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https://expandusceramicsquestions.com/qa/quick-answer-what-percentage-is-a-2-to-1-ratio.html | # Quick Answer: What Percentage Is A 2 To 1 Ratio?
## What is 25% as a ratio?
Following the same logic 25% is 1:3 and not 1:4, else 50% would end up being 1:2 (but 1 in 2 is the proportion and not ratio)..
## What is 2/3 as a percentage?
Some common decimals and fractionsFractionDecimalPercent2/30.666?66.666?%1/40.2525%3/40.7575%1/50.220%21 more rows•Apr 13, 2021
## What is 2/3 as a decimal?
0.66666667Fraction to decimal conversion tableFractionDecimal2/30.666666671/40.252/40.53/40.7551 more rows
## What is 35% as a ratio?
Convert fraction (ratio) 35 / 100 Answer: 35%
## What is a 2 to 1 ratio?
The ratio 2 to 1 is the simplest form of the ratio 4 to 2. And the ratios are equivalent, because the relationship between each pair of numbers is the same. For example, if we have a ratio 250 to 150, we can simplify it by dividing both numbers by 10 and then by 5 to get 5 to 3: 250 : 150 25 : 15 5:3 .
## What is 50% as a ratio?
Percent – a special type of fraction100%=100/10050%= 50/100= 1/225%= 25/100= 1/440%= 40/100= 2/55%= 5/1001 more row
## What is 70% as a ratio?
Convert fraction (ratio) 70 / 100 Answer: 70%
## What is 80% as a ratio?
The answer is “80”. We can say that the ratio 12:15 is the same as 80:100 or 80%. That is, the class has 80% the number of boys has it has girls.
## What is 2 7 as a percentage?
28.571429%Fraction to percent conversion tableFractionPercent5/683.33%1/714.285714%2/728.571429%3/742.857143%41 more rows
## What is 4 50 as a percentage?
8%Now we can see that our fraction is 8/100, which means that 4/50 as a percentage is 8%.
## How do you calculate percentage from a ratio?
We will follow the following steps for converting a ratio into a percentage:Step I: Obtain the ratio. … Step II: Convert the given ratio into the fraction x/y.Step III: Multiply the fraction obtained in step II by 100 and put the percentage sign(%).Express each of the following ratio into percentage:More items…
## What is 2 2 as a percent?
100%How much is – 2 out of 2 written as a percent value? Convert fraction (ratio) – 2 / 2 Answer: -100%
## What does a 1 1 ratio mean?
Answer: 1 : 1 ratio means one-part of the first quantity is equal to one part of the second quantity. The ratio a : b helps us to know how much one part of a is equivalent to one-part of b.
## What is ratio percentage?
A ratio is a comparison of two similar quantities. Given any two similar quantities a and b, the ratio of a to b that is a:b is defined as a:b = a/b, where b≠0. Percentage means ‘by the hundred’ or ‘divide by one hundred’. The percentage is also used to compare quantities, it means ‘per 100’. | 2022-01-20 04:37:05 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8011780977249146, "perplexity": 1362.7931176637421}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301720.45/warc/CC-MAIN-20220120035934-20220120065934-00336.warc.gz"} |
https://www.piping-designer.com/index.php/disciplines/systems/project-management/3291-point-of-total-assumption | Point of Total Assumption
on . Posted in Project Management Engineering
Point of total assumption, abbreviatef as PTA, is the difference between the ceiling and target prices, divided by the buyer’s portion of the share ratio for that price range, plus the target cost.
Point of Total Assumption Formula
$$\large{ PTA = \frac{ CP \;-\; TP }{ BSR} + TC }$$
Symbol
$$\large{ PTA }$$ = point of total assumption
$$\large{ BSR }$$ = buyer's share ratio
$$\large{ CP }$$ = ceiling price
$$\large{ TC }$$ = target cost
$$\large{ TP }$$ = target price | 2023-03-30 14:11:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.330526202917099, "perplexity": 6773.273710252994}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949331.26/warc/CC-MAIN-20230330132508-20230330162508-00367.warc.gz"} |
https://economics.stackexchange.com/questions/18120/whats-the-term-for-elastic-pricing | # What's the term for elastic pricing?
What I've called "elastic pricing", has a true economics name that I believe I once heard.
Here's the notion: I walked into a gas station to buy a fountain drink. I only brought a dollar with me, but when I went to purchase the drink, I found out it was actually \$1.89. The cashier accepted that as payment - making a real-time decision that he was able to capture my demand at only$1. I ended up trying this at a few other gas stations, sometimes bringing 90 cents, and it always works.
An alternative to this is that my University just started pricing football tickets at a variable rate based on the location of the seats. Invariably, they were trying to capture the additional value that the second market was instead capturing.
A second alternative is that a former company of mine negotiated every price. So we would usually price the product at \$500/user/month. But, we would always assess the situation, and with negotiation offer discounts, or increase the pricing. Or, provide value added services for free or at an increased rate.
So how do I talk about this flexible pricing concept – where a business sets it's pricing based on some kind of average demand, but considers an additional spread based on an individual's demand?
Edit: In my first example, the bargaining was only noteworthy because it informed a new mental model of mine – that the pricing was flexible. I don't believe it's an inherent component in the term I'm seeking.
As yet another example, consumer package good brands are known to alter their products slightly for online marketplaces – so that value savvy customers can't compare products directly online with those in the store. E.g. Duracell might offer a 6pk of batteries on Amazon vs. a 4pk at a retail outline. Or, they might package the item differently so it has a different SKU.
• Your edit has made the question very fuzzy - at least for me. The examples before and after seem to have very little in common other than some version of discriminatory pricing. – Giskard Sep 3 '17 at 19:47
• In the gas station example, are we to assume that the cashier, as an employee of what is presumably a big company, has been delegated authority to make a judgement about what each customer can afford? – Adam Bailey Sep 4 '17 at 11:40
Perhaps you may want to look into Price Discrimination? This however is the concept of companies varying their prices on different consumer markets.
1st degree price discrimination, at it's most optimal, is when companies charges the price of each individual consumer's demand. Those willing to pay the most will pay the most. Your description resembles this procedure, but it is not quite exact. Yours implied bargaining, which may or may not lead to 1st degree price discrimination.
2nd degree price discrimination is setting variable prices depending on the product or the quantity sold, playing off of the consumer's preferences.
3rd degree price discrimination is the segmenting of a market into smaller markets (based on some characteristic), and charging a uniform price in that market. The price between these segmented markets vary.
• Thanks for the insightful answer. This isn't the term I was looking for, but I learned something, nonetheless. I gave you an upvote, anyway. – Devin Sep 2 '17 at 23:40
The act where you go in with less money for fountain drinks but still are sold one is called fourth degree price discrimination. This is when instead of the firm discriminating between buyers, the consumer extracts extra surplus from the seller by negotiating the price, and the seller moves closer to their willingness to sell. Often you'll see this happen with negotiating for large appliances for example.
The first alternative you provide however is called vertical product differentiation. The seller here (football venue in your example) provides different quality products (better views/seats) at different rates.
The second alternative you provide is closest to first degree price discrimination, where the firm tries to get a close to the consumer's willingness to pay as they can to extract the most surplus from them.
Your example with selling goods in a way where quality is indistinguishable or difficult, selling online versus in a retail store, sounds like horizontal product differentiation, which involves distinguishing similar products based on characteristics that don't necessarily have to do with quality.
Your many different examples encompass different ideas, but a generic term that best describes the phenomena you are thinking of is called nonlinear pricing.
• I have never encountered the phrase 4th degree price discrimination before. I googled it now but I am getting contradictory explanations. Do you have a good reference for this? If you want, I can ask this as a separate question. (I'll do whatever you want, please don't ban me!!) – Giskard Sep 3 '17 at 19:44
• lollll I am but a benevolent mod I promise! I actually tried to remember where I found the phrase but cannot seem to remember where I got it from. I think it can also be called reverse price discrimination, but given what I'm finding, both terms may just be informal references that I've heard rather than something set in the literature. – Kitsune Cavalry Sep 3 '17 at 20:28 | 2019-07-15 20:14:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4106385409832001, "perplexity": 1567.4979877736712}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195524111.50/warc/CC-MAIN-20190715195204-20190715220451-00061.warc.gz"} |
http://blog.paralleluniverse.co/2013/10/16/spaceships2/ | October 16, 2013
# No More Callbacks: 10,000 Actors, 10,000 Threads, 10,000 Spaceships
## Adopting Ideas from Erlang and Clojure for a Highly Concurrent, Simple and Maintainable Application
I recently stumbled across this quote 1 by Doron Rajwan of Intel: “For the past 30 years, computer performance has been driven by Moore’s Law; from now on, it will be driven by Amdahl’s Law. Writing code that effectively exploits multiple processors can be very challenging.” I could not agree more. Writing correct and efficient multi-threaded code is at once necessary and extremely difficult. The challenge can be met, I believe, by adopting solutions that rest on two legs: languages (or at the very least – programming idioms) designed for concurrency, and appropriate transactional concurrent data-structures.
The former will need to enforce immutability, help manage state, and provide simple and effective concurrency mechanisms, such as message passing. So far, Clojure and Erlang seem to fit the bill. The latter will need to work hand-in-hand with the application, and help it exploit parallelism rather than hinder it, as many databases are prone to do.
Seven months ago, I wrote a blog post describing a simulation of a spaceship battle that uses SpaceBase, our in-memory spatial database, to drive parallelization.
The most common complaint we received about the demo concerned the cumbersome use of callbacks. This, of course, is a problem with many asynchronous computations: you gain concurrency but lose the natural code flow. It’s hard for a programmer to reason about which line of code executes on which thread, and passing information from one callback to another is cumbersome as well.
Callbacks are indeed an annoyance (to say the least), but the alternative – lots of blocking threads – is hard to scale. To solve this, we have developed a lightweight thread library for the JVM called Quasar, along with its Clojure API – Pulsar.
A previous blog post explains in some detail how Quasar lightweight threads (which we call fibers) are implemented. Here I’ll just say that unlike regular threads, you can have hundreds of thousands, or even millions of fibers running concurrently on the same machine. Fibers are optimized for fast context-switches, and are suitable when many operations interact with one another (that is pass information to one another using some mechanism or other). They offer the same scalability afforded by asynchronous callbacks without giving up the simple and natural programming style of synchronous (or single-threaded) code. Instead of a callback, you have fiber-blocking operations, that are as simple as a plain (thread-) blocking operation, only cheaper.
Quasar then builds on the foundation of fibers, and includes Go-like CSP constructs (selectable channels), and an Erlang-like actor system.
The first spaceships demo used only the second component of the two-pillared solution – namely a concurrent, transactional data structure that helps with business logic scaling – but not the first: a concurrency-oriented programming language or paradigm.
To test how well the two parts fit together, we’ve re-written the demo so it uses Quasar actors, as well as the newly released SpaceBase 2.0, which integrates with Quasar. While written in Java rather than in a concurrency-oriented language, the demo uses Quasar’s API which is heavily based on ideas taken from Erlang and Clojure, and I think that the code demonstrates the approach well. If we get the chance, we’ll port the demo to Clojure.
## The Code
Let’s dive into the code. The basic idea is this: we have thousands of spaceships, each modeled as an actor running its logic in a separate fiber (lightweight thread). Each spaceship also stores the publicly-visible portion of its state in the SpaceBase store.
The spaceships find one another by querying their surroundings in the database, then act accordingly – move away, chase, fire – and communicate with other spaceships via messages.
The rendering thread queries the database several (currently, ten) times a second to render a frame, and extrapolates the spaceships’ locations between queries to render 30 (or more) frames per second.
Spawning and Supervising Actors
After setting up the database, the main program spawns the spaceships actors within a supervisor:
new SupervisorActor(SupervisorActor.RestartStrategy.ONE_FOR_ONE) {
@Override
protected void init() throws InterruptedException, SuspendExecution {
for (int i = 0; i < N; i++)
addChild(new Supervisor.ChildSpec("ship-" + i,
Supervisor.ChildMode.PERMANENT, 5, 1, TimeUnit.SECONDS, 3,
ActorSpec.of(Spaceship.class, Spaceships.this, i, phaser)));
}
}.spawn();
A supervisor is an actor that normally monitors other actors for failure, and takes some action – such as restarting the failing actor or all of the supervised actors – when failure occurs. Here we’ll use it to simply create a new spaceship when one is destroyed. A spaceship can be destroyed either as a result of an application event – it blows up after getting hit a number of times – or a software failure – say, an exception occurs. In any case, the supervisor will spawn a new spaceship to replace the dead one (that is the meaning of the ONE_FOR_ONE strategy).
The main thread then creates the application window along with its rendering thread, and then simply loops and prints out the effective rate of simulation cycles every second.
## The Spaceship Actor
The Spaceship class extends BasicActor, which means a spaceship is an actor. As an actor, it implements the doRun method, which is the actor’s main function: it starts running in a separate fiber when the actor is spawned, and when the function returns (or terminates abnormally with an exception), the actor dies (which will result in the supervisor noting the death and spawning a new spaceship).
Pretty much the first thing the spaceship actor does is to insert itself into the database:
global.sb.insert(new TransactionalRecord<>(this, stateRecord), getAABB());
getAABB() returns the (axis-aligned) bounding-box of the spaceship (its location, really), and is used internally by the spatial database; but what is this TransactionalRecord business?
Exposing Public State as Records
Let’s go back to the spaceship’s constructor:
this.state = new State();
this.stateRecord = SpaceshipState.stateType.newInstance(state);
The state field contains the spaceship’s public state (position, velocity etc.). The stateRecord field holds a view of the state field in the form of a record
Just as Erlang teaches us that an actor should expose its operations through a simple, standard interface that allows (pretty-much) only to send it messages, Clojure teaches us that data, or state, should also be exposed through a simple, standard, interface (in Clojure’s case it is the map). A record, then, is such a data-access interface akin to a map. It basically has get(field) and set(field, value) methods, only it preserves the type information of its field to provide type safety at runtime.
The record we’re creating here has fields defined in the SpaceshipState class, while SpaceshipState.stateType.newInstance(state) creates a Record view of the state object by mapping the record’s fields to the state object’s field 2. I should note that accessing an object through the Record interface imposes a negligible performance penalty, because records are implemented using various high-performance techniques like code-generation and HotSpot intrinsics (so r.get($x) is just as fast as o.x). So, instead of calling obj.getX() we call obj.get($x). What does this get us other than re-inventing what is a basic Java functionality, minus the type-safety? Well, both the actor approach and the Clojure standard data-representation approach give up type safety (we preserve the type of the x field, but the compiler can’t tell us whether obj even has an x field; similarly, if we send message m to actor a, the compiler can’t know whether a supports an m operation), they do so at well-defined interface points between separate software components. What we gain is loose coupling. For example, among other things, we gain the ability to swap the implementation of the record or actor at runtime for maintenance (hot code-swapping will be the major feature of the next – 0.4.0 - – release of Quasar).
We gain other things by limiting component interaction to the narrow interfaces of actors and records, and that is an ability to insert cross-cutting concerns. For example, what happens if a method that consumes a resource is called too often? We need to explicitely insert load-handling code into the method. But if we communicate with the component through an actor interface, we can implement a general policy of handling too many messages that are thrown at any actor. Similarly with records. Remember the TransactionalRecord that the spaceships inserts into the database? It applies transactional access permissions to the record. Other spaceships will be able to read our spaceship’s state only when they’re in a transaction, and will be able to modify it only when they’re in a modifying transaction. Any attempt to read or write state outside a transaction will throw a runtime exception.
## The Main Loop
The spacehip’s main loop looks like this:
for (;;) { // loop forever
final long nextCycle = status == Status.ALIVE
? Math.min(state.lastMoved + MIN_PERIOD_MILLIS, nextActionTime())
: nextActionTime();
SpaceshipMessage message = receive(nextCycle - now(), TimeUnit.MILLISECONDS);
if (message != null) {
// handle message
if (message instanceof Shot) {
boolean killed = shot(now, ((Shot) message).x, ((Shot) message).y);
// ...
} else if (message instanceof Blast)
blast(now, ((Blast) message).x, ((Blast) message).y);
} else {
// perform time-based operations
if (status == Status.GONE) {
// ...
return null; // exit loop, destroy ship
} else if (status == Status.ALIVE) {
if (!isLockedOnTarget()) {
if (canFight(now) && wantToFight(now))
searchForTargets();
} else
chaseAndShoot();
applyNeighborRejectionAndMove(now);
}
}
}
// ...
global.sb.delete(state.token);
The receive method returns any messages sent to the spaceships by other spaceships (in the demo, a message telling us we’ve been shot, or that we’re within the blast radius of an exploding ship), and if no messages are available, it waits for a while and then performs time-based operations, like moving the spaceship.
If the spaceship is destroyed (as a result of a Shot message), we exit the loop, delete the spacehisp from the database, and return from the doRun message, resulting in the actor’s termination (and the spawning of a new spaceship by the supervisor).
How do other spaceships send us messages? The state record contains a reference to the ship’s actor. This is an indirect reference of type ActorRef. It has a send method that allows sending messages to the actor, but not much else. This is Quasar actor’s way of providing isolation: no actor can hold a direct reference to another actor, which allows us to change the actor’s implementation at runtime.
## Transactions
Now let’s turn our attention to one of the transactions:
try (ResultSet<Record<SpaceshipState>> rs = global.sb.queryForUpdate(
SpatialQueries.range(myAABB, global.range),
SpatialQueries.equals((Record<SpaceshipState>) stateRecord, myAABB), false)) {
for (ElementUpdater<Record<SpaceshipState>> updater : rs.getResultForUpdate()) {
move(now);
state.status = status;
// ...
updater.update(getAABB());
}
}
queryForUpdate initiates a modifying transaction on the database, and returns a ResultSet. The ResultSet contains, in this case, the state records of the neighboring spaceships. The applyNeighborRejection reads the neighbors’ locations, and steers away from them. Because the neighbors are returned in the ResultSet’s read-only set, attempting to write their fields will result in a runtime exception, courtesy of the TransactionalRecord.
The transaction appears simple: it’s a plain try (with-resources) block, that can access and modify any of the method’s local variables. Behind the scene, the story is more complex. When we issue the call to queryForUpdate, the current fiber blocks, and requests the database to schedule it to continue running when the results are collected. Within the transaction, the fiber runs under the control of the database rather than the regular fiber scheduler. When the transaction completes (at the end of the try block), the database hands the fiber back to the fiber scheduler.
We have essentially transformed an asynchronous operation, normally handled with a callback, into a fiber-blocking operation. The fiber blocks until the query results are available and then resumes, but the task-switch involved is an order-of-magnitude faster than OS controlled thread context switch.
All this is completely transaparent, of course. All you see and care about is a single thread of execution.
Other queries in the code search for targets within a cone extending from the front of the spaceship, or are used to chase after a target we’ve locked onto.
## Synchronizing the Simulation
Many simulations require all simulated objects to work in lock-step: all entities perform a single simulation step and then wait for the cycle to complete before commencing the next one. java.util.concurrent has a synchronization mechanism specifically for this behavior called a Phaser.
Our spaceships are actors, each running in its own fiber (lightweight thread), which exposes an API practically identical to that of a regular Java thread. This allows Quasar to re-use java.util.concurrent constructs designed for threads, and apply them to fibers with hardly any code changes (actually, Quasar’s synchronization constructs ported from java.util.concurrent work for plain threads as well as fibers).
We can configure the demo to use a phaser which is passed to each spaceship. When we do that, every spaceship awaits the beginning of a new cycle once it completes execution of the current one.
Using a phaser forces all spaceships to synchronize execution, but it has its performance price. If we wait for the last spaceship to finish the current cycle, we don’t continuously exploit all cores – we essentially wait for everything to quiet down before starting the whole process again.
## Running the Demo
The demo requires an installation of JDK 7.
To run the demo, clone the GitHub repository, and run ./gradlew on Unix or Mac, or gradlew.bat on Windows.
By default, the demo uses all available cores. To change the default, uncomment and set the co.paralleluniverse.fibers.DefaultFiberPool.parallelism property in gradle.build.
You can set other parameters, such as the number of spaceships, the size of the world or whether or not to use a phaser, by editing src/main/resources/spaceships.properties.
## Performance
On my 4-core (8 virtual cores) i7 MacBook, with 10,000 spaceships, I get close to 10 simulation cycles per second. Every cycle, each of the spaceships executes, on average, two database transactions – one of them is read-only, and one of them includes an update – to a total of 200,000 database queries and 100,000 updates per-second, not including sending and processing messages.
When running the simulation synchronously, i.e. with a phaser, performance drops to about 8 cycles per second on my development machine.
It’s important to mention that the JVM takes a while to warm-up and reach a steady performance level. The warming-up process may take up to two-and-a-half minutes (you’ll see the RATE value printed to the console every second slowly climb), depending on the number of spaceships and the number of cores used. Performance may be improved further by tuning garbage collection (currenctly the JVM defaults are used).
Bear in mind that this implementation is by no means minimal, or optimized for maximum simulation (or game) performance. Every database transaction is monitored, measured and reported (via JMX). Every message passed is counted and reported as well. You can query any actor’s mailbox, or get a current stack-trace of its execution at runtime; and, in the next version of Quasar, you’ll also be able to hot-swap the spaceship logic without stopping or pausing the program.
## Conclusion
The combination of a concurrent, parallelizing database with an actor system on top of lightweight threads gives us several huge advantages:
• Performance – we are able to fully exploit the computing power of modern multi-core hardware.
• Simplicity and familiarity - The code appears completely single-threaded. The programmer need not worry about locks and data races. Just like plain threads, Quasar fibers (and therefore actors) can block on IO or some other synchronization mechanism like the phaser, and handle context-switches faster than plain threads.
• Isolation – every software component is fully isolated from every other component, be it by an ActorRef that only allows message passsing, or a TransactionalRecord. No spaceship can inadvertantly impact another’s correct execution. All shared state is protected by transactions and cannot be modified outside a transaction.
• Fault tolerance – Every error is immediately recognized by the supervisor actor, which can then take immediate action.
This demo also implements, at least partially, John Carmack’s vision for concurrent game programming, outlined in his Quakecon 2013 keynote. We gain efficient concurrency without locks, using a simple and familiar coding style, all while providing good isolation for our components.
There are other actor system for the JVM. The best known ones are probably Akka and Kilim, but neither gives us the same advantages as Quasar. Akka has no true lightweight threads (the actors are actually callbacks), while Kilim does, but both interact very badly with blocking operations like IO, DB calls or synchronization constructs (like the phaser we’ve used).
Of course, the approach used in this demo can – and should – be applied not only to simulations or games, but to any concurrent application, like web services. Stay tuned for more announcements in this area.
Sadly, Quasar’s documentation is still sorely missing (we’re working on it!). But the spaceships demo as well as the examples in the Quasar repository should be enough to get you started. So clone or fork the spaceships demo and/or Quasar and start hacking some super-concurrent code!
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1. Which appears on the back of Java Concurrency in Practice.
2. It is also possible to create a standalone record that is not backed by a plain Java object. | 2019-03-22 12:45:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21051305532455444, "perplexity": 3209.8559336428793}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202658.65/warc/CC-MAIN-20190322115048-20190322141048-00075.warc.gz"} |
http://slideplayer.com/slide/1511338/ | # Heuristic Search Russell and Norvig: Chapter 4 Slides adapted from:
## Presentation on theme: "Heuristic Search Russell and Norvig: Chapter 4 Slides adapted from:"— Presentation transcript:
Heuristic Search Russell and Norvig: Chapter 4 Slides adapted from:
robotics.stanford.edu/~latombe/cs121/2003/home.htm
Heuristic Search Blind search totally ignores where the goals are.
A heuristic function that gives us an estimate of how far we are from a goal. Example: How do we use heuristics?
Heuristic Function Function h(N) that estimate the cost of the cheapest path from node N to goal node. Example: 8-puzzle 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 h(N) = number of misplaced tiles = 6 goal N
Heuristic Function Function h(N) that estimate the cost of the cheapest path from node N to goal node. Example: 8-puzzle 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 h(N) = sum of the distances of every tile to its goal position = = 13 goal N
Greedy Best-First Search
Path search(start, operators, is_goal) { fringe = makeList(start); while (state=fringe.popFirst()) { if (is_goal(state)) return pathTo(state); S = successors(state, operators); fringe = insert(S, fringe); } return NULL; Order the nodes in the fringe in increasing values of h(N)
Robot Navigation f(N) = h(N), with h(N) = Manhattan distance to the goal 2 1 5 8 7 3 4 6
Robot Navigation f(N) = h(N), with h(N) = Manhattan distance to the goal 8 7 6 5 4 3 2 3 4 5 6 7 5 4 3 5 6 3 2 1 1 2 4 7 7 6 5 8 7 6 5 4 3 2 3 4 5 6
Properties of the Greedy Best-First Search
If the state space is finite and we avoid repeated states, the best-first search is complete, but in general is not optimal If the state space is finite and we do not avoid repeated states, the search is in general not complete If the state space is infinite, the search is in general not complete
Admissible heuristic Let h*(N) be the cost of the optimal path from N to a goal node Heuristic h(N) is admissible if: h(N) h*(N) An admissible heuristic is always optimistic
8-Puzzle 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 N goal h1(N) = number of misplaced tiles = 6 is admissible h2(N) = sum of distances of each tile to goal = is admissible h3(N) = (sum of distances of each tile to goal) x (sum of score functions for each tile) = is not admissible
A* Search A* search combines Uniform-cost and Greedy Best-first Search
Evaluation function: f(N) = g(N) + h(N) where: g(N) is the cost of the best path found so far to N h(N) is an admissible heuristic f(N) is the estimated cost of cheapest solution THROUGH N 0 < c(N,N’) (no negative cost steps). Order the nodes in the fringe in increasing values of f(N)
Completeness & Optimality of A*
Claim 1: If there is a path from the initial to a goal node, A* (with no removal of repeated states) terminates by finding the best path, hence is: complete optimal
8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles goal
3+3 3+4 1+5 1+3 2+3 2+4 5+2 5+0 0+4 3+4 3+2 4+1 goal
Robot Navigation f(N) = g(N)+h(N), with h(N) = Manhattan distance to goal 7+2 8+3 2 1 5 8 7 3 4 6 8+3 7+4 7+4 6+5 5+6 6+3 4+7 5+6 3+8 4+7 3+8 2+9 2+9 3+10 7+2 6+1 2+9 3+8 6+1 8+1 7+0 2+9 1+10 1+10 0+11 7+0 7+2 6+1 8+1 7+2 6+3 6+3 5+4 5+4 4+5 4+5 3+6 3+6 2+7 2+7 3+8
Robot navigation f(N) = g(N) + h(N), with h(N) = straight-line distance from N to goal Cost of one horizontal/vertical step = 1 Cost of one diagonal step = 2
Consistent Heuristic The admissible heuristic h is consistent (or satisfies the monotone restriction) if for every node N and every successor N’ of N: h(N) c(N,N’) + h(N’) (triangular inequality) N N’ h(N) h(N’) c(N,N’)
8-Puzzle 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 N goal h1(N) = number of misplaced tiles h2(N) = sum of distances of each tile to goal are both consistent
Claims If h is consistent, then the function f along any path is non-decreasing: f(N) = g(N) + h(N) f(N’) = g(N) +c(N,N’) + h(N’) h(N) c(N,N’) + h(N’) f(N) f(N’) If h is consistent, then whenever A* expands a node it has already found an optimal path to the state associated with this node N N’ h(N) h(N’) c(N,N’)
Avoiding Repeated States in A*
If the heuristic h is consistent, then: Let CLOSED be the list of states associated with expanded nodes When a new node N is generated: If its state is in CLOSED, then discard N If it has the same state as another node in the fringe, then discard the node with the largest f
Complexity of Consistent A*
Let s be the size of the state space Let r be the maximal number of states that can be attained in one step from any state Assume that the time needed to test if a state is in CLOSED is O(1) The time complexity of A* is O(s r log s)
Heuristic Accuracy h(N) = 0 for all nodes is admissible and consistent. Hence, breadth-first and uniform-cost are particular A* !!! Let h1 and h2 be two admissible and consistent heuristics such that for all nodes N: h1(N) h2(N). Then, every node expanded by A* using h2 is also expanded by A* using h1. h2 is more informed than h1 h2 dominates h1 Which heuristic for 8-puzzle is better?
Iterative Deepening A* (IDA*)
Use f(N) = g(N) + h(N) with admissible and consistent h Each iteration is depth-first with cutoff on the value of f of expanded nodes
8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles
4 6 Cutoff=4
8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles
4 6 4 6 Cutoff=4
8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles
4 6 4 5 6 Cutoff=4
8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles
5 4 6 4 5 6 Cutoff=4
8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles
6 5 4 6 4 5 6 Cutoff=4
8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles
4 6 Cutoff=5
8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles
4 6 4 6 Cutoff=5
8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles
4 6 4 5 6 Cutoff=5
8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles
4 6 4 5 6 Cutoff=5 7
8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles
4 5 4 6 5 6 7 Cutoff=5
8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles
4 5 5 6 4 5 6 7 Cutoff=5
8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles
4 5 5 6 4 5 6 7 Cutoff=5
About Heuristics Heuristics are intended to orient the search along promising paths The time spent computing heuristics must be recovered by a better search After all, a heuristic function could consist of solving the problem; then it would perfectly guide the search Deciding which node to expand is sometimes called meta-reasoning Heuristics may not always look like numbers and may involve large amount of knowledge
When to Use Search Techniques?
The search space is small, and There is no other available techniques, or It is not worth the effort to develop a more efficient technique The search space is large, and There is no other available techniques, and There exist “good” heuristics
Summary Heuristic function Greedy Best-first search
Admissible heuristic and A* A* is complete and optimal Consistent heuristic and repeated states Heuristic accuracy IDA* | 2018-02-19 12:27:09 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9355032444000244, "perplexity": 1800.6717063571282}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812584.40/warc/CC-MAIN-20180219111908-20180219131908-00020.warc.gz"} |
http://nlab.mathforge.org/nlab/show/limit+in+a+quasi-category | # nLab limit in a quasi-category
### Context
#### $\left(\infty ,1\right)$-Category theory
(∞,1)-category theory
## Models
#### Limits and colimits
limits and colimits
# Contents
## Idea
The notion of limit and colimit generalize from category theory to (∞,1)-category theory. One model for (∞,1)-categories are quasi-categories. This entry discusses limits and colimits in quasi-categories.
## Definition
###### Definition
For $K$ and $C$ two quasi-categories and $F:K\to C$ an (∞,1)-functor (a morphism of the underlying simplicial sets) , the limit over $F$ is, if it exists, the quasi-categorical terminal object in the over quasi-category ${C}_{/F}$:
$\underset{←}{\mathrm{lim}}F≔\mathrm{TerminalObj}\left({C}_{/F}\right)$\underset{\leftarrow}{\lim} F \coloneqq TerminalObj(C_{/F})
(well defined up to a ontractible space of choices).
A colimit in a quasi-category is accordingly an limit in the opposite quasi-category.
###### Remark
Notice from the discussion at join of quasi-categories that there are two definitions – denoted $\star$ and $♢$ – of join, which yield results that differ as simplicial sets, though are equivalent as quasi-categories.
The notation ${C}_{/F}$ denotes the definition of over quasi-category induced from $*$, while the notation ${C}^{/F}$ denotes that induced from $♢$. Either can be used for the computation of limits in a quasi-category, as for quasi-categorical purposes they are weakly equivalent.
So we also have
$\underset{←}{\mathrm{lim}}F≔\mathrm{TerminalObj}\left({C}^{/F}\right)\phantom{\rule{thinmathspace}{0ex}}.$\underset{\leftarrow}{\lim} F \coloneqq TerminalObj(C^{/F}) \,.
## Properties
### In terms of slice $\infty$-categories
###### Proposition
Let $𝒞$ be a quasi-category and let $f:K\to 𝒞$ be a diagram with $\left(\infty ,1\right)$-colimiting cocone $\stackrel{˜}{f}:K\star {\Delta }^{0}\to 𝒞$. Then the induced map of slice quasi-categories
${𝒞}_{/\stackrel{˜}{f}}\to {𝒞}_{f}$\mathcal{C}_{/\tilde f} \to \mathcal{C}_{f}
is an acyclic Kan fibration.
###### Proposition
For $F:𝒦\to 𝒞$ a diagram in an $\left(\infty ,1\right)$-category and $\underset{←}{\mathrm{lim}}F$ its limit, there is a natural equivalence of (∞,1)-categories
${𝒞}_{/F}\simeq {𝒞}_{/\underset{←}{\mathrm{lim}}F}$\mathcal{C}_{/F} \simeq \mathcal{C}_{/\underset{\leftarrow}{\lim} F}
between the slice (∞,1)-categories over $F$ (the $\left(\infty ,1\right)$-category of $\infty$-cones over $F$) and over just $\underset{←}{\mathrm{lim}}F$.
###### Proof
Let $\stackrel{˜}{F}:{\Delta }^{0}\star 𝒦\to 𝒞$ be the limiting cone. The canonical cospan of $\infty$-functors
$*\to {\Delta }^{0}\star 𝒦←𝒦$\ast \to \Delta^0 \star \mathcal{K} \leftarrow \mathcal{K}
induces a span of slice $\infty$-categories
${𝒞}_{/\underset{←}{\mathrm{lim}}F}←{𝒞}_{/\stackrel{˜}{F}}\to {𝒞}_{/F}\phantom{\rule{thinmathspace}{0ex}}.$\mathcal{C}_{/\underset{\leftarrow}{\lim}F} \leftarrow \mathcal{C}_{/\tilde F} \rightarrow \mathcal{C}_{/F} \,.
The right functor is an equivalence by prop. 2. The left functor is induced by restriction along an op-final (∞,1)-functor (by the Examples discussed there) and hence is an equivalence by the discussion at slice (∞,1)-category (Lurie, prop. 4.1.1.8).
This appears for instance in (Lurie, proof of prop. 1.2.13.8).
### In terms of $\infty$-Hom adjunction
The definition of the limit in a quasi-category in terms of terminal objects in the corresponding over quasi-category is well adapted to the particular nature the incarnation of $\left(\infty ,1\right)$-categories by quasi-categories. But more intrinsically in $\left(\infty ,1\right)$-category theory, it should be true that there is an adjunction characterization of $\left(\infty ,1\right)$-limits : limit and colimit, should be (pointwise or global) right and left adjoint (infinity,1)-functor of the constant diagram $\left(\infty ,1\right)$-functor, $\mathrm{const}:K\to \mathrm{Func}\left(K,C\right)$.
$\left(\mathrm{colim}⊣\mathrm{const}⊣\mathrm{lim}\right):\mathrm{Func}\left(K,C\right)\stackrel{\stackrel{\mathrm{lim}}{\to }}{\stackrel{\stackrel{\mathrm{const}}{←}}{\underset{\mathrm{colim}}{\to }}}\mathrm{Func}\left(*,C\right)\simeq C\phantom{\rule{thinmathspace}{0ex}}.$(colim \dashv const \dashv lim) : Func(K,C) \stackrel{\overset{lim}{\to}}{\stackrel{\overset{const}{\leftarrow}} {\underset{colim}{\to}}} Func(*,C) \simeq C \,.
By the discussion at adjoint (∞,1)-functor (HTT, prop. 5.2.2.8) this requires exhibiitng a morphism $\eta :{\mathrm{Id}}_{\mathrm{Func}\left(K,C\right)}\to \mathrm{const}\mathrm{colim}$ in $\mathrm{Func}\left(\mathrm{Func}\left(K,C\right),\mathrm{Func}\left(K,C\right)\right)$ such that for every $f\in \mathrm{Func}\left(K,C\right)$ and $Y\in C$ the induced morphism
${\mathrm{Hom}}_{C}\left(\mathrm{colim}\left(f\right),Y\right)\to {\mathrm{Hom}}_{\mathrm{Func}\left(K,C\right)}\left(\mathrm{const}\mathrm{colim}\left(f\right),\mathrm{const}Y\right)\stackrel{\mathrm{Hom}\left(\eta ,\mathrm{const}Y\right)}{\to }{\mathrm{Hom}}_{\mathrm{Func}\left(K,Y\right)}\left(f,\mathrm{const}Y\right)$Hom_{C}(colim(f),Y) \to Hom_{Func(K,C)}(const colim(f), const Y) \stackrel{Hom(\eta, const Y)}{\to} Hom_{Func(K,Y)}(f, const Y)
is a weak equivalence in ${\mathrm{sSet}}_{\mathrm{Quillen}}$.
But first consider the following pointwise characterization.
###### Proposition
Let $C$ be a quasi-category, $K$ a simplicial set. A co-cone diagram $\overline{p}:K\star \Delta \left[0\right]\to C$ with cone point $X\in C$ is a colimiting diagram (an initial object in ${C}_{p/}$) precisely if for every object $Y\in C$ the morphism
${\varphi }_{Y}:{\mathrm{Hom}}_{C}\left(X,Y\right)\to {\mathrm{Hom}}_{\mathrm{Func}\left(K,C\right)}\left(p,\mathrm{const}Y\right)$\phi_Y : Hom_C(X,Y) \to Hom_{Func(K,C)}(p, const Y)
induced by the morpism $p\to \mathrm{const}X$ that is encoded by $\overline{p}$ is an equivalence (i.e. a homotopy equivalence of Kan complexes).
###### Proof
This is HTT, lemma 4.2.4.3.
The key step is to realize that ${\mathrm{Hom}}_{\mathrm{Func}\left(K,C\right)}\left(p,\mathrm{const}Y\right)$ is given (up to equivalence) by the pullback ${C}^{p/}{×}_{C}\left\{Y\right\}$ in sSet.
Here is a detailed way to see this, using the discussion at hom-object in a quasi-category.
We have that ${\mathrm{Hom}}_{\mathrm{Func}\left(K,C\right)}\left(p,\mathrm{const}Y\right)$ is given by $\left({C}^{K}{\right)}^{p/}{×}_{{C}^{K}}\mathrm{const}Y$. We compute
$\begin{array}{rl}\left(\left({C}^{K}{\right)}^{p/}{×}_{{C}^{K}}\mathrm{const}Y{\right)}_{n}& ={\mathrm{Hom}}_{\Delta \left[0\right]/\mathrm{sSet}}\left(\Delta \left[0\right]♢\Delta \left[n\right],{C}^{K}\right){×}_{\left({C}^{K}{\right)}_{n}}\left\{\mathrm{const}Y\right\}\\ & ={\mathrm{Hom}}_{\Delta \left[0\right]/\mathrm{sSet}}\left(\Delta \left[0\right]\coprod _{\Delta \left[n\right]}\Delta \left[n\right]×\Delta \left[1\right],{C}^{K}\right){×}_{\left({C}^{K}{\right)}_{n}}\left\{\mathrm{const}Y\right\}& =\left\{p\right\}{×}_{\mathrm{Hom}\left(\Delta \left[0\right],{C}^{K}\right)}\mathrm{Hom}\left(\Delta \left[0\right],{C}^{K}\right){×}_{\mathrm{Hom}\left(\Delta \left[n\right],{C}^{K}\right)}\mathrm{Hom}\left(\Delta \left[n\right]×\Delta \left[1\right],{C}^{K}\text{Unknown character}\right){×}_{\mathrm{Hom}\left(\Delta \left[n\right],{C}^{K}\right)}\left\{\mathrm{const}Y\right\}\\ & =\left\{p\right\}{×}_{\mathrm{Hom}\left(K,C\right)}\mathrm{Hom}\left(K,C\right){×}_{\mathrm{Hom}\left(\Delta \left[n\right]×K,C\right)}\mathrm{Hom}\left(\Delta \left[n\right]×K×\Delta \left[1\right],C\right){×}_{\mathrm{Hom}\left(\Delta \left[n\right]×K,C\right)}\mathrm{Hom}\left(\Delta \left[n\right],C\right){×}_{\Delta \left[n\right],C}\left\{Y\right\}\\ & =\left\{p\right\}{×}_{\mathrm{Hom}\left(K,C\right)}\mathrm{Hom}\left(K♢\Delta \left[n\right],C\right){×}_{\mathrm{Hom}\left(\Delta \left[n\right],C\right)}\left\{Y\right\}\\ & =\left({C}^{p/}{×}_{C}\left\{Y\right\}{\right)}_{n}\end{array}$\begin{aligned} ((C^K)^{p/} \times_{C^K} const Y)_n & = Hom_{{\Delta[0]}/sSet}( \Delta[0] \diamondsuit \Delta[n] , C^K ) \times_{(C^K)_n} \{const Y\} \\ & = Hom_{{\Delta[0]}/sSet}( \Delta[0] \coprod_{\Delta[n]} \Delta[n] \times \Delta[1] , C^K ) \times_{(C^K)_n} \{const Y\} & = \{p\} \times_{Hom(\Delta[0],C^K)} Hom(\Delta[0], C^K) \times_{Hom(\Delta[n], C^K)} Hom(\Delta[n] \times \Delta[1], C^K \) \times_{Hom(\Delta[n], C^K)} \{const Y\} \\ & = \{p\} \times_{Hom(K,C)} Hom(K,C) \times_{Hom(\Delta[n]\times K,C)} Hom(\Delta[n]\times K \times \Delta[1], C) \times_{Hom(\Delta[n]\times K, C)} Hom(\Delta[n],C) \times_{\Delta[n],C} \{Y\} \\ &= \{p\} \times_{Hom(K,C)} Hom(K \diamondsuit \Delta[n], C) \times_{Hom(\Delta[n],C)} \{Y\} \\ &= (C^{p/}\times_C \{Y\})_n \end{aligned}
Under this identification, ${\varphi }_{Y}$ is the morphism
$\left({C}^{X/}\stackrel{\varphi \prime }{\to }{C}^{\overline{p}/}\stackrel{\varphi ″}{\to }{C}^{p/}\right){×}_{C}\left\{Y\right\}\phantom{\rule{thinmathspace}{0ex}},$\left( C^{X/} \stackrel{\phi'}{\to} C^{\bar p/} \stackrel{\phi''}{\to} C^{p/} \right) \times_C \{Y\} \,,
in sSet where $\varphi \prime$ is a section of the map ${C}^{\overline{p}/}\to {C}^{X/}$, (which one checks is an acyclic Kan fibration) obtained by choosing composites of the co-cone components with a given morphism $X\to Y$.
The morphism $\varphi ″$ is a left fibration (using HTT, prop. 4.2.1.6)
One finds that the morphism $\varphi ″$ is a left fibration.
The strategy for the completion of the proof is: realize that the first condition of the proposition is equivalent to $\varphi ″$ being an acyclic Kan fibration, and the second statement equivalent to $\varphi {″}_{Y}$ being an acyclic Kan fibration, then show that these two conditions in turn are equivalent.
### In terms of products and equalizers
A central theorem in ordinary category theory asserts that a category has limits already if it has products and equalizers. The analog statement is true here:
###### Proposition
Let $\kappa$ be a regular cardinal. An (∞,1)-category $C$ has all $\kappa$-small limits precisely if it has equalizers and $\kappa$-small products.
This is HTT, prop. 4.4.3.2.
### In terms of homotopy limits
The notion of homotopy limit, which exists for model categories and in particular for simplicial model categories and in fact in all plain Kan complex-enriched categories – as described in more detail at homotopy Kan extension – is supposed to be a model for $\left(\infty ,1\right)$-categorical limits. In particular, under sending the Kan-complex enriched categories $C$ to quasi-categories $N\left(C\right)$ using the [[homotopy coherent nerve]} functor, homotopy limits should precisely corespond to quasi-categorical limits. That this is indeed the case is asserted by the following statements.
###### Proposition
Let $C$ and $J$ be Kan complex-enriched categories and let $F:J\to C$ be an sSet-enriched functor.
Then a cocone $\left\{{\eta }_{i}:F\left(i\right)\to c{\right\}}_{i\in J}$ under $F$ exhibits the object $c\in C$ as a homotopy colimit (in the sense discussed in detail at homotopy Kan extension) precisely if the induced morphism of quasi-categories
$\overline{N\left(F\right)}:N\left(J{\right)}^{▹}\to N\left(C\right)$\bar {N(F)} : N(J)^{\triangleright} \to N(C)
is a quasi-categorical colimit diagram in $N\left(C\right)$.
Here $N$ is the homotopy coherent nerve, $N\left(J{\right)}^{▹}$ the join of quasi-categories with the point, $N\left(F\right)$ the image of the simplicial functor $F$ under the homotopy coherent nerve and $\overline{N\left(F\right)}$ its extension to the join determined by the cocone maps $\eta$.
###### Proof
This is HTT, theorem 4.2.4.1
A central ingredient in the proof is the fact, discused at (∞,1)-category of (∞,1)-functors and at model structure on functors, that sSet-enriched functors do model (∞,1)-functors, in that for $A$ a combinatorial simplicial model category, $S$ a quasi-category and $\tau \left(S\right)$ the corresponding $\mathrm{sSet}$-category under the left adjoint of the homotopy coherent nerve, we have an equivalence of quasi-categories
$N\left(\left(\left[C,A{\right]}_{\mathrm{proj}}{\right)}^{\circ }\right)\simeq \mathrm{Func}\left(S,N\left({A}^{\circ }\right)\right)$N(([C,A]_{proj})^\circ) \simeq Func(S, N(A^\circ))
and the same is trued for $A$ itself replaced by a chunk? $U\subset A$.
With this and the discussion at homotopy Kan extension, we find that the cocone components $\eta$ induce for each $a\in \left[C,\mathrm{sSet}\right]$ a homotopy equivalence
$C\left(c,a\right)\stackrel{}{\to }\left[{J}^{\mathrm{op}},C\right]\left(jF,\mathrm{const}a\right)$C(c,a) \stackrel{}{\to} [J^{op}, C](j F, const a)
which is hence equivalently an equivalence of the corresponding quasi-categorical hom-objects. The claim follows then from the above discussion of characterization of (co)limits in terms of $\infty$-hom adjunctions.
###### Corollary
The quasi-category $N\left({A}^{\circ }\right)$ presented by a combinatorial simplicial model category $A$ has all small quasi-categorical limits and colimits.
###### Proof
This is HTT, 4.2.4.8.
It follows from the fact that $A$ has (pretty much by definition of model category and combinatorial model category) all homotopy limits and homotopy colimits (in fact all homotopy Kan extensions) by the above proposition.
Since $\left(\infty ,1\right)$-categories equivalent to those of the form $N\left({A}^{\circ }\right)$ for $A$ a combinatorial simplicial model category are precisely the locally presentable (∞,1)-categories, it follows from this in particular that every locally presentable $\left(\infty ,1\right)$-category has all limits and colimits.
### Commutativity of limits
The following proposition says that if for an $\left(\infty ,1\right)$-functor $F:X×Y\to C$ limits (colimits) over each of the two variables exist separately, then they commute.
###### Proposition
Let $X$ and $Y$ be simplicial sets and $C$ a quasi-category. Let $p:{X}^{◃}×{Y}^{◃}\to C$ be a diagram. If
1. for every object $x\in {X}^{◃}$ (including the cone point) the restricted diagram ${p}_{x}:{Y}^{◃}\to C$ is a limit diagram;
2. for every object $y\in Y$ (not including the cone point) the restricted diagram ${p}_{y}:{X}^{◃}\to C$ is a limit diagram;
then, with $c$ denoting the cone point of ${Y}^{◃}$, the restricted diagram, ${p}_{c}:{X}^{◃}\to C$ is also a limit diagram.
###### Proof
This is HTT, lemma 5.5.2.3
In other words, suppose that ${\mathrm{lim}}_{x}F\left(x,y\right)$ exists for all $y$ and ${\mathrm{lim}}_{y}F\left(x,y\right)$ exists for all $x$ and also that ${\mathrm{lim}}_{y}\left({\mathrm{lim}}_{x}F\left(x,y\right)\right)$ exists, then this object is also ${\mathrm{lim}}_{x}{\mathrm{lim}}_{y}F\left(x,y\right)$.
## Examples
### $\infty$-Limits of special shape
#### Pullback / Pushout
The non-degenerate cells of the simplicial set $\Delta \left[1\right]×\Delta \left[1\right]$ obtained as the cartesian product of the simplicial 1-simplex with itself look like
$\begin{array}{ccc}\left(0,0\right)& \to & \left(1,0\right)\\ ↓& ↘& ↓\\ \left(0,1\right)& \to & \left(1,1\right)\end{array}$\array{ (0,0) &\to& (1,0) \\ \downarrow &\searrow& \downarrow \\ (0,1) &\to& (1,1) }
A sqare in a quasi-category $C$ is an image of this in $C$, i.e. a morphism
$s:\Delta \left[1\right]×\Delta \left[1\right]\to C\phantom{\rule{thinmathspace}{0ex}}.$s : \Delta[1] \times \Delta[1] \to C \,.
The simplicial square $\Delta \left[1{\right]}^{×2}$ is isomorphic, as a simplicial set, to the join of simplicial sets of a 2-horn with the point:
$\Delta \left[1\right]×\Delta \left[1\right]\simeq \left\{v\right\}\star \Lambda \left[2{\right]}_{2}=\left(\begin{array}{ccc}v& \to & 1\\ ↓& ↘& ↓\\ 0& \to & 2\end{array}\right)$\Delta[1] \times \Delta[1] \simeq \{v\} \star \Lambda[2]_2 = \left( \array{ v &\to& 1 \\ \downarrow &\searrow& \downarrow \\ 0 &\to& 2 } \right)
and
$\Delta \left[1\right]×\Delta \left[1\right]\simeq \Lambda \left[2{\right]}_{0}\star \left\{v\right\}=\left(\begin{array}{ccc}0& \to & 1\\ ↓& ↘& ↓\\ 2& \to & v\end{array}\right)\phantom{\rule{thinmathspace}{0ex}}.$\Delta[1] \times \Delta[1] \simeq \Lambda[2]_0 \star \{v\} = \left( \array{ 0&\to& 1 \\ \downarrow &\searrow& \downarrow \\ 2 &\to& v } \right) \,.
If a square $\Delta \left[1\right]×\Delta \left[1\right]\simeq \Lambda \left[2{\right]}_{0}\star \left\{v\right\}\to C$ exhibits $\left\{v\right\}\to C$ as a colimit over $F:\Lambda \left[2{\right]}_{0}\to C$, we say the colimit
$v:=\underset{\to }{\mathrm{lim}}F:=F\left(1\right)\coprod _{F\left(0\right)}F\left(2\right)$v := \lim_\to F := F(1) \coprod_{F(0)} F(2)
is the pushout of the diagram $F$.
##### Pasting law of pushouts
We have the following $\left(\infty ,1\right)$-categorical analog of the familiar pasting law of pushouts in ordinary category theory:
###### Proposition
A pasting diagram of two squares is a morphism
$\Delta \left[2\right]×\Delta \left[1\right]\to C\phantom{\rule{thinmathspace}{0ex}}.$\Delta[2] \times \Delta[1] \to C \,.
Schematically this looks like
$\begin{array}{ccccc}x& \to & y& \to & z\\ ↓& & ↓& & ↓\\ x\prime & \to & y\prime & \to & z\prime \end{array}\phantom{\rule{thinmathspace}{0ex}}.$\array{ x &\to& y &\to& z \\ \downarrow && \downarrow && \downarrow \\ x' &\to& y' &\to& z' } \,.
If the left square is a pushout diagram in $C$, then the right square is precisely if the outer square is.
###### Proof
A proof appears as HTT, lemma 4.4.2.1
#### Tensoring and cotensoring with an $\infty$-groupoid
##### Recap of the 1-categorical situation
An ordinary category with limits is canonically cotensored over Set:
For $S,T\in$ Set and ${\mathrm{const}}_{T}:S\to \mathrm{Set}$ the diagram parameterized by $S$ that is constant on $T$, we have
$\underset{←}{\mathrm{lim}}{\mathrm{const}}_{T}\simeq {T}^{S}\phantom{\rule{thinmathspace}{0ex}}.$\lim_{\leftarrow} const_T \simeq T^S \,.
Accordingly the cotensoring
$\left(-{\right)}^{\left(-\right)}:{\mathrm{Set}}^{\mathrm{op}}×C\to C$(-)^{(-)} : Set^{op} \times C \to C
is defined by
${c}^{S}:=\underset{←}{\mathrm{lim}}\left(S\stackrel{{\mathrm{const}}_{c}}{\to }C\right)=\prod _{S}c\phantom{\rule{thinmathspace}{0ex}}.$c^S := \lim_{\leftarrow} (S \stackrel{const_c}{\to} C) = \prod_{S} c \,.
And by continuity of the hom-functor this implies the required natural isomorphisms
${\mathrm{Hom}}_{C}\left(d,{c}^{S}\right)={\mathrm{Hom}}_{C}\left(d,{\underset{←}{\mathrm{lim}}}_{S}c\right)\simeq {\underset{←}{\mathrm{lim}}}_{S}{\mathrm{Hom}}_{C}\left(d,c\right)\simeq \mathrm{Set}\left(S,{\mathrm{Hom}}_{C}\left(d,C\right)\right)\phantom{\rule{thinmathspace}{0ex}}.$Hom_C(d,c^S) = Hom_C(d, {\lim_{\leftarrow}}_S c) \simeq {\lim_{\leftarrow}}_S Hom_C(d,c) \simeq Set(S,Hom_C(d,C)) \,.
Correspondingly if $C$ has colimits, then the tensoring
$\left(-\right)\otimes \left(-\right):\mathrm{Set}×C\to C$(-) \otimes (-) : Set \times C \to C
is given by forming colimits over constant diagrams: $S\otimes c:={{\mathrm{lim}}_{\to }}_{S}c$, and again by continuity of the hom-functor we have the required natural isomorphism
${\mathrm{Hom}}_{C}\left(S\otimes c,d\right)={\mathrm{Hom}}_{C}\left({\underset{\to }{\mathrm{lim}}}_{S}c,d\right)\simeq {\underset{←}{\mathrm{lim}}}_{S}{\mathrm{Hom}}_{C}\left(c,d\right)\simeq \mathrm{Set}\left(S,{\mathrm{Hom}}_{C}\left(c,d\right)\right)\phantom{\rule{thinmathspace}{0ex}}.$Hom_C(S \otimes c, d) = Hom_C({\lim_{\to}}_S c,d) \simeq {\lim_{\leftarrow}}_S Hom_C(c,d) \simeq Set(S,Hom_C(c,d)) \,.
Of course all the colimits appearing here are just coproducts and all limits just products, but for the generalization to $\left(\infty ,1\right)$-categories this is a misleading simplification, it is really the notion of limit and colimit that matters here.
##### Definition
We expect for $S,T\in$ ∞Grpd and for ${\mathrm{const}}_{T}:S\to \infty \mathrm{Grpd}$ the constant diagram, that
$\underset{←}{\mathrm{lim}}{\mathrm{const}}_{T}\simeq {T}^{S}\phantom{\rule{thinmathspace}{0ex}},$\lim_{\leftarrow} const_T \simeq T^S \,,
where on the right we have the internal hom of $\infty$-groupoids, which is modeled in the model structure on simplicial sets ${\mathrm{sSet}}_{\mathrm{Quillen}}$ by the fact that this is a closed monoidal category.
Correspondingly, for $C$ an $\left(\infty ,1\right)$-category with colimits, it is tensored over ∞Grpd by setting
$\left(-\right)\otimes \left(-\right):\infty \mathrm{Grpd}×C\to C$(-)\otimes (-) : \infty Grpd \times C \to C
$S\otimes c:={\underset{\to }{\mathrm{lim}}}_{S}c\phantom{\rule{thinmathspace}{0ex}},$S \otimes c := {\lim_{\to}}_S c \,,
where now on the right we have the $\left(\infty ,1\right)$-categorical colimit over the constant diagram $\mathrm{const}:S\to C$ of shape $S$ on $c$.
Then by the $\left(\infty ,1\right)$-continuity of the hom, and using the above characterization of the internal hom in $\infty \mathrm{Grpd}$ we have the required natural equivalence
${\mathrm{Hom}}_{C}\left(S\otimes c,d\right)={\mathrm{Hom}}_{C}\left({\underset{\to }{\mathrm{lim}}}_{S}c,d\right)\simeq {\underset{←}{\mathrm{lim}}}_{S}{\mathrm{Hom}}_{C}\left(c,d\right)\simeq \infty \mathrm{Grpd}\left(S,{\mathrm{Hom}}_{C}\left(c,d\right)\right)\phantom{\rule{thinmathspace}{0ex}}.$Hom_C(S \otimes c, d) = Hom_C({\lim_{\to}}_S c, d) \simeq {\lim_{\leftarrow}}_S Hom_C(c,d) \simeq \infty Grpd(S,Hom_C(c,d)) \,.
The following proposition should assert that this is all true
###### Proposition
The $\left(\infty ,1\right)$-categorical colimit ${\mathrm{lim}}_{\to }c$ over the diagram of shape $S\in \infty \mathrm{Grpd}$ constant on $c\in C$ is characterized by the fact that it induces natural equivalences
${\mathrm{Hom}}_{C}\left({\underset{\to }{\mathrm{lim}}}_{S}c,d\right)\simeq \infty \mathrm{Grpd}\left(S,{\mathrm{Hom}}_{C}\left(c,d\right)\right)$Hom_C({\lim_{\to}}_S c, d) \simeq \infty Grpd(S, Hom_C(c,d))
for all $d\in C$.
This is essentially HTT, corollary 4.4.4.9.
###### Corollary
Every ∞-groupoid $S$ is the $\left(\infty ,1\right)$-colimit in ∞Grpd of the constant diagram on the point over itself:
$S\simeq {\underset{\to }{\mathrm{lim}}}_{S}{\mathrm{const}}_{*}\phantom{\rule{thinmathspace}{0ex}}.$S \simeq {\lim_{\to}}_S const_* \,.
This justifies the following definition
###### Definition
For $C$ an $\left(\infty ,1\right)$-category with colimits, the tensoring of $C$ over $\infty \mathrm{Grpd}$ is the $\left(\infty ,1\right)$-functor
$\left(-\right)\otimes \left(-\right):\infty \mathrm{Grpd}×C\to C$(-) \otimes (-) : \infty Grpd \times C \to C
given by
$S\otimes c=\underset{\to }{\mathrm{lim}}\left({\mathrm{const}}_{c}:S\to C\right)\phantom{\rule{thinmathspace}{0ex}}.$S \otimes c = \lim_{\to} (const_c : S \to C) \,.
##### Models
We discuss models for $\left(\infty ,1\right)$-(co)limits in terms of ordinary category theory and homotopy theory.
###### Observation
If $C$ is presented by a simplicial model category $A$, in that $C\simeq {A}^{\circ }$, then the $\left(\infty ,1\right)$-tensoring and $\left(\infty ,1\right)$-cotensoring of $C$ over ∞Grpd is modeled by the ordinary tensoring and powering of $A$ over sSet:
For $\stackrel{^}{c}\in A$ cofibant and representing an object $c\in C$ and for $S\in \mathrm{sSet}$ any simplicial set, we have an equivalence
$c\otimes S\simeq \stackrel{^}{C}\cdot S\phantom{\rule{thinmathspace}{0ex}}.$c \otimes S \simeq \hat C \cdot S \,.
###### Proof
The powering in $A$ satisfies the natural isomorphism
$\mathrm{sSet}\left(S,A\left(\stackrel{^}{c},\stackrel{^}{d}\right)\right)\simeq A\left(\stackrel{^}{c}\cdot S,\stackrel{^}{d}\right)$sSet(S,A(\hat c,\hat d)) \simeq A(\hat c \cdot S, \hat d)
in sSet.
For $\stackrel{^}{c}$ a cofibrant and $\stackrel{^}{d}$ a fibrant representative, we have that both sides here are Kan complexes that are equivalent to the corresponding derived hom spaces in the corresponding $\left(\infty ,1\right)$-category $C$, so that this translates into an equivalence
${\mathrm{Hom}}_{C}\left(c\cdot S,d\right)\simeq \infty \mathrm{Grpd}\left(S,{\mathrm{Hom}}_{C}\left(c,d\right)\right)\phantom{\rule{thinmathspace}{0ex}}.$Hom_C(c \cdot S, d) \simeq \infty Grpd(S, Hom_C(c,d)) \,.
The claim then follows from the above proposition.
### Limits in over-$\left(\infty ,1\right)$-categories
###### Proposition
For $C$ an $\left(\infty ,1\right)$-category, $X:D\to C$ a diagram, $C/X$ the over-(∞,1)-category and $F:K\to C/X$ a diagram in the over-$\left(\infty ,1\right)$-category, then the (∞,1)-limit ${\mathrm{lim}}_{←}F$ in $C/X$ coincides with the $\left(\infty ,1\right)$-limit ${\mathrm{lim}}_{←}F/X$ in $C$.
###### Proof
Modelling $C$ as a quasi-category we have that $C/X$ is given by the simplicial set
$C/X:\left[n\right]↦{\mathrm{Hom}}_{X}\left(\left[n\right]\star D,C\right)\phantom{\rule{thinmathspace}{0ex}},$C/X : [n] \mapsto Hom_X([n] \star D, C) \,,
where $\star$ denotes the join of simplicial sets. The limit ${\mathrm{lim}}_{←}F$ is the initial object in $\left(C/X\right)/F$, which is the quasi-category given by the simplicial set
$\left(C/X\right)/F:\left[n\right]↦{\mathrm{Hom}}_{F}\left(\left[n\right]\star K,C/X\right)\phantom{\rule{thinmathspace}{0ex}}.$(C/X)/F : [n] \mapsto Hom_{F}( [n] \star K, C/X) \,.
Since the join preserves colimits of simplicial sets in both arguments, we can apply the co-Yoneda lemma to decompose $\left[n\right]\star K={\mathrm{lim}}_{\underset{\left[r\right]\to \left[n\right]\star K}{\to }}\left[r\right]$, use that the hom-functor sends colimits in the first argument to limits and obtain
$\begin{array}{rl}\mathrm{Hom}\left(\left[n\right]\star K,C/X\right)& \simeq \mathrm{Hom}\left({\underset{\to }{\mathrm{lim}}}_{r}\left[r\right],C/X\right)\\ & \simeq {\underset{←}{\mathrm{lim}}}_{r}\mathrm{Hom}\left(\left[r\right],C/X\right)\\ & \simeq {\underset{←}{\mathrm{lim}}}_{r}{\mathrm{Hom}}_{F}\left(\left[r\right]\star D,C\right)\\ & \simeq {\mathrm{Hom}}_{F}\left({\underset{\to }{\mathrm{lim}}}_{r}\left(\left[r\right]\star D\right),C\right)\\ & \simeq {\mathrm{Hom}}_{F}\left(\left({\underset{\to }{\mathrm{lim}}}_{r}\left[r\right]\right)\star D,C\right)\\ & \simeq {\mathrm{Hom}}_{F}\left(\left(\left[n\right]\star K\right)\star D,C\right)\\ & \simeq {\mathrm{Hom}}_{F}\left(\left[n\right]\star \left(K\star D\right),C\right)\end{array}\phantom{\rule{thinmathspace}{0ex}}.$\begin{aligned} Hom([n] \star K, C/X) &\simeq Hom( {\lim_{\to}}_r [r], C/X) \\ & \simeq {\lim_{\leftarrow}}_r Hom([r], C/X) \\ & \simeq {\lim_{\leftarrow}}_r Hom_F( [r] \star D, C ) \\ & \simeq Hom_F({\lim_{\to}}_r ([r] \star D), C ) \\ & \simeq Hom_F( ({\lim_{\to}}_r[r]) \star D, C ) \\ & \simeq Hom_F(([n] \star K) \star D, C) \\ & \simeq Hom_F([n] \star (K \star D), C) \end{aligned} \,.
Here ${\mathrm{Hom}}_{F}\left(\left[r\right]\star D,C\right)$ is shorthand for the hom in the (ordinary) under category ${\mathrm{sSet}}^{D/}$ from the canonical inclusion $D\to \left[r\right]\star D$ to $X:D\to C$. Notice that we use the 1-categorical analog of the statement that we are proving here when computing the colimit in this under-category as just the colimit in $\mathrm{sSet}$. We also use that the join of simplicial sets, being given by Day convolution is an associative tensor product.
In conclusion we have an isomorphism of simplicial sets
$\left(C/X\right)/F\simeq C/\left(X/F\right)$(C/X)/F \simeq C/(X/F)
and therefore the initial objects of these quasi-categories coincide on both sides. This shows that ${\mathrm{lim}}_{←}F$ is computed as an initial object in $C/\left(X/F\right)$.
### Limits and colimits with values in $\infty \mathrm{Grpd}$
Limits and colimits over a (∞,1)-functor with values in the (∞,1)-category ∞-Grpd of ∞-groupoids may be reformulated in terms of the universal fibration of (∞,1)-categories, hence in terms of the (∞,1)-Grothendieck construction.
Let ∞Grpd be the (∞,1)-category of ∞-groupoids. Let the (∞,1)-functor $Z{\mid }_{\mathrm{Grpd}}\to \infty {\mathrm{Grpd}}^{\mathrm{op}}$ be the universal ∞-groupoid fibration whose fiber over the object denoting some $\infty$-groupoid is that very $\infty$-groupoid.
Then let $X$ be any ∞-groupoid and
$F:X\to \infty \mathrm{Grpd}$F : X \to \infty Grpd
an (∞,1)-functor. Recall that the coCartesian fibration ${E}_{F}\to X$ classified by $F$ is the pullback of the universal fibration of (∞,1)-categories $Z$ along F:
$\begin{array}{ccc}{E}_{F}& \to & Z{\mid }_{\mathrm{Grpd}}\\ ↓& & ↓\\ X& \stackrel{F}{\to }& \infty \mathrm{Grpd}\end{array}$\array{ E_F &\to& Z|_{Grpd} \\ \downarrow && \downarrow \\ X &\stackrel{F}{\to}& \infty Grpd }
###### Proposition
Let the assumptions be as above. Then:
• The $\infty$-colimit of $F$ is equivalent to the (∞,1)-Grothendieck construction ${E}_{F}$:
$\underset{\to }{\mathrm{lim}}F\simeq {E}_{F}$\lim_\to F \simeq E_F
• The $\infty$-limit of $F$ is equivalent to the (∞,1)-groupoid of sections? of ${E}_{F}\to X$
${\Gamma }_{X}\left({E}_{F}\right)\simeq \mathrm{lim}F\phantom{\rule{thinmathspace}{0ex}}.$\Gamma_X(E_F) \simeq lim F \,.
###### Proof
The statement for the colimit is corollary 3.3.4.6 in HTT. The statement for the limit is corollary 3.3.3.4.
### Limits and colimits with values in $\left(\infty ,1\right)$Cat
###### Proposition
For $F:D\to$ (∞,1)Cat an (∞,1)-functor, its $\infty$-colimit is given by forming the (∞,1)-Grothendieck construction $\int F$ of $F$ and then inverting the Cartesian morphisms.
Formally this means, with respect to the model structure for Cartesian fibrations that there is a natural isomorphism
$\underset{\to }{\mathrm{lim}}F\simeq \left(\int F{\right)}^{♯}$\lim_\to F \simeq (\int F)^\sharp
in the homotopy category of the presentation of $\left(\infty ,1\right)$-category by marked simplicial sets.
This is HTT, corollary 3.3.4.3.
For the special case that $F$ takes values in ordinary categories see also at 2-limit the section 2-limits in Cat.
### Limits in $\infty$-functor categories
For $C$ an ordinary category that admits small limits and colimits, and for $K$ a small category, the functor category $\mathrm{Func}\left(D,C\right)$ has all small limits and colimits, and these are computed objectwise. See limits and colimits by example. The analogous statement is true for an (∞,1)-category of (∞,1)-functors.
###### Proposition
Let $K$ and $C$ be quasi-categories, such that $C$ has all colimits indexed by $K$.
Let $D$ be a small quasi-category. Then
• The (∞,1)-category of (∞,1)-functors $\mathrm{Func}\left(D,C\right)$ has all $K$-indexed colimits;
• A morphism ${K}^{▹}\to \mathrm{Func}\left(D,C\right)$ is a colimiting cocone precisely if for each object $d\in D$ the induced morphism ${K}^{▹}\to C$ is a colimiting cocone.
###### Proof
This is HTT, corollary 5.1.2.3
• limit
• 2-limit
• $\left(\infty ,1\right)$-limit
## References
### General
The definition of limit in quasi-categories is due to
• André Joyal, Quasi-categories and Kan complexes Journal of Pure and Applied Algebra 175 (2002), 207-222.
A brief survey is on page 159 of
A detailed account is in definition 1.2.13.4, p. 48 in
### In homotopy type theory
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https://xyz5261941.wordpress.com/2015/03/25/positive-definite-functions/ | # positive definite functions
I have encountered positive definite functions somewhere long before, and I think it should be during a probability course. These days when I attend a seminar on Brownian motions, this concept, positive definite function, recurs many times, and until then I realized that I did not know anything about this kind of function except perhaps its definition.
The most natural way to introduce positive definite function is perhaps to start from positive definite matrices. We all know what a positive definite matrix is. Here I assume always that the matrices are with real valued entries. Now consider a probability space, $(\mathbb{R}^n,\mathfrak{B},d\mu)$ where the $\sigma$-algebra on the space $\mathbb{R}^n$ is just generated by the Borel sets, and $d\mu$ is a finite measure. Then for $i,j=1,2,...,n$, we can define
$a_i=\int_{\mathbb{R}^n}x_id\mu,cov(i,j)=\int_{\mathbb{R}^n}(x_i-a_i)(x_j-a_j)d\mu$
Of course, we should assume that these quantities all exist. Then, we can easily show that the covariance matrix $Cov=(cov(i,j))_{i,j}$ is semi-definite positive.
One can show that, conversely, for any semi-positive definite matrix $Q$, there is a measure $d\mu$ on $\mathbb{R}^n$ such that the above quantities exist and its covariance matrix is just $Q$.
Then, one can ask, what if these quantities, $a_i,cov(i,j)$ do not exist? Then there appears some generalization. Note that the essential obstacle for the existence of these quantities is that these functions $x_i,(x_i-a_i)(x_j-a_j)$ are not bounded. Are there some important bounded functions related to a random variable or simply a finite measure? Yes, there are. And one of them is the characteristic function of a random variable or in other words, the Fourier transform of a finite measure:
$\hat{\mu}(x)=\int_{\mathbb{R}^n}e^{i}d\mu(y)$
where $$ is the inner product on $\mathbb{R}^n$.
Then how could we translate the semi-positive-definiteness of the covariance matrix into the language of characteristic functions? It is not so obvious. I will give it directly. For any positive integer $k$ and for any real numbers $b_1,b_2,...,b_k$ and any vectors $v_1,v_2,...,v_k$, we have that
$\sum_{i,j=1,...,k}\int_{\mathbb{R}^n}e^{i}d\mu(y)\geq0$
This is the definition for a positive definite function: we call a complex valued function $f:\mathbb{R}^n\rightarrow \mathbb{C}$ is semi-positive definite if for any positive integer $k$ and for any real numbers $b_1,b_2,...,b_k$ and any vectors $v_1,v_2,...,v_k$, we have that
$\sum_{i,j}f(v_i-v_j)b_i\bar{b_j}\geq0$
(a little remark is in order: there is another way around in Bayesian analysis which gives some more motivation for the introduction of (semi)positive definite functions, cf the wikipedia article). We drop the prefix ‘semi’ if the equality holds only for the case that $b_1=b_2=...=b_k=0$. So it is clear that the function $f(x)=\int e^{id\mu(y)}$ is a semi-positive definite function. If the measure $d\mu$ admits the existence of the above quantities, then we can show that $f$ is positive definite if and only if $Cov$ is a positive definite matrix. So, in this sense, we say that positive definite functions are generalizations of positive definite matrices.
There is a rather remarkable result which inverses the above process, that is the Bochner’s theorem.
Theorem(Bochner) If $f$ is a positive definite function on $\mathbb{R}^n$, then there is a finite measure $d\mu$ on $\mathbb{R}^n$ such that $f$ is the Fourier transform of $d\mu$.
Note that, according to this theorem, if $f$ is positive definite, then $f(x)$ tends to zero when $x$ tends to infinity. We can not see this point directly from the definition of positive definite functions.
Note that in the definition of positive definite functions, we use only the additive group structure of $\mathbb{R}^n$, this inspires us to again generalize the domain of definition to a general group. This will be the content of the next post. | 2017-11-22 03:59:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 40, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9494500160217285, "perplexity": 173.07322485146574}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806455.2/warc/CC-MAIN-20171122031440-20171122051440-00686.warc.gz"} |
https://brkmnd.com/pages/math/Default.aspx?id=4 | ## 24.12.2018
### Contents/Index
Say that $b$ is our barber. We are quantifying over people, that is $x$. The predicate $S(x,y)$ is interpreted as "$x$ shaves $y$". So if $b$ encumber us with his existence, we can conclude absurdities. What a paradox. | 2021-01-20 21:49:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8778539299964905, "perplexity": 2152.977417195537}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703522133.33/warc/CC-MAIN-20210120213234-20210121003234-00754.warc.gz"} |
http://cms.math.ca/cjm/msc/17C36?fromjnl=cjm&jnl=CJM | Analysis of the Brylinski-Kostant Model for Spherical Minimal Representations We revisit with another view point the construction by R. Brylinski and B. Kostant of minimal representations of simple Lie groups. We start from a pair $(V,Q)$, where $V$ is a complex vector space and $Q$ a homogeneous polynomial of degree 4 on $V$. The manifold $\Xi$ is an orbit of a covering of ${\rm Conf}(V,Q)$, the conformal group of the pair $(V,Q)$, in a finite dimensional representation space. By a generalized Kantor-Koecher-Tits construction we obtain a complex simple Lie algebra $\mathfrak g$, and furthermore a real form ${\mathfrak g}_{\mathbb R}$. The connected and simply connected Lie group $G_{\mathbb R}$ with ${\rm Lie}(G_{\mathbb R})={\mathfrak g}_{\mathbb R}$ acts unitarily on a Hilbert space of holomorphic functions defined on the manifold $\Xi$. Keywords:minimal representation, Kantor-Koecher-Tits construction, Jordan algebra, Bernstein identity, Meijer $G$-functionCategories:17C36, 22E46, 32M15, 33C80 | 2015-07-02 12:34:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9343065023422241, "perplexity": 208.33480952494423}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375095557.73/warc/CC-MAIN-20150627031815-00123-ip-10-179-60-89.ec2.internal.warc.gz"} |
http://quanteda.io/reference/ndoc.html | Get the number of documents or features in an object.
ndoc(x)
nfeat(x)
## Arguments
x a quanteda object: a corpus, dfm, or tokens object, or a readtext object from the readtext package.
## Value
an integer (count) of the number of documents or features
## Details
ndoc returns the number of documents in an object whose texts are organized as "documents" (a corpus, dfm, or tokens object, a readtext object from the readtext package).
nfeat returns the number of features from a dfm; it is an alias for ntype when applied to dfm objects. This function is only defined for dfm objects because only these have "features". (To count tokens, see ntoken.)
ntoken
# number of documents
nfeat(dfm(corpus_subset(data_corpus_inaugural, Year > 1980), remove_punct = FALSE))#> [1] 3260nfeat(dfm(corpus_subset(data_corpus_inaugural, Year > 1980), remove_punct = TRUE))#> [1] 3247 | 2019-06-15 21:29:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21415168046951294, "perplexity": 10935.045908495991}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627997335.70/warc/CC-MAIN-20190615202724-20190615224724-00096.warc.gz"} |
http://www.physicsforums.com/showthread.php?t=515963 | # derivative of sin^2
by elsternj
Tags: derivative, sin2
P: 42 1. The problem statement, all variables and given/known data Derivative of Sin22x 2. Relevant equations dy/dx = dy/du * du/dx y=U2 3. The attempt at a solution Just want to make sure I am doing this right*. Do I let U = Sin2x or U = 2x? Let's say U = Sin2x y=U2 then y = 2Sin2x * cos2x? Or if U = 2x. y = SinU2 y = 2cos2x * 2 y = 4cos2x am i on the right track with either of these? any help is appreciated! thanks!
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P: 9,818
Quote by elsternj am i on the right track with either of these?
You are halfway on the right track .
Sin^2(2x)=F(U(V)): V=2x, U=sin(V), F=U^2.
dF/dx=dF/dU*dU/dV*dV/dx.
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P: 38,879
Quote by elsternj 1. The problem statement, all variables and given/known data Derivative of Sin22x 2. Relevant equations dy/dx = dy/du * du/dx y=U2 3. The attempt at a solution Just want to make sure I am doing this right*. Do I let U = Sin2x or U = 2x?
You first let U= sin 2x so that $y= U^2$, $y'= 2U U'$.
Then, to find U', let V= 2x so U= sin V. U'= cos(V)(V') and, of course, V'= 2.
Put those together.
Let's say U = Sin2x y=U2 then y = 2Sin2x * cos2x?
No, because the derivative of sin2X is not cos2X. Use the chain rule again.
Or if U = 2x. y = SinU2 y = 2cos2x * 2 y = 4cos2x
No, because the derivative of $sin^2(x)$ is not $cos^2(x)$
am i on the right track with either of these? any help is appreciated! thanks!
P: 72
## derivative of sin^2
Essentially, what this entire question boils down to:
We need two applications of the chain rule.
The first one started well.
Instead of
y = 2Sin2x * cos2x
I recommend beginning Calculus students write.
y = 2Sin2x * ( Sin2x )'
The left factor, 2 Sin(2x) is finished.
Then to evaluate the derivative of Sin 2x, apply chain rule a second time, with v =2x
General hint, way to think of chain rule:
Take deriv. of the outside, leave the inside alone , then multiply by deriv. of inside.
Related Discussions Calculus 7 Calculus & Beyond Homework 10 General Physics 5 Advanced Physics Homework 3 Differential Geometry 3 | 2014-04-18 23:33:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6825510263442993, "perplexity": 2559.0129094262875}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609535535.6/warc/CC-MAIN-20140416005215-00305-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://mkweb.bcgsc.ca/scientific.american.graphic.science/ | This love loves love. It's a strange love, strange love.find a way to lovemore quotes
# visualization: beautiful
In Silico Flurries: Computing a world of snow. Scientific American. 23 December 2017
# visualization + design
Working with senior graphics editor at Scientific American Jen Christiansen, I have designed three Graphic Science visualizations for the magazine.
December 2015. Composition of bacteria in household dust.
June 2015. Relationship between genes and traits.
September 2014. Similarity of human, Denisovan, chimp, bonobo, and gorilla genomes.
# Men and Women Alter a Home's Bacteria Differently
## An analysis of dust reveals how the presence of men, women, dogs and cats affects the variety of bacteria in a household
### December 2015, Scientific American Volume 313, Issue 6
This collaboration with Jeanine Hunnicutt explored differences in household dust bacteria based on the gender and pet status of the occupants.
We have also written about the making of the graphic, for those interested in how these things come together.
Graphic by Martin Krzywinski and Barbara Jeanine Hunnicutt.
Catalogue of bacteria shapes by Barbara Jeanine Hunnicutt.
Source: Barberan A et al. (2015) The ecology of microscopic life in household dust. Proc. R. Soc. B 282: 20151139.
# A Road Map to the "Volume Control" of Genes
## Genes, traits and disease are linked in complex and surprising ways
### June 2015, Scientific American Volume 312, Issue 6
Because sometimes only a network hairball will do.
Graphic by Martin Krzywinski.
Source: Integrative analysis of 111 reference human epigenomes. (2015) Nature 518:317.
# Tiny Genetic Differences between Humans and Other Primates Pervade the Genome
## Genome comparisons reveal the DNA that distinguishes Homo sapiens from its kin
### September 2014, Scientific American Volume 311, Issue 3
A Scientific American blog entry "A Monkey's Blueprint" accompanies this piece. I also have a more detailed description with links to data sources.
You can also read more about Hilbert curves and creatures that live on it, Hilbertonians.
This design won a bronze award at Malofiej 23. For more information about Malofiej, see the SA Visual blog entry "There's No Infographic without Info (and other Lessons from Malofiej)".
Graphic by Martin Krzywinski, illustrations by Portia Sloan Rollings.
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# Happy 2018 $\pi$ Day—Boonies, burbs and boutiques of $\pi$
Wed 14-03-2018
Celebrate $\pi$ Day (March 14th) and go to brand new places. Together with Jake Lever, this year we shrink the world and play with road maps.
Streets are seamlessly streets from across the world. Finally, a halva shop on the same block!
A great 10 km run loop between Istanbul, Copenhagen, San Francisco and Dublin. Stop off for halva, smørrebrød, espresso and a Guinness on the way. (details)
Intriguing and personal patterns of urban development for each city appear in the Boonies, Burbs and Boutiques series.
In the Boonies, Burbs and Boutiques of $\pi$ we draw progressively denser patches using the digit sequence 159 to inform density. (details)
No color—just lines. Lines from Marrakesh, Prague, Istanbul, Nice and other destinations for the mind and the heart.
Roads from cities rearranged according to the digits of $\pi$. (details)
The art is featured in the Pi City on the Scientific American SA Visual blog.
Check out art from previous years: 2013 $\pi$ Day and 2014 $\pi$ Day, 2015 $\pi$ Day, 2016 $\pi$ Day and 2017 $\pi$ Day.
# Machine learning: supervised methods (SVM & kNN)
Thu 18-01-2018
Supervised learning algorithms extract general principles from observed examples guided by a specific prediction objective.
We examine two very common supervised machine learning methods: linear support vector machines (SVM) and k-nearest neighbors (kNN).
SVM is often less computationally demanding than kNN and is easier to interpret, but it can identify only a limited set of patterns. On the other hand, kNN can find very complex patterns, but its output is more challenging to interpret.
Nature Methods Points of Significance column: Machine learning: supervised methods (SVM & kNN). (read)
We illustrate SVM using a data set in which points fall into two categories, which are separated in SVM by a straight line "margin". SVM can be tuned using a parameter that influences the width and location of the margin, permitting points to fall within the margin or on the wrong side of the margin. We then show how kNN relaxes explicit boundary definitions, such as the straight line in SVM, and how kNN too can be tuned to create more robust classification.
Bzdok, D., Krzywinski, M. & Altman, N. (2018) Points of Significance: Machine learning: a primer. Nature Methods 15:5–6.
Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120.
# Human Versus Machine
Tue 16-01-2018
Balancing subjective design with objective optimization.
In a Nature graphics blog article, I present my process behind designing the stark black-and-white Nature 10 cover.
Nature 10, 18 December 2017
# Machine learning: a primer
Thu 18-01-2018
Machine learning extracts patterns from data without explicit instructions.
In this primer, we focus on essential ML principles— a modeling strategy to let the data speak for themselves, to the extent possible.
The benefits of ML arise from its use of a large number of tuning parameters or weights, which control the algorithm’s complexity and are estimated from the data using numerical optimization. Often ML algorithms are motivated by heuristics such as models of interacting neurons or natural evolution—even if the underlying mechanism of the biological system being studied is substantially different. The utility of ML algorithms is typically assessed empirically by how well extracted patterns generalize to new observations.
Nature Methods Points of Significance column: Machine learning: a primer. (read)
We present a data scenario in which we fit to a model with 5 predictors using polynomials and show what to expect from ML when noise and sample size vary. We also demonstrate the consequences of excluding an important predictor or including a spurious one.
Bzdok, D., Krzywinski, M. & Altman, N. (2017) Points of Significance: Machine learning: a primer. Nature Methods 14:1119–1120. | 2018-03-20 17:36:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2124570608139038, "perplexity": 5625.586174712503}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647519.62/warc/CC-MAIN-20180320170119-20180320190119-00106.warc.gz"} |
http://greyenlightenment.com/2020/01/ | ## Bernie Sanders’ Immigration Plan is Terrible, but there are some silver linings
The right needs to come to terms with the possibility of Sanders winning the primaries and possibly even becoming president. Upon cursory glance, his immigration policies are terrible, promising free stuff for illegals and pushing Congress for a law that would shield illegals from deportation, in addition to a pathway for citizenship, and also undo… Continue reading Bernie Sanders’ Immigration Plan is Terrible, but there are some silver linings
## No idea what he is talking about
This is why you shouldn’t take investment advice from people who have no idea what they are talking about: Is Boeing going down? Why else is Boeing stock down from $400 in 2018 to$324 now? That loss was anticipated long in advance, unlike Enron in which the loss was sudden and without an obvious… Continue reading No idea what he is talking about
## Online Journalism: Themes of Viral Articles
It has been a while since I wrote about online journalism. In this post I identify characteristics of authors and articles that go viral. There is a tendency to dismiss journalism as not a ‘hard’ or substantive subject, compared to more intellectually rigorous and less ideologically-motivated subjects such has math or computer science (STEM subjects).… Continue reading Online Journalism: Themes of Viral Articles
Not a whole lot in the news. The Trump impeachment Senate trial is a farce. Trump’s approval ratings are climbing again, now at 43% according to 538, which is the highest in months. The left’s gambit has failed. The left hoped that by impeaching Trump, even if on the flimsiest of charges, that enough undecided… Continue reading News Updates
## Smart-Left vs. Regressive-Left
I read lefty publications in order to take the pulse of the entirety culture-war landscape. If I just read right-wing blogs and magazines–the handful that still remain and are updated at at least regular intervals and haven’t yet departed to Twitter, Podcasting, or YouTube–my perspective would be limited. The article What’s the harm in reading?… Continue reading Smart-Left vs. Regressive-Left
## The Great Freeze
A reason why I talk about the stock market and economics a lot is because those are the two issues that policy makers are also most concerned with. We are living in a world increasingly dominated by economics and capital, as opposed to culture, even if the latter gets the most media coverage, and culture… Continue reading The Great Freeze
## Thinking rationally: 3 examples
Rationality is defined as “…the quality or state of being rational – that is, being based on or agreeable to reason. Rationality implies the conformity of one’s beliefs with one’s reasons to believe, and of one’s actions with one’s reasons for action…When the goal or problem involves making a decision, rationality factors in all information… Continue reading Thinking rationally: 3 examples
## 3x Leveraged ETF Strategy Guide, Part 2b
In the prior section, I calculated the volatility parameters for three major market index 3x ETFs: UPRO, UDOW, and TQQQ. In this section, I need to calculate a sample market cycle for the Nasdaq 100 index in order to estimate TQQQ returns. This is harder to do than compared to the the S&P 500, owing… Continue reading 3x Leveraged ETF Strategy Guide, Part 2b
## 3x Leveraged ETF Strategy Guide, Updated for 2020, Part 2
See part one It took longer to complete this section than expected owning to the difficulty of modeling historic stock market returns. Market returns to some degree follow a normal distribution, but ,rather, markets are more characterized by regimes. This means there are long periods in which market does well, followed by long periods in… Continue reading 3x Leveraged ETF Strategy Guide, Updated for 2020, Part 2
## Is a post-scarcity economy possible? It’s already happening
The srticle Education and Men without Work Just skimming the comments, there is the withholding of judgment against young, able-bodied men who, for whatever reason, choose not to work. There is no puritanical moralizing about the ‘virtues of work’, or how ‘people should not be lazy,’ or how ‘one must choose between work or starvation/poverty’;… Continue reading Is a post-scarcity economy possible? It’s already happening | 2021-09-21 15:08:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20036788284778595, "perplexity": 4949.3448851828025}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057225.38/warc/CC-MAIN-20210921131252-20210921161252-00115.warc.gz"} |
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USE CODE: SSPD25
if sinx+sin2x=2
then find,cos2x+cos4x
6 years ago
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### Answers : (1)
Ans:
$sin^{2}x + sinx = 2$
$(sinx+2)(sinx-1) = 0$
$sinx = 1$
is the only solution.
$x = n\pi \pm \frac{\pi }{2}$
$cos2x + cos4x = cos2(n\pi \pm \frac{\pi }{2}) + cos4(n\pi \pm \frac{\pi }{2})$
$cos2x + cos4x = cos(2n\pi \pm \pi ) + cos(4n\pi \pm 2\pi ) = -1 + 1 = 0$
Thanks & Regards
Jitender Singh
IIT Delhi
2 years ago
# Other Related Questions on Trigonometry
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More Questions On Trigonometry | 2016-10-25 14:14:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44511091709136963, "perplexity": 14024.869399609608}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720153.61/warc/CC-MAIN-20161020183840-00070-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://blender.stackexchange.com/questions/103085/how-do-i-make-a-large-set-of-objects-appear-over-a-period-of-time | # How do I make a large set of objects appear over a period of time?
My data assigns a specific time (say a calendar day or shorter) to the appearance of each of its several hundred objects. To show this I'd like to run through say a year of time in about 10 seconds and have the objects appear on the 3D display sequentially. Should I set out to write a python script that simulates time passage and then changes the layer or transparency of each object depending on whether its time has arrived? This sounds like a lot of processing, rechecking the status of all objects every unit of time. Is there some standard efficient strategy for minimizing the processing time so the computing time doesn't slow everything down?
Keyframes or Drivers on hide and hide_render
I would suggest either creating ether a keyframed action, or setting up drivers on the hide and hide_render properties of your object.
How you convert from your time to frames is up to you. In bpy.utils there is a convenience method that converts a datetime object to a frame.
Drivers
Each object from data will be hidden (both in viewer and to render) until the scene frame is greater than the data frame. Test script below.
import bpy
context = bpy.context
scene = context.scene
data = [[0, 0, 1, 12],
[0, 10, 3, 30],
[3, 3, 4, 40],]
for line in data:
x, y, scale, frame = line
location=(x, y, 0))
ob = context.active_object
# set scale
ob.scale *= scale
for dp in ["hide", "hide_render"]: # xxx
driver.driver.expression = "frame < %f" % frame
Keyframes
Keyframe as hidden at frame 1, show at data frame.
# add keyframes
for dp in ["hide", "hide_render"]: # xxx
setattr(ob, dp, 1)
ob.keyframe_insert(dp, frame=0)
setattr(ob, dp, 0)
ob.keyframe_insert(dp, frame=frame) | 2021-12-09 02:00:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18679991364479065, "perplexity": 3150.0940724240695}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363641.20/warc/CC-MAIN-20211209000407-20211209030407-00465.warc.gz"} |
https://nrich.maths.org/public/topic.php?code=71&cl=4&cldcmpid=1952 | # Resources tagged with: Mathematical reasoning & proof
Filter by: Content type:
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### There are 173 results
Broad Topics > Thinking Mathematically > Mathematical reasoning & proof
### Generally Geometric
##### Age 16 to 18 Challenge Level:
Generalise the sum of a GP by using derivatives to make the coefficients into powers of the natural numbers.
### Proof Sorter - Geometric Sequence
##### Age 16 to 18 Challenge Level:
Can you correctly order the steps in the proof of the formula for the sum of the first n terms in a geometric sequence?
### Golden Eggs
##### Age 16 to 18 Challenge Level:
Find a connection between the shape of a special ellipse and an infinite string of nested square roots.
### Archimedes and Numerical Roots
##### Age 14 to 16 Challenge Level:
The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
### Plus or Minus
##### Age 16 to 18 Challenge Level:
Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.
### An Alphanumeric
##### Age 16 to 18
Freddie Manners, of Packwood Haugh School in Shropshire solved an alphanumeric without using the extra information supplied and this article explains his reasoning.
### Geometric Parabola
##### Age 14 to 16 Challenge Level:
Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
### DOTS Division
##### Age 14 to 16 Challenge Level:
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
### Basic Rhythms
##### Age 16 to 18 Challenge Level:
Explore a number pattern which has the same symmetries in different bases.
### Multiplication Square
##### Age 14 to 16 Challenge Level:
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
### Water Pistols
##### Age 16 to 18 Challenge Level:
With n people anywhere in a field each shoots a water pistol at the nearest person. In general who gets wet? What difference does it make if n is odd or even?
### Janine's Conjecture
##### Age 14 to 16 Challenge Level:
Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .
### Fractional Calculus III
##### Age 16 to 18
Fractional calculus is a generalisation of ordinary calculus where you can differentiate n times when n is not a whole number.
### Particularly General
##### Age 16 to 18 Challenge Level:
By proving these particular identities, prove the existence of general cases.
### Shape and Territory
##### Age 16 to 18 Challenge Level:
If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?
### A Biggy
##### Age 14 to 16 Challenge Level:
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
### And So on - and on -and On
##### Age 16 to 18 Challenge Level:
Can you find the value of this function involving algebraic fractions for x=2000?
### Polite Numbers
##### Age 16 to 18 Challenge Level:
A polite number can be written as the sum of two or more consecutive positive integers. Find the consecutive sums giving the polite numbers 544 and 424. What characterizes impolite numbers?
### Thousand Words
##### Age 16 to 18 Challenge Level:
Here the diagram says it all. Can you find the diagram?
### Sixational
##### Age 14 to 18 Challenge Level:
The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
### Mod 3
##### Age 14 to 16 Challenge Level:
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
### Three Ways
##### Age 16 to 18 Challenge Level:
If x + y = -1 find the largest value of xy by coordinate geometry, by calculus and by algebra.
### Common Divisor
##### Age 14 to 16 Challenge Level:
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
### Our Ages
##### Age 14 to 16 Challenge Level:
I am exactly n times my daughter's age. In m years I shall be ... How old am I?
### There's a Limit
##### Age 14 to 18 Challenge Level:
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?
### Symmetric Tangles
##### Age 14 to 16
The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!
### Binomial
##### Age 16 to 18 Challenge Level:
By considering powers of (1+x), show that the sum of the squares of the binomial coefficients from 0 to n is 2nCn
### Triangle Incircle Iteration
##### Age 14 to 16 Challenge Level:
Keep constructing triangles in the incircle of the previous triangle. What happens?
### Iffy Logic
##### Age 14 to 18 Challenge Level:
Can you rearrange the cards to make a series of correct mathematical statements?
### Always Perfect
##### Age 14 to 16 Challenge Level:
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
### Problem Solving, Using and Applying and Functional Mathematics
##### Age 5 to 18 Challenge Level:
Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
### Mechanical Integration
##### Age 16 to 18 Challenge Level:
To find the integral of a polynomial, evaluate it at some special points and add multiples of these values.
### Yih or Luk Tsut K'i or Three Men's Morris
##### Age 11 to 18 Challenge Level:
Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .
##### Age 14 to 16 Challenge Level:
Kyle and his teacher disagree about his test score - who is right?
### Number Rules - OK
##### Age 14 to 16 Challenge Level:
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
### Impossible Sandwiches
##### Age 11 to 18
In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot.
### Euclid's Algorithm II
##### Age 16 to 18
We continue the discussion given in Euclid's Algorithm I, and here we shall discover when an equation of the form ax+by=c has no solutions, and when it has infinitely many solutions.
### Continued Fractions II
##### Age 16 to 18
In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).
### Composite Notions
##### Age 14 to 16 Challenge Level:
A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.
### Transitivity
##### Age 16 to 18
Suppose A always beats B and B always beats C, then would you expect A to beat C? Not always! What seems obvious is not always true. Results always need to be proved in mathematics.
### Matter of Scale
##### Age 14 to 16 Challenge Level:
Prove Pythagoras' Theorem using enlargements and scale factors.
### Magic Squares II
##### Age 14 to 18
An article which gives an account of some properties of magic squares.
### Where Do We Get Our Feet Wet?
##### Age 16 to 18
Professor Korner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.
##### Age 16 to 18 Challenge Level:
Find all positive integers a and b for which the two equations: x^2-ax+b = 0 and x^2-bx+a = 0 both have positive integer solutions.
### Telescoping Functions
##### Age 16 to 18
Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.
### Can it Be?
##### Age 16 to 18 Challenge Level:
When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?
### Proof of Pick's Theorem
##### Age 16 to 18 Challenge Level:
Follow the hints and prove Pick's Theorem.
### Unit Interval
##### Age 14 to 18 Challenge Level:
Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?
### Little and Large
##### Age 16 to 18 Challenge Level:
A point moves around inside a rectangle. What are the least and the greatest values of the sum of the squares of the distances from the vertices?
### Why 24?
##### Age 14 to 16 Challenge Level:
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results. | 2020-08-13 09:16:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5131896734237671, "perplexity": 1322.4099190589732}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738964.20/warc/CC-MAIN-20200813073451-20200813103451-00100.warc.gz"} |
https://wwrenderer-staging.libretexts.org/render-api?sourceFilePath=Library/Michigan/Chap3Sec10/Q15.pg&problemSeed=1234567&courseID=anonymous&userID=anonymous&course_password=anonymous&answersSubmitted=0&showSummary=1&displayMode=MathJax&language=en&outputFormat=nosubmit | Suppose that $f(t)$ is continuous and twice-differentiable for $t\ge 0$. Further suppose $f''(t) \ge 3$ for all $t\ge 0$ and $f(0) = f'(0) = 0$.
Using the Racetrack Principle, what linear function $g(t)$ can we prove is less than $f'(t)$ (for $t\ge 0$)?
$g(t) =$
Then, also using the Racetrack Principle, what quadratic function $h(t)$ can we prove is less than than $f(t)$ (for $t\ge 0$)?
$h(t) =$
For both parts of this problem, be sure you can clearly state how the theorem is applied to prove the indicated inequalities.
You can earn partial credit on this problem. | 2023-03-29 01:24:59 | {"extraction_info": {"found_math": true, "script_math_tex": 13, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9095368385314941, "perplexity": 342.33363953291166}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948900.50/warc/CC-MAIN-20230328232645-20230329022645-00725.warc.gz"} |
http://www.physicsforums.com/showpost.php?p=3047532&postcount=4 | View Single Post
Mentor P: 18,027 Linear transformations - Proving that a set generates the targe space OK, that's good. I'll also assume that you're working with $$\mathbb{R}$$ vector spaces, not that it matters a lot... Now consider the vector space $$E=\mathbb{R}^X$$. Can you find a basis for this vector space? Can you find an easy linear transformation f:E-->F?? | 2014-07-26 13:13:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8134599328041077, "perplexity": 356.7041510875808}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997901589.57/warc/CC-MAIN-20140722025821-00006-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://homework.cpm.org/category/CCI_CT/textbook/cc4/chapter/2/lesson/2.2.1/problem/2-50 | ### Home > CC4 > Chapter 2 > Lesson 2.2.1 > Problem2-50
2-50.
If $f(x)=3x−9$ and $g(x)=−x^2$, calculate the values of: Homework Help ✎
1. $f(−2)$
Substitute the value for $x$.
$f(−2) = 3(−2) − 9$
Continue to simplify.
1. $g(−2)$
Substitute the value for $x$.
$g(−2) = -(−2)^2$
Continue to simplify.
1. $x$ if $f(x)=0$
Substitute $0$ for $f(x)$.
$0 = 3x −9$
Continue solving for $x$
1. $g(m)$
Substitute the value for $x$.
$g(m) = −m^2$ | 2019-12-15 17:52:17 | {"extraction_info": {"found_math": true, "script_math_tex": 17, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7915840744972229, "perplexity": 8576.05097037678}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541309137.92/warc/CC-MAIN-20191215173718-20191215201718-00270.warc.gz"} |
https://tex.stackexchange.com/questions/224004/betababel-you-havent-defined-the-language-polutonikogreek-yet | # betababel: You haven't defined the language polutonikogreek yet
For many years I used the package betababel to combine Latin and Greek letters in one document, but since version 2014.20141024-1 of texlive-lang-greek, the simple example
\documentclass{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[ngerman]{betababel}
\begin{document}
\bcode{lo/gos}
\end{document}
(which worked with the previous version) produces this error when compiling with pdflatex:
Package babel Error: You haven't defined the language polutonikogreek yet.
Any ideas how to solve this?
• Welcome to TeX.SX! Nice question and thanks for the MWE. Maybe, you send a notice to the maintainer of betababel. Jan 20, 2015 at 12:32
I do not know if this runs into some clashes, but as betababel loads babel as well, it should be safe to do:
% arara: pdflatex
\documentclass{scrartcl}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[polutonikogreek, ngerman]{babel}
\usepackage[ngerman]{betababel}
\begin{document}
\bcode{lo/gos}
\end{document}
As written in your output, the babel option polutonikogreek was missing. As betababel does not offer this option, just load it via the original babel.
• The manual for betababel says explicitly not to do this.
– cfr
Oct 31, 2016 at 16:28
• @cfr I fear the betababel documentation is outdated: betababel was last updated 2005, while babel-greek and the babel kernel were last updated 2016. Oct 31, 2016 at 19:11
• @wicho The problem is that betababel wants to load Babel with options. If you load Babel first, that isn't possible.
– cfr
Oct 31, 2016 at 22:16
The packages betababel does not seem to have received updates in the last decade(s). I strongly discourage the use of it. (I could not get it up and running on a TexLive 2021 installation.)
I recommend to directly write Greek in your Tex file. Use Greek stickers on your keyboard and select a Greek layout in your operating system.
An example would look like
\documentclass{article}
% Set the font (output) encodings
\usepackage[T1]{fontenc}
% \usepackage[utf8]{inputenc} is no longer required (since 2018)
% Greek-specific commands
\usepackage[greek,english]{babel}
\begin{document}
\tableofcontents
\begin{abstract}
\textgreek{Αυτή είναι μια σύντομη περιγραφή του θέματος}
\end{abstract}
Latin text can also be added to the document.
\end{document} | 2023-02-09 06:50:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7979090809822083, "perplexity": 6625.377350433228}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764501407.6/warc/CC-MAIN-20230209045525-20230209075525-00093.warc.gz"} |
https://faculty.math.illinois.edu/Macaulay2/doc/Macaulay2/share/doc/Macaulay2/Matroids/html/_hyperplanes.html | # hyperplanes -- hyperplanes of a matroid
## Synopsis
• Usage:
hyperplanes M
• Inputs:
• M, ,
• Outputs:
## Description
The hyperplanes of a matroid are the flats of rank equal to rank M - 1. The complements of the hyperplanes are precisely the circuits of the dual matroid (which is indeed how this method computes hyperplanes), and thus a matroid is determined by its hyperplanes.
i1 : M = matroid({a,b,c,d},{{a,b},{a,c}}) o1 = a matroid of rank 2 on 4 elements o1 : Matroid i2 : hyperplanes M o2 = {set {1, 2, 3}, set {0, 3}} o2 : List | 2021-07-24 01:33:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6762648820877075, "perplexity": 1971.832090241484}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046150067.87/warc/CC-MAIN-20210724001211-20210724031211-00253.warc.gz"} |
http://nbviewer.jupyter.org/github/jrjohansson/sympsi-notebooks/blob/master/lecture-sympsi-resonator.ipynb | # Lecture 3 - Symbolic quantum mechanics using SymPsi - Resonators and cavities¶
Author: J. R. Johansson ([email protected]), http://jrjohansson.github.io.
Status: Preliminary (work in progress)
This notebook is part of a series of IPython notebooks on symbolic quantum mechanics computations using SymPy and SymPsi. SymPsi is an experimental fork and extension of the sympy.physics.quantum module in SymPy. The latest version of this notebook is available at http://github.com/jrjohansson/sympy-quantum-notebooks, and the other notebooks in this lecture series are also indexed at http://jrjohansson.github.io.
Requirements: A recent version of SymPy and the latest development version of SymPsi is required to execute this notebook. Instructions for how to install SymPsi is available here.
Disclaimer: The SymPsi module is still under active development and may change in behavior without notice, and the intention is to move some of its features to sympy.physics.quantum when they matured and have been tested. However, these notebooks will be kept up-to-date the latest versions of SymPy and SymPsi.
## Setup modules¶
In [1]:
from sympy import *
init_printing()
In [2]:
from sympsi import *
from sympsi.boson import *
from sympsi.operatorordering import *
## Introduction¶
In this notebook we will work with cavities and resonators. A single mode of a resonator can be modelled with a quantum harmonic oscillator. Here we look at the effect of classical driving fields, transformation to different rotating frames, and various types of coupling between different modes in a resonator.
## Quantum Harmonic Oscillator¶
First we consider the Hamiltonian for a single harmonic oscillator, which describes a single mode of for example a cavity or a waveguide resonator:
$$H = \hbar \omega_r a^\dagger a$$
To represent this Hamiltonian in sympy we create a symbol omega_r and an instance of the class BosonOp:
In [3]:
omega_r = symbols("omega_r", positive=True)
Hsym = symbols("H")
a = BosonOp("a")
In [4]:
H0 = omega_r * Dagger(a) * a
Eq(Hsym, H0)
Out[4]:
$$H = \omega_{r} {{a}^\dagger} {a}$$
### Classical drive signal¶
A classical driving field of frequency $\omega_d$ and amplitude $A$ and phase $\phi_0$ can be modelled by including an additional term in the Hamiltonian:
$$H = \hbar \omega_r a^\dagger a + A \cos(\omega_dt + \phi_0) (a + a^\dagger)$$
where we have assumed that the driving field couples to the quadrature of the resonator $a + a^\dagger$, which is the canonical case. It is convenient to rewrite the $\cos$ factor
$$H = \hbar \omega_r a^\dagger a + (Ae^{-i\omega_dt}+ A^*e^{i\omega_dt})(a + a^\dagger)$$
where we have redefined $A \rightarrow Ae^{-i\phi_0}$. In Sympy we can represent this Hamiltonian as:
In [5]:
omega_d, t = symbols("omega_d, t")
A = symbols("A")
In [6]:
Hdrive = (A * exp(-I * omega_d * t) + conjugate(A) * exp(I * omega_d * t)) * (a + Dagger(a))
Hdrive
Out[6]:
$$\left(A e^{- i \omega_{d} t} + e^{i \omega_{d} t} \overline{A}\right) \left({{a}^\dagger} + {a}\right)$$
In [7]:
H = H0 + Hdrive
Eq(Hsym, H)
Out[7]:
$$H = \omega_{r} {{a}^\dagger} {a} + \left(A e^{- i \omega_{d} t} + e^{i \omega_{d} t} \overline{A}\right) \left({{a}^\dagger} + {a}\right)$$
When working with Hamiltonians like this one, one common operation is to move to different rotating frames (by performing unitary transformations) where the Hamiltonian takes a simplier form.
Here we want to transform this Hamiltonian to a rotating frame in which the drive term (and all other terms) are no longer explicitly depening on time t. We can accomplish this by performing the unitary transformation
$$U = \exp(i\omega_d a^\dagger a t)$$
In [8]:
U = exp(I * omega_d * t * Dagger(a) * a)
U
Out[8]:
$$e^{i \omega_{d} t {{a}^\dagger} {a}}$$
When doing a unitary basis transformation, the Hamiltonian is transformed as
$$H \rightarrow UHU^\dagger -i U \frac{d}{dt}U^\dagger$$
and we can carry out this transformation using the function hamiltonian_transformation:
In [9]:
H2 = hamiltonian_transformation(U, H.expand())
H2
Out[9]:
$$A {{a}^\dagger} + A e^{- 2 i \omega_{d} t} {a} - \omega_{d} {{a}^\dagger} {a} + \omega_{r} {{a}^\dagger} {a} + e^{2 i \omega_{d} t} \overline{A} {{a}^\dagger} + \overline{A} {a}$$
Now let's introduce the detuning $\Delta = \omega_r - \omega_d$:
In [10]:
Delta = symbols("Delta", positive=True)
In [11]:
H3 = collect(H2, Dagger(a) * a).subs(omega_r - omega_d, Delta)
H3
Out[11]:
$$A {{a}^\dagger} + A e^{- 2 i \omega_{d} t} {a} + \Delta {{a}^\dagger} {a} + e^{2 i \omega_{d} t} \overline{A} {{a}^\dagger} + \overline{A} {a}$$
### Rotating-wave approximation (RWA)¶
Now we invoke the rotating-wave approximation, under which we assume that $\omega_d$ is much larger than $\Delta$, so that the we can neglect the two fast rotating terms which contains factors $\exp(\pm 2i \omega_d t)$:
In [12]:
H3 = drop_terms_containing(H3, [exp( 2 * I * omega_d * t),
exp(-2 * I * omega_d * t)])
Eq(Hsym, H3)
Out[12]:
$$H = A {{a}^\dagger} + \Delta {{a}^\dagger} {a} + \overline{A} {a}$$
This is a time-independent hamiltonian describing the resonator in a rotating frame, where fast rotating terms have been dropped. We can no apply a displacement transformation by applying the unitary transformation:
In [13]:
alpha = symbols("alpha")
H = Dagger(a) * alpha - conjugate(alpha) * a
U = exp(H)
U
Out[13]:
$$e^{\alpha {{a}^\dagger} - \overline{\alpha} {a}}$$
In [14]:
H4 = hamiltonian_transformation(U, H3)
H4 = collect(H4.expand(), [Dagger(a)*a, a, Dagger(a)])
H4
Out[14]:
$$- A \overline{\alpha} + \Delta \alpha \overline{\alpha} + \Delta {{a}^\dagger} {a} - \alpha \overline{A} + \left(A - \Delta \alpha\right) {{a}^\dagger} + \left(- \Delta \overline{\alpha} + \overline{A}\right) {a}$$
If we choose $\alpha = A/\Delta$ and drop c-numbers from the hamiltonian, we obtain a particularly simple form:
In [15]:
H5 = H4.subs(alpha, A/Delta)
H5 = drop_c_number_terms(H5)
H5
Out[15]:
$$\Delta {{a}^\dagger} {a}$$
So a driven harmonic oscillator can be described by the hamiltonian of an undriven harmonic oscillator in a displaced frame.
## Optical parametric oscillator¶
An optical parametric oscillator (OPO) is a two-mode system with a particular nonlinear interaction. The Hamiltonian of the OPO is
$$H = \omega_r a^\dagger a + \omega_p b^\dagger b + (\kappa {a^\dagger}^2 b + \kappa^* a^2 b^\dagger) + (A e^{i\omega_pt} + A^* e^{-i\omega_pt})(b + b^\dagger)$$
where the operators of the two modes are$a$ and $b$, and the nonlinear interaction strength is $\kappa$, and where we have also included a classical drive field applied to mode $b$.
To model this system in SymPy we create two instances of BosonOp, one for each mode, and construct the Hamiltonian:
In [16]:
a, b = BosonOp("a"), BosonOp("b")
In [17]:
kappa, omega_p, omega_a, omega_b, t = symbols("kappa, omega_p, omega_a, omega_b, t")
Delta_a, Delta_b = symbols("Delta_a, Delta_b", positive=True)
In [18]:
Hdrive = (A * exp(-I * omega_p * t) + conjugate(A) * exp(I * omega_p * t)) * (b + Dagger(b))
H1 = omega_a * Dagger(a) * a + omega_b * Dagger(b) * b + kappa * (a ** 2 * Dagger(b) + Dagger(a) ** 2 * b) + Hdrive
Eq(Hsym, H1)
Out[18]:
$$H = \kappa \left(\left({{a}^\dagger}\right)^{2} {b} + \left({a}\right)^{2} {{b}^\dagger}\right) + \omega_{a} {{a}^\dagger} {a} + \omega_{b} {{b}^\dagger} {b} + \left(A e^{- i \omega_{p} t} + e^{i \omega_{p} t} \overline{A}\right) \left({{b}^\dagger} + {b}\right)$$
We first move to a frame rotating with frequency $\omega_p$ with respect to mode $b$:
In [19]:
U = exp(I * omega_p * t * Dagger(b) * b)
U
Out[19]:
$$e^{i \omega_{p} t {{b}^\dagger} {b}}$$
In [20]:
H2 = hamiltonian_transformation(U, H1.expand(), independent=True)
H2
Out[20]:
$$A {{b}^\dagger} + A e^{- 2 i \omega_{p} t} {b} + \kappa e^{i \omega_{p} t} \left({a}\right)^{2} {{b}^\dagger} + \kappa e^{- i \omega_{p} t} \left({{a}^\dagger}\right)^{2} {b} + \omega_{a} {{a}^\dagger} {a} + \omega_{b} {{b}^\dagger} {b} - \omega_{p} {{b}^\dagger} {b} + e^{2 i \omega_{p} t} \overline{A} {{b}^\dagger} + \overline{A} {b}$$
and we can perform the rotating wave approximation and drop the fast rotating terms $\exp{\left(\pm i \omega_p t\right)}$:
In [21]:
H3 = drop_terms_containing(H2, [exp(2 * I * omega_p * t),
exp(-2 * I * omega_p * t)])
H3 = collect(H3, kappa)
H3
Out[21]:
$$A {{b}^\dagger} + \kappa \left(e^{i \omega_{p} t} \left({a}\right)^{2} {{b}^\dagger} + e^{- i \omega_{p} t} \left({{a}^\dagger}\right)^{2} {b}\right) + \omega_{a} {{a}^\dagger} {a} + \omega_{b} {{b}^\dagger} {b} - \omega_{p} {{b}^\dagger} {b} + \overline{A} {b}$$
Introduce a new variable for the detuning $\Delta_b = \omega_b - \omega_p$:
In [22]:
H4 = H3.subs(omega_b, Delta_b + omega_p).expand()
H4
Out[22]:
$$A {{b}^\dagger} + \Delta_{b} {{b}^\dagger} {b} + \kappa e^{i \omega_{p} t} \left({a}\right)^{2} {{b}^\dagger} + \kappa e^{- i \omega_{p} t} \left({{a}^\dagger}\right)^{2} {b} + \omega_{a} {{a}^\dagger} {a} + \overline{A} {b}$$
Next we want to displace the mode $b$ so that the drive terms are eliminated:
In [23]:
beta = symbols("beta")
H = Dagger(b) * beta - conjugate(beta) * b
U = exp(H)
U
Out[23]:
$$e^{\beta {{b}^\dagger} - \overline{\beta} {b}}$$
In [24]:
H5 = hamiltonian_transformation(U, H4.expand(), independent=True)
H5
Out[24]:
$$A \left(- \overline{\beta} + {{b}^\dagger}\right) + \Delta_{b} \left(- \overline{\beta} + {{b}^\dagger}\right) \left(- \beta + {b}\right) + \kappa e^{i \omega_{p} t} \left({a}\right)^{2} \left(- \overline{\beta} + {{b}^\dagger}\right) + \kappa e^{- i \omega_{p} t} \left({{a}^\dagger}\right)^{2} \left(- \beta + {b}\right) + \omega_{a} {{a}^\dagger} {a} + \overline{A} \left(- \beta + {b}\right)$$
In [25]:
H5 = collect(H5.expand(), [Dagger(a) * a, Dagger(b) * b, Dagger(a) ** 2 * b, a ** 2 * Dagger(b), b, Dagger(b)])
H5
Out[25]:
$$- A \overline{\beta} + \Delta_{b} \beta \overline{\beta} + \Delta_{b} {{b}^\dagger} {b} - \beta \kappa e^{- i \omega_{p} t} \left({{a}^\dagger}\right)^{2} - \beta \overline{A} - \kappa e^{i \omega_{p} t} \overline{\beta} \left({a}\right)^{2} + \kappa e^{i \omega_{p} t} \left({a}\right)^{2} {{b}^\dagger} + \kappa e^{- i \omega_{p} t} \left({{a}^\dagger}\right)^{2} {b} + \omega_{a} {{a}^\dagger} {a} + \left(A - \Delta_{b} \beta\right) {{b}^\dagger} + \left(- \Delta_{b} \overline{\beta} + \overline{A}\right) {b}$$
The choice $\beta = A/\Delta_b$ eliminates the drive terms. After dropping c numbers we have:
In [26]:
H6 = H5.subs(beta, A/Delta_b)
H6 = drop_c_number_terms(H6)
H6 = collect(H6, [exp( I * omega_p * t) * kappa * a ** 2,
exp(-I * omega_p * t) * kappa * Dagger(a) ** 2])
H6
Out[26]:
$$\Delta_{b} {{b}^\dagger} {b} + \kappa e^{i \omega_{p} t} \left({a}\right)^{2} \left({{b}^\dagger} - \frac{\overline{A}}{\Delta_{b}}\right) + \kappa e^{- i \omega_{p} t} \left({{a}^\dagger}\right)^{2} \left(- \frac{A}{\Delta_{b}} + {b}\right) + \omega_{a} {{a}^\dagger} {a}$$
If we now assume that the dynamics of the mode $b$ is dominated by the classical drive field, we can neglect the $b$ operators in the hamiltonian (in this displaced frame, which describes deviations from the dynamics induced by the classical driving field):
In [27]:
H7 = drop_terms_containing(H6.expand(), [b, Dagger(b)])
H7 = collect(H7, kappa / Delta_b)
H7
Out[27]:
$$\omega_{a} {{a}^\dagger} {a} + \frac{\kappa}{\Delta_{b}} \left(- A e^{- i \omega_{p} t} \left({{a}^\dagger}\right)^{2} - e^{i \omega_{p} t} \overline{A} \left({a}\right)^{2}\right)$$
To simpify the notation we redefine $- \kappa A / \Delta_b \rightarrow \kappa$, and assume that $A$ is real:
In [28]:
H = omega_a * Dagger(a) * a + kappa * (a ** 2 * exp(I * omega_p * t) + Dagger(a) ** 2 * exp(-I * omega_p * t))
Eq(Hsym, H)
Out[28]:
$$H = \kappa \left(e^{i \omega_{p} t} \left({a}\right)^{2} + e^{- i \omega_{p} t} \left({{a}^\dagger}\right)^{2}\right) + \omega_{a} {{a}^\dagger} {a}$$
To eliminate the time-dependence in the interaction term we move to a rotating frame using the unitary transformation:
In [29]:
U = exp(I * omega_d * t * Dagger(a) * a)
U
Out[29]:
$$e^{i \omega_{d} t {{a}^\dagger} {a}}$$
In [30]:
H2 = hamiltonian_transformation(U, H)
H2
Out[30]:
$$\kappa \left(e^{2 i \omega_{d} t} e^{- i \omega_{p} t} \left({{a}^\dagger}\right)^{2} + e^{- 2 i \omega_{d} t} e^{i \omega_{p} t} \left({a}\right)^{2}\right) + \omega_{a} {{a}^\dagger} {a} - \omega_{d} {{a}^\dagger} {a}$$
Now consider the case $\omega_p = 2 \omega_d$:
In [31]:
H3 = H2.subs(omega_d, omega_p/2)
H3 = collect(H3, Dagger(a) * a)
H3
Out[31]:
$$\kappa \left(\left({{a}^\dagger}\right)^{2} + \left({a}\right)^{2}\right) + \left(\omega_{a} - \frac{\omega_{p}}{2}\right) {{a}^\dagger} {a}$$
Introduce $\Delta_a = \omega_a - \omega_p / 2$:
In [32]:
H4 = H3.subs(omega_a, Delta_a + omega_p/2)
H4
Out[32]:
$$\Delta_{a} {{a}^\dagger} {a} + \kappa \left(\left({{a}^\dagger}\right)^{2} + \left({a}\right)^{2}\right)$$
We can diagonalize this Hamiltonian by introducing the squeezing transformation:
In [33]:
chi = symbols("chi")
In [34]:
U = exp(chi/2 * a **2 - chi/2 * Dagger(a) ** 2)
U
Out[34]:
$$e^{- \frac{\chi \left({{a}^\dagger}\right)^{2}}{2} + \frac{\chi \left({a}\right)^{2}}{2}}$$
which tranforms the operators $a$ and $a^\dagger$ according to the well-known relations:
In [35]:
hamiltonian_transformation(U, a)
Out[35]:
$$\sinh{\left (\chi \right )} {{a}^\dagger} + \cosh{\left (\chi \right )} {a}$$
In [36]:
hamiltonian_transformation(U, Dagger(a))
Out[36]:
$$\sinh{\left (\chi \right )} {a} + \cosh{\left (\chi \right )} {{a}^\dagger}$$
and in this frame the Hamiltonian takes the form:
In [37]:
H5 = hamiltonian_transformation(U, H4)
H5
Out[37]:
$$\Delta_{a} \left(\sinh{\left (\chi \right )} {a} + \cosh{\left (\chi \right )} {{a}^\dagger}\right) \left(\sinh{\left (\chi \right )} {{a}^\dagger} + \cosh{\left (\chi \right )} {a}\right) + \kappa \left(\left(\sinh{\left (\chi \right )} {{a}^\dagger} + \cosh{\left (\chi \right )} {a}\right)^{2} + \left(\sinh{\left (\chi \right )} {a} + \cosh{\left (\chi \right )} {{a}^\dagger}\right)^{2}\right)$$
In [38]:
H6 = normal_ordered_form(H5.expand(), independent=True)
H6 = drop_c_number_terms(H6)
H6 = collect(H6, [Dagger(a) * a, Dagger(a)**2, a**2])
H6
Out[38]:
$$\left(\Delta_{a} \sinh^{2}{\left (\chi \right )} + \Delta_{a} \cosh^{2}{\left (\chi \right )} + 4 \kappa \sinh{\left (\chi \right )} \cosh{\left (\chi \right )}\right) {{a}^\dagger} {a} + \left(\Delta_{a} \sinh{\left (\chi \right )} \cosh{\left (\chi \right )} + \kappa \sinh^{2}{\left (\chi \right )} + \kappa \cosh^{2}{\left (\chi \right )}\right) \left({{a}^\dagger}\right)^{2} + \left(\Delta_{a} \sinh{\left (\chi \right )} \cosh{\left (\chi \right )} + \kappa \sinh^{2}{\left (\chi \right )} + \kappa \cosh^{2}{\left (\chi \right )}\right) \left({a}\right)^{2}$$
In [39]:
H7 = collect(H6, H6.args[1].args[0])
H7
Out[39]:
$$\left(\Delta_{a} \sinh^{2}{\left (\chi \right )} + \Delta_{a} \cosh^{2}{\left (\chi \right )} + 4 \kappa \sinh{\left (\chi \right )} \cosh{\left (\chi \right )}\right) {{a}^\dagger} {a} + \left(\Delta_{a} \sinh{\left (\chi \right )} \cosh{\left (\chi \right )} + \kappa \sinh^{2}{\left (\chi \right )} + \kappa \cosh^{2}{\left (\chi \right )}\right) \left(\left({{a}^\dagger}\right)^{2} + \left({a}\right)^{2}\right)$$
In [40]:
# Trick to simplify the coefficients for the quantum operators
H8 = Add(*(simplify(arg.args[0]) * Mul(*(arg.args[1:])) for arg in H7.args))
H8
Out[40]:
$$\left(\frac{\Delta_{a}}{2} \sinh{\left (2 \chi \right )} + \kappa \cosh{\left (2 \chi \right )}\right) \left(\left({{a}^\dagger}\right)^{2} + \left({a}\right)^{2}\right) + \left(\Delta_{a} \cosh{\left (2 \chi \right )} + 2 \kappa \sinh{\left (2 \chi \right )}\right) {{a}^\dagger} {a}$$
Now if we choose $\chi$ such that the coefficient of $a^2 + {a^\dagger}^2$ is zero:
In [41]:
chi_eq = H8.args[0].args[0]
In [42]:
Eq(chi_eq, 0)
Out[42]:
$$\frac{\Delta_{a}}{2} \sinh{\left (2 \chi \right )} + \kappa \cosh{\left (2 \chi \right )} = 0$$
In [43]:
chi_sol = simplify(solve(chi_eq, chi)[3])
Eq(chi, chi_sol)
Out[43]:
$$\chi = \log{\left (\sqrt[4]{\frac{\Delta_{a} - 2 \kappa}{\Delta_{a} + 2 \kappa}} \right )}$$
we obtain a diagonal Hamiltonian:
In [44]:
H9 = H8.subs(chi_eq.args[0], -chi_eq.args[1])
H9
Out[44]:
$$\left(\Delta_{a} \cosh{\left (2 \chi \right )} + 2 \kappa \sinh{\left (2 \chi \right )}\right) {{a}^\dagger} {a}$$
with frequency:
In [45]:
Eq(Symbol("omega"), H9.args[0])
Out[45]:
$$\omega = \Delta_{a} \cosh{\left (2 \chi \right )} + 2 \kappa \sinh{\left (2 \chi \right )}$$
### Versions¶
In [46]:
%reload_ext version_information
%version_information sympy, sympsi
Out[46]:
SoftwareVersion
Python3.4.1 (default, Sep 20 2014, 19:44:17) [GCC 4.2.1 Compatible Apple LLVM 5.1 (clang-503.0.40)]
IPython2.3.0
OSDarwin 13.4.0 x86_64 i386 64bit
sympy0.7.5-git
sympsi0.1.0.dev-0c6e514
Thu Oct 09 16:01:18 2014 JST | 2017-11-20 18:56:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7244889736175537, "perplexity": 3274.037142135731}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806124.52/warc/CC-MAIN-20171120183849-20171120203849-00157.warc.gz"} |
https://bird.bcamath.org/handle/20.500.11824/667?show=full | dc.contributor.author Biswas I. en_US dc.contributor.author Dan A. en_US dc.contributor.author Paul A. en_US dc.date.accessioned 2017-04-24T10:55:47Z dc.date.available 2017-04-24T10:55:47Z dc.date.issued 2017-04-01 dc.identifier.issn 0025-2611 dc.identifier.uri http://hdl.handle.net/20.500.11824/667 dc.description.abstract A theorem of Weil and Atiyah says that a holomorphic vector bundle $E$ on a compact Riemann surface $X$ admits a holomorphic connection if and only if the degree of every direct summand of $E$ is zero. Fix a finite subset $S$ of $X$, and fix an endomorphism $A(x)\, \in\, \text{End}(E_x)$ for every $x\, \in\, S$. It is natural to ask when there is a logarithmic connection on $E$ singular over $S$ with residue $A(x)$ at every $x\, \in\, S$. We give a necessary and sufficient condition for it under the assumption that the residues $A(x)$ are rigid. en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.publisher Manucripta Mathematica en_US dc.relation info:eu-repo/grantAgreement/EC/FP7/615655 en_US dc.relation ES/1PE/SEV-2013-0323 en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Logarithmic connection en_US dc.subject residue en_US dc.subject rigidity en_US dc.subject logarithmic Atiyah bundle en_US dc.title Criterion for logarithmic connections with prescribed residues en_US dc.type info:eu-repo/semantics/article en_US dc.type info:eu-repo/semantics/publishedVersion en_US dc.identifier.doi 10.1007/s00229-017-0935-6 dc.relation.publisherversion http://link.springer.com/article/10.1007/s00229-017-0935-6 en_US
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Except where otherwise noted, this item's license is described as info:eu-repo/semantics/openAccess | 2019-06-17 13:00:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8068472743034363, "perplexity": 6790.465429649994}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998475.92/warc/CC-MAIN-20190617123027-20190617145027-00186.warc.gz"} |
https://math.stackexchange.com/questions/1372549/shortcuts-for-computing-the-eigenvalues-of-a-linear-transformation | # Shortcuts for computing the eigenvalues of a linear transformation
How would you calculate the eigenvalues of the following matrix?
$A = \begin{pmatrix} -3 & 1 & -1 \\ -7 & 5 & -1\\ -6 & 6 & -2\end{pmatrix}$ $\ \ \ \ \ $$\chi_A(\lambda) = \det(A-\lambda I)= \begin{vmatrix} -3-\lambda & 1 & -1 \\ -7 & 5-\lambda & -1\\ -6 & 6 & -2-\lambda \end{vmatrix}=\ldots =0 I'd really like to avoid using the rule of Sarrus. This will just lead to a huge list of multiplications and finally I may even have to guess the roots of the polynomial (maybe with Vieta's Theorem) and factor them out via polynomial division. - This whole process is tedious and prone to errors so I'd like to take some shortcuts whenever I can. Here are some shortcuts I already know, which may be used in conjunction: • Multiplying two rows by (-1) (this will not change the determinant) • Developing the determinant via a row or column that has a lot of zeros in it (ideally just one factor) to get out linear factors of the polynomial. • Transforming the matrix via gaussian elimination to a matrix which has more zeros in one column or row (ideally: transform it to a lower/upper triangular matrix). • Compute the determinant via the theorem for block-diagonal matrices. However, none of these shortcuts are useful for calculating the eigenvalues of A. How would you approach the computation of the determinant of the matrix of above? What other shortcuts do you have to share? • For dense matrix expanding of determinant is only method, I suppose. – Michael Galuza Jul 24 '15 at 15:25 ## 1 Answer Here's a start: Add column 1 to column 2 (this doesn't change the determinant); then take out a factor from column 2; after that, add column 2 to column 3:$$ \chi_A(\lambda) = \begin{vmatrix} -3-\lambda & 1 & -1 \\ -7 & 5-\lambda & -1 \\ -6 & 6 & -2-\lambda\end{vmatrix} = \begin{vmatrix} -3-\lambda & -2-\lambda & -1 \\ -7 & -2-\lambda & -1 \\ -6 & 0 & -2-\lambda\end{vmatrix} = -(2+\lambda) \begin{vmatrix} -3-\lambda & 1 & -1 \\ -7 & 1 & -1 \\ -6 & 0 & -2-\lambda\end{vmatrix} = -(2+\lambda) \begin{vmatrix} -3-\lambda & 1 & 0 \\ -7 & 1 & 0 \\ -6 & 0 & -2-\lambda\end{vmatrix} = \dotsb$\$
• Thanks! I didn't think of taking out a factor of a column! That's a good idea! I guess there's really no simpler way than doing it that way when the matrix is dense. – ndrizza Jul 25 '15 at 15:56
• In general, you may not be able to avoid multiplying everything out. For tricks like this to work, one needs to be a bit lucky. Or the exercise needs to be rigged. ;-) – Hans Lundmark Jul 25 '15 at 17:25 | 2020-09-27 20:18:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9123045206069946, "perplexity": 319.06762265662604}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401578485.67/warc/CC-MAIN-20200927183616-20200927213616-00578.warc.gz"} |
https://proofwiki.org/wiki/Definition:Linear_Ordering | # Definition:Total Ordering
(Redirected from Definition:Linear Ordering)
## Definition
Let $\mathcal R \subseteq S \times S$ be a relation on a set $S$.
### Definition 1
$\RR$ is a total ordering on $S$ if and only if:
$(1): \quad \RR$ is an ordering on $S$
$(2): \quad \RR$ is connected
That is, $\RR$ is an ordering with no non-comparable pairs:
$\forall x, y \in S: x \mathop \RR y \lor y \mathop \RR x$
### Definition 2
$\RR$ is a total ordering on $S$ if and only if:
$(1): \quad \RR \circ \RR = \RR$
$(2): \quad \RR \cap \RR^{-1} = \Delta_S$
$(3): \quad \RR \cup \RR^{-1} = S \times S$
## Also known as
Some sources call this a linear ordering, or a simple ordering.
If it is necessary to emphasise that a total ordering $\preceq$ is not strict, then the term weak total ordering may be used.
## Also see
• Results about total orderings can be found here. | 2020-07-15 09:19:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8339514136314392, "perplexity": 688.0547317504228}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657163613.94/warc/CC-MAIN-20200715070409-20200715100409-00553.warc.gz"} |
https://halldweb.jlab.org/doc-public/DocDB/ShowDocument?docid=1443 | # GlueX Experiment Document 1443-v1
DocDB Home ] [ Portal Home ] [ Search ] [ Last 20 Days ] [ List Authors ] [ List Topics ] [ List Events ]
# Reconstruction of the $\eta\pi^{0}$ System plus \pyth{} background.
Document #:
GlueX-doc-1443-v1
Document type:
Technical Note
Submitted by:
Blake Leverington
Updated by:
Blake Leverington
Document Created:
14 Mar 2010, 20:31
Contents Revised:
14 Mar 2010, 20:31
14 Mar 2010, 20:37
Viewable by:
• Public document
Modifiable by:
• Same as Viewable by
Abstract:
This is part of Chapter 7 from my thesis draft on reconstructing the eta-pi0 system and examining the background associated with this all neutral system. If anything is amiss don't panic, this is an early draft with several components missing.
Files in Document:
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DocDB Version 8.8.6, contact Document Database Administrators | 2019-07-16 00:58:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2854226231575012, "perplexity": 1969.7556919873398}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195524290.60/warc/CC-MAIN-20190715235156-20190716021156-00330.warc.gz"} |
http://docs.itascacg.com/flac3d700/flac3d/zone/doc/manual/zone_manual/zone_commands/cmd_zone.mechanical.html | # zone mechanical command
Syntax
zone mechanical keyword
Primary keywords:
Sets parameters for a static mechanical analysis, that are specific to zones. The following keywords apply:
active b
Sets mechanical calculation off/on (default is on). The mechanical calculation may be turned off for a thermal-only calculation or a fluid flow-only calculation. Note that in general it is preferable to set mechanical calculations off for the entire model with the model mechanical active command.
damping keyword <range>
Select the damping type for the static, mechanical process (the default damping is local).
combined <f >
combined local damping (default is 0.8).
local <f ><alternate>
local damping (default is 0.8). If the alternate keyword is specified, an experimental alternate implementation of local damping is used that produces less sensitivity to small changes in the model.
energy keyword
allows elastic strain energy and dissipated plastic energy to be calculated (see Energy Calculation in FLAC3D).
active b
Turns the calculations off/on in the stress-strain loop
clear <range>
will set the four zone energy values in every zone back to zero. The zone mechanical active command does not clear these values. This allows you to stop accumulating plastic work over any interval you wish, and resume accumulating at any time from where it left off.
list
shows a summary of current zone mechanical settings in the console. | 2021-09-17 10:41:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41654378175735474, "perplexity": 4642.7573196277735}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780055632.65/warc/CC-MAIN-20210917090202-20210917120202-00096.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/introductory-algebra-for-college-students-7th-edition/chapter-1-section-1-2-fractions-in-algebra-exercise-set-page-29/73 | # Chapter 1 - Section 1.2 - Fractions in Algebra - Exercise Set - Page 29: 73
$\frac{1}{6}$
#### Work Step by Step
$\frac{7}{12} - \frac{5}{12}$ The difference of two fractions with same denominators is the difference of their numerators over the common denominator. $\frac{7-5}{12}$ = $\frac{2}{12}$ Since 2 is the greatest common factor of 2 and 12, divide numerator and denominator by 2 $\frac{1*2}{6*2}$ = $\frac{1}{6}$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 2018-10-19 10:51:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8168852925300598, "perplexity": 421.0686993008429}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512395.23/warc/CC-MAIN-20181019103957-20181019125457-00553.warc.gz"} |
http://www.ams.org/mathscinet-getitem?mr=1956442 | MathSciNet bibliographic data MR1956442 (2004a:32047) 32S65 (37F50 37F75) Brochero Martínez, Fabio Enrique Groups of germs of analytic diffeomorphisms in \$(\Bbb C\sp 2,0)\$$(\Bbb C\sp 2,0)$. J. Dynam. Control Systems 9 (2003), no. 1, 1–32. Article
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews. | 2015-05-29 02:05:42 | {"extraction_info": {"found_math": true, "script_math_tex": 1, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.996381402015686, "perplexity": 14274.9727938526}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207929832.32/warc/CC-MAIN-20150521113209-00111-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://www.storyofmathematics.com/if-a-tank-holds-5000-gallons/ | # If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes.
After time t, the following is the relation that represents the volume V of water that remains in the tank as per Torricelli’s Law.${5000\left(1-\frac{t}{40}\right)}^2=V,\ \ where\ 0\le t\le 40$
As the water is draining from the tank, calculate its rate after (a)5min and (b)10min.
Also, find the time at which the rate of water draining from the tank is fastest and slowest.
The aim of this article is to find the rate of water draining from the tank at a certain instance of time and find the time of fastest and slowest drain rate.
The Rate of Flow of a given volume $V$ is calculated by taking the first derivative of Torricelli’s Equation with respect to time $t$.
$Rate\ of\ Flow=\frac{d}{dt}(Torricelli\prime s\ Equation\ for\ Volume)=\frac{d}{dt}(V)$
Given that:
Torricelli’s Equation for the Volume of Water remaining in the Tank is:
${5000\left(1-\frac{t}{40}\right)}^2=V,\ \ where\ 0\le t\le 40$
To calculate the rate at which water is draining at different instances of time $t$, we will be taking the first derivative of Torricelli’s Equation with respect to time $t$.
$\frac{d}{dt}\left(V\right)=\frac{d}{dt}V(t)$
$\frac{d}{dt}V(t)=\frac{d}{dt}\left[{5000\left(1-\frac{t}{40}\right)}^2\right]$
$V^\prime(t)=5000\times2\left(1-\frac{t}{40}\right)\times\left(-\frac{1}{40}\right)$
$V^\prime(t)=-250\left(1-\frac{t}{40}\right)$
The negative sign indicates that the rate at which the water is draining is decreasing with time.
To calculate the rate at which water is draining from the tank after $5min$, substitute $t=5$ in the above equation:
$V^\prime(5)=-250\left(1-\frac{5}{40}\right)$
$V^\prime(5)=-218.75\frac{Gallons}{Min}$
To calculate the rate at which water is draining from the tank after $10min$, substitute $t=10$ in the above equation:
$V^\prime(10)=-250\left(1-\frac{10}{40}\right)$
$V^\prime(10)=-187.5\frac{Gallons}{Min}$
To calculate the time at which rate of water draining from the tank is fastest or slowest, take the following assumptions from the given minimum and maximum range of $t$
$1st\ Assumption\ t=0\ min$
$2nd\ Assumption\ t=40\ min$
For 1st assumption of $t=0$
$V^\prime(0)=-250\left(1-\frac{0}{40}\right)$
$V^\prime(0)=-250\frac{Gallons}{Min}$
For 2nd assumption of $t=40$
$V^\prime(40)=-250\left(1-\frac{40}{40}\right)$
$V^\prime(40)=0\frac{Gallons}{Min}$
Hence, it proves that the rate at which the water is draining is fastest when $V^\prime(t)$ is maximum and slowest when $V^\prime(t)$ is minimum. Thus, the fastest rate at which the water is draining is at the start when $t=0min$ and the slowest at the end of the drain when $t=40min$. As the time passes, the rate of drain becomes slower until it becomes $0$ at $t=40min$
## Numerical Result
The rate at which water is draining from the tank after $5min$ is:
$V^\prime(5)=-218.75\frac{Gallons}{Min}$
The rate at which water is draining from the tank after $10min$ is:
$V^\prime(10)=-187.5\frac{Gallons}{Min}$
The fastest rate of the drain is at the start when $t=0min$ and the slowest at the end when $t=40min$.
## Example
Water is draining from a tank containing $6000$ gallons of water. After time $t$, the following is the relation that represents the volume $V$ of water that remains in the tank as per Torricelli’s Law.
${6000\left(1-\frac{t}{50}\right)}^2=V,\ \ where\ 0\le t\le 50$
Calculate its rate of drain after $25min$.
Solution
$\frac{d}{dt}V(t)=\frac{d}{dt}\ \left[{\ 6000\left(1-\frac{t}{50}\right)}^2\ \right]$
$V^\prime(t)=-240\left(1-\frac{t}{50}\right)$
To calculate the rate at which water is draining from the tank after $25min$, substitute $t=5$ in the above equation:
$V^\prime(t)=-240\left(1-\frac{25}{50}\right)$
$V^\prime(t)=-120\frac{Gallons}{Min}$ | 2022-08-10 06:04:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9359673857688904, "perplexity": 256.54432419013335}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571147.84/warc/CC-MAIN-20220810040253-20220810070253-00124.warc.gz"} |
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Showing 1 - 200 of 538 Journals sorted alphabetically Abakós (Followers: 4) Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg (Followers: 4) Academic Voices : A Multidisciplinary Journal (Followers: 2) Accounting Perspectives (Followers: 7) ACM Transactions on Algorithms (TALG) (Followers: 15) ACM Transactions on Computational Logic (TOCL) (Followers: 3) ACM Transactions on Mathematical Software (TOMS) (Followers: 6) ACS Applied Materials & Interfaces (Followers: 38) Acta Applicandae Mathematicae (Followers: 1) Acta Mathematica (Followers: 12) Acta Mathematica Hungarica (Followers: 2) Acta Mathematica Scientia (Followers: 5) Acta Mathematica Sinica, English Series (Followers: 6) Acta Mathematica Vietnamica Acta Mathematicae Applicatae Sinica, English Series Advanced Science Letters (Followers: 12) Advances in Applied Clifford Algebras (Followers: 4) Advances in Calculus of Variations (Followers: 6) Advances in Catalysis (Followers: 5) Advances in Complex Systems (Followers: 9) Advances in Computational Mathematics (Followers: 21) Advances in Decision Sciences (Followers: 3) Advances in Difference Equations (Followers: 3) Advances in Fixed Point Theory (Followers: 8) Advances in Geosciences (ADGEO) (Followers: 17) Advances in Linear Algebra & Matrix Theory (Followers: 10) Advances in Materials Science (Followers: 17) Advances in Mathematical Physics (Followers: 7) Advances in Mathematics (Followers: 15) Advances in Nonlinear Analysis Advances in Numerical Analysis (Followers: 7) Advances in Operations Research (Followers: 12) Advances in Porous Media (Followers: 5) Advances in Pure and Applied Mathematics (Followers: 8) Advances in Pure Mathematics (Followers: 9) Advances in Science and Research (ASR) (Followers: 6) Aequationes Mathematicae (Followers: 2) African Journal of Educational Studies in Mathematics and Sciences (Followers: 7) African Journal of Mathematics and Computer Science Research (Followers: 5) Afrika Matematika (Followers: 1) Air, Soil & Water Research (Followers: 13) AKSIOMA Journal of Mathematics Education (Followers: 2) Al-Jabar : Jurnal Pendidikan Matematika (Followers: 1) Algebra and Logic (Followers: 7) Algebra Colloquium (Followers: 4) Algebra Universalis (Followers: 2) Algorithmic Operations Research (Followers: 5) Algorithms (Followers: 11) Algorithms Research (Followers: 1) American Journal of Computational and Applied Mathematics (Followers: 8) American Journal of Mathematical Analysis American Journal of Mathematics (Followers: 6) American Journal of Operations Research (Followers: 6) An International Journal of Optimization and Control: Theories & Applications (Followers: 11) Anadol University Journal of Science and Technology B : Theoritical Sciences Analele Universitatii Ovidius Constanta - Seria Matematica Analysis and Applications (Followers: 1) Analysis and Mathematical Physics (Followers: 6) Analysis Mathematica Analysis. 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Similar Journals
Acta MathematicaJournal Prestige (SJR): 7.066 Citation Impact (citeScore): 3Number of Followers: 12 Hybrid journal (It can contain Open Access articles) ISSN (Print) 1871-2509 - ISSN (Online) 0001-5962 Published by Springer-Verlag [2562 journals]
• A complete classification of homogeneous plane continua
• Authors: Logan C. Hoehn; Lex G. Oversteegen
Pages: 177 - 216
Abstract: We show that the only compact and connected subsets (i.e. continua) X of the plane $${\mathbb{R}^2}$$ which contain more than one point and are homogeneous, in the sense that the group of homeomorphisms of X acts transitively on X, are, up to homeomorphism, the circle $${\mathbb{S}^1}$$ , the pseudo-arc, and the circle of pseudo-arcs. These latter two spaces are fractal-like objects which do not contain any arcs. It follows that any compact and homogeneous space in the plane has the form X × Z, where X is either a point or one of the three homogeneous continua above, and Z is either a finite set or the Cantor set. The main technical result in this paper is a new characterization of the pseudo-arc. Following Lelek, we say that a continuum X has span zero provided for every continuum C and every pair of maps $${f,g\colon C \to X}$$ such that $${f(C) \subset g(C)}$$ there exists $${c_0 \in C}$$ so that f(c 0) = g(c 0). We show that a continuum is homeomorphic to the pseudo-arc if and only if it is hereditarily indecomposable (i.e., every subcontinuum is indecomposable) and has span zero.
PubDate: 2016-06-01
DOI: 10.1007/s11511-016-0138-0
Issue No: Vol. 216, No. 2 (2016)
• Helicoidal minimal surfaces of prescribed genus
• Authors: David Hoffman; Martin Traizet; Brian White
Pages: 217 - 323
Abstract: For every genus g, we prove that $${\mathbf{S}^2\times\mathbf{R}}$$ contains complete, properly embedded, genus-g minimal surfaces whose two ends are asymptotic to helicoids of any prescribed pitch. We also show that as the radius of the $${\mathbf{S}^2}$$ tends to infinity, these examples converge smoothly to complete, properly embedded minimal surfaces in $${\mathbf{R}^3}$$ that are helicoidal at infinity. We prove that helicoidal surfaces in $${\mathbf{R}^3}$$ of every prescribed genus occur as such limits of examples in $${\mathbf{S}^2\times\mathbf{R}}$$ .
PubDate: 2016-06-01
DOI: 10.1007/s11511-016-0139-z
Issue No: Vol. 216, No. 2 (2016)
• Geometric measures in the dual Brunn–Minkowski theory and their
associated Minkowski problems
• Authors: Yong Huang; Erwin Lutwak; Deane Yang; Gaoyong Zhang
Pages: 325 - 388
Abstract: A longstanding question in the dual Brunn–Minkowski theory is “What are the dual analogues of Federer’s curvature measures for convex bodies?” The answer to this is provided. This leads naturally to dual versions of Minkowski-type problems: What are necessary and sufficient conditions for a Borel measure to be a dual curvature measure of a convex body? Sufficient conditions, involving measure concentration, are established for the existence of solutions to these problems.
PubDate: 2016-06-01
DOI: 10.1007/s11511-016-0140-6
Issue No: Vol. 216, No. 2 (2016)
• The Hodge conjecture and arithmetic quotients of complex balls
• Authors: Nicolas Bergeron; John Millson; Colette Moeglin
Pages: 1 - 125
Abstract: Let S be a closed Shimura variety uniformized by the complex n-ball associated with a standard unitary group. The Hodge conjecture predicts that every Hodge class in $${H^{2k} (S, \mathbb{Q})}$$ , $${k=0,\dots, n}$$ , is algebraic. We show that this holds for all degrees k away from the neighborhood $${\bigl]\tfrac13n,\tfrac23n\bigr[}$$ of the middle degree. We also prove the Tate conjecture for the same degrees as the Hodge conjecture and the generalized form of the Hodge conjecture in degrees away from an interval (depending on the codimension c of the subvariety) centered at the middle dimension of S. These results are derived from a general theorem that applies to all Shimura varieties associated with standard unitary groups of any signature. The proofs make use of Arthur’s endoscopic classification of automorphic representations of classical groups. As such our results rely on the stabilization of the trace formula for the (disconnected) groups $${GL (N) \rtimes \langle \theta \rangle}$$ associated with base change.
PubDate: 2016-03-01
DOI: 10.1007/s11511-016-0136-2
Issue No: Vol. 216, No. 1 (2016)
• Regularity of Kähler–Ricci flows on Fano manifolds
• Authors: Gang Tian; Zhenlei Zhang
Pages: 127 - 176
Abstract: In this paper, we will establish a regularity theory for the Kähler–Ricci flow on Fano n-manifolds with Ricci curvature bounded in L p -norm for some $${p > n}$$ . Using this regularity theory, we will also solve a long-standing conjecture for dimension 3. As an application, we give a new proof of the Yau–Tian–Donaldson conjecture for Fano 3-manifolds. The results have been announced in [45].
PubDate: 2016-03-01
DOI: 10.1007/s11511-016-0137-1
Issue No: Vol. 216, No. 1 (2016)
• Local Hodge theory of Soergel bimodules
• Abstract: We prove the local hard Lefschetz theorem and local Hodge–Riemann bilinear relations for Soergel bimodules. Using results of Soergel and Kübel, one may deduce an algebraic proof of the Jantzen conjectures. We observe that the Jantzen filtration may depend on the choice of non-dominant regular deformation direction.
PubDate: 2016-12-01
DOI: 10.1007/s11511-017-0146-8
• Maximum independent sets on random regular graphs
• Abstract: We determine the asymptotics of the independence number of the random d-regular graph for all $${d\geq d_0}$$ . It is highly concentrated, with constant-order fluctuations around $${n\alpha_*-c_*\log n}$$ for explicit constants $${\alpha_*(d)}$$ and $${c_*(d)}$$ . Our proof rigorously confirms the one-step replica symmetry breaking heuristics for this problem, and we believe the techniques will be more broadly applicable to the study of other combinatorial properties of random graphs.
PubDate: 2016-12-01
DOI: 10.1007/s11511-017-0145-9
• Global bifurcation of steady gravity water waves with critical layers
• Abstract: We construct families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed, in particular establishing the existence of waves of large amplitude. A Riemann–Hilbert problem approach is used to recast the governing equations as a one-dimensional elliptic pseudodifferential equation with a scalar constraint. The structural properties of this formulation, which arises as the Euler–Lagrange equation of an energy functional, enable us to develop a theory of analytic global bifurcation.
PubDate: 2016-12-01
DOI: 10.1007/s11511-017-0144-x
• Lower bounds for numbers of real solutions in problems of Schubert
calculus
• Abstract: We give lower bounds for the numbers of real solutions in problems appearing in Schubert calculus in the Grassmannian $${\mathop{\rm Gr}(n,d)}$$ related to osculating flags. It is known that such solutions are related to Bethe vectors in the Gaudin model associated to $${\mathop{\rm gl}_n}$$ . The Gaudin Hamiltonians are self-adjoint with respect to a non-degenerate indefinite Hermitian form. Our bound comes from the computation of the signature of that form.
PubDate: 2016-09-01
DOI: 10.1007/s11511-016-0143-3
• Universality in several-matrix models via approximate transport maps
• Abstract: We construct approximate transport maps for perturbative several-matrix models. As a consequence, we deduce that local statistics have the same asymptotic as in the case of independent GUE or GOE matrices (i.e., they are given by the sine-kernel in the bulk and the Tracy–Widom distribution at the edge), and we show averaged energy universality (i.e., universality for averages of m-points correlation functions around some energy level E in the bulk). As a corollary, these results yield universality for self-adjoint polynomials in several independent GUE or GOE matrices which are close to the identity.
PubDate: 2016-09-01
DOI: 10.1007/s11511-016-0142-4
• Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic
invariant cylinders
• Abstract: We prove a form of Arnold diffusion in the a-priori stable case. Let $$H_{0}(p)+\epsilon H_{1}(\theta,p,t),\quad \theta \in {\mathbb{T}^{n}},\,p \in B^{n},\,t \in \mathbb{T}= \mathbb{R}/\mathbb{T},$$ be a nearly integrable system of arbitrary degrees of freedom $${n \geqslant 2}$$ with a strictly convex H 0. We show that for a “generic” $${\epsilon H_1}$$ , there exists an orbit $${(\theta,p)}$$ satisfying $$\ p(t)-p(0)\ > l(H_{1}) > 0,$$ where $${l(H_1)}$$ is independent of $${\epsilon}$$ . The diffusion orbit travels along a codimension-1 resonance, and the only obstruction to our construction is a finite set of additional resonances. For the proof we use a combination of geometric and variational methods, and manage to adapt tools which have recently been developed in the a-priori unstable case.
PubDate: 2016-09-01
DOI: 10.1007/s11511-016-0141-5
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JournalTOCs © 2009- | 2019-11-12 07:52:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8100200891494751, "perplexity": 8705.521377009636}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496664808.68/warc/CC-MAIN-20191112074214-20191112102214-00156.warc.gz"} |
https://scalability.org/2007/07/gpt-installs-in-opensuse-102-grrrrrr/ | gpt installs in OpenSuSE 10.2 … grrrrrr
Suppose you have a x86_64 box, I dunno, able to put 8+TB usable in 3U. Suppose you want to load OpenSuSE 10.2 on it. Suppose you want to keep the partitioning simple, and not do any fancy tricks to eek out another few percentage of performance, so you build your RAID6 with 2 hot spares. Now you have this big hunk-a-chunk-a disk.
Now install OpenSuSE 10.2 on it. After you are done you discover ….
… it wrote an msdos label to the disk. Not a gpt label.
Which means you have to go back and do it again … though … OpenSuSE 10.2 doesn’t actually write GPT labels to disk. You have to get into rescue mode, then
parted /dev/somethingorother mklabel gpt
sync, reboot, rinse twice, …
and then during partitioning, it cautions you about using gpt.
Yeah, this is helpful.
As soon as Tiburon is done, I am going to automate the loading of these types of units (mostly done, I haven’t had time to finish while I am working on other revenue/… projects) so I don’t have to mess around with design errors and bugs.
I’ll file a bug report with the OpenSuSE folks. I don’t expect them to fix it though (even for 10.3).
Update: Of course, grub doesn’t work with this config. Grub is yet-another open source project that seems to have the “we must throw everything away, recode from scratch, and oh, leave things half finished” disease. When open source is good, it is really good. When it is not, well, … Considering how important boot loaders are, one would think that … maybe … just maybe … they are worth spending time on making work with the newer partitioning schema. Heck, we have terabyte sized disks today. GPT is likely to become the norm.
But this is what we see.
Words fail me. The maintainers of Grub want GPT to be a v2.0 feature. But grub 2 ain’t ready for prime time yet. So we are SOL.
With Tiburon, the problem is solvable, but I need a server to have Tiburon live on. Possible in this configuration, though I would like to avoid setting that up for this particular system. | 2020-04-01 23:57:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5166303515434265, "perplexity": 3194.5582188702497}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370506477.26/warc/CC-MAIN-20200401223807-20200402013807-00372.warc.gz"} |
https://www.physicsforums.com/threads/fibonacci-cubed-recurrence-relation.219378/ | Homework Help: Fibonacci Cubed Recurrence Relation
1. Mar 2, 2008
alec_tronn
1. The problem statement, all variables and given/known data
Find and prove the recurrence relation for the Fibonacci cubed sequence.
2. Relevant equations
By observation (blankly staring at the sequence for an hour) I've decided that the recurrence relation is G$$_{n}$$ = 3G$$_{n-1}$$ + 6G$$_{n-2}$$ - 3G$$_{n-3}$$ - G$$_{n-4}$$
(where G is Fibonacci cubed)
3. The attempt at a solution
My attempt was going to be to prove by induction, but for the n+1 case, I got:
G$$_{n+1}$$ = G$$_{n}$$ + F$$_{n}$$*F$$_{n+1}$$*F$$_{n-1}$$ + G$$_{n-1}$$
Is there an identity that could get me further? Is there a different method anyone could suggest? Is there anything I can do at all?
edit: all that superscript is supposed to be subscript... I'm not sure what happened...
Last edited: Mar 2, 2008
2. Mar 2, 2008
jhicks
I fear your question is esoteric enough that help will be hard to find without a definition of "fibonacci cubed" (or more specifically the sequence, since you do not know the relation). It doesn't seem like a hard question - just an obscure one. (Amusingly enough the first google result for "fibonacci cubed" is this thread!)
My guess is LaTeX fouled up because you didn't properly anchor the subscripts to something.
Last edited: Mar 3, 2008
3. Mar 3, 2008
alec_tronn
Since the Fibonacci sequence is 0,1,1,2,3,5,8,... the Fibonacci Cubed sequence is 0,1,1,8,27,125,512... it's just cubing each element of the Fibonacci sequence. Upon further research, I found that that rule was found and proven by Zeitlin and Parker and published in the Fibonacci Quarterly in 1963... not that I have access to that publication, but if any of you do, or find out how it was done, or have any advice, it'd be greatly appreciated!
4. Mar 3, 2008
jhicks
I think an easier approach would be to solve a simpler case first. Have you tried deriving the equation for a "fibonacci square" sequence? I assume a similar approach would follow for your case:
Let $$H_n$$ denote the nth fibonacci square
$$H_n = (F_n)^2 = (F_{n-1}+F_{n-2})^2 = H_{n-1} + H_{n-2} + 2F_{n-1}F_{n-2}$$
Using the substitution selectively that $$F_{n-1} = F_{n-2} + F_{n-3}$$, $$H_{n-1}+H_{n-2}+2F_{n-1}F_{n-2}=H_{n-1}+H_{n-2}+2(F_{n-2}+F_{n-3})F_{n-2} = H_{n-1}+H_{n-2}+2(F_{n-2})^2 + 2F_{n-2}F_{n-3}$$.
The trick is then to add and subtract $$(F_{n-3})^2$$:
$$H_{n-1}+2H_{n-2}+(F_{n-2})^2 + 2F_{n-2}F_{n-3} + (F_{n-3})^2 - (F_{n-3})^2 = 2H_{n-1}+2H_{n-2}-H_{n-3}$$.
Last edited: Mar 3, 2008 | 2018-05-25 09:48:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8371334671974182, "perplexity": 1366.1375710766597}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867055.20/warc/CC-MAIN-20180525082822-20180525102822-00395.warc.gz"} |
https://docs.klimadao.finance/tokenomics-and-mechanisms/staking | Search…
⌃K
# Staking (🌳,🌳)
Staking is the primary reward distribution mechanism of the protocol. It is intended to be the primary mechanism of value accrual for the majority of users.
Whenever the protocol has an excess of reserves per token (i.e when the CC of the treasury is higher than the assets needed to back KLIMA), the protocol will mint and distribute tokens to the stakers. The amount minted and distributed is controlled by a variable named the reward rate. This is the % of supply that is rebased. This massively slows down how fast the protocol expands supply, as doing so is detrimental to the health (rapid expansion without backing causes a price collapse).
KLIMA and sKLIMA always have a 1:1 ratio, meaning that you will always obtain 1 sKLIMA for every 1 KLIMA and vice versa via staking or unstaking on the KlimaDAO Dapp.
$KLIMA= sKLIMA$
When a rebase occurs, the treasury deposits KLIMA into the distributor contract, which deposits it in the staking contract. Since there is now more KLIMA then there is sKLIMA, the sKLIMA is rebased to keep them in parity.
$Reward Rate=1-KlimaDeposits/sKlimaOutstanding$
Because not all KLIMA is staked, the user gains a larger piece of the share of rebases:
$RewardYield = RewardRate/(\%Staked*\%Circulating)$
This translates to AKR:
$(1+RewardYield)^{(365*24/(BlockTimeInHours)} - 1$ | 2023-01-30 04:17:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 4, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47970396280288696, "perplexity": 3918.4533386417124}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499801.40/warc/CC-MAIN-20230130034805-20230130064805-00617.warc.gz"} |
https://socratic.org/questions/what-is-x-in-the-equation-26-1-x-5#564889 | # What is x in the equation (26-1)/x = 5?
Mar 5, 2018
$x = 5$
#### Explanation:
Fist of all, since $x$ is a denominator, $x \ne 0$
Then we have:
$\frac{26 - 1}{x} = 5$
$\frac{25}{x} = 5$
$25 = 5 x$
$x = 5$ | 2021-10-24 10:05:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9850625395774841, "perplexity": 3071.0257495812143}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585916.29/warc/CC-MAIN-20211024081003-20211024111003-00175.warc.gz"} |
https://math.stackexchange.com/questions/2932641/semidirect-product-command-in-gap | # Semidirect product command in GAP [duplicate]
I need to type the group
in GAP. Is it correct if I type as, "SemidirectProduct(ZmodnZ(3),AbelianGroup([7,7]));"? Will it recognize that AbelianGroup([7,7]) is the normal subgroup?
## marked as duplicate by Matthew Towers, Ivan Neretin, Jeremy Rickard, hardmath, ArsenBerkOct 4 '18 at 19:03
• Here I have considered the internal Semidirect product – Buddhini Angelika Sep 27 '18 at 10:16
• The suggested duplicate can give you a good start on the GAP syntax for this. Note that an internal semidirect product involves a subgroup $H$ "acting" on a normal subgroup $N$ with trivial intersection. It doesn't appear to me that the syntax you've shown allows for this action to be determined, even in principle. – hardmath Oct 4 '18 at 15:20
You will need to also specify the action of $$Z_3$$ on $$Z_7^2$$. Generically, you would do this by specifying as second argument (i.e. arguments are subgroup, map, normal subgroup) a homomorphism from $$Z_3$$ into the automorphism group os $$Z_7^2$$.
gap> m:=[[4,0],[0,2]]*One(GF(7)); | 2019-05-22 19:13:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7376551628112793, "perplexity": 804.0137081034121}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256948.48/warc/CC-MAIN-20190522183240-20190522205240-00537.warc.gz"} |
https://www.zora.uzh.ch/id/eprint/131046/ | Difference operators for partitions under the Littlewood decomposition
Dehaye, Paul-Olivier; Han, Guo-Niu; Xiong, Huan (2017). Difference operators for partitions under the Littlewood decomposition. The Ramanujan Journal, 44(1):197-225.
Abstract
The concept of $\mathit{t}$-difference operator for functions of partitions is introduced to prove a generalization of Stanley’s theorem on polynomiality of Plancherel averages of symmetric functions related to contents and hook lengths. Our extension uses a generalization of the notion of Plancherel measure, based on walks in the Young lattice with steps given by the addition of $\mathit{t}$-hooks. It is well known that the hook lengths of multiples of t can be characterized by the Littlewood decomposition. Our study gives some further information on the contents and hook lengths of other congruence classes modulo $\mathit{t}$.
Abstract
The concept of $\mathit{t}$-difference operator for functions of partitions is introduced to prove a generalization of Stanley’s theorem on polynomiality of Plancherel averages of symmetric functions related to contents and hook lengths. Our extension uses a generalization of the notion of Plancherel measure, based on walks in the Young lattice with steps given by the addition of $\mathit{t}$-hooks. It is well known that the hook lengths of multiples of t can be characterized by the Littlewood decomposition. Our study gives some further information on the contents and hook lengths of other congruence classes modulo $\mathit{t}$.
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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Physical Sciences > Algebra and Number Theory English 2017 01 Feb 2017 07:47 26 Jan 2022 11:28 Springer 1382-4090 Green https://doi.org/10.1007/s11139-016-9807-z : FunderSNSF: Grant IDPP00P2_138906: Project TitleCombinatorics of partitions and number theoretic aspects
Preview
Content: Accepted Version
Language: English
Filetype: PDF
Size: 489kB
View at publisher | 2022-08-11 04:51:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6176756024360657, "perplexity": 1350.8128395210617}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571234.82/warc/CC-MAIN-20220811042804-20220811072804-00221.warc.gz"} |
https://cs.stackexchange.com/questions/71099/how-do-i-normalize-a-push-down-automaton | # How do I normalize a push down automaton?
Looking at the above PDA, I am unsure whether or not it is normalized. Specifically, the loop transition from $q_1$ to $q_1$, because I know a transition must either push OR pop from the stack. Does this mean that there must be two separate transitions to push the * and then pop the *? Or is it normalized as is? Is it okay to have multiple transitions from a single state to another, some of which pop, and some of which push?
• I encourage you to edit your question to include a self-contained definition of what you mean by "normalized". If you don't know what the definition is, you might want to ask whoever is using that term with you to define their terms. Thank you! – D.W. Mar 4 '17 at 0:01
For the example you give, a transition is not represented by a directed edge, but by a directed edge together with a label. If you have an edge with two labels, as in your loop on $q_1$, that represents two transitions. Trying to do it with two separate loop edges would only make your diagram less readable. | 2019-05-19 11:26:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4862113296985626, "perplexity": 277.0428962563741}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232254751.58/warc/CC-MAIN-20190519101512-20190519123512-00317.warc.gz"} |
http://tex.stackexchange.com/questions/59044/moderncv-package-cventry-date-width?answertab=active | Moderncv package - cventry date width
I am writing my CV using moderncv package, everythig is nice but I have a problem with cventry command. I have something like this:
(it means 2010 - now)
I would want to have this in one line, rather than in two lines. I tried looking into the modercv style files but with no success. What can I do to achieve the effect I want?
EDIT: I found the answer, if any one will need it in the future, you need to add
``````\setlength{\hintscolumnwidth}{0.15\textwidth}
``````
and tweak a bit with lengths.
-
You could also write `\llap{2010--now}` to get onto one line. In this case you lap the text the left without taking any official space. – Martin Scharrer Jun 8 '12 at 10:26
It seems I found the solution to my problem, if I add this line
``````\setlength{\hintscolumnwidth}{0.15\textwidth}
``````
and tweak a bit with lengths I can get the results that I wanted.
- | 2014-03-16 06:46:41 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8576056957244873, "perplexity": 1109.9882868351467}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394678702045/warc/CC-MAIN-20140313024502-00082-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://runestone.academy/ns/books/published/APEX/chapter_deriv_apps.html | In the next chapters, we will consider the “reverse” problem to computing the derivative: given a function $$f\text{,}$$ can we find a function whose derivative is $$f\text{?}$$ Being able to do so opens up an incredible world of mathematics and applications. | 2023-01-28 22:51:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6783172488212585, "perplexity": 147.42429278782643}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499695.59/warc/CC-MAIN-20230128220716-20230129010716-00369.warc.gz"} |
https://projecteuclid.org/euclid.aaa/1393449628 | ## Abstract and Applied Analysis
### Characterizations of Nonlinear Lie Derivations of $B(X)$
#### Abstract
Let $X$ be an infinite dimensional Banach space, and $\mathrm{\Phi }:B(X)\to B(X)$ is a nonlinear Lie derivation. Then Φ is the form $\delta +\tau$ where $\delta$ is an additive derivation of $B(X)$ and $\tau$ is a map from $B(X)$ into its center ${Z}_{B(X)}$, which maps commutators into the zero.
#### Article information
Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 245452, 7 pages.
Dates
First available in Project Euclid: 26 February 2014
https://projecteuclid.org/euclid.aaa/1393449628
Digital Object Identifier
doi:10.1155/2013/245452
Mathematical Reviews number (MathSciNet)
MR3035394
Zentralblatt MATH identifier
1271.47029
#### Citation
Huo, Donghua; Zheng, Baodong; Liu, Hongyu. Characterizations of Nonlinear Lie Derivations of $B(X)$. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 245452, 7 pages. doi:10.1155/2013/245452. https://projecteuclid.org/euclid.aaa/1393449628
#### References
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• B. E. Johnson, “Symmetric amenability and the nonexistence of Lie and Jordan derivations,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 120, no. 3, pp. 455–473, 1996.
• F. Y. Lu, “Lie derivations of $I$-subspace lattice algebras,” Proceedings of the American Mathematical Society, vol. 135, no. 8, pp. 2581–2590, 2007.
• F. Y. Lu, “Lie derivations of certain CSL algebras,” Israel Journal of Mathematics, vol. 155, pp. 149–156, 2006.
• M. Mathieu and A. R. Villena, “The structure of Lie derivations on ${C}^{\ast\,\!}$-algebras,” Journal of Functional Analysis, vol. 202, no. 2, pp. 504–525, 2003.
• P. Šemrl, “Additive derivations of some operator algebras,” Illinois Journal of Mathematics, vol. 35, no. 2, pp. 234–240, 1991.
• M. I. Berenguer and A. R. Villena, “Continuity of Lie derivations on Banach algebras,” Proceedings of the Edinburgh Mathematical Society. Series II, vol. 41, no. 3, pp. 625–630, 1998.
• D. Benkovič, “Lie derivations on triangular matrices,” Linear and Multilinear Algebra, vol. 55, no. 6, pp. 619–626, 2007.
• W.-S. Cheung, “Lie derivations of triangular algebras,” Linear and Multilinear Algebra, vol. 51, no. 3, pp. 299–310, 2003.
• A. R. Villena, “Lie derivations on Banach algebras,” Journal of Algebra, vol. 226, no. 1, pp. 390–409, 2000.
• F. Y. Lu and W. Jing, “Characterizations of Lie derivations of $B(X)$,” Linear Algebra and its Applications, vol. 432, no. 1, pp. 89–99, 2010.
• W. Y. Yu and J.H. Zhang, “Nonlinear Lie derivations of triangular algebras,” Linear Algebra and its Applications, vol. 432, no. 11, pp. 2953–2960, 2010.
• P. S. Ji and W. Q. Qi, “Characterizations of Lie derivations of triangular algebras,” Linear Algebra and its Applications, vol. 435, no. 5, pp. 1137–1146, 2011.
• Z. F. Bai and S. P. Du, “The structure of nonlinear Lie derivation on von Neumann algebras,” Linear Algebra and its Applications, vol. 436, no. 7, pp. 2701–2708, 2012.
• D. G. Han, “Continuity and linearity of additive derivations of nest algebras on Banach spaces,” Chinese Annals of Mathematics B, vol. 17, no. 2, pp. 227–236, 1996. | 2019-09-20 07:29:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 9, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40976616740226746, "perplexity": 1239.1409417525792}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573908.70/warc/CC-MAIN-20190920071824-20190920093824-00011.warc.gz"} |
https://math.stackexchange.com/questions/2603996/verifying-v-is-a-vector-space | # verifying V is a vector space
I'm given the following:
Let V be the set of ordered pairs $(x,y)$ of positive real numbers with addition and scalar multiplication defined by
$$(x_1, y_1) + (x_2,y_2) =(x_1x_2,y_1y_2)$$
and
$$a(x,y) = (x^a,y^a)$$
My question is with the 5th addition axiom given by
A5: For each element v in V, an element -v in V exists such that $-v+v=0$ and $v + (-v)=0$
I don't really know how to go about verifying this axiom and judging by the questions wording "Show that V is a vector space by verifying all the axioms" I can't get outta this by saying that V isn't a vector space.
First of all, we need to identify what is $0$, it should refers to the addition identity.
Notice that we have $(x,y)+(1,1)=(x,y)$ and $(1,1)+(x,y)=(x,y)$, hence the addition identity is $(1,1)$.
Remark: note that the addition operation is commutative.
Now let $v=(x,y)$ and we should try to find $-v=(p,q)$.
Hence we need $(x,y)+(p,q)=(1,1)$
That is $(xp,yq)=(1,1)$, try to solve for $p$ and $q$ in terms of $x$ and $y$.
The '0' of a vector space is the identity operator of the addition operator. It has nothing to do with the number 0. For verifying the inverse axiom, you have to first be clear on what 0 the axiom means. Look at the 0 of the axiom based on definition of the addition operator. And then you can find out what -v is for v
In this vector space, $0=(1,1)$. And if $v=(x,y)$, then $-v=\left(\frac1x,\frac1y\right)$, since$$\left(\frac1x,\frac1y\right)+(x,y)=(1,1)=0.$$
• Ah I see, I realized (0,0) become (1,1) but completely forgot about it the second I got to this axiom. Makes so much more sense now, Thank you – AFC Jan 13 '18 at 19:33
There is no contradiction because, due to the addition law, the neutral element instead of being (0,0), is (1,1).
Thus, for the existence of an opposite, you have to check not $-v+v=(0,0)$ but $-v+v=(1,1)$ which is accomplished, if $v:=(a,b)$ by defining $-v:=(1/a,1/b)$. | 2020-02-18 19:44:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9271858930587769, "perplexity": 165.24560088717155}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875143805.13/warc/CC-MAIN-20200218180919-20200218210919-00295.warc.gz"} |
http://appliedclassicalanalysis.net/2016/08/04/integgrateint_0a-a2-x2n-12-mathrmd-x-2/ | # Integrate $$\int_{0}^{a} (a^{2}-x^{2})^{n-1/2} \mathrm{d} x$$
From Victor Moll’s attempt to solve all of the integrals in Gradshteyn and Ryzhik, we have
\int\limits_{0}^{a} (a^{2}-x^{2})^{n-1/2} \mathrm{d} x = a^{2n} \frac{(2n-1)!!}{(2n)!!} \frac{\pi}{2}
\label{eq:1608041}
\tag{1}
Moll’s solution is at the link, so let us solve this another way. We first use the substitution used by Moll, let $$x=av$$ to obtain
\int\limits_{0}^{a} (a^{2}-x^{2})^{n-1/2} \mathrm{d} x = a^{2n} \int\limits_{0}^{1} (1-v^{2})^{n-1/2} \mathrm{d} v
\label{eq:1608042}
\tag{2}
We designate the integral on the right hand side as I and make the substitution $$z = v^{2}$$
\mathrm{I} = \int\limits_{0}^{1} (1-v^{2})^{n-1/2} \mathrm{d} v = \frac{1}{2} \int\limits_{0}^{1} z^{-1/2} (1-z)^{n-1/2} \mathrm{d} z
\label{eq:1608043}
\tag{3}
From the beginning this integral looked like a gamma or beta function, now, in this form it is obviously a beta function. We then have
\mathrm{I} = \frac{1}{2} \mathrm{B}\left(\frac{1}{2}, n + \frac{1}{2} \right)
\label{eq:1608044}
\tag{4}
and thus
\int\limits_{0}^{a} (a^{2}-x^{2})^{n-1/2} \mathrm{d} x = a^{2n} \frac{1}{2} \mathrm{B}\left(\frac{1}{2}, n + \frac{1}{2} \right)
\label{eq:1608045}
\tag{5}
Now we must show that the right hand sides of equations \eqref{eq:1608041} and \eqref{eq:1608045} are equal or
\mathrm{B}\left(\frac{1}{2}, n + \frac{1}{2} \right) \overset{\underset{\mathrm{?}}{}}{=} \pi \frac{(2n-1)!!}{(2n)!!}
\label{eq:1608046}
\tag{6}
We begin by expressing the beta function in terms of gamma functions
\mathrm{B}\left(\frac{1}{2}, n + \frac{1}{2} \right) = \frac{\Gamma(\frac{1}{2}) \Gamma(n + \frac{1}{2})}{\Gamma(n+1)} = \sqrt{\pi}
\frac{\Gamma(n + \frac{1}{2})}{\Gamma(n+1)}
\label{eq:1608047}
\tag{7}
Now we invoke the following two relationships between the gamma function and the double factorial, found at Wikipedia and Wolfram Math World respectively
(2n-1)!! = \frac{2^{n} \Gamma(n + \frac{1}{2})}{\sqrt{\pi}} \quad \mathrm{and} \quad (2n)!! = 2^{n}n! = 2^{n} \Gamma(n+1)
Substituting these expressions into \eqref{eq:1608046} shows that it is indeed an equality.
Putting everything together, we have
\int\limits_{0}^{a} (a^{2}-x^{2})^{n-1/2} \mathrm{d} x = a^{2n} \frac{(2n-1)!!}{(2n)!!} \frac{\pi}{2} = a^{2n} \frac{1}{2} \mathrm{B}\left(\frac{1}{2}, n + \frac{1}{2} \right) | 2018-11-15 15:09:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9995299577713013, "perplexity": 2266.652385148691}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039742779.14/warc/CC-MAIN-20181115141220-20181115163220-00126.warc.gz"} |
https://gowers.wordpress.com/2010/07/ | ## Archive for July, 2010
### EDP17 — are we nearly there?
July 18, 2010
Apologies for the attention-seeking title, but that really is the purpose of this post. I want to draw attention to some ideas that are buried in more comments that most people are likely to want to read, because I think there is a chance that all that stands between where we are now and a solution to EDP is a few soluble technical problems. It goes without saying that that chance is distinctly less than 100%, but I think it is high enough for it to be worth my going to some trouble to lay out as precisely as I can what the current approach is and what remains to be done. I’ll try to write it in such a way that it explains what is going on even to somebody who has not read any of the posts or comments so far. The exception to that is that I shall not repeat very basic things such as what the Erdős discrepancy problem is, what a homogeneous arithmetic progression is, etc. For that kind of information, I refer the reader to the front page of the Polymath5 wiki.
(more…)
### Polymath news
July 13, 2010
If you haven’t already spotted this, you might like to know that Scott Aaronson has just posed a very interesting unsolved combinatorial problem and invited Polymath-style thoughts on it. I’ll give a quick and I hope appetite-whetting account of the problem here, but you could skip it if you want and jump straight to his posts on his blog and at Mathoverflow.
The problem is completely elementary, but it has consequences of great interest to theoretical computer scientists. As Scott says, it also seems to be at a realistic level of difficulty and highly suitable for a Polymath approach. (The first assertion is a coded way of saying that it isn’t a notorious “impossible” complexity assertion in disguise.) It asks this. Suppose you colour the points of $\mathbb{Z}^d$ with two colours in such a way that the origin is red and each of the coordinate axes contains at least one blue point. Do there exist constants $c,\alpha>0$, independent of $d$, such that there must be a point $x$ that has at least $cd^\alpha$ neighbours that are coloured differently from $x$? At the moment, it seems that there isn’t even a proof that for sufficiently large $d$ there must be a point with 100 neighbours of the other colour. There is a non-trivial but not hard example that shows that $\alpha$ cannot be more than $1/2$. (Scott presents this in his Mathoverflow post.) A very brief remark is that if you just assume that not all points are coloured the same way, then the assertion is false: a counterexample is obtained if you colour a point red if its first coordinate is positive and blue otherwise.
### EDP16 — from AP-discrepancy to HAP-discrepancy?
July 4, 2010
In this post I want to elaborate on a strategy for proving EDP that I discussed in EDP15. Briefly, the idea is to take a representation-of-identity proof of Roth’s AP-discrepancy result and modify it so that it becomes a representation-of-diagonal proof of unbounded HAP-discrepancy.
The first step of this programme was an obvious one: obtain a clean and fully detailed proof in the APs case. That has now been completed, and a write-up can be found here. For the benefit of anyone who is interested in thinking about the next stage but doesn’t feel like reading a piece of formal mathematics, let me give a sketch of the argument here. That way, this post will be self-contained. Once I’ve given the sketch, I’ll say what I can about where we might go from here. It is just possible that we are in sight of the finishing line, but that is unlikely as it would depend on various guesses being correct, various potential technical problems not being actual, various calculations giving strong enough bounds, and so on. Thus, the final part of this post will be somewhat speculative, but I will make it as precise as I can in the hope that it will give rise to a fruitful line of enquiry. (more…) | 2015-11-28 04:03:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 9, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6614714860916138, "perplexity": 268.5964899843768}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398450762.4/warc/CC-MAIN-20151124205410-00316-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://chathamtownfc.net/can-a-vector-have-a-negative-magnitude/ | ## 20.3 nature of vectors (ESAGN)
Vectors are mathematical objects and we will currently study some of their math properties.
You are watching: Can a vector have a negative magnitude
If 2 vectors have actually the very same magnitude (size) and the same direction, climate we call them equal to every other. Because that example, if we have two forces, $$\vecF_1 = \text20\text N$$ in the increase direction and also $$\vecF_2 = \text20\text N$$ in the increase direction, then we can say that $$\vecF_1 = \vecF_2$$.
Equality that vectors
Two vectors space equal if they have the same magnitude and also the same direction.
Just like scalars which can have optimistic or an unfavorable values, vectors can also be confident or negative. A an adverse vector is a vector i m sorry points in the direction opposite to the reference positive direction. Because that example, if in a particular situation, we specify the increase direction together the reference confident direction, then a force $$\vecF_1 = \text30\text N$$ downwards would certainly be a negative vector and also could additionally be composed as $$\vecF_1 = -\text30\text N$$. In this case, the negative sign ($$-$$) suggests that the direction of $$\vecF_1$$ is the opposite to the of the reference positive direction.
A an adverse vector is a vector that has actually the opposite direction to the reference hopeful direction.
Like scalars, vectors can likewise be added and subtracted. We will investigate exactly how to carry out this next.
temp message
### Addition and subtraction the vectors (ESAGO)
including vectors
When vectors space added, we need to take right into account both your magnitudes and directions.
For example, imagine the following. You and also a friend space trying to relocate a hefty box. You stand behind it and push forwards v a pressure $$\vecF_1$$ and your friend stands in front and pulls it in the direction of them v a force $$\vecF_2$$. The two pressures are in the same direction (i.e. Forwards) and so the complete force exhilaration on the box is:
It is an extremely easy to understand the principle of vector addition through an task using the displacement vector.
Displacement is the vector which describes the change in one object"s position. That is a vector the points indigenous the initial position to the last position.
### Method
Tape a line of masking ice horizontally throughout the floor. This will certainly be your beginning point.
Take $$\text2$$ steps in the front direction. Usage a item of masking ice cream to mark your end point and label it A. Climate take another $$\text3$$ steps in the forward direction. Use masking ice cream to mark your final position together B. Make certain you shot to keep your steps all the exact same length!
Go earlier to your beginning line. Now take $$\text3$$ measures forward. Usage a item of masking ice cream to note your end point and label it B. Climate take one more $$\text2$$ procedures forward and also use a brand-new piece of masking ice to note your last position as A.
### Discussion
What carry out you notice?
In Task 1, the first $$\text2$$ steps forward stand for a displacement vector and the second $$\text3$$ measures forward also form a displacement vector. If us did not avoid after the first $$\text2$$ steps, we would have actually taken $$\text5$$ procedures in the front direction in total. Therefore, if we add the displacement vectors for $$\text2$$ steps and $$\text3$$ steps, we should obtain a total of $$\text5$$ steps in the forward direction.
It does not matter whether you take it $$\text3$$ measures forward and then $$\text2$$ measures forward, or 2 steps complied with by one more $$\text3$$ measures forward. Your last position is the same! The stimulate of the enhancement does no matter!
We can represent vector addition graphically, based on the activity above. Attract the vector for the very first two steps forward, followed by the vector through the following three steps forward.
We add the 2nd vector at the end of the first vector, since this is whereby we currently are after the very first vector has actually acted. The vector indigenous the tail of the very first vector (the beginning point) to the head that the 2nd vector (the end point) is then the sum of the vectors.
As you can convince yourself, the bespeak in i beg your pardon you include vectors does not matter. In the instance above, if you decided to an initial go $$\text3$$ steps forward and then an additional $$\text2$$ actions forward, the end an outcome would still be $$\text5$$ steps forward.
subtracting vectors
Let"s go back to the difficulty of the heavy box that you and your friend room trying come move. If friend didn"t interact properly first, you both could think that you need to pull in your own directions! Imagine you was standing behind the box and also pull it in the direction of you through a pressure $$\vecF_1$$ and also your friend stands in ~ the former of the box and also pulls it in the direction of them v a force $$\vecF_2$$. In this situation the two forces are in opposite directions. If we specify the direction her friend is pulling in as positive then the force you room exerting should be negative since it is in the contrary direction. We can write the complete force exerted on package as the sum of the separation, personal, instance forces:
What you have done right here is actually to subtract 2 vectors! This is the very same as including two vectors which have actually opposite directions.
See more: How To Prove The Square Root Of 3 Is Irrational ? Proof That The Square Root Of 3 Is Irrational
As us did before, we deserve to illustrate vector individually nicely making use of displacement vectors. If you take it $$\text5$$ actions forward and also then subtract $$\text3$$ measures forward you are left with only two procedures forward:
What did girlfriend physically do to subtract $$\text3$$ steps? You originally took $$\text5$$ procedures forward yet then you took $$\text3$$ steps backward come land up ago with only $$\text2$$ measures forward. The backward displacement is stood for by an arrowhead pointing to the left (backwards) with size $$\text3$$. The net an outcome of adding these two vectors is $$\text2$$ steps forward:
Thus, subtracting a vector from an additional is the same as adding a vector in the opposite direction (i.e. Subtracting $$\text3$$ procedures forwards is the very same as adding $$\text3$$ actions backwards). | 2021-10-28 11:02:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.634781002998352, "perplexity": 697.8887881075874}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588284.71/warc/CC-MAIN-20211028100619-20211028130619-00370.warc.gz"} |
https://qbnets.wordpress.com/2010/12/09/agile-micron-wide-spotlight/ | # Quantum Bayesian Networks
## December 9, 2010
### Agile, Micron-Wide Spotlight
Filed under: Uncategorized — rrtucci @ 10:10 pm
Normally, I don’t say much about experimental stuff, because I’m not an experimental physicist, and I feel uncomfortable teaching outside my area of expertise, but this experiment is easy to explain and really cool. Check out:
“Independent individual addressing of multiple neutral atom qubits
with a micromirror-based beam steering system”
by C. Knoernschild, X. L. Zhang, L. Isenhower, A. T. Gill, F. P. Lu, M. Saffman, and J. Kim (ArXiv version available here)
Some scientists from Saffman’s group at the Univ. of Wisconsin (Madison, Wisc.) and from Duke Univ. (N.Carolina) have built a device that traps 5 NEUTRAL Rubidium-87 atoms and then shines a spotlight on one atom at a time. (so far, the NIST people have used ions)
The five Rb atoms are trapped in a straight line; adjacent ones are 8.7 micrometers apart. The diameter of the spotlight is about 5 micrometers. (bacteria are typically 1 micrometer in size, so this is a spotlight for bacteria) The spotlight can be moved from one atom to another in 10 to 20 microseconds.
The spotlight is so powerful 🙂 that it causes a Rb atom to transition between the $|0\rangle$ and $|1\rangle$ quantum states which define a qubit. In this case, these two states are defined as two hyperfine energy levels of the atom; more specifically, $|0\rangle := | F=1, m_F=0\rangle$ and $|1\rangle := |F=2, m_F=0 \rangle$. It takes about 0.1 microsecs for an atom to go from $|0\rangle$ to $|1\rangle$. This so called Rabi flopping can be induced in a single target atom, with minimal disturbance on the quantum state of adjacent atoms.
In the near future, these researchers plan to produce 2-qubit interactions and 2-dimensional arrays of qubits.
The last sentence of the paper is:
While we have focused on its use in neutral atom QIP, it is applicable to other qubit systems in a periodic lattice including atomic ions, diamond nitrogen-vacancy color centers, and quantum dots.
I find it awesome how good the experimentalists are getting at controlling single qubits. True, qubits floating in the middle of a vacuum cavity, held in place by ephemeral “tractor beams” of light, manipulated by a spotlight which is steered by mechanical means, is probably not the most sturdy and convenient way of implementing a scalable quantum computer. But we can certainly learn a lot of physics from such experiments, and this will illuminate the way towards more convenient devices.
Press release for paper here
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## Leave a Comment »
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Blog at WordPress.com. | 2018-02-19 17:42:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 6, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41415923833847046, "perplexity": 2102.4407315486997}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812758.43/warc/CC-MAIN-20180219171550-20180219191550-00339.warc.gz"} |
http://mathoverflow.net/questions/11082/the-other-classical-limit-of-a-quantum-enveloping-algebra/13794 | # The other classical limit of a quantum enveloping algebra?
Let $\mathbb K$ be a field (of characteristic 0, say), $\mathfrak g$ a Lie bialgebra over $\mathbb K$, and $\mathcal U \mathfrak g$ its usual universal enveloping algebra. Then the coalgebra structure on $\mathfrak g$ is equivalent to a co-Poisson structure on $\mathcal U \mathfrak g$, i.e. a map $\hat\delta : \mathcal U \mathfrak g \to (\mathcal U \mathfrak g)^{\otimes 2}$ satisfying some axioms. A formal quantization of $g$ is a Hopf algebra $\mathcal U_\hbar \mathfrak g$ over $\mathbb K[[\hbar]]$ (topologically free as a $\mathbb K[[\hbar]]$-module) that deforms $\mathcal U \mathfrak g$, in the sense that it comes with an isomorphism $\mathcal U_\hbar \mathfrak g / \hbar \mathcal U_\hbar \mathfrak g \cong \mathcal U \mathfrak g$, and moreover that deforms the comultiplication in the direction of $\hat\delta$: $$\Delta = \Delta_0 + \hbar \hat\delta + O(\hbar^2),$$ where $\Delta$ is the comultiplication on $\mathcal U_\hbar \mathfrak g$ and $\Delta_0$ is the (trivial, i.e. which $\mathfrak g$ is primitive) comultiplication on $\mathcal U\mathfrak g$. This makes precise the "classical limit" criterion: "$\lim_{\hbar \to 0} \mathcal U_\hbar \mathfrak g = \mathcal U \mathfrak g$"
I am wondering about "the other" classical limit of $\mathcal U_\hbar \mathfrak g$. Recall that $\mathcal U\mathfrak g$ is filtered by declaring that $\mathbb K \hookrightarrow \mathcal U\mathfrak g$ has degree $0$ and that $\mathfrak g \hookrightarrow \mathcal U\mathfrak g$ has degree $\leq 1$ (this generates $\mathcal U\mathfrak g$, and so defines the filtration on everything). Then the associated graded algebra of $\mathcal U\mathfrak g$ is the symmetric (i.e. polynomial) algebra $\mathcal S\mathfrak g$. On the other hand, the Lie structure on $\mathfrak g$ induces a Poisson structure on $\mathcal S\mathfrak g$, one should understand $\mathcal U \mathfrak g$ as a "quantization" of $\mathcal S\mathfrak g$ in the direction of the Poisson structure. Alternately, let $k$ range over non-zero elements of $\mathbb K$, and consider the endomorphism of $\mathfrak g$ given by multiplication by $k$. Then for $x,y \in \mathfrak g$, we have $[kx,ky] = k(k[x,y])$. Let $\mathfrak g_k$ be $\mathfrak g$ with $[,]\_k = k[,]$. Then $\lim\_{k\to 0} \mathcal U\mathfrak g_k = \mathcal S\mathfrak g$ with the desired Poisson structure.
I know that there are functorial quantizations of Lie bialgebras, and these quantizations give rise to the Drinfeld-Jimbo quantum groups. So presumably I can just stick $\mathfrak g_k$ into one of these, and watch what happens, but these functors are hard to compute with, in the sense that I don't know any of them explicitly. So:
How should I understand the "other" classical limit of $\mathcal U_\hbar \mathfrak g$, the one that gives a commutative (but not cocommutative) algebra?
If there is any order to the world, in the finite-dimensional case it should give the dual to $\mathcal U(\mathfrak g^\*)$, where $\mathfrak g^\*$ is the Lie algebra with bracket given by the Lie cobracket on $\mathfrak g$. Indeed, B. Enriquez has a series of papers (which I'm in the process of reading) with abstracts like "functorial quantization that respects duals and doubles".
On answer that does not work: there is no non-trivial filtered $\hbar$-formal deformation of $\mathcal U\mathfrak g$. If you demand that the comultiplication $\Delta$ respect the filtration on $\mathcal U\mathfrak g \otimes \mathbb K[[\hbar]]$ and that $\Delta = \Delta_0 + O(\hbar)$, then the coassociativity constraints imply that $\Delta = \Delta_0$.
This makes it hard to do the $\mathfrak g \mapsto \mathfrak g_k$ trick, as well. The most naive thing gives terms of degree $k^{-1}$ in the description of the comultiplication.
-
The answer is already in Drinfeld's "quantum groups" ICM report. To a QUE algebra $U =U_\hbar g$ with classical limit the Lie bialgebra $g$, he associates a QFSH algebra $U^\vee$ which turns out to be a formal deformation of the formal series Hopf algebra $\hat S(g)$; when $g$ is finite dimensional, this is the formal function ring over the formal group $G^\ast$ with Lie algebra $g^\ast$ and indeed the dual to $Ug^*$. All this was later developed in a paper by Gavarini (Ann Inst Fourier).
For example, if the deformation is trivial, so $U=Ug[[\hbar]]$, one finds $U^\vee$ to be the complete subalgebra generated by $\hbar g[[\hbar]]$ which is roughly speaking $U(\hbar g[[\hbar]])$ i.e. $U(g_\hbar)$ where $g_\hbar$ is $g[[\hbar]]$ but with Lie bracket multiplied by $\hbar$. So $U^\vee$ is a quasi-commutative algebra (a flat deformation of $\hat S(g)$ actually).
-
The answer is essentially given in Kassel and Turaev, "Biquantization of Lie bialgebras", Pacific Journal of Mathematics, 2000 vol. 195 (2) pp. 297-369, MR1782170. They do the following: To a finite-dimensional Lie bialgebra $\mathfrak g$ over $\mathbb C$, they define a biassociative bialgebra $A_{u,v}(\mathfrak g)$, (topologically) free over $\mathbb C[u][[v]]$, such that:
1. $A_{u,v}(\mathfrak g)$ is commutative module $u$ and cocommutative modulo $v$.
2. $A_{u,v}(\mathfrak g) / (u,v) = \mathcal S\mathfrak g$, the symmetric algebra, with its induced Poisson and co-Poisson structures.
3. $A_{u,v}(\mathfrak g) / (u)$ is a commutative Poisson bialgebra and its cobracket quantizes $\mathcal S(\mathfrak g)$ in the co-Poisson direction.
4. $A_{u,v}(\mathfrak g) / (v)$ is a cocommutative co-Poisson bialgebra and its bracket quantizes $\mathcal S(\mathfrak g)$ in the Poisson direction. Indeed, $A_{u,v}(\mathfrak g) / (v,u-1) = \mathcal U\mathfrak g$.
5. $A_{u,v}(\mathfrak g)$ is essentially dual to $A_{v,u}(\mathfrak g^*)$.
Thus the Etingof-Kazhdan quantization is $A_{u,v}(\mathfrak g) / (v-\hbar,u-1)$. More generally, we have $\hbar = uv$.
I still don't know if there's some way to look at this construction without variables $u,v$, and rather with (co-)filtrations. But, then again, I've only read the introduction to the paper. I also don't know if it works over other fields. Given that Kassel and Turaev rely on the Etingof-Kazhdan methods, which in turn rely on a Drinfeld associator, I assume that the method requires working over a $\mathbb Q$-algebra.
-
Actually, they are happy to work over any field of characteristic zero. They just call it "$\rm C$" for convenience. – Theo Johnson-Freyd Feb 2 '10 at 5:09 | 2014-12-26 03:02:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9617143273353577, "perplexity": 175.21347128607363}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1419447548601.48/warc/CC-MAIN-20141224185908-00006-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://norcalbiostat.github.io/AppliedStatistics_notes/stratification.html | ## 9.1 Stratification
Stratified models examine the regression equations for each subgroup of the population and seeing if the relationship between the response and explanatory variables changed for at least one subgroup.
Consider the relationship between the length of an iris petal, and the length of it’s sepal. Earlier we found that the iris species modified this relationship. Lets consider a binary indicator variable for species that groups veriscolor and virginica together.
iris$setosa <- ifelse(iris$Species=="setosa", 1, 0)
table(iris$setosa, iris$Species)
##
## setosa versicolor virginica
## 0 0 50 50
## 1 50 0 0
Within the setosa species, there is little to no relationship between sepal and petal length. For the other two species, the relationship looks still significantly positive, but in the combined sample there appears to be a strong positive relationship (blue).
ggplot(iris, aes(x=Sepal.Length, y=Petal.Length, col=as.factor(setosa))) +
geom_point() + theme_bw() + theme(legend.position="top") +
scale_color_manual(name="Species setosa", values=c("red", "darkgreen")) +
geom_smooth(se=FALSE, method="lm") +
geom_smooth(aes(x=Sepal.Length, y=Petal.Length), col="blue", se=FALSE, method='lm')
The mathematical model describing the relationship between Petal length ($$Y$$), and Sepal length ($$X$$), for species setosa ($$s$$) versus not-setosa ($$n$$), is written as follows:
$Y_{is} \sim \beta_{0s} + \beta_{1s}*x_{i} + \epsilon_{is} \qquad \epsilon_{is} \sim \mathcal{N}(0,\sigma^{2}_{s})$ $Y_{in} \sim \beta_{0n} + \beta_{1n}*x_{i} + \epsilon_{in} \qquad \epsilon_{in} \sim \mathcal{N}(0,\sigma^{2}_{n})$
In each model, the intercept, slope, and variance of the residuals can all be different. This is the unique and powerful feature of stratified models. The downside is that each model is only fit on the amount of data in that particular subset. Furthermore, each model has 3 parameters that need to be estimated: $$\beta_{0}, \beta_{1}$$, and $$\sigma^{2}$$, for a total of 6 for the two models. The more parameters that need to be estimated, the more data we need. | 2022-05-26 07:19:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5815578103065491, "perplexity": 1669.0078757046424}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662604495.84/warc/CC-MAIN-20220526065603-20220526095603-00181.warc.gz"} |
http://www.jomsocial.com/forum/guru-pro/35047-some-troubles-with-guru-pro | ### Notice
The forum is in read only mode.
## Support Forum
Welcome! Support Forums have been reactivated
### Some troubles with Guru Pro
3 years 9 months ago
JomSocial Expired GURU Expired
ISSUE SUMMARY:
I have three concerns with GURU PRO:
1. The Informations in current cover page are in an inappropriate color as you can see in the screenshot below
(Think that this is specific to my site)
2. The media-images appear too small in the quiz. Even by setting the width of the image to 500px, 900px, nothing changes. Is it possible to have a setting in % ? So that images can cover the entire width of the screen in the quiz?
3. How to prevent opening a pdf content in a course on google drive?
I'm using :
- Joomla 3.6.2
- JF Social template 2.5
3 years 9 months ago
HI, stankoua.
Thank you for contacting us.
1. Yes, this issue is caused by your current template.
snag.gy/DRBFge.jpg
2. Please, provide me URL and access to that course so I could see what code cause that issue.
3. You can't prevent that as you created media document so it will be opened. If you want your students to download that file you need to add it to media library as URL not a document. but browser (e.g FireFox) will open it by default... so try to zip it.
- Instead of saying: 'it's not working', explain the problem in detail.
- Screenshots with the URL visible in them and the problem marked are more than welcome.
- Tell us how to replicate the problem, we can't fix it if we can't find it.
- Make sure that your site/server meets JomSocial System Requirements
- Make sure to setup JomSocial Cron Job
- Always provide us with access details to the backend and ftp. We need it to debug problems.
- If you have a similar problem, but a solution you found isn't working, open a new thread instead of 'merging' with an existing one.
- Use the "Thank You" feature on any post that helped you
3 years 9 months ago
JomSocial Expired GURU Expired
Hi Michal !
1. Can you provide any help for this issue ? Or maybe check it directly with the admin and ftp account ?
2. Here is the URL to access to that course. You can take the course with the admin account I provide you in m first post.
Here is the URL
Regards
3 years 9 months ago
Hi.
1. All you need is to add this code:
.uk-overlay-background {
color: #fff !important;
}
To your current template main css file.
2. Please, check credentials as I get "Failed login" when I try them.
- Instead of saying: 'it's not working', explain the problem in detail.
- Screenshots with the URL visible in them and the problem marked are more than welcome.
- Tell us how to replicate the problem, we can't fix it if we can't find it.
- Make sure that your site/server meets JomSocial System Requirements
- Make sure to setup JomSocial Cron Job
- Always provide us with access details to the backend and ftp. We need it to debug problems.
- If you have a similar problem, but a solution you found isn't working, open a new thread instead of 'merging' with an existing one.
- Use the "Thank You" feature on any post that helped you
3 years 9 months ago
JomSocial Expired GURU Expired
Thank's much Michal for your help.
the first problem is solved. Great !
For point 2. I just disable the protection access to the administration site and the course to see the problem in the images within the quiz is now freely accessible.
Here is the URL to access to that course
3 years 9 months ago
Hi.
Still no juice as quizzes ar not available for guests.
- Instead of saying: 'it's not working', explain the problem in detail.
- Screenshots with the URL visible in them and the problem marked are more than welcome.
- Tell us how to replicate the problem, we can't fix it if we can't find it.
- Make sure that your site/server meets JomSocial System Requirements
- Make sure to setup JomSocial Cron Job
- Always provide us with access details to the backend and ftp. We need it to debug problems.
- If you have a similar problem, but a solution you found isn't working, open a new thread instead of 'merging' with an existing one.
- Use the "Thank You" feature on any post that helped you
3 years 9 months ago
JomSocial Expired GURU Expired
Hi !.
I sent you an administrator account that can also be used in frontend.
However here is another an account for testing in frontend:
<removed for security reason>
To recap, here's my problem:
"The media-image appear too small in the quiz. Even by setting the width of the image to 500px, ... 900px, nothing changes. Is it possible to have a setting in%? So That image can cover the Entire width of the screen in the quiz question ? "
Here is a course with quiz + images to visualize the problem .
3 years 9 months ago
HI.
Please, click on that small image :)
It will be opened in new window in full size :)
snag.gy/iZP3yv.jpg
This is just a thumbnail... it's possible to have it bigger but this will apply to all images you'll ever use in quiz... even those big ones.
You may add this css to display image in original size straight in quiz:
.guru-quiz__media img {
width: auto !important;
}
But it may distort layout in smaller screens.
- Instead of saying: 'it's not working', explain the problem in detail.
- Screenshots with the URL visible in them and the problem marked are more than welcome.
- Tell us how to replicate the problem, we can't fix it if we can't find it.
- Make sure that your site/server meets JomSocial System Requirements
- Make sure to setup JomSocial Cron Job
- Always provide us with access details to the backend and ftp. We need it to debug problems.
- If you have a similar problem, but a solution you found isn't working, open a new thread instead of 'merging' with an existing one.
- Use the "Thank You" feature on any post that helped you
3 years 9 months ago
JomSocial Expired GURU Expired
Hello Michal !
Thank's very much for your support.
One last question. Where do I have to insert the css code above?
Otherwise it would be interesting for the next version of GURU, thinking to directly display images in full size (better in %) in the quiz, not thumbnails.
3 years 9 months ago
HI.
Try in this file: ROOT/components/com_guru/css/custom.css
- Instead of saying: 'it's not working', explain the problem in detail.
- Screenshots with the URL visible in them and the problem marked are more than welcome.
- Tell us how to replicate the problem, we can't fix it if we can't find it.
- Make sure that your site/server meets JomSocial System Requirements
- Make sure to setup JomSocial Cron Job
- Always provide us with access details to the backend and ftp. We need it to debug problems.
- If you have a similar problem, but a solution you found isn't working, open a new thread instead of 'merging' with an existing one.
- Use the "Thank You" feature on any post that helped you
3 years 9 months ago
JomSocial Expired GURU Expired
Hello !
I've tested without success css code you suggested me.
Otherwise I believe that is a bug!
Indeed when clicking resume testing after failure, the feedback that appears offers quiz images either thumbnail but large visible format.
Moreover, I have some suggestions:
1. It is important to give the opportunity to those who have managed a quiz within 100% to resume and improve their score.
2. It would be cool to have a rich text editor for the quiz with why not a science tool as "WARIS" or "MathJax". Currently the quiz system is too limited to scientists.
Thank you once again for your kind support.
3 years 9 months ago
JomSocial Expired GURU Expired
Hello !
I've tested without success css code you suggested me.
Otherwise I believe that is a bug!
Indeed when clicking resume testing after failure, the feedback that appears offers quiz images either thumbnail but large visible format.
Moreover, I have some suggestions:
1. It is important to give the opportunity to those who have managed a quiz within 100% to resume and improve their score.
2. It would be cool to have a rich text editor for the quiz with why not a science tool as "WARIS" or "MathJax". Currently the quiz system is too limited to scientists.
Thank you once again for your kind support.
3 years 9 months ago
HI.
No, it's not a bug - this is how thumbnails works. The idea of thumbnails is to show small images and larger one after clicking on it.
The same idea as in galleries.
As for suggestions I assign developer and mark thread as feature request.
- Instead of saying: 'it's not working', explain the problem in detail.
- Screenshots with the URL visible in them and the problem marked are more than welcome.
- Tell us how to replicate the problem, we can't fix it if we can't find it.
- Make sure that your site/server meets JomSocial System Requirements
- Make sure to setup JomSocial Cron Job
- Always provide us with access details to the backend and ftp. We need it to debug problems.
- If you have a similar problem, but a solution you found isn't working, open a new thread instead of 'merging' with an existing one.
- Use the "Thank You" feature on any post that helped you
Moderators: Piotr Garasiński
## Join 180,000 websites creating Amazing communities
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full -fledged, social networking site | 2020-07-09 04:22:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18816831707954407, "perplexity": 3373.98419985886}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655898347.42/warc/CC-MAIN-20200709034306-20200709064306-00499.warc.gz"} |
https://math.stackexchange.com/questions/3588449/find-the-remainder-of-3333-divided-by-100 | # Find the remainder of $3^{333}$ divided by $100$
Find the remainder of $$3^{333}$$ divided by $$100$$
So I can find that $$100=2^2\cdot 5^2$$
Then I want to find $$3^{333}$$ mod $$4$$ and mod $$25$$ and use chinese remainder theorem to find a solution mod $$100$$.
I can find that $$3^{333}\equiv (-1)$$ mod $$4$$
But then $$3^{333}=((3^3)^3)^{37}\equiv (27^3)^{37}\equiv (2^3)^{37}\equiv 8^{37}$$ mod $$25$$
But I cannot find $$8^{37}$$ mod $$25$$
• Mar 20 '20 at 20:57
• @WhatsUp I can see I can reduce it to $3^{320}\times 3^{13}\equiv 3^{13}$ mod $100$, but not sure what I do with $3^{13}$ Mar 20 '20 at 21:01
• You used the first link I gave. Now use the second one. Mar 20 '20 at 21:02
• $3^{20}=3 486 784 401\equiv 1 \text{ mod }100$. Just a little hint :)
– user759746
Mar 20 '20 at 21:03
• Hint $\large\ 3^{333} = 3(-1+10)^{166} =\,\ldots$ (Binomial Theorem, only first two terms survive $\bmod 100$) Mar 20 '20 at 21:11
$$3^{333}$$ being divided by 100.
$$=(3^9)^{37}$$
$$=19683^{37}$$
$$=(19700-17)^{37}$$
$$\equiv -17^{37} \quad \bmod 100$$
$$-17^{37} =-17(17^{36})=-17(300-11)^{18}$$
$$\equiv -17(11^{18}) \quad \bmod 100$$
$$-17(11^{18})=-17((1300+31)^6)$$
$$\equiv -17(31^6) \quad \bmod 100$$
$$-17(31^6)=-17(1000-39)^3$$
$$\equiv -17 \cdot -39^3 \quad \bmod 100$$
$$17 \cdot 39^3=17 \cdot 39 \cdot (1500+21)$$
$$=(700-37)(1500+21)$$
And after all the work $$-37 \cdot 21=-777 \equiv -77 (\bmod 100)$$
But if the answer had to be positive then $$100-77=\boxed{23}$$
So you need, as you noted, $$3^{13}\pmod {100}$$. Try successive squaring. $$3^2=9,3^4=9^2=81,3^8=81^2=(-19)^2=61, 3^{12}=3^4\cdot3^8=81\cdot61=41,3^{13}=3\cdot41=23\pmod{100}$$.
We have $$3^{333} \equiv 2^{111}\equiv1024^{11}\times2\equiv-2 \pmod{25}$$ (note that I used your calculation for the first equality here and the well-known fact that $$2^{10}=1024$$)
So, if $$x=3^{333}$$, $$x=-2+25k \equiv-2+k \equiv-1 \pmod4$$
Hence $$k \equiv1 \pmod 4$$
Therefore $$x=-2+25(1+4k')=23+100k' \equiv23 \pmod{100}$$
Use the totient function. $$2$$ and $$5$$ are distinct primes so $$\phi(100)=\phi(2^25^2)=\phi(2^2)\phi(5^2)=[2(2-1)][5(5-1)]=40.$$
Now since $$\gcd(3,100)=1$$ we have $$1\equiv 3^{\phi(100)}\equiv 3^{40} \mod 100.$$
Therefore $$3^{333}\equiv (3^{40})^8\cdot 3^{13}\equiv (1)^8\cdot 3^{13}\equiv 3^{13} \mod 100.$$
To finish, see my comment to the Q.
Using $$\ ab\bmod ac = a\,(b\bmod c) =$$ mod Distributive Law to factor out $$\,a = 4$$
$$3^{\large 333}\!+\!1\bmod 100 = 4\left[\dfrac{\color{#90f}{3^{\large 333}}\!+\!1}4\bmod 25\right] = 4\left[\dfrac{\color{#90f}{23}\!+\!1}4\bmod 25\right] = 4[6],\$$ by
$$\!\bmod 25\!:\,\ \color{#c00}{3^{\large 20}\equiv 1}\ \Rightarrow\ \color{#90f}{3^{\large 333}}\equiv \underbrace{3(\color{#0a0}{3^{\large 3}})^{\large 4}(\color{#c00}{3^{\large 20}})^{\large 16}}_{\textstyle 3\,(\color{#0a0}2)^{\large 4}\,\color{#c00}1^{\large 16}}\equiv \color{#90f}{23},\,$$ by $$\rm\color{#c00}{Euler\ \phi(5^2)=4\cdot 5}$$
Remark The prior line is a special case of modular order reduction - the key to simplifying the computation of large modular powers.
As explained in the first link, the mod Distributive Law is an operational form of CRT. You can use the standard CRT formula along with the above computation mod $$25$$ to obtain the same result. In fact already $$23\equiv -1\pmod{\!4}$$ so we're done - we don't even need to apply the CRT formula.
Another quick way: $$\, 3^{\large 333} = 3(-1+10)^{\large 166} =\,\ldots\,$$ and Binomial expanding only the first $$2$$ terms survive $$\!\bmod 100$$.
Use Euler.
$$\phi(25) = 20$$ so $$8^{20}\equiv 1 \pmod {25}$$
So we need to figure out $$8^{17}\equiv 8^{-3}$$ which is which will be equivalent to $$k^3$$ where $$k$$ is the multiplicative inverse of $$8$$. $$8*3=24\equiv -1$$ so $$8*(-3)\equiv 1 \pmod{25}$$ and $$8^{17} \equiv (-3)^3 \equiv -27\equiv -2\equiv 23 \pmod {25}$$.
.....
Or back to the $$3$$
$$3^{333}=3^{320}3^{13}\equiv 3^{13}\pmod {25}$$.
As $$3^{20}\equiv 1$$ its a good guess that $$3^{10} \equiv \pm 1$$.
Many ways to do this but $$3^{10} = 3^3*3^3*3^3*3\equiv 27*27*27*3\equiv 2*2*2*3\equiv 24 \equiv -1 \pmod {20}$$. So $$3^{13}\equiv -3^3\equiv -27\equiv -2 \equiv 23$$.
.....OR.....
$$100 = 10^2$$
$$3^2 = 10-1$$
So $$3^{10} = (10-1)^5\equiv 50-1$$
$$3^{20} \equiv (50-1)^2 \equiv 1\pmod {100}$$.
So $$3^{333}\equiv 3^{13}\equiv 3^{10}*3^{3}\equiv (50-1)*27\equiv 50*(26+1)-27\equiv 50 - 27 \equiv 23\pmod{100}$$ | 2022-01-29 08:45:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 73, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9217199087142944, "perplexity": 240.1111661280054}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300573.3/warc/CC-MAIN-20220129062503-20220129092503-00123.warc.gz"} |
https://www.sawaal.com/puzzles.htm?page=3&sort= | # Puzzles Questions
• #### Word Puzzles
Q:
Can you arrange 9 numerals - 1, 2, 3, 4, 5, 6, 7, 8 and 9 [using each numeral just once] above and below a division line, to create a fraction equaling to 1/3 [one third]?
Answer
$\inline \frac{5832}{17496}=\frac{1}{3}$
Report Error
Subject: Number Puzzles
6761
Q:
How many letters of the word FAINTS, will their order in the word and that when the letters are arranged in the alphabetical order, remain the same?
A) Two B) One C) Three D) Nil
Answer & Explanation Answer: A) Two
Explanation:
When the letters are arranged in the alphabetical order, two remains the same.
Report Error
Filed Under: Math Puzzles
41 5550
Q:
Logical puzzle
Miss Anne has eleven kids in her class. She has a bowl containing eleven apples. Now Miss Anne want to divide the eleven apples to the kids, in such a way that a apple should remain in her bowl. How can Miss Anne do it?
Answer
Ten kids will get each one apple. The eleventh kid will get the apple with the bowl.
Report Error
Subject: Logic Puzzles
5417
Q:
Arrange four nines(9) and a one(1) and only one mathematical symbol to make it equal to 100 ?
Answer
199 - 99 = 100
Report Error
Subject: Math Puzzles
5262
Q:
Which number multiplied by itself will give the output as 12345678987654321 ?
Answer
11 * 11 = 121
111 * 111 = 12321
what we observe is that the square of the number follows a pattern: 2 1's gives 121. 3 1's gives 12321.
so to get 12345678987654321 we need to get square of 9 1's(111,111,111).
Report Error
Subject: Math Puzzles
5174
Q:
Logical puzzle
You work at a fruit factory.
There are 3 crates in front of you. One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges. And each crate is labeled. One reads "apples", one reads "oranges", and one reads "apples and oranges". But the labeling machine has gone crazy and is now labeling all boxes incorrectly. If you can only take out and look at just one of the pieces of fruit from just one of the crates, how can you label ALL of the crates correctly?
Answer
Our solution:
Take a piece of fruit from the "apples and oranges" crate. If it's an apple then you know that is the "apples" crate since ALL THE CRATES ARE LABELED INCORRECTLY. This means the crate marked "apples" must be "oranges" and the crate marked "oranges" must be "apples and oranges".
Report Error
Subject: Logic Puzzles
5161
Q:
In the below puzzle, a word starts and ends with the same letter. Can you figure out what the word is?
_rus_
Answer
trust
Report Error
Subject: Word Puzzles
5067
Q:
Answer the Following Puzzle.
A) 1 B) 7 C) 3 D) 9
Answer & Explanation Answer: B) 7
Explanation:
In each segment of the circle, multiply the outer two numbers together and subtract the sum of the outer two numbers in the opposite segment to give the value in the inner grey segment
Report Error
Filed Under: Number Puzzles
21 5013 | 2019-01-19 15:15:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2904859483242035, "perplexity": 2349.5323808208677}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583668324.55/warc/CC-MAIN-20190119135934-20190119161934-00487.warc.gz"} |
https://www.fxweek.com/fx-week/news/1534414/candollar-ready-fly | The US dollar has been within a rising trend versus the Canadian dollar from 1991 until the present. This long-term uptrend has encompassed a move from a low of 1.1193 in November 1991 to the recent all-time high of 1.6194, established in January 2002. Interestingly, the all-time high at 1.6194 completed a five-wave Elliott Wave sequence that indicates we are in a longer-term topping pattern in US$/C$. This view is reinforced by the fact that we are currently within a five-year rising wedge | 2018-05-23 22:25:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29365476965904236, "perplexity": 2043.2948757460922}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794865830.35/warc/CC-MAIN-20180523215608-20180523235608-00510.warc.gz"} |
http://www.thusspakeak.com/ak/2016/03/01-TheWeakTheInappropriateAndTheBDShuffle.html | # The Weak, The Inappropriate And The B-D Shuffle
We have been looking[1][2] at how we might approximate random variables with pseudo random number generators, such as the sequences generated with linear congruences of the form
$x_{i+1} = \left(a \times x_i\right)\;\%\;m$
where $$x\;\%\;m$$ represents the remainder of the integer division of $$x$$ by $$m$$, $$a$$ is known as the multiplier, $$c$$ as the increment, $$m$$ as the modulus and $$x_0$$ as the seed.
Whilst these are supremely easy to implement and extremely efficient in terms of both speed of execution and use of memory, choosing appropriate values for $$a$$, $$c$$, $$m$$ and $$x_0$$ is a rather difficult proposition; get it wrong and they will produce weak pseudo random numbers and, unfortunately, the ways in which we can do so are extremely subtle. For example, if we use such sequences to randomly generate two-dimensional vectors then poor choices will result in their lying upon relatively few lines, as demonstrated by program 1 using our ak.congruentialRnd generator which, like Math.random, scales the numbers that it returns so that they are greater than or equal to zero and strictly less than one.
Program 1: Getting It Very, Very Wrong!
Marsaglia's theorem[3] shows that this problem occurs in higher dimensions too, so that in $$n$$ dimensions the vectors might be constrained to a surprisingly small number of $$n-1$$ dimensional subspaces.
### First, Give Them A Good Shuffle...
One thing we might try to improve the randomness of linear congruential pseudo random number generators is to shuffle them, that is to say observe them non-sequentially with
$$\displaystyle{ x^\prime_i = x_{j_i} }$$
where $$j_i$$ is a randomised sequence of integers.
Unfortunately advancing from the seed to a randomly selected element of the sequence at every step would be prohibitively expensive, but we can do almost as well by advancing a random number of elements from the current one instead, as illustrated by program 2.
Program 2: Randomly Advancing Through The Sequence
The randomisation of the advance through the sequence is done here with the lines
d = ak.floor(16*rnd2()); for(j=0;j<d;++j) rnd1();
which throw away between zero and fifteen numbers of the sequence before one is used as a pseudo random number.
Whilst this certainly breaks up the lines rather effectively, on average program 2 uses nine and a half times as many pseudo random numbers as program 1 which, although a good deal better than picking elements from the sequence entirely at random, is hardly ideal.
### The MacLaren-Marsaglia Shuffle
We can significantly reduce the computational expense of shuffling the sequence with a trick developed by MacLaren and Marsaglia[4]. Rather than throwing away any of the pseudo random numbers, they suggested filling a buffer with them and using a second generator to pick which to use at each step. That number is then replaced with a fresh one from the first random number generator, allowing us to jump both forwards and backwards through the sequence, eventually using all of them, as is done in program 3.
Program 3: The MacLaren-Marsaglia Shuffle
This time the randomisation of the progress through the sequence is done with the lines
j = ak.floor(v.length*rnd2()); x1 = v[j]; v[j] = rnd1();
which pick the buffered number to use and replace, breaking up the lines no less effectively than program 2 but with just twice as many pseudo random numbers than were used in program 1.
### The Bays-Durham Shuffle
We can do better still with a trick invented by Bays and Durham[5]; use the previous value taken from the buffer of the pseudo random numbers to pick the next one to use and replace, as demonstrated by program 4.
Program 4: The Bays-Durham Shuffle
Note that now we're randomising the path through the sequence with
j = ak.floor(v.length*x0); x1 = v[j]; v[j] = rnd();
As you can see, this breaks up the lines just as effectively as our previous schemes but only needs one pseudo random number at each step!
### ak.baysDurhamRnd
It's a relatively trivial task to implement a general purpose Bays-Durham shuffle for pseudo random number generators, as illustrated by listing 1.
Listing 1: ak.baysDurhamRnd
ak.baysDurhamRnd = function(rnd, n) {
var v, i, x;
if(ak.nativeType(rnd)!==ak.FUNCTION_T) {
throw new Error('invalid generator in ak.baysDurhamRnd');
}
if(ak.nativeType(n)===ak.UNDEFINED_T) n = 16;
else if(ak.nativeType(n)!==ak.NUMBER_T) {
throw new Error('non-numeric buffer size in ak.baysDurhamRnd');
}
n = Number(n);
if(n!==ak.floor(n) || n<2) {
throw new Error('invalid buffer size in ak.baysDurhamRnd');
}
v = new Array(n);
for(i=0;i<n;++i) v[i] = rnd();
x = rnd();
return function() {
i = ak.floor(n*x);
x = v[i];
v[i] = rnd();
return x;
};
};
This function takes a pseudo random number generator rnd and returns a new one that applies the Bays-Durham shuffle with a buffer length of n to the numbers that it generates in almost exactly the same way as we did in program 4, the principal difference being the tests that the arguments are valid and the defaulting of the buffer length to sixteen if it is not specified.
Program 5 demonstrates how to use ak.baysDurhamRnd to break up the lines in the pseudo random number generator from program 1.
Program 5: Using ak.baysDurhamRnd
The implementation of ak.baysDurhamRnd can be found in BaysDurhamRnd.js.
### References
[1] Pseudo Algorithmical, www.thusspakeak.com, 2016.
[2] Talkin' 'Bout My Generators, www.thusspakeak.com, 2016.
[3] Marsaglia, G., Random Numbers Fall Mainly in the Planes, Proceedings of the National Academy of Sciences, Vol. 61, No. 1, 1968.
[4] MacLaren, M. & Marsaglia, G., Uniform Random Number Generators, Journal of the ACM, Vol. 12, No. 1, 1965.
[5] Bays, C. & Durham, S., Improving a Poor Random Number Generator, ACM Transactions on Mathematical Software, Vol. 2, No. 1, 1976. | 2018-02-21 20:45:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6271612644195557, "perplexity": 1097.317231822213}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813803.28/warc/CC-MAIN-20180221202619-20180221222619-00131.warc.gz"} |
https://hajji.org/en/crypto/riposte/from-mix-nets-to-writable-pir | If you didn't skip the intermission, you'll recall that one necessary, albeit not sufficient, condition to guarantee anonymity was the shuffling of collected user messages before publication. In mix-net based systems, the shuffling was done by the server(s), which we called mixers.
### A Gedankenexperiment
What if we moved the burden of mixing messages from the mixers to the users? Let's do a little silly Gedankenexperiment: Alice selects a random row index $r_a$ to put her message $m_a$ in. She connects to $R_0$, and sends the pair $(r_a, m_a)$. $R_0$ briefly verifies that $0 \le r_a \lt N$ where $N$ is the number of rows in the table, and then updates his table by unconditionally overwriting row $r_a$ with $m_a$. In other words, Alice "mixes" her message $m_a$ into $R_0$'s table at a random location $r_a$. Now, Bob comes along and mixes his message $m_b$ at random location $r_b$ of $R_0$'s table. Then Carol, David, and Eve do the same ... until the period is over, at which point $R_0$ simply publishes the table, and starts a new period with a fresh empty table.
Note that no shuffle was performed, neither by the server, nor by the users. The mixing was implicit by users selecting random rows to add their messages in.
Exercise: Does this system provide anonymity in the sense that we are pursuing, i.e. that at the end of the period, it is impossible to tell who added $m_a$ and $m_b$? If not, what needs to be fixed? Assume that all users connect to $R_0$ with secure channels (providing secrecy and integrity). Assume however that a passive eavesdropper can see who connects to $R_0$ and when. Discuss.
#### Analyzing the Gedankenexperiment
Good news first: the messages at the end of the period are indeed in a random order. A passive eavesdropper watching Alice, Bob, etc. establish secure channels to $R_0$ can't deduce from the order of connections that the first message published by $R_0$ at the end of the period belongs to the user that connected first. The same holds true for the second message and user connecting second, and so on. Since $R_0$ collects a sufficient large number of messages before releasing the table, the passive eavesdropper can't mount a time-based traffic analysis to deanonymize users.
Bad news next: Alice and Bob could both select at random the same row $r$. Alice submits $(r, m_a)$, and Bob submits $(r, m_b)$. Depending on who came last, his or her message will overwrite the other message. Of course, that would be a collision. While pesky, does this collision deanonymize Alice or Bob? Not necessarily, if at least two different rows have been populated by Alice, Bob, and possibly other users. Indeed, the only case where the passive eavesdropper can deanonymize a user is if all users collided on a single row $r$: in this case, the eavesdropper concludes that the last user connecting to $R_0$ must be the author of the message at row $r$. As soon as another row $R_1$ is populated, the eavesdropper can't tell anything with certainty... However, the more collisions occur in one period, the weaker the anonymity guarantee. If enough users submit messages at random locations and if the table is big enough, occasional collisions don't significantly hurt anonymity.
Really bad news last, but no least: If the server $R_0$ is compromized, all users lose their anonymity, because $R_0$ knows exactly on which row Alice, Bob, etc. are mixing their messages in.
### Secret sharing to the rescue?
Remember secret sharing from the high-level introduction to Riposte? This is how Alice could send $m_a$ to $R_0$ and $R_1$, such that neither $R_0$ nor $R_1$ could read $m_a$ without the help of the other server [Y82]:
1. Alice picks a random $r$: $r \overset{R}{\leftarrow} \mathbb F$
2. Alice sends $r$ to $R_0$
3. Alice sends $(-r + m_a)$ to $R_1$
All additions understood modulo $|\mathbb F|$. At the end of the period, $R_0$ and $R_1$ came together and added their messages to reveal the secret $m_a$:
$r + (-r + m_a) = m_a$
Could we somehow integrate secret sharing into our Gedankenexperiment? Let's try it. Assume two non-colluding servers $R_0$ and $R_1$, i.e. at most one of them may be compromized, but not the other.
Alice may want to "blind" her message $m_a$ with a random $r$ just as she did with secret sharing. Therefore, she picks a random blinding $r$ and a random row index $r_a$. She then sends the pair $(r_a, r)$ to $R_0$, and the pair $(r_a, -r + m_a)$ to $R_1$. Then Bob does the same with $m_b$ at location $r_b$, and so on. At the end of the period, $R_0$ and $R_1$ would add their tables row-wise. At row index $r_a$, they'll recover $m_a$, at index $r_b$, they'll recover $m_b$, etc.
Looks like a neat trick! But does it satisfy our anonymity requirements?
Let's assume that $R_1$ is compromized. While Alice successfully hid $m_a$ from the prying eyes of $R_1$, she leaked $r_a$ when she sent $(r_a, -r + m_a)$ to $R_1$. In other words, the attacker at $R_1$ now knows that barring collisions, the message at $r_a$ whatever it is, belongs to Alice. When, at the end of the period, after adding the rows with $R_0$, $m_a$ shows up in row $r_a$, the attacker in $R_1$ will easily deduce that Alice submitted $m_a$.
So, we're getting closer, but we're not there yet: Alice needs not only to blind $m_a$, she also needs to blind $r_a$ somehow.
### The Path to Writable PIR
Effectively blinding the location of the updated row can be extremely tricky. Instead, Alice now decides to update all rows of $R_0$ and of $R_1$, hiding her message $m_a$ in one of these rows. This is what she could do, assuming that the database tables contain $L$ rows:
1. Alice picks $L$ random numbers: $(r_0, r_1, r_2, \cdots, r_{L-1}) \overset{R}{\leftarrow} {\mathbb F}^L$
2. Alice picks a random row index $r_a \overset{R}{\leftarrow} \{0, 1, 2, \cdots, L-1\}$
3. Alice sends $(0, r_0), (1, r_1), \cdots, (r_a-1, r_{r_a-1}), (r_a, r), (r_a+1, r_{r_a+1}), \cdots, (L-1, r_{L-1})$ to $R_0$
4. Alice sends $(0, -r_0), (1, -r_1), \cdots, (r_a-1, -r_{r_a-1}), (r_a, -r + m_a), (r_a+1, -r_{r_a+1}), \cdots, (L-1, -r_{L-1})$ to $R_1$
Since all users now update all rows, we can simplify the protocol, by omitting the indices. Steps 3. and 4. change to:
• Alice sends $(r_0, r_1, \cdots, r_{r_a-1}, r, r_{r_a+1}, \cdots, r_{L-1})$ to $R_0$
• Alice sends $(-r_0, -r_1, \cdots, -r_{r_a-1}, -r + m_a, -r_{r_a+1}, \cdots, -r_{L-1})$ to $R_1$
In other words, she sends different random numbers to all rows except to the row $r_a$ that will contain her blinded message: $r$ for $R_0$ and $-r + m_a$ for $R_1$. An attacker sitting in either $R_0$ or $R_1$ can't tell which row Alice selected for her message, i.e. $r_a$ is well-hidden. Since Alice updated every row with what looks like random values, neither $R_0$ nor $R_1$ knows which row Alice selected for $m_a$, nor do they know $m_a$ before the end of the period.
Unfortunatly, if the servers $R_0$ and $R_1$ overwrote all their rows with the new values provided by Alice as in the Gedankenexperiment, they'll lose all other users' messages (and random numbers) that they previously stored in their tables. Did Alice just thrash the common database by updating all rows? Well, yes, of course she did!
#### Fixing the database thrashing problem
We modify the Gedankenexperiment one last time: instead of overwriting the rows with user-supplied values, $R_0$ and $R_1$ are now supposed to add those values to the already existing values. In other words, the code than $R_0$ and $R_1$ are running looks something like this:
for (int i=0; i != table.size(); ++i) {
// table[i] = user_values[i];
table[i] += user_values[i];
}
Of course, the addition is meant modulo $|\mathbb F|$.
Have you noticed that the random values we've sent to $R_1$ are the additive inverse of those we've sent to $R_0$? This was intentional and not a typo.
What happens when Bob comes along after Alice? Let's run a complete concrete walked example on a set of two servers with only 5 rows to see what happens.
### A Toy Example
Suppose we have 2 Riposte servers, $R_0$ and $R_1$. Each one of them maintains a table in RAM with 5 rows. Each row can store a 160 chars whisp, which we interpret as a number in the finite field $\mathbb F = \{0, 1, 2, \cdots, 2^{8 \times 160} - 1\}$. As usual with finite fields, all additions and subtractions on elements of $\mathbb F$ occur modulo $|\mathbb F|$.
In practice, Riposte servers will store tables with many more rows than 5. Something like 1000000 rows seem appropriate. But for now, 5 rows suffice.
Both $R_0$ and $R_1$ are synchronized in the sense that they agree when a new period starts. At the beginning of a new period, their tables are empty, i.e. all zeroes:
• $R_0: (0, 0, 0, 0, 0)$
• $R_1: (0, 0, 0, 0, 0)$
Alice wants to send message $m_a \in \mathbb F$. She randomly choses a row, and decides that row to be 2 (we start counting rows at index 0). So she generates the vector $(0, 0, m_a, 0, 0)$. Then, she creates a shared secret on this vector like this:
• $v_1 := (r_0, r_1, r_2, r_3, r_4) \overset{R}{\leftarrow} {\mathbb F}^5$
• $v_2 := (-r_0, -r_1, -r_2+m_a, -r_3, -r_4)$
Here, $v_1$ is a vector of random numbers chosen uniformly in $\mathbb F$, and the negative values are understood to be taken modulo $|\mathbb F|$, of course, so they are still in $\mathbb F$.
Note that to an outsider, both $v_1$ and $v_2$ look perfectly random.
Now, Alice logs into $R_0$ and $R_1$, and sends $v_1$ to $R_0$ and $v_2$ to $R_1$. Both Riposte servers first authenticate Alice, and then add the vectors they've just received to their own tables. Since they just started a new period:
• $R_0: (0, 0, 0, 0, 0) + v_1 = (r_0, r_1, r_2, r_3, r_4)$
• $R_1: (0, 0, 0, 0, 0) + v_2 = (-r_0, -r_1, -r_2+m_a, -r_3, -r_4)$
Now, Bob comes along and wants to send message $m_b$. He randomly choses row 4 and computes:
• $w_1 := (s_0, s_1, s_2, s_3, s_4) \overset{R}{\leftarrow} {\mathbb F}^5$
• $w_2 := (-s_0, -s_1, -s_2, -s_3, -s_4+m_b)$
Again, $w_1$ and $w_2$ look perfectly random. You've guessed it: he logs into $R_0$ and into $R_1$ and sends $w_1$ to $R_0$ and $w_2$ to $R_1$. Both servers, having verified Bob's credentials, add $w_1$ and $w_2$ to their tables:
• $R_0: (r_0, r_1, r_2, r_3, r_4) + w_1 = (r_0 + s_0, r_1 + s_1, r_2 + s_2, r_3 + s_3, r_4 + s_5)$
• $R_1: (-r_0, -r_1, -r_2+m_a, -r_3, -r_4) + w_2 = (-r_0-s_0, -r_1-s_1, -r_2+m_a-s_2, -r_3-s_3, -r_4-s_4+m_b)$
Then Carol, David, and Eve would come along and the cycle repeats... until the end of a period. We assume for now that only two whisps were accepted.
At this point, $R_0$ and $R_1$ momentarily stop accepting new vectors. They come together and add their tables. Both compute
$(r_0 + s_0, r_0 + s_1, r_2 + s_2, r_3 + s_3, r_4 + s_4) + (-r_0-s_0, -r_1-s_1, -r_2+m_a-s_2, -r_3-s_3, -r_4-s_4+m_b)$
and lo and behold!, they both get $(0, 0, m_a, 0, m_b)$.
In other words, Alice's $m_a$ and Bob's $m_b$, by the magic of shared secret, materialized there where Alice and Bob have decided to put them. All other rows are empty / unused.
#### How does this provide anonymity?
##### 1. Before the period ends
From the perspective of $R_0$, Alice and Bob are merly sending junk. At no point in time does $R_0$ know that Alice is the author of $m_a$, nor that Bob is the author of $m_b$. More interestingly, neither does $R_1$: even though $m_a$ and $m_b$ are hidden in the vectors submitted by Alice and Bob to $R_1$, since these values are blinded by random junk, $R_1$ still can't distinguish both cases.
Even though it might seem that all users are sending random junk to $R_0$ and blinded messages hidden in random junk to $R_1$, it doesn't have to be that way. In this simple example, Bob could just as well send $w_1$ to $R_1$ and $w_2$ to $R_0$. In this case, the secret sharing method is symmetric, because addition modulo $|\mathbb F|$ is commutative.
The main point though is that Alice touches all rows of $R_0$ and of $R_1$ (and so does Bob). Even if, say, $R_1$ were compromized, knowing that $v_2$ was indeed sent by Alice would still reveal nothing... at least as long as the period is still running its course.
##### 2. After the period ends
When $R_0$ and $R_1$ exchange their tables so that they may add them to their own, the messages $m_a$ by Alice and $m_b$ by Bob are revealed, as well as are the rows where Alice and Bob have put them in. Does this de-anonymize Alice and Bob? Or, asked more precisely since the registered users Alice and Bob are obviously known to the Riposte servers, does it allow $R_0$, $R_1$, or the outside world to tell that $m_a$ was from Alice and that $m_b$ was from Bob?
Let's stop and think about it for a second. What does $R_0$ see w.r.t Alice and Bob?
1. $R_0$ sees $v_1$ from Alice: $(r_0, r_1, r_2, r_3, r_4)$
2. $R_0$ sees $w_1$ from Bob: $(s_0, s_1, s_2, s_3, s_4)$
3. $R_0$ sees $ss_2 := (-r_0-s_0, -r_1-s_1, -r_2+m_a-s_2, -r_3-s_3, -r_4-s_4+m_b)$ from $R_1$
4. $R_0$ computes $v_1 + w_1 + s_2 = (0, 0, m_a, 0, m_b)$
Steps 1. and 2. reveal absolutely nothing about Alice and Bob.
What about $ss_2$? No matter what $R_0$ does with $v_1$, $w_1$, and $so_2$, there's no way to isolate $m_a$ or $m_b$, save form exposing both simultaneously. Therefore, it is impossible to identify Alice's or Bob's message. Think about it if you're not convinced.
The same holds true for $R_1$: by looking at $v_2$, $w_2$ and $ss_1 := (r_0 + s_0, r_1 + s_1, r_2 + s_2, r_3 + s_3, r_4 + s_4)$, $R_1$ can't isolate $m_a$ or $m_b$. Here too, all $R_1$ can do is to expose $m_a$ and $m_b$ simultaneously.
The crucial point is that $R_0$ doesn't reveal the intermediary steps needed to compute $ss_1$ to $R_1$, and vice-versa that $R_1$ doesn't reveal the intermediary steps needed to compute $ss_2$ to $R_0$. By not revealing these steps, and only exposing the aggregated state at the end of the period, both servers are said to not have colluded.
##### 3. What if both servers colluded?
Then, all bets are off. Recall that colluding means to reveal intermediary steps to the other server. The following scenarios come to mind:
• If $R_0$ had seen $v_2$ from $R_1$, this would have immediately exposed Alice as the author of $m_a$ to $R_0$
• If $R_0$ had seen $w_2$ from $R_1$, this would have immediately exposed Bob as the author of $m_b$ to $R_0$
• If $R_1$ had seen $v_1$ from $R_0$, this would have immediately exposed Alice as the author of $m_a$ to $R_1$
• If $R_1$ had seen $w_1$ from $R_0$, this would have immediately exposed Bob as the author of $m_b$ to $R_1$
As long as at least one of the servers stays honest and doesn't collude, Alice and Bob's identities as the authors of a specific message remain hidden.
Of course, the anonymity set (here $\{Alice, Bob\}$) has to contain at least two writers. The more, the better.
The users of the app only see the final state after the period has completed. I.e. they see $(0, 0, m_a, 0, m_b$). In practice, the app may blend out the empty slots, so it would display $(m_a, m_b)$, but this doesn't change anything. As long as Alice and Bob chose their slots randomly in a uniform matter, neither compromized servers, nor users can deduce anything about the writers. Without this requirement, Alice could easily leak her identity, if she had some bias in choosing her rows.
##### 5. What can the NSA do?
The NSA has the following options at her disposal:
1. She could seize $S_1$ or $S_2$. If she seizes both, all bets are off, and Alice and Bob lose. If she seizes only one of both, she's in the same difficult spot we were above, when the other server doesn't collude.
2. She could intercept the synchronization traffic between $S_1$ and $S_2$ at the end of the period. All she would see are the aggregated states of both servers. But since she lacks the intermediary steps (careful here, there be dragons!) she won't be able to associate Alice to $m_a$ or Bob to $m_b$.
3. She could modify that post-period synchronization traffic. This would merely corrupt the end-result, but won't help her at all
4. She could modify the period synchronization signals between $S_1$ and $S_2$, such that both servers, even when not compromized, are no more in sync.
5. She could perform traffic analysis, but since the Riposte servers wait a period for the anonymity set to grow reasonably large before publishing their final state, even if the NSA controls $n-1$ out of $n$ servers, and observes their traffic, it would still be no good (or does it?)
6. Other options
We'll elaborate on the warning in item 2 in just a moment. But let's first concentrate on item 4. I didn't find anything in the Riposte paper about this special kind of attack, and although I didn't try to prove it, my feeling is that even without colluding, even honest servers, just by being mis-synchronized, could leak identites somehow. This should really be investigated in future work.
##### An important caveat
If the NSA, thanks to her trememdous interception capabilites, can passively observe the traffic of all Riposte servers of a cluster, all bets are off. Why is that so? With the current version of the Riposte protocol, all the NSA has to do is run her own sets of shadow Riposte servers, and to send copies of users' traffic to those servers, which would perform the exact same calculations than the legitimate servers. Note that the internal states of those servers would faithfully mirror those of the legitimate servers. But, and that's the kicker, since the NSA would have full control of $n$ out of her $n$ shadow servers, she can have them all collude, and again, it's game over for Alice and Bob (and Carol, and David, and Eve...).
Of course, if the NSA can't eavesdrop on at least one ot the servers of the Riposte cluster, all is well.
The conclusion of this is: at least one non-colluding server is needed, and the traffic to this server needs to be hidden from a global adversary.
IMHO, future work should focus on mitigating this attack. We need to update the Riposte model/protocol in such a way that servers include secret information, so that a passive eavesdropper on that server's traffic still can't clone it. Presently, the only line of defense is that the Riposte clients and servers used secure channels (encrypted and authenticated), which hinders mirroring. But that seems rather fragile. Hardening the Riposte servers against cloning of the full server farm may be needed and should be investigated.
### Improving Riposte v1
We need to take care of the following points in subsequent articles of this mini-series:
• We'll reduce the traffic form clients to the Riposte servers with Distributed Point Functions
• We'll increase the amount of whisps that servers can store, without increasing the number of rows
• We'll prevent malicious users who don't send consistent vectors to the servers from thashing the database by adding an audit server
• We'll move from $2$ to $n$ Riposte servers setup, of which $n - 1$ may collude without adverse effects to the anonymity of the users.
### Literature
• [Y82] Andrew C. Yao: Protocols for Secure Computations (extended abstract). (IEEE (paywalled). full pdf) | 2019-05-23 13:34:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7249593734741211, "perplexity": 922.8095498623715}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257244.16/warc/CC-MAIN-20190523123835-20190523145835-00521.warc.gz"} |
https://volya.xyz/blog/deutsch-algorithm/ | # Deutsch Algorithm
Published 2019-11-04
Implementing 2-qubit Deutsch Algorithm
## Initial Problem
Suppose we have a black box that takes in two input bits and produces two output bits. We would like the query the black box as few times as possible to learn what the black box does.
In Deutsch's problem the black box implements one of the following: $f_1(x,y) = (x,y)$ $f_2(x,y) = (x,\bar{y})$ $f_3(x,y) = (x,x \oplus y)$ $f_4(x,y) = (x,x \oplus \bar{y})$
## Make it Quantum
We write the four possible functions as unitary matrices operating on the standard computational basis.
$U_1 = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$ $U_2 = \begin{bmatrix} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{bmatrix}$ $U_3 = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{bmatrix}$ $U_4 = \begin{bmatrix} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$ These applied to $$\left|00\right\rangle$$, $$\left|01\right\rangle$$, $$\left|10\right\rangle$$, $$\left|11\right\rangle$$ yield the expected result.
Now we can solve this problem in one query if by using a general superposition and manipulation of the two qubits.
## Algorithm
We draw the quantum circuit using qasm2circ:
The Hadamard gate is: $H = \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}$
When we apply the Hadamard gate: $\left|\psi\right\rangle = H\left|0\right\rangle \otimes H \left|1\right\rangle$ $= \frac{1}{\sqrt{2}}(\left|0\right\rangle + \left|1\right\rangle) \otimes \frac{1}{\sqrt{2}}(\left|0\right\rangle - \left|1\right\rangle)$ $= \frac{1}{2} (\left|00\right\rangle - \left|01\right\rangle + \left|10\right\rangle - \left|11\right\rangle)$
Now, once we apply $$U_i$$ we obtain: $\left|\phi_1\right\rangle = U_1 \left|\psi\right\rangle = \frac{1}{2} (\left|00\right\rangle - \left|01\right\rangle + \left|10\right\rangle - \left|11\right\rangle)$ $\left|\phi_2\right\rangle = U_2 \left|\psi\right\rangle = \frac{1}{2} (-\left|00\right\rangle + \left|01\right\rangle - \left|10\right\rangle + \left|11\right\rangle)$ $\left|\phi_3\right\rangle = U_3 \left|\psi\right\rangle = \frac{1}{2} (\left|00\right\rangle - \left|01\right\rangle - \left|10\right\rangle + \left|11\right\rangle)$ $\left|\phi_4\right\rangle = U_4 \left|\psi\right\rangle = \frac{1}{2} (-\left|00\right\rangle + \left|01\right\rangle + \left|10\right\rangle - \left|11\right\rangle)$
We finish off with the final Hadamard Gates: $H \otimes H = \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & -1 & 1 & -1 \\ 1 & 1 & -1 & -1 \\ 1 & -1 & -1 & 1 \end{bmatrix}$
Thus, finally: $\left|o_1\right\rangle = (H\otimes H)U_1\left|\psi\right\rangle = \left|01\right\rangle$ $\left|o_2\right\rangle = (H\otimes H)U_2\left|\psi\right\rangle = -\left|01\right\rangle$ $\left|o_3\right\rangle = (H\otimes H)U_3\left|\psi\right\rangle = \left|11\right\rangle$ $\left|o_4\right\rangle = (H\otimes H)U_4\left|\psi\right\rangle = -\left|11\right\rangle$
This is great, we can figure out the black box by observing the first bit.
## Visualization
Let's draw the states as we evolve in time with the circuit. As an example, lets use $$U_2$$.
We start with $\left|\psi\right\rangle = (H \otimes H) (\left|0\right\rangle \otimes \left|1\right\rangle)$ $= (H \otimes H) \begin{pmatrix} 1 \\ 0 \end{pmatrix} \otimes \begin{pmatrix} 0 \\ 1 \end{pmatrix}$ $= \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & -1 & 1 & -1 \\ 1 & 1 & -1 & -1 \\ 1 & -1 & -1 & 1 \end{bmatrix} \begin{pmatrix} 0 \\ 1 \\ 0 \\ 0 \end{pmatrix}$ $= \frac{1}{\sqrt{2}}\begin{pmatrix} 1 \\ -1 \\ 1 \\ -1 \end{pmatrix}$
The density matrix is $\left|\psi \right\rangle \left\langle\psi\right| = \frac{1}{4}\begin{bmatrix} 1 & -1 & 1 & -1 \\ -1 & 1 & -1 & 1 \\ 1 & -1 & 1 & -1 \\ -1 & 1 & -1 & 1 \end{bmatrix}$
For practice we take the partial trace and draw the mapped density matrix to the Bloch sphere. We then apply $$U_2$$ to $$\left|\psi \right\rangle$$. And once again draw to the Bloch Sphere.
Finally, we apply $$H \otimes H$$ and draw to the Bloch Sphere.
For $$U_2$$ we obtain the following animation:
Following similar procedure for $$U_4$$ we obtain the following animation: | 2022-11-29 10:31:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8814935684204102, "perplexity": 573.5652386797666}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710691.77/warc/CC-MAIN-20221129100233-20221129130233-00057.warc.gz"} |
https://math.stackexchange.com/questions/3311123/in-what-ways-the-letters-of-the-word-puzzle-can-be-arranged-to-form-the-differ | In what ways the letters of the word “PUZZLE” can be arranged to form the different new words so that the vowels always come together?
I tried this way: Taking 'UE' together and remaining 'PZZL'. So, as 'Z' is repeating, I divide it by $$2!$$. My answer: $$(5!/2!)\cdot 2! = 120$$. Is it right? And why do we divide by its factorial if some letters are repeating?
• We divide by $k!$ if a letter appears $k$ times because the factorial at the numerator assumes that all letters are distinguishable, which they are not. – Fabio Somenzi Aug 2 at 5:53
Take 'UE' together and 'PZZLE' is remaining
The $$E$$ should be together with $$UE$$, so in fact you have something like $$(UE)PZZL$$ or $$(EU)PZZL$$.
So, as 'Z' is repeating I divide it by 2!
That's correct. If we call the two letters $$Z_1$$ and $$Z_2$$, there are $$2!$$ ways to arrange the $$Z$$'s, but there is only one distinguishable combination: you cannot tell $$Z_1$$ and $$Z_2$$ apart.
My answer :- (5!/2!)*2! = 120. Is it right?
Yes. There are $$5!$$ ways to arrange the $$5$$ objects $$UE$$, $$P$$, $$Z$$, $$Z$$ and $$L$$. $$U$$ and $$E$$ are interchangeable so we can multiply by $$2!$$, but as earlier said the two $$Z$$'s are not, so we divide by $$2!$$. | 2019-09-20 03:12:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 24, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9426130652427673, "perplexity": 142.71917919035525}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573827.2/warc/CC-MAIN-20190920030357-20190920052357-00413.warc.gz"} |
https://brilliant.org/discussions/thread/iit-2/ | ×
# IIT
I m in 11th. I am an iit aspirant. Will anyone plz guide me how shud I study to clear jee advance with good rank? ?
Note by Lokesh Agrawal
2 years, 4 months ago
Sort by:
Ohho scholy,topper wants advice?! · 2 years ago
Well I am in 11th too :P . But from My experiences, I would like to suggest some books that u must go through very thoroughly, in order to get a decent rank in JEE.
$$Physics$$:-
1) Firstly, stick to your classes notes. They guide you best. 2) Complete DC Pandey "Understanding Physics" series hand in hand with your daily syllabus. It contain Vey good ques alongwith explanations. 3) To get further Good ranks, Try Problems in Physics"- By I.E.Irodov 4) (Suggested Just for Mechanics) H.C.Verma's book
$$Chemistry$$
1) Class notes, as usual. 2) The book I liked the best for chem, with much challenging ques and great explanations, are the books by Ranjit Shahi. Those are 3 BIG Books. Physical,Organic,Inorganic Chemistry. Go through them too
For maths, I never refer anything. Just the notes. Above all, the determination and mental strength, and u will come out with flying colours. :D · 2 years, 4 months ago
Have u done with iit jee,if no den keep quiet,mad! · 2 years ago
Thanks a lot friend fr ur help · 2 years, 4 months ago | 2017-03-29 19:05:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3659168481826782, "perplexity": 11553.993039713412}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218191353.5/warc/CC-MAIN-20170322212951-00077-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/3509477/application-of-pigeonhole-principle-proving-that-two-subsets-include-two-or-mor | # Application of pigeonhole principle: proving that two subsets include two or more common integers
If the proposition below is true, show this. If false, give a counterexample.
From the integers from $$1$$ to $$11$$, make 10 sets $$S_1,S_2, \dots, S_{10}$$ each with 4 integers selected. Within each sets, the same number shall not be chosen twice. No matter how $$S_1,S_2, \dots, S_{10}$$ is selected, two sets $$S_i,S_j$$($$i$$ not equal to $$j$$) include two or more common integers.
Is this related to pigeon principle? $$S_1=\{1,2,3,4\},$$ $$S_2=\{2,3,4,5\},$$ $$S_3=\{4,5,6,7\},$$ $$S_4=\{5,6,7,8\},$$ $$S_5=\{7,8,9,10\},$$ $$S_6=\{8,9,10,11\},$$ $$S_7=\{5,6,2,4\},$$ $$S_8=\{1,5,7,9\},$$ $$S_9=\{4,8,10,11\},$$ $$S_{10}=\{5,7,10,11\}$$
When we choose two of them, there is possibility there are same integer but not all ? If this is related to pigeonhole principle, Is there possibility that sets are hole and number $$1$$-$$11$$ is pigeon but what is the relation with in each sets there are four number?
• Hint: there are $\binom {11}2=55$ possible pairs of integers taken from $\{1, \cdots, 11\}$. There are $\binom 42=6$ pairs in each of the $S_i$ hence there are $60$ pairs between all the ten $S_i$. – lulu Jan 15 at 0:42
• Pigeonhole principle ? – J. W. Tanner Jan 15 at 0:45
• @J.W.Tanner sorry yes i mean pigeonhole principle – vedss Jan 15 at 0:50
• @AdamRubinson The way I understand the question: "From the $11$ integers $\{1, \cdots, 11\}$ we create $10$ sets $S_i$. Each of them contains exactly $4$ of the $11$ integers. Prove that there are at least two of those sets, $S_i, S_j$ with $i\neq j$ such that $|S_i\cap S_j|≥2$." In the example given in the post, $S_1,S_2$ fit the bill. – lulu Jan 15 at 1:00
• Honestly, my initial hint is $95\%$ of a complete solution...I don't see what else I can say other than writing out the answer. Well, do the warm up exercise I proposed. It's considerably easier than the given problem, and the logic behind that is identical. – lulu Jan 15 at 1:48
HINT (different from lulu's)
Lemma: some integer must appear in $$4$$ or more sets.
Proof of Lemma: apply pigeonhole based on there being $$11$$ integers, $$10$$ sets, each of size $$4$$. $$\square$$
Main Claim: some pair $$S_i, S_j$$ must share $$2$$ or more integers.
Proof: By Lemma, there is an integer, call it $$s$$, which appears in (at least) $$4$$ sets, e.g.:
$$\{s,a,b,c\}, \{s,d,e,f\},\{s,g,h,i\}, \{s,j,k,l\}$$
Use pigeonhole principle again to show two of these sets must share $$2$$ or more integers. $$\square$$
Hope you can finish based on the above?
• Thankyou, for the proof some integer must appear in 4 more sets, there are 11 integer, but each sets size 4, so by pigeon hole principle, we need at least 3 sets in order two sets out of three have at least 1 same number on it. since there are 10 sets, $\lceil \frac{10}{3} \rceil =4$ ? but I'm not sure what is the pigeon and pigeonhole in this? and i think there are some integer that only appear in 3 sets too, if i put 1..11 to each sets from S1 to 10 then 8,9,10,11 only appear 3 times in S1..S10 sets(?) – vedss Jan 16 at 14:12
• For the Lemma, count the appearances. There are $10$ sets, each of size $4$, so the integers must collectively appear $40$ times. There are $11$ integers. If each one appeared $3$ times or fewer, that cannot fill the $40$ appearances. – antkam Jan 16 at 14:39
• Thankyou for the hint. But i think it should be that some integer must appear in 3 or 4 more sets ? if all integer appear in 4 sets , it must be 44 appearance and need 11 sets? and for the pair, if one integer appear in 4 sets, there are 3 spot left in every sets, and 10 distinct integer left , by pigeon hole principle, we can put 3 different integer in 3 sets, but in fourth sets there must be integer that we already put in the S1,S2, or S3 , so either $S1 \cap S4$ or $S2 \cap S4$ or $S3 \cap S4$ , it this enough to proof? – vedss Jan 17 at 2:54
• for the lemma, you don't care about integers which appear in $3$ sets. all you need is that some integer appears in at least $4$ sets. and for the second part, yes you are right. – antkam Jan 17 at 4:24
• Thankyou but why it has to be 4? and i dont understand the relation between 11 integer, 10 sets and each size 4, for example there are only 6 sets each 4 integer and 11 integer to put, with only 6 sets, we also can get two sets that share two or more integer? – vedss Jan 17 at 5:09 | 2020-12-02 06:30:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 31, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7698665857315063, "perplexity": 388.64073058720663}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141692985.63/warc/CC-MAIN-20201202052413-20201202082413-00189.warc.gz"} |
https://www.expii.com/t/density-definition-calculation-8071 | Expii
# Density — Definition & Calculation - Expii
Density is a measure of how much of something there is in a given volume. The term density typically refers to mass density, which is given as mass per volume. | 2020-09-20 13:11:00 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9273962378501892, "perplexity": 550.3081530713591}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400198213.25/warc/CC-MAIN-20200920125718-20200920155718-00490.warc.gz"} |
http://hmj2.math.sci.hokudai.ac.jp/page/38-1/HMJ38(2009)0039-0065.html | Hokkaido Mathematical Journal
Hokkaido Mathematical Journal, 38 (2009) pp.39-65
PDF
Abstract
In this paper we study a $C^{1+\alpha}$-partially hyperbolic diffeomorphism f of which restriction on one dimensional center unstable direction behaves as Manneville-Pomeau map. We show that f admits a unique ergodic SRB measure with polynomial upper bounds on correlations for Hölder continuous functions.
MSC(Primary) 37A25 37C40, 37D20 almost Anosov diffeomophism, SRB measure, polynomial upper bounds on correlations, first return map. | 2017-09-26 10:51:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.808976411819458, "perplexity": 2347.0594408802376}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818695439.96/warc/CC-MAIN-20170926103944-20170926123944-00102.warc.gz"} |
https://www.physicsforums.com/threads/finding-the-magnitude-of-the-friction-force.637859/ | # Homework Help: Finding the magnitude of the friction force.
1. Sep 22, 2012
### Ripe
1. The problem statement, all variables and given/known data
An 8kg ball moves down a 12m high inclined plane with a speed of 6m/s. By the time it reaches the bottom, the speed is measured to be 12m/s. What is the frictional force opposing the motion? The inclined plane has an angle of 30 degrees with respect to the ground.
2. Relevant equations
Potential energy = mgh
Kinetic energy = 1/2mv^2
Work done by external forces = ΔE
Work done: Fs (or Fscos(theta))
3. The attempt at a solution
The first step is to calculate the potential energy and kinetic energy, which is 960J and 576J respectively. Hence ΔE=960-576=384J.
Now, since the height is 12m and the angle is 30 degrees, the length of the inclined plane is 12/sin30 or 24m.
Finally, 24f=384 which yields an answer for f as 16N.
I might have gotten the correct answer, but in the book it says that the answer is supposed to be 22N, so I'm assuming I'm missing something, perhaps it has something to do with the initial speed which I haven't included in my calculations.
2. Sep 22, 2012
### azizlwl
I think you forget initial KE.
3. Sep 22, 2012
### Ripe
Please elaborate. I assumed it was 0.
4. Sep 22, 2012
### Ripe
I'd very much like help on this one!
5. Sep 22, 2012
### PhanthomJay
A bit unclear on the wording, but the initial speed is 6 m/s at the top of the ramp. Watch your signage.
6. Sep 23, 2012
### Ripe
Not sure If I follow what you're saying. Could you elaborate?
7. Sep 23, 2012
### PhanthomJay
l think the problem meant to say that the ball is projected down the ramp with an initial speed of 6 m/s, that is, it already had a speed of 6 m/s when it reached the top of the ramp. So re-do your calcs, and see azizlwl post 2.
8. Sep 23, 2012
### Ripe
It doesn't travel up the plane, it travels down the plane. I.e. it has an initial speed of 6m/s when it is at the top (the beginning) and a speed of 12m/s at the bottom (the end). Hence, initial KE=0?
EDIT: Oh! Now I see what you mean. It didn't go from rest to 12m/s meaning it had some kinetic energy at the top as well. In other words, initial KE=144J and hence, initial (total) energy= 144+960=1104J.
Using that, I get an answer of 22N. Thank you for your help!
Last edited: Sep 23, 2012 | 2018-09-24 13:48:38 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8061664700508118, "perplexity": 744.0913488083443}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267160454.88/warc/CC-MAIN-20180924125835-20180924150235-00540.warc.gz"} |
https://www.zbmath.org/?q=an%3A1144.74044 | ## Modelling of fluid-structure interactions with the space-time finite elements: Solution techniques.(English)Zbl 1144.74044
Summary: The space-time fluid-structure interaction (FSI) techniques developed by the Team for Advanced Flow Simulation and Modeling (T$$_\star$$AFSM) have been applied to a wide range of 3D computation of FSI problems, some as early as in 1994 and many with challenging complexities. In this paper, we review these space-time FSI techniques and describe the enhancements introduced recently by the T$$_\star$$AFSM to increase the scope, accuracy, robustness and efficiency of these techniques. The aspects of the FSI solution process enhanced include the deforming-spatial-domain/stabilized space-time (DSD/SST) formulation, the fluid-structure interface conditions, the preconditioning techniques used in iterative solution of the linear equation systems, and a contact algorithm protecting the quality of the fluid mechanics mesh between the structural surfaces coming into contact. We present a number of 3D numerical examples computed with these new stabilized space-time FSI (SSTFSI) techniques.
### MSC:
74S05 Finite element methods applied to problems in solid mechanics 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
Full Text: | 2022-07-06 16:28:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2524523138999939, "perplexity": 1518.4510378416796}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104675818.94/warc/CC-MAIN-20220706151618-20220706181618-00738.warc.gz"} |
https://study.com/academy/answer/find-the-interval-of-convergence-for-f-x-x-0-6-as-a-power-series.html | # Find the interval of convergence for f(x) = x^{0.6} as a power series.
## Question:
Find the interval of convergence for
{eq}f(x) = x^{0.6} {/eq} as a power series.
## Power Series; Interval of Convergence:
The center of expansion for the power series will affect the interval of convergence. To consider a general situation we'll pick a center {eq}x=c>0 {/eq} so that the function {eq}f(x) = x^{0.6} {/eq} is defined in a neighborhood of {eq}c. {/eq} We'll write power series {eq}f(x)=x^{0.6}=\sum_{n=1}^{\infty}a_{n}(x-c)^n {/eq} for some Taylor coefficients {eq}a_n {/eq}.
The problem statement does not specify the center for the power series, so we'll work on the general case of the center at {eq}x=c>0 {/eq} so that the function {eq}f {/eq} is defined on a neighborhood of {eq}c. {/eq}
We'll rewrite {eq}f(x) {/eq} in terms of a new variable {eq}u=x-c {/eq} as follows:
{eq}\begin{align*} f(x)&=x^{0.6}\\ &=(c+(x-c))^{0.6}\\ &=(c+u)^{0.6}\\ &=c^{0.6}\cdot\left (1+\frac{u}{c}\right )^{0.6}\\ &=c^{\frac{3}{5}}\cdot\left (1+\frac{u}{c}\right )^{\frac{3}{5}}. \end{align*} {/eq}
We'll use the binomial expansion:
{eq}\begin{align*} (1+x)^p&=\sum_{n=0}^{\infty}\binom{p}{n}x^n\\ &\text{recalling that }\binom{p}{0}=1\text{ for any }p\ne 0,\\ &=1+\sum_{n=1}^{\infty}\frac{p(p-1)(p-2)\cdots (p-n+1)}{n!}x^n\\ &=1+px+\frac{p(p-1)}{2!}x^2 +\frac{p(p-1)(p-2)}{3!}x^3+\\ &\qquad\cdots+\frac{p(p-1)(p-2)\cdots (p-n+1)}{n!}x^n+\cdots\\ &\text{which in general converges for }|x|<1. \end{align*} {/eq}
In the particular case of a positive exponent {eq}p=0.6=\frac{3}{5}>0 {/eq} the corresponding binomial series also converges at the endpoints, so it has interval of convergence {eq}[-1,1] {/eq}. Thus we have:
{eq}\begin{align*} (1+x)^{\frac{3}{5}}&=\sum_{n=0}^{\infty}\binom{\frac{3}{5}}{n}x^n,\\ &\text{or expanding the binomials,}\\ &=1+\frac{3}{5}x+\frac{\frac{3}{5}(\frac{3}{5}-1)}{2!}x^2 +\frac{\frac{3}{5}(\frac{3}{5}-1)(\frac{3}{5}-2)}{3!}x^3+\\ &\qquad\cdots+\frac{\frac{3}{5}(\frac{3}{5}-1)(\frac{3}{5}-2)\cdots \left (\frac{3}{5}-n+1\right )}{n!}x^n+\cdots.\\ &\text{In abreviated form we write3:}\\ &\boxed{{(1+x)^{\frac{3}{5}}}=\sum_{n=0}^{\infty}\binom{\frac{3}{5}}{n}x^n}, \text{ which converges for }|x|\le 1. \end{align*} {/eq}
We can use the binomial series above, substituting {eq}\frac{u}{c} {/eq} in place of {eq}x {/eq}, to write:
{eq}\begin{align*} f(x)&=x^{0.6}\\ &=c^{\frac{3}{5}}\cdot\left (1+\frac{u}{c}\right )^{\frac{3}{5}}\\ &=c^{\frac{3}{5}}\cdot\sum_{n=0}^{\infty}\binom{\frac{3}{5}}{n}\left(\frac{u}{c}\right)^n,\text{ for }\left|\frac{u}{c}\right|\le1 \\ &=\sum_{n=0}^{\infty}\frac{c^{\frac{3}{5}}\cdot\binom{\frac{3}{5}}{n}}{c^n}\,u^n,\text{ for }\left|u\right|<c,\\ &\text{we return to the original variable making }u=x-c,\\ &\text{and we get,}\\ &\boxed{f(x)=x^{0.6}=\sum_{n=0}^{\infty}\frac{c^{\frac{3}{5}}\cdot\binom{\frac{3}{5}}{n}}{c^n}\,(x-c)^n},\text{ for }\left|x-c\right|\le c. \end{align*} {/eq}
This power series converges for {eq}\left|x-c\right|\le c {/eq} but diverges for {eq}\left|x-c\right|>c, {/eq} thus we can write that the interval of convergence is {eq}\boxed{[0,2c].} {/eq}
Observation: The particular case of the power series with center at {eq}x=1 {/eq} {eq}(c=1) {/eq} we get:
{eq}f(x)=x^{0.6}=\sum_{n=0}^{\infty} \binom{\frac{3}{5}}{n}\,(x-1)^n,\text{ for }\left|x-1\right|\le 1, {/eq}
and the interval of convergence is {eq}\boxed{[0,2].} {/eq} | 2020-01-28 07:30:59 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9951504468917847, "perplexity": 12183.642314157149}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251776516.99/warc/CC-MAIN-20200128060946-20200128090946-00059.warc.gz"} |
http://archive.ambermd.org/200705/0378.html | # Re: AMBER: error in running sander
From: devrani mitra <devranimitra.gmail.com>
Date: Wed, 30 May 2007 16:34:41 -0700
On 5/29/07, Ross Walker <ross.rosswalker.co.uk> wrote:
> Dear Devrani,
>
> This is not the best pdb structure around :-( For starters it is only at 2.5
>
> REMARK 400 COMPOUND
>
> REMARK 400 DELETION MUTANT LEU 127.
>
> REMARK 465
>
> REMARK 465 MISSING RESIDUES
>
> REMARK 465 THE FOLLOWING RESIDUES WERE NOT LOCATED IN THE
>
> REMARK 465 EXPERIMENT. (M=MODEL NUMBER; RES=RESIDUE NAME; C=CHAIN
>
> REMARK 465 IDENTIFIER; SSSEQ=SEQUENCE NUMBER; I=INSERTION CODE.)
>
> REMARK 465
>
> REMARK 465 M RES C SSSEQI
>
> REMARK 465 MET A 274
>
> REMARK 465 GLU A 275
>
> REMARK 465 VAL A 276
>
> REMARK 465 GLU A 277
>
> REMARK 465 ASP A 278
>
> REMARK 465 GLU A 279
>
> REMARK 465 SER A 280
>
> REMARK 465 ILE A 281
>
> REMARK 465 VAL A 282
>
> REMARK 465 GLY A 283
>
> REMARK 465 LYS A 284
>
> REMARK 465 THR A 285
>
> REMARK 465 ALA A 286
>
> REMARK 465 GLU A 287
>
> REMARK 465 GLU A 288
>
> REMARK 465 VAL A 289
>
>
> So residue 127 is missing as you note which should be perfectly fine since
> this is the structure of a mutant of the enzyme where residue 127 has been
> deleted. I assume that you want to simulate the deletion mutant version of
> the enzyme?
>
> Then we have a ton of residues with missing atoms. So a whole chunk of the
> end of the peptide chain is missing from the pdb structure. You will likely
> have to decide what to do with this - do you just ignore these residues? Or
> homology model them in? Or look for a better crystal structure? This is
> really a research decision that you will have to make yourself based on your
> judgement.
>
> With regards to the bad contacts if you look at residue MET 154 (/155) it
> points right out into solvent so I suspect it may be clashing with solvent
> molecules. Did you delete the crystal waters? - if not you probably should
> delete them. Then if this doesn't work follow Carlos's advice and try
> minimizing in gas phase or with GB first and then solvate in leap.
>
> You could also try running 100 steps or so of MD with a very short time
> step, say dt=0.0001. Make sure shake is turned off - then set ntwx=1 and run
> and you can then watch the system blow up in VMD. This way you should be
> able to see visualy where the problem is coming from and hopefully fix it.
>
> All the best
> Ross
>
> /\
> \/
> |\oss Walker
>
> | HPC Consultant and Staff Scientist |
> | San Diego Supercomputer Center |
> | Tel: +1 858 822 0854 | EMail:- ross.rosswalker.co.uk |
> | http://www.rosswalker.co.uk | PGP Key available on request |
>
> Note: Electronic Mail is not secure, has no guarantee of delivery, may not
> be read every day, and should not be used for urgent or sensitive issues.
>
> > -----Original Message-----
> > From: owner-amber.scripps.edu
> > [mailto:owner-amber.scripps.edu] On Behalf Of devrani mitra
> > Sent: Tuesday, May 29, 2007 18:13
> > To: amber.scripps.edu
> > Subject: Re: AMBER: error in running sander
> >
> > Thanks a lot for your replies. Well, the same error msg appears even
> > if I have deleted Mg-ATP from the pdb. As suggested, I looked at my
> > initial pdb structure,
> >
> > ATOM 919 CG1 VAL A 126 15.020 10.602 2.155 1.00
> > 40.87 C
> > ATOM 920 CG2 VAL A 126 14.615 12.941 2.762 1.00
> > 43.82 C
> > ATOM 921 N GLY A 128 17.832 10.976 0.712 1.00
> > 52.78 N
> > ATOM 922 CA GLY A 128 18.873 10.542 -0.212 1.00
> > 59.95 C
> >
> > However, I found that after 126 it is 128, but this sequence has been
> > corrected in 'tleap' as:
> >
> > ATOM 1831 C VAL 126 36.583 33.672 43.611
> > ATOM 1832 O VAL 126 37.744 33.723 44.012
> > ATOM 1833 N GLY 127 36.305 33.201 42.383
> > ATOM 1834 H GLY 127 35.343 33.143 42.082
> >
> > Is this the problem?
> > Surprisingly, the highest energy is seen at
> >
> > ATOM 2239 3HE MET 154 48.483 34.334 23.516
> >
> > This residue is MET 155 at the original starting PDB structure.
> > And I looked at this position and did not find any overlapped atoms.
> > Could you kindly suggest me as how to fix this?
> >
> > Thanks again.
> > Devrani
> >
> > N.B. Accidentally I pressed the 'send' button before sending this
> > mail, please ignore that blank msg.
> >
> > On 5/29/07, Ross Walker <ross.rosswalker.co.uk> wrote:
> > > Dear Devrani,
> > >
> > > Here is the first point from your output file:
> > >
> > > NSTEP ENERGY RMS GMAX
> > NAME NUMBER
> > > 1 1.1843E+11 2.4284E+10 5.5481E+12
> > HE3 2239
> > >
> > > BOND = 156.1910 ANGLE = 724.2956 DIHED =
> > > 2575.2795
> > > VDWAALS = ************* EEL = -129550.8405 HBOND =
> > > 0.0000
> > > 1-4 VDW = 1223.8779 1-4 EEL = 11866.6783 RESTRAINT =
> > > 0.0000
> > >
> > > The *'s mean that the value was too large to fit in the
> > space provided. Thus
> > > your VDW energy is huge and the maximum force GMAX is an
> > astounding 5.5 x
> > > 10^12 KCal/Mol/A. This likely comes about due to problems
> > > structure. You likely have two or more atoms sitting on top
> > of each other.
> > > Note during minimization the atom with the largest force at
> > each step is
> > > printed. Above it is at HE3 with number 2239. I suggest you
> > visualize your
> > > starting structure and look at the area around atome 2239.
> > Once you have
> > > identified the problem you will need to fix your input
> > structure and then
> > > re-run the minimization.
> > >
> > > All the best
> > > Ross
> > >
> > > /\
> > > \/
> > > |\oss Walker
> > >
> > > | HPC Consultant and Staff Scientist |
> > > | San Diego Supercomputer Center |
> > > | Tel: +1 858 822 0854 | EMail:- ross.rosswalker.co.uk |
> > > | http://www.rosswalker.co.uk | PGP Key available on request |
> > >
> > > Note: Electronic Mail is not secure, has no guarantee of
> > delivery, may not
> > > be read every day, and should not be used for urgent or
> > sensitive issues.
> > >
> > > > -----Original Message-----
> > > > From: owner-amber.scripps.edu
> > > > [mailto:owner-amber.scripps.edu] On Behalf Of devrani mitra
> > > > Sent: Tuesday, May 29, 2007 14:27
> > > > To: amber.scripps.edu
> > > > Subject: Re: AMBER: error in running sander
> > > >
> > > > Hello
> > > >
> > > > I'm attaching the output file for the details. Hope this
> > > > simplifies the things.
> > > >
> > > > Thanks,
> > > > Devrani
> > > >
> > > > On 5/29/07, Carlos Simmerling <carlos.simmerling.gmail.com> wrote:
> > > > > does your a_min_water.out file have any information in it?
> > > > >
> > > > > do the test cases pass?
> > > > >
> > > > > you need to give us much more information if you want help.
> > > > >
> > > > >
> > > > > On 5/29/07, devrani mitra <devranimitra.gmail.com> wrote:
> > > > > > Dear AMBER users,
> > > > > >
> > > > > > While running sander (for removing the bad contacts)
> > following the
> > > > > > tutorials, I'm getting the following error message:
> > > > > >
> > > > > > >> sander -O -i a_min.in -p a.parm7 -c a.crd -r a_min.rst -o
> > > > > > a_min_water.out -ref a.rst
> > > > > >
> > > > > > p0_29153: p4_error: interrupt SIGSEGV: 11
> > > > > >
> > > > > > I'm not getting as which file do I need to correct.
> > > > Please suggest.
> > > > > >
> > > > > > Thanks!
> > > > > > Devrani
> > > > > >
> > > > > > Devrani Mitra, UC Davis
> > > > > >
> > > > >
> > > > --------------------------------------------------------------
> > > > ---------
> > > > > > The AMBER Mail Reflector
> > > > > > To post, send mail to amber.scripps.edu
> > > > > > To unsubscribe, send "unsubscribe amber" to
> > majordomo.scripps.edu
> > > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > >
> > >
> > >
> > >
> > --------------------------------------------------------------
> > ---------
> > > The AMBER Mail Reflector
> > > To post, send mail to amber.scripps.edu
> > > To unsubscribe, send "unsubscribe amber" to majordomo.scripps.edu
> > >
> > --------------------------------------------------------------
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> > To unsubscribe, send "unsubscribe amber" to majordomo.scripps.edu
> >
>
>
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>
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Received on Sun Jun 03 2007 - 06:07:17 PDT
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https://www.askiitians.com/forums/Differential-Calculus/see-attachment-and-explain-with-solution_105784.htm | # see attachment and explain with solution
Grade:12
## 1 Answers
Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans: 6 km/hr
Let ‘x’ be the distance of the man from the lamp post at any moment & ‘l’ be the length of the shadow formed.
Distance of man from lamp post = x km
Distance of shadow from lamp post = (x+l) km
Height of the man = 1.5 km
Height of lamp post = 4.5 km
Using similar triangles, we have
$\frac{x+ l}{l} = \frac{4.5}{1.5}$
$\frac{x+ l}{l} = 3$
$x = 2l$
Differentiate on both sides, we have
$\frac{dl}{dt} = \frac{1}{2}.\frac{dx}{dt}$
$\frac{dl}{dt} = \frac{1}{2}.4 = 2 (\frac{km}{hr})$
Velocity of shadow:
$\frac{d(x+l)}{dt} = \frac{dx}{dt} + \frac{dl}{dt} = 4 + 2 = 6(\frac{km}{hr})$
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty
## ASK QUESTION
Get your questions answered by the expert for free | 2022-08-15 21:19:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35138848423957825, "perplexity": 10662.500192647247}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572212.96/warc/CC-MAIN-20220815205848-20220815235848-00344.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/elementary-and-intermediate-algebra-concepts-and-applications-6th-edition/chapter-12-exponential-functions-and-logarithmic-functions-12-1-composite-functions-and-inverse-functions-12-1-exercise-set-page-787/7 | ## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
By definition, $(f^{-1})^{-1}=f$, which means that the inverse of the inverse is the function itself. Therefore the given statement is true. | 2018-06-19 08:58:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8223044872283936, "perplexity": 308.36985004320917}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267861981.50/warc/CC-MAIN-20180619080121-20180619100121-00142.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/3876-calculating-statistical-significance.html | 1. ## Calculating Statistical Significance?
Does anyone know the best Signifinace Test for a dataset following a hypergeometric distribution with sample size over 30?
If you have 100 recipe sheets. And, 10 of these sheets are linked because they all contain the same ingredient. The chance of picking a recipe sheet on it's own with that specific ingredient is 0.408. But, the probability of all 10 sheets picked having the same ingredient is 5.77*10^-14.
I am just trying to figure out whether 5.77*10^-14 is statistically significant?
Thanks for any kind of help
2. Originally Posted by syrivaci
Does anyone know the best Signifinace Test for a dataset following a hypergeometric distribution with sample size over 30?
If you have 100 recipe sheets. And, 10 of these sheets are linked because they all contain the same ingredient. The chance of picking a recipe sheet on it's own with that specific ingredient is 0.408. But, the probability of all 10 sheets picked having the same ingredient is 5.77*10^-14.
I am just trying to figure out whether 5.77*10^-14 is statistically significant?
Thanks for any kind of help
I'm having a bit of trouble understanding exactly what question is being
asked here. Is there a test going on? If so what is being tested?
Also I'm a but puzzled by "The chance of picking a recipe sheet on it's own
with that specific ingredient is 0.408", if 10 sheets of 100 contain this
ingriedient why is the probability not 0.1?
I expect I've missed something obvious here, but I don't understand the
question
RonL
3. ## Thanks
Originally Posted by CaptainBlack
I'm having a bit of trouble understanding exactly what question is being
asked here. Is there a test going on? If so what is being tested?
Also I'm a but puzzled by "The chance of picking a recipe sheet on it's own
with that specific ingredient is 0.408", if 10 sheets of 100 contain this
ingriedient why is the probability not 0.1?
I expect I've missed something obvious here, but I don't understand the
question
RonL
Hi, Captain Black
Sorry for the confusion.
From my understanding:
The number of ways to choose 10 objects out 100 is C(100,10)=17310309456440
1/17310309456440=5.77X10-14
Plus:
(90C9)(10C1)/(100C10)= 0.40799532232929
I just want to work out if 1/17310309456440=5.77X10-14 is statistically significant. I am pretty rusty on p-values and which test to use so please go easy on me.
Thanks again.
4. Originally Posted by syrivaci
Does anyone know the best Signifinace Test for a dataset following a hypergeometric distribution with sample size over 30?
If you have 100 recipe sheets. And, 10 of these sheets are linked because they all contain the same ingredient. The chance of picking a recipe sheet on it's own with that specific ingredient is 0.408. But, the probability of all 10 sheets picked having the same ingredient is 5.77*10^-14.
I am just trying to figure out whether 5.77*10^-14 is statistically significant?
Thanks for any kind of help
With a hypergeometric density $\displaystyle f$ with parameters 100, 10 and 10:
$\displaystyle f(1) = \frac{{10 \choose 1}{90 \choose 9}}{{100 \choose 10}} = .40799.$
$\displaystyle f(10) = \frac{{10 \choose 10}{90 \choose 0}}{{100 \choose 10}} = 5.78 \times 10^{-14}.$
From your later post I gather that you're not sure how to phrase the test. So I'll suggest it is this.
The null hypothesis is that you are drawing recipes from a population of 100 recipes of which 10 have a certain ingredient. The alternative hypothesis is that more than 10 recipes have the ingredient.
You are drawing a sample of 10 (not 30) recipes without replacement from the population. So $\displaystyle x$, the number of recipes in the sample with the ingredient, has a hypergeometric distribution with parameters 90, 10 and 10 under the null hypothesis. A best test would reject the null hypothesis if the p-value for $\displaystyle x$ under the null is less than .05. Since the p-value for $\displaystyle x = 10$ is extremely statistically significant at $\displaystyle 5.78 \times 10^{-14} \ll .05$, the null hypothesis is overwhelmingly rejected.
Put another way, under the null hypothesis it is extremely unlikely that you would draw 10 recipes with the ingredient. So reject the null hypothesis.
5. Originally Posted by JakeD
With a hypergeometric density $\displaystyle f$ with parameters 100, 10 and 10:
$\displaystyle f(1) = \frac{{10 \choose 1}{90 \choose 9}}{{100 \choose 10}} = .40799.$
Ah, so the 0.408 is the probability of finding exactly one of a sample of 10
sheets use the ingredient. That's better
RonL
My comprehension seems to be suffereing in addition to my accuracy
at the moment
6. ## One more thing...
Originally Posted by JakeD
With a hypergeometric density $\displaystyle f$ with parameters 100, 10 and 10:
$\displaystyle f(1) = \frac{{10 \choose 1}{90 \choose 9}}{{100 \choose 10}} = .40799.$
$\displaystyle f(10) = \frac{{10 \choose 10}{90 \choose 0}}{{100 \choose 10}} = 5.78 \times 10^{-14}.$
From your later post I gather that you're not sure how to phrase the test. So I'll suggest it is this.
The null hypothesis is that you are drawing recipes from a population of 100 recipes of which 10 have a certain ingredient. The alternative hypothesis is that more than 10 recipes have the ingredient.
You are drawing a sample of 10 (not 30) recipes without replacement from the population. So $\displaystyle x$, the number of recipes in the sample with the ingredient, has a hypergeometric distribution with parameters 90, 10 and 10 under the null hypothesis. A best test would reject the null hypothesis if the p-value for $\displaystyle x$ under the null is less than .05. Since the p-value for $\displaystyle x = 10$ is extremely statistically significant at $\displaystyle 5.78 \times 10^{-14} \ll .05$, the null hypothesis is overwhelmingly rejected.
Put another way, under the null hypothesis it is extremely unlikely that you would draw 10 recipes with the ingredient. So reject the null hypothesis.
Hi JakeD
Thank you very much that really has helped alot.
I am just wondering does that mean that the p-value never changes.
For instance, if I had another set of 5 recipes from the 100 that were linked by another ingredient how would I calculate whether this was statistically significant.
Thanks again for everybody's help
7. Originally Posted by syrivaci
Hi JakeD
Thank you very much that really has helped alot.
I am just wondering does that mean that the p-value never changes.
For instance, if I had another set of 5 recipes from the 100 that were linked by another ingredient how would I calculate whether this was statistically significant.
Thanks again for everybody's help
The p-value changes. The cutoff for the p-value does not change and is generally set at .05. This cutoff is called the significance level. A result is statistically significant when the p-value of that result is less than the cutoff value (significance level).
The p-value is the probability under the null hypothesis of getting an observation as extreme as the one observed. For example, you drew 10 recipes and got 10 with the one ingredient. The probability of getting 10 or more recipes with the one ingredient is the p-value. (Of course, the "or more" is not possible here since 10 is the max when drawing 10 recipes.)
What was your sample size and null hypothesis when you drew the 5 recipes? In your first post, you indicated you picked 10 out of the 100 at random so your sample size was 10. And your null hypothesis appeared to be there were 10 with the ingredient.
What was your sample size here? Was it still 10, perhaps the same 10? And was your null hypothesis that there were 10 with the other ingredient too? If so, the p-value is the probability of getting 5 or more recipes with the other ingredient out of the sample of 10 using the same hypergeometric density f. So that would be f(5)+f(6)+...+f(10).
Please verify something for me. You are drawing a random sample from the 100 recipes. You have a null hypothesis before you look at the results of the random sample. Everything I said is based on this.
8. ## Thanks
Originally Posted by JakeD
The p-value changes. The cutoff for the p-value does not change and is generally set at .05. This cutoff is called the significance level. A result is statistically significant when the p-value of that result is less than the cutoff value (significance level).
The p-value is the probability under the null hypothesis of getting an observation as extreme as the one observed. For example, you drew 10 recipes and got 10 with the one ingredient. The probability of getting 10 or more recipes with the one ingredient is the p-value. (Of course, the "or more" is not possible here since 10 is the max when drawing 10 recipes.)
What was your sample size and null hypothesis when you drew the 5 recipes? In your first post, you indicated you picked 10 out of the 100 at random so your sample size was 10. And your null hypothesis appeared to be there were 10 with the ingredient.
What was your sample size here? Was it still 10, perhaps the same 10? And was your null hypothesis that there were 10 with the other ingredient too? If so, the p-value is the probability of getting 5 or more recipes with the other ingredient out of the sample of 10 using the same hypergeometric density f. So that would be f(5)+f(6)+...+f(10).
Please verify something for me. You are drawing a random sample from the 100 recipes. You have a null hypothesis before you look at the results of the random sample. Everything I said is based on this.
Hi JakeD
Thanks for the info.
My overall plan is to calculate the significance of each ingredient dependent on how many times they occur in each of the recipes (some ingredients will occur in 10 dishes whereas others will occur in 5 dishes). I want to show whether there is a reason why some could be more significant than others (e.g. comparing a set of Italian Dishes and a set of British dishes e.t.c).
I hope this helps. Thanks again.
9. Originally Posted by syrivaci
Hi JakeD
Thanks for the info.
My overall plan is to calculate the significance of each ingredient dependent on how many times they occur in each of the recipes (some ingredients will occur in 10 dishes whereas others will occur in 5 dishes). I want to show whether there is a reason why some could be more significant than others (e.g. comparing a set of Italian Dishes and a set of British dishes e.t.c).
I hope this helps. Thanks again.
Then I think what you are calculating is inappropriate for what you want
to do (still not entirely clear though). It seems that there is no test.
From what you write it seems to me that an appropriate measure of
the importance of an ingredient to a collection of recipes is something
like the fraction of recipes in the collection that the ingredient appears in.
RonL
10. Originally Posted by syrivaci
Hi JakeD
Thanks for the info.
My overall plan is to calculate the significance of each ingredient dependent on how many times they occur in each of the recipes (some ingredients will occur in 10 dishes whereas others will occur in 5 dishes). I want to show whether there is a reason why some could be more significant than others (e.g. comparing a set of Italian Dishes and a set of British dishes e.t.c).
I hope this helps. Thanks again.
This does help. Now I share Captain Black's concerns about whether your method is an appropriate way to analyze the recipe data. Your method is not standard, but there may be standard methods such the chi-square goodness of fit test that could be used. I'm thinking a multinomial logit analysis is a possibility.
So I suggest turning your questions in the direction of what is a good method for analyzing this data. That requires describing your project in more detail. Here are some things a consultant would need to know to be able to recommend a methodology.
• What is the purpose of the project? Are you writing an article for publication? Is this a term project for a class?
• What are the time constraints? Is it due next week?
• What is your statistical background? Are you willing and do you have time to research methods that may be unfamiliar to you?
• What do the data look like? Give examples.
• What sorts of conclusions do you want to be able to draw from the data?
I think it would be good for a qualified statistician (which I'm not) to look at your requirements and recommend a strategy. You can start here. If you wrote a short description of your project along the above lines, we can review it. Then you could go back to the help sites where you've been posting these questions and try asking for recommendations.
Of course, you may have time for none of this. It goes back to those questions I listed. What is your purpose?
11. ## Details
Originally Posted by JakeD
This does help. Now I share Captain Black's concerns about whether your method is an appropriate way to analyze the recipe data. Your method is not standard, but there may be standard methods such the chi-square goodness of fit test that could be used. I'm thinking a multinomial logit analysis is a possibility.
So I suggest turning your questions in the direction of what is a good method for analyzing this data. That requires describing your project in more detail. Here are some things a consultant would need to know to be able to recommend a methodology.
• What is the purpose of the project? Are you writing an article for publication? Is this a term project for a class?
• What are the time constraints? Is it due next week?
• What is your statistical background? Are you willing and do you have time to research methods that may be unfamiliar to you?
• What do the data look like? Give examples.
• What sorts of conclusions do you want to be able to draw from the data?
I think it would be good for a qualified statistician (which I'm not) to look at your requirements and recommend a strategy. You can start here. If you wrote a short description of your project along the above lines, we can review it. Then you could go back to the help sites where you've been posting these questions and try asking for recommendations.
Of course, you may have time for none of this. It goes back to those questions I listed. What is your purpose?
Purpose
I doubt it will be published (I wish!) but this is a class project.
I am looking into whether there is a reason why particular ingredients are found more often in recipes from particular data sets (each data set representing a particular country). I am pretty sure there is a link but I want to show that some ingredients are more statistically significant than others in a particular data set.
e.g.
Data Set Country ITALY
First Recipe: Ingredient1 Ingredient2 Ingredient3 Ingredient4
Second Recipe: Ingredient5 Ingredient1 Ingredient6
.
.
.
Hundreth Recipe:Ingredient87 Ingredient212
e.t.c
12. Originally Posted by syrivaci
Purpose
I doubt it will be published (I wish!) but this is a class project.
I am looking into whether there is a reason why particular ingredients are found more often in recipes from particular data sets (each data set representing a particular country). I am pretty sure there is a link but I want to show that some ingredients are more statistically significant than others in a particular data set.
e.g.
Data Set Country ITALY
First Recipe: Ingredient1 Ingredient2 Ingredient3 Ingredient4
Second Recipe: Ingredient5 Ingredient1 Ingredient6
.
.
.
Hundreth Recipe:Ingredient87 Ingredient212
e.t.c
Nice project!
The simplest way to compare the use of an ingredient between countries is to calculate the difference in the proportions $\displaystyle p_i$ of the recipes that use the ingredient in country $\displaystyle i$. (Captain Black suggested this before.)
To measure the statistical significance of a difference use the statistic
$\displaystyle Z = \frac{p_1 - p_2}{\sqrt{p(1-p)(1/n_1+1/n_2)}}$
where $\displaystyle n_i$ is the total number of recipes in country $\displaystyle i$ and
$\displaystyle p = \frac{n_1 p_1 + n_2 p_2}{n_1 + n_2}$
is the combined proportion. Treat $\displaystyle Z$ as a standard normal variable. So reject the hypothesis that the two proportions are equal when $\displaystyle |Z| > 1.96$ for a 5% significance level.
Now I don't see how the hypergeometric distribution would apply to this project.
Although I'd like to go into an extensive discussion of all the ways this data could be analyzed, I'll try to restrain myself.
13. Originally Posted by syrivaci
Purpose
I doubt it will be published (I wish!) but this is a class project.
I am looking into whether there is a reason why particular ingredients are found more often in recipes from particular data sets (each data set representing a particular country). I am pretty sure there is a link but I want to show that some ingredients are more statistically significant than others in a particular data set.
e.g.
Data Set Country ITALY
First Recipe: Ingredient1 Ingredient2 Ingredient3 Ingredient4
Second Recipe: Ingredient5 Ingredient1 Ingredient6
.
.
.
Hundreth Recipe:Ingredient87 Ingredient212
e.t.c
Sketch of what might be an appropriate test:
You have a data set with N recipes, using a total of n ingredients.
You have an empirical (observed) distribution of the number of ingriedients
in a recipe for this data set.
Null hypothesis: The data set is a random sample of N recipes from a population
with an appropriate distribution of number of ingredients per recipe, and
with each of the n ingredient appearing with equal frequency*.
Test: Is the frequency of appearance of the most common ingredient/s in
the data set significantly higher than would be expected under the null
hypothesis?
Such a test might well require the extravegant use of the bootstrap to establish
critical values for the test statistic.
That is about all I can say at present. To work out the details would start to
incur serious consultancy fees
RonL
* I intend this to mean that the number of ingredients k is sampled from the
ingredient number distribution then the k ingredients are determined by
sampling without replacement from the list of possible ingredients. | 2018-04-20 08:36:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.513494610786438, "perplexity": 679.6247192007171}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125937193.1/warc/CC-MAIN-20180420081400-20180420101400-00295.warc.gz"} |
https://www.prereview.org/users/2/articles/144-sub-surface-convection-zones-in-hot-massive-stars-and-their-observable-consequences/_show_article | # Sub-surface convection zones in hot massive stars and their observable consequences
Abstract
We study the convection zones in the outer envelope of hot massive stars which are caused by opacity peaks associated with iron and helium ionization. We determine the occurrence and properties of these convection zones as function of the stellar parameters. We then confront our results with observations of OB stars. A stellar evolution code is used to compute a grid of massive star models at different metallicities. In these models, the mixing length theory is used to characterize the envelope convection zones. We find the iron convection zone (FeCZ) to be more prominent for lower surface gravity, higher luminosity and higher initial metallicity. It is absent for luminosities below about $$10^{3.2}{\,{\rm L}_\odot}$$, $$10^{3.9}{\,{\rm L}_\odot}$$, and $$10^{4.2}{\,{\rm L}_\odot}$$ for the Galaxy, LMC and SMC, respectively. We map the strength of the FeCZ on the Hertzsprung-Russell diagram for three metallicities, and compare this with the occurrence of observational phenomena in O stars: microturbulence, non-radial pulsations, wind clumping, and line profile variability. The confirmation of all three trends for the FeCZ as function of stellar parameters by empirical microturbulent velocities argues for a physical connection between sub-photospheric convective motions and small scale stochastic velocities in the photosphere of O- and B-type stars. We further suggest that clumping in the inner parts of the winds of OB stars could be caused by the same mechanism, and that magnetic fields produced in the FeCZ could appear at the surface of OB stars as diagnosed by discrete absorption components in ultraviolet absorption lines.
# Introduction
Massive stars, in a general sense, have convective cores and radiative envelopes (Kippenhahn 1990). The introduction of the so called “iron peak" in stellar opacities (Iglesias 1992) led, however, to the prediction of a small convection zone in the envelope of sufficiently luminous massive main sequence models which originates from an opacity peak associated with partial helium ionization. These two convection zones comprise almost negligible amount of mass. The reality of the iron opacity bump, as predicted by various groups (Iglesias 1992, Badnell 2005), is unambiguous. It is most obvious in the field of stellar pulsations. Only the inclusion of this feature allows an agreement of observed and predicted instability regimes in the HR diagram, from the white dwarf regime (Saio 1993, Charpinet 1997), for main sequence stars (Deng 2001), and up to hot supergiants (Saio 2006).
While the envelope convection zones may, at first glance, be negligible for the internal evolution of hot massive stars, they may cause observable phenomena at the stellar surface. The reason is that the zones are located very close to the photosphere for some mass interval (see below). Here, we will discuss which observed features in hot stars might be produced by these near surface convection zones. In particular, we examine whether a link exists between these convective regions and observable small scale velocity fields at the stellar surface and in the stellar wind,“microturbulence”. A similar idea has been used to explain microturbulence in low mass stars (Edmunds 1978), in which deeper envelope convection zones reach the photosphere. While (Edmunds 1978) concludes that the same mechanism cannot explain microturbulent velocities in O and B stars, the iron-peak induced sub-photospheric convection zones in these stars had not yet been discovered. We demonstrate in this paper that these convection zones may not only cause motions which are observable, but possibly even directly affect the evolution: First, we discuss how photospheric velocity fields may affect the structure of massive star winds by inducing clumping at the base of the wind and thereby affecting the stellar mass-loss. And second, we argue that the near surface convection zones may generate magnetic fields which – if they migrate to the surface – further affect the stellar wind mass-loss and, more significantly, the associated stellar angular momentum loss.
We construct grids of massive main sequence star models, for various metallicities, that allow us to predict the occurrence and properties of sub-surface convection zones as function of the stellar parameters (Sect. \ref{results}). We then compare the model predictions with observed stellar properties, e.g., empirically derived microturbulent velocities and observations of wind clumping in hot massive stars (Sect. \ref{comparison}).
# Method
\label{method} Our stellar models are calculated with a hydrodynamic stellar evolution code. This code can calculate the effect of rotation on the stellar structure, rotationally induced chemical mixing, and the transport of angular momentum by magnetic torques . Compositional mixing is treated as a diffusive process. The rate of change of a nuclear species of mass fraction $$X_i$$ is calculated as where $$D$$ is the diffusion coefficient constructed from the sum of individual diffusion coefficients for the range of mixing processes (see Heger et al., 2000, and references therein). The second term on the right hand side is the schematic symbol to stand for all nuclear reactions. The contributions to the diffusion coefficient are convection, semiconvection and thermohaline mixing. For rotating models also the contributions from rotationally induced mixing and magnetic diffusion are computed. The transport of angular momentum is also treated as a diffusive process (Endal 1978, Pinsonneault 1989, Heger 2000).
${{{{\left({\frac{\partial{X_i}}{\partial{t}}}\right)}}_{{}}}}={{{{\left({\frac{\partial{}}{\partial{m}}}\right)}}_{{}}}}\, {{\left[{(4\pi r^2 \rho)^2 \, D \, {{{{\left({\frac{\partial{X_i}}{\partial{m}}}\right)}}_{{}}}}}\right]}}+{{{{\left({\frac{{{\mathrm d}}{X_i}}{{{\mathrm d}}{t}}}\right)}}_{{\mathrm{nuc}}}}} ,$
The Ledoux criterion is used to determine which regions of the star are unstable to convection. The diffusion coefficient, $$D$$, in convective regions is approximated with where $${\mathrm{H}_{\mathrm{P}}}$$ is the pressure scale height, $${v}_c$$ is the convective velocity, and $$\alpha$$ the mixing length parameter. We fix $$\alpha = 1.5$$, which results from evolutionary tracks of the Sun the $$\alpha$$ dependence of our scenario will be presented in future work. The convective velocity, $${v}_c$$, is calculated using the mixing length theory (Böhm-Vitense 1958) (MLT hereafter) and the convective contribution to the diffusion coefficient becomes: where $$\varkappa$$ is the opacity, $$\rho$$ is the density, $$\beta$$ is the ratio of gas pressure to total pressure, $$g$$ is the local gravitational acceleration, and $$c$$ is the speed of light. Here, $${\nabla_{\mathrm{\!rad}}}$$ and $${\nabla_{\mathrm{\!ad}}}$$ are the radiative and adiabatic gradients, respectively.
${\nabla_{\mathrm{\!ad}}}- {\nabla}+\frac{\varphi}{\delta} \,{\nabla_{\!\mu}}\le 0$
$D=\frac{1}{3} \alpha {\mathrm{H}_{\mathrm{P}}}{v}_c$
$D=\frac{1}{3}\,\alpha^{2/3} {\mathrm{H}_{\mathrm{P}}}\,\Big[\frac{c}{\varkappa \rho}\, g\, \beta\,(1-\beta) {\nabla_{\mathrm{\!ad}}}({\nabla_{\mathrm{\!rad}}}-{\nabla_{\mathrm{\!ad}}}) \Big]^{1/3} ,$
We use the solar composition proposed by (Asplund 2005). The opacities in our code are extracted from the OPAL tables (Iglesias 1996). Fig. \ref{fig:opacity} shows the opacity coefficient as function of temperature in our 60$${\,\mathrm{M}_\odot}$$ models for various metallicities. The peaks at $${\log\, T}\simeq 4.7$$ and $${\log\, T}\simeq 5.3$$ are caused by helium and iron, respectively. The peak at $${\log\, T}\simeq 6.2-6.3$$ is caused by carbon, oxygen and iron. We use the metallicity dependent mass-loss predictions of (Vink 2001) .
\label{fig:opacity} Opacity in the interior of 60 $${\,\mathrm{M}_\odot}$$ zero age main sequence stars of various metallicities (see legend) as a function of temperature, from the surface up to a temperature of $$10^7\,$$K. The different colors refer to different metallicities, as shown in the legend.
## The helium convection zone
\label{he} In the very weak helium convection zone, radiative diffusion is the dominant energy transport mechanism, which may have consequences for the development of convection. In fact, in viscous fluids the Ledoux-criterion is not strictly correct, since it ignores any dissipative effect on the evolution of a perturbation. A more accurate criterion can be expressed in terms of the non-dimensional Rayleigh number, $${\mathrm{Ra}}$$ which for compressible, stratified convection, is Here $$L$$ is the thickness of the convective layer, and $$\kappa$$ and $$\nu$$ are, respectively, the thermal diffusivity and the kinematic (molecular) viscosity (Shore 1992).
${\mathrm{Ra}}\simeq \frac{({\nabla}-{\nabla_{\mathrm{\!ad}}}) L^3 g}{ \kappa\nu} .$
\label{rayleigh}
For convection to develop, $${\mathrm{Ra}}$$ must exceed some critical value, $${\mathrm{Ra}}_c$$. The estimate of $${\mathrm{Ra}}$$ in the helium convective region depends on the choice of the viscosity coefficient. For the Spitzer formula can be considered convective. In contrast, for the radiative viscosity There is an additional uncertainty in these estimates since the expressions for the radiative transport coefficients in our models are strictly correct only in the diffusion limit. Likewise, the value of the heat capacity $${c_{\mathrm{p}}}$$ can vary by an order of magnitude depending on whether the radiative energy reservoir $$a T^4$$ is coupled to the internal energy of the gas or not. Since the helium convection zone occurs very close to the surface in our models, these additional uncertainties could be relevant.
Ideally, the properties of the helium convection zone could be studied through multi-dimensional hydrodynamic calculations. However, the large thermal diffusivity poses a formidable computational challenge since it makes the problem numerically stiff: the diffusive timescale is much shorter than the dynamical one, which leads to very short time steps if an explicit solver is used (unfortunately, most codes used for compressible convection are explicit). Any simulation would have only limited value unless it includes a sufficiently realistic treatment of the coupling between plasma and radiation.
In the presence of strong wind mass-loss, another consideration related to the He convective zone becomes important, due to the fact that it comprises only a tiny amount of mass. Convection can set in only if the turnover time $$\tau_{\rm turn}\simeq {\mathrm{H}_{\mathrm{P}}}/{v}_c$$ is shorter than the time scale for which convection is predicted to prevail at a fixed Lagrangian mass shell inside the convection zone, $$\tau_{\rm conv}$$, which is $$\tau_{\rm conv} \simeq \Delta M_{\rm conv}/\dot M$$. We find a critical mass-loss rate $$\dot{M} \sim 10^{-6} {\,\mathrm{M}_\odot}\rm{yr}^{-1}$$, above which convection has no time to develop in the helium region, since the wind is removing an amount of mass equivalent to the mass of the convection zone before a convective eddy can turn over (see Tab. \ref{clumps}). For a metallicity $$Z$$=0.02, stars above 40 $${\,\mathrm{M}_\odot}$$ cannot develop the He convection zone, and in a 20 $${\,\mathrm{M}_\odot}$$ such a layer is convective only for 10 - 100 turnovers before convection moves to a lower mass coordinate. None of these concerns is significant for the iron convection zone (FeCZ hereafter), where convection is always fully developed. Moreover the convective velocities for the FeCZ are always found to be much higher than those in the helium convection zones. We disregard the occurrence of the helium convection zones unless it is explicitly mentioned.
# Results
\label{results} We calculated a grid of non-rotating stellar evolution sequences for initial masses between $$5{\,\mathrm{M}_\odot}$$ and $$100{\,\mathrm{M}_\odot}$$, at metallicities of $$Z$$=0.02, $$Z$$=0.008 and $$Z$$=0.004, roughly corresponding to the Galaxy, the LMC and the SMC, respectively. Additionally, we computed several models at lower metallicity. Since rapid rotation can change the properties of sub-surface convection (Maeder 2008), we calculated a few rotating models to evaluate the effects of rotation on our results. These effects are discussed in Section \ref{rotation}.
Figures \ref{fig:20zsunsurf} and \ref{fig:60zsunsurf} show the evolution of the radial extent and location of the sub-surface convection zones in 20$${\,\mathrm{M}_\odot}$$ and 60$${\,\mathrm{M}_\odot}$$ models during the main sequence phase.
\label{fig:20zsunsurf} Evolution of the radial extent of the helium and iron convective regions (hatched) as function of time, from the zero age main sequence to roughly the end of core hydrogen burning, for a 20$${\,\mathrm{M}_\odot}$$ star. The top of the plot represents the stellar surface. Only the upper 1$${\,{\rm R}_\odot}$$ of the star is shown in the plot, while the stellar radius itself increases during the evolution. Upper panel: The star has a metallicity of $$Z$$=0.02, and its effective temperature decreases from 35000K to 25000K during the main sequence phase. Lower panel: The star has a metallicity of $$Z$$=0.004, and its effective temperature decreases from 37000K to 27000K during the main sequence phase. The extent of the convection zones is smaller than in the case shown above, and the iron zone is absent for the first 2.5 million years.
\label{fig:60zsunsurf} Same as Fig. \ref{fig:20zsunsurf}, but for a 60$${\,\mathrm{M}_\odot}$$ star at $$Z$$=0.02. Note the different vertical scale, spanning the upper 4$${\,{\rm R}_\odot}$$ of the star. The effective temperature decreases from 48000K to 18000K during the main sequence phase.
As outlined above, the He opacity bump at around $${\log\, T}~\simeq~4.7$$ is responsible for a convective zone which occurs close to the stellar surface and is very inefficient: only a very small fraction of the heat flux is transported by bulk motions in this region. The upper boundary is typically found at an optical depth in the range $$2 \leq \tau \leq 10$$, where $$\tau$$ is the Rosseland mean optical depth. Below this convective zone, the Fe opacity bump at around $${\log\, T}~\simeq~5.3$$ is associated with a more efficient and extended convective region.
${\langle{{v}_{c}}\rangle}:=\frac{1}{\alpha {\mathrm{H}_{\mathrm{P}}}} \int_{{\mathrm{R}_{\mathrm{c}}}-\alpha{\mathrm{H}_{\mathrm{P}}}}^{{\mathrm{R}_{\mathrm{c}}}} {{v}_{c}}(r)\; dr$
\label{aver}
The radial extent of the FeCZ is quite substantial, i.e. a significant fraction of one solar radius, which corresponds typically to 2 - 10 pressure scale heights, comprising a mass on the order of 10$$^{-6}{\,\mathrm{M}_\odot}$$ to 10$$^{-5}{\,\mathrm{M}_\odot}$$, while the amount of mass between the top of the FeCZ and the stellar surface is around several times 10$$^{-7}{\,\mathrm{M}_\odot}$$ (cf. Table 1). In the 20$${\,\mathrm{M}_\odot}$$ model the upper border of the FeCZ is located at $$\tau \approx 140$$ on the ZAMS, and at $$\tau \approx$$ 370 on the cool side of the main sequence band. In the 60$${\,\mathrm{M}_\odot}$$ model the upper border at ZAMS is located at $$\tau \approx$$ 15, reaching $$\tau \approx$$ 260 during the late main sequence evolution. Convective velocities predicted by the MLT are on the order of 10s of $${\, {\rm km}\, {\rm s}^{-1}}$$, where more extended zones achieve higher velocities. For a quantitative analysis, we define an average convective velocity where $${\mathrm{R}_{\mathrm{c}}}$$ is the upper boundary of the convective zone, and where we set $$\alpha = 1.5$$.
\label{tab:tab1}
\label{clumps}
M Zone $${\mathrm{H}_{\mathrm{P}}}$$ $${\langle{{v}_{c}}\rangle}$$ $$\Delta M_{\rm conv}$$1 $$\Delta M_{\rm top}$$2 $$N_{\rm cells}$$3 $$\tau_{\rm turn}$$4 $$\tau_{\rm conv}$$5 $$\dot{M}$$ $${\,\mathrm{M}_\odot}$$ $${\,{\rm R}_\odot}$$ km s$$^{-1}$$ $${\,\mathrm{M}_\odot}$$ $${\,\mathrm{M}_\odot}$$ days days $${\,\mathrm{M}_\odot}\rm{ yr}^{-1}$$ 20 He 0.025 0.08 $$7.6\times10^{-9}$$ $$1.9\times10^{-9}$$ $$1.8\times10^{5}$$ 2.5 38 $$7.3\times10^{-8}$$ 20 Fe 0.08 2.40 $$3.6\times10^{-6}$$ $$5.8\times10^{-7}$$ $$1.8\times10^{4}$$ 0.25 18250 $$7.3\times10^{-8}$$ 60 Fe 0.24 2.25 $$1.6\times10^{-5}$$ $$9.8\times10^{-7}$$ $$8.5\times10^{3}$$ 0.83 1570 $$3.7\times10^{-6}$$
1. Mass contained in the convective region.
2. Mass in the radiative layer between the stellar surface and the upper boundary of the convective zone.
3. Expected number of convective cells, $$N_{\rm cells}:= (R_{\star}/H_{\rm P})^2$$.
4. Convective turnover time, $$\tau_{\rm turn}:= H_{\rm P}/{\langle{{v}_{c}}\rangle}$$.
5. Time that a piece of stellar material spends inside a convective region, $$\tau_{\rm conv}:= \Delta M_{\rm conv}/\dot M$$.
From Figures \ref{fig:20zsunsurf} and \ref{fig:60zsunsurf}, three trends for the extent of the sub-surface convection zones are noticeable. First, with increasing time during the main sequence evolution, these zones become more extended, and are located deeper inside the stellar envelope. This is because the stellar envelope expands, and becomes cooler, while the temperature of the opacity peak remains nearly constant. In our $$20{\,\mathrm{M}_\odot}$$ model at $$Z$$=0.02, the mass of the He convective zone increases from about $$10^{-9}{\,\mathrm{M}_\odot}$$ to $$2\times10^{-7}{\,\mathrm{M}_\odot}$$, and that of the FeCZ is growing from $$2\times10^{-6}{\,\mathrm{M}_\odot}$$ to $$10^{-4}{\,\mathrm{M}_\odot}$$. For sufficiently hot models, the helium convection zones can even vanish (Fig. \ref{fig:20zsunsurf}, lower panel). Second, comparing the 20$${\,\mathrm{M}_\odot}$$ and the 60$${\,\mathrm{M}_\odot}$$ model at $$Z$$=0.02 demonstrates that the FeCZ becomes more prominent for higher luminosity. This is because the opacity is not substantially changing among main sequence models at the same metallicity, such that a higher luminosity renders a larger portion of the envelope convectively unstable (both in radius and mass fraction). Our models show that the FeCZ disappears below a threshold luminosity of about $$10^4{\,{\rm L}_\odot}$$ on the ZAMS at solar metallicity. Third, comparing the two 20$${\,\mathrm{M}_\odot}$$ models in Fig. \ref{fig:20zsunsurf} shows that the extent of the FeCZ, and its presence, depends on the metallicity. We find that for $$Z$$=0.001, it is completely absent below 40$${\,\mathrm{M}_\odot}$$, and at $$Z$$=0.00001 it does not occur for $$\mathrm{M}\leq60{\,\mathrm{M}_\odot}$$. In summary, our models predict an increase of the importance of the FeCZ for cooler surface temperature or lower surface gravity, for higher luminosity, and for higher metallicity.
While in the discussed range of luminosity and effective temperature, the average convective velocity $${\langle{{v}_{c}}\rangle}$$ is on the order of 1 to 10$${\, {\rm km}\, {\rm s}^{-1}}$$ for the FeCZ, we found that the average convective velocity $${\langle{{v}_{c}}\rangle}$$ in the He convective zone is always very low ($$\le 1{\, {\rm km}\, {\rm s}^{-1}}$$). Convection due to hydrogen recombination is absent; this dominates at lower effective temperatures than the ones studied here.
For our grid of stellar evolution models, we map the average convective velocity of the FeCZ (Eq. \ref{eq:aver}) in the HR diagram for the three different metallicities (see Fig. \ref{fig:hrdvel}, and Sect. \ref{sec:mobs}). This figure displays the three qualitative trends of the iron zone we have just described.
• For given luminosity and metallicity, the average convective velocity near the upper boundary of the FeCZs increases with decreasing surface temperature. The convection zones are located deeper inside the star (in radius, not in mass), and the resulting larger pressure scale height leads to higher velocities. At solar metallicity and $$10^5{\,{\rm L}_\odot}$$ (i.e. roughly at $$20{\,\mathrm{M}_\odot}$$) the velocities increase from just a few $${\, {\rm km}\, {\rm s}^{-1}}$$ at the ZAMS to more than $$10{\, {\rm km}\, {\rm s}^{-1}}$$ in the supergiant regime, where $${\langle{{v}_{c}}\rangle}= 2.5{\, {\rm km}\, {\rm s}^{-1}}$$ is achieved at $$T_{\rm eff}\simeq 30\, 000\,$$K. At the lowest considered metallicity, the FeCZ is absent at the ZAMS at $$10^5{\,{\rm L}_\odot}$$, and a level of $${\langle{{v}_{c}}\rangle}= 2.5{\, {\rm km}\, {\rm s}^{-1}}$$ is only reached at $$T_{\rm eff}\simeq 20\, 000\,$$K.
• For fixed effective temperature and metallicity, the iron zone convective velocity increases with increasing luminosity, since a larger flux demanded to be convectively transported requires faster convective motions. Figure \ref{fig:hrdvel} in Sect. \ref{sec:mobs} also shows that there are threshold luminosities below which FeCZs do not occur, i.e., below about $$10^{3.2}{\,{\rm L}_\odot}$$, $$10^{3.9}{\,{\rm L}_\odot}$$, and $$10^{4.2}{\,{\rm L}_\odot}$$ for the Galaxy, LMC and SMC, respectively.
• The FeCZs become weaker for lower metallicities, since due to the lower opacity, more of the flux can be transported by radiation. The threshold luminosity for the occurrence of the FeCZ quoted above for $$Z$$=0.02 is ten times lower than that for $$Z$$=0.004. And above the threshold, for a given point in the HR diagram, the convective velocities are always higher for higher metallicity.
## Rotating models
\label{rotation} We considered two 20$${\,\mathrm{M}_\odot}$$ models with metallicity $$Z$$=0.02, one rotating at birth with an equatorial velocity of 250$${\, {\rm km}\, {\rm s}^{-1}}$$ (corresponding to about 35% of the critical velocity) and one with 350$${\, {\rm km}\, {\rm s}^{-1}}$$ (about 50% of the critical velocity). The evolution of the radial extent of sub-surface convection in the rotating models is very similar to the non-rotating case shown in Fig. \ref{fig:20zsunsurf}. Also the convective velocities inside the FeCZ change only a few percent between rotating and non-rotating models, even if the rotating models show slightly higher convective velocity peaks (see Fig. \ref{fig:feczrotating}). We conclude that rotation is not significantly affecting the structure and the properties of sub-surface convection in the vast majority of OB stars.
As pointed out by (Maeder 2008), the effects of rotation on sub-surface convection become substantial for stars rotating close to critical velocity. While stars rotating with such high velocities exist (e.g. Be stars), their number is modest. The study of sub-surface convection in these very fast rotators is interesting, but may require 2-dimensional stellar models, which is beyond the scope of this paper.
\label{fig:feczrotating} Convective velocity in the FeCZ as function of radial distance from the stellar surface. The dotted line corresponds to a non-rotating 20$${\,\mathrm{M}_\odot}$$ model at $$Z$$=0.02, while the dashed and solid lines refer to the same model rotating at birth with 250$${\, {\rm km}\, {\rm s}^{-1}}$$ and 350 $${\, {\rm km}\, {\rm s}^{-1}}$$ respectively. The values correspond to models having the same effective temperature ($${\log\, T_{\rm }\,}=$$ 4.339) and very similar luminosity ($${\log\, L/ L_\odot \,}=$$ 5.04 for the non-rotating model and $${\log\, L/ L_\odot \,}=$$ 5.03 for the rotating ones). The gray band shows the upper 1.5 pressure scale heights of the FeCZ, which is the region considered for the computation of $${\langle{{v}_{c}}\rangle}$$, cf. Eq. \ref{eq:aver}. Convective velocities in the He convection zone are much lower than 1$${\, {\rm km}\, {\rm s}^{-1}}$$ and are not visible in this plot.
# Comparison with observations
\label{comparison}
In the following, we investigate the idea that these sub-surface convection zones might be related to observable phenomena at the stellar surface. In particular, we investigate potential connections with microturbulence in massive stars, and discuss whether small scale or large scale clumping in massive star winds, magnetic fields, and non-radial pulsations could be related to sub-surface convection. For each point, we first briefly discuss the theoretical motivation, and then the corresponding observational evidence.
## Microturbulence
\label{micro}
The convective cells in the upper part of a convection zone excite acoustic and gravity waves that propagate outward. The generation of sound waves by turbulent motions was first discussed by Lighthill (1952) and extended to a stratified atmosphere by Stein (1967) and Goldreich et al. (1990). In a stratified medium, gravity acts as a restoring force and allows the excitation of gravity waves. For both acoustic and gravity waves, the most important parameter determining the emitted kinetic energy flux is the velocity of the convective motions. This is why, in the following, we use the average convective velocity $${\langle{{v}_{c}}\rangle}$$ as the crucial parameter determining the efficiency of sub-surface convection.
$F_{{\mathrm ac}}\sim F_{c} M_c^{15/2} ,$
$F_{{\mathrm g}}\sim F_{c} M_c ,$
resulting in maximum emission for those waves with horizontal wave vector $$k_h\sim 1/{\mathrm{H}_{\mathrm{P,c}}}$$ and angular frequency $$\omega \sim {v}_c/{\mathrm{H}_{\mathrm{P,c}}}$$, where now $${v}_c$$ and $${\mathrm{H}_{\mathrm{P,c}}}$$ are evaluated at the top of the convective region. They calculated that the amount of convective kinetic energy flux going into acoustic and gravity waves is and respectively, where we take $$F_{c}\sim \rho_c {\langle{{v}_{c}}\rangle}^3$$ and $$M_c$$ is the Mach number in the upper part of the convective region. Since convection in our models is subsonic, gravity waves are expected to extract more energy from the convective region than acoustic waves. These gravity waves can then propagate outward, reach the surface and induce observable density and velocity fluctuations (Fig. \ref{fig:sketch}).
The Brunt-Väisälä frequency in the radiative layer above the FeCZ is about mHz. Molecular viscosity can only damp the highest frequencies, while wavelengths that will be resonant with the scale length of the line forming region should not be affected, see e.g. (Lighthill, 1967). This is the case for the gravity waves stochastically excited by convective motions: they can easily propagate through the sub-surface radiative layer, steepening and becoming dissipative only in the region of line formation.
$\frac{E_{{\mathrm g}}}{E_{\rm s}}\sim M_c\left( \frac{\rho_c}{\rho_s} \right)\left(\frac{{\langle{{v}_{c}}\rangle}}{{v}_{\rm s}}\right)^2\geq 1 ,$
\label{ratio}
${v}_{\rm s} \leq {\langle{{v}_{c}}\rangle}\sqrt{M_c {\rho_c \over \rho_s}}$
Again, multi-dimensional hydrodynamic simulations would be the best way to compute the energy loss of these waves during their propagation through the radiatively stable envelope above the FeCZ, but this is beyond what we can presently do. We can, however, obtain an upper limit to the expected velocity amplitudes at the stellar surface, where we only consider the energy transport through gravity waves. The kinetic energy per unit volume associated with the surface velocity fluctuations $$E_{\rm s}$$ must be comparable to or lower than the kinetic energy density associated with the waves near the sub-surface convection zone, $$E_{\mathrm g}\sim M_c\,\rho_c\,{\langle{{v}_{c}}\rangle}^2$$, or where $$\rho_c$$ is the density at the top of the convective region and $$\rho_s$$ is the surface density, and $${v}_{\rm s}$$ is the surface velocity amplitude. In this ratio we only consider energy density since the volume of the line forming region is comparable to the volume of the upper part of the convective zone. Therefore, we expect In our models with well developed FeCZs, $$\sqrt{M_c \,{\rho_c / \rho_s}} \simeq 1$$ (order of magnitude), and thus $${v}_{\rm s}$$ and $${\langle{{v}_{c}}\rangle}$$ should be on the same order of magnitude. It is difficult to estimate the typical correlation length of the induced velocity field at the stellar surface, but a plausible assumption is that it is about one photospheric pressure scale height, $${\mathrm{H}_{\mathrm{P,s}}}$$, given the proximity of the FeCZ to the surface and the fact that the horizontal wave vector of the emitted waves is $$k_h\sim1/{\mathrm{H}_{\mathrm{P,c}}}$$.
\label{fig:sketch} Schematic representation of the physical processes connected to sub-surface convection. Acoustic and gravity waves emitted in the convective zone travel through the radiative layer and reach the surface, inducing density and velocity fluctuations. In this picture microturbulence and clumping at the base of the wind are a consequence of the presence of sub-surface convection. Buoyant magnetic flux tubes produced in the convection zone could rise to the stellar surface.
$\Delta\lambda_D = \frac{\lambda}{c}\,\sqrt{\frac{2 \mathcal{R} T}{\mu} + {\xi}^2}$
The microturbulent velocity $${\xi}$$ is defined as the microscale nonthermal component of the gas velocity in the region of spectral line formation: Assuming that the gas in this zone has a temperature only slightly different from the effective temperature, one finds empirically that the observed Doppler widths $$\Delta\lambda_D$$ cannot be accounted for by the thermal motions alone (e.g. Cowley, 1970). Regardless of which physical mechanism causes microturbulence, the process of spectral line fitting yields values of $${\xi}$$ in hot massive stars between 0 and about 20$${\, {\rm km}\, {\rm s}^{-1}}$$. In contrast, macroturbulence corresponds to velocity fluctuations which are coherent on a length scale larger than the radial extent of line forming regions. If indeed the length scale of the photospheric velocity fluctuations induced by the iron convection zone are on the order of the photospheric pressure scale height, then this length scale is also comparable to the radial extent of line forming regions, and it is difficult to decide whether the velocity fluctuations would be manifested as micro- or as macroturbulence, or both. Below, we compare our model predictions only to the case of microturbulence since this is the empirical parameter most extensively available in the literature.
Photospheric microturbulence is routinely required, e.g., to derive consistent surface abundances for one element from different photospheric absorption lines through stellar model atmospheres Unfortunately, differences in physical assumptions or atomic physics can require somewhat different microturbulent velocities for the same star in different studies. Here, we restrict our detailed comparison to the data of (Trundle 2007) and (Hunter 2008) from the ESO VLT-FLAMES Survey of Massive Stars (Evans 2005), since it comprises the largest available uniformly analyzed data set. In Fig.\ref{fig:vsinimicro}, we plot the microturbulent velocities derived for the LMC early B type stars analyzed by (Hunter 2008) versus their projected rotational velocity. The error bar on the derived microturbulent velocities is usually quite big, $$\pm 5{\, {\rm km}\, {\rm s}^{-1}}$$, and is often comparable to the measured quantity itself. There seems to be no positive correlation between $${\xi}$$ and the apparent projected rotational velocity $${{v}\sin i}$$. Though $${{v}\sin i}$$ is plotted and not $${v}$$ itself, the lack of a correlation in such a large data set (justifying the assumption of random orientation of the sample) argues against rotation as an important effect in triggering microturbulence in hot stars. To compare microturbulent velocities to properties of sub-photospheric convection we use only data obtained for slow rotators (i.e. $${{v}\sin i}< 80{\, {\rm km}\, {\rm s}^{-1}}$$) as microturbulent velocities are more difficult to measure for faster rotators.
\label{fig:vsinimicro} Projected rotational velocity $${{v}\sin i}$$ versus photospheric microturbulent velocity $${\xi}$$ for the early B-type stars in the LMC analyzed by . Different symbols refer to different luminosity intervals, as explained in the legend. The microturbulent velocities $${\xi}$$ have typical uncertainties of about $$\pm 5{\, {\rm km}\, {\rm s}^{-1}}$$. An uncertainty of 10% or $$\pm 10{\, {\rm km}\, {\rm s}^{-1}}$$, whichever is the larger, should be considered for the rotational velocity measurements.
In Fig.\ref{fig:microlmc}, we show the microturbulent velocities for the LMC stars of Hunter et al. (2008) versus the stellar surface gravity. Trends of the microturbulent velocity with $$\log g$$ have been previously reported for hot stars, e.g. (Gies et al., 1992; Hunter et al., 2007). The figure shows that indeed, for $$\log g < 3.2$$, there is a clear trend. However, the luminosity coding in Fig.\ref{fig:microlmc} suggests that this trend may be largely produced by the increase in convective velocity with increasing luminosity (Sect. \ref{results}). This figure displays a detection threshold of about $$10{\, {\rm km}\, {\rm s}^{-1}}$$ for the microturbulent velocities so in the following we restrict the comparison to $${\xi}\geq 10{\, {\rm km}\, {\rm s}^{-1}}$$.
\label{fig:microlmc} Logarithm of surface gravity versus microturbulent velocity $${\xi}$$ for the LMC early B-type stars studied by ; only stars with $${{v}\sin i}< 80{\, {\rm km}\, {\rm s}^{-1}}$$ are considered here. Different symbols refer to different luminosity intervals, as explained in the legend. The microturbulent velocities $${\xi}$$ have typical uncertainties of about $$\pm 5{\, {\rm km}\, {\rm s}^{-1}}$$. For the surface gravity measurements an uncertainty of $$\pm 0.1$$ should be considered.
In order to compare these observations to our model predictions, we evaluated the ratio of the kinetic energy in the form of gravity waves at the surface of the FeCZ to the kinetic energy of the surface velocity field, $$E_{\mathrm g}/E_{\rm s}$$ (Eq. \ref{ratio}), assuming $${v}_{\rm s} = 10{\, {\rm km}\, {\rm s}^{-1}}$$, in the HR diagram. Fig. \ref{fig:grwplot} shows two different iso-contours of this ratio; the stars of the LMC sample shown in Fig. \ref{fig:microlmc} are over plotted. Notably, all but one of the LMC stars of Fig. \ref{fig:grwplot} with $${\xi}> 10{\, {\rm km}\, {\rm s}^{-1}}$$ are found in that part of the HR diagram where it is energetically possible that the FeCZ-induced gravity waves trigger a significant surface velocity field ($${v}_{\rm s} > 10{\, {\rm km}\, {\rm s}^{-1}}$$). Thus, a physical connection of the FeCZ with the observed microturbulent velocities appears energetically possible. Moreover, that the iso-contour line of $$E_{\mathrm g}/E_{\rm s} = 1$$ in Fig. \ref{fig:grwplot} almost perfectly divides the observed sample in stars with significant ($${\xi}> 10{\, {\rm km}\, {\rm s}^{-1}}$$) and insignificant ($${\xi}< 10{\, {\rm km}\, {\rm s}^{-1}}$$) microturbulence is a further indication of such a physical connection.
\label{fig:grwplot} Values of the ratio $$E_{{\mathrm g}}/E_{\mathrm s}$$ of the kinetic energy in the form of gravity waves above the iron convection zone, to the kinetic energy of the surface velocity field, as a function of the location in the HR diagram (see color scale). This plot is based on evolutionary models between 5$${\,\mathrm{M}_\odot}$$ and 100$${\,\mathrm{M}_\odot}$$ for LMC metallicity. We estimated the ratio $$E_{{\mathrm g}}/E_{\mathrm s}$$ as in Eq. \ref{ratio}, using a value $${v}_s = 10{\, {\rm km}\, {\rm s}^{-1}}$$ for the surface velocity amplitude. Over-plotted as filled circles are stars which have photospheric microturbulent velocities $${\xi}$$ derived in a consistent way by . Here, we use only data for stars with an apparent rotational velocity of $${{v}\sin i}< 80 {\, {\rm km}\, {\rm s}^{-1}}$$. The uncertainty in the determination of $${\xi}$$ is typically $$\pm 5{\, {\rm km}\, {\rm s}^{-1}}$$, which justifies our choice of $${v}_s = 10{\, {\rm km}\, {\rm s}^{-1}}$$. Solid white lines are reference evolutionary tracks. The full drawn black line corresponds to the zero age main sequence.
Figure \ref{fig:hrdvel} shows the iso-contours in the HR diagram of the average convective velocity from our models in the upper layers of the iron convective zone, $${\langle{{v}_{c}}\rangle}$$, at the three considered metallicities. We have over plotted the microturbulent velocities derived by Again, we distinguish between sample stars with significant ($${\xi}> 10{\, {\rm km}\, {\rm s}^{-1}}$$; Group A) and insignificant ($${\xi}< 10{\, {\rm km}\, {\rm s}^{-1}}$$; Group B) microturbulent velocities. Comparing the plot for the LMC in Fig. \ref{fig:hrdvel} with Fig. \ref{fig:grwplot} identifies $${\langle{{v}_{c}}\rangle}\simeq 2.5{\, {\rm km}\, {\rm s}^{-1}}$$ as a critical convection velocity to be able to trigger microturbulence. Interestingly, the contour of $${\langle{{v}_{c}}\rangle}= 2.5{\, {\rm km}\, {\rm s}^{-1}}$$ in our stellar models forms an almost perfect dividing line between Groups A and B for all three considered metallicities.
\label{fig:hrdvel} Average convective velocity within 1.5 pressure scale heights of the upper border of the iron convection zone in our models, as function of the location in the HR diagram (see color scale), based on evolutionary models between 5$${\,\mathrm{M}_\odot}$$ and 100$${\,\mathrm{M}_\odot}$$ (white lines), for three metallicities corresponding to the Galaxy (top panel), the LMC (middle), and the SMC (bottom). The full drawn black line corresponds to the zero age main sequence. Over-plotted as filled circles are photospheric microturbulent velocities $${\xi}$$ derived in a consistent way for hot massive stars by and . Here, we use only data for stars with an apparent rotational velocity of $${{v}\sin i}< 80 {\, {\rm km}\, {\rm s}^{-1}}$$. The uncertainty in the determination of $${\xi}$$ is typically $$\pm 5{\, {\rm km}\, {\rm s}^{-1}}$$.
In fact, Fig. \ref{fig:hrdvel} provides evidence for all three trends found in the average convection velocity as function of stellar parameters (cf., Sect. \ref{results}) to be present also in the empirical data on microturbulent velocities. The LMC data shows that in the luminosity range $$4.5 < {\log\, L/ L_\odot \,}< 5.5$$ microturbulence is found only for $$T_{\rm eff} \le 25\,000\,$$K. The data for all three metallicities clearly suggests a key role of the luminosity, as the stars with $${\xi}> 10{\, {\rm km}\, {\rm s}^{-1}}$$ are the most luminous ones in each sub sample. And finally, the stars with high microturbulent velocities are all comfortably above our theoretical contour line corresponding to $${\langle{{v}_{c}}\rangle}= 2.5{\, {\rm km}\, {\rm s}^{-1}}$$. As the latter trends toward the upper right corner of the HR diagram for lower metallicity, the metallicity dependence is also confirmed by the empirical data.
Interestingly, they found significant microturbulent velocities (i.e., clearly above 5$${\, {\rm km}\, {\rm s}^{-1}}$$) in the mass range 7...11$${\,\mathrm{M}_\odot}$$ for stars with a relative age on the main sequence of $$t/\tau_{\rm MS} > 0.8$$, and in the range 12...19$${\,\mathrm{M}_\odot}$$ for $$t/\tau_{\rm MS} > 0.25$$, but only insignificant microturbulent velocities for younger or less massive stars. Again, these results appear to agree with Fig. \ref{fig:hrdvel} up to a remarkable quantitative level.
In summary, our comparison provides evidence for a physical connection of microturbulence in hot star photospheres with the existence and strength of a sub-photospheric FeCZ.
If microturbulence has a physical origin and is not just a fudge factor, the pressure and energy terms associated with such a velocity field should be included in the calculations of atmospheric models of massive stars. (citation not found: 1991ApJ...377L..33H) have investigated part of these effects by accounting for a constant microturbulent velocity in the pressure term only. They find that for stars with conspicuous $${\xi}$$ values (of 25$${\, {\rm km}\, {\rm s}^{-1}}$$) the inclusion of the pressure term leads to higher values of the surface gravity, which can reduce the mass discrepancy for O stars and O-type central stars of planetary nebula. A similar approach was also studied by Smith et al. (1998). The impact on gravity discussed by (citation not found: 1991ApJ...377L..33H) is likely an upper limit to the effect as, first, the $${\xi}$$ values are in most cases less than 25$${\, {\rm km}\, {\rm s}^{-1}}$$, and, second, a positive gradient in the atmospheric $${\xi}(r)$$ would decrease the pressure gradient due to microturbulence but, to date, the radial stratification of the microturbulent velocity in the atmospheres of hot massive stars has not been studied in detail. From a theoretical perspective, investigating $${\xi}(r)$$ requires hydrodynamic simulations of the stellar atmosphere, including the presence of sub-surface convection.
The mass discrepancy in massive stars is a well documented problem It is typically found that the difference between spectroscopic mass and evolutionary mass is most pronounced in supergiants. In main sequence stars it may not be present at all, but see Hunter et al. (2008). Given that microturbulent velocities are highest in supergiants (see Fig. \ref{fig:microlmc}) an empirical correlation between mass discrepancy and microturbulent velocity is to be expected and is shown in Fig. \ref{fig:discrepancy} using data analysed by Trundle et al. (2007) and Hunter et al. (2008). If indeed microturbulence is related to subsurface convection and supergiants have intrinsically higher microturbulent velocities than dwarfs (see Section \ref{results}) potentially part of the gradient in Fig. \ref{fig:discrepancy} may be explained by the effect discussed by Hubeny et al. (1991).
\label{fig:discrepancy} Values of the mass discrepancy (evolutionary mass divided by spectroscopic mass) as function of microturbulent velocity in the sample of B stars analysed by Trundle et al. (2007) and Hunter et al. (2008). Here, we use only data for stars with an apparent rotational velocity of $${{v}\sin i}< 80{\, {\rm km}\, {\rm s}^{-1}}$$.
## Non-radial pulsation
\label{pulsation}
Several classes of OB star models are found to be linearly unstable against non-radial pulsations, among which are the $$\beta~Cephei$$ stars and the slowly pulsating B stars (citation not found: 2001A&A...366..166D) Pamyatnykh, 1999). The key ingredient required for the pulsational instability is the iron opacity peak described in Sect. \ref{method}. As convection is not required to produce the pulsations in these models, it is not considered in detail as excitation mechanism (Dziembowski, 2008). It is conceivable that the convective excitation could modify the predicted pulsation spectrum and/or extend the instability region of certain linear instabilities. The convective kinetic energy flow into waves could be predominantly directed into those modes for which instability is predicted in the models. In certain parts of the HR diagram, one may thus suspect an intricate connection between the occurrence of a sub-photospheric iron convection zone and the properties of non-radial pulsations.
Non-radial pulsations have also been considered as the origin of various observed small scale (Fullerton 1996, (citation not found: 1997A&A...327..699F) and large scale phenomena components (Prinja 1988, Massa 1995, (citation not found: 1997A&A...327..281K) (citation not found: 2002A&A...388..587P) at the surface or in the wind of massive OB stars. Non-radial g-mode pulsations were also recently proposed as the origin of observable macroturbulence in massive B type stars (Aerts 2008). In Fig. \ref{fig:pulsationplot} we compare the regions where strange mode, g-mode, and p-mode pulsations are predicted to occur in the HR diagram with the region where our models predict a strong FeCZ. Pulsations appear to be almost ubiquitous when all types of variables are accounted for. The strange mode pulsators are predicted to cover the HR diagram at high luminosity, where we plotted only the predictions for the radial strange modes of (Kiriakidis 1993); high-order non-radial strange modes seem to be omnipresent as well for stars above 40$${\,\mathrm{M}_\odot}$$ or so (Glatzel 1996). Non-radial g-mode pulsators are predicted by (Saio 2006) in the B supergiant region. And radial and low order non-radial p-modes are predicted for the $$\beta\,$$Cephei regime by (Deng 2001) and by (Pamyatnykh 1999) and At lower metallicity, many of the predicted areas in the HR diagram are smaller (Kiriakidis 1993, Deng 2001) but the general picture is still incomplete.
Observationally, the classical $$\beta\,$$Cephei stars are concentrated in the region predicted by Deng & Xiong (Stankov 2005), while the B supergiant non-radial g-mode pulsators overlap with the prediction of (Saio 2006) but extend to an effective temperature of $$\sim 10\, 000\,$$K (Lefever 2007). Pulsations are also found for the most luminous stars (van Leeuwen 1998), but there is now no clear evidence for strange mode pulsators. Comparing the prediction for the FeCZ with that for pulsational instability (Fig.\ref{fig:pulsationplot}) shows two things. Firstly, the FeCZ-region is much larger than any region for a particular pulsational instability. Thus, distinguishing whether a certain observational feature is caused by a particular pulsational instability by the FeCZ might, in principle, be possible, since the area in the HR diagram where the latter occurs but the pulsational instability does not is relatively large. Secondly, some regions exist where (so far) no pulsations are predicted but the FeCZ in our models is strong, or where, vice versa, pulsations are predicted but the FeCZ is weak or absent.
Comparing Fig. \ref{fig:pulsationplot} with Fig. \ref{fig:hrdvel}, where we show the observations of microturbulence and the FeCZ predictions, it is unlikely that microturbulence is associated with a particular pulsational instability. Strong microturbulence is observed at too low a luminosity to be attributable to strange mode pulsations alone, while p-mode pulsators are found where microturbulence seems not to occur. Concerning the g-mode pulsators the situation is less clear. Fig. \ref{fig:pulsationplot} shows that, at solar metallicity, g-mode pulsations for post-main sequence stars are expected only in a rather narrow luminosity interval. Unfortunately, the five Galactic stars shown in Fig. \ref{fig:hrdvel} for which strong microturbulence is derived are all inside this luminosity range, so they cannot distinguish between a pulsational or FeCZ origin of microturbulence. However, looking at the LMC data, stars above the g-mode luminosity upper limit with microturbulence are found; whether or not corresponding stellar models are g-mode unstable is currently not known. A connection of microturbulence with non-radial pulsations is thus not impossible, but it is also not very likely.
Comparing Fig. \ref{fig:pulsationplot} with the discrete absorption components (DACs) found in 200 Galactic O stars above $$\sim 20{\,\mathrm{M}_\odot}$$ by Howarth et al. (1989) all the way to the zero age main sequence, seems to argue against non-radial pulsations as the origin of the DACs phenomenon (see also Sect. \ref{magnetic}).
\label{fig:pulsationplot} The plot shows regions of the HR diagram where pulsational instabilities are predicted, compared to our calculations for the occurrence of iron convection. The cloudy region marks the presence of iron sub-surface convection with $${\langle{{v}_{c}}\rangle}\geq 2.5{\, {\rm km}\, {\rm s}^{-1}}$$, while the dotted, blue line divides regions of the HR diagram where iron convection is present (above) from regions where it is absent (below). Different modes of instabilities are shown with different colors and different contour line styles, as explained in the legend. Evolutionary tracks between 7$${\,\mathrm{M}_\odot}$$ and 40$${\,\mathrm{M}_\odot}$$ are plotted as a reference. The straight, full drawn black line corresponds to the zero age main sequence. The Humphrey-Davidson limit is also plotted for reference (top-right corner).
## Wind clumping
\label{clumping} Observational evidence exists for stellar wind inhomogeneities on small and on large scales. While the latter will be discussed in Sect. \ref{magnetic}, here we consider only small scale wind structure, or wind clumping. In Sect. \ref{micro}, we discussed that waves produced by the FeCZ could lead to velocity fluctuations at the stellar surface. In order to induce wind clumping, those waves should induce density fluctuations at the stellar surface. Through the occurrence of porosity or shifts in the ionisation balance of the gas the mass-loss rate may be affected. For this to happen, the amplitude of the velocity fluctuations at the surface should be on the same order of the sound speed. Alternatively, the velocity fluctuations might directly affect the local mass-loss rate through the Doppler effect, if the amplitude of the velocity fluctuations is on the same order as the speed of the wind flow, which, at the base of the wind, is approximately the sound speed. As the sound speed at the surface in our massive main sequence models is on the order of a few times $$10{\, {\rm km}\, {\rm s}^{-1}}$$, we consider here those stellar models potentially capable to produce wind clumping for which the convective velocities in the upper part of the FeCZ $${\langle{{v}_{c}}\rangle}\geq 2.5{\, {\rm km}\, {\rm s}^{-1}}$$, as this allows energetically to have surface velocity amplitudes above $$\sim 10{\, {\rm km}\, {\rm s}^{-1}}$$ (cf. Sect. \ref{micro}).
Assuming the horizontal extent of the clumps to be comparable to the sub-photospheric pressure scale height $$H_{\rm p}$$, we may estimate the number of convective cells by dividing the stellar surface area by the surface area of a convective cell finding that it scales with ($$R/H_{\rm P})^2$$. For our main sequence O star models in the mass range 20-60 $${\,\mathrm{M}_\odot}$$, we find pressure scale heights in the range 0.04-0.24 $${\,{\rm R}_\odot}$$, corresponding to a total number of clumps in the range 6 $$\times 10^3- 6 \times 10^4$$. In principle, this might be testable through linear polarization variability measurements, which can probe wind asphericity at the very base of the wind (Davies et al., 2007).
Evidence has been accumulating that the winds of massive stars may be subject to small scale clumping. So far this is best documented for Wolf-Rayet (WR) stars, where line variability on time scales of minutes to hours is thought to constitute direct evidence of outflows that are clumped already in the acceleration zone near the base of the wind (Lépine et al., 1999). This clumping may be part of the explanation for the wealth of intricate detail seen in nebulae around WR stars (Grosdidier et al., 1998). Recently, the Of supergiants $$\zeta$$Pup (see also Eversberg et al., 1998) and HD93129A. The amplitude of the variation (at the 1-3% level) is similar as in WR stars supporting the notion that clumping is not restricted to WR stars.
Indeed, evidence that O star winds are clumped is given by, among others, behavior of the inner wind (inside about two stellar radii) relative to the clumping in the outer wind (beyond tens of stellar radii) of a large sample of supergiant and giant stars. They find that in stars that have strong winds, the inner wind is more strongly clumped than the outer wind, whereas those having weak winds have similar clumping properties in the inner and outer regions. Their analysis only allows for such a relative statement. In principle, for weak winds the outer part could be homogeneous. If so, weak winds are not clumped. In any case, strong winds - identified as such if H$$\alpha$$ is seen in emission - are clumped near the base of the wind. A measure of the degree of clumping is the clumping factor $$f_{\rm cl} =$$ values (citation not found: 2006A&A...454..625P).
Apparently, this type of radial behavior is not consistent with hydrodynamical predictions of the intrinsic, self-excited line-driven instability . Such models predict a lower clumping in the inner wind than the outer wind. Moreover, if there was any dependence on wind density predicted at all, optically thin winds should be more strongly clumped than optically thick winds (Owocki et al., 1999; Puls et al., 2006). Therefore, the findings on the radial clumping behavior in O stars may point to an additional excitation mechanism of wind structure.
Fig. \ref{fig:clumpvel} shows that the O stars investigated by (Puls 2006) populate the regime in the HR diagram in which our models predict the average convective velocity in the top part of the FeCZ to change from a few to over $$2.5{\, {\rm km}\, {\rm s}^{-1}}$$, indicating that surface velocity fluctuations on the order of the local sound speed are possible (cf. Sect. \ref{tclump}). Though the part of the HR diagram that is covered by the sample is limited ($$4.46 \lt \log\,T_{\rm eff} \lt 4.66$$; $$5.29 \lt \log\,L/{\,{\rm L}_\odot}\lt 6.26$$, the trend is such that stars with relatively strong clumping in the inner winds are in a regime where $${\langle{{v}_{c}}\rangle}$$ is higher. A correlation between clumping at the base of the wind and $${\langle{{v}_{c}}\rangle}$$, i.e., between wind clumping and the properties of the FeCZ, appears therefore possible. To further test the idea that the FeCZ produces wind clumping at the wind base for sufficiently luminous and cool stars it would be desirable to derive the radial clumping profiles for cooler (i.e. B-type) stars. If correct, such stars, both the ones with weak and strong winds, should have relatively strong clumping at the base of the wind.
\label{fig:clumpvel} Average convective velocity within 1.5 pressure scale heights of the upper border of the iron convection zone in our models, as function of the location in the HR diagram (see color scale), based on evolutionary models between 5$${\,\mathrm{M}_\odot}$$ and 120$${\,\mathrm{M}_\odot}$$ (white lines) at solar metallicity. The full drawn black line corresponds to the zero age main sequence. Over-plotted as filled circles are observations of the clumping factor $$f_{cl}^{in}$$ (see text for definition) in the winds of O stars, according to Puls et al. (2006). The data shown here corresponds to objects with well-constrained clumping parameters. Note the different luminosity range with respect to Fig. \ref{fig:hrdvel}.
To derive the spatial scale of the wind clumps from linear polarimetry has not yet been possible for main sequence OB stars. A limitation is that this technique requires very high signal-to-noise observations a more appropriate category of objects to test wind clump sizes, because of a combination of higher mass-loss rates, and lower wind velocities than for O stars polarization variability of P Cygni, the wind should consist of about $$\sim$$ 1000 clumps per wind flow-time ($${\tau_{fl}}\equiv {\,{\rm R}_\star}/{{v}_{\,\mathrm{\infty}}}$$). To see whether this observational result is compatible with sub-surface convection causing wind clumping, we considered the sub-surface convective regions of a massive star model with global properties similar to those of P Cygni (initial mass 60 $${\,\mathrm{M}_\odot}$$, $$\log(L/L_{\odot}$$ = 5.9, and $${\log\, T_{\rm }\,}$$ = 18000 K ). As a result of the lower gravity, the pressure scale height in the FeCZ in this model is about 4$${\,{\rm R}_\odot}$$, which is much bigger than in our O star models. Consequently, the same estimate for the number of clumps as done for the main sequence models in Sect. \ref{tclump} yields about 500 clumps per wind flow time, a number which is quite comparable to that derived for P Cygni observationally (about $$10^3$$ clumps per wind flow time).
Finally, Fullerton et al. (1996) have conducted a spectroscopic survey of O stars and observed intrinsic absorption line profile variability (LPVs) for about 77% of their sample. They report an increase of incidence and amplitude of variability with increasing stellar radius and luminosity, as well as no statistically significant line profile variability for dwarfs earlier than O7. While Fullerton et al. attempt to relate their findings to the predictions of strange-mode pulsation in O stars by (see their Fig. 13) with the occurrence of sub-surface convection as depicted in Fig. \ref{fig:hrdvel} indicates the possibility of a physical connection between line profile variability and sub-surface convection in O stars.
## Magnetic fields
\label{magnetic} In solar-type stars, surface convection zones modified by the stellar rotation are thought of being capable of producing a magnetic field through the so called $$\alpha\Omega$$-dynamo (Parker, 1975; Spiegel et al., 1980; Spiegel et al., 1992). The FeCZ in our massive main sequence stellar models has a spatial extent similar to the Solar convection zone, although its mass is much smaller, and OB stars are rapid rotators, so it is possible that a dynamo may also work in the envelopes of OB stars. If so, the magnetic field may be able to penetrate the radiatively stable layer above the FeCZ, and dynamically significant field strengths might be achievable. To this end, we follow the model by MacGregor et al. (2003) for the rise of buoyant magnetic flux tubes generated at the edge of the convective core of massive stars through their radiative envelope and apply this model to the FeCZ and the overlying radiative layer. The magnetic field strength $$B_0$$ in the iron convection zone is estimated assuming equipartition of kinetic energy density and magnetic energy density inside the convective layers:
$B_0 \simeq 2{v}_c\sqrt{\pi \rho},$
which, for our 60$${\,\mathrm{M}_\odot}$$ star at $$Z$$=0.02, reaches about $$B_0 \simeq 2700\,$$G inside the iron convective zone. The surface field $$B_{\rm s}$$ is then obtained by multiplying this number with the ratio of the surface density $$\rho_{\rm s}$$ and the density in the FeCZ $$\rho_0$$, i.e. $$B_{\rm s} \simeq B_0 \, \rho_{\rm s} / \rho_0 \simeq 60\,{\rm G}$$. Similarly, for the 20$${\,\mathrm{M}_\odot}$$ model at $$Z$$=0.02 we obtain $$B_0 \simeq 1400\,$$G and $$B_{\rm s}\simeq 10\,{\rm G}.$$ Although at the surface, the magnetic pressure in the flux tubes is only on the order of a few percent of the total pressure, it is on the same order as the gas pressure and could thus lead to considerable horizontal density differences. Compared to the situation envisioned by MacGregor et al. (2003), who found that the rise time of the flux tubes from the edge of the convective core to the stellar surface can be comparable to the main sequence life time (but see also MacDonald et al., 2004), the rise time of the flux tubes from the FeCZ to the surface is much shorter. And while the initial magnetic field strength at the edge of the convective core can be considerably higher than our values of $$B_0$$, the surface fields obtainable from the sub-surface convection zones are higher, due to the much lower density contrast between convection zone and surface in this case.
As a consequence, even though we are far from a detailed picture, it seems conceivable that the FeCZs in massive main sequence stars produce localized magnetic fields at their surface. The interaction of the stellar wind with the localized surface magnetic fields could enhance the rate at which the wind induces a loss of stellar angular momentum. Furthermore, co-rotating density patterns in the outflowing wind could be produced by these local magnetic spots.
Rotation may play an important role in the dynamo process, possibly resulting in the appearance of stronger fields at the surface for faster rotating stars. To estimate this effect, a dynamo model accounting for the differential rotation needs to be implemented in the stellar evolution calculations. This will be the discussed in a subsequent paper.
Surface magnetic fields have been linked to several observed phenomena in OB stars, e.g. discrete absorption components (DACs) in UV resonance lines which are thought to diagnose large scale coherent wind anisotropies (Cranmer et al., 1996; Lobel et al., 2008), or the less coherent line profile variability mentioned above (Fullerton et al., 1996; Fullerton et al., 1997). Also non-thermal X-ray emission of OB main sequence stars has been proposed to relate to surface magnetic fields (Babel et al., 1997; ud-Doula et al., 2002).
A connection of the FeCZ in massive stars with the phenomena mentioned above has not yet been considered. However, such a connection becomes testable through our results. While in our comparison to observed microturbulence presented above we discussed when sub-surface convection may lead to detectable surface velocity fluctuations, the presence of surface magnetic fields may simply depend on whether an FeCZ is present in the star or not. Looking at Fig. \ref{fig:hrdvel}, we see that in our models the FeCZ is absent for luminosities below about $$10^{3.2}{\,{\rm L}_\odot}$$, $$10^{3.9}{\,{\rm L}_\odot}$$, and $$10^{4.2}{\,{\rm L}_\odot}$$ for the Galaxy, LMC and SMC, respectively. If DACs or line profile variability were produced by magnetic flux tubes generated in the FeCZ, those phenomena would not be expected for OB stars below those luminosities. in a large Galactic sample, with $${\log\, L/ L_\odot \,}> 4.5$$ and with effective temperatures as high as the zero-age main sequence values of stars above $$\sim 20{\,\mathrm{M}_\odot}$$. Since those stars are well above the luminosity threshold for the occurrence of the iron convection at Galactic metallicity, these observations do not exclude DACs being due to FeCZ induced B-fields. Also, all eleven early B supergiants with DACs in the sample of Prinja et al. (2002) are predicted to have strong FeCZ by our results. Notably, between about $$20{\,\mathrm{M}_\odot}$$ and $$40{\,\mathrm{M}_\odot}$$, stars close to the zero-age main sequence are not predicted to be pulsationally unstable (cf. Fig. \ref{fig:pulsationplot}), which may be in conflict with pulsations as the origin for DACs.
It may be interesting to briefly compare the expectation from surface magnetic fields produced via the FeCZ to that for fields produced by other means. Surface fields produced by convective cores mentioned above, even if for massive stars the buoyant rise of magnetic fields from the convective core seems to be unlikely (MacDonald et al., 2004). In contrast to the sub-surface FeCZ, convective cores are prevalent in all stars above about 1.2$${\,\mathrm{M}_\odot}$$. It has been found that the longer lifetime of stars of lower mass may favor the drift of fields produced in the core to the surface (Schuessler et al., 1978; MacGregor et al., 2003). Therefore, the expected trend is opposite to that found for fields produced by the FeCZ, where surface fields may occur only for stars above a critical mass (or luminosity), and stronger fields are found for more massive stars.
On the other hand, in contrast to fields from the FeCZ, magnetic flux tubes produced in the core may carry CNO-processed material to the surface. This might thus constitute a mechanism to explaining nitrogen enrichment in slowly rotating early B stars (Morel et al., 2006; Morel et al., 2008; Hunter et al., 2008). Strong fossil magnetic fields are thought to persist in only a fraction of massive stars and may lead to, among other phenomena, highly anomalous surface chemical compositions, wind confinement, and variable X-ray emission (Wade et al., 2006; Townsend et al., 2005). Those strong features can clearly not be produced by fields originating from the FeCZs.
Finally, magnetic fields produced in differentially rotating massive stars by the Spruit-Taylor dynamo (Spruit, 2002) may transport angular momentum and chemical species (Heger et al., 2005). These fields are predominantly of toroidal geometry and would quickly decay near the stellar surface, and are thus not thought to lead to observable fields at the stellar surface (but see also Mullan et al. (2005)).
# Concluding remarks
Hot luminous stars show a variety of phenomena at their photosphere and in their winds which still lack a clear physical interpretation at this time. Among these phenomena are photospheric turbulence, spectral line variability (DACs and LPVs; see Sect. \ref{comparison}), wind clumping, variable or constant non-thermal X-ray and radio emission, chemical composition anomalies, and intrinsic slow rotation. In the previous section, we argued that the iron convection zone could be responsible for various of these phenomena.
We proposed in Sect. \ref{micro} that a physical connection may exist between microturbulence in hot star atmospheres and a sub-surface FeCZ. The strength of the FeCZ is predicted to increase with increasing metallicity $$Z$$, decreasing effective temperature $$T$$ and increasing luminosity $$L$$ (Sect. \ref{results}), and all three predicted trends are reflected in the observational data. This suggests that microturbulence corresponds to a physical motion of the gas in hot star atmospheres. This motion may then be connected to wind clumping (Sect. \ref{clumping}), since the empirical microturbulent velocities are comparable to the local sound speed at the stellar surface. In order to verify such a picture, multi-dimensional calculations of the FeCZ and the radiative layers above, including the stellar atmosphere, are required — similar to the recent generation of atmosphere models for cool stars
In Sect. \ref{magnetic}, we proposed that the FeCZ in hot stars might also produce localized surface magnetic fields, in Galactic stars for luminosities above $$\sim 10^{3.2}{\,{\rm L}_\odot}$$. This could explain the occurrence of DACs (discrete absorption components in UV absorption lines), also in very hot main sequence stars for which pulsational instabilities are not predicted. We further argued that there may be regions of the upper HR diagram for which the presence of the FeCZ influences, or even excites, non-radial stellar pulsations (Sect. \ref{pulsation}).
The FeCZ could also turn out to directly affect the evolution of hot massive stars. If it induces wind clumping, it may alter the stellar wind mass-loss rate. Such a change would also influence the angular momentum loss. In addition magnetic fields produced by the iron convection zone could lead to an enhanced rate of angular momentum loss. These effects become weaker for lower metallicity, where the FeCZ is less prominent or absent (see Sect. \ref{results}).
Finally, we note that the consequences of the FeCZ might be strongest in Wolf-Rayet stars. These stars are so hot that the iron opacity peak, and therefore the FeCZ, can be directly at the stellar surface, or — to be more precise — at the sonic point of the wind flow (Heger et al., 1996). This may relate to the very strong clumping found observationally in Wolf-Rayet winds (Lépine et al., 1999; Marchenko et al., 2006), and may be required for an understanding of the very high mass-loss rates of Wolf-Rayet stars (Eichler et al., 1995; Heger et al., 1996).
Acknowledgements
The authors would like to thank Myron Smith, Alex Fullerton, Derk Massa and the members of the VLT-FLAMES consortium. MC wants to thank the STScI for kind hospitality and the Leids Kerkhoven-Bosscha Fonds for financial support. S.-C. Y. is supported by the DOE SciDAC Program (DOE DE-FC02-06ER41438).
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70. I. Hunter, I. Brott, D. J. Lennon, N. Langer, P. L. Dufton, C. Trundle, S. J. Smartt, A. de Koter, C. J. Evans, R. S. I. Ryans. The VLT FLAMES Survey of Massive Stars: Rotation and Nitrogen Enrichment as the Key to Understanding Massive Star Evolution. 676, L29-L32 (2008). Link | 2019-05-23 06:49:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8050817251205444, "perplexity": 1939.2665562759962}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257156.50/warc/CC-MAIN-20190523063645-20190523085645-00179.warc.gz"} |
https://studyadda.com/question-bank/force-and-laws-of-motion_q45/2404/210935 | • # question_answer A bullet of mass $20\,\,g$ is fired from a rifle of $8\,\,kg$ with an initial velocity of$100\,\,m\,\,{{s}^{-1}}$. Find the final velocity of the recoil of the rifle. A) $-0.25\,\,m\,\,{{s}^{-1}}$ B) $2.5\,\,m\,\,{{s}^{-1}}$ C) $25\,\,m\,\,{{s}^{-1}}$ D) $250\,\,m\,\,{{s}^{-1}}$
Initial momentum$=0$ Final momentum$=(0.02\times 100)+8\times v$ According to the law of conservation of momentum, $(0.02\times 100)+8v=0$, $8v=-2$ $v=-\frac{1}{4}m{{s}^{-1}}=-0.25\,\,m\,\,{{s}^{-1}}$ | 2020-08-04 17:38:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8420803546905518, "perplexity": 1977.0229221130553}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735881.90/warc/CC-MAIN-20200804161521-20200804191521-00126.warc.gz"} |
http://math-mprf.org/journal/articles/id1293/ | A Note on the Convergence of Probability Functions of Markov Chains
#### J. Baczynski, M.D. Fragoso
2013, v.19, Issue 1, 141-148
ABSTRACT
Let $P(t)\equiv(p_{ij}(t))_{i,j\in \mathbb{N}}$ stands for a generalized transition matrix function of a continuous-time homogeneous Markov chain with an infinite countable state space and denote $o_{ij} (h) := p_{ij}(h) - p_{ij}(0) - \dot{p}_{ij}(0)h$. In this note we are given conditions to have the convergence $o_{ij} (h)/ h \rightarrow 0$ as $h\rightarrow 0$ performing uniformly with respect to $i$ for each $j$. We also provide some examples where this convergence do not hold. In addition, we identify a liaison between these issues and the uniqueness of solutions of the Kolmogorov forward equation.
Keywords: Markov chains,Kolmogorov forward equation,probability transition matrix function | 2020-06-03 15:50:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8893112540245056, "perplexity": 383.87455100260183}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347435238.60/warc/CC-MAIN-20200603144014-20200603174014-00301.warc.gz"} |
https://zbmath.org/?q=an:0909.58005 | ## Curvature $$h$$-principles.(English)Zbl 0909.58005
This paper derives some properties of the spaces of all metrics on a differentiable manifold $$M$$ which satisfy curvature bounds. In particular, the spaces $$\text{Ric}^{<\alpha}(M)$$ and $$S^{<\alpha}(M)$$ of metrics on $$M$$ with, respectively, Ricci curvature less than $$\alpha$$ and scalar curvature less than $$\alpha$$ for $$\alpha\in\mathbb{R}$$ are investigated. Theorem A says that these spaces are contractible, while Theorem B is an approximation result that these spaces are dense in the space of all metrics in the $$C^0$$ and the Hausdorff topologies. Thus, any metric is $$C^0$$ close to a metric of arbitrarily negative Ricci curvature. Theorems C and D are local versions of these results.
Reviewer: P.Michor (Wien)
### MSC:
58D17 Manifolds of metrics (especially Riemannian) 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
### Keywords:
space of metrics; differentiable manifold; curvature bounds
Full Text: | 2023-03-26 16:02:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.568919837474823, "perplexity": 576.3193493433637}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945473.69/warc/CC-MAIN-20230326142035-20230326172035-00113.warc.gz"} |
https://chemistry.stackexchange.com/questions/4977/how-can-the-equilibrium-shift-while-kc-remains-constant?noredirect=1 | # How can the equilibrium shift, while Kc remains constant?
I understand that when more $\ce{ H+}$ ions are added, the reaction shifts in reverse. So I've understood that this is known as having the equilibrium shift to the left, toward the reactants.
What confuses me is why $K_\mathrm c$ doesn't change. If the equilibrium shifts to the left, I suppose that must mean more reactants are formed in relation to the products, so $K_\mathrm c$ would decrease.
But the answer key says that $K_\mathrm c$ remains unchanged. This is coherent with what I've been taught, but I don't understand how the equilibrium can change yet have $K_\mathrm c$ remain constant.
I'm just afraid I've got some of the theory mixed up, so I wanted to get some clarity. Could someone explain this please?
Kc is related to the ratio of reactants to products AT EQUILIBRIUM.
If the reaction is currently at equilibrium, and you add more products then the reaction is now out of equilibrium and the reverse reaction will happen until it is back in equilibrium.
I don't like the wording of "equilibrium shifts to the left" myself, I would say that reverse reactions occurs to restore equilibrium. But Kc doesn't change based on reactants/products concentrations since its the ratio at equilibrium. Kc will normally depend on temperature though.
Based on the options you have, Kc not changing and the reverse reaction occurring, the closest answer would be D. (If you take Equilibrium shifting to the left to mean the reaction goes in that direction.)
• Agreed. $K_c$ is the equilibrium constant. It does not do us much good if it changes when you add stuff! – Ben Norris May 13 '13 at 11:12
• Agreed. One should recognize that when more products are added, the new concentration of products then decreases by reaction, the concentration of the reactants increase, and the equilibrium ratio is unchanged. – Paul J. Gans May 25 '13 at 21:04
To add to Nick's great answer, I believe you are confusing $K_c$, the equilibrium constant, with $Q_c$, the reaction quotient.
The reaction quotient is defined as the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants, under any conditions or relative amounts of the various species.
$$Q_\mathrm c =\dfrac{[\ce{CrO4^{2-}}]^2[\ce{H+}]}{[\ce{Cr2O7^{2-}}][\ce{H2O}]}$$
The equilibrium constant describes which combinations of reactants and products constitute equilibrium, and there exists an infinite set of such combinations at a given temperature. However, they all must have $Q_\mathrm c = K_\mathrm c$. The difference in the formula for $K_\mathrm c$ below (from the formula for $Q$ above) is the use of equilibrium concentrations. $$K_\mathrm c= Q_\mathrm {c,eq} =\frac{[\ce{CrO4^{2-}}]^2_{\text{eq}}[\ce{H+}]_{\text{eq}}}{[\ce{Cr2O7^{2-}}]_{\text{eq}}[\ce{H2O}]_{\text{eq}}}$$
Let's take an example, where $K_\mathrm c=1$. There are infinitely many concentration combinations that we could have that would work. Three of them are shown below. $$1. \ \ \ [\ce{CrO4^{2-}}]=[\ce{H+}]=[\ce{Cr2O7^{2-}}]=[\ce{H2O}]=\pu{1 M}$$ $$2. \ \ \ [\ce{CrO4^{2-}}]=\pu{4 M};\ \ \ \ [\ce{Cr2O7^{2-}}]=[\ce{H2O}]=\pu{2 M}; \ \ \ \ [\ce{H+}]=\pu{1 M}$$ $$3. \ \ \ [\ce{CrO4^{2-}}]=[\ce{Cr2O7^{2-}}]=\pu{1 M};\ \ \ \ [\ce{H2O}]=[\ce{H+}]=\pu{0.987 M}$$
If we take the first case, where all concentrations are equal, and increase the concentration of $\ce{H+}$ by $\pu{0.5 M}$, now we have the following: $$[\ce{CrO4^{2-}}]=[\ce{Cr2O7^{2-}}]=[\ce{H2O}]=1\ M; \ \ \ \ [\ce{H+}]=\pu{1.5 M}$$
If we calculate $Q_c$, we find that $Q_c=1.5$. Thus, the system is no longer at equilibrium because $Q_c\neq K_c$.
$$Q_c=\frac{(\pu{1 M})^2(\pu{1.5 M})}{(\pu{1 M})(\pu{1 M})}=1.5$$
The system will shift towards the reactants (since $Q_\mathrm c>K_\mathrm c$) to reestablish equilibrium. A little algebra, and we can figure out just how much. The product concentrations will decrease and the reactant concentrations will increase, each by $nx$, where $x$ is the concentration change and $n$ is the stoichiometric coefficient.
$$[\ce{CrO4^{2-}}]_{\text{eq}}=1-2x\ M; \ \ \ \ [\ce{H+}]_{\text{eq}}=1.5-x\ M\ \ \ \ [\ce{Cr2O7^{2-}}]_{\text{eq}}=[\ce{H2O}]_{\text{eq}}=1+x\ M$$
$$K_\mathrm c=\frac{(1-2x\ M)^2(1.5-x\ M)}{(1+x\ M)(1+x\ M)}=1$$ $$K_\mathrm c=\frac{(1-4x+4x^2)(1.5-x)}{(1+2x+x^2)}=\frac{(1.5-7x+10x^2-16x^3)}{(1+2x+x^2)}=1$$ $$(1+2x+x^2)>0\ \ \text{for}\ \ x>0$$ $$1.5-7x+10x^2-16x^3=1+2x+x^2$$ $$0=16x^3-9x^2+9x-0.5$$
The above expression has three roots, two of which are imaginary. The real root is $x=0.0586353$. Thus, the new equilibrium concentrations are:
$$[\ce{CrO4^{2-}}]_{\text{eq}}=0.883\ M; \ \ \ \ [\ce{H+}]_{\text{eq}}=1.441\ M\ \ \ \ [\ce{Cr2O7^{2-}}]_{\text{eq}}=[\ce{H2O}]_{\text{eq}}=1.059\ M$$ | 2019-04-23 21:58:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8398850560188293, "perplexity": 392.8627989203535}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578613888.70/warc/CC-MAIN-20190423214818-20190424000818-00276.warc.gz"} |
https://demo7.dspace.org/items/a848a634-b5a2-4318-9ad3-5bbd9dce8ab5 | ## Statistical Mechanics of Logarithmic REM: Duality, Freezing and Extreme Value Statistics of $1/f$ Noises generated by Gaussian Free Fields
##### Authors
Fyodorov, Yan V
Doussal, Pierre Le
Rosso, Alberto
##### Description
We compute the distribution of the partition functions for a class of one-dimensional Random Energy Models (REM) with logarithmically correlated random potential, above and at the glass transition temperature. The random potential sequences represent various versions of the 1/f noise generated by sampling the two-dimensional Gaussian Free Field (2dGFF) along various planar curves. Our method extends the recent analysis of Fyodorov Bouchaud from the circular case to an interval and is based on an analytical continuation of the Selberg integral. In particular, we unveil a {\it duality relation} satisfied by the suitable generating function of free energy cumulants in the high-temperature phase. It reinforces the freezing scenario hypothesis for that generating function, from which we derive the distribution of extrema for the 2dGFF on the $[0,1]$ interval. We provide numerical checks of the circular and the interval case and discuss universality and various extensions. Relevance to the distribution of length of a segment in Liouville quantum gravity is noted.
Comment: 25 pages, 12 figures Published version. Misprint corrected, references and note added
##### Keywords
Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics | 2022-12-08 13:51:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6548473834991455, "perplexity": 1272.2157838665548}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711336.41/warc/CC-MAIN-20221208114402-20221208144402-00400.warc.gz"} |
https://www.meritnation.com/ask-answer/question/solution-p-has-a-ph-of-13-solution-q-has-a-ph-of-6-and-solut/study-of-acids-bases-and-salts/12659303 | # Solution P has a pH of 13. Solution Q has a pH of 6 and solution R has a pH of 2. Which solution: (a) will liberate ammonia from ammonium sulphate on heating? (b) is a strong acid? (c) contains molecules as well as ions?
The solution is as follows:
1. The solution of P when heated with ammonium sulphate liberates ammonia. The reaction is as follows:
(NH4)2SO4(aq) + BOH (aq) $\underset{∆}{\to }$ 2 NH3(g) + BSO4(aq) + H2O
2. As solution R has pH 2, it is the strongest acid.
3. Solution Q is slightly acidic, thus it has only molecules and ions.
• 1
What are you looking for? | 2022-06-29 13:15:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40190768241882324, "perplexity": 5297.27748067754}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103639050.36/warc/CC-MAIN-20220629115352-20220629145352-00665.warc.gz"} |
http://mathoverflow.net/questions/8560/how-much-choice-is-needed-to-show-that-formally-real-fields-can-be-ordered/8591 | # How much choice is needed to show that formally real fields can be ordered?
Background: a field is formally real if -1 is not a sum of squares of elements in that field. An ordering on a field is a linear ordering which is (in exactly the sense that you would guess if you haven't seen this before) compatible with the field operations.
It is immediate to see that a field which can be ordered is formally real. The converse is a famous result of Artin-Schreier. (For a graceful exposition, see Jacobson's Basic Algebra. For a not particularly graceful exposition which is freely available online, see http://math.uga.edu/~pete/realspectrum.pdf.)
The proof is neither long nor difficult, but it appeals to Zorn's Lemma. One suspects that the reliance on the Axiom of Choice is crucial, because a field which is formally real can have many different orderings (loc. cit. gives a brief introduction to the real spectrum of a field, the set of all orderings endowed with a certain topology making it a compact, totally disconnected topological space).
Can someone give a reference or an argument that AC is required in the technical sense (i.e., there are models of ZF in which it is false)? Does assuming that formally real fields can be ordered recover some weak version of AC, e.g. that any Boolean algebra has a prime ideal? (Or, what seems less likely to me, is it equivalent to AC?)
-
This is equivalent (in ZF) to the Boolean Prime Ideal Theorem (which is equivalent to the Ultrafilter Lemma).
Reference: R. Berr, F. Delon, J. Schmid, Ordered fields and the ultrafilter theorem, Fund Math 159 (1999), 231-241. online
-
Well, that's perfect, thanks. It's amazing to me that this paper is so recent. – Pete L. Clark Dec 11 '09 at 20:11
Yes, one would have thought that all standard theorems that invoke Zorn's Lemma would have been "done" long ago. – Konrad Swanepoel Dec 11 '09 at 20:35
At the very least, it implies the following:
Let $f: A \to B$ be a map of sets where every fiber has cardinality $2$. Then there is a section of $f$.
Proof: Let $V$ be the $\mathbb{R}$-vector space spanned by the elements of $A$, subject to the relation $a_1 = - a_2$ whenever $f(a_1)=f(a_2)$. Let $S$ be $\mathrm{Sym}(V)$ and $K$ be $\mathrm{Frac}(S)$.
Then $K$ is formally real (any proposed sum of squares only uses finitely many elements of $A$, so we can reduce to the case of a finite dimensional vector space, where this is obvious). But to choose an ordering, we need to decide which element of each fiber of $f$ will be positive and which will be negative. The positive elements form a section.
- | 2014-11-26 18:46:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.860541045665741, "perplexity": 221.33668233253206}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931007324.75/warc/CC-MAIN-20141125155647-00091-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://www.doubtnut.com/ncert-solutions/class-11-maths-chapter-15-statistics-1 | # Statistics NCERT Solutions : Class 11 Maths
## NCERT Solutions for Class 11 Maths : Statistics
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### NCERT Class 11 | STATISTICS | Miscellaneous Exercise | Question No. 04
Given that bar x is the mean and sigma^2 is the variance of n observations x_1x_2 , ..., x_n . Prove that the mean and variance of the observations a x_1,""""a x_2 , a x_3,""""dot""""dot""""dot"""",""a x_n are a bar x and a^2sigma^2 ,
### NCERT Class 11 | STATISTICS | Miscellaneous Exercise | Question No. 05
The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. One rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases. (i) If wrong item is omitted (ii) If it is replaced by 12.
### NCERT Class 11 | STATISTICS | Miscellaneous Exercise | Question No. 06
The mean and standard deviation of marks obtained by 50 students of a class in three subject, Mathematics, Physics and Chemistry are given below: Subject Mathematics Physics Chemistry Mean 42 32 40.9 Standard 12 15 20 Deviation Which of the three subjects shows the highest variability in marks and which shows the lowest?
### NCERT Class 11 | STATISTICS | Solved Examples | Question No. 12
Calculate mean, Variance and Standard Deviation for the following distribution.
### NCERT Class 11 | STATISTICS | Solved Examples | Question No. 13
Two plants A and B of a factory show following results about the number of workers and the wages paid to them. A B No. of workers 5000 6000 Average monthly wages Rs 2500 Rs 2500 Variance of distribution 81 100 of wages In which plant, A or B is there greater variability in individual wages? | 2021-06-19 16:12:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5667130947113037, "perplexity": 3581.3806648616624}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487648373.45/warc/CC-MAIN-20210619142022-20210619172022-00554.warc.gz"} |
https://socratic.org/questions/how-do-you-write-the-first-five-terms-of-the-arithmetic-sequence-given-a-1-200-a | # How do you write the first five terms of the arithmetic sequence given a_1=200, a_(k+1)=a_k-10 and find the common difference and write the nth term of the sequence as a function of n?
Jun 8, 2017
First ffive terms are $\left\{200 , 190 , 180 , 170 , 160\right\}$. Common difference is $10$ and ${n}^{t h}$ term ${a}_{n} = 210 - 10 n$
#### Explanation:
As ${a}_{k + 1} = {a}_{k} - 10$, this means that
each succeeding term is $10$ less than the previous term.
Hence $d$ the common difference is given by $d = - 10$
Now first term ${a}_{1}$ is $200$ and as ${n}^{t h}$ term is given by $a + \left(n - 1\right) d = 200 + \left(n - 1\right) \times \left(- 10\right) = 200 - 10 n + 10 = 210 - 10 n$
and hence ${a}_{2} = {a}_{1} - 10 = 200 - 10 = 190$
${a}_{3} = {a}_{2} - 10 = 190 - 10 = 180$
${a}_{4} = {a}_{3} - 10 = 180 - 10 = 170$
qnd ${a}_{5} = {a}_{4} - 10 = 170 - 10 = 160$
Hence first ffive terms are $\left\{200 , 190 , 180 , 170 , 160\right\}$. | 2020-08-06 22:19:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 17, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7211201786994934, "perplexity": 426.5508816763191}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737039.58/warc/CC-MAIN-20200806210649-20200807000649-00397.warc.gz"} |
https://fepujyvynexigyvy.wrcch2016.com/the-construction-of-spin-eigenfunctions-book-9965jq.php | Popular
# The Construction of Spin Eigenfunctions an Exercise Book by Ruben Pauncz
Written in English
The current volume is a very practical book, consisting primarily of many examples and exercises. In particular, The Construction of Spin Eigenfunctions presents all aspects connected with the construction of spin eigenfunctions, and their relationship with many-electron antisymmetric wave functions. This book treats new aligorithms in a way that no previous books have.
The Construction of Spin Eigenfunctions opens with a brief theoretical introduction.
Due to the increasing importance of spin eigenfunctions in quantum chemistry, Dr. Pauncz has followed up with two helpful chapters on the symmetric group and its representations. The author has also calculated matrix elements of the Hamiltonian using spin eigenfunctions. Dr. Pauncz wraps up the book with an important new technique: the spin-coupled valence bond method.
This book should be very useful to graduate students working in the field of molecular quantum mechanics. It also could be used as a text for a one-semester graduate course in physics or in chemistry.
Edition Notes
## Book details
The Physical Object ID Numbers Statement by Ruben Pauncz Format [electronic resource] : Pagination 1 online resource (204 pages) Number of Pages 204 Open Library OL27026894M ISBN 10 146154291X ISBN 10 9781461542919 OCLC/WorldCa 840285491
Since the publication of Spin Eigenfunctions, nearly 20 years ago there have been many interesting developments in the subject; there are quite a few new algorithms for the construction of spin eigenfunctions. Moreover the use of the spin-coupled valence bond method showed the importance of using different constructions for the spin by: In Chapters 2–5 we have discussed the different methods for the construction of spin eigenfunctions.
In Chapters 6 and 7, we presented the basic Author: Ruben Pauncz. The aim of this book is to give a comprehensive treatment of the different methods for the construction of spin eigenfunctions and to show their interrelations. The ultimate goal is the construction of an antisymmetric many-electron wave function that Brand: Springer US.
Since the publication of Spin Eigenfunctions, nearly 20 years ago there have been many interesting developments in the subject; there are quite a few new algorithms for the construction of spin eigenfunctions.
Moreover the use of the spin-coupled valence bond method showed the importance of using different constructions for the spin : Springer US. The aim of this book is to give a comprehensive treatment of the different methods for the construction of spin eigenfunctions and to show their interrelations.
The ultimate goal is the construction of an antisymmetric many-electron wave function that has both spatial and spin parts and the calculation of the matrix elements of the Hamiltonian Cited by: The current volume is a very practical book, consisting primarily of many examples and exercises.
In particular, The Construction of Spin Eigenfunctions presents all aspects connected with the construction of spin eigenfunctions, and their relationship with. Since the publication of Spin Eigenfunctions, nearly 20 years ago there The Construction of Spin Eigenfunctions book been many interesting developments in the subject; there are quite a few new algorithms for the construction of spin eigenfunctions.
Moreover the use of the spin-coupled valence bond method showed the importance of using different constructions for the spin functions. The aim of this book is to give a comprehensive treatment of the different methods for the construction of spin eigenfunctions and to show their interrelations.
The ultimate goal is the construction of an antisymmetric many-electron wave function that has both spatial and spin parts and the calculation of the matrix elements of the Hamiltonian. Note: If you're looking for a free download links of The Construction of Spin Eigenfunctions: An Exercise Book Pdf, epub, docx and torrent then this site is not for you.
only do ebook promotions online The Construction of Spin Eigenfunctions book we does not distribute any free download of ebook on this site. from book The Construction of Spin Eigenfunctions (pp) The Construction of Spin Eigenfunctions.
Chapter January The current volume is a very practical book, consisting primarily of many examples and exercises. In particular, The Construction of Spin Eigenfunctions presents all aspects connected with the construction of spin eigenfunctions, and their relationship with many-electron antisymmetric wave functions.
This book treats new aligorithms in a way. This is the first book to provide comprehensive treatment of the use of the symmetric group in quantum chemical structures of atoms, molecules, and solids. It begins with the conventional Slater determinant approach and proceeds to the basics of the symmetric group and the construction of spin eigenfunctions.
The aim of this book is to give a comprehensive treatment of the different methods for the construction of spin eigenfunctions and to show their interrelations. The ultimate goal is the construction of an antisymmetric many-electron wave function that has both spatial and spin parts and the calculation of the matrix elements of the Hamiltonian over the total wave function.
The. It begins with the conventional Slater determinant approach and proceeds to the basics of the symmetric group and the construction of spin eigenfunctions. The heart of the book is in the chapter dealing with spin-free quantum chemistry showing the great interpretation value of this method.
The last three chapters include the unitary group. This is the first book to provide comprehensive treatment of the use of the symmetric group in quantum chemical structures of atoms, molecules, and solids.
It begins with the conventional Slater determinant approach and proceeds to the basics of the symmetric group and the construction of spin by: The Construction of Spin Eigenfunctions, An Excercise Book, Kluwer Academic / Plenum Publishers New York (). Important Contributions: The spectra of linearly condensed aromatic hydrocarbons on the basis of the elliptical rotator model.
Pauncz: free download. Ebooks library. On-line books store on Z-Library | B–OK. Download books for free. Find books. This option allows users to search by Publication, Volume and Page Selecting this option will search the current publication in context. Book Search tips Selecting this option will search all publications across the Scitation platform Selecting this option will search all publications for the Publisher/Society in contextCited by: This option allows users to search by Publication, Volume and Page Selecting this option will search the current publication in context.
Selecting this option will search all publications across the Scitation platform Selecting this option will search all Cited by: An explicit construction of the eigenfunctions {e 1,e N} of energy operator E B v cannot be obtained in the general case. A finite dimension approximation E B v, n of E B v must be introduced and the eigenfunctions {e 1 ne N n} of E B,n (associated with the N highest eigenvalues) constitute the approximation of {e 1 ,e N}.
This. In quantum chemistry, a configuration state function (CSF), is a symmetry-adapted linear combination of Slater determinants.A CSF must not be confused with a general, one configuration gives rise to several CSFs; all have the same total quantum numbers for spin and spatial parts but differ in their intermediate couplings.
It is possible to construct CSFs by using two-electron spin eigenfunctions denoted as geminal spin functions as the building blocks, as proposed by Serber. In Serber construction, the CSFs of (k + 2)-spin systems are constructed by adding the geminal spin functions to the CSFs of k -spin systems, and four recurrence equations in the Cited by: 2.
solids. The whole book skilfully combines the dual functions of guide to the territory and archive of useful formulae. I G Main Varied functions Spin Eigenfunctions - Construction and Use Ruben Pauncz New York: Plenum xv + pp price £ This is a scholarly book which represents a distinct addition to the literature on many-electron.
Spin states which are eigenfunctions of the total $$S^2 \text{ and } S_z$$ can be formed by using angular momentum coupling methods or the explicit construction methods detailed in. In summary, proper spin eigenfunctions must be constructed from antisymmetric (i.e., determinental) wavefunctions as demonstrated above because the total S 2 and total S z remain valid symmetry operators for many-electron systems.
Technion - Israel Institute of Technology Technion City, HaifaIsrael LIAT - [email protected] Phone: () / Book Description. Quantum Mechanics I: The Fundamentals provides a graduate-level account of the behavior of matter and energy at the molecular, atomic, nuclear, and sub-nuclear levels.
It covers basic concepts, mathematical formalism, and applications to physically important systems. Pauncz, The Construction of Spin Eigenfunctions: An Exercise Book, New York: Kluwer Academic/Plenum Publishers, [15] V. Fock, “Bemerkung zur Quantelung des Harmonischen Oszillators im Magnetfeld,” Zeitschrift fur Physics, 47(), pp.
[16]. Then the book "Ruben Pauncz: The construction of spin eigenfunctions - An exercise book" (it's a Quantum Chemistry book) writes in section on p. 77 that the representation matrix of the conjugate representation $\alpha'$ is given by. Eigenfunctions of energy. Book Author(s): Trygve Helgaker theory of spin tensor operators for angular momentum in quantum mechanics and develops a useful set of tools for the construction and classification of states and operators with definite spin symmetry properties.
This chapter shows how a basis of spin eigenfunctions can set up by taking linear Author: Trygve Helgaker, Poul Jørgensen, Jeppe Olsen. Angular Momentum 1 Angular momentum in Quantum Mechanics The construction of these eigenfunctions by solving the differential main reason for this is that many particles have an intrinsic angular momentum (called spin) that is without a classical analogue, but nonetheless can be described File Size: KB.
Shankar, Principles of Quantum Mechanics, Plenum, New York, Class Procedures Class will meet for lectures two days per week at the scheduled time. CHAPTER 16 The Spin 1. Intrinsic Angular Momentum and the Polarization of ip waves 2. The Quantum Mechanical Description of the Spin 3.
Spin and Rotations 4. The Spin Operators, Pauli Matrices, and Spin Angular Momentum 5. Quantum Dynamics of a Spin System 6. Density Matrix and Spin Polarization 7. The construction of a statistical model for eigenfunctions of the Ising model in transverse and longitudinal elds is discussed in detail for the chaotic case.
When the number of spins is large, each wave function coe cient has the Gaussian distribution with zero mean and the variance calculated from the rst two moments of the Hamiltonian. April, THE NATURE OF THE CHEMICAL BOND 4. The main resonance terms for a single electron-pair bond are those involving only one eigenfunction from each atom.
Of two eigenfunctions with the same defiendence on r, the one the larger value in the bond direction will give rise to the stronger bond, and for a given eigenfunction the bond will tend to be formed in File Size: 1MB.
The subject matter of this book has been presented in a graduate course in the Technion. The author is obliged to the graduate students Averbukh Vitali, Gokhberg Kirill, and Narevicius Edvardas for many helpful comments.
Books > Chemistry. The Construction Of. This book offers a concise introduction to the angular momentum, one of the most fundamental quantities in all of quantum mechanics.
Beginning with the quantization of angular momentum, spin angular momentum, and the orbital angular momentum, the author goes on to discuss the Clebsch-Gordan coefficients for a two-component system. After developing the. It is convenient to define so called spin-angular functions using the Pauli two-component formalism: $${\cal Y}_{l\,m}^{j=l\pm 1/2}\equiv {\cal Y}_{l\,m}^{\pm}$$ \ref{} These functions are eigenfunctions of the total angular momentum for spin one-half particles, just as the spherical harmonics are eigenfunctions of the orbital angular momentum.
The important changes quantum mechanics has undergone in recent years are reflected in this new approach for students. A strong narrative, and over worked problems lead the student from experiment, through general principles of the theory, to modern applications.
Stepping through results allows students to gain a thorough understanding. In the context of the quantum harmonic oscillator, one reinterprets the ladder operators as creation and annihilation operators, adding or subtracting fixed quanta of energy to the oscillator system.
Creation/annihilation operators are different for bosons (integer spin) and fermions (half-integer spin). This is because their wavefunctions have different symmetry properties.Our goal is to apply the principles of quantum mechanics and electronic structure theory to address problems in physical, organic, inorganic, and biological chemistry.
High performance computers are used to solve the complex equations describing the system of interest, yielding predictions of structures, bonding, energetics, reactivity, and other physical properties.
97694 views Thursday, December 3, 2020 | 2021-10-25 06:43:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6848024725914001, "perplexity": 1000.1593459238503}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587655.10/warc/CC-MAIN-20211025061300-20211025091300-00212.warc.gz"} |
https://proofwiki.org/wiki/Metric_Space_is_Weakly_Countably_Compact_iff_Countably_Compact | # Metric Space is Weakly Countably Compact iff Countably Compact
## Theorem
Let $M = \left({A, d}\right)$ be a metric space.
Then $M$ is weakly countably compact if and only if $M$ is countably compact.
## Proof
The result follows from $T_1$ Space is Weakly Countably Compact iff Countably Compact.
$\blacksquare$ | 2019-08-19 01:49:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9967080354690552, "perplexity": 226.3052077630528}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314638.49/warc/CC-MAIN-20190819011034-20190819033034-00266.warc.gz"} |
https://math.stackexchange.com/questions/1070764/set-with-distinct-subset-sums | # Set with distinct subset sums
The problem is as follows : Given a set A with distinct positive integer elements, prove that there always exists another set B consisting of positive integers, s.t.,
1. The size of B is less than or equal to the size of A
2. Each element of A can be represented as the sum of some subset of B
3. The subset sums of all the elements of B are distinct
It's obvious that if we take all powers of 2 less than the largest element in A, we can construct B and the subset sums are distinct. But this doesn't necessarily meet condition 1. Can someone give a construction for this?
• Algorithmically you could start with $B=A$ and remove elements until 3. is met, making sure that 2. always holds. Some work would be required that if 2. holds and $\sum B_1 = \sum B_2$ for some $B_1\ne B_2\subset B$ that we can remove (or replace) at least one element from either $B_1$ or $B_2$ such that 1. is not violated. WLOG we may assume that $B_1\cap B_2 = \emptyset$ – AlexR Dec 16 '14 at 16:36
• The problem is the removal/replacement strategy. How do we replace? For e.g., A = 1,2,3,4 , set B = 1,2,3,4. Now since 4 = 1+3, we remove 4. But the only solution for this case is B = 1,2,4. So, removing 4 is not an option. – ZeroG Dec 16 '14 at 16:56
• Are all the elements of $A$ non-negative? – JimmyK4542 Dec 17 '14 at 7:44
• Yes. All elements of A are strictly positive. Let me add that to the problem statement. – ZeroG Dec 17 '14 at 9:19
• does $B$ also have to be of positive integers? – Jorge Fernández Hidalgo Dec 17 '14 at 18:08
The proof shall be by strong induction over the number of elements of $A$.
So we assume it has been proven for sets with $n$ elements or less.
now notice if we can prove it when the gcd of all the $n$ integers is $1$ we can use this to prove it when the numbers are not relatively prime by dividing all the numbers by the gcd, producing the appropriate generator set and then multiplying the elements of that set by the gcd.
Take elements $x_1,x_2\dots x_n$ and notice at least one of them is odd. Let $x_j$ be the smallest odd one. We define the new set $Y$ constructed as follows:
If $x_i$ is even add $\frac{x_i}{2}$
If $x_i$ is odd add $\frac{x_i-x_j}{2}$
Don't add $x_j$.
This set has less than $n$ elements, so we may use the inductive hypothesis. (Notice this new set may have a gcd different to $1$. But it doesn't matter, since our inductive hypothesis is the strong version of the result).
We construct an appropriate generating set $T'$ for this new set using the inductive hypothesis.
We propose the set $2T'\cup\{x_j\}$ as the desired set.
1. Clearly it satisfies it has $n$ elements or less.
2. If $x_i$ is even we could have created $\frac{x_i}{2}$ from $T'$ so we can do $x_i$ from $2T'$. If $x_i$ is odd we could have created $\frac{x_i-x_j}{2}$ from $T$, so we can create $x_i-x_j$ from $2T$ and $x_i$ from $2T\cup\{x_j\}$
3. The sums containing $x_j$ are all odd, the sums not containing $x_j$ are all even, so there is no overlap. The fact there are no two equal not containg $x_j$ is directly inherited from $T$ being as it is. If two sums containing $x_j$ where equal they would be equal after taking away $x_j$ from each set. Thus all subsets have different sums.
Hence we have proved it for when $A$ has $n$ elements with gcd equal to $1$. Using the method describe above we use this to prove it when $A$ has $n$ elements in general, completing the induction.
• The only niggle(albeit small) I see is that the smaller set that you construct might have repeated elements. For, e.g., $\frac{x_i}{2}$ could be equal to $\frac{x_i-x_j}{2}$. But we can prove that each element occurs at most twice and we can remove repeated elements. Also, the generator for odd and even will have exactly one different element and that would be $x_j$. – ZeroG Dec 20 '14 at 10:23
• Yeah, but the repeated elements are not in the generating set, so it doesn't matter. – Jorge Fernández Hidalgo Dec 20 '14 at 14:27 | 2019-05-19 09:07:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8441186547279358, "perplexity": 151.08467888958663}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232254731.5/warc/CC-MAIN-20190519081519-20190519103519-00051.warc.gz"} |
https://tex.stackexchange.com/questions/471627/pgfgantt-spans-width | # pgfgantt spans width
I would like to draw Gantt chart, where:
is generated by:
\documentclass{article}
\usepackage{pgfgantt}
\begin{document}
\begin{ganttchart}{1}{12}
\gantttitle{2011}{12} \\
\gantttitlelist{1,...,12}{1} \\
\ganttgroup{Group 1}{1}{7} \\
\ganttmilestone{Milestone}{7} \ganttnewline
\end{ganttchart}
\end{document}
I would like it span all the width. So I played with \begin{ganttchart}[x unit=10mm]{1}{12} and got:
How to make pgfgantt span all i.e. \textwidth?
Using \usepackage[showframe]{geometry} to check the position helps, but is there a side effect? Looks like chart moves a bit to the top left.
• One option is to create a separate file, then include the PDF as graphics with \includegraphics[width=\textwidth]{...pdf} – pushpen.paul Jan 24 at 11:52
• I believe you meant span (not spam). Please edit your question.... – pushpen.paul Jan 24 at 11:53
• Also, do you mean \textwidth or something else? – pushpen.paul Jan 24 at 11:57
• It might be difficult to do it automatically, because you need to reserve some space for the labels and pgfgantt does not yet know the size of the labels when the title bar is generated. So it may be easier just to manually play around with the x unit value (for each of your charts if you have more than one). – Marijn Jan 24 at 15:24
• If you add \usepackage[showframe]{geometry} to the preamble of your document, you will realize that you are almost there. I would like to argue that a small distance at the right end is better than overshooting. – user121799 Jan 24 at 15:52 | 2019-10-20 14:51:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6830862760543823, "perplexity": 1380.7901701609892}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986710773.68/warc/CC-MAIN-20191020132840-20191020160340-00130.warc.gz"} |
https://tex.stackexchange.com/questions/215369/tcolorbox-line-numbers | # tcolorbox line numbers
I am trying to make a generic environment to use for all my boxes in my document. I want all my boxes to have line numbers. I can only get this to work some of the time. I don't get line numbers when I use minted content in the box.
\documentclass{article}
\usepackage{lineno}
\usepackage{tcolorbox}
\tcbuselibrary{minted, breakable, skins}
\definecolor{darkgray}{gray}{0.15}
\definecolor{gray}{gray}{0.30}
\newenvironment{mylisting}[1]
{
\begin{tcolorbox}[
title=#1,
listing only,
breakable,
colframe=gray,
colbacktitle=gray,
colback=darkgray,
enhanced,
left=0.3125in,
overlay={
\begin{tcbclipinterior}
\fill[gray] (frame.south west) rectangle ([xshift=0.25in]frame.north west);
\end{tcbclipinterior}}]
\begin{internallinenumbers}
}
{
\end{internallinenumbers}
\end{tcolorbox}
}
\begin{document}
\begin{mylisting}{Test Line Numbers}
Test
the
line
numbers.
\end{mylisting}
\begin{mylisting}{Test Minted Line Numbers}
\mint{cpp}|hi|
\end{mylisting}
\end{document}
The first usage works, but the second usage with the \mint command does not. What am I missing?
PS - I'm aware that minted can do its own line numbering, but I wanted to handle line numbering in a centralized way, and not everything in a listing will be minted, so I figured the line numbering could be decoupled from minted.
• I think that this is purely about interaction between lineno and minted (independent of tcolorbox). I just made some tests and it seems that internallinenumbers has no effect on any minted content. Maybe, someone know how to change that (?) – Thomas F. Sturm Dec 4 '14 at 16:04
• Interesting. I didn't notice that. Good catch. I wonder if it is just minted, or other similar things too. – Aaron Wright Dec 5 '14 at 3:29
• @egreg No, I don't think so. lineno and minted are not compatible as far as I know. – Thomas F. Sturm Sep 15 '15 at 11:07 | 2019-08-17 12:39:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8006410598754883, "perplexity": 2010.1840894618988}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027313259.30/warc/CC-MAIN-20190817123129-20190817145129-00263.warc.gz"} |
https://zxi.mytechroad.com/blog/string/leetcode-2269-find-the-k-beauty-of-a-number/ | The k-beauty of an integer num is defined as the number of substrings of num when it is read as a string that meet the following conditions:
• It has a length of k.
• It is a divisor of num.
Given integers num and k, return the k-beauty of num.
Note:
• 0 is not a divisor of any value.
substring is a contiguous sequence of characters in a string.
Example 1:
Input: num = 240, k = 2
Output: 2
Explanation: The following are the substrings of num of length k:
- "24" from "240": 24 is a divisor of 240.
- "40" from "240": 40 is a divisor of 240.
Therefore, the k-beauty is 2.
Example 2:
Input: num = 430043, k = 2
Output: 2
Explanation: The following are the substrings of num of length k:
- "43" from "430043": 43 is a divisor of 430043.
- "30" from "430043": 30 is not a divisor of 430043.
- "00" from "430043": 0 is not a divisor of 430043.
- "04" from "430043": 4 is not a divisor of 430043.
- "43" from "430043": 43 is a divisor of 430043.
Therefore, the k-beauty is 2.
Constraints:
• 1 <= num <= 109
• 1 <= k <= num.length (taking num as a string)
## Solution: Substring
Note: the substring can be 0, e.g. “00”
Time complexity: O((l-k)*k)
Space complexity: O(l + k) -> O(1)
## C++
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huahualeetcode | 2023-02-08 01:29:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29359203577041626, "perplexity": 4175.237819630295}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500664.85/warc/CC-MAIN-20230207233330-20230208023330-00797.warc.gz"} |
https://www.physicsforums.com/threads/calculus-help.121354/ | # Calculus help
1. May 18, 2006
### Taryn
Hey I have just been tryin to understand limits
I am having a particular problem with these few questions if any1 could please help me understand them and solve them I would be much appreciative
Evaluate the following limits
lim (sin(x))/x
x-> infinity
lim (1-cosx)/x
x->0
I have trouble mainly coz I dunno how to start the problem!
2. May 18, 2006
### jdog
I think the trick for the first limit problem is to recognize that sin is bounded between -1 and 1. So, what happens to a number between -1 and 1 if you divide it by x and let x go to infinity?
I think the second problem may be a little trickier. Have you heard of L'Hopital's Rule? It says that the limit of one function over another function at a point where they both equal zero, is equal to the ratio of the derivitives of those functions evaluated at that limit. In other words the limit of the second problem is the same as the limit of:
sinx/1 at x = 0
If you don't know calculus, or didn't understand my lame explanation of L'Hopital's Rule, you can always graph it and see that it clearly aproaches zero. Does anyone else know a better way?
3. May 18, 2006
### VietDao29
$$\lim_{x \rightarrow \infty} \frac{\sin x}{x}$$
When x increases without bound, the denominator also increases without bound right, while the numerator only oscillates between -1, and 1 right? i.e the whole expression will tend to 0. No?
To prove that, you can use the Squeeze Theorem. Can you go from here? :)
--------------
For your second problem, when you have to evaluate the limit of some expression like this (i.e it contains some trignonometric functions over polynomials, ...), you will often need to use:
$$\lim_{x \rightarrow 0} \frac{\sin x}{x} = 1$$
But in the problem, the numerator is 1 - cos x, not sin x, so we should do some manipulations to change 1 - cos x to sin x. We can use the Power Reduction Formulae to do so, i.e:
$$\sin ^ 2 x = \frac{1 - \cos (2x)}{2}$$
So applying the formula here, we have:
$$\lim_{x \rightarrow 0} \frac{1 - \cos x}{x} = \lim_{x \rightarrow 0} \frac{2 \sin ^ 2 \left( \frac{x}{2} \right)}{x} = ...$$
Can you go from here? :)
Last edited: May 18, 2006
4. May 18, 2006
### Taryn
thanks, that was helpful, our lecturer is really hard to understand in both tutorials and lectures, he doesn't explain or tell us about the rules... I am still a little coonfused on the second one... but I should be able to figure it out after I read up on L'Hopital's rule! Thanks again!
5. May 18, 2006
### Taryn
thats was so helpful, thankyou so much, I understand what I have to do in both of the problems now, much appreciated!
6. May 19, 2006
### sila kara
I dont know if you learn the L'Hopital's rule. The best way to learn the limit is learning the L'Hopital's rule. Then learn that rule as soon as possible:)
7. May 19, 2006
### daveb
In calculus you tend to learn limits before you learn derivatives, so L'Hospital's is generally not adequate when one first encounters limits.
8. May 20, 2006
### arildno
You CAN'T use L'Hopital's rule (differentiating numerator and denominator separately) to "prove" the limit of sin(x)/x, because that limit is needed* in the differentiation of sin(x).
In order to prove the limit, you could either start with a rigorous definition of sin(x) as, say, a solution of a boundary value problem, or you could make a geometric proof of the limit in question.
I'll leave the rigorous construction to, for example, HallsofIvy, and present a geometric approach.
Consider a circle of unit circle with the centre at the origin, and draw a ray with angle x (measured in radians!) to the horizontal axis.
Construct the two right-angled triangles with base&height (cos(x),sin(x)) and (1,tan(x)), respectively.
The area of the circular section is x/2, whereas the least triangle has area 1/2*sin(x)*cos(x); the largest 1/2*tan(x)
Thus, we have the inequality, for non-zero x:
$$\frac{\sin(x)\cos(x)}{2}<\frac{x}{2}<\frac{\tan(x)}{2}\to\cos(x)<\frac{x}{\sin(x)}<\frac{1}{\cos(x)}$$
Assuming cos(x) to be continuous, and taking the limit as x goes to 0, we get:
$$\lim_{x\to{0}}\frac{x}{\sin(x)}=1\to\lim_{x\to{0}}\frac{\sin(x)}{x}=1$$
*Or, at the very least, needed in the most typical limiting expression..
Last edited: May 20, 2006
9. May 21, 2006
### dx
No, you can differentiate sin(x) without knowing the limit sin(x)/x. As long as x is real, sin(x) has a simple geometric interpretation and it is easy to visually differentiate it.
10. May 21, 2006
### arildno
First of all, did you at all bother to read my asterisked caveat?
Secondly, please continue from the DEFINITION of the derivative:
$$\frac{d}{dx}\sin(x)=\lim_{h\to{0}}\frac{\sin(x+h)-\sin(x)}{h}$$
[
11. May 21, 2006
### matt grime
But no one was asked to work out the limit as x tends to zero of sin(x)/x, arildno, though they were asked to effectively work out the derivative of cos(x) at zero. Is there a similar way for doing it for cos rather than sin?
12. May 21, 2006
### arildno
Oh dear..I misread the first one.
However:
Considering the second of the posted limit problems (lim of (1-cos(x))/x),
then it is, IMO, easiest to transform that to lim of (sin(x)/x)^2*(x/(1+cos(x)), but there are probably other ways as well. | 2017-04-23 19:56:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8541470766067505, "perplexity": 716.4004942356956}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118743.41/warc/CC-MAIN-20170423031158-00022-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://cdsweb.cern.ch/collection/ALICE%20Theses?ln=sv | # ALICE Theses
Senast inlagda poster:
2016-09-23
16:15
Measurement of electrons from heavy-flavour hadron decays in p-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV using TPC and EMCal detectors with ALICE at LHC / Jahnke, Cristiane Heavy-ion collisions are a powerful tool to study hot and dense QCD matter, the so-called Quark Gluon Plasma (QGP) [...] CERN-THESIS-2016-106 - 256 p.
Fulltext - U. Sao Paulo server
2016-09-08
11:09
Analysis of D$^0$ and D$^{*+}$-meson production in pp and p-Pb collisions with ALICE at the LHC / Wilkinson, Jeremy This thesis presents measurements of D-meson production in the central barrel of the ALICE detector in pp and p-Pb collisions [...] CERN-THESIS-2016-099 - 160 p.
Fulltext
2016-08-24
16:51
Study of Quark-Gluon Plasma by Measuring the Upsilon Production in p-Pb and Pb-Pb Collisions at Forward Rapidity with ALICE at the LHC / Khan, Palash CERN-THESIS-2015-356 -
Fulltext
2016-08-24
14:12
Photoproduction of $J/\psi$ in ultra-peripheral p-Pb and Pb-Pb collisions with the ALICE detector at the LHC / Adam, Jaroslav The physics of ultra-peripheral collisions is introduced in the first part along with the fundamental concepts of several theoretical models [...] CERN-THESIS-2016-092 - 192 p.
Fulltext
2016-08-23
11:25
Многоканальная система сбора временной и амплитудной информации детектора ТО эксперимента Alice (ЦЕРН, LHC) / Kondratiev, Natalia По общепринятой в настоящее время гипотезе наша Вселенная была создана более 12 миллиардов лет назад во время так называемого «Big Bang» -«Большого Взрыва» [1] [...]
server - Only 1st page
2016-08-11
16:56
Multihadron production in High-Energy collisions and forward rapidity measurement of inclusive photons in Pb+Pb collisions at √sNN = 2.76 TeV in ALICE experiment at LHC / Mishra, Aditya Nath CERN-THESIS-2016-087. -
2016-07-22
21:22
Direct Photon Anisotropy and the Time Evolution of the Quark-Gluon Plasma / Browning, Tyler Allen Historically, the thermal photon inverse slope parameter has been interpreted as the thermalization temperature of the QGP [...] CERN-THESIS-2016-078 - Purdue University : ProQuest Information & Learning, 2016-07-22. - 150 p.
Fulltext
2016-07-08
20:03
Study of $\boldsymbol{J/\psi}$ production dependence with the charged particle multiplicity in p-Pb collisions at $\boldsymbol{\sqrt{s_{_{\mathrm{NN}}}}} =$ 5.02 TeV and pp collisions at $\boldsymbol{\sqrt{s}} =$ 8 TeV with the ALICE experiment at the LHC / Martin Blanco, Javier A suppression of the $J/\psi$ production was found in Pb-Pb collisions at $\sqrt{s_{_{\mathrm{NN}}}} =$ 2.76 TeV, providing further evidence of the formation of a deconfined medium in ultra-relativistic heavy-ion collisions, the so-called Quark-Gluon Plasma [...] CERN-THESIS-2016-070 - 309 p.
Fulltext
2016-06-17
12:00
Elliptic flow at different collision stages / Dubla, Andrea CERN-THESIS-2016-054 - 202 p.
Fulltext
2016-06-14
18:24
$\Lambda/\rm K^0_s$ associated with a jet in central Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV measured with the ALICE detector / Richert, Tuva Ora Herenui In high energy heavy ion collisions, the QCD matter undergoes a phase transition to a hot and dense strongly coupled Quark Gluon Plasma, where quarks and gluons are deconfined in a volume of nuclear dimensions [...] CERN-THESIS-2016-051 - 209 p.
Fulltext | 2016-09-24 20:54:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9698896408081055, "perplexity": 10369.243433566475}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738659496.36/warc/CC-MAIN-20160924173739-00119-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://ehomework-helper.com/mathematics/question16926193 | , 26.06.2020 20:01, shsbbdDnsgs3913
# What is the ratio 28 : 4 in it's simplest form?
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You are looking for your first credit card. you plan to use this credit card only for emergencies and to pay the credit card balance in full each month. which credit card feature is most important? a. no annual fee b. low apr c. generous rewards program d. no balance transfer fee select the best answer from the choices provided
In the next 10 month, colin wants to save $900 for his vacation. he plans to save$75 each of the first 8 months. how much must he save each of the last 2 months in order to meet his goal if he saves the same amount each month ? | 2021-07-31 08:16:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22822967171669006, "perplexity": 2841.317027648181}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154085.58/warc/CC-MAIN-20210731074335-20210731104335-00184.warc.gz"} |
https://dash.harvard.edu/handle/1/11108709 | # Moduli of Galois Representations
Title: Moduli of Galois Representations Author: Wang Erickson, Carl William Citation: Wang Erickson, Carl William. 2013. Moduli of Galois Representations. Doctoral dissertation, Harvard University. Full Text & Related Files: WangErickson_gsas.harvard_0084L_10933.pdf (3.130Mb; PDF) Abstract: The theme of this thesis is the study of moduli stacks of representations of an associative algebra, with an eye toward continuous representations of profinite groups such as Galois groups. The central object of study is the geometry of the map $$\bar{\psi}$$ from the moduli stack of representations to the moduli scheme of pseudorepresentations. The first chapter culminates in showing that $$\bar{\psi}$$ is very close to an adequate moduli space of Alper. In particular, $$\bar{\psi}$$ is universally closed. The second chapter refines the results of the first chapter. In particular, certain projective subschemes of the fibers of $$\bar{\psi}$$ are identified, generalizing a suggestion of Kisin. The third chapter applies the results of the first two chapters to moduli groupoids of continuous representations and pseudorepresentations of profinite algebras. In this context, the moduli formal scheme of pseudorepresentations is semi-local, with each component Spf $$B_\bar{D}$$ being the moduli of deformations of a given finite field-valued pseudorepresentation $$\bar{D}$$. Under a finiteness condition, it is shown that $$\bar{\psi}$$ is not only formally finite type over Spf $$B_\bar{D}$$, but arises as the completion of a finite type algebraic stack over Spec $$B_\bar{D}$$. Finally, the fourth chapter extends Kisin's construction of loci of coefficient spaces for p-adic local Galois representations cut out by conditions from p-adic Hodge theory. The result is extended from the case that the coefficient ring is a complete Noetherian local ring to the more general case that the coefficient space is a Noetherian formal scheme. Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:11108709 Downloads of this work: | 2018-07-20 08:23:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7128859162330627, "perplexity": 585.7504563192847}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591575.49/warc/CC-MAIN-20180720080634-20180720100634-00527.warc.gz"} |
http://us.battle.net/forums/en/wow/1011637/index?page=135 | # World’s End Tavern: Role-play and Fan Fiction
Apr 11, 2013 What is a good realm for beginner rpers? I am bored of raiding pvp is alright what is a good realm for beginner rpers for alliance?Sèthos9
Apr 11, 2013 So im new to rp ...and Ive found myself watching videos of Argent Dawn EU. It looks badass to say the least. So Im looking for an Alliance Military RP guild, that does campaigns, events, etc,. Anyone got something?Hõlyrack3
Apr 11, 2013 Need help with RP name I'm transferring my blood elf paladin to an RP realm. My friend is making our back story, were both blood elf males, brothers. His name is Kalthamir Dawnchaser I need help with a name, last name will be Dawnchaser :)Nelgru4
Apr 11, 2013 warcraft videos hella high sifting through machinima crap on youtube when i came across these and thought i'd share if anyone else cares about warcraft 2 still, cheers! :D will share more if i find cheers you dwarvren bastards! http://www.youtube.com/watch?v=ujNmYFWZ8q8 http://www.youtube.com/watch?v=ToYtfytyMKQ http://www.youtube.com/watch?v=iZc2VOBG9OUButcherr0
Apr 10, 2013 Lore/Lorebreaking vs Opinions This is something that occurs quite a lot on this forum - if an idea is disliked it's stated as breaking lore by those who dislike it while others say it's fine or something similar. This isn't going to be a terribly long post but it's going to hopefully be informative. Lore/Lorebreaking implies that there are hard facts backing up the reason something can or cannot be done. Thus we know, for a fact, Sylvanas is an elf and current ruler of Lordaeron. Thus we know, for a fact, that Varian Wrynn is not an orc in disguise and did not brutally murder Tiffin before blaming it on the populace. If you're going to claim something is a fact, then you need to be prepared to back up your claim with lore supporting your claim. Even if you're 'opposing' an idea, you're proposing that it's breaking lore and are then relying on us, not to disprove you, but to prove you right - which then causes the other side in the argument to scurry off and sift through lore that proves them wrong and - quite honestly - I wouldn't do that and I'm sure most wouldn't. I don't want to lose my argument, so even if I'm wrong when I say 'Thrall is dead and C'thun is the new Warchief' you're not bothering to cite and back-up claims that I'm wrong. That's an extreme example with no grey area to debate, so a more realistic example: 'Edwin VanCleef also had a son who has taken up his father's cause and is working in the shadows and with more cunning than Vanessa.' No one can prove this right, no one can prove this wrong. Vanessa never even mentions what happened to her mother, for all we know this could be true. Those who claim it breaks lore need to bring up proof beyond 'I don't like it, so it's breaking lore'. They need to find arguments that specifically state Edwin could not have had a son. If you want to argue that it breaks lore, not etiquette but lore, then you have to back-up your claims. Now that that is settled, opinions. An opinion is a person's own personal view of a subject. An opinion is not a fact. An opinion is a personal belief. An opinion can, theoretically, be backed by facts but it is not by itself a fact. You can have the opinion that it's wrong for Sylvanas to rule Lordaeron, but the fact is she does currently rule Lordaeron. You can have the opinion that Deathwing isn't dead, but the fact is that he was blasted into next week by some chump named Go'el. You can have the opinion that it's breaking lore to say a gnome cannot be a hunter, but that doesn't mean anything because there's no statement that says gnomes cannot be hunters (inb4 'they can't select it in game' - doesn't mean a gnome can't be RP'd as a hunter). My hope is this post will educate the denizens of the WET forums on the difference and nip long arguments in the bud before they degenerate to ad hominem attacks.Iraelius71
Apr 10, 2013 Alternate reproduction methods? [Gross and educational, tread with caution.] So I'm writing terrible wow fiction and a point of contention I am exploring is a conflict between three siblings over continuing family lineage (responsibility to family), repopulating their nearly exterminated race (social responsibility, albeit in a hedonistic society) verses personal preferences (being a mom conflicts with the sisters' lifestyles, they expect their brother to take responsibility) and sexuality (their brother developed a fancy for another cast member of the same gender over many chapters). One solution, (the most fair solution) would be for one of the sisters to act as a surrogate, sharing the same mitochondrial dna with their brother and all. His partner would be giving material as the father. Of course, that would mean one of the sisters would have to have relations with their brother's partner, something no one would be happy with. (Thankfully no party would actually go through with it, the squick from such a proposal would be hilarious though.) In the reality these conflicts are handled via artificial insemination. But is that plausible in this setting? This made me research. This is what I found: 1780 the first successful recorded procedure was done on animals (britannica). 1785 was the first recorded successful procedure in a human by a Scottish surgeon John Hunter (britannica, internet gives exact year). There are supposedly records stating that this was attempted in the 1400s with King Henry IV of Castile and his wife Juana. Not sure if real or bs. /skeptic There are several methods of AI currently but the crude method of taking the genetic material fresh from one subject and putting it in the other (using a "conception cap") is still practiced. (wikipedia) Said material can survive naturally outside a body for up to a few hours under the right circumstances (mayo clinic). tl;dr: EEEEEeeeew! Given the data gathered I am under the impression that AI's existence in the Warcraft universe is plausible. I think it would be ok for the resident scholar to imply that other methods exist. It's likely not widely in practice among beings of sentience unless there are major fertility problems, though may be used on livestock. It probably isn't widely known and may be a sort of a wild rumor among non-scientific/educated circles. I'd like feedback from other brains though. /nodLeiah0
Apr 10, 2013 As These Words are Bandied About... ... I thought it best to create a thread so people can understand what these words/phrases/what have you are actually intended to mean. Mary Sue - There is the male counterpart to this phrase, Gary Stu or Marty Stu or whatever you want, and this is one of the most common things people cry out when they see a character. Most of the time they aren't saying the right term for the character. A Mary Sue type character is one who fulfills the very definition of the word perfection - this character is so perfect as to be unbelievable. Now maybe the character has flaws? Even the flaws are perfect and do not detract from the character but make the character more perfect than they already were. When this character appears this is when the term Mary Sue should apply. Special Snowflake - http://tvtropes.org/pmwiki/pmwiki.php/Main/SpecialSnowflakeSyndrome this is the best definition I can find on the term and it gives a good example. A special snowflake character isn't necessarily a bad thing, nor is it a good thing, it's entirely left open to the interpretation of those playing the game. The best this can be summed up, for WoW, would be 'characters being roleplayed out of their racial norms'. So every engineering loving Night Elf, earth-hating dwarf, naturalist gnome, skinny pandaren, etc. etc. would be considered a 'special snowflake'. God Moding - Quite simply, this isn't making your character powerful, it is controlling the actions of other players without their prior consent. Metagaming - Using out of character knowledge to influence in character actions. Basically this means, using any knowledge your character shouldn't have in roleplay. So if their character was abused as a child, causing illusions to demonstrate the abuse would be metagaming. Now if your character found a way to draw that information out of their character and then made the illusions, it'd be completely different. Lore-breaking - This means taking established Blizzard lore and changing it. The keyword in that sentence is established. Anything that Blizzard has not touched on, this meaning grey areas in lore, is best tread with caution but is free game. Utilizing the grey area in RP does not break lore. Saying that orcs are in fact orks from Warhammer 40k would be lore-breaking, as it is established that they are not. Saying you are a Balrog is lore-breaking, as this is not Middle Earth. Roleplaying a character who is a member of nobility of any of the Seven Kingdoms? Not lore-breaking. Giving your character braces? Not lore-breaking. I believe that covers the most misused terms, there are a few others but these are the five that have the greatest occurrence rate on the WET forums.Iraelius22
Apr 10, 2013 Eric and the Dread Gazebo I was blathering about in the horde RP channel here on AD and the players in the channel didn't know the story of Eric and the Dread Gazebo. I figured I'd share it here as some of you young whippersnappers might not know it either. (PS: Get off my lawn.) Source: http://www.netfunny.com/rhf/jokes/98/Jul/gazebo.html ...Leiah1
Apr 10, 2013 CRZ and Server type query, Can anyone tell me why All rp-pvp servers arent in the same CRZ?Papilon8
Apr 10, 2013 Bag of Runes [GHI] I like to run plots from time to time and sometimes I like surprises. I might have a basic idea of what I want to do but have no idea about the details. I used to use runes and tarot cards to make these decisions but they're in a box somewhere so I made a very simple crude tool in Gryphonheart Items (GHI) that I've used to make plot decisions in the form of a bag of Norse runes. Typically used for divination, you can use the descriptions of said runes to get ideas for what happens next or for clues or whatever. It's widely up to interpretation which is what makes it such a handy tool. It prints the results on your textbox, only you can see it. I tend to use these definitions: http://www.sunnyway.com/runes/meanings.html Merkstave (/in opposition) runes are the opposite of the normal meaning. You can ignore the merkstave status based on your needs. This is the import code: \bf[cj|34|@Y:|7]|C^|7a[Z^O&itI|BN|7|3|4$T|SY|7|3\$g"sgtqlKn%v""cv+5q|7|3t<!7#,0&(3-t9=@@K,|7|3/a3|7VII?IGBK^i|4lAdXX\_5[T^mN|7|3Qtgg]gei!]|7|3(uivo-i|71_$U$"x&9Dt<$&5&6.6;188H)|7L$9;FOEEILTCNWQPHGHGUIIa^PNXfUSjYeWo^ir[ec^gbb-"-|40|43c+zz#&Q##$wv-#**0;w|7|3zB55+53.7J+|7|3.Q>DJL:H>A$SHD^?|7bw s/,y!L 41#+6&r"Rubhnp^lbeQquxL pl+g|7/&t)+'5@|4C|4Fv>+179'5+.=H)|7|3,^0|7|33VCILRRR]>|7|3A|UF|7|3IlY_XbqR|7uei^]iy |7#vftkwv2=@6j"!%ut%5x7|7:2"0'32ITL%8':9=21=MEIC;R|7U|39[%EIW?alBd=[_eHjuKmEZhf^iXrUw'Xz?msv!_&1b)Zjsot!j1<m4^y(w6t;Fw>d(&4"DO%G"A;8>,NY/Qx7>9E;U8Ze;]/CXXMOaDfqGi6aPLnyOq?[iYUw'XzChhxc"'2c*Yo"%u%#l3>o6V'#&8v=Hy@r4=048&HS)K#9H3M0R]3Uv?MG>LN<^i?a*N^IcFhsIk<Q_TnQs#TvF\crx["-^%Msm#i(f-8i0Sqxs2p7Bs:h3(".$B|4$76:/.:J?C;8BI7KAHHV|7Y|3=_?alBdIdWP^XacQgWnPr|4TgVilogmt)^%'45w spz&o(y%%nvrDEt;v=JK593+")&ST(J*LTgOZ/RJPH>W8|7[RTBVLGbm|4p|4sH|=M|7%(!Qt_nc_yZ|7"7;3JG9<g;OL>FQA2=m5ux/%,,a5*&@!|7D;,<4<A-Z\NY.QEEILwIIJBASIPPV-ScD|7|3GjaTdfbpQ|7|3TwdjprndgJynj)e|7-$r'1<l4((,/^2'#=y|7A44*42-6IT|4W|4Z/RFFJMxJJKCBTJQQW4[[eF|7|3|4wLobiiflllwX|7|3|4.|41|44|47g/q#"#w&-7s|7;<Gw?*9.*D%|7H]aYpm_b2aurdljyXc8|<=|7alA|WF|7RNZbUxMpUijia[ooap \|7|3|42b*nnt%np u3o|7 w(0#Fv|V |7C|8=<,02-0B4:49DBF?R9?S>PE?SWQIXZVVNgrG|LL|7#zOrkg\ZnOboteoehw'c|7|3|49i1q*+*"w00"m./-6,4l/5-<G(|7|3|4Y.|O3|7VWb7|=<|7ork@cP\NW?e]SlM|7$ P|FU|7|3X @deqqVjwUivo-i|71WY[5@p|Yu|7437(K CegF'|7YU*Mm67CC(<Ix;O=Z;|7^olonqdoDgN[\ZS_hpQ|7($T|=Y|713-|40(z!jmv[$rt'3o|77'x02<Gw|I!|7DoB80@JU*|M/|7RS^3VH<IB[<|7_%ELaVNd<ZRalwLoTii^fjG[haz[|7#N!rjz)4d|Qi|7@<l|Kq|7"y*2%Hx@-9+4f87;82F8DJO0|7S8<O;I?BB\g<_DYYNVZ0_TPjK|7n"k$'&'()*+,37/FC58&1|44d|Ji|7@<l4\X7s|7;PTLcRU%TheW_]lKV+N68D:D;AGA$PBKR]>|7|3|4oD|HI|7lmxMpfZWcevW|7z?qgfpw\$Ig#v+6|4 Here is the code if you want to put it together yourself: ...Leiah0
Apr 9, 2013 I'm here because Crabby told me to come here Yup.Notthehair58
Apr 9, 2013 LF experienced RPer Hey you all :) I'm looking for a seasoned & experienced RPer that would be interested in being a part of my blog site. I have multiple bloggers that are interested in different aspects of the game, but I personally have never been on an RP realm nor do I have the interests. Since there is a lot of gamers who enjoy RPing, I was hoping to get a blogger that could appeal to the RPers out here and make this his/her niche. Please add me to real id if you would be interested: shadyshen@yahoo.com Thanks, Pnutbutter <Shady Shenanigans>Pnutbutter8
Apr 9, 2013 Describing characters. As someone who writes fiction as a hobby, I find things like descriptions and just writing in general come easy to me, in that once i get writing, I don't need to plan it out, I can just write freely. The problem I find is getting those first few words onto the page. After that, everything else comes quickly. With that in mind, I'm in the process of re-writing a description for a Forsaken Priest, and I've hit that first road block that comes when one has trouble organizing one's thoughts. Long story short, How does one describe what undeath looks like? Yeah, we see it in our characters, but trying to write it out is a little tricky. Or maybe I'm just thinking too hard.Raydian2
Apr 9, 2013 Backbiter Tavern (Open RP) The Backbiter Tavern is in a small desert village, with very few people living there. Inside the old tavern a mysterious warlock sits. He has black robes with strange purple runes on it. He has blond hair with a black bandana wrapped around his mouth. A strange demon (felhunter) sits by his side. He says to the barman, "Gimme another ale." and hands him a few coins. The dark room has many cobwebs and a couple lanterns in it. --------------------------------------------- Anyone can join, horde or alliance, however only one person can be the barman. Im the warlock. Have fun!Rexxigon44
Apr 9, 2013 Misrepresentation of the Gnomish intrest. Hello my fellow Azerothians, I am here today to discuss an oversight by the producers, directors and filmers of the promotional cinematic features that chronicle the struggle of the people of Azeroth for our future generations. Today I spent the time to watch them from the beginning for the 7th time, now that we have added the meeting of the Panderians to the archive, and I have come across, or I should say, FAILED to come across something very simple. There has not been a single gnome shown in our archives since the start! The first shows a Dwarf, Night Elf, Forsaken, Tauren, Orc, and a Human, the Second introduces our new allies the Draenei and our new enemies the Blood Elves, and the Trolls make their first appearance, however brief. The third shows nothing of either the horde and alliance, and the fourth shows a GIANT STATUE of a Goblin! Nothing of the Worgen, I may add, but that is understandable given their nature. The newest gives an entire fight scene to the Pandariens, showing many more of their race than any single other in any of our archive, unless you wish to count the scourge as a race, they would take that cake for their appearance under the frosty now-dead Lich King. It is shameful to my people, we who have lost our entire GLORIOUS city in our struggle, to not even have a sideways glance in our archive of the history of our world. I will also add that without Gnomish technology none of the moving-picture archives would exist in the first place! I think it is not too much to ask, for the next major event in Azeroth, Gnomes at least be represented as one of the peoples that live on this wonderful planet. Sincerely ShådôwfìrèShådôwfîrè2
Apr 9, 2013 Scars left from magical healing This is an idea I've had rolling around for a while that I thought I'd put out there to get some feedback on. By now, any of our characters have been injured enough to die hundreds of times over, and are pretty much only alive (or clinging to their unlife) thanks to the dedicated efforts of healers. But what if, like how major surgery can leave scars, major healing magic can also leave a lasting mark? I've got some different ideas for the kinds of marks left, and I figure that they would vary depending on the kind of magic used to heal. I figured that Shaman healing could, in some cases, actually replace the ruined flesh / bone with raw elemental matter. This could range from having teeth made of marble to eyes that are actually small orbs of water, or in my character's case a skull (and horns) that are dark iron. Basically any elemental material, as long as it could make sense for the body part in question (bones are more likely to be metal or stone than air or water, for example). Druid healing scars could be kinda similar, except instead of raw elemental material they replace body chunks with plant matter. Where once was a heart could be a pulsating knot of roots, hair could be vines, fingernails could be chips of bark, etc. I'm not 100% sure on what to do for divine healing. Sunwalker (Tauren paladin / priest) healing would be using solar energy, so it could be plants or, as I saw one person playing it, their body slowly being replaced with raw solar energy. He eventually became basically a mass of energy held together by his armour, but he took it to a bit of an extreme. I'm totally open to ideas as to what kinda scars divine healing could leave behind! Anyway, just wanted to get some feedback on this idea, or just put it out there in case anybody else likes it and feels like using it. Just remember, Wolverine might have an adamantium plated skeleton, but only by being beaten to withing an inch of your life and being restored by a shaman can you have a skeleton actually MADE of the stuff!Melahna46
Apr 8, 2013 How to translate IRL to RP Ok so in real life I was a soldier. I am a fairly well rounded person, skilled in hand to hand and well versed and practiced with firearms. I can apply first aid for a large variety of injuries to include gunshot wounds to the head. I can also cook and sew and do other various household tasks. I have devoted myself to learning everything I may need to become a self sufficient warrior. I'd argue that I am more fit to be a soldier then a human being. The question is how would I translate this life to a role play character without coming off as a Rambo type warrior like so many portray? How do you play this type without getting under people skin and whats a good way to start the character off?Bannanaclip3
Apr 7, 2013 Go ahead and poke some holes in my plot :) I want to better my character's storyline so please tell me what you think and let me know if there is any faulty wiring in this Goblin's design ;) Smaragd is sassy but has a dry sense of humor that is sometimes conceived as being rude. She is very materialistic and loves Gems but her passion is Unique daggers She grew up in the Steamwheedle Cartel like most Goblins and is estranged from her family. They grew apart after she went into business against them Ever since she left out on her own she has been determined to make a name for herself as the number one Trade Cartel around and so she founded Tänn Smaragd4
Apr 7, 2013 The Stormwind Archives Royal Library (open Rp Ic :Rayaana was an apprentice at the Royal Library in Stormwind, she spent her long hours at the library writing books, organizing and repairing tomes, and creating glyphs and scrolls. Rayaana was a scholar,scribe, and archivist.She loved books, and deeply enjoyed working at the library.Her co-workers were kind, and so was her boss(played by my other alt, SIndorian), SIndorian. OOC: The Stormwind Archives Royal Library's entrance is located in the courtyard of the Stormwind castle.It is filled to the brim with tomes and scrolls of immense knowledge, and any are free to ask to be hired by SIndorian, you may be hired, and may be not, so do not feel bad, you could always be a reader who loves to visit the library.You can be hired as a page, scribe,archivist, and more.If I do not hire you, it's for a good reason, please role-play an interview with SIndori, I will not be available from tomorrow to Saturday. Please enjoy! P.S, since Stormwind is alliance territory, SIndorian convinced the King to allow approved horde in.Rayaana9
Apr 7, 2013 mrp backup? One my friends lost all of their MRP profiles somehow. not sure on the details, but learning from others misfortunes I started making backups of all my profiles, pretty much Copy pasting everything into a notepad doc for all my characters. This started taking a while, mostly due to pasting it in note pad not carrying over line breaks, so I started looking through the MRP folder of my addons, and I cannot find the file that has all the profiles in it! Does anyone know where the file/folder is that I would have to copy to make backups of all my profiles? Or am I stuck with the tedious task of copying and pasting note pad documents, copying every small field I have available?Masayume5
Apr 7, 2013 trasnmog help I'm trying to find a weapon to match my set, the one I have now is okay, just think I might get a different one. Any ideas?Falanthos2
Apr 7, 2013 RP a Goblin this post is for 2 reasons, 1: to shamelessly redirect you to a previous post in the hopes that someone will reply http://us.battle.net/wow/en/forum/topic/8569857755#1 2: to get some more knowledge on the Goblins as a people. what are some character traits that make a rp`d goblin believable and adhere to proper lore?Smaragd4
Apr 7, 2013 Gnome or Night Elf Monk? I'm having a hard time deciding between the two. Either way I'd like some feedback on their stories. Ginxee was a minor assistant on the irradiator that had destroyed Gnomregan, and after witnessing the horror she had caused she had taken to drinking. She was kicked out of a bar one day and happened to find one of the wandering Pandaren who took her in and taught her temperance. She became enthralled with the special effects that the brews and teas had, and decided to dedicate her life to studying them and the Pandaren martial arts. My night elf monk would be a highborne arcanist with a similar backstory to Ginxee's. As an adding question to this, were the non-Pandaren masters in the Peak of Serenity there after the mists had parted or before?Ginxee5
Apr 6, 2013 (IC) Ask a non-stereotypical Hunter (#1) (I saw something like this in a forum once.) Hello, I'm Enion Boughstrider, of the Anytime Anywhere Messaging Service (Of Cenarion Circle) and I'd like to answer some of your questions for a while. (Make the questions IC please)Enion1
Apr 6, 2013 New RPer seeking guidance Hello all! I'm new to RP and having never written anything on my characters I was wondering if I could get some help. I wanted my character to be an explorer and one who lives off the land. So I was thinking of having her become a scout....here is the story I have so far.. Giselle was taught as a young girl to live off the land. Her mother had passed away in childbirth and her father had raised her the best he knew how. Her father being a game hunter often took Giselle with him on his hunting trips. He taught her the art of tracking, shooting, fishing, and harvesting the skins and meats of their kills. Her father would load the cart with the furs, skins, and meats and sell them at the markets. They were not ritch by no means but they made an honest living and Giselle loved being in the forest. So when Giselle came of age and heared one of the largest land owners in (not sure if I should make him from Duskwoods or Westfall) was looking to hire some scouts to find a large piece of land big enough for a whole town to be built on it. Giselle jumpped at the opportunity! He hired 6 people but not to work together. They were all to split up and scour lands. All findings were to be extensively noted including such things as wildlife found on the land, plants, temperature. And a detailed sketching of the whole area. The person who found the best and safest piece of land would be handsomely reward. This is the only idea I could come up with for an exploding hunter. If I have made a party foul please let me know...the same if its garbage but please try and be kind :)Gíselle10
Apr 6, 2013 The Rise of Strife ...Veptember7
Apr 6, 2013 Fancy RP Names my character was flagged for a name change... a blood elf mage. I was going to transfer her to an RP realm to play with some new friends I made and I was wondering if anyone had some good blood elf mage names. or any good names for that matter please and thanks!Nightfrost3
Apr 6, 2013 Warcraft: Second War just saw a vid called Warcraft: Second War and it got me thinking, I miss the days of arial dogfights between my gryphon riders and the great red dragons of the Horde, on the battlefield beneath is bloodthirsty Orcs, Ogres and Trolls rushing into a glorious clash with humanity's defenders, the holy Knights, while elven rangers launch barrages of arrows into the ranks. I've fought in the second war, and lost my arm!Butcherr1
Apr 5, 2013 Need help deciding a last name Takumi is mainly a warrior, but he's a little bit of his parents' classes too. His father is a shaman, and his mother is a monk. In his RP story, he befriends a group of dwarves, and lives in Ironforge. I've tried really hard to come up with a good last name for Takumi, but I always end up with nothing. I was wondering if anyone had suggestions. Also, I'm thinking of making an addition to his RP story, where he changes his last name to a dwarven-sounding one.Takumi1
Apr 5, 2013 Lore question. May not be the best forum, but I figured RPers would know a good resource. basically I want to know which books cover the major and somewhat major events of each expansion, such as the isle of quel'danas from BC, etc. or domination point in MoP. I honestly dont have a lot of time to quest and get all that lore so I basically wanted to read the book(s) on em or somewhat detailed cliff notes, etc. I havent even been able to do the thunder island dailies and really wanna know the story, preferably in novel form cause of all the detail, but cliff notes are good too. I more or less know the novel order up the the cataclysm one and I can just google the timeline, but wanna know the important lore features etc. Like if you didn't do end time dungeons you wouldn't even have heard of murozond. So I don't wanna miss things like that, wrathgate etc.Kaijin6
Apr 5, 2013 Character Development Hello, Moon Guard. I have a few questions about character development for roleplayers here. I've been tossing around an idea for a book (or... world, rather-- not quite sure what to classify it as). However, I consider myself still relatively new when it comes to developing a character-- goals, beliefs, etc. I encourage the discussion of the following questions within this thread. As always, please try to be respectful of others. Thank you. 1. Where does inspiration, for you as a player, come from when you wrote/write your characters? 2. Sometimes roleplayers find that their real-life personalities and beliefs can interfere with the character's. How can this be avoided? Is it something that should necessarily be avoided at all? 3. What do you think is the key to creating a believable, yet unique character? 4. So the foundation of the character has been laid out. What are other ways that the character can branch out from a set foundation? 5. Do you find writing the character's history before creating the character is more beneficial than fleshing that out as your develop him or her? Is the latter a valid way to do so?Ruthelle7
Apr 5, 2013 Lonely Tavern (Open RP) Upon entering the tavern one may notice the small bar at the other side of the room. A bar-tender wiping the counters from the customers who'd just left. He nods to each new visitor, letting them know he realizes their presence and is willing to help at their command. "Welcome, the names Joe." He had a rusty voice, possibly from all the smoke in the air left by the travelers who'd come and gone. Joe had been the bar keep for many years now, knowing all the tricks and favorite drinks. Putting little spins on his own and creating legendary concoctions. There were tables all around the edges of the wall, and one large one in the middle for big groups. The tables seemed worn down from the many uses, and weight they had held over the years. The place wasn't the nicest place to be, it was more of a hide-a-way for those that needed it. Which would lead to the Priestess, covered in her long gown. Elegant to the sight, sitting properly in one of the far tables. She'd keep her head down, sipping on a glass. What was in the glass was unknown at this time. Her fingers tracing over the rim, a soft humming being heard from the cup. She never looked up from her glass, keeping her head down. Although the Light around her would give off the aura of welcome to any that may sit with her.Merilynn0
Apr 5, 2013 RP on......Nazgrel? Why not?! Yes I know it isn't an RP server but I love my home server of Nazgrel and I can't afford a transfer. So here is what I am pondering, how many of you would be interested in RP in a Traders Guild? When I founded my guild Tänn, my intention was that we would make a name for ourselves as the rulers of the AH. You need something, we have it and if we don't have it, then we can get it for a fee of course /eye glint. We would take orders from other players and fill them for our commission. You could specialize in different fields, from an herbalist to a rare item hunter who tracks down that perfect piece of gear needed to complete a player's xmog. Anything your heart desired so long as you were raking in the cash. ( Time is Money friend). Unfortunately now my sad little guild is down to one other member, my boyfriend who co-founded Tänn with me, and we are lonely. Would anyone like to come join our humble little Traders Guild?Smaragd20
Apr 5, 2013 Putting the WORLD back in Warcraft I started playing WoW because I was interested in the open world-ness of it: the random encounters, the endless possibilities, the world pvp, the rp, etc. The dungeons are battlegrounds were fun for a minute, but they got boring. They didn't seem real. So I decided to roll a new toon that only existed in the world. I've completely eliminated dungeons and battlegrounds from my activities. Total killing blows = world killing blows, etc. I've found it does a couple neat things for my play experience: - Forces me to explore the ridiculously vast world Blizzard has created for us. So much of it is skipped or overlooked when we power level to 90 through dungeons and BGs. Even leveling only in the world, there's still plenty of areas I wasn't able to get to and will likely go back and explore later. - World PVP is my jam. It's what keeps the game fun, entertaining, lively, unpredictable, and challenging. Here's the catch: it only exists in the world. The more time spent in it, the more likely I am to find it. - The challenge. When I hit 90, I'm still going to be playing by these same guidelines. Most of my time is going to be spent in Pandaria, looking for PVP, doing dailies, farming (and actual farming), RPing, etc. But I'm going to be at a disadvantage because I won't be equipped in super easy to attain gear. PVP gear will be earned through world PVP, which is more rewarding, and I'll likely be outgearred. But I'm still going to wreak havoc. That's going to feel good. If anyone is interested in a playstyle like this, and putting the world back in Warcraft, I'd be happy to have people join me. Let me know here, or roll a Horde toon on Emerald Dream and shoot me a message.Johnyawesome6
Apr 5, 2013 In search of an active Rp-PvP community. Was one on Emerald Dream but that has fallen into disrepair. Was told there was one on Ravenholdt but there only seems to be about two dozen active players on the entire server (I am exaggerating of course but, sadly, not that much). Any other suggestions? Ill even do a PvP Realm or an RP realm so long as there is an active RP-PvP community.Papilon11
Apr 4, 2013 How do you deal with trolls? Recently there has been quite a few guilds on WRA who seem to do nothing but troll RPers. Myself and a handfull of others are worried that WRA is going to become another Kirin Tor. What do you do to combat against trolls and make it feel "safe" for RPers again?Aeolidae7
Apr 4, 2013 So, about Vrykul naptime... So I'm planning on tying a new toon's story to the Vrykul in a few ways. The problem is, I want the character to be around 17-18 years old. Rather than just blunder ahead I did some research and found that for him to be 17-18 now, the Vrykul would have been in stasis when he was around the age I would have wanted him to have interaction with them. Is there any way to make this work and still be sound in the lore, or did all of the Vrykul wake up the minute the Alliance and Horde made landfall in Northrend, and not a second before? Thanks in advance. ((Previously posted in wrong section >.>))Helbrenn1
Apr 4, 2013 [A] Bards of Noblegarden - Ravenholdt < Numerous parchments of similar quality may perhaps be seen hung aloft from the winding streets of Stormwind, yet as well the dimly lit corridors of Ironforge. Perhaps less so to have by chance been placed amid other frequently trodden locales...Though, regardless of where, would all state the same; embellishments of faintly shimmering writing therein to seek the eye of passerby. > "To whom it may concern, The season of Noblegarden nears and shall soon be upon all, celebration to herald immense mirth and momentary reprieve from the oppressive circumstances which surround us. Noblegarden's renown seeking and feasting, long founded tradition of Azeroth, will certainly captivate or enthrall many of its denizens in one form or another. It is in such rare moments of peace that open invitation for evening of levity and homage as this may be seen. In festive celebration of community and prosperity, as well to further embody the merits of Noblegarden, does the Twilight Empire and those of Bardic Tales invite all to attend friendly competition! Bardic contest will be held at Goldshire, Elwynn Forest for any interested in well company and prizes! Such will commence at approximately 8:00PM upon the 3rd of April. We encourage all to attend in good spirits and welcome those whom wish participate or merely observe! All desires of submission must be sent to the office of "Minister Erber Spellfixer" via the Alliance post, late given missives to this effect null. All entries must pertain to Noblegarden in suitable and related form, should triumph be awarded by judging panel. That presented may be song, story, or poetic piece! Once more are all welcome to this bidden gathering, we to be hopeful of your timely and generous arrivals. - The Twilight Empire Bardic Tales " (( Greetings! This Ravenholdt event is open for RPers to enjoy and participate in! Ravenholdt is a somewhat smaller CRZ free server! We invite those off-realm to roll character and join in on the fun! - Please, send an in-game mail to Erber should you wish to participate! No late entries accepted! - Entries may either be creative and appropriate song, story, or poetic work! (Noblegarden related!) - Goldshire, Elwynn Forest (8:00PM)! - April 3rd! We hope to see you all there to join in the RP and fun such evening has to offer! ))Erber3
Apr 4, 2013 Can we take ONE server back? Do you Love RP? I do I love PvP as well. And the combination of the two is so synergistic as they fuel one another. Can we just take one RP-PvP Server back from the people who have polluted it? RP-PvP is commonly misunderstood to mean that the roleplaying part is optional. In fact, these servers were started in response to petitioning from roleplayers, who felt that the ability to engage in PvP added realism. I am one of these people. Can we all pick one RP-PvP server and: Report Bad names Ostracize the trolls/greifers and any OOC play. Maintain a positive atmosphere for roleplaying Can we pick one and make a haven a shining ideal of what RP-PvP should be?Papilon55
Apr 3, 2013 any good tribal warrior mogs? i recently rerolled horde from a dwarf and im a little let down my my mog set. it looked better on a dwarf but now im looking for something more tribal and savage, something that says "horde". the problem is, all the tribal looking armor belongs to leather/cloth users. plate cant xmog into anything that dosent make you look like an alliance knight or something. any suggestions?Jotun3
Apr 3, 2013 Looking into trying RP-want advice & have ?'s Oh hi, I'm looking into trying to start up on an RP-PvP realm or an RP realm (first preferred, as I've spent all my WoW career since day 1 on a PvP server. However after reading a lot of the posts about "how to RP" and all of that I have a couple major questions and concerns 1. It seems that a lot of RP groups are tight nit and it might be hard to get into a group especially one that is a good fit with a persons play style etc. 2. I'm a healer by nature and I've seen a lot of posts about toning back heals, etc which makes taking the first step towards RP a bit more daunting 3. I don't really know anything about the RP servers themselves other than Emerald dream is quite full, and ravenholdt is on its own CRZ and didn't know if there were general recomendations or the like Also I'm open to any other advice anyone has, I'm sure I'll have more questions as things go along TLDR: Halp I'm a noob at RP and don't know if its worth taking the plungeAleda6 | 2016-09-26 02:41:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28838926553726196, "perplexity": 2518.310665142427}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738660548.33/warc/CC-MAIN-20160924173740-00190-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://hackage-origin.haskell.org/package/cryptol-2.10.0/candidate/docs/Cryptol-Testing-Random.html | cryptol-2.10.0: Cryptol: The Language of Cryptography
Copyright (c) 2013-2016 Galois Inc. BSD3 cryptol@galois.com provisional portable Trustworthy Haskell2010
Cryptol.Testing.Random
Description
This module generates random values for Cryptol types.
Synopsis
# Documentation
type Gen g x = Integer -> g -> (SEval x (GenValue x), g) Source #
randomValue :: (Backend sym, RandomGen g) => sym -> TValue -> Maybe (Gen g sym) Source #
A generator for values of the given type. This fails if we are given a type that lacks a suitable random value generator.
dumpableType :: forall g. RandomGen g => TValue -> Maybe [Gen g Concrete] Source #
Given a (function) type, compute generators for the function's arguments.
testableType :: RandomGen g => TValue -> Maybe (Maybe Integer, [TValue], [[Value]], [Gen g Concrete]) Source #
Given a (function) type, compute data necessary for random or exhaustive testing.
The first returned component is a count of the number of possible input test vectors, if the input types are finite. The second component is a list of all the types of the function inputs. The third component is a list of all input test vectors for exhaustive testing. This will be empty unless the input types are finite. The final argument is a list of generators for the inputs of the function.
This function will return Nothing if the input type does not eventually return Bit, or if we cannot compute a generator for one of the inputs.
Constructors
TestReport FieldsreportResult :: TestResult reportProp :: StringThe property as entered by the userreportTestsRun :: Integer reportTestsPossible :: Maybe Integer
A test result is either a pass, a failure due to evaluating to False, or a failure due to an exception raised during evaluation
Constructors
Pass FailFalse [Value] FailError EvalError [Value]
Arguments
:: RandomGen g => g The random generator state -> [Gen g Concrete] Generators for the function arguments -> Value The function itself -> Int How many tests? -> IO [([Value], Value)] A list of pairs of random arguments and computed outputs
Return a collection of random tests.
Arguments
:: MonadIO m => (Integer -> m ()) progress callback -> Value function under test -> [[Value]] exhaustive set of test values -> m (TestResult, Integer)
Arguments
:: (MonadIO m, RandomGen g) => (Integer -> m ()) progress callback -> Integer Maximum number of tests to run -> Value function under test -> [Gen g Concrete] input value generators -> g Inital random generator -> m (TestResult, Integer) | 2023-03-26 18:59:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2316451519727707, "perplexity": 7228.223266532594}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296946445.46/warc/CC-MAIN-20230326173112-20230326203112-00424.warc.gz"} |
https://scipost.org/SciPostPhysProc.8.051 | ## Correlations between azimuthal asymmetries and multiplicity and mean transverse momentum in small collisions systems in the CGC
Tolga Altinoluk, Néstor Armesto, Alex Kovner, Michael Lublinsky, Vladimir V. Skokov
SciPost Phys. Proc. 8, 051 (2022) · published 12 July 2022
DIS2021
### Abstract
Considering a dilute-dense situation suitable for pA collisions, we compute in the Color Glass Condensate the correlation between azimuthal asymmetries, specifically the squared second Fourier coefficient $v_2^2$, and the total multiplicity in the event. We also analyse the correlation between $v_2^2$ and the mean squared transverse momentum of particles in the event. In both cases, we find that the correlations are generally very small, consistent with the observations. We also note an interesting sharp change in the value of $v_2^2$ and its correlations as a function of the width of the transverse momentum bin, related with a change of the dominance of Bose and HBT quantum correlations.
### Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.
Funders for the research work leading to this publication | 2022-12-06 07:43:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8695906400680542, "perplexity": 1966.5564355606034}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711074.68/warc/CC-MAIN-20221206060908-20221206090908-00025.warc.gz"} |
https://itectec.com/ubuntu/ubuntu-ubuntu-18-04-authentication-error-on-loging-after-lock/ | # Ubuntu – Ubuntu 18.04: Authentication Error on loging after lock
18.04
I'm on Ubuntu 18.04 and since today whenever I lock my system and try to log back in using my password, it shows the 'in progress' spinner for few seconds then I get the error message "Authentication error". I can successfully log in on the first start though.
I have tried to force disable Wayland by uncommenting the line #WaylandEnable=false to WaylandEnable=false in /etc/gdm3/custom.conf but it had no effect. I was originally using Xorg as well.
I've checked for any available system updates in hope of getting a fix but none are available. What can I do to investigate into and fix this error?
Update: I re-installed Ubuntu 18.04 to get rid of the issue.
What did work was changing fs.inotify.max_user_watches. I used this solution: https://askbot.fedoraproject.org/en/question/115963/gnome-authentication-error-when-logging-in-after-lock/ | 2021-06-18 16:10:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3821132183074951, "perplexity": 3438.3961707984995}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487637721.34/warc/CC-MAIN-20210618134943-20210618164943-00096.warc.gz"} |
https://itk.org/Doxygen/html/itkVectorGradientMagnitudeImageFilter_8h.html | ITK 5.4.0 Insight Toolkit
#include "itkNeighborhoodIterator.h"
#include "itkImageToImageFilter.h"
#include "itkImage.h"
#include "itkVector.h"
#include "vnl/vnl_matrix.h"
#include "vnl/vnl_vector_fixed.h"
#include "vnl/algo/vnl_symmetric_eigensystem.h"
#include "itkMath.h"
This graph shows which files directly or indirectly include this file:
Go to the source code of this file.
Classes
class itk::VectorGradientMagnitudeImageFilter< TInputImage, TRealType, TOutputImage >
itk
Functions
*par Constraints *The filter requires an image with at least two dimensions and a vector *length of at least The theory supports extension to scalar but *the implementation of the itk vector classes do not **The template parameter TRealType must be floating itk::point (float or double) or *a user-defined "real" numerical type with arithmetic operations defined *sufficient to compute derivatives. **\par Performance *This filter will automatically multithread if run with *SetUsePrincipleComponents
Variables
*par Constraints *The filter requires an image with at least two dimensions and a vector *length of at least The theory supports extension to scalar but *the implementation of the itk vector classes do not **The template parameter TRealType must be floating so it cannot multithread for data other than in Anisotropic Diffusion of Multivalued Images *with Application to Color itk::Filtering
*par Constraints *The filter requires an image with at least two dimensions and a vector *length of at least The theory supports extension to scalar itk::images
*par Constraints *The filter requires an image with at least two dimensions and a vector *length of at least The theory supports extension to scalar but *the implementation of the itk vector classes do not **The template parameter TRealType must be floating so it cannot multithread for data other than in Anisotropic Diffusion of Multivalued Images *with Application to Color IEEE Transactions on Image No itk::pp
*par Constraints *The filter requires an image with at least two dimensions and a vector *length of at least The theory supports extension to scalar but *the implementation of the itk vector classes do not **The template parameter TRealType must be floating so it cannot multithread for data other than in Anisotropic Diffusion of Multivalued Images *with Application to Color IEEE Transactions on Image itk::Processing
*par Constraints *The filter requires an image with at least two dimensions and a vector *length of at least The theory supports extension to scalar but *the implementation of the itk vector classes do not **The template parameter TRealType must be floating so it cannot multithread for data other than in * itk::UsePrincipleComponents
*par Constraints *The filter requires an image with at least two dimensions and a vector *length of at least The theory supports extension to scalar but *the implementation of the itk vector classes do not **The template parameter TRealType must be floating so it cannot multithread for data other than in Anisotropic Diffusion of Multivalued Images *with Application to Color IEEE Transactions on Image * itk::Vol | 2023-03-31 06:05:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18183201551437378, "perplexity": 4444.454343373301}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949573.84/warc/CC-MAIN-20230331051439-20230331081439-00304.warc.gz"} |
https://www.climatechange.ai/papers | # Climate Change AI Workshop Papers
On this page, we show accepted works from all our workshops on "Tackling Climate Change with Machine Learning."
Venue Title Subject Areas
NeurIPS 2022 Function Approximations for Reinforcement Learning Controller for Wave Energy Converters (Papers Track)
Abstract and authors: (click to expand)
Abstract: Waves are a more consistent form of clean energy than wind and solar and the latest Wave Energy Converters (WEC) platforms like CETO 6 have evolved into complex multi-generator designs with a high energy capture potential for financial viability. Multi-Agent Reinforcement Learning (MARL) controller can handle these complexities and control the WEC optimally unlike the default engineering controllers like Spring Damper which suffer from lower energy capture and mechanical stress from the spinning yaw motion. In this paper, we look beyond the normal hyper-parameter and MARL agent tuning and explored the most suitable architecture for the neural network function approximators for the policy and critic networks of MARL which act as its brain. We found that unlike the commonly used fully connected network (FCN) for MARL, the sequential models like transformers and LSTMs can model the WEC system dynamics better. Our novel transformer architecture, Skip Transformer-XL (STrXL), with several gated residual connections in and around the transformer block performed better than the state-of-the-art with faster training convergence. STrXL boosts energy efficiency by an average of 25% to 28% over the existing spring damper (SD) controller for waves at different angles and almost eliminated the mechanical stress from the rotational yaw motion, saving costly maintenance on open seas, and thus reducing the Levelized Cost of wave energy (LCOE). Demo: https://tinyurl.com/4s4mmb9v
Authors: Soumyendu Sarkar (Hewlett Packard Enterprise); Vineet Gundecha (Hewlett Packard Enterpise); Alexander Shmakov (UC Irvine); Sahand Ghorbanpour (Hewlett Packard Enterprise); Ashwin Ramesh Babu (Hewlett Packard Enterprise Labs); Alexandre Pichard (Carnegie Clean Energy); mathieu Cocho (Carnegie Clean Energy)
Power and energy systems Reinforcement learning and control
NeurIPS 2022 Image-Based Soil Organic Carbon Estimation from Multispectral Satellite Images with Fourier Neural Operator and Structural Similarity (Papers Track)
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Abstract: Soil organic carbon (SOC) sequestration is the transfer and storage of atmospheric carbon dioxide in soils, which plays an important role in climate change mitigation. SOC concentration can be improved by proper land use, thus it is beneficial if SOC can be estimated at a regional or global scale. As multispectral satellite data can provide SOC-related information such as vegetation and soil properties at a global scale, estimation of SOC through satellite data has been explored as an alternative to manual soil sampling. Although existing works show promising results, most studies are based on pixel-based approaches with traditional machine learning methods, and convolutional neural networks (CNNs) are seldom used. To study the advantages of using CNNs on SOC remote sensing, in this paper, we propose the FNO-DenseNet based on the state-of-the-art Fourier neural operator (FNO). By combining the advantages of the FNO and DenseNet, the FNO-DenseNet outperformed the FNO in our experiments with hundreds of times fewer parameters. The FNO-DenseNet also outperformed a pixel-based random forest by 18% in the mean absolute percentage error. To the best of our knowledge, this is the first work of applying the FNO on SOC remote sensing.
Authors: Ken C. L. Wong (IBM Research – Almaden Research Center); Levente Klein (IBM Research); Ademir Ferreira da Silva (IBM Research); Hongzhi Wang (IBM Almaden Research Center); Jitendra Singh (IBM Research - India); Tanveer Syeda-Mahmood (IBM Research)
Carbon capture and sequestration Classification, regression, and supervised learning Computer vision and remote sensing
NeurIPS 2022 SolarDK: A high-resolution urban solar panel image classification and localization dataset (Papers Track)
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Abstract: The body of research on classification of solar panel arrays from aerial imagery is increasing, yet there are still not many public benchmark datasets. This paper introduces two novel benchmark datasets for classifying and localizing solar panel arrays in Denmark: A human annotated dataset for classification and segmentation, as well as a classification dataset acquired using self-reported data from the Danish national building registry. We explore the performance of prior works on the new benchmark dataset, and present results after fine-tuning models using a similar approach as recent works. Furthermore, we train models of newer architectures and provide benchmark baselines to our datasets in several scenarios. We believe the release of these datasets may improve future research in both local and global geospatial domains for identifying and mapping of solar panel arrays from aerial imagery. The data is accessible at https://osf.io/aj539/.
Authors: Maxim MK Khomiakov (DTU); Julius Radzikowski (DTU); Carl Schmidt (DTU); Mathias Sørensen (DTU); Mads Andersen (DTU); Michael Andersen (Technical University of Denmark); Jes Frellsen (Technical University of Denmark)
Buildings Power and energy systems Computer vision and remote sensing
NeurIPS 2022 Bayesian inference for aerosol vertical profiles (Papers Track)
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Abstract: Aerosol-cloud interactions constitute the largest source of uncertainty in assessments of the anthropogenic climate change. This uncertainty arises in part from the difficulty in measuring the vertical distributions of aerosols. We often have to settle for less informative vertically aggregated proxies such as aerosol optical depth (AOD). In this work, we develop a framework to infer vertical aerosol profiles using AOD and readily available vertically resolved meteorological predictors such as temperature or relative humidity. We devise a simple Gaussian process prior over aerosol vertical profiles and update it with AOD observations. We validate our approach using ECHAM-HAM aerosol-climate model data. Our results show that, while simple, our model is able to reconstruct realistic extinction profiles with well-calibrated uncertainty. In particular, the model demonstrates a faithful reconstruction of extinction patterns arising from aerosol water uptake in the boundary layer.
Authors: Shahine Bouabid (University of Oxford); Duncan Watson-Parris (University of Oxford); Dino Sejdinovic (University of Adelaide)
Climate science and climate modeling Causal and Bayesian methods
NeurIPS 2022 Optimizing toward efficiency for SAR image ship detection (Papers Track)
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Abstract: The detection and prevention of illegal fishing is critical to maintaining a healthy and functional ecosystem. Recent research on ship detection in satellite imagery has focused exclusively on performance improvements, disregarding detection efficiency. However, the speed and compute cost of vessel detection are essential for a timely intervention to prevent illegal fishing. Therefore, we investigated optimization methods that lower detection time and cost with minimal performance loss. We trained an object detection model based on a convolutional neural network (CNN) using a dataset of satellite images. Then, we designed two efficiency optimizations that can be applied to the base CNN or any other base model. The optimizations consist of a fast, cheap classification model and a statistical algorithm. The integration of the optimizations with the object detection model leads to a trade-off between speed and performance. We studied the trade-off using metrics that give different weight to execution time and performance. We show that by using a classification model the average precision of the detection model can be approximated to 99.5% in 44% of the time or to 92.7% in 25% of the time.
Authors: Arthur Van Meerbeeck (KULeuven); Ruben Cartuyvels (KULeuven); Jordy Van Landeghem (KULeuven); Sien Moens (KU Leuven)
Computer vision and remote sensing Ecosystems and biodiversity Oceans and marine systems
NeurIPS 2022 AutoML-based Almond Yield Prediction and Projection in California (Papers Track)
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Abstract: Almonds are one of the most lucrative products of California, but are also among the most sensitive to climate change. In order to better understand the relationship between climatic factors and almond yield, an automated machine learning framework is used to build a collection of machine learning models. The prediction skill is assessed using historical records. Future projections are derived using 17 downscaled climate outputs. The ensemble mean projection displays almond yield changes under two different climate scenarios, along with two technology development scenarios, where the role of technology development is highlighted. The mean projections and distributions provide insightful results to stakeholders and can be utilized by policymakers for climate adaptation.
Authors: Shiheng Duan (Lawrence Livermore National Laboratory); Shuaiqi Wu (University of California, Davis); Erwan Monier (University of California, Davis); Paul Ullrich (University of California, Davis)
Agriculture and food Classification, regression, and supervised learning
NeurIPS 2022 Attention-Based Scattering Network for Satellite Imagery (Papers Track)
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Abstract: Multi-channel satellite imagery, from stacked spectral bands or spatiotemporal data, have meaningful representations for various atmospheric properties. Combining these features in an effective manner to create a performant and trustworthy model is of utmost importance to forecasters. Neural networks show promise, yet suffer from unintuitive computations, fusion of high-level features, and may be limited by the quantity of available data. In this work, we leverage the scattering transform to extract high-level features without additional trainable parameters and introduce a separation scheme to bring attention to independent input channels. Experiments show promising results on estimating tropical cyclone intensity and predicting the occurrence of lightning from satellite imagery.
Earth science Earth observations and monitoring Classification, regression, and supervised learning Interpretable ML
NeurIPS 2022 Discovering Interpretable Structural Model Errors in Climate Models (Papers Track)
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Abstract: Inaccuracies in the models of the Earth system, i.e., structural and parametric model errors, lead to inaccurate climate change projections. Errors in the model can originate from unresolved phenomena due to a low numerical resolution, as well as misrepresentations of physical phenomena or boundaries (e.g., orography). Therefore, such models lead to inaccurate short--term forecasts of weather and extreme events, and more importantly, long term climate projections. While calibration methods have been introduced to address for parametric uncertainties, e.g., by better estimation of system parameters from observations, addressing structural uncertainties, especially in an interpretable manner, remains a major challenge. Therefore, with increases in both the amount and frequency of observations of the Earth system, algorithmic innovations are required to identify interpretable representations of the model errors from observations. We introduce a flexible, general-purpose framework to discover interpretable model errors, and show its performance on a canonical prototype of geophysical turbulence, the two--level quasi--geostrophic system. Accordingly, a Bayesian sparsity--promoting regression framework is proposed, that uses a library of kernels for discovery of model errors. As calculating the library from noisy and sparse data (e.g., from observations) using convectional techniques leads to interpolation errors, here we use a coordinate-based multi--layer embedding to impute the sparse observations. We demonstrate the importance of alleviating spectral bias, and propose a random Fourier feature layer to reduce it in the proposed embeddings, and subsequently enable an accurate discovery. Our framework is demonstrated to successfully identify structural model errors due to linear and nonlinear processes (e.g., radiation, surface friction, advection), as well as misrepresented orography.
Authors: Rambod Mojgani (Rice University); Ashesh K Chattopadhyay (Rice University); Pedram Hassanzadeh (Rice University)
Climate science and climate modeling Earth observations and monitoring Interpretable ML
NeurIPS 2022 Aboveground carbon biomass estimate with Physics-informed deep network (Papers Track)
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Abstract: The global carbon cycle is a key process to understand how our climate is changing. However, monitoring the dynamics is difficult because a high-resolution robust measurement of key state parameters including the aboveground carbon biomass (AGB) is required. We use deep neural network to generate a wall-to-wall map of AGB within the Continental USA (CONUS) with 30-meter spatial resolution for the year 2021. We combine radar and optical hyperspectral imagery, with a physical climate parameter of solar-induced chlorophyll fluorescence (SIF)-based gross primary productivity (GPP). Validation results show that a masked variation of UNet has the lowest validation RMSE of 37.93 ± 1.36 Mg C/ha, as compared to 52.30 ± 0.03 Mg C/ha for random forest algorithm. Furthermore, models that learn from SIF-based GPP in addition to radar and optical imagery reduce validation RMSE by almost 10% and the standard deviation by 40%. Finally, we apply our model to measure losses in AGB from the recent 2021 Caldor wildfire in California, and validate our analysis with Sentinel-based burn index.
Authors: Juan Nathaniel (Columbia University); Levente Klein (IBM Research); Campbell D Watson (IBM Reserch); Gabrielle Nyirjesy (Columbia University); Conrad M Albrecht (IBM Research)
Computer vision and remote sensing Forestry and other land use Hybrid physical models
NeurIPS 2022 Improving the predictions of ML-corrected climate models with novelty detection (Papers Track)
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Abstract: While previous works have shown that machine learning (ML) can improve the prediction accuracy of coarse-grid climate models, these ML-augmented methods are more vulnerable to irregular inputs than the traditional physics-based models they rely on. Because ML-predicted corrections feed back into the climate model’s base physics, the ML-corrected model regularly produces out of sample data, which can cause model instability and frequent crashes. This work shows that adding semi-supervised novelty detection to identify out-of-sample data and disable the ML-correction accordingly stabilizes simulations and sharply improves the quality of predictions. We design an augmented climate model with a one-class support vector machine (OCSVM) novelty detector that provides better temperature and precipitation forecasts in a year-long simulation than either a baseline (no-ML) or a standard ML-corrected run. By improving the accuracy of coarse-grid climate models, this work helps make accurate climate models accessible to researchers without massive computational resources.
Authors: Clayton H Sanford (Columbia); Anna Kwa (Allen Institute for Artificial Intelligence); Oliver Watt-Meyer (Allen Institute for AI); Spencer Clark (Allen Institute for AI); Noah Brenowitz (Allen Institute for AI); Jeremy McGibbon (Allen Institute for AI); Christopher Bretherton (Allen Institute for AI)
Climate science and climate modeling Hybrid physical models Uncertainty quantification and robustness Unsupervised and semi-supervised learning
NeurIPS 2022 Levee protected area detection for improved flood risk assessment in global hydrology models (Papers Track)
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Abstract: Precise flood risk assessment is needed to reduce human societies vulnerability as climate change increases hazard risk and exposure related to floods. Levees are built to protect people and goods from flood, which alters river hydrology, but are still not accounted for by global hydrological model. Detecting and integrating levee structures to global hydrological simulations is thus expected to enable more precise flood simulation and risk assessment, with important consequences for flood risk mitigation. In this work, we propose a new formulation to the problem of identifying levee structures: instead of detecting levees themselves, we focus on segmenting the region of the floodplain they protect. This formulation allows to better identify protected areas, to leverage the structure of hydrological data, and to simplify the integration of levee information to global hydrological models.
Authors: Masato Ikegawa (Kobe University); Tristan E.M Hascoet (Kobe University); Victor Pellet (Observatoire de Paris); Xudong Zhou (The University of Tokyo); Tetsuya Takiguchi (Kobe University); Dai Yamazaki (The University of Tokyo)
Disaster management and relief Classification, regression, and supervised learning
NeurIPS 2022 Scene-to-Patch Earth Observation: Multiple Instance Learning for Land Cover Classification (Papers Track)
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Abstract: Land cover classification (LCC), and monitoring how land use changes over time, is an important process in climate change mitigation and adaptation. Existing approaches that use machine learning with Earth observation data for LCC rely on fully-annotated and segmented datasets. Creating these datasets requires a large amount of effort, and a lack of suitable datasets has become an obstacle in scaling the use of LCC. In this study, we propose Scene-to-Patch models: an alternative LCC approach utilising Multiple Instance Learning (MIL) that requires only high-level scene labels. This enables much faster development of new datasets whilst still providing segmentation through patch-level predictions, ultimately increasing the accessibility of using LCC for different scenarios. On the DeepGlobe-LCC dataset, our approach outperforms non-MIL baselines on both scene- and patch-level prediction. This work provides the foundation for expanding the use of LCC in climate change mitigation methods for technology, government, and academia.
Authors: Joseph Early (University of Southampton); Ying-Jung C Deweese (Georgia Insititute of Technology); Christine Evers (University of Southampton); Sarvapali Ramchurn (University of Southampton)
Earth observations and monitoring Agriculture and food Cities and urban planning Forestry and other land use Classification, regression, and supervised learning Interpretable ML Unsupervised and semi-supervised learning
NeurIPS 2022 Deep learning for downscaling tropical cyclone rainfall (Papers Track)
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Abstract: Flooding is often the leading cause of mortality and damages from tropical cyclones. With rainfall from tropical cyclones set to rise under global warming, better estimates of extreme rainfall are required to better support resilience efforts. While high resolution climate models capture tropical cyclone statistics well, they are computationally expensive leading to a trade-off between accuracy and generating enough ensemble members to generate sufficient high impact, low probability events. Often, downscaling models are used as a computationally cheaper alternative. Here, we develop and evaluate a set of deep learning models for downscaling tropical cyclone rainfall for more robust risk analysis.
Authors: Emily Vosper (University of Bristol); Lucy Harris (University of Oxford); Andrew McRae (University of Oxford); Laurence Aitchison (University of Bristol); Peter Watson (Bristol); Raul Santos Rodriguez (University of Bristol); Dann Mitchell (University of Bristol)
Extreme weather Climate science and climate modeling Interpretable ML
NeurIPS 2022 Short-term Prediction and Filtering of Solar Power Using State-Space Gaussian Processes (Papers Track)
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Abstract: Short-term forecasting of solar photovoltaic energy (PV) production is important for powerplant management. Ideally these forecasts are equipped with error bars, so that downstream decisions can account for uncertainty. To produce predictions with error bars in this setting, we consider Gaussian processes (GPs) for modelling and predicting solar photovoltaic energy production in the UK. A standard application of GP regression on the PV timeseries data is infeasible due to the large data size and non-Gaussianity of PV readings. However, this is made possible by leveraging recent advances in scalable GP inference, in particular, by using the state-space form of GPs, combined with modern variational inference techniques. The resulting model is not only scalable to large datasets but can also handle continuous data streams via Kalman filtering.
Authors: So Takao (UCL); Sean Nassimiha (UCL); Peter Dudfield (Open Climate Fix); Jack Kelly (Open Climate Fix); Marc Deisenroth (University College London)
Time-series analysis Climate science and climate modeling Power and energy systems Causal and Bayesian methods Uncertainty quantification and robustness
NeurIPS 2022 Identifying latent climate signals using sparse hierarchical Gaussian processes (Papers Track)
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Abstract: Extracting latent climate signals from multiple climate model simulations is important to estimate future climate change. To tackle this we develop a sparse hierarchical Gaussian process (SHGP), which probabilistically learns a latent distribution from a set of vectors. We use this to predict the latent surface temperature change globally and for central England from an ensemble of climate models, in a scalable manner and with robust uncertainty propagation.
Authors: Matt Amos (Lancaster University); Thomas Pinder (Lancaster University); Paul Young (Lancaster University)
Climate science and climate modeling Earth science Causal and Bayesian methods Uncertainty quantification and robustness
NeurIPS 2022 Towards dynamical stability analysis of sustainable power grids using Graph Neural Networks (Papers Track)
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Abstract: To mitigate climate change, the share of renewable needs to be increased. Renewable energies introduce new challenges to power grids due to decentralization, reduced inertia and volatility in production. The operation of sustainable power grids with a high penetration of renewable energies requires new methods to analyze the dynamical stability. We provide new datasets of dynamical stability of synthetic power grids, and find that graph neural networks (GNNs) are surprisingly effective at predicting the highly non-linear target from topological information only. To illustrate the potential to scale to real-sized power grids, we demonstrate the successful prediction on a Texan power grid model.
Authors: Christian Nauck (PIK); Michael Lindner (PIK); Konstantin Schürholt (University of St. Gallen); Frank Hellmann (PIK)
Power and energy systems Classification, regression, and supervised learning
NeurIPS 2022 Detecting Methane Plumes using PRISMA: Deep Learning Model and Data Augmentation (Papers Track)
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Abstract: The new generation of hyperspectral imagers, such as PRISMA, has improved significantly our detection capability of methane (CH4) plumes from space at high spatial resolution (∼30m). We present here a complete framework to identify CH4 plumes using images from the PRISMA satellite mission and a deep learning technique able to automatically detect plumes over large areas. To compensate for the sparse database of PRISMA images, we trained our model by transposing high resolution plumes from Sentinel-2 to PRISMA. Our methodology avoids computationally expensive synthetic plume from Large Eddy Simulations while generating a broad and realistic training database, and paves the way for large-scale detection of methane plumes using future hyperspectral sensors (EnMAP, EMIT, CarbonMapper).
Authors: Alexis Groshenry (Kayrros); Clément Giron (Kayrros); Alexandre d'Aspremont (CNRS, DI, Ecole Normale Supérieure; Kayrros); Thomas Lauvaux (University of Reims Champagne Ardenne, GSMA, UMR 7331); Thibaud Ehret (Centre Borelli)
Computer vision and remote sensing Earth observations and monitoring Earth science Classification, regression, and supervised learning Meta- and transfer learning
NeurIPS 2022 Probabilistic forecasting of regional photovoltaic power production based on satellite-derived cloud motion (Papers Track)
Abstract and authors: (click to expand)
Abstract: Solar energy generation drastically increased in the last years, and it is expected to grow even more in the next decades. So, accurate intra-day forecasts are needed to improve the predictability of the photovoltaic power production and associated balancing measures to increase the shares of renewable energy in the power grid. Most forecasting methods require numerical weather predictions, which are slow to compute, or long-term datasets to run the forecast. These issues make the models difficult to implement in an operational setting. To overcome these problems, we propose a novel regional intraday probabilistic PV power forecasting model able to exploit only 2 hours of satellite-derived cloudiness maps to produce the ensemble forecast. The model is easy to implement in an operational setting as it is based on Pysteps, an already-operational Python library for precipitation nowcasting. With few adaptations of the Steps algorithm, we reached state-of-the-art performance, reaching a 71% lower RMSE than the Persistence model and a 50% lower CRPS than the Persistence Ensemble model for forecast lead times up to 4 hours.
Authors: Alberto Carpentieri (Bern University of Applied Science); Doris Folini (Institute for Atmospheric and Climate Science, ETH Zurich); Martin Wild (Institute for Atmospheric and Climate Science, ETH Zurich); Angela Meyer (Bern University of Applied Science)
Power and energy systems Computer vision and remote sensing Uncertainty quantification and robustness
NeurIPS 2022 Robustifying machine-learned algorithms for efficient grid operation (Papers Track)
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Abstract: We propose a learning-augmented algorithm, RobustML, for operation of dispatchable generation that exploits the good performance of a machine-learned algorithm while providing worst-case guarantees on cost. We evaluate the algorithm on a realistic two-generator system, where it exhibits robustness to distribution shift while enabling improved efficiency as renewable penetration increases.
Authors: Nicolas Christianson (California Institute of Technology); Christopher Yeh (California Institute of Technology); Tongxin Li (The Chinese University of Hong Kong (Shenzhen)); Mahdi Torabi Rad (Beyond Limits); Azarang Golmohammadi (Beyond Limits, Inc.); Adam Wierman (California Institute of Technology)
Uncertainty quantification and robustness Power and energy systems Reinforcement learning and control
NeurIPS 2022 Deep Hydrology: Hourly, Gap-Free Flood Maps Through Joint Satellite and Hydrologic Modelling (Papers Track)
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Abstract: Climate change-driven weather disasters are rapidly increasing in both frequency and magnitude. Floods are the most damaging of these disasters, with approximately 1.46 billion people exposed to inundation depths of over 0.15m, a significant life and livelihood risk. Accurate knowledge of flood-extent for ongoing and historical events facilitates climate adaptation in flood-prone communities by enabling near real-time disaster monitoring to support planning, response, and relief during these extreme events. Satellite observations can be used to derive flood-extent maps directly; however, these observations are impeded by cloud and canopy cover, and can be very infrequent and hence miss the flood completely. In contrast, physically-based inundation models can produce spatially complete event maps but suffer from high uncertainty if not frequently calibrated with expensive land and infrastructure surveys. In this study, we propose a deep learning approach to reproduce satellite-observed fractional flood-extent maps given dynamic state variables from hydrologic models, fusing information contained within the states with direct observations from satellites. Our model has an hourly temporal resolution, contains no cloud-gaps, and generalizes to watersheds across the continental United States with a 6% error on held-out areas that never flooded before. We further demonstrate through a case study in Houston, Texas that our model can distinguish tropical cyclones that caused flooding from those that did not within two days of landfall, thereby providing a reliable source for flood-extent maps that can be used by disaster monitoring services.
Authors: Tanya Nair (Cloud To Street); Veda Sunkara (Cloud to Street); Jonathan Frame (Cloud to Street); Philip Popien (Cloud to Street); Subit Chakrabarti (Cloud To Street)
Computer vision and remote sensing Climate justice Climate science and climate modeling Disaster management and relief Earth science Extreme weather Hybrid physical models
NeurIPS 2022 Machine learning emulation of a local-scale UK climate model (Papers Track)
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Abstract: Climate change is causing the intensification of rainfall extremes. Precipitation projections with high spatial resolution are important for society to prepare for these changes, e.g. to model flooding impacts. Physics-based simulations for creating such projections are very computationally expensive. This work demonstrates the effectiveness of diffusion models, a form of deep generative models, for generating much more cheaply realistic high resolution rainfall samples for the UK conditioned on data from a low resolution simulation. We show for the first time a machine learning model that is able to produce realistic high-resolution rainfall predictions based on a physical model that resolves atmospheric convection, a key process behind extreme rainfall. By adding self-learnt, location-specific information to low resolution relative vorticity, quantiles and time-mean of the samples match well their counterparts from the high-resolution simulation.
Authors: Henry Addison (University of Bristol); Elizabeth Kendon (Met Office Hadley Centre); Suman Ravuri (); Laurence Aitchison (University of Bristol); Peter Watson (Bristol)
Climate science and climate modeling Extreme weather Generative modeling
NeurIPS 2022 Bridging the Microwave Data Gap; Using Bayesian Deep Learning to “See” the Unseen (Papers Track)
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Abstract: Having microwave data with the spatial and temporal resolution of infrared data would provide a large positive impact on many climate and weather applications. We demonstrate that Bayesian deep learning is a promising technique for both creating and improving synthetic microwave data from infrared data. We report 0.7% mean absolute percentage error for 183+/-3 GHz microwave brightness temperature and uncertainty metrics and find that more training data is needed to achieve improved performance at 166 GHz, 37 GHz, and 23 GHz. Analysis of the spatial distribution of uncertainty reveals that additional cloud data will provide the greatest increase in skill, which will potentially allow for generation of many secondary products derived from microwave data in the future.
Earth observations and monitoring Climate science and climate modeling Earth science Extreme weather Causal and Bayesian methods Classification, regression, and supervised learning Uncertainty quantification and robustness
NeurIPS 2022 Learning evapotranspiration dataset corrections from water cycle closure supervision (Papers Track)
Abstract and authors: (click to expand)
Abstract: Evapotranspiration (ET) is one of the most uncertain components of the global water cycle. Improving global ET estimates is needed to better our understanding of the global water cycle so as to forecast the consequences of climate change on the future of global water resource distribution. This work presents a methodology to derive monthly corrections of global ET datasets at 0.25 degree resolution. We use ML to generalize sparse catchment-level water cycle closure residual information to global and dense pixel-level residuals. Our model takes a probabilistic view on ET datasets and their correction that we use to regress catchment-level residuals using a sum-aggregated supervision. Using four global ET datasets, we show that our learned model has learned ET corrections that accurately generalize its water cycle-closure results to unseen catchments.
Authors: Tristan E.M Hascoet (Kobe University); Victor Pellet (LERMA); Filipe Aires (LERMA)
Earth observations and monitoring Climate science and climate modeling Causal and Bayesian methods Classification, regression, and supervised learning
NeurIPS 2022 Convolutional Neural Processes for Inpainting Satellite Images: Application to Water Body Segmentation (Papers Track)
Abstract and authors: (click to expand)
Abstract: The widespread availability of satellite images has allowed researchers to monitor the impact of climate on socio-economic and environmental issues through examples like crop and water body classification to measure food scarcity and risk of flooding. However, a common issue of satellite images is missing values due to measurement defects, which render them unusable by existing methods without data imputation. To repair the data, inpainting methods can be employed, which are based on classical PDEs or interpolation methods. Recently, deep learning approaches have shown promise in this realm, however many of these methods do not explicitly take into account the inherent spatio-temporal structure of satellite images. In this work, we cast satellite image inpainting as a meta-learning problem, and implement Convolutional Neural Processes (ConvNPs) in which we frame each satellite image as its own task or 2D regression problem. We show that ConvNPs outperform classical methods and state-of-the-art deep learning inpainting models on a scanline problem for LANDSAT 7 satellite images, assessed on a variety of in- and out-of-distribution images. Our results successfully match the performance of clean images on a downstream water body segmentation task in Canada.
Authors: Alexander Pondaven (Imperial College London); Mart Bakler (Imperial College London); Donghu Guo (Imperial College London); Hamzah Hashim (Imperial College London); Martin G Ignatov (Imperial college London); Samir Bhatt (Imperial College London); Seth Flaxman (Oxford); Swapnil Mishra (Imperial College London); Elie Alhajjar (USMA); Harrison Zhu (Imperial College London)
Computer vision and remote sensing Earth observations and monitoring Generative modeling Meta- and transfer learning
NeurIPS 2022 A POMDP Model for Safe Geological Carbon Sequestration (Papers Track)
Abstract and authors: (click to expand)
Abstract: Geological carbon capture and sequestration (CCS), where CO2 is stored in subsurface formations, is a promising and scalable approach for reducing global emissions.However, if done incorrectly, it may lead to earthquakes and leakage of CO2 back to the surface, harming both humans and the environment. These risks are exacerbated by the large amount of uncertainty in the structure of the storage formation. For these reasons, we propose that CCS operations be modeled as a partially observable Markov decision process (POMDP) and decisions be informed using automated planning algorithms. To this end, we develop a simplified model of CCS operations based on a 2D spillpoint analysis that retains many of the challenges and safety considerations of the real-world problem. We show how off-the-shelf POMDP solvers outperform expert baselines for safe CCS planning. This POMDP model can be used as a test bed to drive the development of novel decision-making algorithms for CCS operations.
Authors: Anthony Corso (Stanford University); Yizheng Wang (Stanford Univerity); Markus Zechner (Stanford University); Jef Caers (Stanford University); Mykel J Kochenderfer (Stanford University)
Carbon capture and sequestration Reinforcement learning and control
NeurIPS 2022 Optimizing Japanese dam reservoir inflow forecast for efficient operation (Papers Track)
Abstract and authors: (click to expand)
Abstract: Despite a climate and topology favorable to hydropower (HP) generation, HP only accounts for 4% of today’s Japanese primary energy consumption mix. In recent years, calls for improving the efficiency of Japanese HP towards achieving a more sustainable energy mix have emerged from prominent voices in the Ministry of Land, Infrastructure, Transport and Tourism (MILT). Among potential optimizations, data-driven dam operation policies using accurate river discharge forecasts have been advocated for. In the meantime, Machine Learning (ML) has recently made important strides in hydrological modeling, with forecast accuracy improvements demonstrated on both precipitation nowcasting and river discharge prediction. We are motivated by the convergence of these societal and technological contexts: our final goal is to provide scientific evidence and actionable insights for dam infrastructure managers and policy makers to implement more energy-efficient and flood-resistant dam operation policies on a national scale. Towards this goal this work presents a preliminary study of ML-based dam inflow forecasts on a dataset of 127 Japanese public dams we assembled. We discuss our preliminary results and lay out a path for future studies.
Authors: Keisuke Yoshimi (Kobe University); Tristan E.M Hascoet (Kobe University); Rousslan F. Julien Dossa (Kobe University); Ryoichi Takashima (Kobe University); Tetsuya Takiguchi (Kobe University); Satoru Oishi (Kobe University)
Earth science Time-series analysis
NeurIPS 2022 Deep Climate Change: A Dataset and Adaptive domain pre-trained Language Models for Climate Change Related Tasks (Papers Track)
Abstract and authors: (click to expand)
Abstract: The quantity and quality of literature around climate change (CC) and its impacts are increasing yearly. Yet, this field has received limited attention in the Natural Language Processing (NLP) community. With the help of large Language Models (LMs) and transfer learning, NLP can support policymakers, researchers, and climate activists in making sense of large-scale and complex CC-related texts. CC-related texts include specific language that general language models cannot represent accurately. Therefore we collected a climate change corpus consisting of over 360 thousand abstracts of top climate scientists' articles from trustable sources covering large temporal and spatial scales. Comparison of the performance of GPT2 LM and our 'climateGPT2 models', fine-tuned on the CC-related corpus, on claim generation (text generation) and fact-checking, downstream tasks show the better performance of the climateGPT2 models compared to the GPT2. The climateGPT2 models decrease the validation loss to 1.08 for claim generation from 43.4 obtained by GPT2. We found that climateGPT2 models improved the masked language model objective for the fact-checking task by increasing the F1 score from 0.67 to 0.72.
Authors: Saeid Vaghefi (University of Zürich); Veruska Muccione (University of Zürich); Christian Huggel (University of Zürich); Hamed Khashehchi (2w2e GmbH); Markus Leippold (University of Zurich)
Natural language processing Meta- and transfer learning
NeurIPS 2022 Data-Driven Optimal Solver for Coordinating a Sustainable and Stable Power Grid (Papers Track)
Abstract and authors: (click to expand)
Abstract: With today's pressing climate change concerns, the widespread integration of low-carbon technologies such as sustainable generation systems (e.g. photovoltaics, wind turbines, etc.) and flexible consumer devices (e.g. storage, electric vehicles, smart appliances, etc.) into the electric grid is vital. Although these power entities can be deployed at large, these are highly variable in nature and must interact with the existing grid infrastructure without violating electrical limits so that the system continues to operate in a stable manner at all times. In order to ensure the integrity of grid operations while also being economical, system operators will need to rapidly solve the optimal power flow (OPF) problem in order to adapt to these fluctuations. Inherent non-convexities in the OPF problem do not allow traditional model-based optimization techniques to offer guarantees on optimality, feasibility and convergence. In this paper, we propose a data-driven OPF solver built on information-theoretic and semi-supervised machine learning constructs. We show that this solver is able to rapidly compute solutions (i.e. in sub-second range) that are within 3\% of optimality with guarantees on feasibility on a benchmark IEEE 118-bus system.
Authors: Junfei Wang (York University); Pirathayini Srikantha (York University)
Power and energy systems Climate finance and economics Unsupervised and semi-supervised learning
NeurIPS 2022 Don't Waste Data: Transfer Learning to Leverage All Data for Machine-Learnt Climate Model Emulation (Papers Track)
Abstract and authors: (click to expand)
Abstract: How can we learn from all available data when training machine-learnt climate models, without incurring any extra cost at simulation time? Typically, the training data comprises coarse-grained high-resolution data. But only keeping this coarse-grained data means the rest of the high-resolution data is thrown out. We use a transfer learning approach, which can be applied to a range of machine learning models, to leverage all the high-resolution data. We use three chaotic systems to show it stabilises training, gives improved generalisation performance and results in better forecasting skill. Our code is at https://github.com/raghul-parthipan/dont_waste_data
Authors: Raghul Parthipan (University of Cambridge); Damon Wischik (Univeristy of Cambridge)
Climate science and climate modeling Generative modeling Meta- and transfer learning Time-series analysis
NeurIPS 2022 Explainable Multi-Agent Recommendation System for Energy-Efficient Decision Support in Smart Homes (Papers Track)
Abstract and authors: (click to expand)
Abstract: Transparent, understandable, and persuasive recommendations support the electricity consumers’ behavioral change to tackle the energy efficiency problem. This paper proposes an explainable multi-agent recommendation system for load shifting for household appliances. First, we extend a novel multi-agent approach by designing an Explainability Agent that provides explainable recommendations for optimal appliance scheduling in a textual and visual manner. Second, we enhance the predictive capacity of other agents by including weather data and applying state-of-the-art models (i.e., k-nearest-neighbours, extreme gradient boosting, adaptive boosting, random forest, logistic regression, and explainable boosting machines). Since we want to help the user understand a single recommendation, we focus on local explainability approaches. In particular, we apply post-model approaches LIME (local, interpretable, model-agnostic explanation) and SHAP (Shapley additive explanations) as model-agnostic tools that can explain the predictions of the chosen classifiers. We further provide an overview of the predictive and explainability performance. Our results show a substantial improvement in the performance of the multi-agent system while at the same time opening up the “black box” of recommendations. To show the pathway to positive impact regarding climate change, we provide a discussion on the potential impact of the suggested approach.
Authors: Alona Zharova (Humboldt University of Berlin); Annika Boer (Humboldt University of Berlin); Julia Knoblauch (Humboldt University of Berlin); Kai Ingo Schewina (Humboldt University of Berlin); Jana Vihs (Humboldt University of Berlin)
Recommender systems Buildings Power and energy systems Interpretable ML
NeurIPS 2022 FIRO: A Deep-neural Network for Wildfire Forecast with Interpretable Hidden States (Papers Track)
Abstract and authors: (click to expand)
Abstract: Several wildfire danger systems have emerged from decades of research. One such system is the National Fire-Danger Rating System (NFDRS), which is used widely across the United States and is a key predictor in the Global ECMWF Fire Forecasting (GEFF) model. The NFDRS is composed of over 100 equations relating wildfire risk to weather conditions, climate and land cover characteristics, and fuel. These equations and the corresponding 130+ parameters were developed via field and lab experiments. These parameters, which are fixed in the standard NFDRS and GEFF implementations, may not be the most appropriate for a climate-changing world. In order to adjust the NFDRS parameters to current climate conditions and specific geographical locations, we recast NFDRS in PyTorch to create a new deep learning-based Fire Index Risk Optimizer (FIRO). FIRO predicts the ignition component, or the probability a wildfire would require suppression in the presence of a firebrand, and calibrates the uncertain parameters for a specific region and climate conditions by training on observed fires. Given the rare occurrence of wildfires, we employed the extremal dependency index (EDI) as the loss function. Using ERA5 reanalysis and MODIS burned area data, we trained FIRO models for California, Texas, Italy, and Madagascar. Across these four geographies, the average EDI improvement was 175% above the standard NFDRS implementation
Authors: Eduardo R Rodrigues (MSR); Campbell D Watson (IBM Reserch); Bianca Zadrozny (IBM Research); Gabrielle Nyirjesy (Columbia University)
Disaster management and relief Forestry and other land use Interpretable ML
NeurIPS 2022 Towards a spatially transferable super resolution model for downscaling Antarctic surface melt (Papers Track)
Abstract and authors: (click to expand)
Abstract: Surface melt on the Antarctic Ice Sheet is an important climate indicator, yet the spatial scale of modeling and observing surface melt is insufficient to capture crucial details and understand local processes. High-resolution climate models could provide a solution, but they are computationally expensive and require finetuning for some model parameters. An alternative method, pioneering in geophysics, is single-image super resolution (SR) applied on lower-resolution model output. However, often input and output of such SR models are available on the same, fixed spatial domain. High-resolution model simulations over Antarctica are available only in some regions. To be able to apply an SR model elsewhere, we propose to make the single-image SR model physics-aware, using surface albedo and elevation as additional input. Our results show a great improvement in the spatial transferability of the conventional SR model. Although issues with the input satellite-derived albedo remain, adding physics awareness paves a way toward a spatially transferable SR model for downscaling Antarctic surface melt.
Authors: Zhongyang Hu (IMAU); Yao Sun (TUM); Peter Kuipers Munneke (IMAU); Stef Lhermitte (TU Delft); Xiaoxiang Zhu (Technical University of Munich,Germany)
Climate science and climate modeling Earth science Classification, regression, and supervised learning Computer vision and remote sensing
NeurIPS 2022 Forecasting European Ozone Air Pollution With Transformers (Papers Track)
Abstract and authors: (click to expand)
Abstract: Surface ozone is an air pollutant that contributes to hundreds of thousands of premature deaths annually. Accurate short-term ozone forecasts may allow improved policy to reduce the risk to health, such as air quality warnings. However, forecasting ozone is a difficult problem, as surface ozone concentrations are controlled by a number of physical and chemical processes which act on varying timescales. Accounting for these temporal dependencies appropriately is likely to provide more accurate ozone forecasts. We therefore deploy a state-of-the-art transformer-based model, the Temporal Fusion Transformer, trained on observational station data from three European countries. In four-day test forecasts of daily maximum 8-hour ozone, the novel approach is highly skilful (MAE = 4.6 ppb, R2 = 0.82), and generalises well to two European countries unseen during training (MAE = 4.9 ppb, R2 = 0.79). The model outperforms standard machine learning models on our data, and compares favourably to the published performance of other deep learning architectures tested on different data. We illustrate that the model pays attention to physical variables known to control ozone concentrations, and that the attention mechanism allows the model to use relevant days of past ozone concentrations to make accurate forecasts.
Authors: Seb Hickman (University of Cambridge); Paul Griffiths (University of Cambridge); Alex Archibald (University of Cambridge); Peer Nowack (Imperial College London); Elie Alhajjar (USMA)
Climate science and climate modeling Earth science Extreme weather Health Public policy Societal adaptation and resilience Classification, regression, and supervised learning Interpretable ML Time-series analysis
NeurIPS 2022 Stability Constrained Reinforcement Learning for Real-Time Voltage Control (Papers Track)
Abstract and authors: (click to expand)
Abstract: This paper is a summary of a recently submitted work. Deep Reinforcement Learning (DRL) has been recognized as a promising tool to address the challenges in real-time control of power systems. However, its deployment in real-world power systems has been hindered by a lack of explicit stability and safety guarantees. In this paper, we propose a stability constrained reinforcement learning method for real-time voltage control in both single-phase and three-phase distribution grids. The key idea underlying our approach is an explicitly constructed Lyapunov function that certifies stability. We demonstrate the effectiveness of our approach with IEEE test feeders, where the proposed method achieves the best overall performance, while always achieving voltage stability. In contrast, standard RL methods often fail to achieve voltage stability.
Authors: Jie Feng (UCSD); Yuanyuan Shi (University of California San Diego); Guannan Qu (Carnegie Mellon University); Steven Low (California Institute of Technology); Animashree Anandkumar (Caltech); Adam Wierman (California Institute of Technology)
Power and energy systems Reinforcement learning and control
NeurIPS 2022 Land Use Prediction using Electro-Optical to SAR Few-Shot Transfer Learning (Papers Track)
Abstract and authors: (click to expand)
Abstract: Satellite image analysis has important implications for land use, urbanization, and ecosystem monitoring. Deep learning methods can facilitate the analysis of different satellite modalities, such as electro-optical (EO) and synthetic aperture radar (SAR) imagery, by supporting knowledge transfer between the modalities to compensate for individual shortcomings. Recent progress has shown how distributional alignment of neural network embeddings can produce powerful transfer learning models by employing a sliced Wasserstein distance (SWD) loss. We analyze how this method can be applied to Sentinel-1 and -2 satellite imagery and develop several extensions toward making it effective in practice. In an application to few-shot Local Climate Zone (LCZ) prediction, we show that these networks outperform multiple common baselines on datasets with a large number of classes. Further, we provide evidence that instance normalization can significantly stabilize the training process and that explicitly shaping the embedding space using supervised contrastive learning can lead to improved performance.
Authors: Marcel Hussing (University of Pennsylvania); Karen Li (University of Pennsylvania); Eric Eaton (University of Pennsylvania)
Meta- and transfer learning Cities and urban planning Earth observations and monitoring
NeurIPS 2022 Exploring Randomly Wired Neural Networks for Climate Model Emulation (Papers Track)
Abstract and authors: (click to expand)
Abstract: Exploring the climate impacts of various anthropogenic emissions scenarios is key to making informed decisions for climate change mitigation and adaptation. State-of-the-art Earth system models can provide detailed insight into these impacts, but have a large associated computational cost on a per-scenario basis. This large computational burden has driven recent interest in developing cheap machine learning models for the task of climate model emulation. In this manuscript, we explore the efficacy of randomly wired neural networks for this task. We describe how they can be constructed and compare them to their standard feedforward counterparts using the ClimateBench dataset. Specifically, we replace the dense layers in multilayer perceptrons, convolutional neural networks, and convolutional long short-term memory networks with randomly wired ones and assess the impact on model performance for models with 1 million and 10 million parameters. We find average performance improvements of 4.2% across model complexities and prediction tasks, with substantial performance improvements of up to 16.4% in some cases. Furthermore, we find no significant difference in prediction speed between networks with standard feedforward dense layers and those with randomly wired layers. These findings indicate that randomly wired neural networks may be suitable direct replacements for traditional dense layers in many standard models.
Authors: William J Yik (Harvey Mudd College); Sam J Silva (The University of Southern California); Andrew Geiss (Pacific Northwest National Laboratory); Duncan Watson-Parris (University of Oxford)
Climate science and climate modeling Earth observations and monitoring Earth science Extreme weather Classification, regression, and supervised learning Computer vision and remote sensing Time-series analysis
NeurIPS 2022 Closing the Domain Gap -- Blended Synthetic Imagery for Climate Object Detection (Papers Track)
Abstract and authors: (click to expand)
Abstract: Object detection models have great potential to increase both the frequency and cost-efficiency of assessing climate-relevant infrastructure in satellite imagery. However, model performance can suffer when models are applied to stylistically different geographies. We propose a technique to generate synthetic imagery using minimal labeled examples of the target object at a low computational cost. Our technique blends example objects onto unlabeled images of the target domain. We show that including these synthetic images improves the average precision of a YOLOv3 object detection model when compared to a baseline and other popular domain adaptation techniques.
Authors: Caleb Kornfein (Duke University); Frank Willard (Duke University); Caroline Tang (Duke University); Yuxi Long (Duke University); Saksham Jain (Duke University); Jordan Malof (Duke University); Simiao Ren (); Kyle Bradbury (Duke University)
Computer vision and remote sensing Meta- and transfer learning
NeurIPS 2022 SustainGym: A Benchmark Suite of Reinforcement Learning for Sustainability Applications (Papers Track)
Abstract and authors: (click to expand)
Abstract: The lack of standardized benchmarks for reinforcement learning (RL) in sustainability applications has made it difficult to both track progress on specific domains and identify bottlenecks for researchers to focus their efforts on. In this paper, we present SustainGym, a suite of two environments designed to test the performance of RL algorithms on realistic sustainability tasks. The first environment simulates the problem of scheduling decisions for a fleet of electric vehicle (EV) charging stations, and the second environment simulates decisions for a battery storage system bidding in an electricity market. We describe the structure and features of the environments and show that standard RL algorithms have significant room for improving performance. We discuss current challenges in introducing RL to real-world sustainability tasks, including physical constraints and distribution shift.
Authors: Christopher Yeh (California Institute of Technology); Victor Li (California Institute of Technology); Rajeev Datta (California Institute of Technology); Yisong Yue (Caltech); Adam Wierman (California Institute of Technology)
Reinforcement learning and control Power and energy systems
NeurIPS 2022 Remote estimation of geologic composition using interferometric synthetic-aperture radar in California’s Central Valley (Papers Track)
Abstract and authors: (click to expand)
Abstract: California's Central Valley is the national agricultural center, producing 1/4 of the nation’s food. However, land in the Central Valley is sinking at a rapid rate (as much as 20 cm per year) due to continued groundwater pumping. Land subsidence has a significant impact on infrastructure resilience and groundwater sustainability. In this study, we aim to identify specific regions with different temporal dynamics of land displacement and find relationships with underlying geological composition. Then, we aim to remotely estimate geologic composition using interferometric synthetic aperture radar (InSAR)-based land deformation temporal changes using machine learning techniques. We identified regions with different temporal characteristics of land displacement in that some areas (e.g., Helm) with coarser grain geologic compositions exhibited potentially reversible land deformation (elastic land compaction). We found a significant correlation between InSAR-based land deformation and geologic composition using random forest and deep neural network regression models. We also achieved significant accuracy with 1/4 sparse sampling to reduce any spatial correlations among data, suggesting that the model has the potential to be generalized to other regions for indirect estimation of geologic composition. Our results indicate that geologic composition can be estimated using InSAR-based land deformation data. In-situ measurements of geologic composition can be expensive and time consuming and may be impractical in some areas. The generalizability of the model sheds light on high spatial resolution geologic composition estimation utilizing existing measurements.
Authors: KYONGSIK YUN (California Institute of Technology); Kyra Adams (California Institute of Technology); John Reager (California Institute of Technology); Zhen Liu (California Institute of Technology); Caitlyn Chavez (California Institute of Technology); Michael Turmon (California Institute of Technology); Thomas Lu (California Institute of Technology)
Earth observations and monitoring Classification, regression, and supervised learning Interpretable ML
NeurIPS 2022 AutoML for Climate Change: A Call to Action (Papers Track)
Abstract and authors: (click to expand)
Abstract: The challenge that climate change poses to humanity has spurred a rapidly developing field of artificial intelligence research focused on climate change applications. The climate change AI (CCAI) community works on a diverse, challenging set of problems which often involve physics-constrained ML or heterogeneous spatiotemporal data. It would be desirable to use automated machine learning (AutoML) techniques to automatically find high-performing architectures and hyperparameters for a given dataset. In this work, we benchmark popular AutoML libraries on three high-leverage CCAI applications: climate modeling, wind power forecasting, and catalyst discovery. We find that out-of-the-box AutoML libraries currently fail to meaningfully surpass the performance of human-designed CCAI models. However, we also identify a few key weaknesses, which stem from the fact that most AutoML techniques are tailored to computer vision and NLP applications. For example, while dozens of search spaces have been designed for image and language data, none have been designed for spatiotemporal data. Addressing these key weaknesses can lead to the discovery of novel architectures that yield substantial performance gains across numerous CCAI applications. Therefore, we present a call to action to the AutoML community, since there are a number of concrete, promising directions for future work in the space of AutoML for CCAI. We release our code and a list of resources at https://anonymous.4open.science/r/climate-change-automl.
Authors: Renbo Tu (University of Toronto); Nicholas Roberts (University of Wisconsin-Madison); Vishak Prasad C (Indian Institute Of Technology, Bombay); Sibasis Nayak (Indian Institute of Technology, Bombay); Paarth Jain (Indian Institute of Technology Bombay); Frederic Sala (University of Wisconsin-Madison); Ganesh Ramakrishnan (IIT Bombay); Ameet Talwalkar (CMU); Willie Neiswanger (Stanford University); Colin White (Abacus.AI)
Other Climate science and climate modeling Materials science and discovery Power and energy systems
NeurIPS 2022 Temperature impacts on hate speech online: evidence from four billion tweets (Papers Track)
Abstract and authors: (click to expand)
Abstract: Human aggression is no longer limited to the physical space but exists in the form of hate speech on social media. Here, we examine the effect of temperature on the occurrence of hate speech on Twitter and interpret the results in the context of climate change, human behavior and mental health. Employing supervised machine learning models, we identify hate speech in a data set of four billion geolocated tweets from over 750 US cities (2014 – 2020). We statistically evaluate the changes in daily hate tweets against changes in local temperature, isolating the temperature influence from confounding factors using binned panel-regression models. We find a low prevalence of hate tweets in moderate temperatures and observe sharp increases of up to 12% for colder and up to 22% for hotter temperatures, indicating that not only hot but also cold temperatures increase aggressive tendencies. Further, we observe that for extreme temperatures hate speech also increases as a percentage of total tweeting activity, crowding out non-hate speech. The quasi-quadratic shape of the temperature-hate tweet curve is robust across varying climate zones, income groups, religious and political beliefs. The prevalence of the results across climatic and socioeconomic splits points to limits in adaptation. Our results illuminate hate speech online as an impact channel through which temperature alters societal aggression.
Authors: Annika Stechemesser (Potsdam Insitute for Climate Impact Research); Anders Levermann (Potsdam Institute for Climate Impact Research); Leonie Wenz (Potsdam Institute for Climate Impact Research)
Classification, regression, and supervised learning Health Societal adaptation and resilience Data mining Natural language processing
NeurIPS 2022 Cross Modal Distillation for Flood Extent Mapping (Papers Track)
Abstract and authors: (click to expand)
Abstract: The increasing intensity and frequency of floods is one of the many consequences of our changing climate. In this work, we explore ML techniques that improve the flood detection module of an operational early flood warning system. Our method exploits an unlabelled dataset of paired multi-spectral and Synthetic Aperture Radar (SAR) imagery to reduce the labeling requirements of a purely supervised learning method. Past attempts have used such unlabelled data by creating weak labels out of them, but end up learning the label mistakes in those weak labels. Motivated by knowledge distillation and semi supervised learning, we explore the use of a teacher to train a student with the help of a small hand labeled dataset and a large unlabelled dataset. Unlike the conventional self distillation setup, we propose a cross modal distillation framework that transfers supervision from a teacher trained on richer modality (multi-spectral images) to a student model trained on SAR imagery. The trained models are then tested on the Sen1Floods11 dataset. Our model outperforms the Sen1Floods11 SAR baselines by an absolute margin of 4.15% pixel wise Intersection-over-Union (IoU) on the test split.
Computer vision and remote sensing Disaster management and relief Earth observations and monitoring Unsupervised and semi-supervised learning
NeurIPS 2022 Transformer Neural Networks for Building Load Forecasting (Papers Track)
Abstract and authors: (click to expand)
Abstract: Accurate electrical load forecasts of buildings are needed to optimize local energy storage and to make use of demand-side flexibility. We study the usage of Transformer neural networks for short-term electrical load forecasting of 296 buildings from a public dataset. Transformer neural networks trained on many buildings give the best forecasts on 115 buildings, and multi-layer perceptrons trained on a single building are better on 161 buildings. In addition, we evaluate the models on buildings that were not used for training, and find that Transformer neural networks generalize better than multi-layer perceptrons and our statistical baselines. This shows that the usage of Transformer neural networks for building load forecasting could reduce training resources due to the good generalization to unseen buildings, and they could be useful for cold-start scenarios.
Authors: Matthias Hertel (KIT); Simon Ott (KIT); Oliver Neumann (KIT); Benjamin Schäfer (KIT); Ralf Mikut (Karlsruhe Institute of Technology); Veit Hagenmeyer (Karlsruhe Institute of Technology (KIT))
Time-series analysis Buildings Classification, regression, and supervised learning
NeurIPS 2022 Estimating Chicago’s tree cover and canopy height using multi-spectral satellite imagery (Papers Track)
Abstract and authors: (click to expand)
Abstract: Information on urban tree canopies is fundamental to mitigating climate change as well as improving quality of life. Urban tree planting initiatives face a lack of up-to-date data about the horizontal and vertical dimensions of the tree canopy in cities. We present a pipeline that utilizes LiDAR data as ground-truth and then trains a multi-task machine learning model to generate reliable estimates of tree cover and canopy height in urban areas using multi-source multi-spectral satellite imagery for the case study of Chicago.
Authors: John Francis (University College London)
Cities and urban planning Ecosystems and biodiversity Public policy Computer vision and remote sensing
NeurIPS 2022 Reconstruction of Grid Measurements in the Presence of Adversarial Attacks (Papers Track)
Abstract and authors: (click to expand)
Abstract: In efforts to mitigate the adverse effects of climate change, policymakers have set ambitious goals to reduce the carbon footprint of all sectors - including the electric grid. To facilitate this, sustainable energy systems like renewable generation must { be} deployed at high numbers throughout the grid. As these are highly variable in nature, the grid must be closely monitored so that system operators will have elevated situational awareness and can execute timely actions to maintain stable grid operations. With the widespread deployment of sensors like phasor measurement units (PMUs), an abundance of data is available for conducting accurate state estimation. However, due to the cyber-physical nature of the power grid, measurement data can be perturbed in an adversarial manner to enforce incorrect decision-making. In this paper, we propose a novel reconstruction method that leverages on machine learning constructs like CGAN and gradient search to recover the original states when subjected to adversarial perturbations. Experimental studies conducted on the practical IEEE 118-bus benchmark power system show that the proposed method can reduce errors due to perturbation by large margins (i.e. up to 100%).
Authors: amirmohammad naeini (York University); Samer El Kababji (Western University); Pirathayini Srikantha (York University)
Generative modeling Other Unsupervised and semi-supervised learning
NeurIPS 2022 Heat Demand Forecasting with Multi-Resolutional Representation of Heterogeneous Temporal Ensemble (Papers Track)
Abstract and authors: (click to expand)
Abstract: One of the primal challenges faced by utility companies is ensuring efficient supply with minimal greenhouse gas emissions. The advent of smart meters and smart grids provide an unprecedented advantage in realizing an optimised supply of thermal energies through proactive techniques such as load forecasting. In this paper, we propose a forecasting framework for heat demand based on neural networks where the time series are encoded as scalograms equipped with the capacity of embedding exogenous variables such as weather, and holiday/non-holiday. Subsequently, CNNs are utilized to predict the heat load multi-step ahead. Finally, the proposed framework is compared with other state-of-the-art methods, such as SARIMAX and LSTM. The quantitative results from retrospective experiments show that the proposed framework consistently outperforms the state-of-the-art baseline method with real-world data acquired from Denmark. A minimal mean error of 7.54% for MAPE and 417kW for RMSE is achieved with the proposed framework in comparison to all other methods.
Authors: Satyaki Chatterjee (Pattern Recognition Lab, FAU Erlangen-Nuremberg); Adithya Ramachandran (Pattern Recognition Lab, Friedrich Alexander University, Erlangen); Thorkil Flensmark Neergaard (Brønderslev Forsyning A/S); Andreas K Maier (Pattern Recognition Lab, FAU Erlangen-Nuremberg); Siming Bayer (Pattern Recognition Lab, Friedrich-Alexander University)
Time-series analysis Cities and urban planning Power and energy systems Classification, regression, and supervised learning Interpretable ML
NeurIPS 2022 Generalized Ice Detection on Wind Turbine Rotor Blades with Neural Style Transfer (Papers Track)
Abstract and authors: (click to expand)
Abstract: Wind energy’s ability to liberate the world of conventional sources of energy relies on lowering the significant costs associated with the maintenance of wind turbines. Since icing events on turbine rotor blades are a leading cause of operational failures, identifying icing in advance is critical. Some recent studies focus on specific wind parks and fail to generalize to unseen scenarios (e.g. new rotor blade designs). We propose the utilisation of synthetic data augmentation via neural style transfer to improve the generalization of existing ice prediction models. We show that training models with augmented data that captures domain-invariant icing characteristics can help improve predictive performance across multiple wind parks. Through efficient identification of icing, this study can support preventive maintenance of wind energy sources by making them more reliable towards tackling climate change.
Authors: Joyjit Chatterjee (University of Hull); Maria Teresa Alvela Nieto (University of Bremen); Hannes Gelbhardt (University of Bremen); Nina Dethlefs (University of Hull); Jan Ohlendorf (University of Bremen); Klaus-Dieter Thoben (University of Bremen)
Power and energy systems Classification, regression, and supervised learning Computer vision and remote sensing Meta- and transfer learning
NeurIPS 2022 Identifying Compound Climate Drivers of Forest Mortality with β-VAE (Papers Track)
Abstract and authors: (click to expand)
Abstract: Climate change is expected to lead to higher rates of forest mortality. Forest mortality is a complex phenomenon driven by the interaction of multiple climatic variables at multiple temporal scales, further modulated by the current state of the forest (e.g. age, stem diameter, and leaf area index). Identifying the compound climate drivers of forest mortality would greatly improve understanding and projections of future forest mortality risk. Observation data are, however, limited in accuracy and sample size, particularly in regard to forest state variables and mortality events. In contrast, simulations with state-of-the-art forest models enable the exploration of novel machine learning techniques for associating forest mortality with driving climate conditions. Here we simulate 160,000 years of beech, pine and spruce forest dynamics with the forest model FORMIND. We then apply β-VAE to learn disentangled latent representations of weather conditions and identify those that are most likely to cause high forest mortality. The learned model successfully identifies three characteristic climate representations that can be interpreted as different compound drivers of forest mortality.
Authors: Mohit Anand (Helmholtz Centre for Environmental Research - UFZ); Lily-belle Sweet (Helmholtz Centre for Environmental Research - UFZ); Gustau Camps-Valls (Universitat de València); Jakob Zscheischler (Helmholtz Centre for Environmental Research - UFZ)
Generative modeling Climate science and climate modeling Earth observations and monitoring Earth science Ecosystems and biodiversity Extreme weather Forestry and other land use Classification, regression, and supervised learning Interpretable ML Time-series analysis
NeurIPS 2022 TCFD-NLP: Assessing alignment of climate disclosures using NLP for the financial markets (Papers Track)
Abstract and authors: (click to expand)
Abstract: Climate-related disclosure is increasing in importance as companies and stakeholders alike aim to reduce their environmental impact and exposure to climate-induced risk. Companies primarily disclose this information in annual or other lengthy documents where climate information is not the sole focus. To assess the quality of a company's climate-related disclosure, these documents, often hundreds of pages long, must be reviewed manually by climate experts. We propose a more efficient approach to assessing climate-related financial information. We construct a model leveraging TF-IDF, sentence transformers and multi-label k nearest neighbors (kNN). The developed model is capable of assessing alignment of climate disclosures at scale, with a level of granularity and transparency that will support decision-making in the financial markets with relevant climate information. In this paper, we discuss the data that enabled this project, the methodology, and how the resulting model can drive climate impact.
Authors: Rylen Sampson (Manifest Climate); Aysha Cotterill (Manifest Climate); Quoc Tien Au (Manifest Climate)
Climate finance and economics Classification, regression, and supervised learning Natural language processing
NeurIPS 2022 Deep Learning for Rapid Landslide Detection using Synthetic Aperture Radar (SAR) Datacubes (Papers Track)
Abstract and authors: (click to expand)
Abstract: With climate change predicted to increase the likelihood of landslide events, there is a growing need for rapid landslide detection technologies that help inform emergency responses. Synthetic Aperture Radar (SAR) is a remote sensing technique that can provide measurements of affected areas independent from weather or lighting conditions. Usage of SAR, however, is hindered by domain knowledge that is necessary for the pre-processing steps and its interpretation requires expert knowledge. We provide simplified, pre-processed, machine-learning ready SAR datacubes for four globally located landslide events obtained from several Sentinel-1 satellite passes before and after a landslide triggering event together with segmentation maps of the landslides. From this dataset, using the Hokkaido, Japan datacube, we study the feasibility of SAR-based landslide detection with supervised deep learning (DL). Our results demonstrate that DL models can be used to detect landslides from SAR data, achieving an Area under the Precision-Recall curve exceeding 0.7. We find that additional satellite visits enhance detection performance, but that early detection is possible when SAR data is combined with terrain information from a digital elevation model. This can be especially useful for time-critical emergency interventions.
Authors: Vanessa Boehm (UC Berkeley); Wei Ji Leong (The Ohio State University); Ragini Bal Mahesh (German Aerospace Center DLR); Ioannis Prapas (National Observatory of Athens); Siddha Ganju (Nvidia); Freddie Kalaitzis (University of Oxford); Edoardo Nemni (United Nations Satellite Centre (UNOSAT)); Raul Ramos-Pollan (Universidad de Antioquia)
Disaster management and relief Earth observations and monitoring Classification, regression, and supervised learning Computer vision and remote sensing
NeurIPS 2022 Hybrid Recurrent Neural Network for Drought Monitoring (Papers Track)
Abstract and authors: (click to expand)
Abstract: Droughts are pervasive hydrometeorological phenomena and global hazards, whose frequency and intensity are expected to increase in the context of climate change. Drought monitoring is of paramount relevance. Here we propose a hybrid model for drought detection that integrates both climatic indices and data-driven models in a hybrid deep learning approach. We exploit time-series of multi-scale Standardized Precipitation Evapotranspiration Index together with precipitation and temperature as inputs. We introduce a dual-branch recurrent neural network with convolutional lateral connections for blending the data. Experimental and ablative results show that the proposed system outperforms both the considered drought index and purely data-driven deep learning models. Our results suggest the potential of hybrid models for drought monitoring and open the door to synergistic systems that learn from data and domain knowledge altogether.
Authors: Mengxue Zhang (Universitat de València); Miguel-Ángel Fernández-Torres (Universitat de València); Gustau Camps-Valls (Universitat de València)
Climate science and climate modeling Extreme weather Computer vision and remote sensing Hybrid physical models Time-series analysis
NeurIPS 2022 Deep Learning for Global Wildfire Forecasting (Papers Track)
Abstract and authors: (click to expand)
Abstract: Climate change is expected to aggravate wildfire activity through the exacerbation of fire weather. Improving our capabilities to anticipate wildfires on a global scale is of uttermost importance for mitigating their negative effects. In this work, we create a global fire dataset and demonstrate a prototype for predicting the presence of global burned areas on a sub-seasonal scale with the use of segmentation deep learning models. Particularly, we present an open-access global analysis-ready datacube, which contains a variety of variables related to the seasonal and sub-seasonal fire drivers (climate, vegetation, oceanic indices, human-related variables), as well as the historical burned areas and wildfire emissions for 2001-2021. We train a deep learning model, which treats global wildfire forecasting as an image segmentation task and skillfully predicts the presence of burned areas 8, 16, 32 and 64 days ahead of time. Our work motivates the use of deep learning for global burned area forecasting and paves the way towards improved anticipation of global wildfire patterns.
Authors: Ioannis Prapas (National Observatory of Athens); Akanksha Ahuja (NOA); Spyros Kondylatos (National Observatory of Athens); Ilektra Karasante (National Observatory of Athens); Lazaro Alonso (Max Planck Institute for Biogeochemistry); Eleanna Panagiotou (Harokopio University of Athens); Charalampos Davalas (Harokopio University of Athens); Dimitrios Michail (Harokopio University of Athens); Nuno Carvalhais (Max Planck Institute for Biogeochemistry); IOANNIS PAPOUTSIS (National Observatory of Athens)
Earth observations and monitoring Climate science and climate modeling Disaster management and relief Earth science Extreme weather Classification, regression, and supervised learning Computer vision and remote sensing
NeurIPS 2022 Causal Modeling of Soil Processes for Improved Generalization (Papers Track)
Abstract and authors: (click to expand)
Abstract: Measuring and monitoring soil organic carbon is critical for agricultural productivity and for addressing critical environmental problems. Soil organic carbon not only enriches nutrition in soil, but also has a gamut of co-benefits such as improving water storage and limiting physical erosion. Despite a litany of work in soil organic carbon estimation, current approaches do not generalize well across soil conditions and management practices. We empirically show that explicit modeling of cause-and-effect relationships among the soil processes improves the out-of-distribution generalizability of prediction models. We provide a comparative analysis of soil organic carbon estimation models where the skeleton is estimated using causal discovery methods. Our framework provide an average improvement of 81% in test mean squared error and 52% in test mean absolute error.
Authors: Somya Sharma (U. Minnesota); Swati Sharma (Microsoft Research); Emre Kiciman (Microsoft Research); Andy Neal (Rothamstead); Ranveer Chandra (Microsoft Research); John Crawford (University of Glasgow); Sara Malvar (Microsoft); Eduardo R Rodrigues (MSR)
Agriculture and food Causal and Bayesian methods
NeurIPS 2022 Machine Learning for Activity-Based Road Transportation Emissions Estimation (Papers Track)
Abstract and authors: (click to expand)
Abstract: Measuring and attributing greenhouse gas (GHG) emissions remains a challenging problem as the world strives towards meeting emissions reductions targets. As a significant portion of total global emissions, the road transportation sector represents an enormous challenge for estimating and tracking emissions at a global scale. To meet this challenge, we have developed a hybrid approach for estimating road transportation emissions that combines the strengths of machine learning and satellite imagery with localized emissions factors data to create an accurate, globally scalable, and easily configurable GHG monitoring framework.
Authors: Derek Rollend (JHU); Kevin Foster (JHU); Tomek Kott (JHU); Rohita Mocharla (JHU); Rodrigo Rene Rai Munoz Abujder (Johns Hopkins Applied Physics Laboratory); Neil Fendley (JHU/APL); Chace Ashcraft (JHU/APL); Frank Willard (JHU); Marisa Hughes (JHU); Derek Rollend (Unaffiliated)
Transportation Cities and urban planning Classification, regression, and supervised learning Computer vision and remote sensing
NeurIPS 2022 Bayesian State-Space SCM for Deforestation Baseline Estimation for Forest Carbon Credit (Papers Track)
Abstract and authors: (click to expand)
Abstract: In forest carbon credit, the concept of dynamic (or ex-post) baseline has been discussed to overcome the criticism of junk carbon credit, while an ex-ante baseline is still necessary in terms of project finance and risk assessment. We propose a Bayesian state-space SCM, which integrates both ex-ante and ex-post baseline estimation in a time-series causal inference framework. We apply the proposed model to a REDD+ project in Brazil, and show that it might have had a small, positive effect but had been over-credited and that the 90% predictive interval of the ex-ante baseline included the ex-post baseline, implying our ex-ante estimation can work effectively.
Authors: Keisuke Takahata (sustainacraft, Inc.); Hiroshi Suetsugu (sustainacraft, Inc.); Keiichi Fukaya (National Institute for Environmental Studies); Shinichiro Shirota (Hitotsubashi University)
Forestry and other land use Causal and Bayesian methods
NeurIPS 2022 Estimating Corporate Scope 1 Emissions Using Tree-Based Machine Learning Methods (Papers Track)
Abstract and authors: (click to expand)
Abstract: Companies worldwide contribute to climate change, emitting significant amounts of greenhouse gases (GHGs). Yet, most do not report their direct or Scope 1 emissions, resulting in a large data gap in corporate emissions. This study aims to fill this gap by training several decision-tree machine learning models to predict company-level Scope 1 emissions. Our results demonstrate that the Extreme Gradient Boosting and LightGBM models perform best, where the former shows a 19% improvement in prediction error over a benchmark model. Our model is also of reduced complexity and greater computational efficiency; it does not require meta-learners and is trained on a smaller number of features, for which data is more common and accessible compared to prior works. Our features are uniquely chosen based on concepts of environmental pollution in economic theory. Predicting corporate emissions with machine learning can be used as a gap-filling approach, which would allow for better GHG accounting and tracking, thus facilitating corporate decarbonization efforts in the long term. It can also impact representations of a company’s carbon performance and carbon risks, thereby helping to funnel investments towards companies with lower emissions and those making true efforts to decarbonize.
Authors: Elham Kheradmand (University of Montreal); Maida Hadziosmanovic (Concordia University); Nazim Benguettat (Concordia); H. Damon Matthews (Concordia University); Shannon M. Lloyd (Concordia University)
Classification, regression, and supervised learning Climate finance and economics Interpretable ML
NeurIPS 2022 Analyzing Micro-Level Rebound Effects of Energy Efficient Technologies (Papers Track)
Abstract and authors: (click to expand)
Abstract: Energy preservation is central to prevent resource depletion, climate change and environment degradation. Investment in raising efficiency of appliances is among the most significant attempts to save energy. Ironically, introduction of many such energy saving appliances increased the total energy consumption instead of reducing it. This effect in literature is attributed to the inherent Jevons paradox (JP) and optimism bias (OB) in consumer behavior. However, the magnitude of these instincts vary among different people. Identification of this magnitude for each household can enable the development of appropriate policies that induce desired energy saving behaviour. Using the RECS 2015 dataset, the paper uses machine learning for each electrical appliance to determine the dependence of their total energy consumption on their energy star rating. This shows that only substitutable appliances register increase in energy demand upon boosted efficiency. Lastly, an index is noted to indicate the varying influence of JP and OB on different households.
Authors: Mayank Jain (University College Dublin); Mukta Jain (Delhi School of Economics); Tarek T. Alskaif (Wageningen University); Soumyabrata Dev (University College Dublin)
Behavioral and social science Cities and urban planning Power and energy systems Classification, regression, and supervised learning
NeurIPS 2022 Comparing the carbon costs and benefits of low-resource solar nowcasting (Papers Track)
Abstract and authors: (click to expand)
Abstract: Mitigating emissions in line with climate goals requires the rapid integration of low carbon energy sources, such as solar photovoltaics (PV) into the electricity grid. However, the energy produced from solar PV fluctuates due to clouds obscuring the sun's energy. Solar PV yield nowcasting is used to help anticipate peaks and troughs in demand to support grid integration. This paper compares multiple low-resource approaches to nowcasting solar PV yield. To do so, we use a dataset of UK satellite imagery and solar PV energy readings over a 1 to 4-hour time range. Our work investigates the performance of multiple nowcasting models. The paper also estimates the carbon emissions generated and averted by deploying models such as these, and finds that short-term PV forecasting may have a benefit several orders of magnitude greater than its carbon cost and that this benefit holds for small models that could be deployable in low-resource settings around the globe.
Authors: Ben Dixon (UCL); Jacob Bieker (Open Climate Fix); Maria Perez-Ortiz (University College London)
Computer vision and remote sensing Climate science and climate modeling Time-series analysis
NeurIPS 2022 Climate Policy Tracker: Pipeline for automated analysis of public climate policies (Papers Track)
Abstract and authors: (click to expand)
Abstract: The number of standardized policy documents regarding climate policy and their publication frequency is significantly increasing. The documents are long and tedious for manual analysis, especially for policy experts, lawmakers, and citizens who lack access or domain expertise to utilize data analytics tools. Potential consequences of such a situation include reduced citizen governance and involvement in climate policies and an overall surge in analytics costs, rendering less accessibility for the public. In this work, we use a Latent Dirichlet Allocation-based pipeline for the automatic summarization and analysis of 10-years of national energy and climate plans (NECPs) for the period from 2021 to 2030, established by 27 Member States of the European Union. We focus on analyzing policy framing, the language used to describe specific issues, to detect essential nuances in the way governments frame their climate policies and achieve climate goals. The methods leverage topic modeling and clustering for the comparative analysis of policy documents across different countries. It allows for easier integration in potential user-friendly applications for the development of theories and processes of climate policy. This would further lead to better citizen governance and engagement over climate policies and public policy research.
Authors: Artur Żółkowski (Warsaw University of Technology); Mateusz Krzyziński (Warsaw University of Technology); Piotr Wilczyński (Warsaw University of Technology); Stanisław Giziński (University of Warsaw); Emilia Wiśnios (University of Warsaw); Bartosz Pieliński (University of Warsaw); Julian Sienkiewicz (Warsaw University of Technology); Przemysław Biecek (Warsaw University of Technology)
Public policy Natural language processing
NeurIPS 2022 Topic correlation networks inferred from open-ended survey responses reveal signatures of ideology behind carbon tax opinion (Papers Track)
Abstract and authors: (click to expand)
Abstract: Ideology can often render policy design ineffective by overriding what, at face value, are rational incentives. A timely example is carbon pricing, whose public support is strongly influenced by ideology. As a system of ideas, ideology expresses itself in the way people explain themselves and the world. As an object of study, ideology is then amenable to a generative modelling approach within the text-as-data paradigm. Here, we analyze the structure of ideology underlying carbon tax opinion using topic models. An idea, termed a topic, is operationalized as the fixed set of proportions with which words are used when talking about it. We characterize ideology through the relational structure between topics. To access this latent structure, we use the highly expressive Structural Topic Model to infer topics and the weights with which individual opinions mix topics. We fit the model to a large dataset of open-ended survey responses of Canadians elaborating on their support of or opposition to the tax. We propose and evaluate statistical measures of ideology in our data, such as dimensionality and heterogeneity. Finally, we discuss the implications of the results for transition policy in particular, and of our approach to analyzing ideology for computational social science in general.
Authors: Maximilian Puelma Touzel (Mila)
Behavioral and social science Climate finance and economics Public policy Generative modeling Natural language processing
NeurIPS 2022 Controllable Generation for Climate Modeling (Papers Track)
Abstract and authors: (click to expand)
Abstract: Recent years have seen increased interest in modeling future climate trends, especially from the point of view of accurately predicting, understanding and mitigating downstream impacts. For instance, current state-of-the-art process-based agriculture models rely on high-resolution climate data during the growing season for accurate estimation of crop yields. However, high-resolution climate data for future climates is unavailable and needs to be simulated, and that too for multiple possible climate scenarios, which becomes prohibitively expensive via traditional methods. Meanwhile, deep generative models leveraging the expressivity of neural networks have shown immense promise in modeling distributions in high dimensions. Here, we cast the problem of simulation of climate scenarios in a generative modeling framework. Specifically, we leverage the GAN (Generative Adversarial Network) framework for simulating synthetic climate scenarios. We condition the model by quantifying the degree of extremeness" of the observed sample, which allows us to sample from different parts of the distribution. We demonstrate the efficacy of the proposed method on the CHIRPS precipitation dataset.
Authors: Moulik Choraria (University of Illinois at Urbana-Champaign); Daniela Szwarcman (IBM Research); Bianca Zadrozny (IBM Research); Campbell D Watson (IBM Reserch); Lav Varshney (UIUC: ECE)
Climate science and climate modeling Extreme weather Generative modeling
NeurIPS 2022 Learn to Bid: Deep Reinforcement Learning with Transformer for Energy Storage Bidding in Energy and Contingency Reserve Markets (Papers Track)
Abstract and authors: (click to expand)
Abstract: As part of efforts to tackle climate change, grid-scale battery energy storage systems (BESS) play an essential role in facilitating reliable and secure power system operation with variable renewable energy (VRE). BESS can balance time-varying electricity demand and supply in the spot market through energy arbitrage and in the frequency control ancillary services (FCAS) market through service enablement or delivery. Effective algorithms are needed for the optimal participation of BESS in multiple markets. Using deep reinforcement learning (DRL), we present a BESS bidding strategy in the joint spot and contingency FCAS markets, leveraging a transformer-based temporal feature extractor to exploit the temporal trends of volatile energy prices. We validate our strategy on real-world historical energy prices in the Australian National Electricity Market (NEM). We demonstrate that the novel DRL-based bidding strategy significantly outperforms benchmarks. The simulation also reveals that the joint bidding in both the spot and contingency FCAS markets can yield a much higher profit than in individual markets. Our work provides a viable use case for the BESS, contributing to the power system operation with high penetration of renewables.
Authors: Jinhao Li (Monash University); Changlong Wang (Monash University); Yanru Zhang (University of Electronic Science and Technology of China); Hao Wang (Monash University)
Power and energy systems Reinforcement learning and control
NeurIPS 2022 Curriculum Based Reinforcement Learning to Avert Cascading Failures in the Electric Grid (Papers Track)
Abstract and authors: (click to expand)
Abstract: We present an approach to integrate the domain knowledge of the electric power grid operations into reinforcement learning (RL) frameworks for effectively learning RL agents to prevent cascading failures. A curriculum-based approach with reward tuning is incorporated into the training procedure by modifying the environment using the network physics. Our procedure is tested on an actor-critic-based agent on the IEEE 14-bus test system using the RL environment developed by RTE, the French transmission system operator (TSO). We observed that naively training the RL agent without the curriculum approach failed to prevent cascading for most test scenarios, while the curriculum based RL agents succeeded in most test scenarios, illustrating the importance of properly integrating domain knowledge of physical systems for real-world RL applications.
Authors: Amarsagar Reddy Ramapuram Matavalam (Arizona State University); Kishan Guddanti (Pacific Northwest National Lab); Yang Weng (Arizona State University)
Power and energy systems Reinforcement learning and control
NeurIPS 2022 Short-range forecasts of global precipitation using deep learning-augmented numerical weather prediction (Papers Track)
Abstract and authors: (click to expand)
Abstract: Precipitation drives the hydroclimate of Earth and its spatiotemporal changes on a day to day basis have one of the most notable socioeconomic impacts. The success of numerical weather prediction (NWP) is measured by the improvement of forecasts for various physical fields such as temperature and pressure. Large biases however exist in the precipitation predictions. Pure deep learning based approaches lack the advancements acheived by NWP in the past two to three decades. Hybrid methodology using NWP outputs as inputs to the deep learning based refinement tool offer an attractive means taking advantage of both NWP and state of the art deep learning algorithms. Augmenting the output from a well-known NWP model: Coupled Forecast System ver.2 (CFSv2) with deep learning for the first time, we demonstrate a hybrid model capability (DeepNWP) which shows substantial skill improvements for short-range global precipitation at 1-, 2- and 3-days lead time. To achieve this hybridization, we address the sphericity of the global data by using modified DLWP-CS architecture which transforms all the fields to cubed-sphere projection. The dynamical model outputs corresponding to precipitation and surface temperature are ingested to a UNET for predicting the target ground truth precipitation. While the dynamical model CFSv2 shows a bias in the range of +5 to +7 mm/day over land, the multivariate deep learning model reduces it to -1 to +1 mm/day over global land areas. We validate the results by taking examples from Hurricane Katrina in 2005, Hurricane Ivan in 2004, Central European floods in 2010, China floods in 2010, India floods in 2005 and the Myanmar cyclone Nargis in 2008.
Authors: Manmeet Singh (The University of Texas at Austin); Vaisakh SB (Indian Institute of Tropical Meteorology); Nachiketa Acharya (Department of Meteorology and Atmospheric Science,Pennsylvania State University); Aditya Grover (UCLA); Suryachandra A. Rao (Indian Institute of Tropical Meteorology); Bipin Kumar (Indian Institute of Tropical Meteorology); Zong-Liang Yang (The University of Texas at Austin); Dev Niyogi (The University of Texas at Austin)
Climate science and climate modeling Hybrid physical models
NeurIPS 2022 A Multi-Scale Deep Learning Framework for Projecting Weather Extremes (Papers Track)
Abstract and authors: (click to expand)
Abstract: Weather extremes are a major societal and economic hazard, claiming thousands of lives and causing billions of dollars in damage every year. Under climate change, their impact and intensity are expected to worsen significantly. Unfortunately, general circulation models (GCMs), which are currently the primary tool for climate projections, cannot characterize weather extremes accurately. To address this, we present a multi-resolution deep-learning framework that, firstly, corrects a GCM's biases by matching low-order and tail statistics of its output with observations at coarse scales; and secondly, increases the level of detail of the debiased GCM output by reconstructing the finer scales as a function of the coarse scales. We use the proposed framework to generate statistically realistic realizations of the climate over Western Europe from a simple GCM corrected using observational atmospheric reanalysis. We also discuss implications for probabilistic risk assessment of natural disasters in a changing climate.
Authors: Antoine Blanchard (MIT); Nishant Parashar (Verisk Analytics); Boyko Dodov (Verisk Analytics); Christian Lessig (Otto-von-Guericke-Universitat Magdeburg); Themis Sapsis (MIT)
Extreme weather Hybrid physical models
NeurIPS 2022 A Global Classification Model for Cities using ML (Papers Track)
Abstract and authors: (click to expand)
Abstract: This paper develops a novel data set for three key resources use; namely, food, water, and energy, for 9000 cities globally. The data set is then utilized to develop a clustering approach as a starting point towards a global classification model. This novel clustering approach aims to contribute to developing an inclusive view of resource efficiency for all urban centers globally. The proposed clustering algorithm is comprised of three steps: first, outlier detection to address specific city characteristics, then a Variational Autoencoder (VAE), and finally, Agglomerative Clustering (AC) to improve the classification results. Our results show that this approach is more robust and yields better results in creating delimited clusters with high Calinski-Harabasz Index scores and Silhouette Coefficient than other baseline clustering methods.
Authors: Doron Hazan (MIT); Mohamed Habashy (Massachusetts Institute of Technology); Mohanned ElKholy (Massachusetts Institute of Technology); Omer Mousa (American University in Cairo); Norhan M Bayomi (MIT Environmental Solutions Initiative); Matias Williams (Massachusetts Institute of Technology); John Fernandez (Massachusetts Institute of Technology)
Cities and urban planning Classification, regression, and supervised learning Data mining
NeurIPS 2022 EnhancedSD: Downscaling Solar Irradiance from Climate Model Projections (Papers Track)
Abstract and authors: (click to expand)
Abstract: Renewable energy-based electricity systems are seen as a keystone of future decarbonization efforts. However, power system planning does not currently consider the impacts of climate change on renewable energy resources such as solar energy, chiefly due to a paucity of climate-impacted high-resolution solar power data. Existing statistical downscaling (SD) methods that learn to map coarse-resolution versions of historical reanalysis data to generate finer resolution outputs are of limited use when applied to future climate model projections due to the domain gap between climate models and reanalysis data. In contrast, we present EnhancedSD, a deep learning-based framework for downscaling coarse-scale climate model outputs to high-resolution observational (reanalysis) data. Our proposed ML based downscaling allows for future reanalysis projections, which can be pivotal for mitigating climate change’s impacts on power systems planning.
Authors: Nidhin Harilal (University of Colorado, Boulder); Bri-Mathias S Hodge (University of Colorado Boulder); Claire Monteleoni (University of Colorado Boulder); Aneesh Subramanian (University of California, San Diego)
Computer vision and remote sensing Climate science and climate modeling Power and energy systems
NeurIPS 2022 Positional Encoder Graph Neural Networks for Geographic Data (Papers Track)
Abstract and authors: (click to expand)
Abstract: Modeling spatial dependencies in geographic data is of crucial importance for the modeling of our planet. Graph neural networks (GNNs) provide a powerful and scalable solution for modeling continuous spatial data. However, in the absence of further context on the geometric structure of the data, they often rely on Euclidean distances to construct the input graphs. This assumption can be improbable in many real-world settings, where the spatial structure is more complex and explicitly non-Euclidean (e.g., road networks). In this paper, we propose PE-GNN, a new framework that incorporates spatial context and correlation explicitly into the models. Building on recent advances in geospatial auxiliary task learning and semantic spatial embeddings, our proposed method (1) learns a context-aware vector encoding of the geographic coordinates and (2) predicts spatial autocorrelation in the data in parallel with the main task. We show the effectiveness of our approach on two climate-relevant regression tasks: 3d spatial interpolation and air temperature prediction. The code for this study can be accessed via: https://bit.ly/3xDpfyV.
Authors: Konstantin Klemmer (Microsoft Research); Nathan S Safir (University of Georgia); Daniel B Neill (New York University)
Classification, regression, and supervised learning Climate science and climate modeling Earth observations and monitoring Extreme weather
NeurIPS 2022 Image-based Early Detection System for Wildfires (Papers Track)
Abstract and authors: (click to expand)
Abstract: Wildfires are a disastrous phenomenon which cause damage to land, loss of property, air pollution, and even loss of human life. Due to the warmer and drier conditions created by climate change, more severe and uncontrollable wildfires are expected to occur in the coming years. This could lead to a global wildfire crisis and have dire consequences on our planet. Hence, it has become imperative to use technology to help prevent the spread of wildfires. One way to prevent the spread of wildfires before they become too large is to perform early detection i.e, detecting the smoke before the actual fire starts. In this paper, we present our Wildfire Detection and Alert System which use machine learning to detect wildfire smoke with a high degree of accuracy and can send immediate alerts to users. Our technology is currently being used in the USA to monitor data coming in from hundreds of cameras daily. We show that our system has a high true detection rate and a low false detection rate. Our performance evaluation study also shows that on an average our system detects wildfire smoke faster than an actual person.
Authors: Omkar Ranadive (Alchera X); Jisu Kim (Alchera); Serin Lee (Alchera X); Youngseo Cha (Alchera); Heechan Park (Alchera); Minkook Cho (Alchera); Young Hwang (Alchera)
Computer vision and remote sensing Disaster management and relief Other Classification, regression, and supervised learning
NeurIPS 2022 Towards Global Crop Maps with Transfer Learning (Papers Track)
Abstract and authors: (click to expand)
Abstract: The continuous increase in global population and the impact of climate change on crop production are expected to affect the food sector significantly. In this context, there is need for timely, large-scale and precise mapping of crops for evidence-based decision making. A key enabler towards this direction are new satellite missions that freely offer big remote sensing data of high spatio-temporal resolution and global coverage. During the previous decade and because of this surge of big Earth observations, deep learning methods have dominated the remote sensing and crop mapping literature. Nevertheless, deep learning models require large amounts of annotated data that are scarce and hard-to-acquire. To address this problem, transfer learning methods can be used to exploit available annotations and enable crop mapping for other regions, crop types and years of inspection. In this work, we have developed and trained a deep learning model for paddy rice detection in South Korea using Sentinel-1 VH time-series. We then fine-tune the model for i) paddy rice detection in France and Spain and ii) barley detection in the Netherlands. Additionally, we propose a modification in the pre-trained weights in order to incorporate extra input features (Sentinel-1 VV). Our approach shows excellent performance when transferring in different areas for the same crop type and rather promising results when transferring in a different area and crop type.
Authors: Hyun-Woo Jo (Korea University); Alkiviadis Marios Koukos (National Observatory of Athens); Vasileios Sitokonstantinou (National Observatory of Athens); Woo-Kyun Lee (Korea University); Charalampos Kontoes (National Observatory of Athens)
Meta- and transfer learning Agriculture and food Earth observations and monitoring Forestry and other land use Classification, regression, and supervised learning Computer vision and remote sensing
NeurIPS 2022 Pyrocast: a Machine Learning Pipeline to Forecast Pyrocumulonimbus (PyroCb) Clouds (Papers Track)
Abstract and authors: (click to expand)
Abstract: Pyrocumulonimbus (pyroCb) clouds are storm clouds generated by extreme wildfires. PyroCbs are associated with unpredictable, and therefore dangerous, wildfire spread. They can also inject smoke particles and trace gases into the upper troposphere and lower stratosphere, affecting the Earth's climate. As global temperatures increase, these previously rare events are becoming more common. Being able to predict which fires are likely to generate pyroCb is therefore key to climate adaptation in wildfire-prone areas. This paper introduces Pyrocast, a pipeline for pyroCb analysis and forecasting. The pipeline's first two components, a pyroCb database and a pyroCb forecast model, are presented. The database brings together geostationary imagery and environmental data for over 148 pyroCb events across North America, Australia, and Russia between 2018 and 2022. Random Forests, Convolutional Neural Networks (CNNs), and CNNs pretrained with Auto-Encoders were tested to predict the generation of pyroCb for a given fire six hours in advance. The best model predicted pyroCb with an AUC of 0.90±0.04.
Authors: Kenza Tazi (University of Cambridge); Emiliano Díaz Salas-Porras (University of Valencia); Ashwin Braude (Institut Pierre-Simon Laplace); Daniel Okoh (National Space Research and Development Agency\); Kara D. Lamb (Columbia University); Duncan Watson-Parris (University of Oxford); Paula Harder (Fraunhofer ITWM); Nis Meinert (Pasteur Labs)
Classification, regression, and supervised learning Earth observations and monitoring Computer vision and remote sensing
NeurIPS 2022 Evaluating Digital Tools for Sustainable Agriculture using Causal Inference (Papers Track)
Abstract and authors: (click to expand)
Abstract: In contrast to the rapid digitalization of several industries, agriculture suffers from low adoption of climate-smart farming tools. Even though AI-driven digital agriculture can offer high-performing predictive functionalities, they lack tangible quantitative evidence on their benefits to the farmers. Field experiments can derive such evidence, but are often costly and time consuming. To this end, we propose an observational causal inference framework for the empirical evaluation of the impact of digital tools on target farm performance indicators. This way, we can increase farmers' trust via enhancing the transparency of the digital agriculture market, and in turn accelerate the adoption of technologies that aim to increase productivity and secure a sustainable and resilient agriculture against a changing climate. As a case study, we perform an empirical evaluation of a recommendation system for optimal cotton sowing, which was used by a farmers' cooperative during the growing season of 2021. We leverage agricultural knowledge to develop the causal graph of the farm system, we use the back-door criterion to identify the impact of recommendations on the yield and subsequently we estimate it using several methods on observational data. The results showed that a field sown according to our recommendations enjoyed a significant increase in yield 12% to 17%.
Authors: Ilias Tsoumas (National Observatory of Athens); Georgios Giannarakis (National Observatory of Athens); Vasileios Sitokonstantinou (National Observatory of Athens); Alkiviadis Marios Koukos (National Observatory of Athens); Dimitra A Loka (Hellenic Agricultural Organization ELGO DIMITRA); Nikolaos S Bartsotas (National Observatory of Athens); Charalampos Kontoes (National Observatory of Athens); Ioannis N Athanasiadis (Wageningen University and Research)
Causal and Bayesian methods Agriculture and food Earth observations and monitoring Extreme weather Societal adaptation and resilience
NeurIPS 2022 Generating physically-consistent high-resolution climate data with hard-constrained neural networks (Papers Track)
Abstract and authors: (click to expand)
Abstract: The availability of reliable, high-resolution climate and weather data is important to inform long-term decisions on climate adaptation and mitigation and to guide rapid responses to extreme events. Forecasting models are limited by computational costs and therefore often can only make coarse resolution predictions. Statistical downscaling can provide an efficient method of upsampling low-resolution data. In this field, deep learning has been applied successfully, often using image super-resolution methods from computer vision. Despite achieving visually compelling results in some cases, such models often violate conservation laws when predicting physical variables. In order to conserve important physical quantities, we developed a deep downscaling method that guarantees physical constraints are satisfied, by adding a renormalization layer at the end of the neural network. Furthermore, the constrained model also improves the performance according to standard metrics. We show the applicability of our methods across different popular architectures and upsampling factors using ERA5 reanalysis data.
Authors: Paula Harder (Mila); Qidong Yang (New York University); Venkatesh Ramesh (Mila); Prasanna Sattigeri (IBM Research); Alex Hernandez-Garcia (Mila - Quebec AI Institute); Campbell D Watson (IBM Reserch); Daniela Szwarcman (IBM Research); David Rolnick (McGill University, Mila)
Climate science and climate modeling Classification, regression, and supervised learning
NeurIPS 2022 Transformers for Fast Emulation of Atmospheric Chemistry Box Models (Papers Track)
Abstract and authors: (click to expand)
Abstract: When modeling atmospheric chemistry, concentrations are determined by numerically solving large systems of ordinary differential equations that represent a set of chemical reactions. These solvers can be very computationally intensive, particularly those with the thousands or tens of thousands of chemical species and reactions that make up the most accurate models. We demonstrate the application of a deep learning transformer architecture to emulate an atmospheric chemistry box model, and show that this attention-based model outperforms LSTM and autoencoder baselines while providing interpretable predictions that are more than 2 orders of magnitude faster than a numerical solver. This work is part of a larger study to replace the numerical solver in a 3D global chemical model with a machine learned emulator and achieve significant speedups for global climate simulations.
Authors: Herbie Bradley (University of Cambridge); Nathan Luke Abraham (National Centre for Atmospheric Science, UK); Peer Nowack (Imperial College London); Doug McNeall (Met Office Hadley Centre, UK)
Climate science and climate modeling Earth science Hybrid physical models Time-series analysis
NeurIPS 2022 Flood Prediction with Graph Neural Networks (Papers Track)
Abstract and authors: (click to expand)
Abstract: Climate change is increasing the frequency of flooding around the world. As a consequence, there is a growing demand for effective flood prediction. Machine learning is a promising alternative to hydrodynamic models for flood prediction. However, existing approaches focus on capturing either the spatial or temporal flood patterns using CNNs or RNNs, respectively. In this work, we propose FloodGNN, which is a graph neural network (GNN) for flood prediction. Compared to existing approaches, FloodGNN (i) employs a graph-based model (GNN); (ii) operates on both spatial and temporal dimensions; and (iii) processes the water flow velocities as vector features, instead of scalar features. Experiments show that FloodGNN achieves promising results, outperforming an RNN-based baseline.
Authors: Arnold N Kazadi (Rice University); James Doss-Gollin (Rice University); Antonia Sebastian (UNC Chapel Hill); Arlei Silva (Rice University)
Extreme weather Classification, regression, and supervised learning
NeurIPS 2022 Neural Representation of the Stratospheric Ozone Layer (Papers Track)
Abstract and authors: (click to expand)
Abstract: In climate modeling, the stratospheric ozone layer is typically only considered in a highly simplified form due to computational constraints. For climate projections, it would be of advantage to include the mutual interactions between stratospheric ozone, temperature, and atmospheric dynamics to accurately represent radiative forcing. The overarching goal of our research is to replace the ozone chemistry in climate models with a machine-learned neural representation of the stratospheric ozone chemistry that allows for a particularly fast, but accurate and stable simulation. We created a benchmark data set from pairs of input and output variables that we stored from simulations of a chemistry and transport model. We analyzed several variants of multilayer perceptrons suitable for physical problems to learn a neural representation of a function that predicts 24-hour ozone tendencies based on input variables. We performed a comprehensive hyperparameter optimization of the multilayer perceptron using Bayesian search and Hyperband early stopping. We validated our model by implementing it in a chemistry and transport model and comparing computation time, accuracy, and stability with the full chemistry module. We found that our model had a computation time that was a factor of 700 faster than the full chemistry module. The accuracy of our model compares favorably to the full chemistry module within a two-year simulation run, also outperforms a previous polynomial approach for fast ozone chemistry, and reproduces seasonality well in both hemispheres. In conclusion, the neural representation of stratospheric ozone chemistry in simulation resulted in an ozone layer that showed a high accuracy, significant speed-up, and stability in a long-term simulation.
Authors: Helge Mohn (Alfred Wegener Institute for Polar and Marine Research); Daniel Kreyling (Alfred Wegener Institute for Polar and Marine Research); Ingo Wohltmann (Alfred Wegener Institute for Polar and Marine Research); Ralph Lehmann (Alfred Wegener Institute for Polar and Marine Research); Peter Maaß (University of Bremen); Markus Rex (Alfred Wegener Institute for Polar and Marine Research)
Climate science and climate modeling Classification, regression, and supervised learning
NeurIPS 2022 DL-Corrector-Remapper: A grid-free bias-correction deep learning methodology for data-driven high-resolution global weather forecasting (Papers Track)
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Abstract: Data-driven models, such as FourCastNet (FCN), have shown exemplary performance in high-resolution global weather forecasting. This performance, however, is based on supervision on mesh-gridded weather data without the utilization of raw climate observational data, the gold standard ground truth. In this work we develop a methodology to correct, remap, and fine-tune gridded uniform forecasts of FCN so it can be directly compared against observational ground truth, which is sparse and non-uniform in space and time. This is akin to bias-correction and post-processing of numerical weather prediction (NWP), a routine operation at meteorological and weather forecasting centers across the globe. The Adaptive Fourier Neural Operator (AFNO) architecture is used as the backbone to learn continuous representations of the atmosphere. The spatially and temporally non-uniform output is evaluated by the non-uniform discrete inverse Fourier transform (NUIDFT) given the output query locations. We call this network the Deep-Learning-Corrector-Remapper (DLCR). The improvement in DLCR’s performance against the gold standard ground truth over the baseline’s performance shows its potential to correct, remap, and fine-tune the mesh-gridded forecasts under the supervision of observations.
Authors: Tao Ge (Washington University in St. Louis); Jaideep Pathak (NVIDIA Corporation); Akshay Subramaniam (NVIDIA); Karthik Kashinath (NVIDIA)
Classification, regression, and supervised learning Climate science and climate modeling Extreme weather
NeurIPS 2022 Industry-scale CO2 Flow Simulations with Model-Parallel Fourier Neural Operators (Papers Track)
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Abstract: Carbon capture and storage (CCS) is one of the most promising technologies for reducing greenhouse gas emissions and relies on numerical reservoir simulations for identifying and monitoring CO2 storage sites. In many commercial settings however, numerical reservoir simulations are too computationally expensive for important downstream application such as optimization or uncertainty quantification. Deep learning-based surrogate models offer the possibility to solve PDEs many orders of magnitudes faster than conventional simulators, but they are difficult to scale to industrial-scale problem settings. Using model-parallel deep learning, we train the largest CO2 surrogate model to date on a 3D simulation grid with two million grid points. To train the 3D simulator, we generate a new training dataset based on a real-world CCS simulation benchmark. Once trained, each simulation with the network is five orders of magnitude faster than a numerical reservoir simulator and 4,500 times cheaper. This paves the way to applications that require thousands of (sequential) simulations, such as optimizing the location of CO2 injection wells to maximize storage capacity and minimize risk of leakage.
Authors: Philipp A Witte (Microsoft); Russell Hewett (Microsoft); Ranveer Chandra (Microsoft Research)
Carbon capture and sequestration Classification, regression, and supervised learning
NeurIPS 2022 Adaptive Bias Correction for Improved Subseasonal Forecasting (Papers Track)
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Abstract: Subseasonal forecasting — predicting temperature and precipitation 2 to 6 weeks ahead — is critical for effective water allocation, wildfire management, and drought and flood mitigation. Recent international research efforts have advanced the subseasonal capabilities of operational dynamical models, yet temperature and precipitation prediction skills remains poor, partly due to stubborn errors in representing atmospheric dynamics and physics inside dynamical models. To counter these errors, we introduce an adaptive bias correction (ABC) method that combines state-of-the-art dynamical forecasts with observations using machine learning. When applied to the leading subseasonal model from the European Centre for Medium-Range Weather Forecasts (ECMWF), ABC improves temperature forecasting skill by 60-90% and precipitation forecasting skill by 40-69% in the contiguous U.S. We couple these performance improvements with a practical workflow, based on Cohort Shapley, for explaining ABC skill gains and identifying higher-skill windows of opportunity based on specific climate conditions.
Authors: Soukayna Mouatadid (University of Toronto); Paulo Orenstein (IMPA); Genevieve E Flaspohler (MIT); Judah Cohen (AER); Miruna Oprescu (Cornell University); Ernest Fraenkel (MIT); Lester Mackey (Microsoft Research New England)
Climate science and climate modeling Extreme weather
NeurIPS 2022 Nowformer : A Locally Enhanced Temporal Learner for Precipitation Nowcasting (Papers Track)
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Abstract: The precipitation video datasets have distinctive meteorological patterns where a mass of fluid moves in a particular direction across the entire frames, and each local area of the fluid has an individual life cycle from initiation to maturation to decay. This paper proposes a novel transformer-based model for precipitation nowcasting that can extract global and local dynamics within meteorological characteristics. The experimental results show our model achieves state-of-the-art performances on the precipitation nowcasting benchmark.
Authors: jinyoung park (KAIST); Inyoung Lee (KAIST); Minseok Son (KAIST); Seungju Cho (KAIST); Changick Kim (KAIST)
Computer vision and remote sensing Earth observations and monitoring
NeurIPS 2022 An Unsupervised Learning Perspective on the Dynamic Contribution to Extreme Precipitation Changes (Papers Track)
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Abstract: Despite the importance of quantifying how the spatial patterns of extreme precipitation will change with warming, we lack tools to objectively analyze the storm-scale outputs of modern climate models. To address this gap, we develop an unsupervised machine learning framework to quantify how storm dynamics affect precipitation extremes and their changes without sacrificing spatial information. Over a wide range of precipitation quantiles, we find that the spatial patterns of extreme precipitation changes are dominated by spatial shifts in storm regimes rather than intrinsic changes in how these storm regimes produce precipitation.
Authors: Griffin S Mooers (UC Irvine); Tom Beucler (University of Lausanne); Michael Pritchard (UCI); Stephan Mandt (University of California, Irivine)
Climate science and climate modeling Unsupervised and semi-supervised learning
NeurIPS 2022 An Interpretable Model of Climate Change Using Correlative Learning (Papers Track)
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Abstract: Determining changes in global temperature and precipitation that may indicate climate change is complicated by annual variations. One approach for finding potential climate change indicators is to train a model that predicts the year from annual means of global temperatures and precipitations. Such data is available from the CMIP6 ensemble of simulations. Here a two-hidden-layer neural network trained on this data successfully predicts the year. Differences among temperature and precipitation patterns for which the model predicts specific years reveal changes through time. To find these optimal patterns, a new way of interpreting what the neural network has learned is explored. Alopex, a stochastic correlative learning algorithm, is used to find optimal temperature and precipitation maps that best predict a given year. These maps are compared over multiple years to show how temperature and precipitations patterns indicative of each year change over time.
Climate science and climate modeling Interpretable ML
NeurIPS 2022 Multimodal Wildland Fire Smoke Detection (Papers Track)
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Abstract: Research has shown that climate change creates warmer temperatures and drier conditions, leading to longer wildfire seasons and increased wildfire risks in the United States. These factors have in turn led to increases in the frequency, extent, and severity of wildfires in recent years. Given the danger posed by wildland fires to people, property, wildlife, and the environment, there is an urgency to provide tools for effective wildfire management. Early detection of wildfires is essential to minimizing potentially catastrophic destruction. In this paper, we present our work on integrating multiple data sources in SmokeyNet, a deep learning model using spatio-temporal information to detect smoke from wildland fires. Camera image data is integrated with weather sensor measurements and processed by SmokeyNet to create a multimodal wildland fire smoke detection system. Our results show that incorporating multimodal data in SmokeyNet improves performance in terms of both F1 and time-to-detection over the baseline with a single data source. With a time-to-detection of only a few minutes, SmokeyNet can serve as an automated early notification system, providing a useful tool in the fight against destructive wildfires.
Authors: Mai Nguyen (University of California San Diego); Shreyas Anantha Ramaprasad (University of California San Diego); Jaspreet Kaur Bhamra (University of California San Diego); Siddhant Baldota (University of California San Diego); Garrison Cottrell (UC San Diego)
Disaster management and relief Computer vision and remote sensing
NeurIPS 2022 Using uncertainty-aware machine learning models to study aerosol-cloud interactions (Papers Track)
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Abstract: Aerosol-cloud interactions (ACI) include various effects that result from aerosols entering a cloud, and affecting cloud properties. In general, an increase in aerosol concentration results in smaller droplet sizes which leads to larger, brighter, longer-lasting clouds that reflect more sunlight and cool the Earth. The strength of the effect is however heterogeneous, meaning it depends on the surrounding environment, making ACI one of the most uncertain effects in our current climate models. In our work, we use causal machine learning to estimate ACI from satellite observations by reframing the problem as a treatment (aerosol) and outcome (change in droplet radius). We predict the causal effect of aerosol on clouds with uncertainty bounds depending on the unknown factors that may be influencing the impact of aerosol. Of the three climate models evaluated, we find that only one plausibly recreates the trend, lending more credence to its estimate cooling due to ACI.
Authors: Maëlys Solal (University of Oxford); Andrew Jesson (University of Oxford); Yarin Gal (University of Oxford); Alyson Douglas (University of Oxford)
Causal and Bayesian methods Climate science and climate modeling Earth observations and monitoring Uncertainty quantification and robustness
NeurIPS 2022 Accessible Large-Scale Plant Pathology Recognition (Papers Track)
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Abstract: Plant diseases are costly and threaten agricultural production and food security worldwide. Climate change is increasing the frequency and severity of plant diseases and pests. Therefore, detection and early remediation can have a significant impact, especially in developing countries. However, AI solutions are yet far from being in production. The current process for plant disease diagnostic consists of manual identification and scoring by humans, which is time-consuming, low-supply, and expensive. Although computer vision models have shown promise for efficient and automated plant disease identification, there are limitations for real-world applications: a notable variation in visual symptoms of a single disease, different light and weather conditions, and the complexity of the models. In this work, we study the performance of efficient classification models and training "tricks" to solve this problem. Our analysis represents a plausible solution for these ecological disasters and might help to assist producers worldwide. More information available at: https://github.com/mv-lab/mlplants
Authors: Marcos V. Conde (University of Würzburg); Dmitry Gordeev (H2O.ai)
Computer vision and remote sensing Disaster management and relief Forestry and other land use Health Active learning Classification, regression, and supervised learning
NeurIPS 2022 Dynamic weights enabled Physics-Informed Neural Network for simulating the mobility of Engineered Nano Particles in a contaminated aquifer (Papers Track)
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Abstract: Numerous polluted groundwater sites across the globe require an active remediation strategy for the restoration of natural environmental conditions and local ecosystem. The Engineered Nanoparticles (ENPs) has emerged as an efficient reactive agent for the in-situ degradation of groundwater contaminants. While the performance of these ENPs has been highly promising on the laboratory scale, their application in a real field case conditions is still limited. The optimized injection of the ENPs in the contaminated aquifer and its subsequent monitoring are hindered by the complex transport and retention mechanisms of ENPs. Therefore, a predictive tool for understanding the transport and retention behavior of ENPs becomes highly important. The existing tools in the literature are dominated with numerical simulators, which have limited flexibility and accuracy in the presence of sparse dataset. In this work, a dynamic weights enabled Physics-Informed Neural network (dw-PINN) framework is applied to model the nano-particle´s behavior within an aquifer. The result from the forward model demonstrates the effective capability of dw-PINN in accurately predicting the ENPs mobility. The model verification step shows that the mean squared error of the predicted ENPs concentration using dw-PINN converges to a minimum value of 1.3e-5. In the subsequent step, the result from the inverse model estimates the governing parameters of ENPs mobility with reasonable accuracy. The research work demonstrates the tool´s capability in providing predictive insights for the development of an efficient groundwater remediation strategy.
Authors: shikhar Nilabh (Amphos21)
Earth science Hybrid physical models
NeurIPS 2022 Calibration of Large Neural Weather Models (Papers Track)
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Abstract: Uncertainty quantification of weather forecasts is a necessity for reliably planning for and responding to extreme weather events in a warming world. This motivates the need for well-calibrated ensembles in probabilistic weather forecasting. We present initial results for the calibration of large-scale deep neural weather models for data-driven probabilistic weather forecasting. By explicitly accounting for uncertainties about the forecast's initial condition and model parameters, we generate ensemble forecasts that show promising results on standard diagnostics for probabilistic forecasts. Specifically, we are approaching the Integrated Forecasting System (IFS), the gold standard on probabilistic weather forecasting, on: (i) the spread-error agreement; and (ii) the Continuous Ranked Probability Score (CRPS). Our approach scales to state-of-the-art data-driven weather models, enabling cheap post-hoc calibration of pretrained models with tens of millions of parameters and paving the way towards the next generation of well-calibrated data-driven weather models.
Authors: Andre Graubner (Nvidia); Kamyar Kamyar Azizzadenesheli (Nvidia); Jaideep Pathak (NVIDIA Corporation); Morteza Mardani (Nvidia); Mike Pritchard (Nvidia); Karthik Kashinath (Nvidia); Anima Anandkumar (NVIDIA/Caltech)
Uncertainty quantification and robustness Climate science and climate modeling
NeurIPS 2022 Learning to forecast vegetation greenness at fine resolution over Africa with ConvLSTMs (Papers Track)
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Abstract: Forecasting the state of vegetation in response to climate and weather events is a major challenge. Its implementation will prove crucial in predicting crop yield, forest damage, or more generally the impact on ecosystems services relevant for socio-economic functioning, which if absent can lead to humanitarian disasters. Vegetation status depends on weather and environmental conditions that modulate complex ecological processes taking place at several timescales. Interactions between vegetation and different environmental drivers express responses at instantaneous but also time-lagged effects, often showing an emerging spatial context at landscape and regional scales. We formulate the land surface forecasting task as a strongly guided video prediction task where the objective is to forecast the vegetation developing at very fine resolution using topography and weather variables to guide the prediction. We use a Convolutional LSTM (ConvLSTM) architecture to address this task and predict changes in the vegetation state in Africa using Sentinel-2 satellite NDVI, having ERA5 weather reanalysis, SMAP satellite measurements, and topography (DEM of SRTMv4.1) as variables to guide the prediction. Ours results highlight how ConvLSTM models can not only forecast the seasonal evolution of NDVI at high resolution, but also the differential impacts of weather anomalies over the baselines. The model is able to predict different vegetation types, even those with very high NDVI variability during target length.
Authors: Claire Robin (Biogeochemical Integration, Max-Planck-Institute for Biogeochemistry, Jena, Germany); Christian Requena-Mesa (Computer Vision Group, Friedrich Schiller University Jena; DLR Institute of Data Science, Jena; Max Planck Institute for Biogeochemistry, Jena); Vitus Benson (Max-Planck-Institute for Biogeochemistry); Jeran Poehls (Max-Planck-Institute for Biogeochemistry); Lazaro Alonzo (Max-Planck-Institute for Biogeochemistry Max-Planck-Institute for Biogeochemistry); Nuno Carvalhais (Max-Planck-Institute for Biogeochemistry); Markus Reichstein (Max Planck Institute for Biogeochemistry, Jena; Michael Stifel Center Jena for Data-Driven and Simulation Science, Jena)
Computer vision and remote sensing Agriculture and food Ecosystems and biodiversity Extreme weather Time-series analysis
NeurIPS 2022 Generative Modeling of High-resolution Global Precipitation Forecasts (Papers Track)
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Abstract: Forecasting global precipitation patterns and, in particular, extreme precipitation events is of critical importance to preparing for and adapting to climate change. Making accurate high-resolution precipitation forecasts using traditional physical models remains a major challenge in operational weather forecasting as they incur substantial computational costs and struggle to achieve sufficient forecast skill. Recently, deep-learning-based models have shown great promise in closing the gap with numerical weather prediction (NWP) models in terms of precipitation forecast skill, opening up exciting new avenues for precipitation modeling. However, it is challenging for these deep learning models to fully resolve the fine-scale structures of precipitation phenomena and adequately characterize the extremes of the long-tailed precipitation distribution. In this work, we present several improvements to the architecture and training process of a current state-of-the art deep learning precipitation model (FourCastNet) using a novel generative adversarial network (GAN) to better capture fine scales and extremes. Our improvements achieve superior performance in capturing the extreme percentiles of global precipitation, while comparable to state-of-the-art NWP models in terms of forecast skill at 1--2 day lead times. Together, these improvements set a new state-of-the-art in global precipitation forecasting.
Authors: James Duncan (University of California, Berkeley); Peter Harrington (Lawrence Berkeley National Laboratory (Berkeley Lab)); Shashank Subramanian (Lawrence Berkeley National Laboratory)
Climate science and climate modeling Extreme weather Computer vision and remote sensing Generative modeling
NeurIPS 2022 Learning Surrogates for Diverse Emission Models (Papers Track)
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Abstract: Transportation plays a major role in global CO2 emission levels, a factor that directly connects with climate change. Roadway interventions that reduce CO2 emission levels have thus become a timely requirement. An integral need in assessing the impact of such roadway interventions is access to industry-standard programmatic and instantaneous emission models with various emission conditions such as fuel types, vehicle types, cities of interest, etc. However, currently, there is a lack of well-calibrated emission models with all these properties. Addressing these limitations, this paper presents 1100 programmatic and instantaneous vehicular CO2 emission models with varying fuel types, vehicle types, road grades, vehicle ages, and cities of interest. We hope the presented emission models will facilitate future research in tackling transportation-related climate impact. The released version of the emission models can be found here.
Authors: Edgar Ramirez Sanchez (MIT); Catherine H Tang (Massachusetts Institute of Technology); Vindula Jayawardana (MIT); Cathy Wu ()
Transportation Cities and urban planning Classification, regression, and supervised learning Data mining
NeurIPS 2022 Continual VQA for Disaster Response Systems (Papers Track)
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Abstract: Visual Question Answering (VQA) is a multi-modal task that involves answering questions from an input image, semantically understanding the contents of the image and answering it in natural language. Using VQA for disaster management is an important line of research due to the scope of problems that are answered by the VQA system. However, the main challenge is the delay caused by the generation of labels in the assessment of the affected areas. To tackle this, we deployed pre-trained CLIP model, which is trained on visual-image pairs. however, we empirically see that the model has poor zero-shot performance. Thus, we instead use pre-trained embeddings of text and image from this model for our supervised training and surpass previous state-of-the-art results on the FloodNet dataset. We expand this to a continual setting, which is a more real-life scenario. We tackle the problem of catastrophic forgetting using various experience replay methods.
Authors: Aditya Kane (Pune Institute of Computer Technology); V Manushree (Manipal Institute Of Technology); Sahil S Khose (Georgia Institute of Technology)
Disaster management and relief Active learning
NeurIPS 2022 Performance evaluation of deep segmentation models on Landsat-8 imagery (Papers Track)
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Abstract: Contrails, short for condensation trails, are line-shaped ice clouds produced by aircraft engine exhaust when they fly through the cold and humid air. They generate a greenhouse effect by absorbing or directing back to Earth approximately 33% of emitted outgoing longwave radiation. They account for over half of the climate change resulting from aviation activities. Avoiding contrails and adjusting flight routes could be an inexpensive and effective way to reduce their impact. An accurate, automated, and reliable detection algorithm is required to develop and evaluate contrail avoidance strategies. Advancement in contrail detection has been severely limited due to several factors, primarily due to a lack of quality-labelled data. Recently, McCloskey et al. proposed a large human-labelled Landsat-8. Each contrail is carefully labelled with various inputs in various scenes of Landsat-8 satellite imagery. In this work, we benchmark several popular segmentation models with combinations of different loss functions and encoder backbones. This work is the first to apply state-of-the-art segmentation techniques to detect contrails in low-orbit satellite imagery. Our work can also be used as an open benchmark for contrail segmentation.
Authors: Akshat Bhandari (Manipal Institute of Technology, Manipal); Pratinav Seth (Manipal Institute of Technology); Sriya Rallabandi (Manipal Institute of Technology); Aditya Kasliwal (Manipal Institute of Technology); Sanchit Singhal (Manipal Institute of Technology)
Earth observations and monitoring Computer vision and remote sensing
NeurIPS 2022 Synthesis of Realistic Load Data: Adversarial Networks for Learning and Generating Residential Load Patterns (Papers Track)
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Abstract: Responsible energy consumption plays a key role in reducing carbon footprint and CO2 emissions to tackle climate change. A better understanding of the residential consumption behavior using smart meter data is at the heart of the mission, which can inform residential demand flexibility, appliance scheduling, and home energy management. However, access to high-quality residential load data is still limited due to the cost-intensive data collection process and privacy concerns of data shar- ing. In this paper, we develop a Generative Adversarial Network (GAN)-based method to model the complex and diverse residential load patterns and generate synthetic yet realistic load data. We adopt a generation-focused weight selection method to select model weights to address the mode collapse problem and generate diverse load patterns. We evaluate our method using real-world data and demon- strate that it outperforms three representative state-of-the-art benchmark models in better preserving the sequence level temporal dependencies and aggregated level distributions of load patterns.
Authors: Xinyu Liang (Monash University); Hao Wang (Monash University)
Power and energy systems Generative modeling
NeurIPS 2022 Guided Transformer Network for Detecting Methane Emissions in Sentinel-2 Satellite Imagery (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Methane (CH_4) is the chief contributor to global climate change and its mitigation is targeted by the EU, US and jurisdictions worldwide~\cite{methane-reduction}. Recent studies have shown that imagery from the multi-spectral instrument on Sentinel-2 satellites is capable of detecting and estimating large methane emissions. However, most of the current methods rely on temporal relations between a ratio of shortwave-infrared spectra and assume relatively constant ground conditions, and availability of ground information on when there was no methane emission on site. To address such limitations we propose a guided query-based transformer neural network architecture, that will detect and quantify methane emissions without dependence on temporal information. The guided query aspect of our architecture is driven by a Sentinel Enhanced Matched Filter (SEMF) approach, also discussed in this paper. Our network uses all 12 spectral channels of Sentinel-2 imagery to estimate ground terrain and detect methane emissions. No dependence on temporal data makes it more robust to changing ground and terrain conditions and more computationally efficient as it reduces the need to process historical time-series imagery to compute a single date emissions analysis.
Authors: Satish Kumar (University of California, Santa Barbara); William Kingwill (Orbio Earth); Rozanne Mouton (Orbio Earth); Wojciech Adamczyk (ETH, Zurich); Robert Huppertz (Orbio Earth); Evan D Sherwin (Stanford University, Energy and Resources Engineering)
Carbon capture and sequestration Earth observations and monitoring Computer vision and remote sensing
NeurIPS 2022 Identification of medical devices using machine learning on distribution feeder data for informing power outage response (Proposals Track)
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Abstract: Power outages caused by extreme weather events due to climate change have doubled in the United States in the last two decades. Outages pose severe health risks to over 4.4 million individuals dependent on in-home medical devices. Data on the number of such individuals residing in a given area is limited. This study proposes a load disaggregation model to predict the number of medical devices behind an electric distribution feeder. This data can be used to inform planning and response to power outages and other emergencies. The proposed solution serves as a measure for climate change adaptation.
Authors: Paraskevi Kourtza (University of Edinburgh); Maitreyee Marathe (University of Wisconsin-Madison); Anuj Shetty (Stanford University); Diego Kiedanski (Yale University)
Power and energy systems Disaster management and relief Health Classification, regression, and supervised learning Time-series analysis
NeurIPS 2022 Analyzing the global energy discourse with machine learning (Proposals Track)
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Abstract: To transform our economy towards net-zero emissions, industrial development of clean energy technologies (CETs) to replace fossil energy technologies (FETs) is crucial. Although the media has great power in influencing consumer behavior and decision making in business and politics, its role in the energy transformation is still underexplored. In this paper, we analyze the global energy discourse via machine learning. For this, we collect a large-scale dataset with ~5 million news articles from seven of the world’s major CO2 emitting countries, covering eight CETs and four FETs. Using machine learning, we then analyze the content of news articles on a highly granular level and along several dimensions, namely relevance (for the energy discourse), context (e.g., costs, regulation, investment), and connotations (e.g., high/increasing vs. low/decreasing costs). By linking empirical discourse patterns to investment and deployment data of CETs and FETs, this study advances the current understanding about the role of the media in the energy transformation. Thereby, it enables businesses, investors, and policy makers to respond more effectively to sensitive topics in the media discourse and leverage windows of opportunity for scaling CETs.
Authors: Malte Toetzke (ETH Zurich); Benedict Probst (ETH Zurich); Yasin Tatar (ETH Zurich); Stefan Feuerriegel (LMU Munich); Volker Hoffmann (ETH Zurich)
Public policy Behavioral and social science Natural language processing
NeurIPS 2022 Deep-S2SWind: A data-driven approach for improving Sub-seasonal wind predictions (Proposals Track)
Abstract and authors: (click to expand)
Abstract: A major transformation to mitigate climate change implies a rapid decarbonisation of the energy system and thus, increasing the use of renewable energy sources, such as wind power. However, renewable resources are strongly dependent on local and large-scale weather conditions, which might be influenced by climate change. Weather-related risk assessments are essential for the energy sector, in particular, for power system management decisions, for which forecasts of climatic conditions from several weeks to months (i.e. sub-seasonal scales) are of key importance. Here, we propose a data-driven approach to predict wind speed at longer lead-times that can benefit the energy sector. The main goal of this study is to assess the potential of machine learning algorithms to predict periods of low wind speed conditions that have a strong impact on the energy sector.
Authors: Noelia Otero Felipe (University of Bern); Pascal Horton (University of Bern)
Climate science and climate modeling Earth observations and monitoring Interpretable ML Time-series analysis
NeurIPS 2022 Towards Low Cost Automated Monitoring of Life Below Water to De-risk Ocean-Based Carbon Dioxide Removal and Clean Power (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Oceans will play a crucial role in our efforts to combat the growing climate emergency. Researchers have proposed several strategies to harness greener energy through oceans and use oceans as carbon sinks. However, the risks these strategies might pose to the ocean and marine ecosystem are not well understood. It is imperative that we quickly develop a range of tools to monitor ocean processes and marine ecosystems alongside the technology to deploy these solutions on a large scale into the oceans. Large arrays of inexpensive cameras placed deep underwater coupled with machine learning pipelines to automatically detect, classify, count and estimate fish populations have the potential to continuously monitor marine ecosystems and help study the impacts of these solutions on the ocean. In this proposal, we discuss the challenges presented by a dark artificially lit underwater video dataset captured 500m below the surface, propose potential solutions to address these challenges, and present preliminary results from detecting and classifying 6 species of fish in deep underwater camera data.
Authors: Kameswari Devi Ayyagari (Dalhousie University); Christopher Whidden (Dalhousie University); Corey Morris (Department of Fisheries and Oceans); Joshua Barnes (National Research Council Canada)
Oceans and marine systems Climate science and climate modeling Classification, regression, and supervised learning Computer vision and remote sensing
NeurIPS 2022 Towards the Automatic Analysis of Ceilometer Backscattering Profiles using Unsupervised Learning (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Ceilometers use a laser beam to capture certain phenomena in the atmosphere like clouds, precipitation, or aerosol layers. These measurements can be visualized in so-called quick looks that at the moment are mostly analyzed manually by meteorology experts. In this work, we illustrate the path towards the automatic analysis of quick looks by using a hybrid approach combining an image segmentation algorithm with unsupervised representation learning and clustering. We present a first proof of concept and give an outlook on possible future work.
Authors: Michael Dammann (HAW Hamburg); Ina Mattis (Deutscher Wetterdienst); Michael Neitzke (HAW Hamburg); Ralf Möller (University of Lübeck)
Climate science and climate modeling Extreme weather Computer vision and remote sensing Unsupervised and semi-supervised learning
NeurIPS 2022 Modelling the performance of delivery vehicles across urban micro-regions to accelerate the transition to cargo-bike logistics (Proposals Track)
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Abstract: Light goods vehicles (LGV) used extensively in the last mile of delivery are one of the leading polluters in cities. Cargo-bike logistics has been put forward as a high impact candidate for replacing LGVs, with experts estimating over half of urban van deliveries being replaceable by cargo bikes, due to their faster speeds, shorter parking times and more efficient routes across cities. By modelling the relative delivery performance of different vehicle types across urban micro-regions, machine learning can help operators evaluate the business and environmental impact of adding cargo-bikes to their fleets. In this paper, we introduce two datasets, and present initial progress in modelling urban delivery service time (e.g. cruising for parking, unloading, walking). Using Uber’s H3 index to divide the cities into hexagonal cells, and aggregating OpenStreetMap tags for each cell, we show that urban context is a critical predictor of delivery performance.
Authors: Max C Schrader (University of Alabama); Navish Kumar (IIT Kharagpur); Nicolas Collignon (University of Edinburgh); Maria S Astefanoaei (IT University of Copenhagen); Esben Sørig (Kale Collective); Soonmyeong Yoon (Kale Collective); Kai Xu (University of Edinburgh); Akash Srivastava (MIT-IBM)
Cities and urban planning Transportation Classification, regression, and supervised learning Data mining Unsupervised and semi-supervised learning
NeurIPS 2022 An Inversion Algorithm of Ice Thickness and InSAR Data for the State of Friction at the Base of the Greenland Ice Sheet (Proposals Track)
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Abstract: With the advent of climate change and global warming, the Greenland Ice Sheet (GrIS) has been melting at an alarming rate, losing over 215 Gt per yr, and accounting for 10% of mean global sea level rise since the 1990s. It is imperative to understand what dynamics are causing ice loss and influencing ice flow in order to successfully project mass changes of ice sheets and associated sea level rise. This work applies machine learning, ice thickness data, and horizontal ice velocity measurements from satellite radar data to quantify the magnitudes and distributions of the basal traction forces that are holding the GrIS back from flowing into the ocean. Our approach uses a hybrid model: InSAR velocity data trains a linear regression model, and these model coefficients are fed into a geophysical algorithm to estimate basal tractions that capture relationships between the ice motion and physical variables. Results indicate promising model performance and reveal significant presence of large basal traction forces around the coastline of the GrIS.
Authors: Aryan Jain (Amador Valley High School); Jeonghyeop Kim (Stony Brook University); William Holt (Stony Brook University)
Earth science Earth observations and monitoring Classification, regression, and supervised learning Hybrid physical models
NeurIPS 2022 Deep learning-based bias adjustment of decadal climate predictions (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Decadal climate predictions are key to inform adaptation strategies in a warming climate. Coupled climate models used for decadal predictions are, however, imperfect representations of the climate system leading to forecast biases. Biases can also result from a poor model initialization that, when combined with forecast drift, can produce errors depending non-linearly on lead time. We propose a deep learning-based bias correction approach for the post-processing of gridded forecasts to enhance the accuracy of decadal predictions.
Authors: Reinel Sospedra-Alfonso (Environment and Climate Change Canada); Johannes Exenberger (Graz University of Technology); Marie C McGraw (Cooperative Institute for Research in the Atmosphere | CIRA); Trung Kien Dang (National University of Singapore)
Climate science and climate modeling Classification, regression, and supervised learning
NeurIPS 2022 Surrogate Modeling for Methane Dispersion Simulations Using Fourier Neural Operator (Proposals Track)
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Abstract: Methane leak detection and remediation are critical for tackling climate change, where methane dispersion simulations play an important role in emission source attribution. As 3D modeling of methane dispersion is often costly and time-consuming, we train a deep-learning-based surrogate model using the Fourier Neural Operator to learn the PDE solver in our study. Our preliminary result shows that our surrogate modeling provides a fast, accurate and cost-effective solution to methane dispersion simulations, thus reducing the cycle time of methane leak detection.
Authors: Qie Zhang (Microsoft); Mirco Milletari (Microsoft); YAGNA DEEPIKA ORUGANTI (MICROSOFT); Philipp A Witte (Microsoft)
Climate science and climate modeling Earth observations and monitoring Classification, regression, and supervised learning
NeurIPS 2022 Detecting Floods from Cloudy Scenes: A Fusion Approach Using Sentinel-1 and Sentinel-2 Imagery (Proposals Track)
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Abstract: As the result of climate change, extreme flood events are becoming more frequent. To better respond to such disasters, and to test and calibrate flood models, we need accurate real-world data on flooding extent. Detection of floods from remote sensed imagery suffers from a widespread problem: clouds block flood scenes in images, leading to degraded and fragmented flood datasets. To address this challenge, we propose a workflow based on U-Net, and a dataset that detects flood in cloud-prone areas by fusing information from the Sentinel-1 and Sentinel-2 satellites. The expected result will be a reliable and detailed catalogue of flood extents and how they change through time, allowing us to better understand flooding in different morphological settings and climates.
Authors: Qiuyang Chen (University of Edinburgh)
Computer vision and remote sensing Disaster management and relief Extreme weather Classification, regression, and supervised learning Other Time-series analysis
NeurIPS 2022 Urban Heat Island Detection and Causal Inference Using Convolutional Neural Networks (Proposals Track)
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Abstract: Compared to rural areas, urban areas experience higher temperatures for longer periods of time because of the urban heat island (UHI) effect. This increased heat stress leads to greater mortality, increased energy demand, regional changes to precipitation patterns, and increased air pollution. Urban developers can minimize the UHI effect by incorporating features that promote air flow and heat dispersion (e.g., increasing green space). However, understanding which urban features to implement is complex, as local meteorology strongly dictates how the environment responds to changes in urban form. In this proposal we describe a methodology for estimating the causal relationship between changes in urban form and changes in the UHI effect. Changes in urban form and temperature changes are measured using convolutional neural networks, and a causal inference matching approach is proposed to estimate causal relationships. The success of this methodology will enable urban developers to implement city-specific interventions to mitigate the warming planet's impact on cities.
Authors: Zachary D Calhoun (Duke University); Ziyang Jiang (Duke University); Mike Bergin (Duke University); David Carlson (Duke University)
Cities and urban planning Buildings Climate justice Climate science and climate modeling Disaster management and relief Extreme weather Health Causal and Bayesian methods Classification, regression, and supervised learning Computer vision and remote sensing Time-series analysis
NeurIPS 2022 Forecasting Global Drought Severity and Duration Using Deep Learning (Proposals Track)
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Abstract: Drought detection and prediction is challenging due to the slow onset of the event and varying degrees of dependence on numerous physical and socio-economic factors that differentiate droughts from other natural disasters. In this work, we propose DeepXD (Deep learning for Droughts), a deep learning model with 26 physics-informed input features for SPI (Standardised Precipitation Index) forecasting to identify and classify droughts using monthly oceanic indices, global meteorological and vegetation data, location (latitude, longitude) and land cover for the years 1982 to 2018. In our work, we propose extracting features by considering the atmosphere and land moisture and energy budgets and forecasting global droughts on a seasonal and an annual scale at 1, 3, 6, 9, 12 and 24 months lead times. SPI helps us to identify the severity and the duration of the drought to classify them as meteorological, agricultural and hydrological.
Authors: Akanksha Ahuja (NOA); Xin Rong Chua (Centre for Climate Research Singapore)
Classification, regression, and supervised learning Agriculture and food Climate science and climate modeling Disaster management and relief Earth observations and monitoring Earth science Extreme weather Societal adaptation and resilience Data mining
NeurIPS 2022 ForestBench: Equitable Benchmarks for Monitoring, Reporting, and Verification of Nature-Based Solutions with Machine Learning (Proposals Track)
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Abstract: Restoring ecosystems and reducing deforestation are necessary tools to mitigate the anthropogenic climate crisis. Current measurements of forest carbon stock can be inaccurate, in particular for underrepresented and small-scale forests in the Global South, hindering transparency and accountability in the Monitoring, Reporting, and Verification (MRV) of these ecosystems. There is thus need for high quality datasets to properly validate ML-based solutions. To this end, we present ForestBench, which aims to collect and curate geographically-balanced gold-standard datasets of small-scale forest plots in the Global South, by collecting ground-level measurements and visual drone imagery of individual trees. These equitable validation datasets for ML-based MRV of nature-based solutions shall enable assessing the progress of ML models for estimating above-ground biomass, ground cover, and tree species diversity.
Authors: Lucas Czech (Carnegie Institution for Science); Björn Lütjens (MIT); David Dao (ETH Zurich)
Earth observations and monitoring Carbon capture and sequestration Climate finance and economics Climate justice Ecosystems and biodiversity Forestry and other land use Local and indigenous knowledge systems Public policy Classification, regression, and supervised learning Computer vision and remote sensing Other
NeurIPS 2022 Estimating Heating Loads in Alaska using Remote Sensing and Machine Learning Methods (Proposals Track)
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Abstract: Alaska and the larger Arctic region are in much greater need of decarbonization than the rest of the globe as a result of the accelerated consequences of climate change over the past ten years. Heating for homes and businesses accounts for over 75% of the energy used in the Arctic region. However, the lack of thorough and precise heating load estimations in these regions poses a significant obstacle to the transition to renewable energy. In order to accurately measure the massive heating demands in Alaska, this research pioneers a geospatial-first methodology that integrates remote sensing and machine learning techniques. Building characteristics such as height, size, year of construction, thawing degree days, and freezing degree days are extracted using open-source geospatial information in Google Earth Engine (GEE). These variables coupled with heating load forecasts from the AK Warm simulation program are used to train models that forecast heating loads on Alaska’s Railbelt utility grid. Our research greatly advances geospatial capability in this area and considerably informs the decarbonization activities currently in progress in Alaska.
Authors: Madelyn Gaumer (University of Washington); Nick Bolten (Paul G. Allen School of Computer Science and Engineering, University of Washington); Vidisha Chowdhury (Heinz College of Information Systems and Public Policy, Carnegie Mellon University); Philippe Schicker (Heinz College of Information Systems and Public Policy, Carnegie Mellon University); Shamsi Soltani (Department of Epidemiology and Population Health, Stanford University School of Medicine); Erin D Trochim (University of Alaska Fairbanks)
Classification, regression, and supervised learning Buildings Cities and urban planning Earth observations and monitoring Computer vision and remote sensing
NeurIPS 2022 Interpretable Spatiotemporal Forecasting of Arctic Sea Ice Concentration at Seasonal Lead Times (Proposals Track)
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Abstract: There are many benefits from the accurate forecasting of Arctic sea ice, however existing models struggle to reliably predict sea ice concentration at long lead times. Many numerical models exist but can be sensitive to initial conditions, and while recent deep learning-based methods improve overall robustness, they either do not utilize temporal trends or rely on architectures that are not performant at learning long-term sequential dependencies. We propose a method of forecasting sea ice concentration using neural circuit policies, a form of continuous time recurrent neural architecture, which improve the learning of long-term sequential dependencies compared to existing techniques and offer the added benefits of adaptability to irregular sequence intervals and high interpretability.
Authors: Matthew Beveridge (Independent Researcher); Lucas Pereira (ITI, LARSyS, Técnico Lisboa)
Computer vision and remote sensing Climate science and climate modeling Earth observations and monitoring Earth science Oceans and marine systems Classification, regression, and supervised learning Interpretable ML Time-series analysis Uncertainty quantification and robustness
NeurIPS 2022 CliMedBERT: A Pre-trained Language Model for Climate and Health-related Text (Proposals Track)
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Abstract: Climate change is threatening human health in unprecedented orders and many ways. These threats are expected to grow unless effective and evidence-based policies are developed and acted upon to minimize or eliminate them. Attaining such a task requires the highest degree of the flow of knowledge from science into policy. The multidisciplinary, location-specific, and vastness of published science makes it challenging to keep track of novel work in this area, as well as making the traditional knowledge synthesis methods inefficient in infusing science into policy. To this end, we consider developing multiple domain-specific language models (LMs) with different variations from Climate- and Health-related information, which can serve as a foundational step toward capturing available knowledge to enable solving different tasks, such as detecting similarities between climate- and health-related concepts, fact-checking, relation extraction, evidence of health effects to policy text generation, and more. To our knowledge, this is the first work that proposes developing multiple domain-specific language models for the considered domains. We will make the developed models, resources, and codebase available for the researchers.
Health Natural language processing
NeurIPS 2022 Improving accuracy and convergence of federated learning edge computing methods for generalized DER forecasting applications in power grid (Proposals Track)
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Abstract: This proposal aims to develop more accurate federated learning (FL) methods with faster convergence properties and lower communication requirements, specifically for forecasting distributed energy resources (DER) such as renewables, energy storage, and loads in modern, low-carbon power grids. This will be achieved by (i) leveraging recently developed extensions of FL such as hierarchical and iterative clustering to improve performance with non-IID data, (ii) experimenting with different types of FL global models well-suited to time-series data, and (iii) incorporating domain-specific knowledge from power systems to build more general FL frameworks and architectures that can be applied to diverse types of DERs beyond just load forecasting, and with heterogeneous clients.
Power and energy systems Buildings Time-series analysis
NeurIPS 2022 Personalizing Sustainable Agriculture with Causal Machine Learning (Proposals Track)
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Abstract: To fight climate change and accommodate the increasing population, global crop production has to be strengthened. To achieve the "sustainable intensification" of agriculture, transforming it from carbon emitter to carbon sink is a priority, and understanding the environmental impact of agricultural management practices is a fundamental prerequisite to that. At the same time, the global agricultural landscape is deeply heterogeneous, with differences in climate, soil, and land use inducing variations in how agricultural systems respond to farmer actions. The "personalization" of sustainable agriculture with the provision of locally adapted management advice is thus a necessary condition for the efficient uplift of green metrics, and an integral development in imminent policies. Here, we formulate personalized sustainable agriculture as a Conditional Average Treatment Effect estimation task and use Causal Machine Learning for tackling it. Leveraging climate data, land use information and employing Double Machine Learning, we estimate the heterogeneous effect of sustainable practices on the field-level Soil Organic Carbon content in Lithuania. We thus provide a data-driven perspective for targeting sustainable practices and effectively expanding the global carbon sink.
Authors: Georgios Giannarakis (National Observatory of Athens); Vasileios Sitokonstantinou (National Observatory of Athens); Roxanne Suzette Lorilla (National Observatory of Athens); Charalampos Kontoes (National Observatory of Athens)
Causal and Bayesian methods Agriculture and food Carbon capture and sequestration Earth observations and monitoring Ecosystems and biodiversity Public policy Societal adaptation and resilience Classification, regression, and supervised learning Data mining
NeurIPS 2022 Disaster Risk Monitoring Using Satellite Imagery (Tutorials Track)
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Abstract: Natural disasters such as flood, wildfire, drought, and severe storms wreak havoc throughout the world, causing billions of dollars in damages, and uprooting communities, ecosystems, and economies. Unfortunately, flooding events are on the rise due to climate change and sea level rise. The ability to detect and quantify them can help us minimize their adverse impacts on the economy and human lives. Using satellites to study flood is advantageous since physical access to flooded areas is limited and deploying instruments in potential flood zones can be dangerous. We are proposing a hands-on tutorial to highlight the use of satellite imagery and computer vision to study natural disasters. Specifically, we aim to demonstrate the development and deployment of a flood detection model using Sentinel-1 satellite data. The tutorial will cover relevant fundamental concepts as well as the full development workflow of a deep learning-based application. We will include important considerations such as common pitfalls, data scarcity, augmentation, transfer learning, fine-tuning, and details of each step in the workflow. Importantly, the tutorial will also include a case study on how the application was used by authorities in response to a flood event. We believe this tutorial will enable machine learning practitioners of all levels to develop new technologies that tackle the risks posed by climate change. We expect to deliver the below learning outcomes: • Develop various deep learning-based computer vision solutions using hardware-accelerated open-source tools that are optimized for real-time deployment • Create an optimized pipeline for the machine learning development workflow • Understand different performance metrics for model evaluation that are relevant for real world datasets and data imbalances • Understand the public sector’s efforts to support climate action initiatives and point out where the audience can contribute
Authors: kevin lee (NVIDIA); Siddha Ganju (Nvidia)
Disaster management and relief Climate science and climate modeling Earth observations and monitoring Extreme weather Active learning Classification, regression, and supervised learning Computer vision and remote sensing Data mining Meta- and transfer learning
NeurIPS 2022 Machine Learning for Predicting Climate Extremes (Tutorials Track)
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Abstract: Climate change has led to a rapid increase in the occurrence of extreme weather events globally, including floods, droughts, and wildfires. In the longer term, some regions will experience aridification while others will risk sinking due to rising sea levels. Typically, such predictions are done via weather and climate models that simulate the physical interactions between the atmospheric, oceanic, and land surface processes that operate at different scales. Due to the inherent complexity, these climate models can be inaccurate or computationally expensive to run, especially for detecting climate extremes at high spatiotemporal resolutions. In this tutorial, we aim to introduce the participants to machine learning approaches for addressing two fundamental challenges. We will walk the participants through a hands-on tutorial for predicting climate extremes relating to temperature and precipitation in 2 setups: (1) temporal forecasting: the goal is to predict climate variables into the future (both direct single step approaches and iterative approaches that roll out the model for several timesteps), and (2) spatial downscaling: the goal is to learn a mapping that transforms low-resolution outputs of climate models into high-resolution regional forecasts. Through introductory presentations and colab notebooks, we aim to expose the participants to (a) APIs for accessing and navigating popular repositories that host global climate data, such as the Copernicus data store, (b) identifying relevant datasets, including auxiliary data (e.g., other climate variables such as geopotential), (c) scripts for downloading and preprocessing relevant datasets, (d) algorithms for training machine learning models, (d) metrics for evaluating model performance, and (e) visualization tools for both the dataset and predicted outputs. The coding notebooks will be in Python. No prior knowledge of climate science is required.
Authors: Hritik Bansal (UCLA); Shashank Goel (University of California Los Angeles); Tung Nguyen (University of California, Los Angeles); Aditya Grover (UCLA)
Climate science and climate modeling Earth observations and monitoring Earth science Extreme weather Classification, regression, and supervised learning Data mining Hybrid physical models
NeurIPS 2022 FourCastNet: A practical introduction to a state-of-the-art deep learning global weather emulator (Tutorials Track)
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Abstract: Accurate, reliable, and efficient means of forecasting global weather patterns are of paramount importance to our ability to mitigate and adapt to climate change. Currently, real-time weather forecasting requires repeated numerical simulation and data assimilation cycles on dedicated supercomputers, which restricts the ability to make reliable, high-resolution forecasts to a handful of organizations. However, recent advances in deep learning, specifically the FourCastNet model, have shown that data-driven approaches can forecast important atmospheric variables with excellent skill and comparable accuracy to standard numerical methods, but at orders-of-magnitude lower computational and energy cost during inference, enabling larger ensembles for better probabilistic forecasts. In this tutorial, we demonstrate various applications of FourCastNet for high-resolution global weather forecasting, with examples including real-time forecasts, uncertainty quantification for extreme events, and adaptation to specific variables or localized regions of interest. The tutorial will provide examples that will demonstrate the general workflow for formatting and working with global atmospheric data, running autoregressive inference to obtain daily global forecasts, saving/visualizing model predictions of atmospheric events such as hurricanes and atmospheric rivers, and computing quantitative evaluation metrics for weather models. The exercises will primarily use PyTorch and do not require detailed understanding of the climate and weather system. With this tutorial, we hope to equip attendees with basic knowledge about building deep learning-based weather model surrogates and obtaining forecasts of crucial atmospheric variables using these models.
Authors: Jaideep Pathak (NVIDIA Corporation); Shashank Subramanian (Lawrence Berkeley National Laboratory); Peter Harrington (Lawrence Berkeley National Laboratory (Berkeley Lab)); Thorsten Kurth (Nvidia); Andre Graubner (Nvidia); Morteza Mardani (NVIDIA Corporation); David M. Hall (NVIDIA); Karthik Kashinath (Lawrence Berkeley National Laboratory); Anima Anandkumar (NVIDIA/Caltech)
Earth science Climate science and climate modeling Extreme weather Classification, regression, and supervised learning Uncertainty quantification and robustness
NeurIPS 2022 Automating the creation of LULC datasets for semantic segmentation (Tutorials Track)
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Abstract: High resolution and accurate Land Use and Land Cover mapping (LULC) datasets are increasingly important and can be widely used in monitoring climate change impacts in agriculture, deforestation, and the carbon cycle. These datasets represent physical classifications of land types and spatial information over the surface of the Earth. These LULC datasets can be leveraged in a plethora of research topics and industries to mitigate and adapt to environmental changes. High resolution urban mappings can be used to better monitor and estimate building albedo and urban heat island impacts, and accurate representation of forests and vegetation can even be leveraged to better monitor the carbon cycle and climate change through improved land surface modelling. The advent of machine learning (ML) based CV techniques over the past decade provides a viable option to automate LULC mapping. One impediment to this has been the lack of large ML datasets. Large vector datasets for LULC are available, but can’t be used directly by ML practitioners due to a knowledge gap in transforming the input into a dataset of paired satellite images and segmentation masks. We demonstrate a novel end-to-end pipeline for LULC dataset creation that takes vector land cover data and provides a training-ready dataset. We will use Sentinel-2 satellite imagery and the European Urban Atlas LULC data. The pipeline manages everything from downloading satellite data, to creating and storing encoded segmentation masks and automating data checks. We then use the resulting dataset to train a semantic segmentation model. The aim of the pipeline is to provide a way for users to create their own custom datasets using various combinations of multispectral satellite and vector data. In addition to presenting the pipeline, we aim to provide an introduction to multispectral imagery, geospatial data and some of the challenges in using it for ML.
Authors: Sambhav S Rohatgi (Spacesense.ai); Anthony Mucia (Spacesense.ai)
Computer vision and remote sensing Cities and urban planning Climate science and climate modeling Forestry and other land use Classification, regression, and supervised learning Other
AAAI FSS 2022 AI-Based Text Analysis for Evaluating Food Waste Policies
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Abstract: Food waste is a major contributor to climate change, making the reduction of food waste one of the most important strategies to preserve threatened ecosystems and increase economic benefits. To evaluate the impact of food waste policies in this arena and provide actionable guidance to policymakers, we conducted an AI-based text analysis of food waste policy provisions. Specifically, we a) identified commonalities across state policy texts, b) clustered states by shared policy text, and c) examined relationships between state cluster memberships and food waste . This approach generated state clusters but demonstrated very limited convergent validity with policy ratings provided by subject matter experts and no predictive validity with food waste. We discuss the potential of using supervised machine learning to analyze food waste policy text as a next step.
Authors: John Aitken (The MITRE Corporation), Denali Rao (The MITRE Corporation), Balca Alaybek (The MITRE Corporation), Amber Sprenger (The MITRE Corporation), Grace Mika (The MITRE Corporation), Rob Hartman (The MITRE Corporation) and Laura Leets (The MITRE Corporation)
AAAI FSS 2022 Data-Driven Reduced-Order Model for Atmospheric CO2 Dispersion
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Abstract: Machine learning frameworks have emerged as powerful tools for the enhancement of computational fluid dynamics simulations and the construction of reduced-order models (ROMs). The latter are particularly desired when their full-order counterparts portray multiple spatiotemporal features and demand high processing power and storage capacity, such as climate models. In this work, a ROM for CO2 dispersion across Earth‘s atmosphere was built from NASA’s gridded daily OCO-2 carbon dioxide assimilated dataset. For that, a proper orthogonal decomposition was performed, followed by a non-intrusive operator inference (OpInf). This scientific machine learning technique was capable of accurately representing and predicting the detailed CO2 concentration field for about one year ahead, with a normalized root-mean-square error below 5%. It suggests OpInf-based ROMs may be a reliable alternative for fast response climate-related predictions.
Authors: Pedro Roberto Barbosa Rocha (IBM Research), Marcos Sebastião de Paula Gomes (Pontifical Catholic University of Rio de Janeiro), João Lucas de Sousa Almeida (IBM Research), Allan Moreira Carvalho (IBM Research) and Alberto Costa Nogueira Junior (IBM Research)
AAAI FSS 2022 KnowUREnvironment: An Automated Knowledge Graph for Climate Change and Environmental Issues
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Abstract: Despite climate change being one of the greatest threats to humanity, many people are still in denial or lack motivation for appropriate action. A structured source of knowledge can help increase public awareness while also helping crucial natural language understanding tasks such as information retrieval, question answering, and recommendation systems. We introduce KnowUREnvironment – a knowledge graph for climate change and related environmental issues, extracted from the scientific literature. We automatically identify 210,230 domain-specific entities/concepts and encode how these concepts are interrelated with 411,860 RDF triples backed up with evidence from the literature, without using any supervision or human intervention. Human evaluation shows our extracted triples are syntactically and factually correct (81.69% syntactic correctness and 75.85% precision). The proposed framework can be easily extended to any domain that can benefit from such a knowledge graph.
Authors: Md Saiful Islam (University of Rochester), Adiba Proma (University of Rochester), Yilin Zhou (University of Rochester), Syeda Nahida Akter (Carnegie Mellon University), Caleb Wohn (University of Rochester) and Ehsan Hoque (University of Rochester)
AAAI FSS 2022 Towards Generating Large Synthetic Phytoplankton Datasets for Efficient Monitoring of Harmful Algal Blooms
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Abstract: Climate change is increasing the frequency and severity of harmful algal blooms (HABs), which cause significant fish deaths in aquaculture farms. This contributes to ocean pollution and greenhouse gas (GHG) emissions since dead fish are either dumped into the ocean or taken to landfills, which in turn negatively impacts the climate. Currently, the standard method to enumerate harmful algae and other phytoplankton is to manually observe and count them under a microscope. This is a time-consuming, tedious and error-prone process, resulting in compromised management decisions by farmers. Hence, automating this process for quick and accurate HAB monitoring is extremely helpful. However, this requires large and diverse datasets of phytoplankton images, and such datasets are hard to produce quickly. In this work, we explore the feasibility of generating novel high-resolution photorealistic synthetic phytoplankton images, containing multiple species in the same image, given a small dataset of real images. To this end, we employ Generative Adversarial Networks (GANs) to generate synthetic images. We evaluate three different GAN architectures: ProjectedGAN, FastGAN, and StyleGANv2 using standard image quality metrics. We empirically show the generation of high-fidelity synthetic phytoplankton images using a training dataset of only 961 real images. Thus, this work demonstrates the ability of GANs to create large synthetic datasets of phytoplankton from small training datasets, accomplishing a key step towards sustainable systematic monitoring of harmful algal blooms.
Authors: Nitpreet Bamra (University of Waterloo), Vikram Voleti (Mila, University of Montreal), Alexander Wong (University of Waterloo) and Jason Deglint (University of Waterloo)
AAAI FSS 2022 Generating physically-consistent high-resolution climate data with hard-constrained neural networks
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Abstract: The availability of reliable, high-resolution climate and weather data is important to inform long-term decisions on climate adaptation and mitigation and to guide rapid responses to extreme events. Forecasting models are limited by computational costs and therefore often predict quantities at a coarse spatial resolution. Statistical downscaling can provide an efficient method of upsampling low-resolution data. In this field, deep learning has been applied successfully, often using methods from the super-resolution domain in computer vision. Despite often achieving visually compelling results, such models often violate conservation laws when predicting physical variables. In order to conserve important physical quantities, we develop methods that guarantee physical constraints are satisfied by a deep downscaling model while also increasing their performance according to traditional metrics. We introduce two ways of constraining the network: a renormalization layer added to the end of the neural network and a successive approach that scales with increasing upsampling factors. We show the applicability of our methods across different popular architectures and upsampling factors using ERA5 reanalysis data.
Authors: Paula Harder (Fraunhofer Institute ITWM, Mila Quebec AI Institute), Qidong Yang (Mila Quebec AI Institute, New York University), Venkatesh Ramesh (Mila Quebec AI Institute, University of Montreal), Alex Hernandez-Garcia (Mila Quebec AI Institute, University of Montreal), Prasanna Sattigeri (IBM Research), Campbell D. Watson (IBM Research), Daniela Szwarcman (IBM Research) and David Rolnick (Mila Quebec AI Institute, McGill University).
AAAI FSS 2022 Discovering Transition Pathways Towards Coviability with Machine Learning
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Abstract: This paper presents our ongoing French-Brazilian collaborative project which aims at: (1) establishing a diagnosis of socio-ecological coviability for several sites of interest in Nordeste, the North-East region of Brazil (in the states of Paraiba, Ceara, Pernambuco, and Rio Grande do Norte known for their biodiversity hotspots and vulnerabilities to climate change) using advanced data science techniques for multisource and multimodal data fusion and (2) finding transition pathways towards coviability equilibrium using machine learning techniques. Data collected in the field by scientists, ecologists, local actors combined with volunteered information, pictures from smart-phones, and data available on-line from satellite imagery, social media, surveys, etc. can be used to compute various coviability indicators of interest for the local actors. These indicators are useful to characterize and monitor the socio-ecological coviability status along various dimensions of anthropization, human welfare, ecological and biodiversity balance, and ecosystem intactness and vulnerabilities.
Authors: Laure Berti-Equille (IRD) and Rafael Raimundo (UFPB)
AAAI FSS 2022 Wildfire Forecasting with Satellite Images and Deep Generative Model
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Abstract: Wildfire prediction has been one of the most critical tasks that humanities want to thrive at. While it plays a vital role in protecting human life, it is also difficult because of its stochastic and chaotic properties. We tackled the problem by interpreting a series of wildfire images into a video and used it to anticipate how the fire would behave in the future. However, creating video prediction models that account for the inherent uncertainty of the future is challenging. The bulk of published attempts are based on stochastic image-autoregressive recurrent networks, which raise various performance and application difficulties such as computational cost and limited efficiency on massive datasets. Another possibility is to use entirely latent temporal models that combine frame synthesis with temporal dynamics. However, due to design and training issues, no such model for stochastic video prediction has yet been proposed in the literature. This paper addresses these issues by introducing a novel stochastic temporal model whose dynamics are driven in a latent space. It naturally predicts video dynamics by allowing our lighter, more interpretable latent model to beat previous state-of-the-art approaches on the GOES-16 dataset. Results are compared using various benchmarking models.
Authors: Thai-Nam Hoang (University of Wisconsin - Madison), Sang Truong (Stanford University) and Chris Schmidt (University of Wisconsin - Madison)
AAAI FSS 2022 From Ideas to Deployment - A Joint Industry-University Research Effort on Tackling Carbon Storage Challenges with AI
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Abstract: Carbon capture and storage (CCS) offers a promising means for significant reductions in greenhouse gas emissions and climate change mitigation at a large scale. Modeling CO2 transport and pressure buildup is central to understanding the responses of geosystems after CO2 injection and assessing the suitability and safety of CO2 storage. However, numerical simulations of geological CO2 storage often suffer from its multi-physics nature and complex non-linear governing equations, and is further complicated by flexible injection designs including changes in injection rates, resulting in formidable computational costs. New ideas have emerged such as data-driven models to tackle such challenges but very few have been fully developed and deployed as reliable tools. With the joint efforts of industry and universities, we are currently working on a new mechanism of fostering cross-disciplinary collaboration, developing, deploying, and scaling data-driven tools for CCS. A deep learning suite that can act as an alternative to CCS variable rate injection simulation will be the first tool developed under this mechanism. Based on the surrogate model, optimal design of injection strategy under pressure buildup constraints will be enabled with machine learning.
Authors: Junjie Xu (Tsinghua University), Jiesi Lei (Tsinghua University), Yang Li (Tsinghua University), Junfan Ren (College of Petroleum Engineering, China University of Petroleum (Beijing), Beijing, China), Jian Qiu (Product and Solution & Website Business Unit, Alibaba Cloud, Hangzhou, Zhejiang, China), Biao Luo (Product and Solution & Website Business Unit, Alibaba Cloud, Hangzhou, Zhejiang, China), Lei Xiao (Product and Solution & Website Business Unit, Alibaba Cloud, Hangzhou, Zhejiang, China) and Wenwen Zhou (Product and Solution & Website Business Unit, Alibaba Cloud, Hangzhou, Zhejiang, China)
AAAI FSS 2022 NADBenchmarks - a compilation of Benchmark Datasets for Machine Learning Tasks related to Natural Disasters
Abstract and authors: (click to expand)
Abstract: Climate change has increased the intensity, frequency, and duration of extreme weather events and natural disasters across the world. While the increased data on natural disasters improves the scope of machine learning(ML) for this field, progress is relatively slow. One bottleneck is the lack of benchmark datasets that would allow ML researchers to quantify their progress against a standard metric. The objective of this short paper is to explore the state of benchmark datasets for ML tasks related to natural disasters, categorizing the datasets according to the disaster management cycle. We compile a list of existing benchmark datasets that have been introduced in the past five years. We propose a web platform where researchers can search for benchmark datasets in this domain, and develop a preliminary version of such a platform using our compiled list. This paper is intended to aid researchers in finding benchmark datasets to train their ML models on, and provide general directions in for topics where they can contribute new benchmark datasets.
Authors: Adiba Proma (University of Rochester), Md Saiful Islam (University of Rochester), Stela Ciko (University of Rochester), Raiyan Abdul Baten (University of Rochester) and Ehsan Hoque (University of Rochester)
AAAI FSS 2022 Contrastive Learning for Climate Model Bias Correction and Super-Resolution
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Abstract: Climate models often require post-processing in order to make accurate estimates of local climate risk. The most common post-processing applied is bias-correction and spatial resolution enhancement. However, the statistical methods typically used for this not only are incapable of capturing multivariate spatial correlation information but are also reliant on rich observational data often not available outside of developed countries, limiting their potential. Here we propose an alternative approach to this challenge based on a combination of image super resolution (SR) and contrastive learning generative adversarial networks (GANs). We benchmark performance against NASA’s flagship post-processed CMIP6 climate model product, NEX-GDDP. We find that our model successfully reaches a spatial resolution double that of NASA’s product while also achieving comparable or improved levels of bias correction in both daily precipitation and temperature. The resulting higher fidelity simulations of present and forward-looking climate can enable more local, accurate models of hazards like flooding, drought, and heatwaves.
Authors: Tristan Ballard (Sust Global) and Gopal Erinjippurath (Sust Global)
AAAI FSS 2022 Employing Deep Learning to Quantify Power Plant Greenhouse Gas Emissions via Remote Sensing Data
Abstract and authors: (click to expand)
Abstract: Greenhouse gasses (GHG) emitted from fossil-fuel-burning power plants pose a global threat to climate and public health. GHG emissions degrade air quality and increase the frequency of natural disasters five-fold, causing 8.7 million deaths per year. Quantifying GHG emissions is crucial for the success of the planet. However, current methods to track emissions cost upwards of 520,000/plant. These methods are cost prohibitive for developing countries, and are not globally standardized, leading to inaccurate emissions reports from nations and companies. I developed a low-cost solution via an end-to-end deep learning pipeline that utilizes observations of emitted smoke plumes in satellite imagery to provide an accurate, precise system for quantifying power plant GHG emissions by segmentation of power plant smoke plumes, classification of the plant fossil fuels, and algorithmic prediction of power generation and CO2 emissions. The pipeline was able to achieve a segmentation Intersection Over Union (IoU) score of 0.841, fuel classification accuracy of 92%, and quantify power generation and CO2 emission rates with R2 values of 0.852 and 0.824 respectively. The results of this work serve as a step toward the low-cost monitoring and detection of major sources of GHG emissions, helping limit their catastrophic impacts on climate and our planet. Authors: Aryan Jain (Amador Valley High School) AAAI FSS 2022 ClimateBert: A Pretrained Language Model for Climate-Related Text Abstract and authors: (click to expand) Abstract: Over the recent years, large pretrained language models (LM) have revolutionized the field of natural language processing (NLP). However, while pretraining on general language has been shown to work very well for common language, it has been observed that niche language poses problems. In particular, climate-related texts include specific language that common LMs can not represent accurately. We argue that this shortcoming of today's LMs limits the applicability of modern NLP to the broad field of text processing of climate-related texts. As a remedy, we propose ClimateBert, a transformer-based language model that is further pretrained on over 2 million paragraphs of climate-related texts, crawled from various sources such as common news, research articles, and climate reporting of companies. We find that ClimateBert leads to a 48% improvement on a masked language model objective which, in turn, leads to lowering error rates by 3.57% to 35.71% for various climate-related downstream tasks like text classification, sentiment analysis, and fact-checking Authors: Nicolas Webersinke (FAU Erlangen-Nürnberg), Mathias Kraus (FAU Erlangen-Nürnberg), Julia Anna Bingler (ETH Zurich) and Markus Leippold (UZH Zurich) AAAI FSS 2022 Curator: Creating Large-Scale Curated Labelled Datasets using Self-Supervised Learning Abstract and authors: (click to expand) Abstract: Applying Machine learning to domains like Earth Sciences is impeded by the lack of labeled data, despite a large corpus of raw data available in such domains. For instance, training a wildfire classifier on satellite imagery requires curating a massive and diverse dataset, which is an expensive and time-consuming process that can span from weeks to months. Searching for relevant examples in over 40 petabytes of unlabelled data requires researchers to manually hunt for such images, much like finding a needle in a haystack. We present a no-code end-to-end pipeline, Curator, which dramatically minimizes the time taken to curate an exhaustive labeled dataset. Curator is able to search massive amounts of unlabelled data by combining self-supervision, scalable nearest neighbor search, and active learning to learn and differentiate image representations. The pipeline can also be readily applied to solve problems across different domains. Overall, the pipeline makes it practical for researchers to go from just one reference image to a comprehensive dataset in a diminutive span of time. Authors: Tarun Narayanan (SpaceML), Ajay Krishnan (SpaceML), Anirudh Koul (Pinterest, SpaceML, FDL) and Siddha Ganju (NVIDIA, SpaceML, FDL) AAAI FSS 2022 De-risking Carbon Capture and Sequestration with Explainable CO2 Leakage Detection in Time-lapse Seismic Monitoring Images Abstract and authors: (click to expand) Abstract: With the growing global deployment of carbon capture and sequestration technology to combat climate change, monitoring and detection of potential CO2 leakage through existing or storage induced faults are critical to the safe and long-term viability of the technology. Recent work on time-lapse seismic monitoring of CO2 storage has shown promising results in its ability to monitor the growth of the CO2 plume from surface recorded seismic data. However, due to the low sensitivity of seismic imaging to CO2 concentration, additional developments are required to efficiently interpret the seismic images for leakage. In this work, we introduce a binary classification of time-lapse seismic images to delineate CO2 plumes (leakage) using state-of-the-art deep learning models. Additionally, we localize the leakage region of CO2 plumes by leveraging Class Activation Mapping (CAM) methods. Authors: Huseyin Tuna Erdinc (Georgia Institute of Technology), Abhinav Prakash Gahlot (Georgia Institute of Technology), Ziyi Yin (Georgia Institute of Technology), Mathias Louboutin (Georgia Institute of Technology) and Felix J. Herrmann (Georgia Institute of Technology) AAAI FSS 2022 Predicting Wildfire Risk Under Novel 21st-Century Climate Conditions Abstract and authors: (click to expand) Abstract: Wildfires are one of the most impactful hazards associated with climate change, and in a hotter, drier world, wildfires will be much more common than they have historically been. However, the exact severity and frequency of future wildfires are difficult to estimate, because climate change will create novel combinations of vegetation and fire weather outside what has been historically observed. This provides a challenge for AI-based approaches to long-term fire risk modeling, as much future fire risk is outside of the available feature space provided by the historical record. Here, we give an overview of this problem that is inherent to many climate change impacts and propose a restricted model form that makes monotonic and interpretable predictions in novel fire weather environments. We then show how our model outperforms other neural networks and logistic regression models when making predictions on unseen data from a decade into the future. Authors: Matthew Cooper (Sust Global). AAAI FSS 2022 Probabilistic Machine Learning in Polar Earth and Climate Science: A Review of Applications and Opportunities Abstract and authors: (click to expand) Abstract: Our world’s climate future is on thin ice. The study of longterm weather patterns in the polar regions is an important building block in tackling Climate Change. Our understanding of the past, the present and the future of the earth system, and the inherent uncertainty, informs planning, mitigation, and adaptation strategies. In this work we review previous applications of machine learning and statistical computing to polar climate research, and we highlight promising probabilistic machine learning methods that address the modelling needs of climate-related research in the Arctic and the Antarctic. We discuss common challenges in this interdisciplinary field and provide an overview of opportunities for future work in this novel area of research. Authors: Kim Bente (The University of Sydney), Judy Kay (The University of Sydney) and Roman Marchant (Commonwealth Scientific and Industrial Research Organisation (CSIRO)) AAAI FSS 2022 Rethinking Machine Learning for Climate Science: A Dataset Perspective Abstract and authors: (click to expand) Abstract: The growing availability of data sources is a predominant factor enabling the widespread success of machine learning (ML) systems across a wide range of applications. Typically, training data in such systems constitutes a source of ground-truth, such as measurements about a physical object (e.g., natural images) or a human artifact (e.g., natural language). In this position paper, we take a critical look at the validity of this assumption for datasets for climate science. We argue that many such climate datasets are uniquely biased due to the pervasive use of external simulation models (e.g., general circulation models) and proxy variables (e.g., satellite measurements) for imputing and extrapolating in-situ observational data. We discuss opportunities for mitigating the bias in the training and deployment of ML systems using such datasets. Finally, we share views on improving the reliability and accountability of ML systems for climate science applications. Authors: Aditya Grover (UCLA) AAAI FSS 2022 Graph Representation Learning for Energy Demand Data: Application to Joint Energy System Planning under Emissions Constraints Abstract and authors: (click to expand) Abstract: To meet the mid-century goal of CO2 emissions reduction requires a rapid transformation of current electric power and natural gas (NG) infrastructure. This necessitates a long-term planning of the joint power-NG system under representative demand patterns, operational constraints, and policy considerations. Our work is motivated by the computational and practical challenges associated with solving the generation and transmission expansion problem (GTEP) for joint planning of power-NG systems. Specifically, we focus on efficiently extracting a set of representative days from power and NG demand data in respective networks and using this set to reduce the computational burden required to solve the GTEP. We propose a Graph Autoencoder for Multiple time resolution Energy Systems (GAMES) to capture the spatio-temporal demand patterns in interdependent networks and account for differences in the temporal resolution of available data. The resulting embeddings are used in a clustering algorithm to select representative days. We evaluate the effectiveness of our approach in solving a GTEP formulation calibrated for the joint power-NG system in New England. This formulation accounts for the physical interdependencies between power and NG systems, including the joint emissions constraint. Our results show that the set of representative days obtained from GAMES not only allows us to tractably solve the GTEP formulation, but also achieves a lower cost of implementing the joint planning decisions. Authors: Aron Brenner (MIT), Rahman Khorramfar (MIT), Dharik Mallapragada (MIT) and Saurabh Amin (MIT) AAAI FSS 2022 Modeling Global Climate Negotiations, Agreements, and Long-Term Cooperation in RICE-N Abstract and authors: (click to expand) Abstract: Comprehensive global cooperation is essential to limit global temperature increases while continuing economic development, e.g., reducing severe inequality or achieving long-term economic growth. Achieving long-term cooperation on climate change mitigation with n strategic agents poses a complex game-theoretic problem. For example, agents may negotiate and reach climate agreements, but there is no central authority to enforce adherence to those agreements. Hence, it is critical to design negotiation and agreement frameworks that foster cooperation, allow all agents to meet their individual policy objectives, and incentivize long-term adherence. This is an interdisciplinary challenge that calls for collaboration between researchers in machine learning, economics, climate science, law, policy, ethics, and other fields. In particular, we argue that machine learning is a critical tool to address the complexity of this domain. To facilitate this research, here we introduce RICE-N, a multi-region integrated assessment model that simulates the global climate and economy, and which can be used to design and evaluate the strategic outcomes for different negotiation and agreement frameworks. We also describe how to use multi-agent reinforcement learning to train rational agents using RICE-N. This framework underpins AI for Global Climate Cooperation, a working group collaboration and competition on climate negotiation and agreement design. Here, we invite the scientific community to design and evaluate their solutions using RICE-N, machine learning, economic intuition, and other domain knowledge. More information can be found on www.ai4climatecoop.org. Authors: Tianyu Zhang (Université de Montréal, MILA), Andrew Williams (Université de Montréal, MILA), Soham Phade (Salesforce Research), Sunil Srinivasa (Salesforce Research), Yang Zhang (MILA), Prateek Gupta (MILA, University of Oxford, The Alan Turing Institute), Yoshua Bengio (Université de Montréal, MILA, CIFAR) and Stephan Zheng (Salesforce Research) AAAI FSS 2022 Self-Supervised Representations of Geo-located Weather Time Series - an Evaluation and Analysis Abstract and authors: (click to expand) Abstract: Self-supervised learning (SSL) is gaining traction in various domains, and demonstrated their potential particularly in tasks where labelled data is limited and costly to collect. In this work, we evaluate the performance existing self-supervised multivariate time series learning algorithms on weather-driven applications involving regression, classification and forecasting tasks. We experiment with a two-step protocol. In the first step, we employ and SSL algorithm and learn generic weather representations from multivariate weather data. Then, in the next step, we use these representations and fine-tune them for multiple downstream tasks. Through our initial experiments on air quality prediction and renewable energy generation tasks, we highlight the benefits of self-supervised weather representations, including improved performance in such tasks, ability to generalize with limited in-task data, and reduction in training time and carbon emissions. We expect such a direction to be relevant in multiple weather-driven applications supporting climate change mitigation and adaptation efforts. Authors: Arjun Ashok (IBM Research), Devyani Lambhate (IBM Research) and Jitendra Singh (IBM Research) AAAI FSS 2022 Predicting Daily Ozone Air Pollution With Transformers Abstract and authors: (click to expand) Abstract: Surface ozone is an air pollutant that contributes to hundreds of thousands of premature deaths annually. Ozone at the surface also has considerable negative impacts on vegetation and crop yields. Ozone concentrations are affected by environmental factors, including temperature, which means that ozone concentrations are likely to change in future climates, posing risks to human health. This effect is known as the ozone climate penalty, and recent work suggests that currently polluted areas are likely to become more polluted by ozone in future climates. In light of recent stricter WHO regulations on surface ozone concentrations, we aim to build a predictive data-driven model for recent ozone concentrations, which could be used to make predictions of ozone concentrations in future climates, better quantifying future risks to human health and gaining insight into the variables driving ozone concentrations. We use observational station data from three European countries to train a transformer-based model to make predictions of daily maximum 8-hour ozone. Authors: Sebastian Hickman (University of Cambridge), Paul Griffiths (University of Cambridge), Peer Nowack (University of East Anglia) and Alex Archibald (University of Cambridge) AAAI FSS 2022 The Impact of TCFD Reporting - A New Application of Zero-Shot Analysis to Climate-Related Financial Disclosures Abstract and authors: (click to expand) Abstract: We examine climate-related disclosures in 3,335 reports based on a sample of 188 banks that officially endorsed the recommendations of the Task Force for Climate-related Financial Disclosures (TCFD). In doing so, we introduce a new application of zero-shot text classification based on the BART model and a MNLI task. By developing a set of robust and fine-grained labels, we show that zero-shot analysis provides high accuracy in analyzing companies’ climate-related reporting without further model training. We are able to demonstrate that banks that support the TCFD increase their level of disclosure after officially declaring their support for the guidelines, although we also find significant differences depending on the topic of disclosure. Our findings yield important conclusions for the design of climate-related disclosures. Authors: Alix Auzepy (Justus-Liebig-Universität Gießen), Elena Tönjes (Justus-Liebig-Universität Gießen) and Christoph Funk (Justus-Liebig-Universität Gießen) AAAI FSS 2022 Using Natural Language Processing for Automating the Identification of Climate Action Interlinkages within the Sustainable Development Goals Abstract and authors: (click to expand) Abstract: Climate action, Goal 13 of the UN Sustainable Development Goals (SDG), cuts across almost all SDGs. Achieving climate goals can reinforce the achievements in many other goals, but at the same time climate mitigation and adaptation measures may generate trade-offs, such as levelling the cost of energy and transitioning away from fossil fuels. Leveraging the synergies and minimizing the trade-offs among the climate goals and other SDGs is an imperative task for ensuring policy coherence. Understanding the interlinkages between climate action and other SDGs can help inform about the synergies and trade-offs. This paper presents a novel methodology by using natural language processing (NLP) to automate the process of systematically identifying the key interlinkages between climate action and SDGs from a large amount of climate literature. A qualitative SDG interlinkages model for climate action was automatically generated and visualized in a network graph. This work contributes to the conference thematic topic on using AI for policy alignment for climate change goals, SDGs and associated environmental, social and governance (ESG) frameworks. Authors: Xin Zhou (Institute for Global Environmental Strategies (IGES)), Kshitij Jain (Google Inc.), Mustafa Moinuddin (Institute for Global Environmental Strategies (IGES)) and Patrick McSharry (Carnegie Mellon University Africa; Oxford Man Institute of Quantitative Finance, Oxford University) AAAI FSS 2022 Imputation of Missing Streamflow Data at Multiple Gauging Stations in Benin Republic Abstract and authors: (click to expand) Abstract: Streamflow observation data is vital for flood monitoring, agricultural, and settlement planning. However, such streamflow data are commonly plagued with missing observations due to various causes such as harsh environmental conditions and constrained operational resources. This problem is often more pervasive in under-resourced areas such as Sub-Saharan Africa. In this work, we reconstruct streamflow time series data through bias correction of the GEOGloWS ECMWF streamflow service (GESS) forecasts at ten river gauging stations in Benin. We perform bias correction by fitting Quantile Mapping, Gaussian Process, and Elastic Net regression in a constrained training period. We show by simulating missingness in a testing period that GESS forecasts have a significant bias that results in low predictive skill over the ten Beninese stations. Our findings suggest that overall bias correction by Elastic Net and Gaussian Process regression achieves superior skill relative to traditional imputation by Random Forest, k-Nearest Neighbour, and GESS lookup. The findings of this work provide a basis for integrating global GESS streamflow data into operational early-warning decision-making systems (e.g., flood alert) in countries vulnerable to drought and flooding due to extreme weather events. Authors: Rendani Mbuvha (Queen Mary University of London), Julien Yise Peniel Adounkpe (International Water Management Institute (IWMI)), Wilson Tsakane Mongwe (University of Johannesburg), Mandela Houngnibo (Agence Nationale de la Météorologie du Benin Meteo Benin), Nathaniel Newlands (Summerland Research and Development Centre, Agriculture and Agri-Food Canada) and Tshilidzi Marwala (University of Johannesburg) AAAI FSS 2022 Intermediate and Future Frame Prediction of Geostationary Satellite Imagery With Warp and Refine Network Abstract and authors: (click to expand) Abstract: Geostationary satellite imagery has applications in climate and weather forecasting, planning natural energy resources, and predicting extreme weather events. For precise and accurate prediction, higher spatial and temporal resolution of geostationary satellite imagery is important. Although recent geostationary satellite resolution has improved, the long-term analysis of climate applications is limited to using multiple satellites from the past to the present due to the different resolutions. To solve this problem, we proposed warp and refine network (WR-Net). WR-Net is divided into an optical flow warp component and a warp image refinement component.We used the TV-L1 algorithm instead of deep learning-based approaches to extract the optical flow warp component. The deep-learning-based model is trained on the human-centric view of the RGB channel and does not work on geostationary satellites, which is gray-scale one-channel imagery.The refinement network refines the warped image through a multi-temporal fusion layer. We evaluated WR-Net by interpolation of temporal resolution at 4 min intervals to 2 min intervals in large-scale GK2A geostationary meteorological satellite imagery. Furthermore, we applied WR-Net to the future frame prediction task and showed that the explicit use of optical flow can help future frame prediction. Authors: Minseok Seo (SI Analytics), Yeji Choi (SI Analytics), Hyungon Ryu (NVIDIA), Heesun Park (National Institute of Meteorological Science), Hyungkun Bae (SI Analytics), Hyesook Lee (National Institute of Meteorological Science) and Wanseok Seo (NVIDIA) AAAI FSS 2022 Machine Learning Methods in Climate Finance: A Systematic Review Abstract and authors: (click to expand) Abstract: Preventing the materialization of climate change is one of the main challenges of our time. The involvement of the financial sector is a fundamental pillar in this task, which has led to the emergence of a new field in the literature, climate finance. In turn, the use of Machine Learning (ML) as a tool to analyze climate finance is on the rise, due to the need to use big data to collect new climate-related information and model complex non-linear relationships. Considering the potential for the use of ML in climate finance and the proliferation of articles in this field, we propose a survey of the academic literature to assess how ML is enabling climate finance to scale up. The contribution of this paper is threefold. First, we do a systematic search in three scientific databases to assemble a corpus of relevant studies. Using topic modeling (Latent Dirichlet Allocation) we uncover representative thematic clusters. This allows us to statistically identify seven granular application domains where ML is playing a significant role in climate finance literature: natural hazards, biodiversity, agricultural risk, carbon markets, energy economics, ESG factors & investing, and climate data. Secondly, we do an analysis highlighting publication trends; and thirdly, we show a breakdown of ML methods applied by research area, aiming to spur further innovative work from ML experts. Authors: Andres Alonso-Robisco (Banco de España), Jose Manuel Carbo (Banco de España) and Jose Manuel Marques (Banco de España) NeurIPS 2021 Flood Segmentation on Sentinel-1 SAR Imagery with Semi-Supervised Learning (Papers Track) Abstract and authors: (click to expand) Abstract: Floods wreak havoc throughout the world, causing billions of dollars in damages, and uprooting communities, ecosystems and economies. The NASA Impact Emerging Techniques in Computational Intelligence (ETCI) competition on Flood Detection tasked participants with predicting flooded pixels after training with synthetic aperture radar (SAR) images in a supervised setting. We propose a semi-supervised learning pseudo-labeling scheme that derives confidence estimates from U-Net ensembles, thereby progressively improving accuracy. Concretely, we use a cyclical approach involving multiple stages (1) training an ensemble model of multiple U-Net architectures with the provided high confidence hand-labeled data and, generated pseudo labels or low confidence labels on the entire unlabeled test dataset, and then, (2) filter out quality generated labels and, (3) combine the generated labels with the previously available high confidence hand-labeled dataset. This assimilated dataset is used for the next round of training ensemble models. This cyclical process is repeated until the performance improvement plateaus. Additionally, we post process our results with Conditional Random Fields. Our approach sets a high score, and a new state-of-the-art on the Sentinel-1 dataset for the ETCI competition with 0.7654 IoU, an impressive improvement over the 0.60 IOU baseline. Our method, which we release with all the code including trained models, can also be used as an open science benchmark for the Sentinel-1 released dataset. Authors: Siddha Ganju (Nvidia Corporation); Sayak Paul (Carted) Unsupervised and semi-supervised learning Disaster prediction, management, and relief Earth science and monitoring Computer vision and remote sensing NeurIPS 2021 Short-term Solar Irradiance Prediction from Sky Images (Papers Track) Abstract and authors: (click to expand) Abstract: Solar irradiance forecasting is essential for the integration of the solar power into the power grid system while maintaining its stability. This paper focuses on short-term solar irradiance forecasting (upto 4-hour ahead-of-time prediction) from a past sky image sequence. Most existing work aims for the prediction of the most likely future of the solar irradiance. While it is likely deterministic for intra-hourly prediction, the future solar irradiance is naturally diverse over a relatively long-term horizon (>1h). We therefore introduce approaches to deterministic and stochastic predictions to capture the most likely as well as the diverse future of the solar irradiance. To enable the autoregressive prediction capability of the model, we proposed deep neural networks to predict the future sky images in a deterministic as well as stochastic manner. We evaluate our approaches on benchmark datasets and demonstrate that our approaches achieve superior performance. Authors: Hoang Chuong Nguyen (Australia National University); Miaomiao Liu (The Australian National University) Computer vision and remote sensing Power and energy NeurIPS 2021 Towards Representation Learning for Atmospheric Dynamics (Papers Track) Abstract and authors: (click to expand) Abstract: The prediction of future climate scenarios under anthropogenic forcing is critical to understand climate change and to assess the impact of potentially counter-acting technologies. Machine learning and hybrid techniques for this prediction rely on informative metrics that are sensitive to pertinent but often subtle influences. For atmospheric dynamics, a critical part of the climate system, no well established metric exists and visual inspection is currently still often used in practice. However, this eyeball metric'' cannot be used for machine learning where an algorithmic description is required. Motivated by the success of intermediate neural network activations as basis for learned metrics, e.g. in computer vision, we present a novel, self-supervised representation learning approach specifically designed for atmospheric dynamics. Our approach, called AtmoDist, trains a neural network on a simple, auxiliary task: predicting the temporal distance between elements of a randomly shuffled sequence of atmospheric fields (e.g. the components of the wind field from reanalysis or simulation). The task forces the network to learn important intrinsic aspects of the data as activations in its layers and from these hence a discriminative metric can be obtained. We demonstrate this by using AtmoDist to define a metric for GAN-based super resolution of vorticity and divergence. Our upscaled data matches both visually and in terms of its statistics a high resolution reference closely and it significantly outperform the state-of-the-art based on mean squared error. Since AtmoDist is unsupervised, only requires a temporal sequence of fields, and uses a simple auxiliary task, it has the potential to be of utility in a wide range of applications. Authors: Sebastian Hoffmann (University of Magdeburg); Christian Lessig (Otto-von-Guericke-Universitat Magdeburg) Climate and Earth science Earth science and monitoring Generative modeling Time-series analysis NeurIPS 2021 Addressing Deep Learning Model Uncertainty in Long-Range Climate Forecasting with Late Fusion (Papers Track) Abstract and authors: (click to expand) Abstract: Global warming leads to the increase in frequency and intensity of climate extremes that cause tremendous loss of lives and property. Accurate long-range climate prediction allows more time for preparation and disaster risk management for such extreme events. Although machine learning approaches have shown promising results in long-range climate forecasting, the associated model uncertainties may reduce their reliability. To address this issue, we propose a late fusion approach that systematically combines the predictions from multiple models to reduce the expected errors of the fused results. We also propose a network architecture with the novel denormalization layer to gain the benefits of data normalization without actually normalizing the data. The experimental results on long-range 2m temperature forecasting show that the framework outperforms the 30-year climate normals, and the accuracy can be improved by increasing the number of models. Authors: Ken C. L. Wong (IBM Research – Almaden Research Center); Hongzhi Wang (IBM Almaden Research Center); Etienne E Vos (IBM); Bianca Zadrozny (IBM Research); Campbell D Watson (IBM Reserch); Tanveer Syeda-Mahmood (IBM Research) Uncertainty quantification and robustness Climate and Earth science Classification, regression, and supervised learning Time-series analysis NeurIPS 2021 Predicting Discharge in Catchment Outlet Using Deep Learning: Case Study of the Ansongo-Niamey Basin (Papers Track) Abstract and authors: (click to expand) Abstract: Hydrological models are one of the key challenges in hydrology. Their goal is to understand, predict and manage water resources. Most of the hydrological models so far were either physical or conceptual models. But in the past two decades, fully data-driven (empirical) models started to emerge with the breakthroughs of novel deep learning methods in runoff prediction. These breakthroughs were mostly favored by the large volume, variety and velocity of water-related data. Long Short-Term Memory and Gated Recurrent Unit neural networks, particularly achieved the outstanding milestone of outperforming classic hydrological models in less than a decade. Moreover, they have the potential to change the way hydrological modeling is performed. In this study, precipitation, minimal and maximum temperature at the Ansongo-Niamey basin combined with the discharge at Ansongo and Kandadji were used to predict the discharge at Niamey using artificial neural networks. After data preprocessing and hyperparameter optimization, the deep learning models performed well with the LSTM and GRU respectively scoring a Nash-Sutcliffe Efficiency of 0.933 and 0.935. This performance matches those of well-known physically-based models used to simulate Niamey’s discharge and therefore demonstrates the efficiency of deep learning methods in a West African context, especially in Niamey which has been facing severe floods due to climate change. Authors: Peniel J. Y. Adounkpe (WASCAL); Eric Alamou (Université d'Abomey-Calavi); Belko Diallo (WASCAL); Abdou Ali (AGRHYMET Regional Centre) Disaster prediction, management, and relief Causal and Bayesian methods Classification, regression, and supervised learning Time-series analysis NeurIPS 2021 Accurate and Timely Forecasts of Geologic Carbon Storage using Machine Learning Methods (Papers Track) Abstract and authors: (click to expand) Abstract: Carbon capture and storage is one strategy to reduce greenhouse gas emissions. One approach to storing the captured CO2 is to inject it into deep saline aquifers. However, dynamics of the injected CO2 plume is uncertain and the potential for leakage back to the atmosphere must be assessed. Thus, accurate and timely forecasts of CO2 storage via real-time measurements integration becomes very crucial. This study proposes a learning-based, inverse-free prediction method that can accurately and rapidly forecast CO2 movement and distribution with uncertainty quantification based on limited simulation and observation data. The machine learning techniques include dimension reduction, multivariate data analysis, and Bayesian learning. The outcome is expected to provide CO2 storage site operators with an effective tool for real-time decision making. Authors: Dan Lu (Oak Ridge National Laboratory); Scott Painter (Oak Ridge National Laboratory); Nicholas Azzolina (University of North Dakota); Matthew Burton-Kelly (University of North Dakota) Carbon capture and sequestration Uncertainty quantification and robustness NeurIPS 2021 Towards debiasing climate simulations using unsuperviserd image-to-image translation networks (Papers Track) Abstract and authors: (click to expand) Abstract: Climate models form the basis of a vast portion of earth system research, and inform our climate policy. Due to the complex nature of our climate system, and the approximations which must necessarily be made in simulating it, these climate models may not perfectly match observations. For further research, these outputs must be bias corrected against observations, but current methods of debiasing do not take into account spatial correlations. We evaluate unsupervised image-to-image translation networks, specifically the UNIT model architecture, for their ability to produce more spatially realistic debiasing than the standard techniques used in the climate community. Authors: James Fulton (University of Edinburgh); Ben Clarke (Oxford University) Climate and Earth science Generative modeling NeurIPS 2021 Using Non-Linear Causal Models to Study Aerosol-Cloud Interactions in the Southeast Pacific (Papers Track) Abstract and authors: (click to expand) Abstract: Aerosol-cloud interactions include a myriad of effects that all begin when aerosol enters a cloud and acts as cloud condensation nuclei (CCN). An increase in CCN results in a decrease in the mean cloud droplet size (r_{e}). The smaller droplet size leads to brighter, more expansive, and longer lasting clouds that reflect more incoming sunlight, thus cooling the earth. Globally, aerosol-cloud interactions cool the Earth, however the strength of the effect is heterogeneous over different meteorological regimes. Understanding how aerosol-cloud interactions evolve as a function of the local environment can help us better understand sources of error in our Earth system models, which currently fail to reproduce the observed relationships. In this work we use recent non-linear, causal machine learning methods to study the heterogeneous effects of aerosols on cloud droplet radius. Authors: Andrew Jesson (University of Oxford); Peter Manshausen (University of Oxford); Alyson Douglas (University of Oxford); Duncan Watson-Parris (University of Oxford); Yarin Gal (University of Oxford); Philip Stier (University of Oxford) Climate and Earth science Causal and Bayesian methods NeurIPS 2021 Memory to Map: Improving Radar Flood Maps With Temporal Context and Semantic Segmentation (Papers Track) Abstract and authors: (click to expand) Abstract: Global flood risk has increased due to worsening extreme weather events and human migration into growing flood-prone areas. Accurate, high-resolution, and near-real time flood maps can address flood risk by reducing financial loss and damage. We propose Model to Map, a novel machine learning approach that utilizes bi-temporal context to improve flood water segmentation performance for Sentinel-1 imagery. We show that the inclusion of unflooded context for the area, or "memory," allows the model to tap into a "prior state" of pre-flood conditions, increasing performance in geographic regions in which single-image radar-based flood mapping methods typically underperform (e.g. deserts). We focus on accuracy across different biomes to ensure global performance. Our experiments and novel data processing technique show that the confluence of pre-flood and permanent water context provides a 21% increase in mIoU over the baseline overall, and over 87% increase in deserts. Authors: Veda Sunkara (Cloud to Street); Nicholas Leach (Cloud to Street); Siddha Ganju (Nvidia) Computer vision and remote sensing Climate justice Earth science and monitoring NeurIPS 2021 Hurricane Forecasting: A Novel Multimodal Machine Learning Framework (Papers Track) Abstract and authors: (click to expand) Abstract: This paper describes a machine learning (ML) framework for tropical cyclone intensity and track forecasting, combining multiple distinct ML techniques and utilizing diverse data sources. Our framework, which we refer to as Hurricast (HURR), is built upon the combination of distinct data processing techniques using gradient-boosted trees and novel encoder-decoder architectures, including CNN, GRU and Transformers components. We propose a deep-learning feature extractor methodology to mix spatial-temporal data with statistical data efficiently. Our multimodal framework unleashes the potential of making forecasts based on a wide range of data sources, including historical storm data, and visual data such as reanalysis atmospheric images. We evaluate our models with current operational forecasts in North Atlantic (NA) and Eastern Pacific (EP) basins on 2016-2019 for 24-hour lead time, and show our models consistently outperform statistical-dynamical models and compete with the best dynamical models. Furthermore, the inclusion of Hurricast into an operational forecast consensus model leads to a significant improvement of 5% - 15% over NHC's official forecast, thus highlighting the complementary properties with existing approaches. Authors: Léonard Boussioux (MIT, CentraleSupélec); Cynthia Zeng (MIT); Dimitris Bertsimas (MIT); Théo J Guenais (Harvard University) Hybrid physical models Climate and Earth science Disaster prediction, management, and relief Classification, regression, and supervised learning Computer vision and remote sensing Time-series analysis Unsupervised and semi-supervised learning NeurIPS 2021 Improved Drought Forecasting Using Surrogate Quantile And Shape (SQUASH) Loss (Papers Track) Abstract and authors: (click to expand) Abstract: Droughts are amongst the most damaging natural hazard with cascading impacts across multiple sectors of the economy and society. Improved forecasting of drought conditions ahead of time can significantly improve strategic planning to mitigate the impacts and enhance resilience. Though significant progress in forecasting approaches has been made, the current approaches focus on the overall improvement of the forecast, with less attention on the extremeness of drought events. In this paper, we focus on improving the accuracy of forecasting extreme and severe drought events by introducing a novel loss function Surrogate Quantile and Shape loss (SQUASH) that combines weighted quantile loss and dynamic time-warping-based shape loss. We show the effectiveness of the proposed loss functions for imbalanced time-series drought forecasting tasks on two regions in India and the USA. Authors: Devyani Lambhate Lambhate (Indian Institute of Science); Smit Marvaniya (IBM Research India); Jitendra Singh (IBM Research - India); David Gold (IBM) Disaster prediction, management, and relief Agriculture, forestry and other land use Climate and Earth science Time-series analysis NeurIPS 2021 Global ocean wind speed estimation with CyGNSSnet (Papers Track) Abstract and authors: (click to expand) Abstract: The CyGNSS (Cyclone Global Navigation Satellite System) satellite system measures GNSS signals reflected off the Earth's surface. A global ocean wind speed dataset is derived, which fills a gap in Earth observation data, will improve cyclone forecasting, and could be used to mitigate effects of climate change. We propose CyGNSSnet, a deep learning model for predicting wind speed from CyGNSS observables, and evaluate its potential for operational use. With CyGNSSnet, performance improves by 29\% over the current operational model. We further introduce a hierarchical model, that combines an extreme value classifier and a specialized CyGNSSnet and slightly improves predictions for high winds. Authors: Caroline Arnold (German Climate Computing Center); Milad Asgarimehr (German Research Centre for Geosciences) Computer vision and remote sensing Disaster prediction, management, and relief Earth science and monitoring Classification, regression, and supervised learning NeurIPS 2021 Predicting Critical Biogeochemistry of the Southern Ocean for Climate Monitoring (Papers Track) Abstract and authors: (click to expand) Abstract: The Biogeochemical-Argo (BGC-Argo) program is building a network of globally distributed, sensor-equipped robotic profiling floats, improving our understanding of the climate system and how it is changing. These floats, however, are limited in the number of variables measured. In this study, we train neural networks to predict silicate and phosphate values in the Southern Ocean from temperature, pressure, salinity, oxygen, nitrate, and location and apply these models to earth system model (ESM) and BGC-Argo data to expand the utility of this ocean observation network. We trained our neural networks on observations from the Global Ocean Ship-Based Hydrographic Investigations Program (GO-SHIP) and use dropout regularization to provide uncertainty bounds around our predicted values. Our neural network significantly improves upon linear regression but shows variable levels of uncertainty across the ranges of predicted variables. We explore the generalization of our estimators to test data outside our training distribution from both ESM and BGC-Argo data. Our use of out-of-distribution test data to examine shifts in biogeochemical parameters and calculate uncertainty bounds around estimates advance the state-of-the-art in oceanographic data and climate monitoring. We make our data and code publicly available. Authors: Ellen Park (MIT); Jae Deok Kim (MIT-WHOI); Nadege Aoki (MIT); Yumeng Cao (MIT); Yamin Arefeen (Massachusetts Institute of Technology); Matthew Beveridge (Massachusetts Institute of Technology); David P Nicholson (Woods Hole Oceanographic Institution); Iddo Drori (MIT) Earth science and monitoring Ecosystems and natural systems Classification, regression, and supervised learning Other NeurIPS 2021 On the Generalization of Agricultural Drought Classification from Climate Data (Papers Track) Abstract and authors: (click to expand) Abstract: Climate change is expected to increase the likelihood of drought events, with severe implications for food security. Unlike other natural disasters, droughts have a slow onset and depend on various external factors, making drought detection in climate data difficult. In contrast to existing works that rely on simple relative drought indices as ground-truth data, we build upon soil moisture index (SMI) obtained from a hydrological model. This index is directly related to insufficiently available water to vegetation. Given ERA5-Land climate input data of six months with land use information from MODIS satellite observation, we compare different models with and without sequential inductive bias in classifying droughts based on SMI. We use PR-AUC as the evaluation measure to account for the class imbalance and obtain promising results despite a challenging time-based split. We further show in an ablation study that the models retain their predictive capabilities given input data of coarser resolutions, as frequently encountered in climate models. Authors: Julia Gottfriedsen (1Deutsches Zentrum für Luft- und Raumfahrt (DLR), LMU); Max Berrendorf (Ludwig-Maximilians-Universität München); Pierre Gentine (Columbia University); Markus Reichstein (Max Planck Institute for Biogeochemistry, Jena; Michael Stifel Center Jena for Data-Driven and Simulation Science, Jena); Katja Weigel (niversity of Bremen, Institute of Environmental Physics (IUP), Bremen, Germany); Birgit Hassler (Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany); Veronika Eyring (Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany; University of Bremen, Institute of Environmental Physics (IUP), Bremen, Germany) Climate and Earth science Agriculture, forestry and other land use Disaster prediction, management, and relief NeurIPS 2021 Mapping Post-Climate Change Biogeographical Regions with Deep Latent Variable Models (Papers Track) Abstract and authors: (click to expand) Abstract: Forecasting future changes to biodiversity due to shifts in climate is challenging due to nonlinear interactions between species as recorded in their presence/absence data. This work proposes using variational autoencoders with environmental covariates to identify low-dimensional structure in species’ joint co-occurrence patterns and leveraging this simplified representation to provide multivariate predictions of their habitat extent under future climate scenarios. We pursue a latent space clustering approach to map biogeographical regions of frequently co-occurring species and apply this methodology to a dataset from northern Belgium, generating predictive maps illustrating how these regions may expand or contract with changing temperature under a future climate scenario. Authors: Christopher Krapu (Oak Ridge National Lab - Oak Ridge, TN) Generative modeling Agriculture, forestry and other land use Causal and Bayesian methods NeurIPS 2021 Rotation Equivariant Deforestation Segmentation and Driver Classification (Papers Track) Abstract and authors: (click to expand) Abstract: Deforestation has become a significant contributing factor to climate change and, due to this, both classifying the drivers and predicting segmentation maps of deforestation has attracted significant interest. In this work, we develop a rotation equivariant convolutional neural network model to predict the drivers and generate segmentation maps of deforestation events from Landsat 8 satellite images. This outperforms previous methods in classifying the drivers and predicting the segmentation map of deforestation, offering a 9% improvement in classification accuracy and a 7% improvement in segmentation map accuracy. In addition, this method predicts stable segmentation maps under rotation of the input image, which ensures that predicted regions of deforestation are not dependent upon the rotational orientation of the satellite. Authors: Joshua Mitton (University of Glasgow); Roderick Murray-Smith (University of Glasgow) Computer vision and remote sensing Classification, regression, and supervised learning NeurIPS 2021 WiSoSuper: Benchmarking Super-Resolution Methods on Wind and Solar Data (Papers Track) Abstract and authors: (click to expand) Abstract: The transition to green energy grids depends on detailed wind and solar forecasts to optimize the siting and scheduling of renewable energy generation. Operational forecasts from numerical weather prediction models, however, only have a spatial resolution of 10 to 20-km, which leads to sub-optimal usage and development of renewable energy farms. Weather scientists have been developing super-resolution methods to increase the resolution, but often rely on simple interpolation techniques or computationally expensive differential equation-based models. Recently, machine learning-based models, specifically the physics-informed resolution-enhancing generative adversarial network (PhIREGAN), have outperformed traditional downscaling methods. We provide a thorough and extensible benchmark of leading deep learning-based super-resolution techniques, including the enhanced super-resolution generative adversarial network (ESRGAN) and an enhanced deep super-resolution (EDSR) network, on wind and solar data. We accompany the benchmark with a novel public, processed, and machine learning-ready dataset for benchmarking super-resolution methods on wind and solar data. Authors: Rupa Kurinchi-Vendhan (Caltech); Björn Lütjens (MIT); Ritwik Gupta (University of California, Berkeley); Lucien D Werner (California Institute of Technology); Dava Newman (MIT); Steven Low (California Institute of Technology) Computer vision and remote sensing Climate and Earth science Earth science and monitoring Power and energy Classification, regression, and supervised learning Generative modeling NeurIPS 2021 Meta-Learned Bayesian Optimization for Calibrating Building Simulation Models with Multi-Source Data (Papers Track) Abstract and authors: (click to expand) Abstract: Well-calibrated building simulation models are key to reducing greenhouse gas emissions and optimizing building performance. Current calibration algorithms do not leverage data collected during previous calibration tasks. In this paper, we employ attentive neural processes (ANP) to meta-learn a distribution using multi-source data acquired during previously seen calibration tasks. The ANP informs a meta-learned Bayesian optimizer to accelerate calibration of new, unseen tasks. The few-shot nature of our proposed algorithm is demonstrated on a library of residential buildings validated by the United States Department of Energy (USDoE). Authors: Sicheng Zhan (NUS); Gordon Wichern (Mitsubishi Electric Research Laboratories (MERL)); Christopher Laughman (Mitsubishi Electric Research Laboratories); Ankush Chakrabarty (Mitsubishi Electric Research Labs) Buildings and cities Meta- and transfer learning NeurIPS 2021 MS-nowcasting: Operational Precipitation Nowcasting with Convolutional LSTMs at Microsoft Weather (Papers Track) Abstract and authors: (click to expand) Abstract: We present the encoder-forecaster convolutional long short-term memory (LSTM) deep-learning model that powers Microsoft Weather's operational precipitation nowcasting product. This model takes as input a sequence of weather radar mosaics and deterministically predicts future radar reflectivity at lead times up to 6 hours. By stacking a large input receptive field along the feature dimension and conditioning the model's forecaster with predictions from the physics-based High Resolution Rapid Refresh (HRRR) model, we are able to outperform optical flow and HRRR baselines by 20-25% on multiple metrics averaged over all lead times. Authors: Sylwester Klocek (Microsoft Corporation); Haiyu Dong (Microsoft); Matthew Dixon (Microsoft Corporation); Panashe Kanengoni (Microsoft Corporation); Najeeb Kazmi (Microsoft); Pete Luferenko (Microsoft Corporation); Zhongjian Lv (Microsoft Corporation); Shikhar Sharma (); Jonathan Weyn (Microsoft); Siqi Xiang (Microsoft Corporation) Computer vision and remote sensing Climate and Earth science Disaster prediction, management, and relief Earth science and monitoring Classification, regression, and supervised learning Hybrid physical models NeurIPS 2021 SunCast: Solar Irradiance Nowcasting from Geosynchronous Satellite Data (Papers Track) Abstract and authors: (click to expand) Abstract: When cloud layers cover photovoltaic (PV) panels, the amount of power the panels produce fluctuates rapidly. Therefore, to maintain enough energy on a power grid to match demand, utilities companies rely on reserve power sources that typically come from fossil fuels and therefore pollute the environment. Accurate short-term PV power prediction enables operators to maximize the amount of power obtained from PV panels and safely reduce the reserve energy needed from fossil fuel sources. While several studies have developed machine learning models to predict solar irradiance at specific PV generation facilities, little work has been done to model short-term solar irradiance on a global scale. Furthermore, models that have been developed are proprietary and have architectures that are not publicly available or rely on computationally demanding Numerical Weather Prediction (NWP) models. Here, we propose a Convolutional Long Short-Term Memory Network model that treats solar nowcasting as a next frame prediction problem, is more efficient than NWP models and has a straightforward, reproducible architecture. Our models can predict solar irradiance for entire North America for up to 3 hours in under 60 seconds on a single machine without a GPU and has a RMSE of 120 W/m^2 when evaluated on 2 months of data. Authors: Dhileeban Kumaresan (UC Berkeley); Richard Wang (UC Berkeley); Ernesto A Martinez (UC Berkeley); Richard Cziva (UC Berkeley); Alberto Todeschini (UC Berkeley); Colorado J Reed (University of California, Berkeley); Puya Vahabi (UC Berkeley) Power and energy Classification, regression, and supervised learning Computer vision and remote sensing NeurIPS 2021 Synthetic Imagery Aided Geographic Domain Adaptation for Rare Energy Infrastructure Detection in Remotely Sensed Imagery (Papers Track) Abstract and authors: (click to expand) Abstract: Object detection in remotely sensed data is frequently stymied by applications in geographies that are different from that of the training data. When objects are rare, the problem is exacerbated further. This is true of assessments of energy infrastructure such as generation, transmission, and end-use consumption; key to electrification planning as well as for effective assessment of natural disaster impacts which are varying in frequency and intensity due to climate change. We propose an approach to domain adaptation that requires only unlabeled samples from the target domain and generates synthetic data to augment training data for targeted domain adaptation. This approach is shown to work consistently across four geographically diverse domains, improving object detection average precision by 15.5\% on average for small sample sizes. Authors: Wei Hu (Duke University); Tyler Feldman (Duke University); Eddy Lin (Duke University); Jose Luis Moscoso (Duke); Yanchen J Ou (Duke University); Natalie Tarn (Duke University); Baoyan Ye (Duke University); Wendy Zhang (Duke University); Jordan Malof (Duke University); Kyle Bradbury (Duke University) Computer vision and remote sensing Earth science and monitoring Power and energy Classification, regression, and supervised learning NeurIPS 2021 Being the Fire: A CNN-Based Reinforcement Learning Method to Learn How Fires Behave Beyond the Limits of Physics-Based Empirical Models (Papers Track) Abstract and authors: (click to expand) Abstract: Wildland fires pose an increasing threat in light of anthropogenic climate change. Fire-spread models play an underpinning role in many areas of research across this domain, from emergency evacuation to insurance analysis. We study paths towards advancing such models through deep reinforcement learning. Aggregating 21 fire perimeters from the Western United States in 2017, we construct 11-layer raster images representing the state of the fire area. A convolution neural network based agent is trained offline on one million sub-images to create a generalizable baseline for predicting the best action - burn or not burn - given the then-current state on a particular fire edge. A series of online, TD(0) Monte Carlo Q-Learning based improvements are made with final evaluation conducted on a subset of holdout fire perimeters. We examine the performance of the learned agent/model against the FARSITE fire-spread model. We also make available a novel data set and propose more informative evaluation metrics for future progress. Authors: William L Ross (Stanford) Disaster prediction, management, and relief Societal adaptation Computer vision and remote sensing Reinforcement learning and control NeurIPS 2021 Subseasonal Solar Power Forecasting via Deep Sequence Learning (Papers Track) Abstract and authors: (click to expand) Abstract: To help mitigate climate change, power systems need to integrate renewable energy sources, such as solar, at a rapid pace. Widespread integration of solar energy into the power system requires major improvements in solar irradiance forecasting, in order to reduce the uncertainty associated with solar power output. While recent works have addressed short lead-time forecasting (minutes to hours ahead), week(s)-ahead and longer forecasts, coupled with uncertainty estimates, will be extremely important for storage applications in future power systems. In this work, we propose machine learning approaches for these longer lead-times as an important new application area in the energy domain. We demonstrate the potential of several deep sequence learning techniques for both point predictions and probabilistic predictions at these longer lead-times. We compare their performance for subseasonal forecasting (forecast lead-times of roughly two weeks) using the SURFRAD data set for 7 stations across the U.S. in 2018. The results are encouraging; the deep sequence learning methods outperform the current benchmark for machine learning-based probabilistic predictions (previously applied at short lead-times in this domain), along with relevant baselines. Authors: Saumya Sinha (University of Colorado, Boulder); Bri-Mathias S Hodge (University of Colorado Boulder); Claire Monteleoni (University of Colorado Boulder) Power and energy Time-series analysis NeurIPS 2021 A Transfer Learning-Based Surrogate Model for Geological Carbon Storage with Multi-Fidelity Training Data (Papers Track) Abstract and authors: (click to expand) Abstract: Geologic carbon storage (GCS) entails injecting large volumes of carbon dioxide (CO2) in deep geologic formations to prevent its release to the atmosphere. Reservoir simulation is widely used in GCS applications to predict subsurface pressure and CO2 saturation. High fidelity numerical models are prohibitively expensive for data assimilation and uncertainty quantification, which require a large number of simulation runs. Deep learning-based surrogate models have shown a great promise to alleviate the high computational cost. However, the training cost is high as thousands of high-fidelity simulations are often necessary for generating the training data. In this work, we explore the use of a transfer learning approach to reduce the training cost. Compared with the surrogate model trained with high-fidelity simulations, our new transfer learning-based model shows comparable accuracy but reduces the training cost by 80%. Authors: Su Jiang (Stanford University) Carbon capture and sequestration Computer vision and remote sensing NeurIPS 2021 National Cropland Classification with Agriculture Census Information and EO Datasets (Papers Track) Abstract and authors: (click to expand) Abstract: National cropland classification is critical to monitor food security, comprehend environmental circumstances and climate change, and participate in agricultural policy development. The increasing earth observation datasets, especially the free available Sentinel and Landsat, open unprecedented large-scale mapping opportunities. However, most applied machine learning techniques have relied on substantial training datasets, which are not always available and may be expensive to create or collect. Focusing on Japan, this work indicates what kinds of information can be extracted from agriculture census information then used for mapping different crop types. Different classification approaches of pixel-based and parcel-based are compared. Then, the efficient method is used to generate Japan's first national cropland classification with Sentinel-1 C-band and Landsat-8 time series. For 2015, the overall accuracies for the prefectures range between 71\% and 94\%. This national cropland classification map, which particularly succeeds in extracting high-precision rice products for the whole of Japan and other classes for different prefectures, can be treated as the base map of Japan for future studies related to agriculture, environment, and climate change. Authors: Junshi Xia (RIKEN); Naoto Yokoya (The University of Tokyo); Bruno Adriano (RIKEN Center for Advanced Intelligence Project (AIP)) Agriculture, forestry and other land use Classification, regression, and supervised learning NeurIPS 2021 FIgLib & SmokeyNet: Dataset and Deep Learning Model for Real-Time Wildland Fire Smoke Detection (Papers Track) Abstract and authors: (click to expand) Abstract: The size and frequency of wildland fires in the western United States have dramatically increased in recent years. On high fire-risk days, a small fire ignition can rapidly grow and get out of control. Early detection of fire ignitions from initial smoke can assist response to such fires before they become difficult to manage. Past deep learning approaches for wildfire smoke detection have suffered from small or unreliable datasets that make it difficult to extrapolate performance to real-world scenarios. In this work, we present the Fire Ignition Library (FIgLib), a publicly-available dataset of nearly 25,000 labeled wildfire smoke images as seen from fixed-view cameras deployed in Southern California. We also introduce SmokeyNet, a novel deep learning architecture using spatio-temporal information from camera imagery for real-time wildfire smoke detection. When trained on the FIgLib dataset, SmokeyNet outperforms comparable baselines. We hope that the availability of the FIgLib dataset and the SmokeyNet architecture will inspire further research into deep learning methods for wildfire smoke detection, leading to automated notification systems to reduce the time to wildfire response. Authors: Anshuman Dewangan (University of California, San Diego); Mai Nguyen (University of California, San Diego); Garrison Cottrell (UC San Diego) Disaster prediction, management, and relief Computer vision and remote sensing NeurIPS 2021 Multitask Learning for Estimating Power Plant Greenhouse Gas Emissions from Satellite Imagery (Papers Track) Abstract and authors: (click to expand) Abstract: The burning of fossil fuels produces large amounts of carbon dioxide (CO2), a major Greenhouse Gas (GHG) and a main driver of Climate Change. Quantifying GHG emissions is crucial for accurate predictions of climate effects and to enforce emission trading schemes. The reporting of such emissions is only required in some countries, resulting in insufficient global coverage. In this work, we propose an end-to-end method to predict power generation rates for fossil fuel power plants from satellite images based on which we estimate GHG emission rates. We present a multitask deep learning approach able to simultaneously predict: (i) the pixel-area covered by plumes from a single satellite image of a power plant, (ii) the type of fired fuel, and (iii) the power generation rate. We then convert the predicted power generation rate into estimates for the rate at which CO2 is being emitted. Experimental results show that our model approach allows us to estimate the power generation rate of a power plant to within 139 MW (MAE, for a mean sample power plant capacity of 1177 MW) from a single satellite image and CO2 emission rates to within 311 t/h. This multitask learning approach improves the power generation estimation MAE by 39 % compared to a single-task network trained on the same dataset. Authors: Joëlle Hanna (University of St. Gallen); Michael Mommert (University of St. Gallen); Linus M. Scheibenreif (University of St. Gallen); Damian Borth (University of St. Gallen) Computer vision and remote sensing Power and energy NeurIPS 2021 ClimART: A Benchmark Dataset for Emulating Atmospheric Radiative Transfer in Weather and Climate Models (Papers Track) Abstract and authors: (click to expand) Abstract: Numerical simulations of Earth's weather and climate require substantial amounts of computation. This has led to a growing interest in replacing subroutines that explicitly compute physical processes with approximate machine learning (ML) methods that are fast at inference time. Within weather and climate models, atmospheric radiative transfer (RT) calculations are especially expensive. This has made them a popular target for neural network-based emulators. However, prior work is hard to compare due to the lack of a comprehensive dataset and standardized best practices for ML benchmarking. To fill this gap, we introduce the \climart dataset, with more than \emph{10 million samples from present, pre-industrial, and future climate conditions}. ClimART poses several methodological challenges for the ML community, such as multiple out-of-distribution test sets, underlying domain physics, and a trade-off between accuracy and inference speed. We also present several novel baselines that indicate shortcomings of the datasets and network architectures used in prior work. Authors: Salva Rühling Cachay (Technical University of Darmstadt); Venkatesh Ramesh (MILA); Jason N. S. Cole (Environment and Climate Change Canada); Howard Barker (Environment and Climate Change Canada); David Rolnick (McGill University, Mila) Climate and Earth science Classification, regression, and supervised learning NeurIPS 2021 A GNN-RNN Approach for Harnessing Geospatial and Temporal Information: Application to Crop Yield Prediction (Papers Track) Best Paper: ML Innovation Abstract and authors: (click to expand) Abstract: Climate change poses new challenges to agricultural production, as crop yields are extremely sensitive to climatic variation. Accurately predicting the effects of weather patterns on crop yield is crucial for addressing issues such as food insecurity, supply stability, and economic planning. Recently, there have been many attempts to use machine learning models for crop yield prediction. However, these models either restrict their tasks to a relatively small region or a short time-period (e.g. a few years), which makes them hard to generalize spatially and temporally. They also view each location as an i.i.d sample, ignoring spatial correlations in the data. In this paper, we introduce a novel graph-based recurrent neural network for crop yield prediction, which incorporates both geographical and temporal structure. Our method is trained, validated, and tested on over 2000 counties from 41 states in the US mainland, covering years from 1981 to 2019. As far as we know, this is the first machine learning method that embeds geographical knowledge in crop yield prediction and predicts crop yields at the county level nationwide. Experimental results show that our proposed method consistently outperforms a wide variety of existing state-of-the-art methods, validating the effectiveness of geospatial and temporal information. Authors: Joshua Fan (Cornell University); Junwen Bai (Cornell University); Zhiyun Li (Cornell University); Ariel Ortiz-Bobea (Cornell); Carla P Gomes (Cornell University) Agriculture, forestry and other land use Classification, regression, and supervised learning Time-series analysis NeurIPS 2021 Learned Benchmarks for Subseasonal Forecasting (Papers Track) Abstract and authors: (click to expand) Abstract: We develop a subseasonal forecasting toolkit of simple learned benchmark models that outperform both operational practice and state-of-the-art machine learning and deep learning methods. Our new models include (a) Climatology++, an adaptive alternative to climatology that, for precipitation, is 9% more accurate and 250\% more skillful than the United States operational Climate Forecasting System (CFSv2); (b) CFSv2++, a learned CFSv2 correction that improves temperature and precipitation accuracy by 7-8% and skill by 50-275%; and (c) Persistence++, an augmented persistence model that combines CFSv2 forecasts with lagged measurements to improve temperature and precipitation accuracy by 6-9% and skill by 40-130%. Across the contiguous U.S., these models consistently outperform standard meteorological baselines, state-of-the-art learning methods, and the European Centre for Medium-Range Weather Forecasts ensemble. Overall, we find that augmenting traditional forecasting approaches with learned enhancements yields an effective and computationally inexpensive strategy for building the next generation of subseasonal forecasting benchmarks. Authors: Soukayna Mouatadid (University of Toronto); Paulo Orenstein (IMPA); Genevieve E Flaspohler (MIT); Miruna Oprescu (Microsoft Research); Judah Cohen (AER); Franklyn Wang (Harvard University); Sean Knight (MIT); Maria Geogdzhayeva (MIT); Sam Levang (Salient Predictions Inc.); Ernest Fraenkel (MIT); Lester Mackey (Microsoft Research) Climate and Earth science Classification, regression, and supervised learning NeurIPS 2021 Emissions-aware electricity network expansion planning via implicit differentiation (Papers Track) Abstract and authors: (click to expand) Abstract: We consider a variant of the classical problem of designing or expanding an electricity network. Instead of minimizing only investment and production costs, however, we seek to minimize some mixture of cost and greenhouse gas emissions, even if the underlying dispatch model does not tax emissions. This enables grid planners to directly minimize consumption-based emissions, when expanding or modifying the grid, regardless of whether or not the carbon market incorporates a carbon tax. We solve this problem using gradient descent with implicit differentiation, a technique recently popularized in machine learning. To demonstrate the method, we optimize transmission and storage resources on the IEEE 14-bus test network and compare our solution to one generated by standard planning with a carbon tax. Our solution significantly reduces emissions for the same levelized cost of electricity. Authors: Anthony Degleris (Stanford University); Lucas Fuentes (Stanford); Abbas El Gamal (Stanford University); Ram Rajagopal (Stanford University) Power and energy Climate policy Other NeurIPS 2021 Amortized inference of Gaussian process hyperparameters for improved concrete strength trajectory prediction (Papers Track) Abstract and authors: (click to expand) Abstract: Designing and utilizing alternative concrete formulations which supplant the use of ordinary portland cement with alternative binders have been identified as central goals in reducing the greenhouse gas impact of the concrete industry. Given the variability in availability and quality of alternatives, these goals call for an optimal design of experiment approach to designing formulations, which can be adapted to local needs. The realization of this goal hinges on an ability to predict key properties. Here, we present and benchmark a Gaussian process (GP) model for predicting the trajectory of concrete strength, an essential performance measure. GPs are a desirable model class for the application because of their ability to estimate uncertainty and update predictions given additional data. In this work, rather than manually tuning hyperparameters for different concrete mix models, we propose a new method based on amortized inference leveraging mixture attributes, leading to models which are better fit for use in Bayesian optimization of concrete formulation. We demonstrate the success of the approach using a large, industrial concrete dataset. Authors: Kristen Severson (Microsoft Research); Olivia Pfeiffer (MIT); Jie Chen (IBM Research); Kai Gong (MIT); Jeremy Gregory (Massachusetts Institute of Technology); Richard Goodwin (IBM Research); Elsa Olivetti (Massachusetts Institute of Technology) Causal and Bayesian methods Industry NeurIPS 2021 A data integration pipeline towards reliable monitoring of phytoplankton and early detection of harmful algal blooms (Papers Track) Abstract and authors: (click to expand) Abstract: Climate change is making oceans warmer and more acidic. Under these conditions phytoplankton can produce harmful algal blooms which cause rapid oxygen depletion and consequent death of marine plants and animals. Some species are even capable of releasing toxic substances endangering water quality and human health. Monitoring of phytoplankton and early detection of harmful algal blooms is essential for protection of marine flaura and fauna. Recent technological advances have enabled in-situ plankton image capture in real-time at low cost. However, available phytoplankton image databases have several limitations that prevent the practical usage of artificial intelligent models. We present a pipeline for integration of heterogeneous phytoplankton image datasets from around the world into a unified database that can ultimately serve as a benchmark dataset for phytoplankton research and therefore act as an important tool in building versatile machine learning models for climate adaptation planning. A machine learning model for early detection of harmful algal blooms is part of ongoing work. Authors: Bruna Guterres (Universidade Federal do Rio Grande - FURG); Sara khalid (University of Oxford); Marcelo Pias (Federal University of Rio Grande); Silvia Botelho (Federal University of Rio Grande) Disaster prediction, management, and relief Ecosystems and natural systems Classification, regression, and supervised learning NeurIPS 2021 Identifying Distributional Differences in Convective Evolution Prior to Rapid Intensification in Tropical Cyclones (Papers Track) Abstract and authors: (click to expand) Abstract: Tropical cyclone (TC) intensity forecasts are issued by human forecasters who evaluate spatio-temporal observations (e.g., satellite imagery) and model output (e.g., numerical weather prediction, statistical models) to produce forecasts every 6 hours. Within these time constraints, it can be challenging to draw insight from such data. While high-capacity machine learning methods are well suited for prediction problems with complex sequence data, extracting interpretable scientific information with such methods is difficult. Here we leverage powerful AI prediction algorithms and classical statistical inference to identify patterns in the evolution of TC convective structure leading up to the rapid intensification of a storm, hence providing forecasters and scientists with key insight into TC behavior. Authors: Irwin H McNeely (Carnegie Mellon University); Galen Vincent (Carnegie Mellon University); Rafael Izbicki (UFSCar); Kimberly Wood (Mississippi State University); Ann B. Lee (Carnegie Mellon University) Disaster prediction, management, and relief Interpretable ML NeurIPS 2021 Predicting Atlantic Multidecadal Variability (Papers Track) Best Paper: Pathway to Impact Abstract and authors: (click to expand) Abstract: Atlantic Multidecadal Variability (AMV) describes variations of North Atlantic sea surface temperature with a typical cycle of between 60 and 70 years. AMV strongly impacts local climate over North America and Europe, therefore prediction of AMV, especially the extreme values, is of great societal utility for understanding and responding to regional climate change. This work tests multiple machine learning models to improve the state of AMV prediction from maps of sea surface temperature, salinity, and sea level pressure in the North Atlantic region. We use data from the Community Earth System Model 1 Large Ensemble Project, a state-of-the-art climate model with 3,440 years of data. Our results demonstrate that all of the models we use outperform the traditional persistence forecast baseline. Predicting the AMV is important for identifying future extreme temperatures and precipitation as well as hurricane activity, in Europe and North America up to 25 years in advance. Authors: Glenn Liu (Massachusetts Institute of Technology); Peidong Wang (MIT); Matthew Beveridge (Massachusetts Institute of Technology); Young-Oh Kwon (Woods Hole Oceanographic Institution); Iddo Drori (MIT) Climate and Earth science Classification, regression, and supervised learning Other NeurIPS 2021 Identifying the atmospheric drivers of drought and heat using a smoothed deep learning approach (Papers Track) Abstract and authors: (click to expand) Abstract: Europe was hit by several, disastrous heat and drought events in recent summers. Besides thermodynamic influences, such hot and dry extremes are driven by certain atmospheric situations including anticyclonic conditions. Effects of climate change on atmospheric circulations are complex and many open research questions remain in this context, e.g., on future trends of anticyclonic conditions. Based on the combination of a catalog of labeled circulation patterns and spatial atmospheric variables, we propose a smoothed convolutional neural network classifier for six types of anticyclonic circulations that are associated with drought and heat. Our work can help to identify important drivers of hot and dry extremes in climate simulations, which allows to unveil the impact of climate change on these drivers. We address various challenges inherent to circulation pattern classification that are also present in other climate patterns, e.g., subjective labels and unambiguous transition periods. Authors: Magdalena Mittermeier (Ludwig-Maximilians-Universität München); Maximilian Weigert (Ludwig-Maximilians-Universität München); David Ruegamer (LMU Munich) Climate and Earth science Classification, regression, and supervised learning NeurIPS 2021 Learning to identify cracks on wind turbine blade surfaces using drone-based inspection images (Papers Track) Abstract and authors: (click to expand) Abstract: Wind energy is expected to be one of the leading ways to achieve the goals of the Paris Agreement but it in turn heavily depends on effective management of its operations and maintenance (O&M) costs. Blade failures account for one-third of all O&M costs thus making accurate detection of blade damages, especially cracks, very important for sustained operations and cost savings. Traditionally, damage inspection has been a completely manual process thus making it subjective, error-prone, and time-consuming. Hence in this work, we bring more objectivity, scalability, and repeatability in our damage inspection process, using deep learning, to miss fewer cracks. We build a deep learning model trained on a large dataset of blade damages, collected by our drone-based inspection, to correctly detect cracks. Our model is already in production and has processed more than a million damages with a recall of 0.96. We also focus on model interpretability using class activation maps to get a peek into the model workings. The model not only performs as good as human experts but also better in certain tricky cases. Thus, in this work, we aim to increase wind energy adoption by decreasing one of its major hurdles - the O&M costs resulting from missing blade failures like cracks. Authors: Akshay B Iyer (SkySpecs, Inc.); Linh V Nguyen (SkySpecs Inc); Shweta Khushu (SkySpecs Inc.) Power and energy Climate finance and economics Classification, regression, and supervised learning Computer vision and remote sensing NeurIPS 2021 Evaluating Pretraining Methods for Deep Learning on Geophysical Imaging Datasets (Papers Track) Abstract and authors: (click to expand) Abstract: Machine learning has the potential to automate the analysis of vast amounts of raw geophysical data, allowing scientists to monitor changes in key aspects of our climate such as cloud cover in real-time and at fine spatiotemporal scales. However, the lack of large labeled training datasets poses a significant barrier for effectively applying machine learning to these applications. Transfer learning, which involves first pretraining a neural network on an auxiliary “source” dataset and then finetuning on the “target” dataset, has been shown to improve accuracy for machine learning models trained on small datasets. Across prior work on machine learning for geophysical imaging, different choices are made about what data to pretrain on, and the impact of these choices on model performance is unclear. To address this, we systematically explore various settings of transfer learning for cloud classification, cloud segmentation, and aurora classification. We pretrain on different source datasets, including the large ImageNet dataset as well as smaller geophysical datasets that are more similar to the target datasets. We also experiment with multiple transfer learning steps where we pretrain on more than one source dataset. Despite the smaller source datasets’ similarity to the target datasets, we find that pretraining on the large, general-purpose ImageNet dataset yields significantly better results across all of our experiments. Transfer learning is especially effective for smaller target datasets, and in these cases, using multiple source datasets can give a marginal added benefit. Authors: James Chen (Kirby School) Computer vision and remote sensing Earth science and monitoring Meta- and transfer learning NeurIPS 2021 An Automated System for Detecting Visual Damages of Wind Turbine Blades (Papers Track) Abstract and authors: (click to expand) Abstract: Wind energy’s ability to compete with fossil fuels on a market level depends on lowering wind’s high operational costs. Since damages on wind turbine blades are the leading cause for these operational problems, identifying blade damages is critical. However, recent works in visual identification of blade damages are still experimental and focus on optimizing the traditional machine learning metrics such as IoU. In this paper, we argue that pushing models to production long before achieving the "optimal" model performance can still generate real value for this use case. We discuss the performance of Blue, our damage’s suggestion model in production and how this system works in coordination with humans as part of a commercialized product and how it can contribute towards lowering wind energy’s operational costs. Authors: Linh V Nguyen (SkySpecs Inc); Akshay B Iyer (SkySpecs, Inc.); Shweta Khushu (SkySpecs Inc.) Computer vision and remote sensing Climate finance and economics Classification, regression, and supervised learning NeurIPS 2021 Predicting Power System Dynamics and Transients: A Frequency Domain Approach (Papers Track) Abstract and authors: (click to expand) Abstract: With the ambition of reducing carbon emissions and mitigating climate change, many regions have set up the goal to generate electricity with close to 100% renewables. However, actual renewable generations are often curtailed by operators because it is too hard to check the dynamic stability of the electric grid under the high uncertainties introduced by the renewables. The dynamics of a power grid are governed by a large number of nonlinear ordinary differential equations (ODEs). To safely operate the system, operators need to check that the states described by this set of ODEs stay within prescribed limits after various potential faults. Limited by the size and stiffness of the ODEs, current numerical integration techniques are often too slow to be useful in real-time or large-scale resource allocation problems. In addition, detailed system parameters are often not exactly known. Machine learning approaches have been proposed to reduce the computational efforts, but existing methods generally suffer from overfitting and failures to predict unstable behaviors. This paper proposes a novel framework for power system dynamic predictions by learning in the frequency domain. The intuition is that although the system behavior is complex in the time domain, there are relatively few dominate modes in the frequency domain. Therefore, we learn to predict by constructing neural networks with Fourier transform and filtering layers. System topology and fault information are encoded by taking a multi-dimensional Fourier transform, allowing us to leverage the fact that the trajectories are sparse both in time and spatial (across different buses) frequencies. We show that the proposed approach does not need detailed system parameters, speeds up prediction computations by orders of magnitude and is highly accurate for different fault types. Authors: Wenqi Cui (University of Washington); Weiwei Yang (Microsoft Research); Baosen Zhang (University of Washington) Power and energy Classification, regression, and supervised learning NeurIPS 2021 HyperionSolarNet: Solar Panel Detection from Aerial Images (Papers Track) Abstract and authors: (click to expand) Abstract: With the effects of global climate change impacting the world, collective efforts are needed to reduce greenhouse gas emissions. The energy sector is the single largest contributor to climate change and many efforts are focused on reducing dependence on carbon-emitting power plants and moving to renewable energy sources, such as solar power. A comprehensive database of the location of solar panels is important to assist analysts and policymakers in defining strategies for further expansion of solar energy. In this paper we focus on creating a world map of solar panels. We identify locations and total surface area of solar panels within a given geographic area. We use deep learning methods for automated detection of solar panel locations and their surface area using aerial imagery. The framework, which consists of a two-branch model using an image classifier in tandem with a semantic segmentation model, is trained on our created dataset of satellite images. Our work provides an efficient and scalable method for detecting solar panels, achieving an accuracy of 0.96 for classification and an IoU score of 0.82 for segmentation performance. Authors: Poonam Parhar (UCBerkeley); Ryan Sawasaki (UCBerkeley); Alberto Todeschini (UC Berkeley); Colorado Reed (UC Berkeley); Hossein Vahabi (University California Berkeley); Nathan Nusaputra (UC Berkeley); Felipe Vergara (UC Berkeley) Power and energy Buildings and cities Climate policy Classification, regression, and supervised learning Computer vision and remote sensing NeurIPS 2021 Prediction of Household-level Heat-Consumption using PSO enhanced SVR Model (Papers Track) Abstract and authors: (click to expand) Abstract: In combating climate change, an effective demand-based energy supply operation of the district energy system (DES) for heating or cooling is indispensable. As a consequence, an accurate forecast of heat consumption on the consumer side poses an important first step towards an optimal energy supply. However, due to the non-linearity and non-stationarity of heat consumption data, the prediction of the thermal energy demand of DES remains challenging. In this work, we propose a forecasting framework for thermal energy consumption within a district heating system (DHS) based on kernel Support Vector Regression (kSVR) using real-world smart meter data. Particle Swarm Optimization (PSO) is employed to find the optimal hyper-parameter for the kSVR model which leads to the superiority of the proposed methods when compared to a state-of-the-art ARIMA model. The average MAPE is reduced to 2.07% and 2.64% for the individual meter-specific forecasting and for forecasting of societal consumption, respectively. Authors: Satyaki Chatterjee (Pattern Recognition Lab, FAU Erlangen-Nuremberg); Siming Bayer (Pattern Recognition Lab, Friedrich-Alexander University); Andreas K Maier (Pattern Recognition Lab, FAU Erlangen-Nuremberg) Classification, regression, and supervised learning Power and energy Other Time-series analysis NeurIPS 2021 EcoLight: Reward Shaping in Deep Reinforcement Learning for Ergonomic Traffic Signal Control (Papers Track) Abstract and authors: (click to expand) Abstract: Mobility, the environment, and human health are all harmed by sub-optimal control policies in transportation systems. Intersection traffic signal controllers are a crucial part of today's transportation infrastructure, as sub-optimal policies may lead to traffic jams and as a result increased levels of air pollution and wasted time. Many adaptive traffic signal controllers have been proposed in the literature, but research on their relative performance differences is limited. On the other hand, to the best of our knowledge there has been no work that directly targets CO2 emission reduction, even though pollution is currently a critical issue. In this paper, we propose a reward shaping scheme for various RL algorithms that not only produces lowers CO2 emissions, but also produces respectable outcomes in terms of other metrics such as travel time. We compare multiple RL algorithms --- sarsa, and A2C --- as well as diverse scenarios with a mix of different road users emitting varied amounts of pollution. Authors: Pedram Agand (Simon Fraser University); Alexey Iskrov (Breeze Labs Inc.); Mo Chen (Simon Fraser University) Transportation Power and energy Reinforcement learning and control NeurIPS 2021 Data Driven Study of Estuary Hypoxia (Papers Track) Abstract and authors: (click to expand) Abstract: This paper presents a data driven study of dissolved oxygen times series collected in Atlantic Canada. The main motivation of presented work was to evaluate if machine learning techniques could help to understand and anticipate hypoxic episodes in nutrient-impacted estuaries, a phenomenon that is exacerbated by increasing temperature expected to arise due to changes in climate. A major constraint was to limit ourselves to the use of dissolved oxygen time series only. Our preliminary findings shows that recurring neural networks and in particular LSTM may be suitable to predict short horizon levels while traditional results could benefit in longer range hypoxia prevention. Authors: Md Monwer Hussain (University of New-Brunswick); Guillaume Durand (National Research Council Canada); Michael Coffin (Department of Fisheries and Oceans Canada); Julio J Valdés (National Research Council Canada); Luke Poirier (Department of Fisheries and Oceans Canada) Ecosystems and natural systems Time-series analysis NeurIPS 2021 Decentralized Safe Reinforcement Learning for Voltage Control (Papers Track) Abstract and authors: (click to expand) Abstract: Inverter-based distributed energy resources provide the possibility for fast time-scale voltage control by quickly adjusting their reactive power. The power-electronic interfaces allow these resources to realize almost arbitrary control law, but designing these decentralized controllers is nontrivial. Reinforcement learning (RL) approaches are becoming increasingly popular to search for policy parameterized by neural networks. It is difficult, however, to enforce that the learned controllers are safe, in the sense that they may introduce instabilities into the system. This paper proposes a safe learning approach for voltage control. We prove that the system is guaranteed to be exponentially stable if each controller satisfies certain Lipschitz constraints. The set of Lipschitz bound is optimized to enlarge the search space for neural network controllers. We explicitly engineer the structure of neural network controllers such that they satisfy the Lipschitz constraints by design. A decentralized RL framework is constructed to train local neural network controller at each bus in a model-free setting. Authors: Wenqi Cui (University of Washington); Jiayi Li (University of Washington); Baosen Zhang (University of Washington) Power and energy Reinforcement learning and control NeurIPS 2021 NoFADE: Analyzing Diminishing Returns on CO2 Investment (Papers Track) Abstract and authors: (click to expand) Abstract: Climate change continues to be a pressing issue that currently affects society at-large. It is important that we as a society, including the Computer Vision (CV) community take steps to limit our impact on the environment. In this paper, we (a) analyze the effect of diminishing returns on CV methods, and (b) propose a \textit{NoFADE''}: a novel entropy-based metric to quantify model--dataset--complexity relationships. We show that some CV tasks are reaching saturation, while others are almost fully saturated. In this light, NoFADE allows the CV community to compare models and datasets on a similar basis, establishing an agnostic platform. Authors: Andre Fu (University of Toronto); Justin B Tran (University of Toronto); Andy Xie (University of Toronto); Jonathan T Spraggett (University of Toronto); Elisa Ding (University of Toronto); Chang-Won Lee (University of Toronto); Kanav Singla (University of Toronto); Mahdi S. Hosseini (University of New Brunswick); Konstantinos N Plataniotis (UofT) Carbon capture and sequestration Computer vision and remote sensing NeurIPS 2021 High-resolution rainfall-runoff modeling using graph neural network (Papers Track) Abstract and authors: (click to expand) Abstract: Time-series modeling has shown great promise in recent studies using the latest deep learning algorithms such as LSTM (Long Short-Term Memory). These studies primarily focused on watershed-scale rainfall-runoff modeling or streamflow forecasting, but the majority of them only considered a single watershed as a unit. Although this simplification is very effective, it does not take into account spatial information, which could result in significant errors in large watersheds. Several studies investigated the use of GNN (Graph Neural Networks) for data integration by decomposing a large watershed into multiple sub-watersheds, but each sub-watershed is still treated as a whole, and the geoinformation contained within the watershed is not fully utilized. In this paper, we propose the GNRRM (Graph Neural Rainfall-Runoff Model), a novel deep learning model that makes full use of spatial information from high-resolution precipitation data, including flow direction and geographic information. When compared to baseline models, GNRRM has less over-fitting and significantly improves model performance. Our findings support the importance of hydrological data in deep learning-based rainfall-runoff modeling, and we encourage researchers to include more domain knowledge in their models. Authors: Zhongrun Xiang (University of Iowa); Ibrahim Demir (The University of Iowa) Time-series analysis Agriculture, forestry and other land use Climate and Earth science Disaster prediction, management, and relief Earth science and monitoring Ecosystems and natural systems Classification, regression, and supervised learning Data mining NeurIPS 2021 Machine Learning for Snow Stratigraphy Classification (Papers Track) Abstract and authors: (click to expand) Abstract: Snow-layer segmentation and classification is an essential diagnostic task for a wide variety of cryospheric science and climate research applications. To this end a Snow Micro Pen (SMP) can be used - a portable high-resolution snow penetrometer. However, the penetration-force measurements of the SMP must be labeled manually, which is a time-intensive task that requires training and becomes infeasible for large datasets. Here, we evaluate how well machine learning models can automatically segment and classify SMP profiles. Fourteen different models are trained on the MOSAiC SMP dataset, a unique and large SMP dataset of snow on Arctic sea-ice profiles. Depending on the user's task and needs, the long short-term memory neural network and the random forests are performing the best. The findings presented here facilitate and accelerate SMP data analysis and in consequence, help scientists to analyze the effects of climate change on the cryosphere more efficiently. Authors: Julia Kaltenborn (McGill University); Viviane Clay (Osnabrück University); Amy R. Macfarlane (WSL Institute for Snow and Avalanche Research SLF); Martin Schneebeli (WSL Institute for Snow and Avalanche Research SLF) Other Earth science and monitoring Classification, regression, and supervised learning Time-series analysis NeurIPS 2021 DEM Super-Resolution with EfficientNetV2 (Papers Track) Abstract and authors: (click to expand) Abstract: Efficient climate change monitoring and modeling rely on high-quality geospatial and environmental datasets. Due to limitations in technical capabilities or resources, the acquisition of high-quality data for many environmental disciplines is costly. Digital Elevation Model (DEM) datasets are such examples whereas their low-resolution versions are widely available, high-resolution ones are scarce. In an effort to rectify this problem, we propose and assess an EfficientNetV2 based model. The proposed model increases the spatial resolution of DEMs up to 16 times without additional information. Authors: Bekir Z Demiray (University of Iowa); Muhammed A Sit (The University of Iowa); Ibrahim Demir (The University of Iowa) Computer vision and remote sensing Disaster prediction, management, and relief Earth science and monitoring Classification, regression, and supervised learning NeurIPS 2021 Learning to Dissipate Traffic Jams with Piecewise Constant Control (Papers Track) Abstract and authors: (click to expand) Abstract: Greenhouse gases (GHGs), particularly carbon dioxide, are a key contributor to climate change. The transportation sector makes up 35% of CO2 emissions in the US and more than 70% of it is due to land transport. Previous work shows that simple driving interventions have the ability to significantly improve traffic flow on the road. Recent work shows that 5% of vehicles using piecewise constant controllers, designed to be compatible to the reaction times of human drivers, can prevent the formation of stop-and-go traffic congestion on a single-lane circular track, thereby mitigating land transportation emissions. Our work extends these results to consider more extreme traffic settings, where traffic jams have already formed, and environments with limited cooperation. We show that even with the added realism of these challenges, piecewise constant controllers, trained using deep reinforcement learning, can essentially eliminate stop-and-go traffic when actions are held fixed for up to 5 seconds. Even up to 10-second action holds, such controllers show congestion benefits over a human driving baseline. These findings are a stepping-stone for near-term deployment of vehicle-based congestion mitigation. Authors: Mayuri Sridhar (MIT); Cathy Wu () Transportation Reinforcement learning and control NeurIPS 2021 Multi-objective Reinforcement Learning Controller for Multi-Generator Industrial Wave Energy Converter (Papers Track) Abstract and authors: (click to expand) Abstract: Waves are one of the greatest sources of renewable energy and are a promising resource to tackle climate challenges by decarbonizing energy generation. Lowering the Levelized Cost of Energy (LCOE) for wave energy converters is key to competitiveness with other forms of clean energy like wind and solar. Also, the complexity of control has gone up significantly with the state-of-the-art multi-generator multi-legged industrial Wave Energy Converters (WEC). This paper introduces a Multi-Agent Reinforcement Learning controller (MARL) architecture that can handle these multiple objectives for LCOE, helping the increase in energy capture efficiency, boosting revenue, reducing structural stress to limit maintenance and operating cost, and adaptively and proactively protect the wave energy converter from catastrophic weather events, preserving investments and lowering effective capital cost. We use a MARL implementing proximal policy optimization (PPO) with various optimizations to help sustain the training convergence in the complex hyperplane. The MARL is able to better control the reactive forces of the generators on multiple tethers (legs) of WEC than the commonly deployed spring damper controller. The design for trust is implemented to assure the operation of WEC within a safe zone of mechanical compliance and guarantee mechanical integrity. This is achieved through reward shaping for multiple objectives of energy capture and penalty for harmful motions to minimize stress and lower the cost of maintenance. We achieved double-digit gains in energy capture efficiency across the waves of different principal frequencies over the baseline Spring Damper controller with the proposed MARL controllers. Authors: Soumyendu Sarkar (Hewlett Packard Enterprise); Vineet Gundecha (Hewlett Packard Enterpise); Alexander Shmakov (UC Irvine); Sahand Ghorbanpour (Hewlett Packard Enterprise); Ashwin Ramesh Babu (Hewlett Packard Enterprise Labs); Paolo Faraboschi (HPE); mathieu Cocho (Carnegie Clean Energy); Alexandre Pichard (Carnegie Clean Energy); Jonathan Fievez (Carnegie Clean Energy) Power and energy Reinforcement learning and control NeurIPS 2021 Resolving Super Fine-Resolution SIF via Coarsely-Supervised U-Net Regression (Papers Track) Abstract and authors: (click to expand) Abstract: Climate change presents challenges to crop productivity, such as increasing the likelihood of heat stress and drought. Solar-Induced Chlorophyll Fluorescence (SIF) is a powerful way to monitor how crop productivity and photosynthesis are affected by changing climatic conditions. However, satellite SIF observations are only available at a coarse spatial resolution (e.g. 3-5km) in most places, making it difficult to determine how individual crop types or farms are doing. This poses a challenging coarsely-supervised regression task; at training time, we only have access to SIF labels at a coarse resolution (3 km), yet we want to predict SIF at a very fine spatial resolution (30 meters), a 100x increase. We do have some fine-resolution input features (such as Landsat reflectance) that are correlated with SIF, but the nature of the correlation is unknown. To address this, we propose Coarsely-Supervised Regression U-Net (CSR-U-Net), a novel approach to train a U-Net for this coarse supervision setting. CSR-U-Net takes in a fine-resolution input image, and outputs a SIF prediction for each pixel; the average of the pixel predictions is trained to equal the true coarse-resolution SIF for the entire image. Even though this is a very weak form of supervision, CSR-U-Net can still learn to predict accurately, due to its inherent localization abilities, plus additional enhancements that facilitate the incorporation of scientific prior knowledge. CSR-U-Net can resolve fine-grained variations in SIF more accurately than existing averaging-based approaches, which ignore fine-resolution spatial variation during training. CSR-U-Net could also be useful for a wide range of "downscaling'" problems in climate science, such as increasing the resolution of global climate models. Authors: Joshua Fan (Cornell University); Di Chen (Cornell University); Jiaming Wen (Cornell University); Ying Sun (Cornell University); Carla P Gomes (Cornell University) Agriculture, forestry and other land use Ecosystems and natural systems Computer vision and remote sensing Unsupervised and semi-supervised learning NeurIPS 2021 PreDisM: Pre-Disaster Modelling With CNN Ensembles for At-Risk Communities (Papers Track) Abstract and authors: (click to expand) Abstract: The machine learning community has recently had increased interest in the climate and disaster damage domain due to a marked increased occurrences of natural hazards (e.g., hurricanes, forest fires, floods, earthquakes). However, not enough attention has been devoted to mitigating probable destruction from impending natural hazards. We explore this crucial space by predicting building-level damages on a before-the-fact basis that would allow state actors and non-governmental organizations to be best equipped with resource distribution to minimize or preempt losses. We introduce PreDisM that employs an ensemble of ResNets and fully connected layers over decision trees to capture image-level and meta-level information to accurately estimate weakness of man-made structures to disaster-occurrences. Our model performs well and is responsive to tuning across types of disasters and highlights the space of preemptive hazard damage modelling. Authors: Vishal Anand (Columbia University); Yuki Miura (Columbia University) Disaster prediction, management, and relief Buildings and cities Computer vision and remote sensing Interpretable ML NeurIPS 2021 A hybrid convolutional neural network/active contour approach to segmenting dead trees in aerial imagery (Papers Track) Abstract and authors: (click to expand) Abstract: The stability and ability of an ecosystem to withstand climate change is directly linked to its biodiversity. Dead trees are a key indicator of overall forest health, housing one-third of forest ecosystem biodiversity, and constitute 8% of the global carbon stocks. They are decomposed by several natural factors, e.g. climate, insects and fungi. Accurate detection and modeling of dead wood mass is paramount to understanding forest ecology, the carbon cycle and decomposers. We present a novel method to construct precise shape contours of dead trees from aerial photographs by combining established convolutional neural networks with a novel active contour model in an energy minimization framework. Our approach yields superior performance accuracy over state-of-the-art in terms of precision, recall, and intersection over union of detected dead trees. This improved performance is essential to meet emerging challenges caused by climate change (and other man-made perturbations to the systems), particularly to monitor and estimate carbon stock decay rates, monitor forest health and biodiversity, and the overall effects of dead wood on and from climate change. Authors: Jacquelyn Shelton (Hong Kong Polytechnic University); Przemyslaw Polewski (TomTom Location Technology Germany GmbH); Wei Yao (The Hong Kong Polytechnic University); Marco Heurich (Bavarian Forest National Park) Computer vision and remote sensing Carbon capture and sequestration Ecosystems and natural systems Agriculture, forestry and other land use NeurIPS 2021 Semi-Supervised Classification and Segmentation on High Resolution Aerial Images (Papers Track) Abstract and authors: (click to expand) Abstract: FloodNet is a high-resolution image dataset acquired by a small UAV platform, DJI Mavic Pro quadcopters, after Hurricane Harvey. The dataset presents a unique challenge of advancing the damage assessment process for post-disaster scenarios using unlabeled and limited labeled dataset. We propose a solution to address their classification and semantic segmentation challenge. We approach this problem by generating pseudo labels for both classification and segmentation during training and slowly incrementing the amount by which the pseudo label loss affects the final loss. Using this semi-supervised method of training helped us improve our baseline supervised loss by a huge margin for classification, allowing the model to generalize and perform better on the validation and test splits of the dataset. In this paper, we compare and contrast the various methods and models for image classification and semantic segmentation on the FloodNet dataset. Authors: Sahil S Khose (Manipal Institute of Technology); Abhiraj Tiwari (Manipal Institute of Technology); Ankita Ghosh (Manipal Institute of Technology) Disaster prediction, management, and relief Classification, regression, and supervised learning Meta- and transfer learning Unsupervised and semi-supervised learning NeurIPS 2021 Reducing the Barriers of Acquiring Ground-truth from Biodiversity Rich Audio Datasets Using Intelligent Sampling Techniques (Papers Track) Abstract and authors: (click to expand) Abstract: The potential of passive acoustic monitoring (PAM) as a method to reveal the consequences of climate change on the biodiversity that make up natural soundscapes can be undermined by the discrepancy between the low barrier of entry to acquire large field audio datasets and the higher barrier of acquiring reliable species level training, validation, and test subsets from the field audio. These subsets from a deployment are often required to verify any machine learning models used to assist researchers in understanding the local biodiversity. Especially as many models convey promising results from various sources that may not translate to the collected field audio. Labeling such datasets is a resource intensive process due to the lack of experts capable of identifying bioacoustics at a species level as well as the overwhelming size of many PAM audiosets. To address this challenge, we have tested different sampling techniques on an audio dataset collected over a two-week long August audio array deployment on the Scripps Coastal Reserve (SCR) Biodiversity Trail in La Jolla, California. These sampling techniques involve creating four subsets using stratified random sampling, limiting samples to the daily bird vocalization peaks, and using a hybrid convolutional neural network (CNN) and recurrent neural network (RNN) trained for bird presence/absence audio classification. We found that a stratified random sample baseline only achieved a bird presence rate of 44% in contrast with a sample that randomly selected clips with high hybrid CNN-RNN predictions that were collected during bird activity peaks at dawn and dusk yielding a bird presence rate of 95%. The significantly higher bird presence rate demonstrates how intelligent, machine learning-assisted selection of audio data can significantly reduce the amount of time that domain experts listen to audio without vocalizations of interest while building a ground truth for machine learning models. Authors: Jacob G Ayers (UC San Diego); Sean Perry (UC San Diego); Vaibhav Tiwari (UC San Diego); Mugen Blue (Cal Poly San Luis Obispo); Nishant Balaji (UC San Diego); Curt Schurgers (UC San Diego); Ryan Kastner (University of California San Diego); Mathias Tobler (San Diego Zoo Wildlife Alliance); Ian Ingram (San Diego Zoo Wildlife Alliance) Ecosystems and natural systems Computer vision and remote sensing NeurIPS 2021 Two-phase training mitigates class imbalance for camera trap image classification with CNNs (Papers Track) Abstract and authors: (click to expand) Abstract: By leveraging deep learning to automatically classify camera trap images, ecologists can monitor biodiversity conservation efforts and the effects of climate change on ecosystems more efficiently. Due to the imbalanced class-distribution of camera trap datasets, current models are biased towards the majority classes. As a result, they obtain good performance for a few majority classes but poor performance for many minority classes. We used two-phase training to increase the performance for these minority classes. We trained, next to a baseline model, four models that implemented a different versions of two-phase training on a subset of the highly imbalanced Snapshot Serengeti dataset. Our results suggest that two-phase training can improve performance for many minority classes, with limited loss in performance for the other classes. We find that two-phase training based on majority undersampling increases class-specific F1-scores up to 3.0%. We also find that two-phase training outperforms using only oversampling or undersampling by 6.1% in F1-score on average. Finally, we find that a combination of over- and undersampling leads to a better performance than using them individually. Authors: Farjad Malik (KU Leuven); Simon Wouters (KU Leuven); Ruben Cartuyvels (KULeuven); Erfan Ghadery (KU Leuven); Sien Moens (KU Leuven) Ecosystems and natural systems Computer vision and remote sensing NeurIPS 2021 Capturing Electricity Market Dynamics in the Optimal Trading of Strategic Agents using Neural Network Constrained Optimization (Papers Track) Abstract and authors: (click to expand) Abstract: In competitive electricity markets the optimal trading problem of an electricity market agent is commonly formulated as a bi-level program, and solved as mathematical program with equilibrium constraints (MPEC). In this paper, an alternative paradigm, labeled as mathematical program with neural network constraint (MPNNC), is developed to incorporate complex market dynamics in the optimal bidding strategy. This method uses input-convex neural networks (ICNNs) to represent the mapping between the upper-level (agent) decisions and the lower-level (market) outcomes, i.e., to replace the lower-level problem by a neural network. In a comparative analysis, the optimal bidding problem of a load agent is formulated via the proposed MPNNC and via the classical bi-level programming method, and compared against each other. Authors: Mihály Dolányi (KU Leuven); Kenneth Bruninx (KU Leuven); Jean-François Toubeau (Faculté Polytechnique (FPMs), Université de Mons (UMONS)); Erik Delaue (KU Leuven) Hybrid physical models Climate finance and economics Recommender systems NeurIPS 2021 Leveraging Machine Learning to Predict the Autoconversion Rates from Satellite Data (Papers Track) Abstract and authors: (click to expand) Abstract: One way of reducing the uncertainty involved in determining the radiative forcing of climate change is by understanding the interaction between aerosols, clouds, and precipitation processes. This can be studied using high-resolution simulations such as the ICOsahedral Non-hydrostatic Large-Eddy Model (ICON-LEM). However, due to the extremely high computational cost required, this simulation-based approach can only be run for a limited amount of time within a limited area. To address this, we developed new models using emerging machine learning approaches that leverage a plethora of satellite observations providing long-term global spatial coverage. In particular, our machine learning models are capable of capturing the key process of precipitation formation which greatly control cloud lifetime, namely autoconversion rates -- the term used to describe the collision and coalescence of cloud droplets responsible for raindrop formation. We validate the performance of our models against simulation data, showing that our models are capable of predicting the autoconversion rates fairly well. Authors: Maria C Novitasari (University College London); Johannes Quaas (University of Leipzig); Miguel Rodrigues (University College London) Classification, regression, and supervised learning Climate and Earth science Computer vision and remote sensing NeurIPS 2021 Towards Automatic Transformer-based Cloud Classification and Segmentation (Papers Track) Abstract and authors: (click to expand) Abstract: Clouds have been demonstrated to have a huge impact on the energy balance, temperature, and weather of the Earth. Classification and segmentation of clouds and coverage factors is crucial for climate modelling, meteorological studies, solar energy industry, and satellite communication. For example, clouds have a tremendous impact on short-term predictions or 'nowcasts' of solar irradiance and can be used to optimize solar power plants and effectively exploit solar energy. However even today, cloud observation requires the intervention of highly-trained professionals to document their findings, which introduces bias. To overcome these issues and contribute to climate change technology, we propose, to the best of our knowledge, the first two transformer-based models applied to cloud data tasks. We use the CCSD Cloud classification dataset and achieve 90.06% accuracy, outperforming all other methods. To demonstrate the robustness of transformers in this domain, we perform Cloud segmentation on SWIMSWG dataset and achieve 83.2% IoU, also outperforming other methods. With this, we signal a potential shift away from pure CNN networks. Authors: Roshan Roy (Birla Institute of Technology and Science, Pilani); Ahan M R (BITS Pilani); Vaibhav Soni (MANIT Bhopal); Ashish Chittora (BITS Pilani) Computer vision and remote sensing Climate and Earth science Earth science and monitoring Classification, regression, and supervised learning Data mining NeurIPS 2021 Scalable coastal inundation mapping using machine learning (Papers Track) Abstract and authors: (click to expand) Abstract: Coastal flooding is a significant climate hazard with impacts across economic sectors and society. This study provides a proof of concept for data-driven models for coastal flood inundation at the country scale, incorporating storm dynamics and geospatial characteristics to improve upon simpler geomorphological models. The best fit machine learning model scores an AUC of 0.92 in predicting flooded locations. For a case study storm event in December 2013 we find that all models over-predict flood extents, but that the machine learning model extents were closest to those observed. Authors: Ophelie Meuriot (IBM Research Europe); Anne Jones (IBM Research) Classification, regression, and supervised learning Climate and Earth science Other NeurIPS 2021 Machine Learning in Automating Carbon Sequestration Site Assessment (Proposals Track) Abstract and authors: (click to expand) Abstract: Carbon capture and sequestration are viewed as an indispensable component to achieve the Paris Agreement climate goal, i.e., keep the global warming within 2 degrees Celsius from pre-industrial levels. Once captured, most CO2 needs to be stored securely for at least decades, preferably in deep underground geological formations. It is economical to inject and store CO2 near/around a depleted gas/oil reservoir or well, where a geological trap for CO2 with good sealing properties and some minimum infrastructure exist. In this proposal, with our preliminary work, it is shown that Machine Learning tools like Optical Character Recognition and Natural Language Processing can aid in screening and selection of injection sites for CO2 storage, facilitate identification of possible CO2 leakage paths in the subsurface, and assist in locating a depleted gas/oil well suitable for CO2 injection and long-term storage. The automated process based on ML tools can also drastically decrease the decision-making cycle time in site selection and assessment phase by reducing human effort. In the longer term, we expect ML tools like Deep Neural Networks to be utilized in CO2 storage monitoring, injection optimization etc. By injecting CO2 into a trapping geological underground formation in a safe and sustainable manner, the Energy industry can contribute substantially to reducing global warming and achieving the goals of the Paris Agreement by the end of this century. Authors: Jay Chen (Shell); Ligang Lu (Shell); Mohamed Sidahmed (Shell); Taixu Bai (Shell); Ilyana Folmar (Shell); Puneet Seth (Shell); Manoj Sarfare (Shell); Duane Mikulencak (Shell); Ihab Akil (Shell) Carbon capture and sequestration Climate finance and economics Active learning Computer vision and remote sensing NeurIPS 2021 A Risk Model for Predicting Powerline-induced Wildfires in Distribution System (Proposals Track) Abstract and authors: (click to expand) Abstract: The power grid is one of the most common causes of wildfires that result in tremendous economic loss and significant life risk. In this study, we propose to use machine learning techniques to build a risk model for predicting powerline-induced wildfires in distribution system. We collect weather, vegetation, and infrastructure data for all feeders in Pacific Gas & Electricity territory. This study will contribute to a deeper understanding of powerline-induced wildfire prediction and provide valuable suggestions for wildfire mitigation planning. Authors: Mengqi Yao (University of California Berkeley) Disaster prediction, management, and relief Power and energy Classification, regression, and supervised learning Data mining NeurIPS 2021 Detecting Abandoned Oil And Gas Wells Using Machine Learning And Semantic Segmentation (Proposals Track) Abstract and authors: (click to expand) Abstract: Around the world, there are millions of unplugged abandoned oil and gas wells, leaking methane into the atmosphere. The locations of many of these wells, as well as their greenhouse gas emissions impacts, are unknown. Machine learning methods in computer vision and remote sensing, such as semantic segmentation, have made it possible to quickly analyze large amounts of satellite imagery to detect salient information. This project aims to automatically identify undocumented oil and gas wells in the province of Alberta, Canada to aid in documentation, estimation of emissions and maintenance of high-emitting wells. Authors: Michelle Lin (McGill University); David Rolnick (McGill University, Mila) Power and energy Classification, regression, and supervised learning Computer vision and remote sensing NeurIPS 2021 Machine learning-enabled model-data integration for predicting subsurface water storage (Proposals Track) Abstract and authors: (click to expand) Abstract: Subsurface water storage (SWS) is a key variable of the climate system and a storage component for precipitation and radiation anomalies, inducing persistence in the climate system. It plays a critical role in climate-change projections and can mitigate the impacts of climate change on ecosystems. However, because of the difficult accessibility of the underground, hydrologic properties and dynamics of SWS are poorly known. Direct observations of SWS are limited, and accurate incorporation of SWS dynamics into Earth system land models remains challenging. We propose a machine learning-enabled model-data integration framework to improve the SWS prediction at local to conus scales in a changing climate by leveraging all the available observation and simulation resources, as well as to inform the model development and guide the observation collection. The accurate prediction will enable an optimal decision of water management and land use and improve the ecosystem's resilience to the climate change. Authors: Dan Lu (Oak Ridge National Laboratory); Eric Pierce (Oak Ridge National Laboratory); Shih-Chieh Kao (Oak Ridge National Laboratory); David Womble (Oak Ridge National Laboratory); LI LI (Pennsylvania State University); Daniella Rempe (The University of Texas at Austin) Ecosystems and natural systems Earth science and monitoring NeurIPS 2021 Hybrid physics-based and data-driven modeling with calibrated uncertainty for lithium-ion battery degradation diagnosis and prognosis (Proposals Track) Abstract and authors: (click to expand) Abstract: Advancing lithium-ion batteries (LIBs) in both design and usage is key to promoting electrification in the coming decades to mitigate human-caused climate change. Inadequate understanding of LIB degradation is an important bottleneck that limits battery durability and safety. Here, we propose hybrid physics-based and data-driven modeling for online diagnosis and prognosis of battery degradation. Compared to existing battery modeling efforts, we aim to build a model with physics as its backbone and statistical learning techniques as enhancements. Such a hybrid model has better generalizability and interpretability together with a well-calibrated uncertainty associated with its prediction, rendering it more valuable and relevant to safety-critical applications under realistic usage scenarios. Authors: Jing Lin (Institute for Infocomm Research); Yu Zhang (I2R); Edwin Khoo (Institute for Infocomm Research) Hybrid physical models Power and energy Causal and Bayesian methods Classification, regression, and supervised learning Time-series analysis Uncertainty quantification and robustness NeurIPS 2021 On the use of Deep Generative Models for "Perfect" Prognosis Climate Downscaling (Proposals Track) Abstract and authors: (click to expand) Abstract: Deep Learning has recently emerged as a "perfect" prognosis downscaling technique to compute high-resolution fields from large-scale coarse atmospheric data. Despite their promising results to reproduce the observed local variability, they are based on the estimation of independent distributions at each location, which leads to deficient spatial structures, especially when downscaling precipitation. This study proposes the use of generative models to improve the spatial consistency of the high-resolution fields, very demanded by some sectoral applications (e.g., hydrology) to tackle climate change. Authors: Jose González-Abad (Institute of Physics of Cantabria); Jorge Baño-Medina (Institute of Physics of Cantabria); Ignacio Heredia (Institute of Physics of Cantabria) Climate and Earth science Classification, regression, and supervised learning Generative modeling NeurIPS 2021 A Deep Learning application towards transparent communication for Payment for Forest Environmental Services (PES) (Proposals Track) Abstract and authors: (click to expand) Abstract: Deforestation accounts for more than 20% of global emission. Payments for Environmental Services (PES) is seen by both policy makers and practitioners as an effective market-based instrument to provide financial incentives for forest owners, particularly poor and indigenous households in developing countries. It is a critical instrument to protect forests, and ultimately to mitigate climate change and reduce emission from deforestation. However, previous studies have pointed out a key challenge for PES is to ensure transparent payment to local people, due to i) weak monitoring and evaluation and ii) indigenous inaccessibility to e-banking and complying with procedural and administrative paper works to receive payments. Specifically, the amount and the complexity of forms along with the language barriers is a key issue; and most transactions need several intermediaries and transaction costs which reduce the payments reaching landowners. To address these issues, we propose a communication platform that links across the stakeholders and processes. Our proposal will utilize Machine Learning techniques to lower the language barrier and provide technology solutions to help indigenous people to access payments. This would also help improve the effectiveness and transparency of PES schemes. Specifically, we propose the use of Natural Language Processing techniques in providing a speech-to-text and auto translation capability, and the use of Graph Neural Network to provide link predictions of transaction types, volumes and values. The pathway to impact will be forest protection and local livelihood through providing financial incentives, and subsequently contribution to more carbon sequestration and storage – a key issue in climate change mitigation. Authors: Lan HOANG (IBM Research); Thuy Thu Phan (Center for International Forestry Research (CIFOR)) Agriculture, forestry and other land use Natural language processing NeurIPS 2021 A NLP-based Analysis of Alignment of Organizations' Climate-Related Risk Disclosures with Material Risks and Metrics (Proposals Track) Abstract and authors: (click to expand) Abstract: The Sustainability Accounting Standards Board (SASB) establishes standards to guide the disclosures of material sustainability and ESG (Environment, Social, Governance)-related information across industries. The availability of quality, comparable and decision-useful information is required to assess risks and opportunities later integrated into financial decision-making. Particularly, standardized, industry-specific climate risk metrics and topics can support these efforts. SASB’s latest climate risk technical bulletin introduces three climate-related risks that are financially material - physical, transition and regulatory risks - and maps these across industries. The main objective of this work is to create a framework that can analyze climate related risk disclosures using an AI-based tool that automatically extracts and categorizes climate-related risks and related metrics from company disclosures based on SASB’s latest climate risk guidance. This process will help with automating large-scale analysis and add much-needed transparency vis-a-vis the current state of climate-related disclosures, while also assessing how far along companies are currently disclosing information on climate risks relevant to their industry. As it stands, this much needed type of analysis is made mostly manually or using third-party metrics, often opaque and biased, as proxies. In this work, we will first create a climate risk glossary that will be trained on a large amount of climate risk text. By combining climate risk keywords in this glossary with recent advances in natural language processing (NLP), we will then be able to quantitatively and qualitatively compare climate risk information in different sectors and industries using a novel climate risk score that will be based on SASB standards. Authors: Elham Kheradmand (University of Montreal); Didier Serre (Clearsum); Manuel Morales (University of Montreal); Cedric B Robert (Clearsum) Climate finance and economics Classification, regression, and supervised learning Natural language processing NeurIPS 2021 Unsupervised Machine Learning framework for sensor placement optimization: analyzing methane leaks (Proposals Track) Abstract and authors: (click to expand) Abstract: Methane is one of the most potent greenhouse gases, with the global oil and gas industry being the second largest source of anthropogenic methane emissions, accounting for about 63% of the whole energy sector. This underscores the importance of detecting and remediating methane leaks for the entire oil and gas value chain. Methane sensor networks are a promising technology to detect methane leaks in a timely manner. While they provide near-real-time monitoring of an area of interest, the density of the network can be cost prohibitive, and the identification of the source of the leak is not apparent, especially where there could be more than one source. To address these issues, we developed a machine learning framework that leverages various data sources including oil and gas facilities data, historical methane leak rate distribution and meteorological data, to optimize sensor placement. The determination of sensor locations follows the objective to maximize the detection of possible methane leaks with a limited sensor budget. Authors: Shirui Wang (University of Houston); Sara Malvar (Microsoft); Leonardo Nunes (Microsoft); Kim Whitehall (Microsoft); YAGNA DEEPIKA ORUGANTI (MICROSOFT); Yazeed Alaudah (Microsoft); Anirudh Badam (Microsoft) Earth science and monitoring Other Unsupervised and semi-supervised learning NeurIPS 2021 Multi-agent reinforcement learning for renewable integration in the electric power grid (Proposals Track) Abstract and authors: (click to expand) Abstract: As part of the fight against climate change, the electric power system is transitioning from fuel-burning generators to renewable sources of power like wind and solar. To allow for the grid to rely heavily on renewables, important operational changes must be done. For example, novel approaches for frequency regulation, i.e., for balancing in real-time demand and generation, are required to ensure the stability of a renewable electric system. Demand response programs in which loads adjust in part their power consumption for the grid's benefit, can be used to provide frequency regulation. In this proposal, we present and motivate a collaborative multi-agent reinforcement learning approach to meet the algorithmic requirements for providing real-time power balancing with demand response. Authors: Vincent Mai (Mila, Université de Montréal); Tianyu Zhang (Mila, Université de Montréal); Antoine Lesage-Landry (Polytechnique Montréal & GERAD) Power and energy Reinforcement learning and control NeurIPS 2021 Machine Learning Speeding Up the Development of Portfolio of New Crop Varieties to Adapt to and Mitigate Climate Change (Proposals Track) Abstract and authors: (click to expand) Abstract: Climate change poses serious challenges to achieving food security in a time of a need to produce more food to keep up with the world’s increasing demand for food. There is an urgent need to speed up the development of new high yielding varieties with traits of adaptation and mitigation to climate change. Mathematical approaches, including ML approaches, have been used to search for such traits, leading to unprecedented results as some of the traits, including heat traits that have been long sought-for, have been found within a short period of time. Authors: Abdallah Bari (OperAI Canada - Operational AI); Hassan Ouabbou (INRA); Abderrazek Jilal (INRA); Frederick Stoddard (University of Helsinki); Mikko Sillanpää (University of Oulu); Hamid Khazaei (World Vegetable Center) Agriculture, forestry and other land use Carbon capture and sequestration Causal and Bayesian methods Classification, regression, and supervised learning Time-series analysis Unsupervised and semi-supervised learning NeurIPS 2021 Toward Foundation Models for Earth Monitoring: Proposal for a Climate Change Benchmark (Proposals Track) Abstract and authors: (click to expand) Abstract: Recent progress in self-supervision shows that pre-training large neural networks on vast amounts of unsupervised data can lead to impressive increases in generalisation for downstream tasks. Such models, recently coined as foundation models, have been transformational to the field of natural language processing. While similar models have also been trained on large corpuses of images, they are not well suited for remote sensing data. To stimulate the development of foundation models for Earth monitoring, we propose to develop a new benchmark comprised of a variety of downstream tasks related to climate change. We believe that this can lead to substantial improvements in many existing applications and facilitate the development of new applications. This proposal is also a call for collaboration with the aim of developing a better evaluation process to mitigate potential downsides of foundation models for Earth monitoring. Authors: Alexandre Lacoste (ServiceNow); Evan D Sherwin (Stanford University, Energy and Resources Engineering); Hannah R Kerner (University of Maryland); Hamed Alemohammad (Radiant Earth Foundation); Björn Lütjens (MIT); Jeremy A Irvin (Stanford); David Dao (ETH Zurich); Alex Chang (Service Now); Mehmet Gunturkun (Element Ai); Alexandre Drouin (ServiceNow); Pau Rodriguez (Element AI); David Vazquez (ServiceNow) Computer vision and remote sensing Agriculture, forestry and other land use Climate and Earth science Disaster prediction, management, and relief Ecosystems and natural systems Meta- and transfer learning NeurIPS 2021 Optimization of Agricultural Management for Soil Carbon Sequestration based on Deep Reinforcement Learning and Large-Scale Simulations (Proposals Track) Abstract and authors: (click to expand) Abstract: Soil carbon sequestration in croplands has tremendous potential to help mitigate climate change; however, it is challenging to develop the optimal management practices for maximization of the sequestered carbon as well as the crop yield. This project aims to develop an intelligent agricultural management system using deep reinforcement learning (RL) and large-scale soil and crop simulations. To achieve this, we propose to build a simulator to model and simulate the complex soil-water-plant-atmosphere interaction. By formulating the management decision as an RL problem, we can leverage the state-of-the-art algorithms to train management policies through extensive interactions with the simulated environment. The trained policies are expected to maximize the stored organic carbon while maximizing the crop yield in the presence of uncertain weather conditions. The whole system will be tested using data of soil and crops in both mid-west of the United States and the central region of Portugal. The proposed research will impact food security and climate change, two of the most significant challenges currently facing humanity. Authors: Jing Wu (University of Illinois Urbana-Champaign); Pan Zhao (University of Illinois Urbana-Champaign); Ran Tao (University of Illinois Urbana-Champaign); Naira Hovakimyan (UIUC); Guillermo Marcillo (University of Illinois at Urbana-Champaign); Nicolas Martin (University of Illinois at Urbana-Champaign); Carla Ferreira (Royal Institute of Technology); Zahra Kalantari (Royal Institute of Technology); Jennifer Hobbs (IntelinAir Inc.) Reinforcement learning and control Carbon capture and sequestration NeurIPS 2021 Leveraging machine learning for identify hydrological extreme events under global climate change (Proposals Track) Abstract and authors: (click to expand) Abstract: Hydrological extreme events, such as droughts and floods, are highly destructive natural disasters and its occurrence is expected to increase under the future climate change. Accurate and efficient approach to detect such events will provide timely information to assist management strategies for minimizing socio-economic damages. Despite the threshold approach has established to detect extreme events, the missing data from hydroclimate data and accurately identifying these events are still major challenges. The advent of machine learning models can help to identify the occurrence of droughts and floods events accurately and efficiently. Therefore, this proposed study will develop a machine learning model with semi-supervised anomaly detection approach to identify hydrological extreme events with ground-based data. As a test case, we will use 45-years record of hydroclimate data in coastal California, where was the driest region in 2012-2015, following with flash floods events. The expected results will increase communities’ awareness for hydrological extreme events and enable environmental planning and resource management under climate change Authors: Ying-Jung C Deweese (Georgia Insititute of Technology) Earth science and monitoring Classification, regression, and supervised learning NeurIPS 2021 Predicting Cascading Failures in Power Systems using Graph Convolutional Networks (Proposals Track) Abstract and authors: (click to expand) Abstract: Worldwide targets are set for the increase of renewable power generation in electricity networks on the way to combat climate change. Consequently, a secure power system that can handle the complexities resulted from the increased renewable power integration is crucial. One particular complexity is the possibility of cascading failures — a quick succession of multiple component failures that takes down the system and might also lead to a blackout. Viewing the prediction of cascading failures as a binary classification task, we explore the efficacy of Graph Convolution Networks (GCNs), to detect the early onset of a cascading failure. We perform experiments based on simulated data from a benchmark IEEE test system. Our preliminary findings show that GCNs achieve higher accuracy scores than other baselines which bodes well for detecting cascading failures. It also motivates a more comprehensive study of graph-based deep learning techniques for the current problem. Authors: Tabia Ahmad (University of Strathclyde); Yongli Zhu (Texas A&M Universersity); Panagiotis Papadopoulos (University of Strathclyde) Power and energy Carbon capture and sequestration Classification, regression, and supervised learning Data mining Unsupervised and semi-supervised learning NeurIPS 2021 DeepQuake: Artificial Intelligence for Earthquake Forecasting Using Fine-Grained Climate Data (Proposals Track) Best Paper: Proposals Abstract and authors: (click to expand) Abstract: Earthquakes are one of the most catastrophic natural disasters, making accurate, fine-grained, and real-time earthquake forecasting extremely important for the safety and security of human lives. In this work, we propose DeepQuake, a hybrid physics and deep learning model for fine-grained earthquake forecasting using time-series data of the horizontal displacement of earth’s surface measured from continuously operating Global Positioning System (cGPS) data. Recent studies using cGPS data have established a link between transient deformation within earth's crust to climate variables. DeepQuake’s physics-based pre-processing algorithm extracts relevant features including the x, y, and xy components of strain in earth’s crust, capturing earth’s elastic response to these climate variables, and feeds it into a deep learning neural network to predict key earthquake variables such as the time, location, magnitude, and depth of a future earthquake. Results across California show promising correlations between cGPS derived strain patterns and the earthquake catalog ground truth for a given location and time. Authors: Yash Narayan (The Nueva School) Time-series analysis Climate and Earth science Earth science and monitoring Other NeurIPS 2021 A day in a sustainable life (Tutorials Track) Abstract and authors: (click to expand) Abstract: In this notebook, we show the reader how to use an electrical battery to minimize the operational carbon intensity of a building. The central idea is to charge the battery when the carbon intensity of the grid energy mix is low, and vice versa. The same methodology is used in practice to optimise for a number of different objective functions, including energy costs. Taking the hypothetical case of Pi, an eco-conscious and tech-savvy householder in the UK, we walk the reader through getting carbon intensity data, and how to use this with a number of different optimisation algorithms to decarbonise. Starting off with easy-to-understand, brute force search, we establish a baseline for subsequent (hopefully smarter) optimization algorithms. This should come naturally, since in their day job Pi is a data scientist where they often use grid and random search to tune hyperparameters of ML models. The second optimization algorithm we explore is a genetic algorithm, which belongs to the class of derivative free optimizers and is consequently extremely versatile. However, the flexibility of these algorithms comes at the cost of computational speed and effort. In many situations, it makes sense to utilize an optimization method which can make use of the special structure in the problem. As the final step, we see how Pi can optimally solve the problem of minimizing their carbon intensity by formulating it as a linear program. Along the way, we also keep an eye out for some of the most important challenges that arise in practice. Authors: Hussain Kazmi (KU Leuven); Attila Balint (KU Leuven); Jolien Despeghel (KU Leuven) Buildings and cities Power and energy Classification, regression, and supervised learning Other Time-series analysis NeurIPS 2021 Open Catalyst Project: An Introduction to ML applied to Molecular Simulations (Tutorials Track) Abstract and authors: (click to expand) Abstract: As the world continues to battle energy scarcity and climate change, the future of our energy infrastructure is a growing challenge. Renewable energy technologies offer the opportunity to drive efficient carbon-neutral means for energy storage and generation. Doing so, however, requires the discovery of efficient and economic catalysts (materials) to accelerate associated chemical processes. A common approach in discovering high performance catalysts is using molecular simulations. Specifically, each simulation models the interaction of a catalyst surface with molecules that are commonly seen in electrochemical reactions. By predicting these interactions accurately, the catalyst's impact on the overall rate of a chemical reaction may be estimated. The Open Catalyst Project (OCP) aims to develop new ML methods and models to accelerate the catalyst simulation process for renewable energy technologies and improve our ability to predict properties across catalyst composition. The initial release of the Open Catalyst 2020 (OC20) dataset presented the largest open dataset of molecular combinations, spanning 55 unique elements and over 130M+ data points. We will present a comprehensive tutorial of the Open Catalyst Project repository, including (1) Accessing & visualizing the dataset, (2) Overview of the various tasks, (3) Training graph neural network (GNN) models, (4) Developing your own model for OCP, (5) Running ML-driven simulations, and (6) Visualizing the results. Primary tools include PyTorch and PyTorch Geometric. No background in chemistry is assumed. Following this tutorial we hope to better equip attendees with a basic understanding of the data and repository. Authors: Muhammed Shuaibi (Carnegie Mellon University); Anuroop Sriram (Facebook); Abhishek Das (Facebook AI Research); Janice Lan (Facebook AI Research); Adeesh Kolluru (Carnegie Mellon University); Brandon Wood (NERSC); Zachary Ulissi (Carnegie Mellon University); Larry Zitnick (Facebook AI Research) Carbon capture and sequestration Other Power and energy ICML 2021 Examining the nexus of environmental policy, climate physics, and maritime shipping with deep learning models and space-borne data (Papers Track) Abstract and authors: (click to expand) Abstract: Ship-tracks are produced by ship exhaust interacting with marine low clouds. They provide an ideal lab for constraining a critical climate forcing. However, no global survey of ship ship-tracks has been made since its discovery 55 years ago, which limits research progress. Here we present the first global map of ship-tracks produced by applying deep segmentation models to large satellite data. Our model generalizes well and is validated against independent data. Large-scale ship-track data are at the nexus of environmental policy, climate physics, and maritime shipping industry: they can be used to study aerosol-cloud interactions, the largest uncertainty source in climate forcing; to evaluate compliance and impacts of environmental policies; and to study the impact of significant socioeconomic events on maritime shipping. Based on twenty years of global data, we show cloud physics responses in ship-tracks strongly depend on the cloud regime. Inter-annual fluctuation in ship-track frequency clearly reflects international trade/economic trends. Emission policies strongly affect the pattern of shipping routes and ship-track occurrence. The combination of stricter fuel standard and the COVID-19 pandemic pushed global ship-track frequency to the lowest level in the record. More applications of our technique and data are envisioned such as detecting illicit shipping activity and checking policy compliance of individual ships. Authors: Tianle Yuan (University of Maryland, NASA); Hua Song (NASA, SSAI); Chenxi Wang (University of Maryland, NASA); Kerry Meyer (NASA); Siobhan Light (University of Maryland); Sophia von Hippel (University of Arizona); Steven Platnick (NASA); Lazaros Oreopoulos (NASA); Robert Wood (University of Washington); Hans Mohrmann (University of Washington) Computer vision and remote sensing Climate policy Meta- and transfer learning ICML 2021 A human-labeled Landsat-8 contrails dataset (Papers Track) Abstract and authors: (click to expand) Abstract: Contrails (condensation trails) are the ice clouds that trail behind aircraft as they fly through cold and moist regions of the atmosphere. Avoiding these regions could potentially be an inexpensive way to reduce over half of aviation's impact on global warming. Development and evaluation of these avoidance strategies greatly benefits from the ability to detect contrails on satellite imagery. Since little to no public data is available to develop such contrail detectors, we construct and release a dataset of several thousand Landsat-8 scenes with pixel-level annotations of contrails. The dataset will continue to grow, but currently contains 4289 scenes (of which 47% have at least one contrail) representing 950+ person-hours of labeling time. Authors: Kevin McCloskey (Google); Scott Geraedts (Google); Brendan Jackman (Google); Vincent R. Meijer (Laboratory for Aviation and the Environment, Massachusetts Institute of Technology); Erica Brand (Google); Dave Fork (Google); John C. Platt (Google); Carl Elkin (Google); Christopher Van Arsdale (Google) Computer vision and remote sensing Climate and Earth science ICML 2021 Urban Tree Species Classification Using Aerial Imagery (Papers Track) Abstract and authors: (click to expand) Abstract: Urban trees help regulate temperature, reduce energy consumption, improve urban air quality, reduce wind speeds, and mitigating the urban heat island effect. Urban trees also play a key role in climate change mitigation and global warming by capturing and storing atmospheric carbon-dioxide which is the largest contributor to greenhouse gases. Automated tree detection and species classification using aerial imagery can be a powerful tool for sustainable forest and urban tree management. Hence, This study first offers a pipeline for generating labelled dataset of urban trees using Google Map's aerial images and then investigates how state of the art deep Convolutional Neural Network models such as VGG and ResNet handle the classification problem of urban tree aerial images under different parameters. Experimental results show our best model achieves an average accuracy of 60% over 6 tree species. Authors: Emily Waters (Anglia Ruskin University); Mahdi Maktabdar Oghaz (Anglia Ruskin University); Lakshmi Babu Saheer (Anglia Ruskin University) Carbon capture and sequestration Buildings and cities Climate and Earth science Agriculture, forestry and other land use Computer vision and remote sensing ICML 2021 Estimation of Corporate Greenhouse Gas Emissions via Machine Learning (Papers Track) Abstract and authors: (click to expand) Abstract: As an important step to fulfill the Paris Agreement and achieve net-zero emissions by 2050, the European Commission adopted the most ambitious package of climate impact measures in April 2021 to improve the flow of capital towards sustainable activities. For these and other international measures to be successful, reliable data is key. The ability to see the carbon footprint of companies around the world will be critical for investors to comply with the measures and hit climate neutrality. However, with only a small portion of companies volunteering to disclose their greenhouse gas (GHG) emissions, it is nearly impossible for investors to align their investment strategies with the measures. By training a machine learning model on disclosed GHG emissions, we are able to estimate the emissions of other companies globally who do not disclose their emissions. In this paper, we show that our model provides accurate estimates of corporate GHG emissions to investors such that they are able to align their investments with the regulatory measures and achieve net-zero goals. Authors: You Han (Bloomberg L.P.); Achintya Gopal (Bloomberg LP); Liwen Ouyang (Bloomberg L.P.); Aaron Key (Bloomberg LP) Climate finance and economics Industry Climate policy Classification, regression, and supervised learning Generative modeling Uncertainty quantification and robustness Unsupervised and semi-supervised learning ICML 2021 ANP-BBO: Attentive Neural Processes and Batch Bayesian Optimization for Scalable Calibration of Physics-Informed Digital Twins (Papers Track) Abstract and authors: (click to expand) Abstract: Physics-informed dynamical system models form critical components of digital twins of the built environment. These digital twins enable the design of energy-efficient infrastructure, but must be properly calibrated to accurately reflect system behavior for downstream prediction and analysis. Dynamical system models of modern buildings are typically described by a large number of parameters and incur significant computational expenditure during simulations. To handle large-scale calibration of digital twins without exorbitant simulations, we propose ANP-BBO: a scalable and parallelizable batch-wise Bayesian optimization (BBO) methodology that leverages attentive neural processes (ANPs). Authors: Ankush Chakrabarty (Mitsubishi Electric Research Labs); Gordon Wichern (Mitsubishi Electric Research Laboratories (MERL)); Christopher Laughman (Mitsubishi Electric Research Laboratories (MERL)) Buildings and cities Causal and Bayesian methods ICML 2021 Seasonal Sea Ice Presence Forecasting of Hudson Bay using Seq2Seq Learning (Papers Track) Abstract and authors: (click to expand) Abstract: Accurate and timely forecasts of sea ice conditions are crucial for safe shipping operations in the Canadian Arctic and other ice-infested waters. Given the advancement of machine-learning methods and the recent observations on the declining trend of Arctic sea ice extent over the past decades due to global warming, new machine learning approaches are deployed to provide additional sea ice forecasting products. This study is novel in comparison with previous machine learning (ML) approaches in the sea-ice forecasting domain as it provides a daily spatial map of probability of ice presence in the domain up to 90 days. The predictions are further used to predict freeze-up/breakup dates and show their capability to capture both the variability and the increasing trend of open water season in the domain over the past decades. Authors: Nazanin Asadi (University of Waterloo); K Andrea Scott (University of Waterloo); Philippe Lamontagne (National Research Council Canada) Climate and Earth science Classification, regression, and supervised learning Computer vision and remote sensing Time-series analysis ICML 2021 Semantic Segmentation on Unbalanced Remote Sensing Classes for Active Fire (Papers Track) Abstract and authors: (click to expand) Abstract: Wildfires generate considerable research interest due to their high frequency of occurrence along with global climate change. Future wildfire detection sensors would equip an on-orbit processing module that filters the useless raw images before data transmission. To efficiently detect heat anomalies from the single large scene, we need to handle the unbalanced sample sets between small active fire pixels and large-size complex background information. In this study, we contribute to solving this problem by enhancing the target feature representation in three ways. We first preprocess training images by constraining sampling ranges and removing background patches. Then we use the object-contextual representation (OCR) module to strengthen the active fire pixel representation based on the self-attention unit. The HRNet backbone provides multi-scale pixel representation as input to the OCR module. Finally, the combined loss of weighted cross-entropy loss and Lovasz hinge loss improve the segmentation accuracy further by optimizing the IoU of the foreground class. The performance is tested on the aerial FLAME dataset, whose ratio between labeled active fire and background pixels is 5.6%. The proposed framework improves the mIoU from 83.10% (baseline U-Net) to 90.81%. Future research will expand the technique for active fire detection using satellite images. Authors: Xikun Hu (KTH Royal Institute of Technology); Alberto Costa Nogueira Junior (IBM Research Brazil); Tian Jin (College of Electronic Science, National University of Defense Technology) Disaster prediction, management, and relief Computer vision and remote sensing ICML 2021 Improving Image-Based Characterization of Porous Media with Deep Generative Models (Papers Track) Abstract and authors: (click to expand) Abstract: Micro- and nanoscale imaging are important for characterizing subsurface formations for carbon sequestration, shale gas recovery, and hydrogen storage. Common imaging techniques, however, are often sample-destructive, expensive, require high levels of expertise, or only acquire planar data. The resulting image datasets therefore may not allow for a representative estimation of rock properties. In this work, we address these challenges in image-based characterization of porous media using deep generative models. We present a machine learning workflow for characterizing porous media from limited imaging data. We develop methods for 3D image volume translation and synthesis from 2D training data, apply this method to grayscale and multimodal image datasets of sandstones and shales, and simulate flow through the generated volumes. Results show that the proposed image reconstruction and generation approaches produce realistic pore-scale 3D representations of rock samples using only 2D training data. The models proposed here expand our capabilities for characterization of rock samples and enable new understanding of pore-scale storage and recovery processes. Authors: Timothy Anderson (Stanford University); Kelly Guan (Stanford University); Bolivia Vega (Stanford University); Laura Froute (Stanford University); Anthony Kovscek (Stanford University) Generative modeling Carbon capture and sequestration ICML 2021 Forest Terrain Identification using Semantic Segmentation on UAV Images (Papers Track) Abstract and authors: (click to expand) Abstract: Beavers' habitat is known to alter the terrain, providing biodiversity in the area, and recently their lifestyle is linked to climatic changes by reducing greenhouse gases levels in the region. To analyse the impact of beavers’ habitat on the region, it is, therefore, necessary to estimate the terrain alterations caused by beaver actions. Furthermore, such terrain analysis can also play an important role in domains like wildlife ecology, deforestation, land-cover estimations, and geological mapping. Deep learning models are known to provide better estimates on automatic feature identification and classification of a terrain. However, such models require significant training data. Pre-existing terrain datasets (both real and synthetic) like CityScapes, PASCAL, UAVID, etc, are mostly concentrated on urban areas and include roads, pathways, buildings, etc. Such datasets, therefore, are unsuitable for forest terrain analysis. This paper contributes, by providing a finely labelled novel dataset of forest imagery around beavers’ habitat, captured from a high-resolution camera on an aerial drone. The dataset consists of 100 such images labelled and classified based on 9 different classes. Furthermore, a baseline is established on this dataset using state-of-the-art semantic segmentation models based on performance metrics including Intersection Over Union (IoU), Overall Accuracy (OA), and F1 score. Authors: Muhammad Umar (Anglia Ruskin University); Lakshmi Babu Saheer (Anglia Ruskin University); Javad Zarrin (Anglia Ruskin University) Agriculture, forestry and other land use Ecosystems and natural systems Classification, regression, and supervised learning Computer vision and remote sensing ICML 2021 Climate-based ensemble machine learning model to forecast Dengue epidemics (Papers Track) Abstract and authors: (click to expand) Abstract: Dengue fever is one of the most common and rapidly spreading arboviral diseases in the world, with major public health and economic consequences in tropical and sub-tropical regions. Countries such as Peru, 17.143 cases of dengue were reported in 2019, where 81.4% of cases concentrated in five of the 25 departments. When predicting infectious disease outbreaks, it is crucial to model the long-term dependency in time series data. However, this is challenging when performed on a countrywide level since dengue incidence varies across administrative areas. Therefore, this study developed and applied a climate-based ensemble model using multiple machine learning (ML) approaches to forecast dengue incidence rate (DIR) by department. The ensemble combined the outputs from Long Short-Term Memory (LSTM) recurrent neural network and Categorical Boosting (CatBoost) methods to predict DIR one month ahead for each department in Peru. Monthly dengue cases stratified by Peruvian departments were analysed in conjunction with associated demographic, geographic, and satellite-based meteorological data for the period January 2010–December 2019. The results demonstrated that the ensemble model was able to forecast DIR in low-transmission departments, while the model was less able to detect sudden DIR peaks in some departments. Air temperature and wind components demonstrated to be the significant predictors for DIR predictions. This dengue forecast model is timely and can help local governments to implement effective control measures and mitigate the effects of the disease. This study advances the state-of-the-art of climate services for the public health sector, by informing what are the key climate factors responsible for triggering dengue transmission. Finally, this project summarises how important it is to perform collaborative work with complementary expertise from intergovernmental organizations and public health universities to advance knowledge and address societal challenges. Authors: Rochelle Schneider (European Space Agency); Alessandro Sebastianelli (European Space Agency); Dario Spiller (Italian Space Agency); James Wheeler (European Space Agency); Raquel Carmo (European Space Agency); Artur Nowakowski (Warsaw University of Technology); Manuel Garcia-Herranz (UNICEF); Dohyung Kim (UNICEF); Hanoch Barlevi (UNICEF LACRO); Zoraya El Raiss Cordero (UNICEF LACRO); Silvia Liberata Ullo (University of Sannio); Pierre-Philippe Mathieu (European Space Agency); Rachel Lowe (London School of Hygiene & Tropical Medicine) Societal adaptation Climate Change and Health ICML 2021 Physics-Informed Graph Neural Networks for Robust Fault Location in Power Grids (Papers Track) Best Paper: ML Innovation Abstract and authors: (click to expand) Abstract: The reducing cost of renewable energy resources, such as solar photovoltaics (PV) and wind farms, is accelerating global energy transformation to mitigate climate change. However, a high level of intermittent renewable energy causes power grids to have more stability issues. This accentuates the need for quick location of system failures and follow-up control actions. In recent events such as in California, line failures have resulted in large-scale wildfires leading to loss of life and property. In this article, we propose a two-stage graph learning framework to locate power grid faults in the challenging but practical regime characterized by (a) sparse observations, (b) low label rates, and (c) system variability. Our approach embeds the geometrical structure of power grids into the graph neural networks (GNN) in stage I for fast fault location, and then stage II further enhances the location accuracy by employing the physical similarity of the labeled and unlabeled data samples. We compare our approach with three baselines in the IEEE 123-node benchmark system and show that it outperforms the others by significant margins in various scenarios. Authors: Wenting Li (Los Alamos National Laboratory); Deepjyoti Deka (Los Alamos National Laboratory) Power and energy Classification, regression, and supervised learning Hybrid physical models Interpretable ML Uncertainty quantification and robustness Unsupervised and semi-supervised learning ICML 2021 Prediction of Boreal Peatland Fires in Canada using Spatio-Temporal Methods (Papers Track) Abstract and authors: (click to expand) Abstract: Peat fires are the largest fires on earth in terms of fuel consumption and are responsible for a significant portion of global carbon emissions. Predicting fires in the peatlands can help decision-makers and researchers monitor and prevent peat fires. Despite this, research on predicting peatland fires remains largely understudied as compared to the prediction of other forms of fires. However, peatland fires are unique among fires and therefore require datasets and architectures attuned to their particular characteristics. In this paper, we present a new dataset, PeatSet, designed specifically for the problem of peatland fire prediction. In addition, we propose several models to tackle the problem of fire prediction for the peatlands. We develop novel neural architectures for peatland fire prediction, PeatNet, and PT-Net, with a graph-based and a transformer-based architecture, respectively. Our results indicate that these new deep-learning architectures outperform a regression baseline from existing peatland research. Among all the tested models, PT-Net achieves the highest F1 score of 0.1006 and an overall accuracy of 99.84%. Authors: Shreya Bali (Carnegie Mellon University); Sydney Zheng (Carnegie Mellon University); Akshina Gupta (Carnegie Mellon University); Yue Wu (None); Blair Chen (Carnegie Mellon University); Anirban Chowdhury (Carnegie Mellon University); Justin Khim (Carnegie Mellon University) Disaster prediction, management, and relief Climate and Earth science Classification, regression, and supervised learning ICML 2021 Revealing the impact of global warming on climate modes using transparent machine learning and a suite of climate models (Papers Track) Abstract and authors: (click to expand) Abstract: The ocean is key to climate through its ability to store and transport heat and carbon. From studies of past climates, it is clear that the ocean can exhibit a range of dramatic variability that could have catastrophic impacts on society, such as changes in rainfall, severe weather, sea level rise and large scale climate patterns. The mechanisms of change remain obscure, but are explored using a transparent machine learning method, Tracking global Heating with Ocean Regimes (THOR) presented here. We investigate two future scenarios, one where CO2 is increased by 1% per year, and one where CO2 is abruptly quadrupled. THOR is engineered combining interpretable and explainable methods to reveal its source of predictive skill. At the core of THOR, is the identification of dynamically coherent regimes governing the circulation, a fundamental question within oceanography. Three key regions are investigated here. First, the North Atlantic circulation that delivers heat to the higher latitudes is seen to weaken and we identify associated dynamical changes. Second, the Southern Ocean circulation, the strongest circulation on earth, is seen to intensify where we reveal the implications for interactions with the ice on Antarctica. Third, shifts in ocean circulation regimes are identified in the tropical Pacific region, with potential impacts on the El Nino Southern Oscillation, Earth’s dominant source of year-to-year climate variations affecting weather extremes, ecosystems, agriculture, and fisheries. Together with revealing these climatically relevant ocean dynamics, THOR also constitutes a step towards trustworthy machine learning called for within oceanography and beyond because its predictions are physically tractable. We conclude with by highlighting open questions and potentially fruitful avenues of further machine learning applications to climate research. Authors: Maike Sonnewald (Princeton University); Redouane Lguensat (LSCE-IPSL); Aparna Radhakrishnan (Geophysical Fluid Dynamics Laboratory); Zoubero Sayibou (Bronx Community College); Venkatramani Balaji (Princeton University); Andrew Wittenberg (NOAA) Climate and Earth science Interpretable ML ICML 2021 Challenges in Applying Audio Classification Models to Datasets Containing Crucial Biodiversity Information (Papers Track) Abstract and authors: (click to expand) Abstract: The acoustic signature of a natural soundscape can reveal consequences of climate change on biodiversity. Hardware costs, human labor time, and expertise dedicated to labeling audio are impediments to conducting acoustic surveys across a representative portion of an ecosystem. These barriers are quickly eroding away with the advent of low-cost, easy to use, open source hardware and the expansion of the machine learning field providing pre-trained neural networks to test on retrieved acoustic data. One consistent challenge in passive acoustic monitoring (PAM) is a lack of reliability from neural networks on audio recordings collected in the field that contain crucial biodiversity information that otherwise show promising results from publicly available training and test sets. To demonstrate this challenge, we tested a hybrid recurrent neural network (RNN) and convolutional neural network (CNN) binary classifier trained for bird presence/absence on two Peruvian bird audiosets. The RNN achieved an area under the receiver operating characteristics (AUROC) of 95% on a dataset collected from Xeno-canto and Google’s AudioSet ontology in contrast to 65% across a stratified random sample of field recordings collected from the Madre de Dios region of the Peruvian Amazon. In an attempt to alleviate this discrepancy, we applied various audio data augmentation techniques in the network’s training process which led to an AUROC of 77% across the field recordings. Authors: Jacob G Ayers (UC San Diego); Yaman Jandali (University of California, San Diego); Yoo-Jin Hwang (Harvey Mudd College); Erika Joun (University of California, San Diego); Gabriel Steinberg (Binghampton University); Mathias Tobler (San Diego Zoo Wildlife Alliance); Ian Ingram (San Diego Zoo Wildlife Alliance); Ryan Kastner (University of California San Diego); Curt Schurgers (University of California San Diego) Ecosystems and natural systems Natural language processing ICML 2021 Learning Optimal Power Flow with Infeasibility Awareness (Papers Track) Abstract and authors: (click to expand) Abstract: Optimal power flow provides an energy-efficient operating point for power grids and therefore supports climate change mitigation. This function has to be run every few minutes day and night, thus a reliable and computationally efficient solution method is of vital importance. Deep learning seems a promising direction, and related works have emerged recently. However, considering feasible scenarios only during the learning process, existing works will mislead system operators in infeasible scenarios and pose a new threat to system resilience. Paying attention to infeasibility in the decision making process, this paper tackles this emerging threat with multi-task learning. Case studies on the IEEE test system validate the effectiveness of the proposed method. Authors: Gang Huang (Zhejiang Lab); Longfei Liao (Zhejiang Lab); Lechao Cheng (Zhejiang Lab); Wei Hua (Zhejiang Lab) Power and energy ICML 2021 Reconstructing Aerosol Vertical Profiles with Aggregate Output Learning (Papers Track) Abstract and authors: (click to expand) Abstract: Aerosol-cloud interactions constitute the largest source of uncertainty in assessments of the anthropogenic climate change. This uncertainty arises in part from the inability to observe aerosol amounts at the cloud formation levels, and, more broadly, the vertical distribution of aerosols. Hence, we often have to settle for less informative two-dimensional proxies, i.e. vertically aggregated data. In this work, we formulate the problem of disaggregation of vertical profiles of aerosols. We propose some initial solutions for such aggregate output regression problem and demonstrate their potential on climate model data. Authors: Sofija Stefanovic (University of Oxford); Shahine Bouabid (University of Oxford); Philip Stier (University of Oxford); Athanasios Nenes (EPFL); Dino Sejdinovic (University of Oxford) Climate and Earth science Classification, regression, and supervised learning Unsupervised and semi-supervised learning ICML 2021 Self-Attentive Ensemble Transformer: Representing Ensemble Interactions in Neural Networks for Earth System Models (Papers Track) Abstract and authors: (click to expand) Abstract: Ensemble data from Earth system models has to be calibrated and post-processed. I propose a novel member-by-member post-processing approach with neural networks. I bridge ideas from ensemble data assimilation with self-attention, resulting into the self-attentive ensemble transformer. Here, interactions between ensemble members are represented as additive and dynamic self-attentive part. As proof-of-concept, I regress global ECMWF ensemble forecasts to 2-metre-temperature fields from the ERA5 reanalysis. I demonstrate that the ensemble transformer can calibrate the ensemble spread and extract additional information from the ensemble. As it is a member-by-member approach, the ensemble transformer directly outputs multivariate and spatially-coherent ensemble members. Therefore, self-attention and the transformer technique can be a missing piece for a non-parametric post-processing of ensemble data with neural networks. Authors: Tobias S Finn (Universität Hamburg) Climate and Earth science Classification, regression, and supervised learning ICML 2021 DeepOPF-NGT: A Fast Unsupervised Learning Approach for Solving AC-OPF Problems without Ground Truth (Papers Track) Abstract and authors: (click to expand) Abstract: AC optimal power flow (AC-OPF) problems need to be solved more frequently in the future to maintain the reliable and cost-effective operation of power systems. Recently, supervised-learning approaches have been developed to speed up the solving time of AC-OPF problems without incurring infeasibility or much optimality loss by learning the load-solution mapping embedded in the training dataset. However, it is non-trivial and computationally expensive to prepare the training dataset with single embedded mapping, due to that AC-OPF problems are non-convex and may admit multiple optimal solutions. In this paper, we develop an unsupervised learning approach (DeepOPF-NGT) for solving AC-OPF problems, which does not require training datasets with ground truth to operate. Instead, it uses a properly designed loss function to guide the tuning of the neural network parameters to directly learn one load-solution mapping. Preliminary results on the IEEE 30-bus test system show that the unsupervised DeepOPF-NGT approach can achieve comparable optimality, feasibility, and speedup performance against an existing supervised learning approach. Authors: Wanjun Huang (City University of Hong Kong); Minghua Chen (City University of Hong Kong) Power and energy Unsupervised and semi-supervised learning ICML 2021 Commercial Vehicle Traffic Detection from Satellite Imagery with Deep Learning (Papers Track) Abstract and authors: (click to expand) Abstract: Road freight traffic is a major greenhouse gas emitter: commercial vehicles (CVs) contribute ∼7% to the global CO 2 emission budget, a fraction that is likely to increase in the future. The quantitative monitoring of CV traffic rates, while essential for the implementation of targeted road emission regulations, is costly and as such only available in developed regions. In this work, we investigate the feasibility of estimating hourly CV traffic rates from freely available Sentinel-2 satellite imagery. We train a modified Faster R-CNN object detection model to detect individual CVs in satellite images and feed the resulting counts into a regression model to predict hourly CV traffic rates. This architecture, when trained on ground-truth data for Switzerland, is able to estimate hourly CV traffic rates for any freeway section within 58% (MAPE) of the actual value; for freeway sections with historic information on CV traffic rates, we can predict hourly CV traffic rates up to within 4% (MAPE). We successfully apply our model to freeway sections in other coun tries and show-case its utility by quantifying the change in traffic patterns as a result of the first CoVID-19 lockdown in Switzerland. Our results show that it is possible to estimate hourly CV traffic rates from satellite images, which can guide civil engineers and policy makers, especially in developing countries, in monitoring and reducing greenhouse gas emissions from CV traffic. Authors: Moritz Blattner (University of St. Gallen); Michael Mommert (University of St. Gallen); Damian Borth (University of St. Gallen) Computer vision and remote sensing Transportation ICML 2021 Probabilistic Short-Term Low-Voltage Load Forecasting using Bernstein-Polynomial Normalizing Flows (Papers Track) Abstract and authors: (click to expand) Abstract: The transition to a fully renewable energy grid requires better forecasting of demand at the low-voltage level. However, high fluctuations and increasing electrification cause huge forecast errors with traditional point estimates. Probabilistic load forecasts take future uncertainties into account and thus enables various applications in low-carbon energy systems. We propose an approach for flexible conditional density forecasting of short-term load based on Bernstein-Polynomial Normalizing Flows where a neural network controls the parameters of the flow. In an empirical study with 363 smart meter customers, our density predictions compare favorably against Gaussian and Gaussian mixture densities and also outperform a non-parametric approach based on the pinball loss for 24h-ahead load forecasting for two different neural network architectures. Authors: Marcel Arpogaus (Konstanz University of Applied Sciences); Marcus Voß (Technische Universität Berlin (DAI-Labor)); Beate Sick (ZHAW and University of Zurich); Mark Nigge-Uricher (Bosch.IO GmbH); Oliver Dürr (Konstanz University of Applied Sciences) Power and energy Buildings and cities Industry Classification, regression, and supervised learning Generative modeling Interpretable ML Time-series analysis Uncertainty quantification and robustness ICML 2021 Guided A* Search for Scheduling Power Generation Under Uncertainty (Papers Track) Abstract and authors: (click to expand) Abstract: Increasing renewables penetration motivates the development of new approaches to operating power systems under uncertainty. We apply a novel approach combining self-play reinforcement learning (RL) and traditional planning to solve the unit commitment problem, an essential power systems scheduling task. Applied to problems with stochastic demand and wind generation, our results show significant cost reductions and improvements to security of supply as compared with an industry-standard mixed-integer linear programming benchmark. Applying a carbon price of \50/tCO$_2$ achieves carbon emissions reductions of up to 10\%. Our results demonstrate scalability to larger problems than tackled in existing literature, and indicate the potential for RL to contribute to decarbonising power systems.
Authors: Patrick de Mars (UCL); Aidan O'Sullivan (UCL)
Power and energy Reinforcement learning and control
ICML 2021 DroughtED: A dataset and methodology for drought forecasting spanning multiple climate zones (Papers Track)
Abstract and authors: (click to expand)
Abstract: Climate change exacerbates the frequency, duration and extent of extreme weather events such as drought. Previous attempts to forecast drought conditions using machine learning have focused on regional models which have two major limitations for national drought management: (i) they are trained on localised climate data and (ii) their architectures prevent them from being applied to new heterogeneous regions. In this work, we present a new large-scale dataset for training machine learning models to forecast national drought conditions, named DroughtED. The dataset consists of globally available meteorological features widely used for drought prediction, paired with location meta-data which has not previously been utilised for drought forecasting. Here we also establish a baseline on DroughtED and present the first research to apply deep learning models - Long Short-Term Memory (LSTMs) and Transformers - to predict county-level drought conditions across the full extent of the United States. Our results indicate that DroughtED enables deep learning models to learn cross-region patterns in climate data that contribute to drought conditions and models trained on DroughtED compare favourably to state-of-the-art drought prediction models trained on individual regions.
Authors: Christoph D Minixhofer (The University of Edinburgh); Mark Swan (The University of Edinburgh); Calum McMeekin (The University of Edinburgh); Pavlos Andreadis (The University of Edinburgh)
Disaster prediction, management, and relief Agriculture, forestry and other land use Climate and Earth science Classification, regression, and supervised learning Data mining Meta- and transfer learning Time-series analysis
ICML 2021 Estimation of Air Pollution with Remote Sensing Data: Revealing Greenhouse Gas Emissions from Space (Papers Track)
Abstract and authors: (click to expand)
Abstract: Air pollution is a major driver of climate change. Anthropogenic emissions from the burning of fossil fuels for transportation and power generation emit large amounts of problematic air pollutants, including Greenhouse Gases (GHGs). Despite the importance of limiting GHG emissions to mitigate climate change, detailed information about the spatial and temporal distribution of GHG and other air pollutants is difficult to obtain. Existing models for surface-level air pollution rely on extensive land-use datasets which are often locally restricted and temporally static. This work proposes a deep learning approach for the prediction of ambient air pollution that only relies on remote sensing data that is globally available and frequently updated. Combining optical satellite imagery with satellite-based atmospheric column density air pollution measurements enables the scaling of air pollution estimates (in this case NO2) to high spatial resolution (up to ~10m) at arbitrary locations and adds a temporal component to these estimates. The proposed model performs with high accuracy when evaluated against air quality measurements from ground stations (mean absolute error <6 microgram/m^3). Our results enable the identification and temporal monitoring of major sources of air pollution and GHGs.
Authors: Linus M. Scheibenreif (University of St. Gallen); Michael Mommert (University of St. Gallen); Damian Borth (University of St. Gallen)
Computer vision and remote sensing Climate and Earth science
ICML 2021 Emulating Aerosol Microphysics with a Machine Learning (Papers Track)
Abstract and authors: (click to expand)
Abstract: Aerosol particles play an important role in the climate system by absorbing and scattering radiation and influencing cloud properties. They are also one of the biggest sources of uncertainty for climate modeling. Many climate models do not include aerosols in sufficient detail. In order to achieve higher accuracy, aerosol microphysical properties and processes have to be accounted for. This is done in the ECHAM-HAM global climate aerosol model using the M7 microphysics model, but increased computational costs make it very expensive to run at higher resolutions or for a longer time. We aim to use machine learning to approximate the microphysics model at sufficient accuracy and reduce the computational cost by being fast at inference time. The original M7 model is used to generate data of input-output pairs to train a neural network on it. By using a special logarithmic transform we are able to learn the variables tendencies achieving an average $R^2$ score of $89\%$. On a GPU we achieve a speed-up of 120 compared to the original model.
Authors: Paula Harder (Fraunhofer ITWM); Duncan Watson-Parris (University of Oxford); Dominik Strassel (Fraunhofer ITWM); Nicolas Gauger (TU Kaiserslautern); Philip Stier (University of Oxford); Janis Keuper (hs-offenburg)
Climate and Earth science Classification, regression, and supervised learning
ICML 2021 Automated Identification of Climate Risk Disclosures in Annual Corporate Reports (Papers Track)
Abstract and authors: (click to expand)
Abstract: It is important for policymakers to understand which financial policies are effective in increasing climate risk disclosure in corporate reporting. We use machine learning to automatically identify disclosures of five different types of climate-related risks. For this purpose, we have created a dataset of over 120 manually-annotated annual reports by European firms. Applying our approach to reporting of 337 firms over the last 20 years, we find that risk disclosure is increasing. Disclosure of transition risks grows more dynamically than physical risks, and there are marked differences across industries. Country-specific dynamics indicate that regulatory environments potentially have an important role to play for increasing disclosure.
Authors: David Friederich (University of Bern); Lynn Kaack (ETH Zurich); Sasha Luccioni (Mila); Bjarne Steffen (ETH Zurich)
Climate finance and economics Natural language processing
ICML 2021 Forecasting Black Sigatoka Infection Risks with Latent Neural ODEs (Papers Track)
Abstract and authors: (click to expand)
Abstract: Black Sigatoka is the most widely-distributed and destructive disease affecting banana plants. Due to the heavy financial burden of managing this infectious disease, farmers in developing countries face significant banana crop losses. The spread of black Sigatoka is highly dependent on weather conditions and though scientists have produced mathematical models of infectious diseases, adapting these models to incorporate climate effects is difficult. We present MR. NODE (Multiple predictoR Neural ODE), a neural network that models the dynamics of black Sigatoka infection learnt directly from data via Neural Ordinary Differential Equations. Our method encodes external predictor factors into the latent space in addition to the variable that we infer, and it can also predict the infection risk at an arbitrary point in time. Empirically, we demonstrate on historical climate data that our method has superior generalization performance on time points up to one month in the future and unseen irregularities. We believe that our method can be a useful tool to control the spread of black Sigatoka.
Authors: Yuchen Wang (University of Toronto); Matthieu Chan Chee (University of Toronto); Ziyad Edher (University of Toronto); Minh Duc Hoang (University of Toronto); Shion Fujimori (University of Toronto); Jesse Bettencourt (University of Toronto)
Agriculture, forestry and other land use Time-series analysis
ICML 2021 A Reinforcement Learning Approach to Home Energy Management for Modulating Heat Pumps and Photovoltaic Systems (Papers Track)
Abstract and authors: (click to expand)
Abstract: Efficient sector coupling in residential buildings plays a key role in supporting the energy transition. In this study, we analyze the potential of using reinforcement learning (RL) to control a home energy management system. We conduct this study by modeling a representative building with a modulating air-sourced heat pump, a photovoltaic system, a battery, and thermal storage systems for floor heating and hot-water supply. In our numerical analysis, we benchmark our reinforcement learning results using DDPG with the optimal solution generated with model predictive control using a mixed-integer linear model under full information. Our input data, models, and the RL environment, developed using the Julia programming language, will be available in an open-source manner.
Authors: Lissy Langer (TU Berlin)
Buildings and cities Reinforcement learning and control
ICML 2021 Reinforcement Learning for Optimal Frequency Control: A Lyapunov Approach (Papers Track)
Abstract and authors: (click to expand)
Abstract: Renewable energy resources play a vital role in reducing carbon emissions and are becoming increasingly common in the grid. On one hand, they are challenging to integrate into a power system because the lack of rotating mechanical inertia can lead to frequency instabilities. On the other hand, these resources have power electronic interfaces that are capable of implementing almost arbitrary control laws. To design these controllers, reinforcement learning has emerged as a popular method to search for policy parameterized by neural networks. The key challenge with learning based approaches is enforcing the constraint that the learned controller need to be stabilizing. Through a Lyapunov function, we explicitly identify the structure of neural network-based controllers such that they guarantee system stability by design. A recurrent RL architecture is used to efficiently train the controllers and they outperform other approaches as demonstrated by simulations.
Authors: Wenqi Cui (University of Washington); Baosen Zhang (University of Washington)
Power and energy Reinforcement learning and control
ICML 2021 Modeling Bird Migration by Disaggregating Population Level Observations (Papers Track)
Abstract and authors: (click to expand)
Abstract: Birds are shifting migratory routes and timing in response to climate change, but modeling migration to better understand these changes is difficult. Some recent work leverages fluid dynamics models, but this requires individual flight speed and directional data which may not be readily available. We developed an alternate modeling method which only requires population level positional data and use it to model migration routes of the American Woodcock (Scolopax minor). We use our model to sample simulated bird trajectories and compare them to real trajectories in order to evaluate the model.
Authors: Miguel Fuentes (University of Massachusetts, Amherst); Benjamin Van Doren (Cornell University); Daniel Sheldon (University of Massachusetts, Amherst)
Ecosystems and natural systems Other
ICML 2021 Power Grid Cascading Failure Mitigation by Reinforcement Learning (Papers Track)
Abstract and authors: (click to expand)
Abstract: This paper proposes a cascading failure mitigation strategy based on Reinforcement Learning (RL) method. Firstly, the principles of RL are introduced. Then, the Multi-Stage Cascading Failure (MSCF) problem is formulated, and its challenges are investigated. The problem is then tackled by the RL based on DCOPF (Direct Current Optimal Power Flow). Designs of the RL framework (rewards, states, etc.) are illustrated in detail. Experiments on the IEEE 118-bus system by the proposed RL method demonstrate promising performance in reducing system collapses.
Authors: Yongli Zhu (Texas A&M University)
Disaster prediction, management, and relief Power and energy
ICML 2021 Decadal Forecasts with ResDMD: a residual DMD neural network (Papers Track)
Abstract and authors: (click to expand)
Abstract: Significant investment is being made by operational forecasting centers to produce decadal (1-10 year) forecasts that can support long-term decision making for a more climate-resilient society. One method that has been employed for this task is the Dynamic Mode Decomposition (DMD) algorithm – also known as the Linear Inverse Model– which is used to fit linear dynamical models to data. While the DMD usually approximates non-linear terms in the true dynamics as a linear system with random noise, we investigate an extension to the DMD to explicitly represent the non-linear terms as a neural network. Our weight initialization allows the network to produce sensible results before training and then improve the prediction after training as data becomes available. In this short paper, we evaluate the proposed architecture for simulating global sea surface temperatures and compare the results with the standard DMD and seasonal forecasts produced by the state-of-the-art dynamical model, CFSv2.
Authors: EDUARDO ROCHA RODRIGUES (IBM Research); Campbell Watson (IBM Reserch); Bianca Zadrozny (IBM Research); David Gold (IBM Global Business Services)
Classification, regression, and supervised learning Climate and Earth science Time-series analysis
ICML 2021 TweetDrought: A Deep-Learning Drought Impacts Recognizer based on Twitter Data (Papers Track)
Abstract and authors: (click to expand)
Abstract: Acquiring a better understanding of drought impacts becomes increasingly vital under a warming climate. Traditional drought indices describe mainly biophysical variables and not impacts on social, economic, and environmental systems. We utilized natural language processing and bidirectional encoder representation from Transformers (BERT) based transfer learning to fine-tune the model on the data from the news-based Drought Impact Report (DIR) and then apply it to recognize seven types of drought impacts based on the filtered Twitter data from the United States. Our model achieved a satisfying macro-F1 score of 0.89 on the DIR test set. The model was then applied to California tweets and validated with keyword-based labels. The macro-F1 score was 0.58. However, due to the limitation of keywords, we also spot-checked tweets with controversial labels. 83.5% of BERT labels were correct compared to the keyword labels. Overall, the fine-tuned BERT-based recognizer provided proper predictions and valuable information on drought impacts. The interpretation and analysis of the model were consistent with experiential domain expertise.
Authors: Beichen Zhang (University of Nebraska-Lincoln); Frank Schilder (Thomson Reuters); Kelly Smith (National Drought Mitigation Center); Michael Hayes (University of Nebraska-Lincoln); Sherri Harms (University of Nebraska-Kearney); Tsegaye Tadesse (University of Nebraska-Lincoln)
Disaster prediction, management, and relief Natural language processing
ICML 2021 Graph Neural Networks for Learning Real-Time Prices in Electricity Market (Papers Track)
Abstract and authors: (click to expand)
Abstract: Solving the optimal power flow (OPF) problem in real-time electricity market improves the efficiency and reliability in the integration of low-carbon energy resources into the power grids. To address the scalability and adaptivity issues of existing end-to-end OPF learning solutions, we propose a new graph neural network (GNN) framework for predicting the electricity market prices from solving OPFs. The proposed GNN-for-OPF framework innovatively exploits the locality property of prices and introduces physics-aware regularization, while attaining reduced model complexity and fast adaptivity to varying grid topology. Numerical tests have validated the learning efficiency and adaptivity improvements of our proposed method over existing approaches.
Authors: Shaohui Liu (University of Texas at Austin); Chengyang Wu (University of Texas at Austin); Hao Zhu (University of Texas at Austin)
Power and energy Classification, regression, and supervised learning
ICML 2021 Learning Granger Causal Feature Representations (Papers Track)
Abstract and authors: (click to expand)
Abstract: Tackling climate change needs to understand the complex phenomena occurring on the Planet. Discovering teleconnection patterns is an essential part of the endeavor. Events like El Niño Southern Oscillation (ENSO) impact essential climate variables at large distances, and influence the underlying Earth system dynamics. However, their automatic identification from the wealth of observational data is still unresolved. Nonlinearities, nonstationarities and the (ab)use of correlation analyses hamper the discovery of true causal patterns. We here introduce a deep learning methodology that extracts nonlinear latent functions from spatio-temporal Earth data and that are Granger causal with the index altogether. We illustrate its use to study the impact of ENSO on vegetation, which allows for a more rigorous study of impacts on ecosystems globally.
Authors: Gherardo Varando (Universitat de València); Miguel-Ángel Fernández-Torres (Universitat de València); Gustau Camps-Valls (Universitat de València)
Climate and Earth science Interpretable ML Unsupervised and semi-supervised learning
ICML 2021 DeepPolicyTracker: Tracking Changes In Environmental Policy In The Brazilian Federal Official Gazette With Deep Learning (Papers Track)
Abstract and authors: (click to expand)
Abstract: Even though most of its energy generation comes from renewable sources, Brazil is one of the largest emitters of greenhouse gases in the world, due to intense farming and deforestation of biomes, such as the Amazon Rainforest, whose preservation is essential for compliance with the Paris Agreement. Still, regardless of lobbies or prevailing political orientation, all government legal actions are published daily in the Federal Official Gazette. However, with hundreds of decrees issued every day by the authorities, it is absolutely burdensome to manually analyze all these processes and find out which ones can pose serious environmental hazards. In this paper, we propose the DeepPolicyTracker, a promising deep learning model that uses a state-of-the-art pre-trained natural language model to classify government acts and track harmful changes in the environmental policies. We also provide the used dataset annotated by domain experts and show some results already obtained. In the future, this system should serve to scale up the high-quality tracking of all oficial documents with a minimum of human supervision and contribute to increasing society's awareness of every government action.
Authors: Flávio N Cação (University of Sao Paulo); Anna Helena Reali Costa (Universidade de São Paulo); Natalie Unterstell (Política por Inteiro); Liuca Yonaha (Política por Inteiro); Taciana Stec (Política por Inteiro); Fábio Ishisaki (Política por Inteiro)
Natural language processing Agriculture, forestry and other land use Classification, regression, and supervised learning
ICML 2021 Fast-Slow Streamflow Model Using Mass-Conserving LSTM (Papers Track)
Abstract and authors: (click to expand)
Abstract: Streamflow forecasting is key to effectively managing water resources and preparing for the occurrence of natural calamities being exacerbated by climate change. Here we use the concept of fast and slow flow components to create a new mass-conserving Long Short-Term Memory (LSTM) neural network model. It uses hydrometeorological time series and catchment attributes to predict daily river discharges. Preliminary results evidence improvement in skills for different scores compared to the recent literature.
Authors: Miguel Paredes Quinones (IBM Research); Maciel Zortea (IBM Research); Leonardo Martins (IBM Research)
Climate and Earth science Time-series analysis
ICML 2021 Attention For Damage Assessment (Papers Track)
Abstract and authors: (click to expand)
Abstract: Due to climate change the hurricanes are getting stronger and having longer impacts. To reduce the detrimental effects of these hurricanes faster and accurate assessments of damages are essential to the rescue teams. Like other computer vision techniques semantic segmentation can identify the damages and help in proper and prompt damage assessment. Current segmentation methods can be classified into attention and non-attention based methods. Existing non-attention based methods suffers from low accuracy and therefore attention based methods are becoming popular. Self-attention based methods can map the mutual relationship and dependencies among pixels of an image and thus improve semantic segmentation accuracy. In this paper, we present a self-attention semantic segmentation method on UAV imageries to assess the damages inflicted by a natural disaster. The proposed method outperforms four state-of-art segmentation methods both quantitatively and qualitatively with a mean IoU score of 84.03 %.
Authors: Tashnim Chowdhury (University of Maryland Baltimore County); Maryam Rahnemoonfar (University of Maryland Baltimore County)
Disaster prediction, management, and relief Buildings and cities Computer vision and remote sensing
ICML 2021 Online LSTM Framework for Hurricane Trajectory Prediction (Papers Track)
Abstract and authors: (click to expand)
Abstract: Hurricanes are high-intensity tropical cyclones that can cause severe damages when the storms make landfall. Accurate long-range prediction of hurricane trajectories is an important but challenging problem due to the complex interactions between the ocean and atmosphere systems. In this paper, we present a deep learning framework for hurricane trajectory forecasting by leveraging the outputs from an ensemble of dynamical (physical) models. The proposed framework employs a temporal decay memory unit for imputing missing values in the ensemble member outputs, coupled with an LSTM architecture for dynamic path prediction. The framework is extended to an online learning setting to capture concept drift present in the data. Empirical results suggest that the proposed framework significantly outperforms various baselines including the official forecasts from U.S. National Hurricane Center (NHC).
Authors: Ding Wang (Michigan State University); Pang-Ning Tan (MSU)
Disaster prediction, management, and relief Data mining
ICML 2021 Controlling Weather Field Synthesis Using Variational Autoencoders (Papers Track)
Abstract and authors: (click to expand)
Abstract: One of the consequences of climate change is an observed increase in the frequency of extreme climate events. That poses a challenge for weather forecast and generation algorithms, which learn from historical data but should embed an often uncertain bias to create correct scenarios. This paper investigates how mapping climate data to a known distribution using variational autoencoders might help explore such biases and control the synthesis of weather fields towards more extreme climate scenarios. We experimented using a monsoon-affected precipitation dataset from southwest India, which should give a roughly stable pattern of rainy days and ease our investigation. We report compelling results showing that mapping complex weather data to a known distribution implements an efficient control for weather field synthesis towards more (or less) extreme scenarios.
Authors: Dario Augusto Borges Oliveira (IBM Research); Jorge Luis Guevara Diaz (IBM Research); Bianca Zadrozny (IBM Research); Campbell Watson (IBM Reserch)
Climate and Earth science Generative modeling
ICML 2021 ForestViT: A Vision Transformer Network for Convolution-free Multi-label Image Classification in Deforestation Analysis (Papers Track)
Abstract and authors: (click to expand)
Abstract: Understanding the dynamics of deforestation as well as land uses of neighboring areas is of vital importance for the design and development of appropriate forest conservation and management policies. In this paper, we approach deforestation as a multi-label classification problem in an endeavor to capture the various relevant land uses from satellite images. To this end, we propose a multi-label vision transformer model, ForestViT, which leverages the benefits of self-attention mechanism, obviating any convolution operations involved in commonly used deep learning models utilized for deforestation detection.
Authors: Maria Kaselimi (National Technical University of Athens); Athanasios Voulodimos (University of West Attica); Ioannis Daskalopoulos (University of West Attica); Nikolaos Doulamis (National Technical University of Athens); Anastasios Doulamis (Technical University of Crete)
Agriculture, forestry and other land use Computer vision and remote sensing
ICML 2021 Reducing Carbon in the Design of Large Infrastructure Scheme with Evolutionary Algorithms (Papers Track)
Abstract and authors: (click to expand)
Abstract: The construction and operations of large infrastructure schemes such as railways, roads, pipelines and power lines account for a significant proportion of global carbon emissions. Opportunities to reduce the embodied and operational carbon emissions of new infrastructure schemes are greatest during the design phase. However, schedule and cost constraints limit designers from assessing a large number of design options in detail to identify the solution with the lowest lifetime carbon emissions using conventional methods. Here, we develop an evolutionary algorithm to rapidly evaluate in detail the lifetime carbon emissions of thousands of possible design options for new water transmission pipeline schemes. Our results show that this approach can help designers in some cases to identify design solutions with more than 10% lower operational carbon emissions compared with conventional methods, saving more than 1 million tonnes in lifetime carbon emissions for a new water transmission pipeline scheme. We also find that this evolutionary algorithm can be applied to design other types of infrastructure schemes such as non-water pipelines, railways, roads and power lines.
Authors: Matt Blythe (Continuum Industries)
Buildings and cities Industry Power and energy Transportation
ICML 2021 An Accurate and Scalable Subseasonal Forecasting Toolkit for the United States (Papers Track)
Abstract and authors: (click to expand)
Abstract: We develop a subseasonal forecasting toolkit of accurate and highly scalable benchmarks that outperform both the United States operational Climate Forecasting System (CFSv2) and state-of-the-art learning methods from the literature. Our new learned benchmarks include (a) Climatology++, an enhanced form of climatology using knowledge of only the day of the year; (b) CFSv2++, a learned correction for CFSv2; and (c) Persistence++, an augmented persistence model that combines lagged measurements with CFSv2forecasts. These methods alone improve upon CFSv2 accuracy by 9% for US precipitation and 6% for US temperature over 2011-2020. Ensembling our benchmarks with diverse forecasting methods leads to even further gains. Overall, we find that augmenting classical forecasting approaches with learned corrections yields an effective, low-cost strategy for building next-generation subseasonal forecasting models.
Authors: Soukayna Mouatadid (University of Toronto); Paulo Orenstein (IMPA); Genevieve E Flaspohler (MIT); Miruna Oprescu (Microsoft Research); Judah Cohen (AER); Franklyn Wang (Harvard); Sean Knight (MIT); Ernest Fraenkel (MIT); Lester Mackey (Microsoft Research)
Classification, regression, and supervised learning
ICML 2021 Self-supervised Contrastive Learning for Irrigation Detection in Satellite Imagery (Papers Track)
Abstract and authors: (click to expand)
Abstract: Climate change has caused reductions in river runoffs and aquifer recharge resulting in an increasingly unsustainable crop water demand from reduced freshwater availability. Achieving food security while deploying water in a sustainable manner will continue to be a major challenge necessitating careful monitoring and tracking of agricultural water usage. Historically, monitoring water usage has been a slow and expensive manual process with many imperfections and abuses. Ma-chine learning and remote sensing developments have increased the ability to automatically monitor irrigation patterns, but existing techniques often require curated and labelled irrigation data, which are expensive and time consuming to obtain and may not exist for impactful areas such as developing countries. In this paper, we explore an end-to-end real world application of irrigation detection with uncurated and unlabeled satellite imagery. We apply state-of-the-art self-supervised deep learning techniques to optical remote sensing data, and find that we are able to detect irrigation with up to nine times better precision, 90% better recall and 40% more generalization ability than the traditional supervised learning methods.
Authors: Chitra Agastya (UC Berkeley, IBM); Sirak Ghebremusse (UC Berkeley); Ian Anderson (UC Berkeley); Colorado Reed (UC Berkeley); Hossein Vahabi (University California Berkeley); Alberto Todeschini (UC Berkeley)
Unsupervised and semi-supervised learning Agriculture, forestry and other land use Climate and Earth science Classification, regression, and supervised learning Computer vision and remote sensing Meta- and transfer learning
ICML 2021 Extreme Precipitation Seasonal Forecast Using a Transformer Neural Network (Papers Track)
Abstract and authors: (click to expand)
Abstract: An impact of climate change is the increase in frequency and intensity of extreme precipitation events. However, confidently predicting the likelihood of extreme precipitation at seasonal scales remains an outstanding challenge. Here, we present an approach to forecasting the quantiles of the maximum daily precipitation in each week up to six months ahead using the temporal fusion transformer (TFT) model. Through experiments in two regions, we compare TFT predictions with those of two baselines: climatology and a calibrated ECMWF SEAS5 ensemble forecast (S5). Our results show that, in terms of quantile risk at six month lead time, the TFT predictions significantly outperform those from S5 and show an overall small improvement compared to climatology. The TFT also responds positively to departures from normal that climatology cannot.
Authors: Daniel Salles Civitarese (IBM Research, Brazil); Daniela Szwarcman (IBM Research); Bianca Zadrozny (IBM Research); Campbell Watson (IBM Reserch)
Disaster prediction, management, and relief Climate and Earth science Time-series analysis
ICML 2021 BERT Classification of Paris Agreement Climate Action Plans (Papers Track)
Abstract and authors: (click to expand)
Abstract: As the volume of text-based information on climate policy increases, natural language processing (NLP) tools can distill information from text to better inform decision making on climate policy. We investigate how large pretrained transformers based on the BERT architecture classify sentences on a dataset of climate action plans which countries submitted to the United Nations following the 2015 Paris Agreement. We use the document header structure to assign noisy policy-relevant labels such as mitigation, adaptation, energy, and land use to text elements. Our models provide an improvement in out-of-sample classification over simple heuristics though fall short of the consistency observed between human annotators. We hope to extend this framework to a wider class of textual climate change data such as climate legislation and corporate social responsibility filings and build tools to streamline the extraction of information from these documents for climate change researchers.
Authors: Tom Corringham (Scripps Institution of Oceanography); Daniel Spokoyny (Carnegie Mellon University); Eric Xiao (University of California San Diego); Christopher Cha (University of California San Diego); Colin Lemarchand (University of California San Diego); Mandeep Syal (University of California San Diego); Ethan Olson (University of California San Diego); Alexander Gershunov (Scripps Institution of Oceanography)
Natural language processing Climate policy
ICML 2021 Quantification of Carbon Sequestration in Urban Forests (Papers Track)
Abstract and authors: (click to expand)
Abstract: Vegetation, trees in particular, sequester carbon by absorbing carbon dioxide from the atmosphere, however, the lack of efficient quantification methods of carbon stored in trees renders it difficult to track the process. Here we present an approach to estimate the carbon storage in trees based on fusing multispectral aerial imagery and LiDAR data to identify tree coverage, geometric shape, and tree species, which are crucial attributes in carbon storage quantification. We demonstrate that tree species information and their three-dimensional geometric shapes can be estimated from remote imagery in order to calculate the tree's biomass. Specifically, for Manhattan, New York City, we estimate a total of 52,000 tons of carbon sequestered in trees.
Authors: Levente Klein (IBM Research); Wang Zhou (IBM Research); Conrad M Albrecht (IBM Research)
Carbon capture and sequestration Climate and Earth science Agriculture, forestry and other land use
ICML 2021 A comparative study of stochastic and deep generative models for multisite precipitation synthesis (Papers Track)
Abstract and authors: (click to expand)
Abstract: Future climate change scenarios are usually hypothesized using simulations from weather generators. However, there only a few works comparing and evaluating multisite weather generators, and there is no existing work contrasting promising deep learning approaches for weather generation against classical stochastic weather generators. This study shows preliminary results evaluating stochastic weather generators and deep generative models for multisite precipitation synthesis. Using a variety of metrics, we compare two open source weather generators: XWeathergen (an extension of the Weathergen library) and RGeneratePrec, and two deep generative models: GAN and VAE. Our preliminary results can serve as a guide for improving the design of deep learning architectures and algorithms for the multisite precipitation synthesis task.
Authors: Jorge Luis Guevara Diaz (IBM Research); Dario Augusto Borges Oliveira (IBM Research); Bianca Zadrozny (IBM Research); Campbell Watson (IBM Reserch)
Generative modeling Other
ICML 2021 Self-Supervised Learning on Multispectral Satellite Data for Near-Term Solar Forecasting (Papers Track)
Abstract and authors: (click to expand)
Abstract: With the unprecedented increase in distributed photovoltaic (PV) capacity across the globe, there is an increasing need for reliable and accurate forecasting of solar power generation. While PV output is affected by many factors, the atmosphere, i.e., cloud cover, plays a dominant role in determining the amount of downwelling solar irradiance that reaches PV modules. This paper demonstrates that self-supervised learning of multispectral satellite data from the recently launched GOES-R series of satellites can improve near-term (15 minutes) solar forecasting. We develop deep auto-regressive models using convolutional neural networks (CNN) and long short-term memory networks (LSTM) that are globally trained across many solar sites on the raw spatio-temporal data from GOES-R satellites. This self-supervised model provides estimates of future solar irradiance that can be fed directly to a regression model trained on smaller site-specific solar data to provide near-term solar PV forecasts at the site. The regression implicitly models site-specific characteristics, such as capacity, panel tilt, orientation, etc, while the self-supervised CNN-LSTM implicitly captures global atmospheric patterns affecting a site's solar irradiation. Results across 25 solar sites show the utility of such self-supervised modeling by providing accurate near-term forecast with errors close to that of a model using current ground-truth observations.
Authors: Akansha Singh Bansal (University of Massachusetts Amherst); Trapit Bansal (University of Massachusetts Amherst); David Irwin (University of Massachusetts Amherst)
Unsupervised and semi-supervised learning Other Time-series analysis
ICML 2021 Refining Ice Layer Tracking through Wavelet combined Neural Networks (Papers Track)
Abstract and authors: (click to expand)
Abstract: Rise in global temperatures is resulting in polar ice caps to melt away, which can lead to drastic sea level rise and coastal floods. Accurate calculation of the ice cap reduction is necessary in order to project its climatic impact. Ice sheets are monitored through Snow Radar sensors which give noisy profiles of subsurface ice layers. The sensors take snapshots of the entire ice sheet regularly, and thus result in large datasets. In this work, we use convolutional neural networks (CNNs) for their property of feature extraction and generalizability on large datasets. We also use wavelet transforms and embed them as a layer in the architecture to help in denoising the radar images and refine ice layer detection. Our results show that incorporating wavelets in CNNs helps in detecting the position of deep subsurface ice layers, which can be used to analyse their change overtime.
Authors: Debvrat Varshney (University of Maryland Baltimore County); Masoud Yari (College of Engineering and Information Technology, University of Maryland Balitimore County); Tashnim Chowdhury (University of Maryland Baltimore County); Maryam Rahnemoonfar (University of Maryland Baltimore County)
Computer vision and remote sensing Climate and Earth science
ICML 2021 Forecasting Sea Ice Concentrations using Attention-based Ensemble LSTM (Papers Track)
Abstract and authors: (click to expand)
Abstract: Accurately forecasting Arctic sea ice from sub-seasonal to seasonal scales has been a major scientific effort with fundamental challenges at play. In addition to physics-based earth system models, researchers have been applying multiple statistical and machine learning models for sea ice forecasting. Looking at the potential of data-driven sea ice forecasting, we propose an attention-based Long Short Term Memory (LSTM) ensemble method to predict monthly sea ice extent up to 1 month ahead. Using daily and monthly satellite retrieved sea ice data from NSIDC and atmospheric and oceanic variables from ERA5 reanalysis product for 39 years, we show that our multi-temporal ensemble method outperforms several baseline and recently proposed deep learning models. This will substantially improve our ability in predicting future Arctic sea ice changes, which is fundamental for forecasting transporting routes, resource development, coastal erosion, threats to Arctic coastal communities and wildlife.
Authors: Sahara Ali (University of Maryland, Baltimore County); Yiyi Huang (University of Maryland, Baltimore County); Xin Huang (University of Maryland, Baltimore County); Jianwu Wang (University of Maryland, Baltimore County)
Climate and Earth science Ecosystems and natural systems Classification, regression, and supervised learning Time-series analysis
ICML 2021 Toward efficient calibration of higher-resolution Earth System Models (Papers Track) Best Paper: Pathway to Impact
Abstract and authors: (click to expand)
Abstract: Projections of future climate change to support decision-making require high spatial resolution, but this is computationally prohibitive with modern Earth system models (ESMs). A major challenge is the calibration (parameter tuning) process, which requires running large numbers of simulations to identify the optimal parameter values. Here we train a convolutional neural network (CNN) on simulations from two lower-resolution (and thus much less expensive) versions of the same ESM, and a smaller number of higher-resolution simulations. Cross-validated results show that the CNN's skill exceeds that of a climatological baseline for most variables with as few as 5-10 examples of the higher-resolution ESM, and for all variables (including precipitation) with at least 20 examples. This proof-of-concept study offers the prospect of significantly more efficient calibration of ESMs, by reducing the required CPU time for calibration by 20-40 %.
Authors: Christopher Fletcher (University of Waterloo); William McNally (University of Waterloo); John Virgin (University of Waterloo)
Generative modeling Climate and Earth science
ICML 2021 Visual Question Answering: A Deep Interactive Framework for Post-Disaster Management and Damage Assessment (Papers Track)
Abstract and authors: (click to expand)
Abstract: Each natural disaster has left a trail of destruction and damage, which must be managed very effectively to reduce the disaster's impact. Lack of proper decision making in post-disaster managerial level can increase human suffering and waste a great amount of money. Our objective is to incorporate a deep interactive approach in the decision-making system especially in a rescue mission after any natural disaster for the systematic distribution of the limited resources and accelerating the recovery process. We believe that Visual Question Answering (VQA) is the finest way to address this issue. In visual question answering, a query-based answer regarding the situation of the affected area can add value to the decision-making system. Our main purpose of this study is to develop a Visual Question Answering model for post-disaster damage assessment purposes. With this aim, we collect the images by UAV (Unmanned Aerial Vehicle) after Hurricane Harvey and develop a dataset that includes the questions that are very important in the decision support system after a natural disaster. In addition, We propose a supervised attention-based approach in the modeling segment. We compare our approach with the two other baseline attention-based VQA algorithms namely Multimodal Factorized Bilinear (MFB) and Stacked Attention Network (SAN). Our approach outperforms in providing answers for several types of queries including simple counting, complex counting compares to the baseline models.
Authors: Argho Sarkar (University of Maryland, Baltimore County); Maryam Rahnemoonfar (University of Maryland Baltimore County)
Disaster prediction, management, and relief Computer vision and remote sensing
ICML 2021 Designing Bounded min-knapsack Bandits algorithm for Sustainable Demand Response (Papers Track)
Abstract and authors: (click to expand)
Abstract: Around 40% of global energy produced is consumed by buildings. By using renewable energy resources we can alleviate the dependence on electrical grids. Recent trends focus on incentivizing consumers to reduce their demand consumption during peak hours for sustainable demand response. To minimize the loss, the distributor companies should target the right set of consumers and demand the right amount of electricity reductions. This paper proposes a novel bounded integer min-knapsack algorithm and shows that the algorithm, while allowing for multiple unit reduction, also optimizes the loss to the distributor company within a factor of two (multiplicative) and a problem-dependent additive constant. Existing CMAB algorithms fail to work in this setting due to non-monotonicity of reward function and time-varying optimal sets. We propose a novel algorithm Twin-MinKPDR-CB to learn these compliance probabilities efficiently. Twin-MinKPDR-CB works for non-monotone reward functions bounded min-knapsack constraints and time-varying optimal sets. We find that Twin-MinKPDR-CB achieves sub-linear regret of O(log T) with T being the number of rounds demand response is run.
Authors: Akansha Singh (Indian Institute of Technology, Ropar); Meghana Reddy (Indian Institute of Technology, Ropar); Zoltan Nagy (University of Texas); Sujit P. Gujar (Machine Learning Laboratory, International Institute of Information Technology, Hyderabad); Shweta Jain (Indian Institute of Technology Ropar)
Power and energy Buildings and cities Reinforcement learning and control Uncertainty quantification and robustness
ICML 2021 Sky Image Prediction Using Generative Adversarial Networks for Solar Forecasting (Papers Track)
Abstract and authors: (click to expand)
Abstract: Large-scale integration of solar photovoltaics (PV) is challenged by high variability in its power output, mainly due to local and short-term cloud events. To achieve accurate solar forecasting, it is paramount to accurately predict the movement of clouds. Here, we use generative adversarial networks (GANs) to predict future sky images based on past sky image sequences and show that our trained model can generate realistic future sky images and capture the dynamics of clouds in the context frames. The generated images are then evaluated for a downstream solar forecasting task; results show promising performance.
Authors: Yuhao Nie (Stanford University); Andea Scott (Stanford University); Eric Zelikman (Stanford University); Adam Brandt (Stanford University)
Generative modeling Climate and Earth science Computer vision and remote sensing
ICML 2021 EVGen: Adversarial Networks for Learning Electric Vehicle Charging Loads and Hidden Representations (Papers Track)
Abstract and authors: (click to expand)
Abstract: The nexus between transportation, the power grid, and consumer behavior is much more pronounced than ever before as the race to decarbonize intensifies. Electrification in the transportation sector has led to technology shifts and rapid deployment of electric vehicles (EVs). The potential increase in stochastic and spatially heterogeneous charging load presents a unique challenge that is not well studied, and will have significant impacts on grid operations, emissions, and system reliability if not managed effectively. Realistic scenario generators can help operators prepare, and machine learning can be leveraged to this end. In this work, we develop generative adversarial networks (GANs) to learn distributions of electric vehicle (EV) charging sessions and disentangled representations. We show that this model successfully parameterizes unlabeled temporal and power patterns and is able to generate synthetic data conditioned on these patterns. We benchmark the generation capability of this model with Gaussian Mixture Models (GMMs), and empirically show that our proposed model framework is better at capturing charging distributions and temporal dynamics.
Authors: Robert Buechler (Stanford University); Emmanuel O Balogun (Stanford University); Arun Majumdar (Stanford University); Ram Rajagopal (Stanford University)
Power and energy Transportation Generative modeling Unsupervised and semi-supervised learning
ICML 2021 Reconstruction of Long-Term Historical Electricity Demand Data (Papers Track)
Abstract and authors: (click to expand)
Abstract: Long-term planning of a robust power system requires the understanding of changing demand patterns. Electricity demand is highly weather sensitive. Thus, the supply side variation from introducing intermittent renewable sources, juxtaposed with variable demand, will introduce additional challenges in the grid planning process. By understanding the spatial and temporal variability of temperature over the US, the response of demand to natural variability and climate change-related effects on temperature can be separated, especially because the effects due to the former factor are not known. Through this project, we aim to better support the technology& policy development process for power systems by developing machine and deep learning ’back-forecasting’ models to reconstruct multidecadaldemand records and study the natural variabilityof temperature and its influence on demand.
Authors: Reshmi Ghosh (Carnegie Mellon University); Michael Craig (University of Michigan); H.Scott Matthews (Carnegie Mellon University); Laure Berti-Equille (IRD)
Classification, regression, and supervised learning Deep Learning
ICML 2021 A Set-Theoretic Approach to Safe Reinforcement Learning in Power Systems (Papers Track)
Abstract and authors: (click to expand)
Abstract: Reducing the carbon footprint of the energy sector will be a vital part of the fight against climate change, and doing so will require the widespread adoption of renewable energy resources. Optimally integrating a large number of these resources requires new control techniques that can both compensate for the variability of renewables and satisfy hard engineering constraints. Reinforcement learning (RL) is a promising approach to data-driven control, but it is difficult to verify that the policies derived from data will be safe. In this paper, we combine RL with set-theoretic control to propose a computationally efficient approach to safe RL. We demonstrate the method on a simplified power system model and compare it with other RL techniques.
Authors: Daniel Tabas (University of Washington); Baosen Zhang (University of Washington)
Reinforcement learning and control Power and energy
ICML 2021 A study of battery SoC scheduling using machine learning with renewable sources (Papers Track)
Abstract and authors: (click to expand)
Abstract: An open energy system (OES) enables the shared distribution of energy resources within a community autonomously and efficiently. For this distributed system a rooftop solar panel and a battery are installed in each house of the community. The OES system monitors the State of Charge (SoC) of each battery independently, arbitrates energy-exchange requests from each house, and physically controls peer-to-peer energy exchanges. In this study, our goal is to optimize those energy exchanges to maximize the renewable energy penetration within the community using machine learning techniques. Future household electricity consumption is predicted using machine learning from the past time series. The predicted consumption is used to determine the next energy-exchange strategy, i.e. when and how much energy should be exchanged to minimize the surplus of solar energy. The simulation results show that the proposed method can increase the amount of renewable energy penetration within the community.
Authors: Daisuke Kawamoto (Sony Computer Science Laboratories, Inc.); Gopinath Rajendiran (CSIR Central Scientific Instruments Organisation, Chennai)
Power and energy Time-series analysis
ICML 2021 Multivariate climate downscaling with latent neural processes (Papers Track)
Abstract and authors: (click to expand)
Abstract: Statistical downscaling is a vital tool in generating high resolution projections for climate impact studies. This study applies convolutional latent neural processes to multivariate downscaling of maximum temperature and precipitation. In contrast to existing downscaling methods, this model is shown to produce spatially coherent predictions at arbitrary locations specified at test time, regardless of whether training data are available at these points.
Authors: Anna Vaughan (Univeristy of Cambridge); Nic Lane (University of Cambridge); Michael Herzog (University of Cambridge)
Climate and Earth science Causal and Bayesian methods
ICML 2021 FIRE-ML: A Remotely-sensed Daily Wildfire Forecasting Dataset for the Contiguous United States (Papers Track)
Abstract and authors: (click to expand)
Abstract: Wildfires are natural phenomena that can have devastating effects on ecosystems, urban developments, and the environment. Improving the scientific understanding of these events and the ability to forecast how they will evolve in the short- and long-term are ongoing multi-decadal challenges. We present a large-scale dataset, well-suited to machine learning, that aggregates and aligns multiple remotely-sensed and forecasted data products to provide a holistic set of features for forecasting wildfires on daily timescales. This dataset includes 4.2 million unique active fire detections, covers the majority of the contiguous United States from 2012 to 2020, and includes active fire detections, land cover, topography, and meteorology.
Authors: Casey A Graff (UC Irvine)
Computer vision and remote sensing Agriculture, forestry and other land use Classification, regression, and supervised learning
ICML 2021 IowaRain: A Statewide Rain Event Dataset Based on Weather Radars and Quantitative Precipitation Estimation (Papers Track)
Abstract and authors: (click to expand)
Abstract: Effective environmental planning and management to address climate change could be achieved through extensive environmental modeling with machine learning and conventional physical models. In order to develop and improve these models, practitioners and researchers need comprehensive benchmark datasets that are prepared and processed with environmental expertise that they can rely on. This study presents an extensive dataset of rainfall events for the state of Iowa (2016-2019) acquired from the National Weather Service Next Generation Weather Radar (NEXRAD) system and processed by a quantitative precipitation estimation system. The dataset presented in this study could be used for better disaster monitoring, response and recovery by paving the way for both predictive and prescriptive modeling.
Authors: Muhammed A Sit (The University of Iowa); Bongchul Seo (IIHR—Hydroscience & Engineering, The University of Iowa); Ibrahim Demir (The University of Iowa)
Data mining Benchmark Datasets
ICML 2021 Short-term Hourly Streamflow Prediction with Graph Convolutional GRU Networks (Papers Track)
Abstract and authors: (click to expand)
Abstract: The frequency and impact of floods are expected to increase due to climate change. It is crucial to predict streamflow, consequently flooding, in order to prepare and mitigate its consequences in terms of property damage and fatalities. This paper presents a Graph Convolutional GRUs based model to predict the next 36 hours of streamflow for a sensor location using the upstream river network. As shown in experiment results, the model presented in this study provides better performance than the persistence baseline and a Convolutional Bidirectional GRU network for the selected study area in short-term streamflow prediction.
Authors: Muhammed A Sit (The University of Iowa); Bekir Demiray (The University of Iowa); Ibrahim Demir (The University of Iowa)
Disaster prediction, management, and relief Climate and Earth science Computer vision and remote sensing Interpretable ML Time-series analysis
ICML 2021 Wildfire Smoke Plume Segmentation Using Geostationary Satellite Imagery (Papers Track)
Abstract and authors: (click to expand)
Abstract: Wildfires have increased in frequency and severity over the past two decades, especially in the Western United States. Beyond physical infrastructure damage caused by these wildfire events, researchers have increasingly identified harmful impacts of particulate matter generated by wildfire smoke on respiratory, cardiovascular, and cognitive health. This inference is difficult due to the spatial and temporal uncertainty regarding how much particulate matter is specifically attributable to wildfire smoke. One factor contributing to this challenge is the reliance on manually drawn smoke plume annotations, which are often noisy representations limited to the United States. This work uses deep convolutional neural networks to segment smoke plumes from geostationary satellite imagery. We compare the performance of predicted plume segmentations versus the noisy annotations using causal inference methods to estimate the amount of variation each explains in Environmental Protection Agency (EPA) measured surface level particulate matter <2.5μm in diameter (PM2.5).
Authors: Jeffrey L Wen (Stanford University); Marshall Burke (Stanford University)
Computer vision and remote sensing Behavioral and social science Climate and Earth science Disaster prediction, management, and relief Societal adaptation Classification, regression, and supervised learning
ICML 2021 Deep Spatial Temporal Forecasting of Electrical Vehicle Charging Demand (Papers Track)
Abstract and authors: (click to expand)
Abstract: Electric vehicles can offer a low carbon emission solution to reverse rising emission trends. However, this requires that the energy used to meet the demand is green. To meet this requirement, accurate forecasting of the charging demand is vital. Short and long-term charging demand forecasting will allow for better optimisation of the power grid and future infrastructure expansions. In this paper, we propose to use publicly available data to forecast the electric vehicle charging demand. To model the complex spatial-temporal correlations between charging stations, we argue that Temporal Graph Convolution Models are the most suitable to capture the correlations. The proposed Temporal Graph Convolutional Networks provide the most accurate forecasts for short and long-term forecasting compared with other forecasting methods.
Authors: Frederik B Hüttel (Technical University of Denmark (DTU)); Filipe Rodrigues (Technical University of Denmark (DTU)); Inon Peled (Technical University of Denmark (DTU)); Francisco Pereira (DTU)
Transportation Power and energy Classification, regression, and supervised learning Time-series analysis
ICML 2021 Powering Effective Climate Communication with a Climate Knowledge Base (Proposals Track)
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Abstract: While many accept climate change and its growing impacts, few converse about it well, limiting the adoption speed of societal changes necessary to address it. In order to make effective climate communication easier, we aim to build a system that presents to any individual the climate information predicted to best motivate and inspire them to take action given their unique set of personal values. To alleviate the cold-start problem, the system relies on a knowledge base (ClimateKB) of causes and effects of climate change, and their associations to personal values. Since no such comprehensive ClimateKB exists, we revisit knowledge base construction techniques and build a ClimateKB from free text. We plan to open source the ClimateKB and associated code to encourage future research and applications.
Authors: Kameron B. Rodrigues (Stanford University); Shweta Khushu (SkySpecs Inc); Mukut Mukherjee (ClimateMind); Andrew Banister (Climate Mind); Anthony Hevia (ClimateMind); Sampath Duddu (ClimateMind); Nikita Bhutani (Megagon Labs)
Natural language processing Knowledge engineering
ICML 2021 Solar PV Maps for Estimation and Forecasting of Distributed Solar Generation (Proposals Track)
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Abstract: Rapid uptake of distributed solar PV is starting to make the operation of grids and energy markets more challenging, and better methods are needed for measuring and forecasting distributed solar PV generation across entire regions. We propose a method for converting time series data from a number of point sources (power measurements at individual sites) into 2-dimensional maps that estimate total solar PV generation across large areas. These maps may be used on their own, or in conjunction with additional data sources (such as satellite imagery) in a deep learning framework that enables improved regional solar PV estimation and forecasting. We provide some early validation and results, discuss anticipated benefits of this approach, and argue that this method has the potential to further enable significant uptake of solar PV, assisting a shift away from fossil fuel-based generation.
Authors: Julian de Hoog (The University of Melbourne); Maneesha Perera (The University of Melbourne); Kasun Bandara (The University of Melbourne); Damith Senanayake (The University of Melbourne); Saman Halgamuge (University of Melbourne)
Power and energy Classification, regression, and supervised learning Time-series analysis
ICML 2021 An Iterative Approach to Finding Global Solutions of AC Optimal Power Flow Problems (Proposals Track)
Abstract and authors: (click to expand)
Abstract: To achieve a cleaner energy system, a diverse set of energy resources such as solar PV, battery storage and electric vehicles are entering the electric grid. Their operation is typically controlled by solving a resource allocation problem, called the AC optimal power flow (ACOPF) problem. This problem minimizes the cost of generation subject to supply/demand balance and various other engineering constraints. It is nonlinear and nonconvex, and existing solvers are generally successful in finding local solutions. As the share of renewable energy resources increases, it is becoming increasingly important to find globally optimal solutions to utilize these resources to the full extent. In this paper, we propose a simple iterative approach to find globally optimal solutions to ACOPF problems. First, we call an existing solver for the ACOPF problem and we form a partial Lagrangian from the associated dual variables. This partial Lagrangian has a much better optimization landscape and we use its solution as a warm start for the ACOPF problem. By repeating this process, we can iteratively improve the solution quality, moving from local solutions to global ones. We demonstrate the effectiveness of our algorithm on standard benchmarks. We also show how the dual variables could be found by using a neural network to further speed up the algorithm.
Authors: Ling Zhang (University of Washington); Baosen Zhang (University of Washington)
Power and energy
ICML 2021 Deep learning applied to sea surface semantic segmentation: Filtering sunglint from aerial imagery (Proposals Track)
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Abstract: Water waves are an ubiquitous feature of the oceans, which serve as a pathway for interactions with the atmosphere. Wave breaking in particular is crucial in developing better understanding of the exchange of momentum, heat, and gas fluxes between the ocean and the atmosphere. Characterizing the properties of wave breaking using orbital or suborbital imagery of the surface of the ocean can be challenging, due to contamination from sunglint, a persistent feature in certain lighting conditions. Here we propose a supervised learning approach to accurately detect whitecaps from airborne imagery obtained under a broad range of lighting conditions. Finally, we discuss potential applications for improving ocean and climate models.
Authors: Teodor Vrecica (UCSD); Quentin Paletta (University of Cambridge); Luc Lenain (UCSD)
Climate and Earth science Classification, regression, and supervised learning Computer vision and remote sensing
ICML 2021 Technical support project and analysis of the dissemination of carbon dioxide and methane from Lake Kivu in nature and its impact on biodiversity in the Great Lakes region since 2012 (Proposals Track)
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Abstract: Straddling the Democratic Republic of the Congo and Rwanda, at an altitude of 1,460 m, Lake Kivu is one of the ten great lakes in Africa, alongside the main ones that are Victoria and Tanganyika. Kivu contains very high concentrations of gases (carbon dioxide and methane in particular), produced by volcanic activity in the region and the decomposition of organic matter. It has 2,700 km2 of this body of water, a depth that approaches 500 meters in places. It is estimated to contain 60 billion cubic meters of dissolved methane and about 300 billion cubic meters of carbon dioxide accumulated over time. Lake Kivu, located north of Lake Tanganyika and contains a very high amount of carbon dioxide and methane. Carbon dioxide (CO2) and methane (CH4) are both greenhouse gases that affect how well the planet works. The first stays in the atmosphere for a hundred years while the second stays there only for a dozen years. The effect of the dissemination of these in nature prompts me to collect as much data as possible on their circulation and to suggest possible solutions that are consistent with the Paris Agreement. In addition, many wastes come from households and/or small industries in the towns of Bukavu, Goma for the DRC and those of Gyangugu and Gisenyi for Rwanda constitute a high source of CH4 emissions which also contribute to global warming. The exploitation of methane expected in the near future is an additional threat to the sustainable development of ecosystem resources. For various reasons, Lake Kivu constitutes an adequate model for studying the responses of large tropical lakes to changes linked to human activity: indeed, despite its physical and biogeochemical peculiarities, the limnological and ecological processes of its pelagic waters are subject to the same forcings as in other large lakes in the same region, as shown by recent studies.
Reinforcement learning and control Carbon capture and sequestration
ICML 2021 Virtual Screening for Perovskites Discovery (Proposals Track)
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Abstract: Re-inventing the global energy harvesting system from fossil fuels to renewables is essential for reducing greenhouse gas emissions in line with current climate targets. Perovskite photovoltaics (PVs), the class of materials with relatively unexplored material configurations, play key role in solar energy generation due to their low manufacturing cost and exceptional optoelectronic properties. Without the efficient utilisation of machine learning, the discovery and manufacturing process could take a dangerously long time. We present a high-throughput computational design that leverages machine learning algorithms at various steps in order to assess the suitability of the organic molecules for the perovskite crystals.
Authors: Andrea Karlova (UCL); Cameron C.L. Underwood (University of Surrey); Ravi Silva (University of Surrey)
Power and energy Photovoltaics
ICML 2021 Leveraging Machine Learning for Equitable Transition of Energy Systems (Proposals Track)
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Abstract: Our planet is facing overlapping crises of climate change, global pandemic, and systemic inequality. To respond climate change, the energy system is in the midst of its most foundational transition since its inception, from traditional fuel-based energy sources to clean renewable sources. While the transition to a low-carbon energy system is in progress, there is an opportunity to make the new system more just and equitable than the current one that is inequitable in many forms. Measuring inequity in the energy system is a formidable task since it is large scale and the data is coming from abundant data sources. In this work, we lay out a plan to leverage and develop scalable machine learning (ML) tools to measure the equity of the current energy system and to facilitate a just transition to a clean energy system. We focus on two concrete examples. First, we explore how ML can help to measure the inequity in the energy inefficiency of residential houses in the scale of a town or a country. Second, we explore how deep learning techniques can help to estimate the solar potential of residential buildings to facilitate a just installation and incentive allocation of solar panels. The application of ML for energy equity is much broader than the above two examples and we highlight some others as well. The result of this research could be used by policymakers to efficiently allocate energy assistance subsidies in the current energy systems and to ensure justice in their energy transition plans.
Authors: Enea Dodi (UMass Amherst); Anupama A Sitaraman (University of Massachusetts Amherst); Mohammad Hajiesmaili (UMass Amherst); Prashant Shenoy (University of Massachusetts Amherst)
Classification, regression, and supervised learning Climate justice Time-series analysis
ICML 2021 Long-term Burned Area Reconstruction through Deep Learning (Proposals Track)
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Abstract: Wildfire impact studies are significantly hampered by the absence of a global long-term burned area dataset. This prevents conclusive statements on the role of anthropogenic activity on wildfire impacts over the last century. Here, we propose a workflow to construct a 1901-2014 reanalysis of monthly global burned area at a 0.5° by 0.5° scale. A neural network will be trained with weather-related, vegetational, societal and economic input parameters, and burned area as output label for the 1982-2014 time period. This model can then be applied to the whole 1901-2014 time period to create a data-driven, long-term burned area reanalysis. This reconstruction will allow to investigate the long-term effect of anthropogenic activity on wildfire impacts, will be used as basis for detection and attribution studies and could help to reduce the uncertainties in future predictions.
Authors: Seppe Lampe (Vrije Universiteit Brussel); Bertrand Le Saux (European Space Agency (ESA)); Inne Vanderkelen (Vrije Universiteit Brussel); Wim Thiery (Vrije Universiteit Brussel)
Disaster prediction, management, and relief Classification, regression, and supervised learning Computer vision and remote sensing
ICML 2021 Preserving the integrity of the Canadian northern ecosystems through insights provided by reinforcement learning-based Arctic fox movement models (Proposals Track)
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Abstract: Realistic modeling of the movement of the Arctic fox, one of the main predators of the circumpolar world, is crucial to understand the processes governing the distribution of the Canadian Arctic biodiversity. Current methods, however, are unable to adequately account for complex behaviors as well as intra- and interspecific relationships. We propose to harness the potential of reinforcement learning to develop innovative models that will address these shortcomings and provide the backbone to predict how vertebrate communities may be affected by environmental changes in the Arctic, an essential step towards the elaboration of rational conservation actions.
Authors: Catherine Villeneuve (Université Laval); Frédéric Dulude-De Broin (Université Laval); Pierre Legagneux (Université Laval); Dominique Berteaux (Université du Québec à Rimouski); Audrey Durand (Université Laval)
Ecosystems and natural systems Reinforcement learning and control
ICML 2021 Street2Sat: A Machine Learning Pipeline for Generating Ground-truth Geo-referenced Labeled Datasets from Street-Level Images (Proposals Track)
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Abstract: Ground-truth labels on crop type and other variables are critically needed to develop machine learning methods that use satellite observations to combat climate change and food insecurity. These labels difficult and costly to obtain over large areas, particularly in Sub-Saharan Africa where they are most scarce. We propose Street2Sat, a new framework for obtaining large data sets of geo-referenced crop type labels obtained from vehicle-mounted cameras that can be extended to other applications. Using preliminary data from Kenya, we present promising results from this approach and identify future to improve the method before operational use in 5 countries.
Authors: Madhava Paliyam (University of Maryland); Catherine L Nakalembe (University of Maryland); Kevin Liu (University of Maryland); Richard Nyiawung (University of Guelph); Hannah R Kerner (University of Maryland)
Agriculture, forestry and other land use Classification, regression, and supervised learning Computer vision and remote sensing
ICML 2021 From Talk to Action with Accountability: Monitoring the Public Discussion of Policy Makers with Deep Neural Networks and Topic Modelling (Proposals Track)
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Abstract: Decades of research on climate have provided a consensus that human activity has changed the climate and we are currently heading into a climate crisis. While public discussion and research efforts on climate change mitigation have increased, potential solutions need to not only be discussed but also effectively deployed. For preventing mismanagement and holding policy makers accountable, transparency and degree of information about government processes have been shown to be crucial. However, currently the quantity of information about climate change discussions and the range of sources make it increasingly difficult for the public and civil society to maintain an overview to hold politicians accountable. In response, we propose a multi-source topic aggregation system (MuSTAS) which processes policy makers speech and rhetoric from several publicly available sources into an easily digestible topic summary. MuSTAS uses novel multi-source hybrid latent Dirichlet allocation to model topics from a variety of documents. This topic digest will serve the general public and civil society in assessing where, how, and when politicians talk about climate and climate policies, enabling them to hold politicians accountable for their actions to mitigate climate change and lack thereof.
Authors: Vili Hätönen (Emblica); Fiona Melzer (University of Edinburgh)
Natural language processing Behavioral and social science Climate policy Unsupervised and semi-supervised learning
ICML 2021 NeuralNERE: Neural Named Entity Relationship Extraction for End-to-End Climate Change Knowledge Graph Construction (Proposals Track)
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Abstract: This paper proposes an end-to-end Neural Named Entity Relationship Extraction model (called NeuralNERE) for climate change knowledge graph (KG) construction, directly from the raw text of relevant news articles. The proposed model will not only remove the need for any kind of human supervision for building knowledge bases for climate change KG construction (used in the case of supervised or dictionary-based KG construction methods), but will also prove to be highly valuable for analyzing climate change by summarising relationships between different factors responsible for climate change, extracting useful insights & reasoning on pivotal events, and helping industry leaders in making more informed future decisions. Additionally, we also introduce the Science Daily Climate Change dataset (called SciDCC) that contains over 11k climate change news articles scraped from the Science Daily website, which could be used for extracting prior knowledge for constructing climate change KGs.
Authors: Prakamya Mishra (Independent Researcher); Rohan Mittal (Independent Researcher)
Natural language processing Behavioral and social science Climate policy Unsupervised and semi-supervised learning
ICML 2021 A multi-task learning approach to enhance sustainable biomolecule production in engineered microorganisms (Proposals Track)
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Abstract: A sustainable alternative to sourcing many materials humans need is metabolic engineering: a field that aims to engineer microorganisms into biological factories that convert renewable feedstocks into valuable biomolecules (i.e., jet fuel, medicine). Microorganism factories must be genetically optimized using predictable DNA sequence tools, however, for many organisms, the exact DNA sequence signals defining their genetic control systems are poorly understood. To better decipher these DNA signals, we propose a multi-task learning approach that uses deep learning and feature attribution methods to identify DNA sequence signals that control gene expression in the methanotroph M. buryatense. This bacterium consumes methane, a potent greenhouse gas. If successful, this work would enhance our ability to build gene expression tools to more effectively engineer M. buryatense into an efficient biomolecule factory that can divert methane pollution into valuable, everyday materials.
Authors: Erin Wilson (University of Washington); Mary Lidstrom (University of Washington); David Beck (University of Washington)
Other Sustainable molecule production
ICML 2021 MethaNet - an AI-driven approach to quantifying methane point-source emission from high-resolution 2-D plume imagery (Proposals Track)
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Abstract: Methane (CH4) is one of the most powerful anthropogenic greenhouse gases with a significant impact on global warming trajectory and tropospheric air quality. Quantifying an emission rate of observed CH4 plumes from aerial or satellite images is a critical step for understanding the local distributions and subsequently prioritizing mitigation target sites. However, there exists no method that can reliably predict emission rates from detected plumes in real-time without ancillary data. Here, we trained a convolutional neural network model, called MethaNet, to predict methane point-source emission directly from high-resolution 2-D plume images without relying on other local measurements such as background wind speeds. Our results support the basis for the applicability of using deep learning techniques to quantify CH4 point sources in an automated manner over large geographical areas. MethaNet opens the way for real-time monitoring systems, not only for present and future airborne field campaigns but also for upcoming space-based observations in this decade.
Authors: Siraput Jongaramrungruang (Caltech)
Computer vision and remote sensing Carbon capture and sequestration Climate and Earth science Classification, regression, and supervised learning
ICML 2021 Tackling the Overestimation of Forest Carbon with Deep Learning and Aerial Imagery (Proposals Track)
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Abstract: Forest carbon offsets are increasingly popular and can play a significant role in financing climate mitigation, forest conservation, and reforestation. Measuring how much carbon is stored in forests is, however, still largely done via expensive, time-consuming, and sometimes unaccountable field measurements. To overcome these limitations, many verification bodies are leveraging machine learning (ML) algorithms to estimate forest carbon from satellite or aerial imagery. Aerial imagery allows for tree species or family classification, which improves on the satellite imagery-based forest type classification. However, aerial imagery is significantly more expensive to collect and it is unclear by how much the higher resolution improves the forest carbon estimation. This proposal paper describes the first systematic comparison of forest carbon estimation from aerial imagery, satellite imagery, and “ground-truth“ field measurements via deep learning-based algorithms for a tropical reforestation project. Our initial results show that forest carbon estimates from satellite imagery can overestimate above-ground biomass by more than 10-times for tropical reforestation projects. The significant difference between aerial and satellite-derived forest carbon measurements shows the potential for aerial imagery-based ML algorithms and raises the importance to extend this study to a global benchmark between options for carbon measurements.
Authors: Gyri Reiersen (TUM); David Dao (ETH Zurich); Björn Lütjens (MIT); Konstantin Klemmer (University of Warwick); Xiaoxiang Zhu (Technical University of Munich,Germany); Ce Zhang (ETH)
Carbon capture and sequestration Computer vision and remote sensing
ICML 2021 Learning Why: Data-Driven Causal Evaluations of Climate Models (Proposals Track)
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Abstract: We plan to use nascent data-driven causal discovery methods to find and compare causal relationships in observed data and climate model output. We will look at ten different features in the Arctic climate collected from public databases and from the Energy Exascale Earth System Model (E3SM). In identifying and comparing the resulting causal networks, we hope to find important differences between observed causal relationships and those in climate models. With these, climate modeling experts will be able to improve the coupling and parameterization of E3SM and other climate models.
Authors: Jeffrey J Nichol (University of New Mexico); Matthew Peterson (Sandia National Laboratories); George M Fricke (UNM); Kara Peterson (Sandia National Laboratories)
Climate and Earth science Causal and Bayesian methods
ICML 2021 Enhancing Laboratory-scale Flow Imaging of Fractured Geological Media with Deep Learning Super Resolution (Proposals Track)
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Abstract: Injection into deep geological formations is a promising approach for the utilization, sequestration, and removal from the atmosphere of CO2 emissions. Laboratory experiments are essential to characterize how CO2 flows and reacts in various types of geological media. We reproduce such dynamic injection processes while imaging using Computed Tomography (CT) at sufficient temporal resolution to visualize changes in the flow field. The resolution of CT, however, is on the order of 100's of micrometers and insufficient to characterize fine-scale reaction-induced alterations to micro-fractures. Super resolution deep learning is, therefore, an essential tool to improve spatial resolution of dynamic CT images. We acquired and processed pairs of multi-scale low- and high-resolution CT rock images. We also show the performance of our baseline model on fractured rock images using peak signal to noise ratio and structural similarity index. Coupling dynamic CT imaging with deep learning results in visualization with enhanced spatial resolution of about a factor of 4 thereby enabling improved interpretation.
Authors: Manju Pharkavi Murugesu (Stanford University); Timothy Anderson (Stanford University); Niccolo Dal Santo (MathWorks, Inc.); Vignesh Krishnan (The MathWorks Ltd); Anthony Kovscek (Stanford University)
Carbon capture and sequestration Climate and Earth science Computer vision and remote sensing Generative modeling Unsupervised and semi-supervised learning
ICML 2021 Forecasting emissions through Kaya identity using Neural ODEs (Proposals Track)
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Abstract: Starting from Kaya identity, we used a Neural ODE model to predict the evolution of several indicators related to carbon emissions, on a country-level : population, GDP per capita, energy intensity of GDP, carbon intensity of energy. We compared the model with a baseline statistical model - VAR - and obtained good performances. We conclude that this machine-learning approach can be used to produce a wide range of results and give relevant insight to policymakers.
Authors: Pierre Browne (Imperial College London)
Time-series analysis Climate policy Power and energy
ICML 2021 On the Role of Spatial Clustering Algorithms in Building Species Distribution Models from Community Science Data (Proposals Track) Best Paper: Proposals
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Abstract: This paper discusses opportunities for developments in spatial clustering methods to help leverage broad scale community science data for building species distribution models (SDMs). SDMs are tools that inform the science and policy needed to mitigate the impacts of climate change on biodiversity. Community science data span spatial and temporal scales unachievable by expert surveys alone, but they lack the structure imposed in smaller scale studies to allow adjustments for observational biases. Spatial clustering approaches can construct the necessary structure after surveys have occurred, but more work is needed to ensure that they are effective for this purpose. In this proposal, we describe the role of spatial clustering for realizing the potential of large biodiversity datasets, how existing methods approach this problem, and ideas for future work.
Authors: Mark Roth (Oregon State University); Tyler Hallman (Swiss Ornithological Institute); W. Douglas Robinson (Oregon State University); Rebecca Hutchinson (Oregon State University)
Ecosystems and natural systems Unsupervised and semi-supervised learning
ICML 2021 Machine Learning for Climate Change: Guiding Discovery of Sorbent Materials for Direct Air Capture of CO2 (Proposals Track)
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Abstract: The global climate crisis requires interdisciplinary collaboration. The same is true for making significant strides in materials discovery for direct air capture (DAC) of carbon dioxide (CO2). DAC is an emerging technology that captures CO2 directly from the atmosphere and it is part of the solution to achieving carbon neutrality by 2050. The proposed project is a collaborative effort that tackles climate change by using machine learning to guide scientists to novel, optimized, advanced sorbent materials for direct air capture of CO2. Immediate impacts will include high throughput machine learning tools for developing new, cost-effective CO2 sorption materials, and continued, expanded collaborations with potential domestic and international stakeholders.
Authors: Diana L Ortiz-Montalvo (NIST); Aaron Gilad Kusne (NIST); Austin McDannald (NIST); Daniel Siderius (NIST); Kamal Choudhary (NIST); Taner Yildirim (NIST)
Carbon capture and sequestration Active learning
ICML 2021 Reducing greenhouse gas emissions by optimizing room temperature set-points (Proposals Track)
Abstract and authors: (click to expand)
Abstract: We design a learning and optimization framework to mitigate greenhouse gas emissions associated with heating and cooling buildings. The framework optimizes room temperature set-points based on forecasts of weather, occupancy, and the greenhouse gas intensity of electricity. We compare two approaches: the first one combines a linear load forecasting model with convex optimization that offers a globally optimal solution, whereas the second one combines a nonlinear load forecasting model with nonconvex optimization that offers a locally optimal solution. The project explores the two approaches with a simulation testbed in EnergyPlus and experiments in university-campus buildings.
Authors: Yuan Cai (MIT); Subhro Das (MIT-IBM Watson AI Lab, IBM Research); Leslie Norford (Massachusetts Institute of Technology); Jeremy Gregory (Massachusetts Institute of Technology); Julia Wang (Massachusetts Institute of Technology); Kevin J Kircher (MIT); Jasmina Burek (Massachusetts Institute of Technology)
Buildings and cities Power and energy Classification, regression, and supervised learning Time-series analysis
ICML 2021 Deep learning network to project future Arctic ocean waves (Proposals Track)
Abstract and authors: (click to expand)
Abstract: The Arctic Ocean is warming at an alarming rate and will likely become ice-free in summer by mid-century. This will be accompanied by higher ocean surface waves, which pose a risk to coastal communities and marine operations. In order to develop climate change adaptation strategies, it is imperative to robustly assess the future changes in the Arctic ocean wave climate. This requires a large ensemble of regional ocean wave projections to properly capture the range of climate modeling uncertainty in the Arctic region. This has been proven challenging, as ocean wave information is typically not provided by climate models, ocean wave numerical modeling is computationally expensive, and most global wave climate ensembles exclude the Arctic region. Here we present a framework to develop a deep learning network based on CNN and LSTM which could be potentially used to obtain such a large ensemble of Arctic wave projections with an affordable cost.
Authors: Merce Casas Prat (Environment and Climate Change Canada); Lluis Castrejon (Mila, Université de Montréal, Facebook AI Research); Shady Moahmmed (University of Ottawa)
Climate and Earth science Computer vision and remote sensing
ICML 2021 Deep Learning for Spatiotemporal Anomaly Forecasting: A Case Study of Marine Heatwaves (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Spatiotemporal data have unique properties and require specific considerations. Forecasting spatiotemporal processes is a difficult task because the data are high-dimensional, often are limited in extent, and temporally correlated. Hence, we propose to evaluate several deep learning-based approaches that are relevant to spatiotemporal anomaly forecasting. We will use marine heatwaves as a case study. Those are observed around the world and have strong impacts on marine ecosystems. The evaluated deep learning methods will be integrated for the task of marine heatwave prediction in order to overcome the limitations of spatiotemporal data and improve data-driven seasonal marine heatwave forecasts.
Authors: Ding Ning (University of Canterbury); Varvara Vetrova (University of Canterbury); Karin Bryan (University of Waikato); Sébastien Delaux (Meteorological Service of New Zealand)
Classification, regression, and supervised learning Climate and Earth science
ICML 2021 Leveraging Domain Adaptation for Low-Resource Geospatial Machine Learning (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Machine learning in remote sensing has matured alongside a proliferation in availability and resolution of geospatial imagery, but its utility is bottlenecked by the need for labeled data. What's more, many labeled geospatial datasets are specific to certain regions, instruments, or extreme weather events. We investigate the application of modern domain-adaptation to multiple proposed geospatial benchmarks, uncovering unique challenges and proposing solutions to them.
Authors: John M Lynch (NC State University); Sam Wookey (Masterful AI)
Unsupervised and semi-supervised learning Ecosystems and natural systems Computer vision and remote sensing
ICML 2021 APPLYING TRANSFORMER TO IMPUTATION OF MULTI-VARIATE ENERGY TIME SERIES DATA (Proposals Track)
Abstract and authors: (click to expand)
Abstract: To reduce the greenhouse gas emissions from electricity production, it is necessaryto switch to an energy system based on renewable energy sources (RES). However,intermittent electricity generation from RES poses challenges for energy systems.The primary input for data-driven solutions is data on electricity generation fromRES, which usually contain many missing values. This proposal studies the useof attention-based algorithms to impute missing values of electricity production,electricity demand and electricity prices. Since attention mechanisms allow us totake into account dependencies between time series across multiple dimensionsefficiently, our approach goes beyond classic statistical methods and incorporatesmany related variables, such as electricity price, demand and production by othersources. Our preliminary results show that while transformers can come at highercomputational costs, they are more precise than classical imputation methods.
Authors: Hasan Ümitcan Yilmaz (Karlsruhe Institute of Technology); Max Kleinebrahm (Karlsruhe Institut für Technologie); Christopher Bülte (Karlsruhe Institute of Technology); Juan Gómez-Romero (Universidad de Granada)
Power and energy Time-series analysis Unsupervised and semi-supervised learning
NeurIPS 2020 Electric Vehicle Range Improvement by Utilizing Deep Learning to Optimize Occupant Thermal Comfort (Papers Track)
Abstract and authors: (click to expand)
Abstract: Heating, ventilation and air-conditioning (HVAC) systems can have a significant impact on the driving range of battery electric vehicles (EV’s). Predicting thermal comfort in an automotive vehicle cabin’s highly asymmetric and dynamic thermal environment is critical for developing energy-efficient HVAC systems. In this study we have coupled high-fidelity Computational Fluid Dynamics (CFD) simulations and Artificial Neural Networks (ANN) to predict vehicle occupant thermal comfort for any combination of steady-state boundary conditions. A vehicle cabin CFD model, validated against climatic wind tunnel measurements, was used to systematically generate training and test data that spanned the entire range of boundary conditions which impact occupant thermal comfort in an electric vehicle. Artificial neural networks (ANN) were applied to the simulation data to predict the overall Equivalent Homogeneous Temperature (EHT) comfort index for each occupant. An ensemble of five neural network models was able to achieve a mean absolute error of 2 ºC or less in predicting the overall EHT for all occupants in the vehicle on unseen or test data, which is acceptable for rapid evaluation and optimization of thermal comfort energy demand. The deep learning model developed in this work enables predictions of thermal comfort for any combination of steady-state boundary conditions in real-time without being limited by time-consuming and expensive CFD simulations or climatic wind tunnel tests. This model has been deployed as an easy-to-use web application within the organization for HVAC engineers to optimize thermal comfort energy demand and, thereby, driving range of electric vehicle programs.
Authors: Alok Warey (General Motors Global Research and Development); Shailendra Kaushik (General Motors Global Research and Development); Bahram Khalighi (General Motors Global Research and Development); Michael Cruse (Siemens Digital Industries Software); Ganesh Venkatesan (Siemens Digital Industries Software)
Transportation Classification, regression, and supervised learning
NeurIPS 2020 Is Africa leapfrogging to renewables or heading for carbon lock-in? A machine-learning-based approach to predicting success of power-generation projects (Papers Track)
Abstract and authors: (click to expand)
Abstract: Several extant energy-planning studies, comprising wide-ranging assumptions about the future, feature projections of Africa’s rapid transition in the next decade towards renewables-based power generation. Here, we develop a novel empirical approach to predicting medium-term generation mix that can complement traditional energy planning. Relying on the largest dataset on historic and planned power plants available for Africa, combined with country-level characteristics, we build a machine-learning-based model, using gradient boosted trees, that demonstrates high predictive performance. Training our model on past successful and failed projects, we find that the most relevant factors for commissioning are plant-level: capacity, fuel, ownership and grid connection type. We then apply the trained model to predict the realisation of the current project pipeline. Contrary to the rapid transition scenarios, our results show that the share of non-hydro renewables in generation is likely to remain below 10% in 2030, despite total generation more than doubling. These findings point to high carbon lock-in risks in Africa, highlighting the urgency to shift its pipeline of projects towards low-carbon energy and improve the realisation chances of renewable energy plants.
Authors: Galina Alova (University of Oxford); Philipp Trotter (University of Oxford); Alex Money (University of Oxford)
Power and energy Climate finance and economics Classification, regression, and supervised learning Interpretable ML
NeurIPS 2020 pymgrid: An Open-Source Python Microgrid Simulator for Applied Artificial Intelligence Research (Papers Track)
Abstract and authors: (click to expand)
Abstract: Microgrids – self-contained electrical grids that are capable of disconnecting from the main grid – hold potential in both tackling climate change mitigation via reducing CO$_2$ emissions and adaptation by increasing infrastructure resiliency. Due to their distributed nature, microgrids are often idiosyncratic; as a result, control of these systems is nontrivial. While microgrid simulators exist, many are limited in scope and in the variety of microgrids they can simulate. We propose \HL{pymgrid}, an open-source Python package to generate and simulate a large number of microgrids, and the first open-source tool that can generate more than 600 different microgrids. \HL{pymgrid} abstracts most of the domain expertise, allowing users to focus on control algorithms. In particular, \HL{pymgrid} is built to be a reinforcement learning (RL) platform, and includes the ability to model microgrids as Markov decision processes. \HL{pymgrid} also introduces two pre-computed list of microgrids, intended to allow for research reproducibility in the microgrid setting.
Authors: Gonzague Henri (Total); Tanguy Levent (Ecole Polytechnique); Avishai Halev (Total, UC Davis); Reda ALAMI (Total R&D); Philippe Cordier (Total S.A.)
Power and energy Reinforcement learning and control
NeurIPS 2020 Towards Optimal District Heating Temperature Control in China with Deep Reinforcement Learning (Papers Track)
Abstract and authors: (click to expand)
Abstract: Achieving efficiency gains in Chinese district heating networks, thereby reducing their carbon footprint, requires new optimal control methods going beyond current industry tools. Focusing on the secondary network, we propose a data-driven deep reinforcement learning (DRL) approach to address this task. We build a recurrent neural network, trained on simulated data, to predict the indoor temperatures. This model is then used to train two DRL agents, with or without expert guidance, for the optimal control of the supply water temperature. Our tests in a multi-apartment setting show that both agents can ensure a higher thermal comfort and at the same time a smaller energy cost, compared to an optimized baseline strategy.
Authors: Adrien Le Coz (EDF); Tahar Nabil (EDF); Francois Courtot (EDF)
Buildings and cities Reinforcement learning and control
NeurIPS 2020 Deep Reinforcement Learning in Electricity Generation Investment for the Minimization of Long-Term Carbon Emissions and Electricity Costs (Papers Track)
Abstract and authors: (click to expand)
Abstract: A change from a high-carbon emitting electricity power system to one based on renewables would aid in the mitigation of climate change. Decarbonization of the electricity grid would allow for low-carbon heating, cooling and transport. Investments in renewable energy must be made over a long time horizon to maximise return of investment of these long life power generators. Over these long time horizons, there exist multiple uncertainties, for example in future electricity demand and costs to consumers and investors. To mitigate for imperfect information of the future, we use the deep deterministic policy gradient (DDPG) deep reinforcement learning approach to optimize for a low-cost, low-carbon electricity supply using a modified version of the FTT:Power model. In this work, we model the UK and Ireland electricity markets. The DDPG algorithm is able to learn the optimum electricity mix through experience and achieves this between the years of 2017 and 2050. We find that a change from fossil fuels and nuclear power to renewables, based upon wind, solar and wave would provide a cheap and low-carbon alternative to fossil fuels.
Authors: Alexander J. M. Kell (Newcastle University); Pablo Salas (University of Cambridge); Jean-Francois Mercure (University of Exeter); Matthew Forshaw (Newcastle University); A. Stephen McGough (Newcastle University)
Power and energy Reinforcement learning and control
NeurIPS 2020 Short-Term Solar Irradiance Forecasting Using Calibrated Probabilistic Models (Papers Track)
Abstract and authors: (click to expand)
Abstract: Advancing probabilistic solar forecasting methods is essential to supporting the integration of solar energy into the electricity grid. In this work, we develop a variety of state-of-the-art probabilistic models for forecasting solar irradiance. We investigate the use of post-hoc calibration techniques for ensuring well-calibrated probabilistic predictions. We train and evaluate the models using public data from seven stations in the SURFRAD network, and demonstrate that the best model, NGBoost, achieves higher performance at an intra-hourly resolution than the best benchmark solar irradiance forecasting model across all stations. Further, we show that NGBoost with CRUDE post-hoc calibration achieves comparable performance to a numerical weather prediction model on hourly-resolution forecasting.
Authors: Eric Zelikman (Stanford University); Sharon Zhou (Stanford University); Jeremy A Irvin (Stanford); Cooper Raterink (Stanford University); Hao Sheng (Stanford University); Avati Anand (Stanford University); Jack Kelly (Open Climate Fix); Ram Rajagopal (Stanford University); Andrew Ng (Stanford University); David J Gagne (National Center for Atmospheric Research)
Power and energy Climate and Earth science Causal and Bayesian methods Uncertainty quantification and robustness
NeurIPS 2020 Deep Learning for Climate Model Output Statistics (Papers Track) Best ML Innovation
Abstract and authors: (click to expand)
Abstract: Climate models are an important tool for the assessment of prospective climate change effects but they suffer from systematic and representation errors, especially for precipitation. Model output statistics (MOS) reduce these errors by fitting the model output to observational data with machine learning. In this work, we explore the feasibility and potential of deep learning with convolutional neural networks (CNNs) for MOS. We propose the CNN architecture ConvMOS specifically designed for reducing errors in climate model outputs and apply it to the climate model REMO. Our results show a considerable reduction of errors and mostly improved performance compared to three commonly used MOS approaches.
Authors: Michael Steininger (University of Würzburg); Daniel Abel (University of Würzburg); Katrin Ziegler (University of Würzburg); Anna Krause (Universität Würzburg, Department of Computer Science, CHair X Data Science); Heiko Paeth (University of Würzburg); Andreas Hotho (Universitat Wurzburg)
Climate and Earth science Classification, regression, and supervised learning
NeurIPS 2020 A Temporally Consistent Image-based Sun Tracking Algorithm for Solar Energy Forecasting Applications (Papers Track)
Abstract and authors: (click to expand)
Abstract: Improving irradiance forecasting is critical to further increase the share of solar in the energy mix. On a short time scale, fish-eye cameras on the ground are used to capture cloud displacements causing the local variability of the electricity production. As most of the solar radiation comes directly from the Sun, current forecasting approaches use its position in the image as a reference to interpret the cloud cover dynamics. However, existing Sun tracking methods rely on external data and a calibration of the camera, which requires access to the device. To address these limitations, this study introduces an image-based Sun tracking algorithm to localise the Sun in the image when it is visible and interpolate its daily trajectory from past observations. We validate the method on a set of sky images collected over a year at SIRTA's lab. Experimental results show that the proposed method provides robust smooth Sun trajectories with a mean absolute error below 1% of the image size.
Authors: Quentin Paletta (University of Cambridge); Joan Lasenby (University of Cambridge)
Power and energy Classification, regression, and supervised learning Computer vision and remote sensing Time-series analysis
NeurIPS 2020 Characterization of Industrial Smoke Plumes from Remote Sensing Data (Papers Track)
Abstract and authors: (click to expand)
Abstract: The major driver of global warming has been identified as the anthropogenic release of greenhouse gas (GHG) emissions from industrial activities. The quantitative monitoring of these emissions is mandatory to fully understand their effect on the Earth’s climate and to enforce emission regulations on a large scale. In this work, we investigate the possibility to detect and quantify industrial smoke plumes from globally and freely available multi-band image data from ESA’s Sentinel-2 satellites. Using a modified ResNet-50, we can detect smoke plumes of different sizes with an accuracy of 94.3%. The model correctly ignores natural clouds and focuses on those imaging channels that are related to the spectral absorption from aerosols and water vapor, enabling the localization of smoke. We exploit this localization ability and train a U-Net segmentation model on a labeled sub-sample of our data, resulting in an Intersection-over-Union (IoU) metric of 0.608 and an overall accuracy for the detection of any smoke plume of 94.0%; on average, our model can reproduce the area covered by smoke in an image to within 5.6%. The performance of our model is mostly limited by occasional confusion with surface objects, the inability to identify semi-transparent smoke, and human limitations to properly identify smoke based on RGB-only images. Nevertheless, our results enable us to reliably detect and qualitatively estimate the level of smoke activity in order to monitor activity in industrial plants across the globe. Our data set and code base are publicly available.
Authors: Michael Mommert (University of St. Gallen); Mario Sigel (Sociovestix Labs Ltd.); Marcel Neuhausler (ISS Technology Innovation Lab); Linus M. Scheibenreif (University of St. Gallen); Damian Borth (University of St. Gallen)
Computer vision and remote sensing Industry
NeurIPS 2020 Learning the distribution of extreme precipitation from atmospheric general circulation model variables (Papers Track)
Abstract and authors: (click to expand)
Abstract: Precipitation extremes are projected to become more frequent and severe in a warming atmosphere over the coming decades. However, the accurate prediction of precipitation, in particular of extremes, remains a challenge for numerical weather prediction models. A large source of error are subgrid-scale parameterizations of processes that play a crucial role in the complex, multi-scale dynamics of precipitation, but are not explicitly resolved in the model formulation. Here we follow a hybrid, data-driven approach, in which atmospheric variables such as wind fields are forecast in time by a general circulation model (GCM) ensemble and then mapped to precipitation using a deep convolutional autoencoder. A frequency-based weighting of the loss function is introduced to improve the learning with regard to extreme values. Our results show an improved representation of extreme precipitation frequencies, as well as better error and correlation statistics compared to a state-of-the-art GCM ensemble.
Authors: Philipp Hess (Free University Berlin); Niklas Boers (Free University Berlin)
Climate and Earth science Hybrid physical models
NeurIPS 2020 Towards Tracking the Emissions of Every Power Plant on the Planet (Papers Track) Best Pathway to Impact
Abstract and authors: (click to expand)
Abstract: Greenhouse gases emitted from fossil-fuel-burning power plants are a major contributor to climate change. Current methods to track emissions from individual sources are expensive and only used in a few countries. While carbon dioxide concentrations can be measured globally using remote sensing, background fluctuations and low spatial resolution make it difficult to attribute emissions to individual sources. We use machine learning to infer power generation and emissions from visible and thermal power plant signatures in satellite images. By training on a data set of power plants for which we know the generation or emissions, we are able to apply our models globally. This paper demonstrates initial progress on this project by predicting whether a power plant is on or off from a single satellite image.
Authors: Heather D Couture (Pixel Scientia Labs); Joseph O'Connor (Carbon Tracker); Grace Mitchell (WattTime); Isabella Söldner-Rembold (Carbon Tracker); Durand D'souza (Carbon Tracker); Krishna Karra (WattTime); Keto Zhang (WattTime); Ali Rouzbeh Kargar (WattTime); Thomas Kassel (WattTime); Brian Goldman (Google); Daniel Tyrrell (Google); Wanda Czerwinski (Google); Alok Talekar (Google); Colin McCormick (Georgetown University)
Power and energy Classification, regression, and supervised learning Computer vision and remote sensing
NeurIPS 2020 Spatio-Temporal Learning for Feature Extraction inTime-Series Images (Papers Track)
Abstract and authors: (click to expand)
Abstract: Earth observation programs have provided highly useful information in global climate change research over the past few decades and greatly promoted its development, especially through providing biological, physical, and chemical parameters on a global scale. Programs such as Landsat, Sentinel, SPOT, and Pleiades can be used to acquire huge volume of medium to high resolution images every day. In this work, we organize these data in time series and we exploit both temporal and spatial information they provide to generate accurate and up-to-date land cover maps that can be used to monitor vulnerable areas threatened by the ongoing climatic and anthropogenic global changes. For this purpose, we combine a fully convolutional neural network with a convolutional long short-term memory. Implementation details of the proposed spatio-temporal neural network architecture are described. Examples are provided for the monitoring of roads and mangrove forests on the West African coast.
Authors: Gael Kamdem De Teyou (Huawei)
Agriculture, forestry and other land use Ecosystems and natural systems
NeurIPS 2020 Meta-modeling strategy for data-driven forecasting (Papers Track)
Abstract and authors: (click to expand)
Abstract: Accurately forecasting the weather is a key requirement for climate change mitigation. Data-driven methods offer the ability to make more accurate forecasts, but lack interpretability and can be expensive to train and deploy if models are not carefully developed. Here, we make use of two historical climate data sets and tools from machine learning, to accurately predict temperature fields. Furthermore, we are able to use low fidelity models that are cheap to train and evaluate, to selectively avoid expensive high fidelity function evaluations, as well as uncover seasonal variations in predictive power. This allows for an adaptive training strategy for computationally efficient geophysical emulation.
Authors: Dominic J Skinner (MIT); Romit Maulik (Argonne National Laboratory)
Climate and Earth science Interpretable ML Time-series analysis
NeurIPS 2020 Short-term prediction of photovoltaic power generation using Gaussian process regression (Papers Track)
Abstract and authors: (click to expand)
Abstract: Photovoltaic (PV) power is affected by weather conditions, making the power generated from the PV systems uncertain. Solving this problem would help improve the reliability and cost effectiveness of the grid, and could help reduce reliance on fossil fuel plants. The present paper focuses on evaluating predictions of the energy generated by PV systems in the United Kingdom using Gaussian process regression (GPR). Gaussian process regression is a Bayesian non-parametric model that can provide predictions along with the uncertainty in the predicted value, which can be very useful in applications with a high degree of uncertainty. The model is evaluated for short-term forecasts of 48 hours against three main factors – training period, sky area coverage and kernel model selection – and for very short-term forecasts of four hours against sky area. We also compare very short-term forecasts in terms of cloud coverage within the prediction period and only initial cloud coverage as a predictor.
Authors: Yahya Hasan Al Lawati (Queen Mary University of London); Jack Kelly (Open Climate Fix); Dan Stowell (Queen Mary University of London)
Classification, regression, and supervised learning Causal and Bayesian methods
NeurIPS 2020 Formatting the Landscape: Spatial conditional GAN for varying population in satellite imagery (Papers Track)
Abstract and authors: (click to expand)
Abstract: Climate change is expected to reshuffle the settlement landscape: forcing people in affected areas to migrate, to change their lifeways, and continuing to affect demographic change throughout the world. Changes to the geographic distribution of population will have dramatic impacts on land use and land cover and thus constitute one of the major challenges of planning for climate change scenarios. In this paper, we explore a generative model framework for generating satellite imagery conditional on gridded population distributions. We make additions to the existing ALAE [30] architecture, creating a spatially conditional version: SCALAE. This method allows us to explicitly disentangle population from the model’s latent space and thus input custom population forecasts into the generated imagery. We postulate that such imagery could then be directly used for land cover and land use change estimation using existing frameworks, as well as for realistic visualisation of expected local change. We evaluate the model by comparing pixel and semantic reconstructions, as well as calculate the standard FID metric. The results suggest the model captures population distributions accurately and delivers a controllable method to generate realistic satellite imagery.
Authors: Tomas Langer (Intuition Machines); Natalia Fedorova (Max Planck Institute for Evolutionary Anthropology); Ron Hagensieker (Osir.io)
Generative modeling Behavioral and social science Buildings and cities Societal adaptation Computer vision and remote sensing
NeurIPS 2020 Storing Energy with Organic Molecules: Towards a Metric for Improving Molecular Performance for Redox Flow Batteries (Papers Track)
Abstract and authors: (click to expand)
Abstract: Energy storage is an important tool in the decarbonization of energy systems, particularly when coupled with intermittent forms of energy. However, storage technologies are still not commercially competitive to garner mainstream adoption. This work focuses on the cost reduction of organic redox flow batteries (ORFBs) via materials discovery. We identify macroscopic metrics of interest to optimize for lowering their cost and relate them to the molecular properties of the materials involved. Furthermore, we consolidate a benchmark set of experimental data for building predictive models for these materials properties. Building more accurate models will aid practitioners in the rational design of new ORFB.
Authors: Luis M Mejia Mendoza (University of Toronto); Alan Aspuru-Guzik (Harvard University); Martha Flores Leonar (University of Toronto)
Classification, regression, and supervised learning Other Meta- and transfer learning
NeurIPS 2020 Predicting Landsat Reflectance with Deep Generative Fusion (Papers Track)
Abstract and authors: (click to expand)
Abstract: Public satellite missions are commonly bound to a trade-off between spatial and temporal resolution as no single sensor provides fine-grained acquisitions with frequent coverage. This hinders their potential to assist vegetation monitoring or humanitarian actions, which require detecting rapid and detailed terrestrial surface changes. In this work, we probe the potential of deep generative models to produce high-resolution optical imagery by fusing products with different spatial and temporal characteristics. We introduce a dataset of co-registered Moderate Resolution Imaging Spectroradiometer (MODIS) and Landsat surface reflectance time series and demonstrate the ability of our generative model to blend coarse daily reflectance information into low-paced finer acquisitions. We benchmark our proposed model against state-of-the-art reflectance fusion algorithms.
Authors: Shahine Bouabid (University of Oxford); Jevgenij Gamper (Cervest Ltd.)
Generative modeling Agriculture, forestry and other land use Computer vision and remote sensing
NeurIPS 2020 Quantitative Assessment of Drought Impacts Using XGBoost based on the Drought Impact Reporter (Papers Track)
Abstract and authors: (click to expand)
Abstract: Under climate change, the increasing frequency, intensity, and spatial extent of drought events lead to higher socio-economic costs. However, the relationships between the hydro-meteorological indicators and drought impacts are not identified well yet because of the complexity and data scarcity. In this paper, we proposed a framework based on the extreme gradient model (XGBoost) for Texas to predict multi-category drought impacts and connected a typical drought indicator, Standardized Precipitation Index (SPI), to the text-based impacts from the Drought Impact Reporter (DIR). The preliminary results of this study showed an outstanding performance of the well-trained models to assess drought impacts on agriculture, fire, society & public health, plants & wildlife, as well as relief, response & restrictions in Texas. It also provided a possibility to appraise drought impacts using hydro-meteorological indicators with the proposed framework in the United States, which could help drought risk management by giving additional information and improving the updating frequency of drought impacts. Our interpretation results using the Shapley additive explanation (SHAP) interpretability technique revealed that the rules guiding the predictions of XGBoost comply with domain expertise knowledge around the role that SPI indicators play around drought impacts.
Authors: Beichen Zhang (University of Nebraska-Lincoln); Fatima K Abu Salem (American University of Beirut); Michael Hayes (University of Nebraska-Lincoln); Tsegaye Tadesse (University of Nebraska-Lincoln)
Disaster prediction, management, and relief Interpretable ML
NeurIPS 2020 Estimating Forest Ground Vegetation Cover From Nadir Photographs Using Deep Convolutional Neural Networks (Papers Track)
Abstract and authors: (click to expand)
Abstract: Forest fires, such as those on the US west coast in September 2020, are an important factor in climate change. Wildfire modeling and mitigation require mapping vegetation ground cover over large plots of land. The current forestry practice is to send out human ground crews to collect photos of the forest floor at precisely determined locations, then manually calculate the percent cover of ground fuel types. In this work, we propose automating this process using a supervised learning-based deep convolutional neural network to perform image segmentation. Experimental results on a real dataset show this approach delivers very promising performance.
Authors: Pranoy Panda (Indian Institute of Technology, Hyderabad); Martin Barczyk (University of Alberta); Jen Beverly (University of Alberta)
Agriculture, forestry and other land use Classification, regression, and supervised learning
NeurIPS 2020 A Machine Learning Approach to Methane Emissions Mitigation in the Oil and Gas Industry (Papers Track) Overall Best Paper
Abstract and authors: (click to expand)
Abstract: Reducing methane emissions from the oil and gas sector is a key component of climate policy in the United States. Methane leaks across the supply chain are stochastic and intermittent, with a small number of sites (‘super-emitters’) responsible for a majority of emissions. Thus, cost-effective emissions reduction critically relies on effectively identifying the super-emitters from thousands of well-sites and millions of miles of pipelines. Conventional approaches such as walking surveys using optical gas imaging technology are slow and time-consuming. In addition, several variables contribute to the formation of leaks such as infrastructure age, production, weather conditions, and maintenance practices. Here, we develop a machine learning algorithm to predict high-emitting sites that can be prioritized for follow-up repair. Such prioritization can significantly reduce the cost of surveys and increase emissions reductions compared to conventional approaches. Our results show that the algorithm using logistic regression performs the best out of several algorithms. The model achieved a 70% accuracy rate with a 57% recall and a 66% balanced accuracy rate. Compared to the conventional approach, the machine learning model reduced the time to achieve a 50% emissions mitigation target by 42%. Correspondingly, the mitigation cost reduced from $85/t CO2e to$49/t CO2e.
Authors: Jiayang Wang (Harrisburg University); Selvaprabu Nadarajah (University of Illinois at Chicago); Jingfan Wang (Stanford University); Arvind Ravikumar (Harrisburg University)
Power and energy Classification, regression, and supervised learning
NeurIPS 2020 Monitoring the Impact of Wildfires on Tree Species with Deep Learning (Papers Track)
Abstract and authors: (click to expand)
Abstract: One of the impacts of climate change is the difficulty of tree regrowth after wildfires over areas that traditionally were covered by certain tree species. Here a deep learning model is customized to classify land covers from four-band aerial imagery before and after wildfires to study the prolonged consequences of wildfires on tree species. The tree species labels are generated from manually delineated maps for five land cover classes: Conifer, Hardwood, Shrub, ReforestedTree, and Barren land. With an accuracy of 92% on the test split, the model is applied to three wildfires on data from 2009 to 2018. The model accurately delineates areas damaged by wildfires, changes in tree species, and regrowth in burned areas. The result shows clear evidence of wildfires impacting the local ecosystem and the outlined approach can help monitor reforested areas, observe changes in forest composition, and track wildfire impact on tree species.
Authors: Wang Zhou (IBM Research); Levente Klein (IBM Research)
Agriculture, forestry and other land use Disaster prediction, management, and relief Computer vision and remote sensing
NeurIPS 2020 ForestNet: Classifying Drivers of Deforestation in Indonesia using Deep Learning on Satellite Imagery (Papers Track)
Abstract and authors: (click to expand)
Abstract: Characterizing the processes leading to deforestation is critical to the development and implementation of targeted forest conservation and management policies. In this work, we develop a deep learning model called ForestNet to classify the drivers of primary forest loss in Indonesia, a country with one of the highest deforestation rates in the world. Using satellite imagery, ForestNet identifies the direct drivers of deforestation in forest loss patches of any size. We curate a dataset of Landsat 8 satellite images of known forest loss events paired with driver annotations from expert interpreters. We use the dataset to train and validate the models and demonstrate that ForestNet substantially outperforms other standard driver classification approaches. In order to support future research on automated approaches to deforestation driver classification, the dataset curated in this study is publicly available at https://stanfordmlgroup.github.io/projects/forestnet .
Authors: Jeremy A Irvin (Stanford); Hao Sheng (Stanford University); Neel Ramachandran (Stanford University); Sonja Johnson-Yu (Stanford University); Sharon Zhou (Stanford University); Kyle Story (Descartes Labs); Rose Rustowicz (Descartes Labs); Cooper Elsworth (Descartes Labs); Kemen Austin (RTI International); Andrew Ng (Stanford University)
Agriculture, forestry and other land use Computer vision and remote sensing
NeurIPS 2020 Mangrove Ecosystem Detection using Mixed-Resolution Imagery with a Hybrid-Convolutional Neural Network (Papers Track)
Abstract and authors: (click to expand)
Abstract: Mangrove forests are rich in biodiversity and are a large contributor to carbon sequestration critical in the fight against climate change. However, they are currently under threat from anthropogenic activities, so monitoring their health, extent, and productivity is vital to our ability to protect these important ecosystems. Traditionally, lower resolution satellite imagery or high resolution unmanned air vehicle (UAV) imagery has been used independently to monitor mangrove extent, both offering helpful features to predict mangrove extent. To take advantage of both of these data sources, we propose the use of a hybrid neural network, which combines a Convolutional Neural Network (CNN) feature extractor with a Multilayer-Perceptron (MLP), to accurately detect mangrove areas using both medium resolution satellite and high resolution drone imagery. We present a comparison of our novel Hybrid CNN with algorithms previously applied to mangrove image classification on a data set we collected of dwarf mangroves from consumer UAVs in Baja California Sur, Mexico, and show a 95\% intersection over union (IOU) score for mangrove image classification, outperforming all our baselines.
Authors: Dillon Hicks (Engineers for Exploration); Ryan Kastner (University of California San Diego); Curt Schurgers (University of California San Diego); Astrid Hsu (University of California San Diego); Octavio Aburto (University of California San Diego)
Computer vision and remote sensing Carbon capture and sequestration Ecosystems and natural systems Agriculture, forestry and other land use Classification, regression, and supervised learning
NeurIPS 2020 Context-Aware Urban Energy Efficiency Optimization Using Hybrid Physical Models (Papers Track)
Abstract and authors: (click to expand)
Abstract: Buildings produce more U.S. greenhouse gas emissions through electricity generation than any other economic sector. To improve the energy efficiency of buildings, engineers often rely on physics-based building simulations to predict the impacts of retrofits in individual buildings. In dense urban areas, these models suffer from inaccuracy due to imprecise parameterization or external, unmodeled urban context factors such as inter-building effects and urban microclimates. In a case study of approximately 30 buildings in Sacramento, California, we demonstrate how our hybrid physics-driven deep learning framework can use these external factors advantageously to identify a more optimal energy efficiency retrofit installation strategy and achieve significant savings in both energy and cost.
Authors: Benjamin Choi (Stanford University); Alex Nutkiewicz (Stanford University); Rishee Jain (Stanford University)
Hybrid physical models Buildings and cities
NeurIPS 2020 Deep learning architectures for inference of AC-OPF solutions (Papers Track)
Abstract and authors: (click to expand)
Abstract: We present a systematic comparison between neural network (NN) architectures for inference of AC-OPF solutions. Using fully connected NNs as a baseline we demonstrate the efficacy of leveraging network topology in the models by constructing abstract representations of electrical grids in the graph domain, for both convolutional and graph NNs. The performance of the NN architectures is compared for regression (predicting optimal generator set-points) and classification (predicting the active set of constraints) settings. Computational gains for obtaining optimal solutions are also presented.
Authors: Thomas Falconer (University College London); Letif Mones (Invenia Labs)
Classification, regression, and supervised learning Power and energy
NeurIPS 2020 Predicting the Solar Potential of Rooftops using Image Segmentation and Structured Data (Papers Track)
Abstract and authors: (click to expand)
Abstract: Estimating the amount of electricity that can be produced by rooftop photovoltaic systems is a time-consuming process that requires on-site measurements, a difficult task to achieve on a large scale. In this paper, we present an approach to estimate the solar potential of rooftops based on their location and architectural characteristics, as well as the amount of solar radiation they receive annually. Our technique uses computer vision to achieve semantic segmentation of roof sections and roof objects on the one hand, and a machine learning model based on structured building features to predict roof pitch on the other hand. We then compute the azimuth and maximum number of solar panels that can be installed on a rooftop with geometric approaches. Finally, we compute precise shading masks and combine them with solar irradiation data that enables us to estimate the yearly solar potential of a rooftop.
Authors: Daniel de Barros Soares (nam.R); François ANDRIEUX (nam.R); Bastien HELL (nam.R); Julien LENHARDT (nam.R; ENSTA); JORDI BADOSA (Ecole Polytechnique); Sylvain GAVOILLE (nam.R); Stéphane GAIFFAS (nam.R; LPSM (Université de Paris)); Emmanuel BACRY (nam.R; CEREMADE (Université Paris Dauphine, PSL))
Buildings and cities Power and energy Classification, regression, and supervised learning Computer vision and remote sensing
NeurIPS 2020 Revealing the Oil Majors' Adaptive Capacity to the Energy Transition with Deep Multi-Agent Reinforcement Learning (Papers Track)
Abstract and authors: (click to expand)
Abstract: A low-carbon energy transition is transpiring to combat climate change, posing an existential threat to oil and gas companies, particularly the Majors. Though Majors yield the resources and expertise to adapt to low-carbon business models, meaningful climate-aligned strategies have yet to be enacted. A 2-degrees pathways (2DP) wargame was developed to assess climate-compatible pathways for the oil Majors. Recent advances in deep multi-agent reinforcement learning (MARL) have achieved superhuman-level performance in solving high-dimensional continuous control problems. Modeling within a Markovian framework, we present the novel 2DP-MARL model which applies deep MARL methods to solve the 2DP wargame across a multitude of transition scenarios. Designed to best mimic Majors in real- life competition, the model reveals all Majors quickly adapt to low-carbon business models to remain robust amidst energy transition uncertainty. The purpose of this work is provide tangible metrics to support the call for oil Majors to diversify into low-carbon business models and, thus, accelerate the energy transition.
Authors: Dylan Radovic (Imperial College London); Lucas Kruitwagen (University of Oxford); Christian Schroeder de Witt (University of Oxford)
Industry Climate finance and economics Reinforcement learning and control Uncertainty quantification and robustness
NeurIPS 2020 Quantifying the presence of air pollutants over a road network in high spatio-temporal resolution (Papers Track)
Abstract and authors: (click to expand)
Abstract: Monitoring air pollution plays a key role when trying to reduce its impact on the environment and on human health. Traditionally, two main sources of information about the quantity of pollutants over a city are used: monitoring stations at ground-level (when available), and satellites' remote sensing. In addition to these two, other methods have been developed in the last years that aim at understanding how traffic emissions behave in space and time at a finer scale, taking into account the human mobility patterns. We present a simple and versatile framework for estimating the quantity of four air pollutants (CO2, NOx, PM, VOC) emitted by private vehicles moving on a road network, starting from raw GPS traces and information about vehicles' fuel type, and use this framework for analyses on how such pollutants distribute over the road networks of different cities.
Authors: Matteo Bohm (Sapienza University of Rome); Mirco Nanni (ISTI-CNR Pisa, Italy); Luca Pappalardo (ISTI)
Transportation Data mining
NeurIPS 2020 Annual and in-season mapping of cropland at field scale with sparse labels (Papers Track)
Abstract and authors: (click to expand)
Abstract: Spatial information about where crops are being grown, known as cropland maps, are critical inputs for analyses and decision-making related to food security and climate change. Despite a widespread need for readily-updated annual and in-season cropland maps at the management (field) scale, these maps are unavailable for most regions at risk of food insecurity. This is largely due to lack of in-situ labels for training and validating machine learning classifiers. Previously, we developed a method for binary classification of cropland that learns from sparse local labels and abundant global labels using a multi-headed LSTM and time-series multispectral satellite inputs over one year. In this work, we present a new method that uses an autoregressive LSTM to classify cropland during the growing season (i.e., partially-observed time series). We used these methods to produce publicly-available 10m-resolution cropland maps in Kenya for the 2019-2020 and 2020-2021 growing seasons. These are the highest-resolution and most recent cropland maps publicly available for Kenya. These methods and associated maps are critical for scientific studies and decision-making at the intersection of food security and climate change.
Authors: Gabriel Tseng (NASA Harvest); Hannah R Kerner (University of Maryland); Catherine L Nakalembe (University of Maryland); Inbal Becker-Reshef (University of Maryland)
Agriculture, forestry and other land use Computer vision and remote sensing
NeurIPS 2020 NightVision: Generating Nighttime Satellite Imagery from Infra-Red Observations (Papers Track)
Abstract and authors: (click to expand)
Abstract: The recent explosion in applications of machine learning to satellite imagery often rely on visible images and therefore suffer from a lack of data during the night. The gap can be filled by employing available infra-red observations to generate visible images. This work presents how Deep Learning can be applied successfully to create those images by using U-Net based architectures. The proposed methods show promising results, achieving a structural similarity index (SSIM) up to 86\% on an independent test set and providing visually convincing output images, generated from infra-red observations.
Authors: Paula Harder (Fraunhofer ITWM); William Jones (University of Oxford); Redouane Lguensat (LSCE-IPSL); Shahine Bouabid (University of Oxford); James Fulton (University of Edinburgh); Dánnell Quesada-Chacón (Technische Universität Dresden); Aris Marcolongo (University of Bern); Sofija Stefanovic (University of Oxford); Yuhan Rao (North Carolina Institute for Climate Studies); Peter Manshausen (University of Oxford); Duncan Watson-Parris (University of Oxford)
Computer vision and remote sensing Climate and Earth science Generative modeling
NeurIPS 2020 Analyzing Sustainability Reports Using Natural Language Processing (Papers Track)
Abstract and authors: (click to expand)
Abstract: Climate change is a far-reaching, global phenomenon that will impact many aspects of our society, including the global stock market. In recent years, companies have increasingly been aiming to both mitigate their environmental impact and adapt their practices the changing climate context. This is reported via increasingly exhaustive reports, which cover many types of sustainability measures, often under the umbrella of Environmental, Social, and Governance (ESG) disclosures. However, given this abundance of data, sustainability analysts are obliged to comb through hundreds of pages of reports in order to find relevant information. We have leveraged recent progress in Natural Language Processing (NLP) to create a custom model, ClimateQA, which allows the analysis of financial reports in order to identify climate-relevant sections using a question answering approach. We present this tool and the methodology that we used to develop it in the present article.
Authors: Sasha Luccioni (Mila); Emi Baylor (McGill); Nicolas Duchene (Universite de Montreal)
Climate finance and economics Natural language processing
NeurIPS 2020 Automated Identification of Oil Field Features using CNNs (Papers Track)
Abstract and authors: (click to expand)
Abstract: Oil and gas production sites have been identified as a major source of anthropogenic methane emissions. Emissions studies utilize counts of equipment to estimate emissions from production facilities. However these counts are poorly documented, including both information about well pad locations and major equipment on each well pad. While these data can be found by manually reviewing satellite imagery, it is prohibitively difficult and time consuming. This work, part of a larger study of methane emission studies in Colorado, US, adapted a machine learning (ML) algorithm to detect well pads and associated equipment. Our initial model showed an average well pad detection accuracy of 95% on the Denver-Julesburg (DJ) basin in northeastern Colorado. Our example demonstrates the potential for this type of automated detection from satellite imagery, leading to more accurate and complete models of production emissions.
Authors: SONU DILEEP (Colorado State University); Daniel Zimmerle (Colorado State University); Ross Beveridge (CSU); Timothy Vaughn (Colorado State University)
Climate and Earth science Computer vision and remote sensing
NeurIPS 2020 Using attention to model long-term dependencies in occupancy behavior (Papers Track)
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Abstract: Over the past years, more and more models have been published that aim to capture relationships in human residential behavior. Most of these models are different Markov variants or regression models that have a strong assumption bias and are therefore unable to capture complex long-term dependencies and the diversity in occupant behavior. This work shows that attention based models are able to capture complex long-term dependencies in occupancy behavior and at the same time adequately depict the diversity in behavior across the entire population and different socio-demographic groups. By combining an autoregressive generative model with an imputation model, the advantages of two data sets are combined and new data are generated which are beneficial for multiple use cases (e.g. generation of consistent household energy demand profiles). The two step approach generates synthetic activity schedules that have similar statistical properties as the empirical collected schedules and do not contain direct information about single individuals. Therefore, the presented approach forms the basis to make data on occupant behavior freely available, so that further investigations based on the synthetic data can be carried out without a large data application effort. In future work it is planned to take interpersonal dependencies into account in order to be able to generate entire household behavior profiles.
Authors: Max Kleinebrahm (Karlsruhe Institut für Technologie); Jacopo Torriti (University Reading); Russell McKenna (University of Aberdeen); Armin Ardone (Karlsruhe Institut für Technologie); Wolf Fichtner (Karlsruhe Institute of Technology)
Behavioral and social science Buildings and cities Power and energy Transportation Natural language processing Time-series analysis
NeurIPS 2020 Street to Cloud: Improving Flood Maps With Crowdsourcing and Semantic Segmentation (Papers Track)
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Abstract: To address the mounting destruction caused by floods in climate-vulnerable regions, we propose Street to Cloud, a machine learning pipeline for incorporating crowdsourced ground truth data into the segmentation of satellite imagery of floods. We propose this approach as a solution to the labor-intensive task of generating high-quality, hand-labeled training data, and demonstrate successes and failures of different plausible crowdsourcing approaches in our model. Street to Cloud leverages community reporting and machine learning to generate novel, near-real time insights into the extent of floods to be used for emergency response.
Authors: Veda Sunkara (Cloud to Street); Matthew Purri (Rutgers University); Bertrand Le Saux (European Space Agency (ESA)); Jennifer Adams (European Space Agency (ESA))
Disaster prediction, management, and relief Computer vision and remote sensing
NeurIPS 2020 Accurate river level predictions using a Wavenet-like model (Papers Track)
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Abstract: The effects of climate change on river levels are noticeable through a higher occurrence of floods with disastrous social and economic impacts. As such, river level forecasting is essential in flood mitigation, infrastructure management and secure shipping. Historical records of river levels and influencing factors such as rainfall or soil conditions are used for predicting future river levels. The current state-of-the-art time-series prediction model is the LSTM network, a recurrent neural network. In this work we study the efficiency of convolutional models, and specifically the WaveNet model in forecasting one-day ahead river levels. We show that the additional benefit of the WaveNet model is the computational ease with which other input features can be included in the predictions of river stage and river flow. The conditional WaveNet models outperformed conditional LSTM models for river level prediction by capturing short-term, non-linear dependencies between input data. Furthermore, the Wavenet model offers a faster computation time, stable results and more possibilities for fine-tuning.
Authors: Shannon Doyle (UvA); Anastasia Borovykh (Imperial College London)
Disaster prediction, management, and relief Other Classification, regression, and supervised learning
NeurIPS 2020 Movement Tracks for the Automatic Detection of Fish Behavior in Videos (Papers Track)
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Abstract: Global warming is predicted to profoundly impact ocean ecosystems. Fish behavior is an important indicator of changes in such marine environments. Thus, the automatic identification of key fish behavior in videos represents a much needed tool for marine researchers, enabling them to study climate change-related phenomena. We offer a dataset of sablefish (Anoplopoma fimbria) startle behaviors in underwater videos, and investigate the use of deep learning (DL) methods for behavior detection on it. Our proposed detection system identifies fish instances using DL-based frameworks, determines trajectory tracks, derives novel behavior-specific features, and employs Long Short-Term Memory (LSTM) networks to identify startle behavior in sablefish. Its performance is studied by comparing it with a state-of-the-art DL-based video event detector.
Authors: Declan GD McIntosh (University Of Victoria); Tunai Porto Marques (University of Victoria); Alexandra Branzan Albu (University of Victoria); Rodney Rountree (University of Victoria); Fabio De Leo Cabrera (Ocean Networks Canada)
Computer vision and remote sensing Ecosystems and natural systems Other Classification, regression, and supervised learning Time-series analysis
NeurIPS 2020 Counting Cows: Tracking Illegal Cattle Ranching From High-Resolution Satellite Imagery (Papers Track)
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Abstract: Cattle farming is responsible for 8.8\% of greenhouse gas emissions worldwide. In addition to the methane emitted due to their digestive process, the growing need for grazing areas is an important driver of deforestation. While some regulations are in place for preserving the Amazon against deforestation, these are being flouted in various ways. Hence the need to scale and automate the monitoring of cattle ranching activities. Through a partnership with \textit{Anonymous under review}, we explore the feasibility of tracking and counting cattle at the continental scale from satellite imagery. With a license from Maxar Technologies, we obtained satellite imagery of the Amazon at 40cm resolution, and compiled a dataset of 903 images containing a total of 28498 cattle. Our experiments show promising results and highlight important directions for the next steps on both counting algorithms and the data collection processes for solving such challenges.
Authors: Issam Hadj Laradji (Element AI); Pau Rodriguez (Element AI); Alfredo Kalaitzis (University of Oxford); David Vazquez (Element AI); Ross Young (Element AI); Ed Davey (Global Witness); Alexandre Lacoste (Element AI)
Computer vision and remote sensing Agriculture, forestry and other land use Climate and Earth science Ecosystems and natural systems
NeurIPS 2020 RainBench: Enabling Data-Driven Precipitation Forecasting on a Global Scale (Papers Track)
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Abstract: Climate change is expected to aggravate extreme precipitation events, directly impacting the livelihood of millions. Without a global precipitation forecasting system in place, many regions -- especially those constrained in resources to collect expensive groundstation data -- are left behind. To mitigate such unequal reach of climate change, a solution is to alleviate the reliance on numerical models (and by extension groundstation data) by enabling machine-learning-based global forecasts from satellite imagery. Though prior works exist in regional precipitation nowcasting, there lacks work in global, medium-term precipitation forecasting. Importantly, a common, accessible baseline for meaningful comparison is absent. In this work, we present RainBench, a multi-modal benchmark dataset dedicated to advancing global precipitation forecasting. We establish baseline tasks and release PyRain, a data-handling pipeline to enable efficient processing of decades-worth of data by any modeling framework. Whilst our work serves as a basis for a new chapter on global precipitation forecast from satellite imagery, the greater promise lies in the community joining forces to use our released datasets and tools in developing machine learning approaches to tackle this important challenge.
Authors: Catherine Tong (University of Oxford); Christian A Schroeder de Witt (University of Oxford); Valentina Zantedeschi (GE Global Research); Daniele De Martini (University of Oxford); Alfredo Kalaitzis (University of Oxford); Matthew Chantry (University of Oxford); Duncan Watson-Parris (University of Oxford); Piotr Bilinski (University of Warsaw / University of Oxford)
Climate and Earth science Classification, regression, and supervised learning
NeurIPS 2020 Machine learning for advanced solar cell production: adversarial denoising, sub-pixel alignment and the digital twin (Papers Track)
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Abstract: Photovoltaic is a main pillar to achieve the transition towards a renewable energy supply. In order to continue the tremendous cost decrease of the last decades, novel cell techologies and production processes are implemented into mass production to improve cell efficiency. Raising their full potential requires novel techniques of quality assurance and data analysis. We present three use-cases along the value chain where machine learning techniques are investigated for quality inspection and process optimization: Adversarial learning to denoise wafer images, alignment of surface structuring processes via sub-pixel coordinate regression, and the development of a digital twin for wafers and solar cells for material and process analysis.
Authors: Matthias Demant (Fraunhofer ISE); Leslie Kurumundayil (Fraunhofer ISE); Philipp Kunze (Fraunhofer ISE); Aditya Kovvali (Fraunhofer ISE); Alexandra Woernhoer (Fraunhofer ISE); Stefan Rein (Fraunhofer ISE)
Power and energy Industry Classification, regression, and supervised learning Computer vision and remote sensing Unsupervised and semi-supervised learning
NeurIPS 2020 Climate Change Driven Crop Yield Failures (Papers Track)
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Abstract: The effect of extreme temperatures, precipitation and variations in other meteorological factors affect crop yields, and hence climate change jeopardizes the entire food supply chain and dependent economic activities. We utilize Deep Neural Networks and Gaussian Processes for understanding crop yields as functions of climatological variables, and use change detection techniques to identify climatological thresholds where yield drops significantly.
Authors: Somya Sharma (U. Minnesota); Deepak Ray (University of Minnesota); Snigdhansu Chatterjee (University of Minnesota)
Agriculture, forestry and other land use Spatial deep learning
NeurIPS 2020 Physics-constrained Deep Recurrent Neural Models of Building Thermal Dynamics (Papers Track)
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Abstract: We develop physics-constrained and control-oriented predictive deep learning models for the thermal dynamics of a real-world commercial office building. The proposed method is based on the systematic encoding of physics-based prior knowledge into a structured recurrent neural architecture. Specifically, our model mimics the structure of the building thermal dynamics model and leverages penalty methods to model inequality constraints. Additionally, we use constrained matrix parameterization based on the Perron-Frobenius theorem to bound the eigenvalues of the learned network weights. We interpret the stable eigenvalues as dissipativeness of the learned building thermal model. We demonstrate the effectiveness of the proposed approach on a dataset obtained from an office building with 20 thermal zones.
Authors: Jan Drgona (Pacific Northwest National Laboratory); Aaron R Tuor (Pacific Northwest National Laboratory); Vikas Chandan (PNNL); Draguna Vrabie (PNNL)
Hybrid physical models Buildings and cities
NeurIPS 2020 Narratives and Needs: Analyzing Experiences of Cyclone Amphan Using Twitter Discourse (Papers Track)
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Abstract: People often turn to social media to comment upon and share information about major global events. Accordingly, social media is receiving increasing attention as a rich data source for understanding people's social, political and economic experiences of extreme weather events. In this paper, we contribute two novel methodologies that leverage Twitter discourse to characterize narratives and identify unmet needs in response to Cyclone Amphan, which affected 18 million people in May 2020.
Authors: Ancil S Crayton (Booz Allen Hamilton); Joao Fonseca (NOVA Information Management School); Kanav Mehra (Independent Researcher); Jared Ross (Booz Allen Hamilton); Marcelo Sandoval-Castañeda (New York University Abu Dhabi); Michelle Ng (International Water Management Institute); Rachel von Gnechten (International Water Management Institute)
Disaster prediction, management, and relief Natural language processing Other Unsupervised and semi-supervised learning
NeurIPS 2020 FlowDB: A new large scale river flow, flash flood, and precipitation dataset (Papers Track)
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Abstract: Flooding results in 8 billion dollars of damage annually in the US and causes the most deaths of any weather related event. Due to climate change scientists expect more heavy precipitation events in the future. However, no current datasets exist that contain both hourly precipitation and river flow data. We introduce a novel hourly river flow and precipitation dataset and a second subset of flash flood events with damage estimates and injury counts. Using these datasets we create two challenges (1) general stream flow forecasting and (2) flash flood damage estimation. We also create a public benchmark and an Python package to enable easy adding of new models . Additionally, in the future we aim to augment our dataset with snow pack data and soil index moisture data to improve predictions
Authors: Isaac Godfried (CoronaWhy)
Time-series analysis Climate and Earth science Data mining
NeurIPS 2020 Can Federated Learning Save The Planet ? (Papers Track)
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Abstract: Despite impressive results, deep learning-based technologies also raise severe privacy and environmental concerns induced by the training procedure often conducted in data centers. In response, alternatives to centralized training such as Federated Learning (FL) have emerged. Perhaps unexpectedly, FL in particular is starting to be deployed at a global scale by companies that must adhere to new legal demands and policies originating from governments and the civil society for privacy protection. \textit{However, the potential environmental impact related to FL remains unclear and unexplored. This paper offers the first-ever systematic study of the carbon footprint of FL.} First, we propose a rigorous model to quantify the carbon footprint, hence facilitating the investigation of the relationship between FL design and carbon emissions. Then, we compare the carbon footprint of FL to traditional centralized learning. Our findings show FL, despite being slower to converge, can be a greener technology than data center GPUs. Finally, we highlight and connect the reported results to the future challenges and trends in FL to reduce its environmental impact, including algorithms efficiency, hardware capabilities, and stronger industry transparency.
Authors: Xinchi Qiu (University of Cambridge); Titouan Parcollet (University of Oxford); Daniel J Beutel (Adap GmbH / University of Cambridge); Taner Topal (Adap GmbH); Akhil Mathur (Nokia Bell Labs); Nicholas Lane (University of Cambridge and Samsung AI)
Power and energy Federated Learning
NeurIPS 2020 FireSRnet: Geoscience-driven super-resolution of future fire risk from climate change (Papers Track)
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Abstract: With fires becoming increasingly frequent and severe across the globe in recent years, understanding climate change’s role in fire behavior is critical for quantifying current and future fire risk. However, global climate models typically simulate fire behavior at spatial scales too coarse for local risk assessments. Therefore, we propose a novel approach towards super-resolution (SR) enhancement of fire risk exposure maps that incorporates not only 2000 to 2020 monthly satellite observations of active fires but also local information on land cover and temperature. Inspired by SR architectures, we propose an efficient deep learning model trained for SR on fire risk exposure maps. We evaluate this model on resolution enhancement and find it outperforms standard image interpolation techniques at both 4x and 8x enhancement while having comparable performance at 2x enhancement. We then demonstrate the generalizability of this SR model over northern California and New South Wales, Australia. We conclude with a discussion and application of our proposed model to climate model simulations of fire risk in 2040 and 2100, illustrating the potential for SR enhancement of fire risk maps from the latest state-of-the-art climate models.
Authors: Tristan C Ballard (Sust Global, Stanford University); Gopal Erinjippurath (Sust Global)
Computer vision and remote sensing Climate and Earth science Societal adaptation
NeurIPS 2020 An Enriched Automated PV Registry: Combining Image Recognition and 3D Building Data (Papers Track)
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Abstract: While photovoltaic (PV) systems are installed at an unprecedented rate, reliable information on an installation level remains scarce. As a result, automatically created PV registries are a timely contribution to optimize grid planning and operations. This paper demonstrates how aerial imagery and three-dimensional building data can be combined to create an address-level PV registry, specifying area, tilt, and orientation angles. We demonstrate the benefits of this approach for PV capacity estimation. In addition, this work presents, for the first time, a comparison between automated and officially-created PV registries. Our results indicate that our enriched automated registry proves to be useful to validate, update, and complement official registries.
Authors: Benjamin Rausch (Stanford); Kevin Mayer (Stanford); Marie-Louise Arlt (Stanford); Gunther Gust (University of Freiburg); Philipp Staudt (KIT); Christof Weinhardt (Karlsruhe Institute of Technology); Dirk Neumann (Universität Freiburg); Ram Rajagopal (Stanford University)
Power and energy Buildings and cities Classification, regression, and supervised learning Computer vision and remote sensing
NeurIPS 2020 Satellite imagery analysis for Land Use, Land Use Change and Forestry: A pilot study in Kigali, Rwanda (Papers Track)
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Abstract: Estimating greenhouse gases from the Agriculture, Forestry and Other land Use (AFOLU) sector is very challenging partly due to the unavailability of data (particularly for land use and land use change sectors) and inadequate experts to analyze this data in case it is available. We used Collect Earth together with Machine Learning techniques to be able to predict and classify all the land use types based on some few points collected using Collect Earth. We investigated the adoption of this tool and technology in Rwanda to help its national and sub-national inventories. The use of Collect Earth and the Machine Learning (ML) implementation will help Rwanda monitor and predict its Land Use, Land Use Change, and Forestry in a cost-effective manner whiles enhancing the quality of reports submitted to national and international bodies whiles introducing a new approach. Among the classification algorithms we tested, we had an overall classification accuracy of 97% using the Classification and Regression Trees (CART) algorithm to to predict the six land Use classes across the country.
Authors: Bright Aboh (African Institute for Mathematical Sciences); Alphonse Mutabazi (UN Environment Program)
Agriculture, forestry and other land use Classification, regression, and supervised learning
NeurIPS 2020 EarthNet2021: A novel large-scale dataset and challenge for forecasting localized climate impacts (Papers Track)
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Abstract: Climate change is global, yet its concrete impacts can strongly vary between different locations in the same region. Seasonal weather forecasts currently operate at the mesoscale (> 1 km). For more targeted mitigation and adaptation, modelling impacts to < 100 m is needed. Yet, the relationship between driving variables and Earth’s surface at such local scales remains unresolved by current physical models. Large Earth observation datasets now enable us to create machine learning models capable of translating coarse weather information into high-resolution Earth surface forecasts encompassing localized climate impacts. Here, we define high-resolution Earth surface forecasting as video prediction of satellite imagery conditional on mesoscale weather forecasts. Video prediction has been tackled with deep learning models. Developing such models requires analysis-ready datasets. We introduce EarthNet2021, a new, curated dataset containing target spatio-temporal Sentinel 2 satellite imagery at 20 m resolution, matched with high-resolution topography and mesoscale (1.28 km) weather variables. With over 32000 samples it is suitable for training deep neural networks. Comparing multiple Earth surface forecasts is not trivial. Hence, we define the EarthNetScore, a novel ranking criterion for models forecasting Earth surface reflectance. For model intercomparison we frame EarthNet2021 as a challenge with four tracks based on different test sets. These allow evaluation of model validity and robustness as well as model applicability to extreme events and the complete annual vegetation cycle. In addition to forecasting directly observable weather impacts through satellite-derived vegetation indices, capable Earth surface models will enable downstream applications such as crop yield prediction, forest health assessments, coastline management, or biodiversity monitoring. Find data, code, and how to participate at www.earthnet.tech .
Authors: Christian Requena-Mesa (Computer Vision Group, Friedrich Schiller University Jena; DLR Institute of Data Science, Jena; Max Planck Institute for Biogeochemistry, Jena); Vitus Benson (Max-Planck-Institute for Biogeochemistry); Jakob Runge (Institute of Data Science, German Aerospace Center (DLR)); Joachim Denzler (Computer Vision Group, Friedrich Schiller University Jena, Germany); Markus Reichstein (Max Planck Institute for Biogeochemistry, Jena; Michael Stifel Center Jena for Data-Driven and Simulation Science, Jena)
Climate and Earth science Agriculture, forestry and other land use Disaster prediction, management, and relief Ecosystems and natural systems Computer vision and remote sensing Data mining Generative modeling Hybrid physical models
NeurIPS 2020 DeepWaste: Applying Deep Learning to Waste Classification for a Sustainable Planet (Papers Track)
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Abstract: Accurate waste disposal, at the point of disposal, is crucial to fighting climate change. When materials that could be recycled or composted get diverted into landfills, they cause the emission of potent greenhouse gases such as methane. Current attempts to reduce erroneous waste disposal are expensive, inaccurate, and confusing. In this work, we propose DeepWaste, an easy-to-use mobile app, that utilizes highly optimized deep learning techniques to provide users instantaneous waste classification into trash, recycling, and compost. We experiment with several convolution neural network architectures to detect and classify waste items. Our best model, a deep learning residual neural network with 50 layers, achieves an average precision of 0.881 on the test set. We demonstrate the performance and efficiency of our app on a set of real-world images.
Authors: Yash Narayan (The Nueva School)
Other Classification, regression, and supervised learning
NeurIPS 2020 Machine Learning Climate Model Dynamics: Offline versus Online Performance (Papers Track)
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Abstract: Climate models are complicated software systems that approximate atmospheric and oceanic fluid mechanics at a coarse spatial resolution. Typical climate forecasts only explicitly resolve processes larger than 100 km and approximate any process occurring below this scale (e.g. thunderstorms) using so-called parametrizations. Machine learning could improve upon the accuracy of some traditional physical parametrizations by learning from so-called global cloud-resolving models. We compare the performance of two machine learning models, random forests (RF) and neural networks (NNs), at parametrizing the aggregate effect of moist physics in a 3 km resolution global simulation with an atmospheric model. The NN outperforms the RF when evaluated offline on a testing dataset. However, when the ML models are coupled to an atmospheric model run at 200 km resolution, the NN-assisted simulation crashes with 7 days, while the RF-assisted simulations remain stable. Both runs produce more accurate weather forecasts than a baseline configuration, but globally averaged climate variables drift over longer timescales.
Authors: Noah D Brenowitz (Vulcan Inc.); Brian Henn (Vulcan, Inc.); Spencer Clark (Vulcan, Inc.); Anna Kwa (Vulcan, Inc.); Jeremy McGibbon (Vulcan, Inc.); W. Andre Perkins (Vulcan, Inc.); Oliver Watt-Meyer (Vulcan, Inc.); Christopher S. Bretherton (Vulcan, Inc.)
Climate and Earth science Hybrid physical models
NeurIPS 2020 OGNet: Towards a Global Oil and Gas Infrastructure Database using Deep Learning on Remotely Sensed Imagery (Papers Track)
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Abstract: At least a quarter of the warming that the Earth is experiencing today is due to anthropogenic methane emissions. There are multiple satellites in orbit and planned for launch in the next few years which can detect and quantify these emissions; however, to attribute methane emissions to their sources on the ground, a comprehensive database of the locations and characteristics of emission sources worldwide is essential. In this work, we develop deep learning algorithms that leverage freely available high-resolution aerial imagery to automatically detect oil and gas infrastructure, one of the largest contributors to global methane emissions. We use the best algorithm, which we call OGNet, together with expert review to identify the locations of oil refineries and petroleum terminals in the U.S. We show that OGNet detects many facilities which are not present in four standard public datasets of oil and gas infrastructure. All detected facilities are associated with characteristics critical to quantifying and attributing methane emissions, including the types of infrastructure and number of storage tanks. The data curated and produced in this study is freely available at https://link/provided/in/camera/ready/version.
Authors: Hao Sheng (Stanford University); Jeremy A Irvin (Stanford); Sasankh Munukutla (Stanford University); Shawn Zhang (Stanford University); Christopher Cross (Stanford University); Zutao Yang (Stanford University); Kyle Story (Descartes Labs); Rose Rustowicz (Descartes Labs); Cooper Elsworth (Descartes Labs); Mark Omara (Environmental Defense Fund); Ritesh Gautam (Environmental Defense Fund); Rob Jackson (Stanford University); Andrew Ng (Stanford University)
Power and energy Computer vision and remote sensing
NeurIPS 2020 VConstruct: Filling Gaps in Chl-a Data Using a Variational Autoencoder (Papers Track)
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Abstract: Remote sensing of Chlorophyll-a is vital in monitoring climate change. Chlorphylla measurements give us an idea of the algae concentrations in the ocean, which lets us monitor ocean health. However, a common problem is that the satellites used to gather the data are commonly obstructed by clouds and other artifacts. This means that time series data from satellites can suffer from spatial data loss. There are a number of algorithms that are able to reconstruct the missing parts of these images to varying degrees of accuracy, with Data INterpolating Empirical Orthogonal Functions (DINEOF) being the current standard. However, DINEOF is slow, suffers from accuracy loss in temporally homogenous waters, reliant on temporal data, and only able to generate a single potential reconstruction. We propose a machine learning approach to reconstruction of Chlorophyll-a data using a Variational Autoencoder (VAE). Our accuracy results to date are competitive with but slightly less accurate than DINEOF. We show the benefits of our method including vastly decreased computation time and ability to generate multiple potential reconstructions. Lastly, we outline our planned improvements and future work.
Authors: Matthew Ehrler (University of Victoria); Neil Ernst (University of Victoria)
Computer vision and remote sensing Climate and Earth science Ecosystems and natural systems Generative modeling
NeurIPS 2020 A Comparison of Data-Driven Models for Predicting Stream Water Temperature (Papers Track)
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Abstract: Changes to the Earth's climate are expected to negatively impact water resources in the future. It is important to have accurate modelling of river flow and water quality to make optimal decisions for water management. Machine learning and deep learning models have become promising methods for making such hydrological predictions. Using these models, however, requires careful consideration both of data constraints and of model complexity for a given problem. Here, we use machine learning (ML) models to predict monthly stream water temperature records at three monitoring locations in the Northwestern United States with long-term datasets, using meteorological data as predictors. We fit three ML models: a Multiple Linear Regression, a Random Forest Regression, and a Support Vector Regression, and compare them against two baseline models: a persistence model and historical model. We show that all three ML models are reasonably able to predict mean monthly stream temperatures with root mean-squared errors (RMSE) ranging from 0.63-0.91 degrees Celsius. Of the three ML models, Support Vector Regression performs the best with an error of 0.63-0.75 degrees Celsius. However, all models perform poorly on extreme values of water temperature. We identify the need for machine learning approaches for predicting extreme values for variables such as water temperature, since it has significant implications for stream ecosystems and biota.
Authors: Helen Weierbach (Lawrence Berkeley); Aranildo Lima (Aquatic Informatics); Danielle Christianson (Lawrence Berkeley National Lab); Boris Faybishenko (Lawrence Berkeley National Lab); Val Hendrix (Lawrence Berkeley National Lab); Charuleka Varadharajan (Lawrence Berkeley National Lab)
Ecosystems and natural systems Climate and Earth science Classification, regression, and supervised learning Time-series analysis
NeurIPS 2020 Automated Salmonid Counting in Sonar Data (Papers Track)
Abstract and authors: (click to expand)
Abstract: The prosperity of salmonids is crucial for several ecological and economic functions. Accurately counting spawning salmonids during their seasonal migration is essential in monitoring threatened populations, assessing the efficacy of recovery strategies, guiding fishing season regulations, and supporting the management of commercial and recreational fisheries. While several different methods exist for counting river fish, they all rely heavily on human involvement, introducing a hefty financial and time burden. In this paper we present an automated fish counting method that utilizes data captured from ARIS sonar cameras to detect and track salmonids migrating in rivers. Our results show that our fully automated system has a 19.3% per-clip error when compared to human counting performance. There is room to improve, but our system can already decrease the amount of time field biologists and fishery managers need to spend manually watching ARIS clips.
Authors: Peter Kulits (Caltech); Angelina Pan (Caltech); Sara M Beery (Caltech); Erik Young (Trout Unlimited); Pietro Perona (California Institute of Technology); Grant Van Horn (Cornell University)
Ecosystems and natural systems Agriculture, forestry and other land use Climate and Earth science Industry Computer vision and remote sensing Time-series analysis
NeurIPS 2020 Short-term PV output prediction using convolutional neural network: learning from an imbalanced sky images dataset via sampling and data augmentation (Papers Track)
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Abstract: Integrating photovoltaics (PV) into electricity grids is one of the major pathways towards a low-carbon energy system. However, the biggest challenge is the strong fluctuation in PV power generation. In recent years, sky-image-based PV output prediction using deep neural networks has emerged as a promising approach to alleviate the uncertainty. Despite the research surge in exploring different model architectures, there is currently no study addressing the issue of learning from an imbalanced sky images dataset, the outcome of which would be highly beneficial for improving the reliability of existing and new solar forecasting models. In this study, we train convolutional neural network (CNN) models from an imbalanced sky images dataset for two disparate PV output prediction tasks, i.e., nowcast and forecast. We empirically examine the efficacy of using different sampling and data augmentation approaches to create synthesized dataset for model development. We further apply a three-stage selection approach to determine the optimal sampling approach, data augmentation technique and oversampling rate.
Authors: Yuhao Nie (Stanford University); Ahmed S Zamzam (The National Renewable Energy Laboratory); Adam Brandt (Stanford University)
Computer vision and remote sensing Climate and Earth science Classification, regression, and supervised learning
NeurIPS 2020 OfficeLearn: An OpenAI Gym Environment for Building Level Energy Demand Response (Papers Track)
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Abstract: Energy Demand Response (DR) will play a crucial role in balancing renewable energy generation with demand as grids decarbonize. There is growing interest in developing Reinforcement Learning (RL) techniques to optimize DR pricing, as pricing set by electric utilities often cannot take behavioral irrationality into account. However, so far, attempts to standardize RL efforts in this area do not exist. In this paper, we present a first of the kind OpenAI gym environment for testing DR with occupant level building dynamics. We demonstrate the variety of parameters built into our office environment allowing the researcher to customize a building to meet their specifications of interest. We hope that this work enables future work in DR in buildings.
Authors: Lucas Spangher (U.C. Berkeley); Akash Gokul (University of California at Berkeley); Utkarsha Agwan (U.C. Berkeley); Joseph Palakapilly (UC Berkeley); Manan Khattar (University of California at Berkeley); Akaash Tawade (University of California at Berkeley); Costas J. Spanos (University of California at Berkeley)
Buildings and cities Power and energy Reinforcement learning and control Time-series analysis
NeurIPS 2020 Machine Learning for Glacier Monitoring in the Hindu Kush Himalaya (Papers Track)
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Abstract: Glacier mapping is key to ecological monitoring in the Hindu Kush Himalaya region. Climate change poses a risk to individuals whose livelihoods depend on the health of glacier ecosystems. In this work, we present a machine learning based approach to support ecological monitoring, with a focus on glaciers. Our approach is based on semi-automated mapping from satellite images. We utilize readily available remote sensing data to create a model to identify and outline both clean ice and debris-covered glaciers from satellite imagery. We also release data and develop a web tool that allows experts to visualize and correct model predictions, with the ultimate aim of accelerating the glacier mapping process.
Authors: Shimaa Baraka (Mila); Benjamin Akera (Makerere University); Bibek Aryal (The University of Texas at El Paso); Tenzing Sherpa (International Centre for Integrated Mountain Development); Finu Shrestha (International Centre for Integrated Mountain Development); Anthony Ortiz (Microsoft); Kris Sankaran (University of Wisconsin-Madison); Juan M Lavista Ferres (Microsoft); Mir A Matin (International Center for Integrated Mountain Development); Yoshua Bengio (Mila)
Ecosystems and natural systems Computer vision and remote sensing
NeurIPS 2020 Data-driven modeling of cooling demand in a commercial building (Papers Track)
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Abstract: Heating, ventilation, and air conditioning (HVAC) systems account for 30% of the total energy consumption in buildings. Design and implementation of energy-efficient schemes can play a pivotal role in minimizing energy usage. As an important first step towards improved HVAC system controls, this study proposes a new framework for modeling the thermal response of buildings by leveraging data measurements and formulating a data-driven system identification model. The proposed method combines principal component analysis (PCA) to identify the most significant predictors that influence the cooling demand of a building with an auto-regressive integrated moving average with exogenous variables (ARIMAX) model. The performance of the developed model was evaluated both analytically and visually. It was found that our PCA-based ARIMAX (2-0-5) model was able to accurately forecast the cooling demand for the prediction horizon of 7 days. In this work, the actual measurements from a university campus building are used for model development and validation.
Authors: Aqsa Naeem (Stanford University); Sally Benson (Stanford University); Jacques de Chalendar (Stanford University)
Buildings and cities Power and energy Hybrid physical models
NeurIPS 2020 Investigating two super-resolution methods for downscaling precipitation: ESRGAN and CAR (Papers Track)
Abstract and authors: (click to expand)
Abstract: In an effort to provide optimal inputs to downstream modeling systems (e.g., a hydrodynamics model that simulates the water circulation of a lake), we hereby strive to enhance resolution of precipitation fields from a weather model by up to 9x. We test two super-resolution models: the enhanced super-resolution generative adversarial networks (ESRGAN) proposed in 2017, and the content adaptive resampler (CAR) proposed in 2020. Both models outperform simple bicubic interpolation, with the ESRGAN exceeding expectations for accuracy. We make several proposals for extending the work to ensure it can be useful tool for quantifying the impact of climate change on local ecosystems while removing reliance on energy-intensive, high-resolution weather model simulations.
Authors: Campbell Watson (IBM); Chulin Wang (Northwestern University); Tim Lynar (University of New South Wales); Komminist Weldemariam (IBM Research)
Classification, regression, and supervised learning Ecosystems and natural systems
NeurIPS 2020 Emerging Trends of Sustainability Reporting in the ICT Industry: Insights from Discriminative Topic Mining (Papers Track)
Abstract and authors: (click to expand)
Abstract: The Information and Communication Technologies (ICT) industry has a considerable climate change impact and accounts for approximately 3 percent of global carbon emissions. Despite the increasing availability of sustainability reports provided by ICT companies, we still lack a systematic understanding of what has been disclosed at an industry level. In this paper, we make the first major effort to use modern unsupervised learning methods to investigate the sustainability reporting themes and trends of the ICT industry over the past two decades. We build a cross-sector dataset containing 22,534 environmental reports from 1999 to 2019, of which 2,187 are ICT specific. We then apply CatE, a text embedding based topic modeling method, to mine specific keywords that ICT companies use to report on climate change and energy. As a result, we identify (1) important shifts in ICT companies' climate change narratives from physical metrics towards climate-related disasters, (2) key organizations with large influence on ICT companies, and (3) ICT companies' increasing focus on data center and server energy efficiency.
Authors: Lin Shi (Stanford University); Nhi Truong Vu (Stanford University)
Industry Climate policy Data mining Natural language processing Unsupervised and semi-supervised learning
NeurIPS 2020 Loosely Conditioned Emulation of Global Climate Models With Generative Adversarial Networks (Papers Track)
Abstract and authors: (click to expand)
Abstract: Climate models encapsulate our best understanding of the Earth system, allowing research to be conducted on its future under alternative assumptions of how human-driven climate forces are going to evolve. An important application of climate models is to provide metrics of mean and extreme climate changes, particularly under these alternative future scenarios, as these quantities drive the impacts of climate on society and natural systems. Because of the need to explore a wide range of alternative scenarios and other sources of uncertainties in a computationally efficient manner, climate models can only take us so far, as they require significant computational resources, especially when attempting to characterize extreme events, which are rare and thus demand long and numerous simulations in order to accurately represent their changing statistics. Here we use deep learning in a proof of concept that lays the foundation for emulating global climate model output for different scenarios. We train two "loosely conditioned" Generative Adversarial Networks (GANs) that emulate daily precipitation output from a fully coupled Earth system model: one GAN modeling Fall-Winter behavior and the other Spring-Summer. Our GANs are trained to produce spatiotemporal samples: 32 days of precipitation over a 64x128 regular grid discretizing the globe. We evaluate the generator with a set of related performance metrics based upon KL divergence, and find the generated samples to be nearly as well matched to the test data as the validation data is to test. We also find the generated samples to accurately estimate the mean number of dry days and mean longest dry spell in the 32 day samples. Our trained GANs can rapidly generate numerous realizations at a vastly reduced computational expense, compared to large ensembles of climate models, which greatly aids in estimating the statistics of extreme events.
Authors: Alex Ayala (Western Washington University); Chris Drazic (Western Washington University); Brian Hutchinson (Western Washington University); Ben Kravitz (Indiana University); Claudia Tebaldi (Joint Global Change Research Institute)
Generative modeling Climate and Earth science
NeurIPS 2020 The Peruvian Amazon Forestry Dataset: A Leaf Image Classification Corpus (Papers Track)
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Abstract: This paper introduces the Peruvian Amazon Forestry Dataset, which includes 59,441 leaves samples from ten of the most profitable and endangered Amazon timber-tree species. Besides, the proposal includes a background removal algorithm to feed a fine-tuned CNN. We evaluate the quantitative (accuracy metric) and qualitative (visual interpretation) impacts of each stage by ablation experiments. The results show a 96.64 % training accuracy and 96.52 % testing accuracy on the VGG-19 model. Furthermore, the visual interpretation of the model evidences that leaf venations have the highest correlation in the plant recognition task.
Authors: Gerson Waldyr Vizcarra Aguilar (San Pablo Catholic University); Danitza Bermejo (Universidad Nacional del Altiplano); Manasses A. Mauricio (Universidad Católica San Pablo); Ricardo Zarate (Instituto de Investigaciones de la Amazonía Peruana); Erwin Dianderas (Instituto de Investigaciones de la Amazonía Peruana)
Agriculture, forestry and other land use Meta- and transfer learning
NeurIPS 2020 Spatiotemporal Features Improve Fine-Grained Butterfly Image Classification (Papers Track)
Abstract and authors: (click to expand)
Abstract: Understanding the changing distributions of butterflies gives insight into the impacts of climate change across ecosystems and is a prerequisite for conservation efforts. eButterfly is a citizen science website created to allow people to track the butterfly species around them and use these observations to contribute to research. However, correctly identifying butterfly species is a challenging task for non-specialists and currently requires the involvement of entomologists to verify the labels of novice users on the website. We have developed a computer vision model to label butterfly images from eButterfly automatically, decreasing the need for human experts. We employ a model that incorporates geographic and temporal information of where and when the image was taken, in addition to the image itself. We show that we can successfully apply this spatiotemporal model for fine-grained image recognition, significantly improving the accuracy of our classification model compared to a baseline image recognition system trained on the same dataset.
Authors: Marta Skreta (University of Toronto); Sasha Luccioni (Mila); David Rolnick (McGill University, Mila)
Ecosystems and natural systems Classification, regression, and supervised learning Computer vision and remote sensing
NeurIPS 2020 High-resolution global irrigation prediction with Sentinel-2 30m data (Papers Track)
Abstract and authors: (click to expand)
Abstract: An accurate and precise understanding of global irrigation usage is crucial for a variety of climate science efforts. Irrigation is highly energy-intensive, and as population growth continues at its current pace, increases in crop need and water usage will have an impact on climate change. Precise irrigation data can help with monitoring water usage and optimizing agricultural yield, particularly in developing countries. Irrigation data, in tandem with precipitation data, can be used to predict water budgets as well as climate and weather modeling. With our research, we produce an irrigation prediction model that combines unsupervised clustering of Normalized Difference Vegetation Index (NDVI) temporal signatures with a precipitation heuristic to label the months that irrigation peaks for each cropland cluster in a given year. We have developed a novel irrigation model and Python package ("Irrigation30") to generate 30m resolution irrigation predictions of cropland worldwide. With a small crowdsourced test set of cropland coordinates and irrigation labels, using a fraction of the resources used by the state-of-the-art NASA-funded GFSAD30 project with irrigation data limited to India and Australia, our model was able to achieve consistency scores in excess of 97% and an accuracy of 92% in a small geo-diverse randomly sampled test set.
Authors: Will Hawkins (UC Berkeley); Weixin Wu (UC Berkeley); Sonal Thakkar (UC Berkeley); Puya Vahabi (UC Berkeley); Alberto Todeschini (UC Berkeley)
Agriculture, forestry and other land use Unsupervised and semi-supervised learning
NeurIPS 2020 Do Occupants in a Building exhibit patterns in Energy Consumption? Analyzing Clusters in Energy Social Games (Papers Track)
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Abstract: Energy use in buildings account for approximately half of global electricity consumption and a significant amount of CO2 emissions. To encourage energy efficient behavior among occupants in a building, energy social games have emerged to be a successful strategy leveraging human-in-the-loop strategy and engaging users in a competitive game with incentives for energy efficient behavior. Prior works involve an incentive design mechanism which is dependent on knowledge of utility functions (energy use behavior) for the users, which is hard to compute when the number of users is high, common in buildings. We propose that the utilities can be grouped to a relatively small number of clusters, which can then be targeted with tailored incentives. Proposed work performs the above segmentation by learning the features leading to human decision making towards energy usage in competitive environment. We propose a graphical lasso based approach with explainable nature for such segmentation, by studying the feature correlations in a real-world energy social game dataset.
Authors: Hari Prasanna Das (UC Berkeley); Ioannis C. Konstantakopoulos (UC Berkeley); Aummul Baneen Manasawala (UC Berkeley); Tanya Veeravalli (UC Berkeley); Huihan Liu (UC Berkeley); Costas J. Spanos (University of California at Berkeley)
Buildings and cities Other
NeurIPS 2020 In-N-Out: Pre-Training and Self-Training using Auxiliary Information for Out-of-Distribution Robustness (Papers Track)
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Abstract: Many machine learning applications used to tackle climate change involve lots of unlabeled data (such as satellite imagery) along with auxiliary information such as climate data. In this work, we show how to use auxiliary information in a semi-supervised setting to improve both in-distribution and out-of-distribution (OOD) accuracies (e.g. for countries in Africa where we have very little labeled data). We show that 1) on real-world datasets, the common practice of using auxiliary information as additional input features improves in-distribution error but can hurt OOD. Oppositely, we find that 2) using auxiliary information as outputs of auxiliary tasks to pre-train a model improves OOD error. 3) To get the best of both worlds, we introduce In-N-Out, which first trains a model with auxiliary inputs and uses it to pseudolabel all the in-distribution inputs, then pre-trains a model on OOD auxiliary outputs and fine-tunes this model with the pseudolabels (self-training). We show both theoretically and empirically on remote sensing datasets for land cover prediction and cropland prediction that In-N-Out outperforms auxiliary inputs or outputs alone on both in-distribution and OOD error.
Authors: Robbie M Jones (Stanford University); Sang Michael Xie (Stanford University); Ananya Kumar (Stanford University); Fereshte Khani (Stanford); Tengyu Ma (Stanford University); Percy Liang (Stanford University)
Meta- and transfer learning Agriculture, forestry and other land use Computer vision and remote sensing Unsupervised and semi-supervised learning
NeurIPS 2020 Climate-FEVER: A Dataset for Verification of Real-World Climate Claims (Papers Track)
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Abstract: Our goal is to introduce \textsc{climate-fever}, a new publicly available dataset for verification of climate change-related claims. By providing a dataset for the research community, we aim to help and encourage work on improving algorithms for retrieving climate-specific information and detecting fake news in social and mass media to reduce the impact of misinformation on the formation of public opinion on climate change. We adapt the methodology of \textsc{fever} \cite{thorne2018fever}, the largest dataset of artificially designed claims, to real-life claims collected from the Internet. Although during this process, we could count on the support of renowned climate scientists, it turned out to be no easy task. We discuss the surprising, subtle complexity of modeling real-world climate-related claims within the \textsc{fever} framework, which provides a valuable challenge for general natural language understanding. We hope that our work will mark the beginning of an exciting long-term joint effort by the climate science and \textsc{ai} community to develop robust algorithms to verify the facts for climate-related claims.
Authors: Markus Leippold (University of Zurich); Thomas Diggelmann (ETH Zurich)
Natural language processing Behavioral and social science Climate finance and economics Other
NeurIPS 2020 Understanding global fire regimes using Artificial Intelligence (Papers Track)
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Abstract: Improved understanding of fire activity and its influencing factors will impact the way we interact and coexist with not only the fire itself but also with the ecosystem as a whole. We consolidate more than 20 million wildfire records between 2000 and 2018 across the six continents. This data is processed with artificial intelligence methods to discover global fire regimes, areas with characteristic fire behavior over long periods. We discover 15 groups with clear differences in fire-related historical behavior. Despite sharing historical fire behavior, regions belonging to the same group present significant differences in location and influencing factors. Groups are further divided into 62 regimes based on spatial aggregation patterns, providing a comprehensive characterization. This allows an interpretation of how a combination of vegetation, climate, and demographic features results in a specific fire regime. The current work expands on existing classification efforts and is a step forward in addressing the complex challenge of characterizing global fire regimes.
Authors: Cristobal Pais (University of California Berkeley); Jose-Ramon Gonzalez (CTFC); Pelagy Moudio (University of California Berkeley); Jordi Garcia-Gonzalo (CTFC); Marta C. González (Berkeley); Zuo-Jun Shen (University of California, Berkeley)
Climate and Earth science Disaster prediction, management, and relief
NeurIPS 2020 ClimaText: A Dataset for Climate Change Topic Detection (Papers Track)
Abstract and authors: (click to expand)
Abstract: Climate change communication in the mass media and other textual sources may affect and shape public perception. Extracting climate change information from these sources is an important task, e.g., for filtering content and e-discovery, sentiment analysis, automatic summarization, question-answering, and fact-checking. However, automating this process is a challenge, as climate change is a complex, fast-moving, and often ambiguous topic with scarce resources for popular text-based AI tasks. In this paper, we introduce \textsc{ClimaText}, a dataset for sentence-based climate change topic detection, which we make publicly available. We explore different approaches to identify the climate change topic in various text sources. We find that popular keyword-based models are not adequate for such a complex and evolving task. Context-based algorithms like BERT~\cite{devlin2018bert} can detect, in addition to many trivial cases, a variety of complex and implicit topic patterns. Nevertheless, our analysis reveals a great potential for improvement in several directions, such as, e.g., capturing the discussion on indirect effects of climate change. Hence, we hope this work can serve as a good starting point for further research on this topic.
Authors: Markus Leippold (University of Zurich); Francesco Saverio Varini (ETH)
Natural language processing Behavioral and social science Other
NeurIPS 2020 Towards Data-Driven Physics-Informed Global Precipitation Forecasting from Satellite Imagery (Papers Track)
Abstract and authors: (click to expand)
Abstract: Under the effects of global warming, extreme events such as floods and droughts are increasing in frequency and intensity. This trend directly affects communities and make all the more urgent widening the access to accurate precipitation forecasting systems for disaster preparedness. Nowadays, weather forecasting relies on numerical models necessitating massive computing resources that most developing countries cannot afford. Machine learning approaches are still in their infancy but already show the promise for democratizing weather predictions, by leveraging any data source and requiring less compute. In this work, we propose a methodology for data-driven and physics-aware global precipitation forecasting from satellite imagery. To fully take advantage of the available data, we design the system as three elements: 1. The atmospheric state is estimated from recent satellite data. 2. The atmospheric state is propagated forward in time. 3. The atmospheric state is used to derive the precipitation intensity within a nearby time interval. In particular, our use of stochastic methods for forecasting the atmospheric state represents a novel application in this domain.
Authors: Valentina Zantedeschi (GE Global Research); Daniele De Martini (University of Oxford); Catherine Tong (University of Oxford); Christian A Schroeder de Witt (University of Oxford); Piotr Bilinski (University of Warsaw / University of Oxford); Alfredo Kalaitzis (University of Oxford); Matthew Chantry (University of Oxford); Duncan Watson-Parris (University of Oxford)
Climate and Earth science Agriculture, forestry and other land use Disaster prediction, management, and relief Ecosystems and natural systems Classification, regression, and supervised learning Computer vision and remote sensing
NeurIPS 2020 A Generative Adversarial Gated Recurrent Network for Power Disaggregation & Consumption Awareness (Papers Track)
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Abstract: Separating the household aggregated power signal into its additive sub-components is called energy (power) disaggregation or Non-Intrusive Load Monitoring. NILM can play an instrumental role as a driver towards consumer energy consumption awareness and behavioral change. In this paper, we propose EnerGAN++, a model based on GANs for robust energy disaggregation. We propose a unified autoencoder (AE) and GAN architecture, in which the AE achieves a non-linear power signal source separation. The discriminator performs sequence classification, using a recurrent CNN to handle the temporal dynamics of an appliance energy consumption time series. Experimental results indicate the proposed method’s superiority compared to the current state of the art.
Authors: Maria Kaselimi (National Technical University of Athens); Athanasios Voulodimos (University of West Attica); Nikolaos Doulamis (National Technical University of Athens); Anastasios Doulamis (Technical University of Crete); Eftychios Protopapadakis (National Technical University of Athens)
Power and energy Generative modeling
NeurIPS 2020 Deep Fire Topology: Understanding the role of landscape spatial patterns in wildfire susceptibility (Papers Track)
Abstract and authors: (click to expand)
Abstract: Increasing wildfire activity across the globe has become an urgent issue with enormous ecological and social impacts. While there is evidence that landscape topology affects fire growth, no study has yet reported its potential influence on fire ignition. This study proposes a deep learning framework focused on understanding the impact of different landscape topologies on the ignition of a wildfire and the rationale behind these results. Our model achieves an accuracy of above 90\% in fire occurrence prediction, detection, and classification of risky areas by only exploiting topological pattern information from 17,579 landscapes. This study reveals the strong potential of landscape topology in wildfire occurrence prediction and its implications for similar research. The proposed methodology can be applied to multiple fields/studies to understand and capture the role and impact of different topological features and their interactions.
Authors: Cristobal Pais (University of California Berkeley); Alejandro Miranda (University of Chile); Jaime Carrasco (University of Chile); Zuo-Jun Shen (University of California, Berkeley)
Computer vision and remote sensing Disaster prediction, management, and relief Agriculture, forestry and other land use
NeurIPS 2020 Interpretability in Convolutional Neural Networks for Building Damage Classification in Satellite Imagery (Papers Track)
Abstract and authors: (click to expand)
Abstract: Natural disasters ravage the world's cities, valleys, and shores on a monthly basis. Having precise and efficient mechanisms for assessing infrastructure damage is essential to channel resources and minimize the loss of life. Using a dataset that includes labeled pre- and post- disaster satellite imagery, we train multiple convolutional neural networks to assess building damage on a per-building basis. In order to investigate how to best classify building damage, we present a highly interpretable deep-learning methodology that seeks to explicitly convey the most useful information required to train an accurate classification model. We also delve into which loss functions best optimize these models. Our findings include that ordinal-cross entropy loss is the most optimal loss function to use and that including the type of disaster that caused the damage in combination with a pre- and post-disaster image best predicts the level of damage caused. Our research seeks to computationally contribute to aiding in this ongoing and growing humanitarian crisis, heightened by climate change.
Authors: Thomas Y Chen (The Academy for Mathematics, Science, and Engineering)
Computer vision and remote sensing Buildings and cities Interpretable ML
NeurIPS 2020 Long-Range Seasonal Forecasting of 2m-Temperature with Machine Learning (Papers Track)
Abstract and authors: (click to expand)
Abstract: A significant challenge in seasonal climate prediction is whether a prediction can beat climatology. We hereby present results from two data-driven models - a convolutional (CNN) and a recurrent (RNN) neural network - that predict 2m temperature out to 52 weeks for six geographically-diverse locations. The motivation for testing the two classes of ML models is to allow the CNN to leverage information related to teleconnections and the RNN to leverage long-term historical temporal signals. The ML models boast improved accuracy of long-range temperature forecasts up to a lead time of 30 weeks for PCC and up 52 weeks for RMSESS, however only for select locations. Further iteration is required to ensure the ML models have value beyond regions where the climatology has a noticeably reduced correlation skill, namely the tropics.
Authors: Etienne E Vos (IBM); Ashley Gritzman (IBM); Sibusisiwe Makhanya (IBM Research); Thabang Mashinini (IBM); Campbell Watson (IBM)
Classification, regression, and supervised learning Climate and Earth science
NeurIPS 2020 Explaining Complex Energy Systems: A Challenge (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Designing future low-carbon, sector-coupled energy systems is a complex task. The work is therefore often supported by software tools that model and optimize possible energy systems. These tools typically have high dimensional inputs and outputs and are tailored towards domain experts. The final investment decisions to implement a certain system, however, are mostly made by people with little time and prior knowledge, thus unable to understand models and their input data used in these tools. Since such decisions are often connected to significant personal consequences for the decision makers, it is not enough for them to rely on experts only. They need an own, at least rough understanding. Explaining the key rationales behind complex energy system designs to non-expert decision makers in a short amount of time is thus a critical task for realizing projects of the energy transition in practice. It is also an interesting, novel challenge for the explainable AI community.
Interpretable ML Climate finance and economics Power and energy
NeurIPS 2020 The Human Effect Requires Affect: Addressing Social-Psychological Factors of Climate Change with Machine Learning (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Machine learning has the potential to aid in mitigating the human effects of climate change. Previous applications of machine learning to tackle the human effects in climate change include approaches like informing individuals of their carbon footprint and strategies to reduce it. For these methods to be the most effective they must consider relevant social-psychological factors for each individual. Of social-psychological factors at play in climate change, affect has been previously identified as a key element in perceptions and willingness to engage in mitigative behaviours. In this work, we propose an investigation into how affect could be incorporated to enhance machine learning based interventions for climate change. We propose using affective agent-based modelling for climate change as well as the use of a simulated climate change social dilemma to explore the potential benefits of affective machine learning interventions. Behavioural and informational interventions can be a powerful tool in helping humans adopt mitigative behaviours. We expect that utilizing affective ML can make interventions an even more powerful tool and help mitigative behaviours become widely adopted.
Authors: Kyle Tilbury (University of Waterloo); Jesse Hoey (University of Waterloo)
Behavioral and social science Societal adaptation Causal and Bayesian methods
NeurIPS 2020 A Way Toward Low-Carbon Shipping: Improving Port Operations Planning using Machine Learning (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Despite being the most carbon-efficient way of transportation, shipping is an important contributor to air pollution especially in coastal areas. The sector’s impact on the environment still need mitigation, through different measures undertaken so far. Operational optimization of ports and ships is a step in shipping progress towards reducing the pollution. The main purpose of this research is to reduce the degree of error and uncertainty of some operational parameters using Machine Learning models, and provide port managers with accurate information to assist them in their decision-making process. Therefore, they will be able to manage ships speed and port times for a better monitoring of ships emissions during sea voyage and port stay.
Authors: Sara El Mekkaoui (EMI Engineering School); Loubna Benabou (UQAR); Abdelaziz Berrado (EMI Engineering School)
Transportation
NeurIPS 2020 Privacy Preserving Demand Forecasting to Encourage Consumer Acceptance of Smart Energy Meters (Proposals Track)
Abstract and authors: (click to expand)
Abstract: In this proposal paper we highlight the need for privacy preserving energy demand forecasting to allay a major concern consumers have about smart meter installations. High resolution smart meter data can expose many private aspects of a consumer’s household such as occupancy, habits and individual appliance usage. Yet smart metering infrastructure has the potential to vastly reduce carbon emissions from the energy sector through improved operating efficiencies. We propose the application of a distributed machine learning setting known as federated learning for energy demand forecasting at various scales to make load prediction possible whilst retaining the privacy of consumers’ raw energy consumption data.
Authors: Christopher Briggs (Keele University); Zhong Fan (Keele University); Peter Andras (Keele University, School of Computing and Mathematics, Newcastle-under-Lyme, UK)
Power and energy Buildings and cities Societal adaptation Classification, regression, and supervised learning Time-series analysis
NeurIPS 2020 Leveraging Machine learning for Sustainable and Self-sufficient Energy Communities (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Community Energies (CEs) are the next-generation energy management techniques that empowers citizens to interact with the energy market as self-consumers or prosumers actively. Successful implementation of CEs will promote sustainable energy production and consumption practices; thus, contributing to affordable and clean energy (SDG7) and climate action (SDG 13). Despite the potential of CEs, managing the overall power production and demand is challenging. This is because power is generated, distributed and controlled by several producers, each of which with different, and potentially conflicting, objectives. Thus, this project will investigate the role of machine learning approaches in smartening CEs, increasing energy awareness and enabling distributed energy resources planning and management. The project implementation will be centered around proof of concept development and capacity development in Africa.
Authors: Anthony Faustine (University College Dublin); Lucas Pereira (ITI, LARSyS, Técnico Lisboa); Loubna Benabou (UQAR); Daniel Ngondya (The University of Dodoma)
Power and energy
NeurIPS 2020 Structural Forecasting for Tropical Cyclone Intensity Prediction: Providing Insight with Deep Learning (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Tropical cyclone (TC) intensity forecasts are ultimately issued by human forecasters. The human in-the-loop pipeline requires that any forecasting guidance must be easily digestible by TC experts if it is to be adopted at operational centers like the National Hurricane Center. Our proposed framework leverages deep learning to provide forecasters with something neither end-to-end prediction models nor traditional intensity guidance does: a powerful tool for monitoring high-dimensional time series of key physically relevant predictors and the means to understand how the predictors relate to one another and to short-term intensity changes.
Authors: Irwin H McNeely (Carnegie Mellon University); Kimberly Wood (Mississippi State University); Niccolo Dalmasso (Carnegie Mellon University); Ann Lee (Carnegie Mellon University)
Disaster prediction, management, and relief Interpretable ML
NeurIPS 2020 Hyperspectral Remote Sensing of Aquatic Microbes to Support Water Resource Management (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Harmful algal blooms in drinking water supply and at recreational sites endanger human health. Excessive algal growth can result in low oxygen environments, making them uninhabitable for fish and other aquatic life. Harmful algae and algal blooms are predicted to increase in frequency and extent due to the warming climate, but microbial dynamics remain difficult to predict. Existing satellite remote sensing monitoring technologies are ill-equipped to discriminate harmful algae, while models do not adequately capture the complex controls on algal populations. This proposal explores the potential for Bayesian neural networks to detect phytoplankton pigments from hyperspectral remote sensing reflectance retrievals. Once developed, such a model could enable hyperspectral remote sensing retrievals to support decision making in water resource management as more advanced ocean color satellites are launched in the coming decade. While uncertainty quantification motivates the proposed use of Bayesian models, the interpretation of these uncertainties in an operational context must be carefully considered.
Authors: Grace E Kim (Booz Allen Hamilton); Evan Poworoznek (NASA GSFC); Susanne Craig (NASA GSFC)
Ecosystems and natural systems Climate and Earth science
NeurIPS 2020 Wildfire Smoke and Air Quality: How Machine Learning Can Guide Forest Management (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Prescribed burns are currently the most effective method of reducing the risk of widespread wildfires, but a largely missing component in forest management is knowing which fuels one can safely burn to minimize exposure to toxic smoke. Here we show how machine learning, such as spectral clustering and manifold learning, can provide interpretable representations and powerful tools for differentiating between smoke types, hence providing forest managers with vital information on effective strategies to reduce climate-induced wildfires while minimizing production of harmful smoke.
Authors: Lorenzo Tomaselli (Carnegie Mellon University); Coty Jen (Carnegie Mellon University); Ann Lee (Carnegie Mellon University)
Disaster prediction, management, and relief Agriculture, forestry and other land use Interpretable ML Unsupervised and semi-supervised learning
NeurIPS 2020 HECT: High-Dimensional Ensemble Consistency Testing for Climate Models (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Climate models play a crucial role in understanding the effect of environmental and man-made changes on climate to help mitigate climate risks and inform governmental decisions. Large global climate models such as the Community Earth System Model (CESM), developed by the National Center for Atmospheric Research, are very complex with millions of lines of code describing interactions of the atmosphere, land, oceans, and ice, among other components. As development of the CESM is constantly ongoing, simulation outputs need to be continuously controlled for quality. To be able to distinguish a climate-changing'' modification of the code base from a true climate-changing physical process or intervention, there needs to be a principled way of assessing statistical reproducibility that can handle both spatial and temporal high-dimensional simulation outputs. Our proposed work uses probabilistic classifiers like tree-based algorithms and deep neural networks to perform a statistically rigorous goodness-of-fit test of high-dimensional spatio-temporal data.
Authors: Niccolo Dalmasso (Carnegie Mellon University); Galen Vincent (Carnegie Mellon University); Dorit Hammerling (Colorado School of Mines); Ann Lee (Carnegie Mellon University)
Climate and Earth science Classification, regression, and supervised learning Uncertainty quantification and robustness
NeurIPS 2020 Towards DeepSentinel: An extensible corpus of labelled Sentinel-1 and -2 imagery and a proposed general purpose sensor-fusion semantic embedding model (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Earth observation offers new insight into anthropogenic changes to nature, and how these changes are effecting (and are effected by) the built environment and the real economy. With the global availability of medium-resolution (10-30m) synthetic aperature radar (SAR) Sentinel-1 and multispectral Sentinel-2 imagery, machine learning can be employed to offer these insights at scale, unbiased to company- and country-level reporting. In this proposal, we document the development of an extensible corpus of labelled and unlabelled Sentinel-1 and Sentinel-2 imagery for the purposes of sensor fusion research. We make a large corpus and supporting code publicly available. We propose our own experiment design for the development of \emph{DeepSentinel}, a general-purpose semantic embedding model. Our aspiration is to provide pretrained models for transfer learning applications, significantly accelerating the impact of machine learning-enhanced earth observation on climate change mitigation.
Authors: Lucas Kruitwagen (University of Oxford)
Computer vision and remote sensing Agriculture, forestry and other land use
NeurIPS 2020 Monitoring Shorelines via High-Resolution Satellite Imagery and Deep Learning (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Twentieth-century has seen an overall sea-level rise of 0.5m [7, 11] and the studies for the twenty-first-century project the overall increment within a range of 0.5m to 2m, considering high emission scenarios and rapid melting of major Antarctic glaciers. Naturally, this has a severe impact on a major percentage of the population inhabiting coastal land zones], with a recent study placing 110million people living below the local high tide line. Of all the different coastline types, sandy shores, forming 31% of the world’s beaches, undergo major erosion and accretion changes and hence are of special focus in this paper. Because of these reasons, it is paramount to regularly monitor the coastline changes across the world for better understanding and to create necessary preparation and mitigation strategies.
Authors: Venkatesh Ramesh (HyperVerge); Digvijay Singh (HyperVerge)
Computer vision and remote sensing
NeurIPS 2020 Graph Neural Networks for Improved El Niño Forecasting (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Deep learning-based models have recently outperformed state-of-the-art seasonal forecasting models, such as for predicting El Ni\~no-Southern Oscillation (ENSO). However, current deep learning models are based on convolutional neural networks which are difficult to interpret and can fail to model large-scale atmospheric patterns called teleconnections. Hence, we propose the application of spatiotemporal Graph Neural Networks (GNN) to forecast ENSO at long lead times, finer granularity and improved predictive skill than current state-of-the-art methods. The explicit modeling of information flow via edges may also allow for more interpretable forecasts. Preliminary results are promising and outperform state-of-the art systems for projections 1 and 3 months ahead.
Authors: Salva Rühling Cachay (Technical University of Darmstadt); Emma Erickson (University of Illinois at Urbana-Champaign); Arthur F C Bucker (University of São Paulo); Ernest J Pokropek (Warsaw University of Techology); Willa Potosnak (Duquesne University); Salomey Osei (African Master's of Machine Intelligence(AMMI-GH)); Björn Lütjens (MIT)
Climate and Earth science Agriculture, forestry and other land use Disaster prediction, management, and relief Classification, regression, and supervised learning Interpretable ML Time-series analysis
NeurIPS 2020 Residue Density Segmentation for Monitoring and Optimizing Tillage Practices (Proposals Track)
Abstract and authors: (click to expand)
Abstract: "No-till" and cover cropping are often identified as the leading simple, best management practices for carbon sequestration in agriculture. However, the root of the problem is more complex, with the potential benefits of these approaches depending on numerous factors including a field's soil type(s), topography, and management history. Instead of using computer vision approaches to simply classify a field as till vs. no-till, we instead seek to identify the degree of residue coverage across a field through a probabilistic deep learning segmentation approach to enable more accurate analysis of carbon holding potential and realization. This approach will not only provide more precise insights into currently implemented practices, but also enable a more accurate identification process of fields with the greatest potential for adopting new practices to significantly impact carbon sequestration in agriculture.
Authors: Jennifer Hobbs (IntelinAir); Ivan A Dozier (IntelinAir); Naira Hovakimyan (UIUC)
Agriculture, forestry and other land use Carbon capture and sequestration Computer vision and remote sensing
NeurIPS 2020 Machine Learning Informed Policy for Environmental Justice in Atlanta with Climate Justice Implications (Proposals Track)
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Abstract: Environmental hazards are not evenly distributed between the privileged and the protected classes in the U.S. Neighborhood zoning and planning of hazardous treatment, storage, and disposal facilities (TSDs) play a significant role in this sanctioned environmental racism. TSDs and toxic chemical releases into the air are accounted for by the U.S. Environmental Protection Agency’s (EPA) Toxic Release Inventories (TRIs) [2,4,7, 14]. TSDs and toxic chemical releases not only emit carbon dioxide and methane, which are the top two drivers of climate change, but also emit contaminants, such as arsenic, lead, and mercury into the water, air, and crops [12]. Studies on spatial disparities in TRIs and TSDs based on race/ethnicity and socioeconomic status (SES) in U.S. cities, such as Charleston, SC, San Joaquin Valley, CA, and West Oakland, CA showed that there are more TRIs and TSDs in non-white and low SES areas in those cities [2,4,7]. Environmental justice recognizes that the impacts of environmental burdens, such as socioeconomic and public health outcomes, are not equitably distributed, and in fact bear the heaviest burden on marginalized people, including communities of color and low-income communities [12]. In our case, environmental justice has a strong tie to climate justice since the TRIs release carbon dioxide and methane into the atmosphere.
Authors: Lelia Hampton (Massachusetts Institute of Technology)
Climate policy Behavioral and social science Climate justice Classification, regression, and supervised learning Unsupervised and semi-supervised learning
NeurIPS 2020 A Multi-source, End-to-End Solution for Tracking Climate Change Adaptation in Agriculture (Proposals Track)
Abstract and authors: (click to expand)
Abstract: The impact of climate change on tropical agri-food systems will depend on both the direction and magnitude of climate change, and the agricultural sector’s adaptive capacity, the latter being affected by the chosen adaptation strategies. By extending SEIRS, a Satellite Remote Sensing (SRS) based system originally developed by the International Center for Tropical Agriculture - CIAT for monitoring U.S. Government-funded development programs across cropping areas in Africa, this research proposes the development and deployment of a scalable AI-based platform exploiting free-of-charge SRS data that will enable the agri-food sector to monitor a wide range of climate change adaptation (CCA) interventions in a timely, evidence-driven and comparable manner. The main contributions of the platform are i) ingesting and processing variety sources of SRS data with a considerable record (> 5 years) of vegetation greenness and precipitation (input data); ii) operating an end-to-end system by exploiting AI-based models suited to time series analysis such as Seq2Seq and Transformers; iii) providing customised proxies informing the success or failure of a given local CCA intervention(s).
Authors: Alejandro Coca-Castro (Kings College London); Aaron Golden (NUI Galway); Louis Reymondin (The Alliance of Bioversity International and the International Center for Tropical Agriculture)
Computer vision and remote sensing Agriculture, forestry and other land use Climate finance and economics Climate policy Classification, regression, and supervised learning Time-series analysis
NeurIPS 2020 Expert-in-the-loop Systems Towards Safety-critical Machine Learning Technology in Wildfire Intelligence (Proposals Track)
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Abstract: With the advent of climate change, wildfires are becoming more frequent and severe across several regions worldwide. To prevent and mitigate its effects, wildfire intelligence plays a pivotal role, e.g. to monitor the evolution of wildfires and for early detection in high-risk areas such as wildland-urban-interface regions. Recent works have proposed deep learning solutions for fire detection tasks, however the current limited databases prevent reliable real-world deployments. We propose the development of expert-in-the-loop systems that combine the benefits of semi-automated data annotation with relevant domain knowledge expertise. Through this approach we aim to improve the data curation process and contribute to the generation of large-scale image databases for relevant wildfire tasks and empower the application of machine learning techniques in wildfire intelligence in real scenarios.
Authors: Maria João Sousa (IDMEC, Instituto Superior Técnico, Universidade de Lisboa); Alexandra Moutinho (IDMEC, Instituto Superior Técnico, Universidade de Lisboa); Miguel Almeida (ADAI, University of Coimbra)
Computer vision and remote sensing Carbon capture and sequestration Disaster prediction, management, and relief Agriculture, forestry and other land use Classification, regression, and supervised learning Interpretable ML Meta- and transfer learning Natural language processing Uncertainty quantification and robustness Unsupervised and semi-supervised learning
NeurIPS 2020 ACED: Accelerated Computational Electrochemical systems Discovery (Proposals Track)
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Abstract: Large-scale electrification is vital to addressing the climate crisis, but many engineering challenges remain to fully electrifying both the chemical industry and transportation. In both of these areas, new electrochemical materials and systems will be critical, but developing these systems currently relies heavily on computationally expensive first-principles simulations as well as human-time-intensive experimental trial and error. We propose to develop an automated workflow that accelerates these computational steps by introducing both automated error handling in generating the first-principles training data as well as physics-informed machine learning surrogates to further reduce computational cost. It will also have the capacity to include automated experiments in the loop'' in order to dramatically accelerate the overall materials discovery pipeline.
Authors: Rachel C Kurchin (CMU); Eric Muckley (Citrine Informatics); Lance Kavalsky (CMU); Vinay Hegde (Citrine Informatics); Dhairya Gandhi (Julia Computing); Xiaoyu Sun (CMU); Matthew Johnson (MIT); Alan Edelman (MIT); James Saal (Citrine Informatics); Christopher V Rackauckas (Massachusetts Institute of Technology); Bryce Meredig (Citrine Informatics); Viral Shah (Julia Computing); Venkat Viswanathan (Carnegie Mellon University)
Power and energy Agriculture, forestry and other land use Transportation Active learning Classification, regression, and supervised learning Hybrid physical models Interpretable ML Uncertainty quantification and robustness
NeurIPS 2020 Forecasting Marginal Emissions Factors in PJM (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Many climate change applications rely on accurate forecasts of power grid emissions, but many forecasting methods can be expensive, sensitive to input errors, or lacking in domain knowledge. Motivated by initial experiments using deep learning and power system modeling techniques, we propose a method that combines the strengths of both of these approaches to forecast hourly day-ahead MEFs for the PJM region of the United States.
Authors: Amy H Wang (Western University); Priya L Donti (Carnegie Mellon University)
Power and energy Hybrid physical models Time-series analysis
NeurIPS 2020 Artificial Intelligence, Machine Learning and Modeling for Understanding the Oceans and Climate Change (Proposals Track)
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Abstract: These changes will have a drastic impact on almost all forms of life in the ocean with further consequences on food security, ecosystem services in coastal and inland communities. Despite these impacts, scientific data and infrastructures are still lacking to understand and quantify the consequences of these perturbations on the marine ecosystem. Understanding this phenomenon is not only an urgent but also a scientifically demanding task. Consequently, it is a problem that must be addressed with a scientific cohort approach, where multi-disciplinary teams collaborate to bring the best of different scientific areas. In this proposal paper, we describe our newly launched four-years project focused on developing new artificial intelligence, machine learning, and mathematical modeling tools to contribute to the understanding of the structure, functioning, and underlying mechanisms and dynamics of the global ocean symbiome and its relation with climate change. These actions should enable the understanding of our oceans and predict and mitigate the consequences of climate change.
Authors: Nayat Sánchez Pi (Inria); Luis Martí (Inria); André Abreu (Fountation Tara Océans); Olivier Bernard (Inria); Colomban de Vargas (CNRS); Damien Eveillard (Univ. Nantes); Alejandro Maass (CMM, U. Chile); Pablo Marquet (PUC); Jacques Sainte-Marie (Inria); Julien Salomin (Inria); Marc Schoenauer (INRIA); Michele Sebag (LRI, CNRS, France)
Interpretable ML Carbon capture and sequestration Ecosystems and natural systems Active learning Causal and Bayesian methods Computer vision and remote sensing Hybrid physical models Meta- and transfer learning Time-series analysis
NeurIPS 2020 Machine Learning towards a Global Parameterisation of Atmospheric New Particle Formation and Growth (Proposals Track)
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Abstract: New particle formation (NPF) and growth in the atmosphere affects climate, weather, air quality, and human health. It is the first step of the complex process leading to cloud condensation nuclei (CCN) formation. Even though there is a wealth of observations from field measurements (in forests, high-altitude, polar regions, coastal and urban sites, aircraft campaigns), as well as laboratory studies of multi-component nucleation (including the CLOUD chamber at CERN), and improved nucleation theories, the NPF parameterisations in regional and global models are lacking. These deficiencies make the impacts of aerosols one of the highest sources of uncertainty in global climate change modelling, and associated impacts on weather and human health. We propose to use Machine Learning methods to overcome the challenges in modelling aerosol nucleation and growth, by ingesting the data from the multitude of available sources to create a single parameterisation applicable throughout the modelled atmosphere (troposphere and stratosphere at all latitudes) that efficiently encompasses all input ambient conditions and concentrations of relevant species.
Authors: Theodoros Christoudias (Cyprus Institute); Mihalis A Nicolaou (Cyprus Institute)
Climate and Earth science Classification, regression, and supervised learning
ICLR 2020 BISCUIT: Building Intelligent System Customer Investment Tools (Papers Track)
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Abstract: Energy use in buildings account for approximately half of global electricity consumption and a significant amount of CO2 emissions. Often, the higher energy usage in buildings are accounted to old and poorly maintained infrastructure and equipments. On the other hand, Smart buildings are capable of achieving energy efficiency by using intelligent services such as indoor positioning, personalized lighting, demand-based heating ventilation and air-conditioning, automatic fault detection and recovery etc. However, most buildings nowadays lack the basic components and infrastructure to support such services. The investment decision of intelligent system design and retrofit can be a daunting task, because it involves both hardware (sensors, actuators, servers) and software (operating systems, service algorithms), which have issues of compatibility, functionality constraints, and opportunities of co-design of synergy. Our work proposes a user-oriented investment decision toolset using optimization and machine learning techniques aimed at handling the complexity of exploration in the large design space and to enhance cost-effectiveness, energy efficiency, and human-centric values. The toolset is demonstrated in a case study to retrofit a medium-sized building, where it is shown to propose a design that significantly lowers the overall investment cost while achieving user specifications.
Authors: Ming Jin (U.C. Berkeley); Ruoxi Jia (UC Berkeley); Hari Prasanna Das (UC Berkeley); Wei Feng (Lawrence Berkeley National Laboratory); Costas J. Spanos (University of California at Berkeley)
Buildings and cities
ICLR 2020 Deep Reinforcement Learning based Renewable Energy Error Compensable Forecasting (Papers Track)
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Abstract: Recently, renewable energy is rapidly integrated into the power grid to prevent climate change, and accurate forecasting of renewable generation becomes critical for reliable power system operation. However, existing forecasting algorithms only focused on reducing forecasting errors without considering error compensability by using a large-scale battery. In this paper, we propose a novel strategy called error compensable forecasting. We switch the objective of forecasting from reducing errors to making errors compensable by leveraging a battery. Specifically, we propose a deep reinforcement learning based framework having forecasting in the loop of control. Extensive simulations show that the proposed one-hour ahead forecasting achieves zero error for more than 98% of time while reducing the operational expenditure by up to 44%.
Authors: Jaeik Jeong (Sogang University); Hongseok Kim (Sogang University)
Power and energy Data presentation and management
ICLR 2020 Missing-insensitive Short-term Load Forecasting Leveraging Autoencoder and LSTM (Papers Track)
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Abstract: Short-term load forecasting (STLF) is fundamental for power system operation, demand response, and also greenhouse gas emission reduction. So far, most deep learning-based STLF techniques require intact data, but many real-world datasets contain missing values due to various reasons, and thus missing imputation using deep learning is actively studied. However, missing imputation and STLF have been considered independently so far. In this paper, we jointly consider missing imputation and STLF and propose a family of autoencoder/LSTM combined models to realize missing-insensitive STLF. Specifically, autoencoder (AE), denoising autoencoder (DAE), and convolutional autoencoder (CAE) are investigated for extracting features, which is directly fed into the input of LSTM. Our results show that three proposed autoencoder/LSTM combined models significantly improve forecasting accuracy compared to the baseline models of deep neural network and LSTM. Furthermore, the proposed CAE/LSTM combined model outperforms all other models for 5%-25% of random missing data.
Authors: Kyungnam Park (Sogang University); Jaeik Jeong (Sogang University); Hongseok Kim (Sogang University)
Power and energy Data presentation and management
ICLR 2020 A Machine Learning Pipeline to Predict Vegetation Health (Papers Track)
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Abstract: Agricultural droughts can exacerbate poverty and lead to famine. Timely distribution of disaster relief funds is essential to help minimise the impact of drought. Indices of vegetation health are indicative of higher risk of agricultural drought, but their prediction remains challenging, particularly in Africa. Here, we present an open-source machine learning pipeline for climate-related data. Specifically, we train and analyse a recurrent model to predict pixel-wise vegetation health in Kenya.
Authors: Thomas Lees (University of Oxford); Gabriel Tseng (Okra Solar); Simon Dadson (University of Oxford); Alex Hernández (University of Osnabrück); Clement G. Atzberger (University of Natural Resources and Life Sciences); Steven Reece (University of Oxford)
Disaster prediction, management, and relief Extreme weather events
ICLR 2020 Understanding the dynamics of climate-crucial food choice behaviours using Distributional Semantics (Papers Track)
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Abstract: Developed countries must make swift movements toward plant-based diets in order to mitigate climate change and maintain food security. However, researchers currently lack clear insight into the psychological dimensions that influence food choice, which is necessary to encourage the societal adaptation of new diets. In this project, we use Skip-gram word embeddings trained on the ukWaC corpus as a lens to study the implicit mental representations people have of foods. Our data-driven insights expand on findings from traditional, interview-based studies by uncovering implicit mental representations, allowing a better understanding the complex combination of conscious and sub-conscious processes surrounding food choice. In particular, our findings shed light on the pervasiveness of meat as the ‘centre’ of the meal in the UK.
Authors: Claudia Haworth (University of Sheffield); Gabriella Viglioco (University College London)
Societal adaptation Climate change and diet
ICLR 2020 SolarNet: A Deep Learning Framework to Map Solar Plants In China From Satellite Imagery (Papers Track)
Abstract and authors: (click to expand)
Abstract: Renewable energy such as solar power is critical to fight the ever more serious climate, how to effectively detect renewable energy has became an important issue for governments. In this paper, we proposed a deep learning framework named SolarNet which is designed to perform semantic segmentation on large scale satellite imagery data to detect solar farms. SolarNet has successfully mapped 439 solar farms in China, covering near 2000 square kilometers, equivalent to the size of whole Shenzhen city or two and a half of New York city. To the best of our knowledge, it is the first time that we used deep learning to reveal the locations and sizes of solar farms in China, which could provide insights for solar power companies, climate finance and markets.
Authors: Xin Hou (WeBank); Biao Wang (WeBank); Wanqi Hu (WeBank); lei yin (WeBank); Anbu Huang (WeBank); Haishan Wu (WeBank)
Power and energy Ecosystems and natural systems
ICLR 2020 Embedding Hard Physical Constraints in Convolutional Neural Networks for 3D Turbulence (Papers Track)
Abstract and authors: (click to expand)
Abstract: Deep learning approaches have shown much promise for climate sciences, especially in dimensionality reduction and compression of large datasets. A major issue in deep learning of climate phenomena, like geophysical turbulence, is the lack of physical guarantees. In this work, we propose a general framework to directly embed the notion of incompressible fluids into Convolutional Neural Networks, for coarse-graining of turbulence. These \textbf{physics-embedded neural networks} leverage interpretable strategies from numerical methods and computational fluid dynamics to enforce physical laws and boundary conditions by taking advantage the mathematical properties of the underlying equations. We demonstrate results on 3D fully-developed turbulence, showing that the \textit{physics-aware inductive bias} drastically improves local conservation of mass, without sacrificing performance according to several other metrics characterizing the fluid flow.
Authors: Arvind T Mohan (Los Alamos National Laboratory); NIcholas Lubbers (Los Alamos National Laboratory); Daniel Livescu (Los Alamos National Laboratory); Misha Chertkov (University of Arizona)
Climate and Earth science Extreme weather events
ICLR 2020 DETECTION OF HOUSING AND AGRICULTURE AREAS ON DRY-RIVERBEDS FOR THE EVALUATION OF RISK BY LANDSLIDES USING LOW-RESOLUTION SATELLITE IMAGERY BASED ON DEEP LEARNING. STUDY ZONE: LIMA, PERU (Papers Track)
Abstract and authors: (click to expand)
Abstract: The expansion of human settlements in Peru has caused risk exposure to landslides. However, this risk could increase because the intensity of the El niño phenomenon will be greater in the coming years, increasing rainfall on the Peruvian coast. In this paper, we present a novel methodology for detecting housing areas and agricultural lands in low-resolution satellite imagery in order to analyze potential risk in case of unexpected landslides. It was developed by creating two datasets from Lima Metropolitana in Peru, one of which is for detecting dry riverbeds and agriculture lands, and the other for classifying housing areas. We applied data augmentation based on geometrical methods and trained architectures based on U-net methods separately and then, overlap the results for risk assessment. We found that there are areas with significant potential risk that have been classified by the Peruvian government as medium or low risk areas. On this basis, it is recommended obtain a dataset with better resolution that can identify how many housing areas will be affected and take the appropriate prevention measures. Further research in post-processing is needed for suppress noise in our results.
Authors: Brian Cerrón (National University of Engineering); Cristopher Bazan (National University of Engineering); Alberto Coronado (National University of Engineering)
Buildings and cities Agriculture, forestry and other land use Climate and Earth science Industry
ICLR 2020 Non-linear interlinkages and key objectives amongst the Paris Agreement and the Sustainable Development Goals (Papers Track)
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Abstract: The United Nations' ambitions to combat climate change and prosper human development are manifested in the Paris Agreement and the Sustainable Development Goals (SDGs), respectively. These are inherently inter-linked as progress towards some of these objectives may accelerate or hinder progress towards others. We investigate how these two agendas influence each other by defining networks of 18 nodes, consisting of the 17 SDGs and climate change, for various groupings of countries. We compute a non-linear measure of conditional dependence, the partial distance correlation, given any subset of the remaining 16 variables. These correlations are treated as weights on edges, and weighted eigenvector centralities are calculated to determine the most important nodes. We find that SDG 6, clean water and sanitation, and SDG 4, quality education, are most central across nearly all groupings of countries. In developing regions, SDG 17, partnerships for the goals, is strongly connected to the progress of other objectives in the two agendas whilst, somewhat surprisingly, SDG 8, decent work and economic growth, is not as important in terms of eigenvector centrality.
Authors: Felix Laumann (Imperial College London); Julius von Kügelgen (MPI for Intelligent Systems, Tübingen & University of Cambridge); Mauricio Barahona (Imperial College London)
Climate policy Data presentation and management Societal adaptation
ICLR 2020 A CONTINUAL LEARNING APPROACH FOR LOCAL LEVEL ENVIRONMENTAL MONITORING IN LOW-RESOURCE SETTINGS (Papers Track)
Abstract and authors: (click to expand)
Abstract: An increasingly important dimension in the quest for mitigation and monitoring of environmental change is the role of citizens. The crowd-based monitoring of local level anthropogenic alterations is essential towards measurable changes in different contributing factors to climate change. With the proliferation of mobile technologies here in the African continent, it is useful to have machine learning based models that are deployed on mobile devices and that can learn continually from streams of data over extended time, possibly pertaining to different tasks of interest. In this paper, we demonstrate the localisation of deforestation indicators using lightweight models and extend to incorporate data about wildfires and smoke detection. The idea is to show the need and potential of continual learning approaches towards building robust models to track local environmental alterations.
Authors: Arijit Patra (University of Oxford)
Agriculture, forestry and other land use Disaster prediction, management, and relief Ecosystems and natural systems Societal adaptation
ICLR 2020 WeatherBench: A benchmark dataset for data-driven weather forecasting (Papers Track) Best Paper Award
Abstract and authors: (click to expand)
Abstract: Accurate weather forecasts are a crucial prerequisite for climate change adaptation. Can these be provided by deep learning? First studies show promise, but the lack of a common dataset and evaluation metrics make inter-comparison between the proposed models difficult. In fact, despite the recent research surge in data-driven weather forecasting, there is currently no standard approach for evaluating the proposed models. Here we introduce WeatherBench, a benchmark dataset for data-driven medium-range weather forecasting. We provide data derived from an archive of assimilated earth observations for the last 40 years that has been processed to facilitate the use in machine learning models. We propose a simple and clear evaluation metric which will enable a direct comparison between different proposed methods. Further, we provide baseline scores from simple linear regression techniques, purely physical forecasting models as well as existing deep learning weather forecasting models. All data and code are made publicly available along with tutorials for getting started. We believe WeatherBench will provide a useful and reproducible way of evaluating data-driven weather forecasting models and we hope that it will accelerate research in this direction.
Authors: Stephan Rasp (Technical University of Munich); Soukayna Mouatadid (University of Toronto); Peter Dueben (European Centre for Medium-Range Weather Forecasts (ECMWF)); Sebastian Scher (Stockholm University); Jonathan Weyn (University of Washington); Nils Thuerey (nils.thuerey@tum.de)
Climate and Earth science Extreme weather events
ICLR 2020 Modeling Cloud Reflectance Fields using Conditional Generative Adversarial Networks (Papers Track)
Abstract and authors: (click to expand)
Abstract: We introduce a conditional Generative Adversarial Network (cGAN) approach to generate cloud reflectance fields (CRFs) conditioned on large scale meteorological variables such as sea surface temperature and relative humidity. We show that our trained model can generate realistic CRFs from the corresponding meteorological observations, which represents a step towards a data-driven framework for stochastic cloud parameterization.
Authors: Victor Schmidt (Mila); Mustafa Alghali Muhammed (University of Khartoum); Kris Sankaran (Montreal Institute for Learning Algorithms); Tianle Yuan (NASA); Yoshua Bengio (Mila)
Climate and Earth science
ICLR 2020 SMArtCast: Predicting soil moisture interpolations into the future using Earth observation data in a deep learning framework (Papers Track)
Abstract and authors: (click to expand)
Abstract: Soil moisture is critical component of crop health and monitoring it can enable further actions for increasing yield or preventing catastrophic die off. As climate change increases the likelihood of extreme weather events and reduces the predictability of weather, and non-optimal soil moistures for crops may become more likely. In this work, we use a series of LSTM architectures to analyze measurements of soil moisture and vegetation indices derived from satellite imagery. The system learns to predict the future values of these measurements. These spatially sparse values and indices are used as input features to an interpolation method that infer spatially dense moisture maps at multiple depths for a future time point. This has the potential to provide advance warning for soil moistures that may be inhospitable to crops across an area with limited monitoring capacity.
Authors: Conrad J Foley (Deep Planet); Sagar Vaze (deepplanet.ai); Mohamed El Amine Seddiq (Deep Planet); Aleksei Unagaev (Deep Planet); Natalia Efremova (University of Oxford)
Agriculture, forestry and other land use Ecosystems and natural systems Extreme weather events
ICLR 2020 Prediction of Bayesian Intervals for Tropical Storms (Papers Track)
Abstract and authors: (click to expand)
Abstract: Building on recent research for prediction of hurricane trajectories using recurrent neural networks (RNNs), we have developed improved methods and generalized the approach to predict a confidence interval region of the trajectory utilizing Bayesian methods. Tropical storms are capable of causing severe damage, so accurately predicting their trajectories can bring significant benefits to cities and lives, especially as they grow more intense due to climate change effects. By implementing the Bayesian confidence interval using dropout in an RNN, we improve the actionability of the predictions, for example by estimating the areas to evacuate in the landfall region. We used an RNN to predict the trajectory of the storms at 6-hour intervals. We used latitude, longitude, windspeed, and pressure features from a Statistical Hurricane Intensity Prediction Scheme (SHIPS) dataset of about 500 tropical storms in the Atlantic Ocean. Our results show how neural network dropout values affect our predictions and Bayesian intervals.
Authors: Max Chiswick (Independent); Sam Ganzfried (Ganzfried Research)
Extreme weather events Climate and Earth science
ICLR 2020 MobilityNet: Towards a Public Dataset for Multi-modal Mobility Research (Papers Track)
Abstract and authors: (click to expand)
Abstract: Influencing transportation demand can significantly reduce CO2 emissions. Individual user mobility models are key to influencing demand at the personal and structural levels. Constructing such models is a challenging task that depends on a number of interdependent steps. Progress on this task is hamstrung by the lack of high quality public datasets. We introduce MobilityNet: the first step towards a common ground for multi-modal mobility research. MobilityNet solves the holistic evaluation, privacy preservation and fine grained ground truth problems through the use of artificial trips, control phones, and repeated travel. It currently includes 1080 hours of data from both Android and iOS, representing 16 different travel contexts and 4 different sensing configurations.
Authors: K. Shankari (UC Berkeley); Jonathan Fürst (NEC Laboratories Europe); Mauricio Fadel Argerich (NEC Laboratories Europe); Eleftherios Avramidis (DFKI GmbH); Jesse Zhang (UC Berkeley)
Transportation Buildings and cities
ICLR 2020 Wavelet-Powered Neural Networks for Turbulence (Papers Track)
Abstract and authors: (click to expand)
Abstract: One of the fundamental driving phenomena for climate effects is fluid turbulence in geophysical flows. Modeling these flows and explaining its associated spatio-temporal phenomena are notoriously difficult tasks. Navier-Stokes (NS) equations describe all the details of the fluid motions, but require accounting for unfeasibly many degrees of freedom in the regime of developed turbulence. Model reduction and surrogate modeling of turbulence is a general methodology aiming to circumvent this curse of dimensionality. Originally driven by phenomenological considerations, multiple attempts to model-reduce NS equations got a new boost recently with Deep Learning (DL), trained on the ground truth data, e.g. extracted from high-fidelity Direct Numerical Simulations (DNS). However, early attempts of building NNs to model turbulence has also revealed its lack of interpretability as the most significant shortcoming. In this paper we address the key challenge of devising reduced but, at least partially, interpretable model. We take advantage of the balance between strong mathematical foundations and the physical interpretability of wavelet theory to build a spatio-temporally reduced dynamical map which fuses wavelet based spatial decomposition with spatio-temporal modeling based on Convolutional Long Short Term Memory (C-LSTM) architecture. It is shown that the wavelet-based NN makes progress in scaling to large flows, by reducing computational costs and GPU memory requirements.
Authors: Arvind T Mohan (Los Alamos National Laboratory); Daniel Livescu (Los Alamos National Laboratory); Misha Chertkov (University of Arizona)
Climate and Earth science Data presentation and management
ICLR 2020 Benchmarks for Grid Flexibility Prediction: Enabling Progress and Machine Learning Applications (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Decarbonizing the grid is recognized worldwide as one of the objectives for the next decades. Its success depends on our ability to massively deploy renewable resources, but to fully benefit from those, grid flexibility is needed. In this paper we put forward the design of a benchmark that will allow for the systematic measurement of demand response programs' effectiveness, information that we do not currently have. Furthermore, we explain how the proposed benchmark will facilitate the use of Machine Learning techniques in grid flexibility applications.
Authors: Diego Kiedansk (Telecom ParisTech); Lauren Kuntz (Gaiascope); Daniel Kofman (Telecom ParisTech)
Power and energy Data presentation and management
ICLR 2020 Machine Learning Approaches to Safeguarding Continuous Water Supply in the Arid and Semi-arid Lands of Northern Kenya (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Arid and semi-arid regions (ASALs) in developing countries are heavily affected by the effects of global warming and climate change, leading to adverse climatic conditions such as drought and flooding. This paper explores the problem of fresh-water access in northern Kenya and measures being taken to safeguard water access despite these harsh climatic changes. We present an integrated water management and decision-support platform, eMaji Manager, that we developed and deployed in five ASAL counties in northern Kenya to manage waterpoint access for people and livestock. We then propose innovative machine learning methods for understanding waterpoint usage and repair patterns for sensor-instrumented waterpoints (e.g., boreholes). We explore sub-sequence discriminatory models and recurrent neural networks to predict water-point failures, improve repair response times and ultimately support continuous access to water.
Authors: Fred Otieno (IBM); Timothy Nyota (IBM); Isaac Waweru (IBM); Celia Cintas (IBM Research); Samuel C Maina (IBM Research); William Ogallo (IBM Research); Aisha Walcott-Bryant (IBM Research - Africa)
Climate and Earth science Data presentation and management Societal adaptation
ICLR 2020 Accelerated Data Discovery for Scalable Climate Action (Proposals Track)
Abstract and authors: (click to expand)
Abstract: According to the Intergovernmental Panel on Climate Change (IPCC), the planet must decarbonize by 50% by 2030 in order to keep global warming below 1.5C. This goal calls for a prompt and massive deployment of solutions in all societal sectors - research, governance, finance, commerce, health care, consumption. One challenge for experts and non-experts is access to the rapidly growing body of relevant information, which is currently scattered across many weakly linked domains of expertise. We propose a large-scale, semi-automatic, AI-based discovery system to collect, tag, and semantically index this information. The ultimate goal is a near real-time, partially curated data catalog of global climate information for rapidly scalable climate action.
Authors: Henning Schwabe (Private); Sumeet Sandhu (Elementary IP LLC); Sergy Grebenschikov (Private)
Data presentation and management Climate and Earth science Climate finance and economics Industry Climate policy
ICLR 2020 YOU FORGOT IT IN THE GENOTYPE, MODELING TOWARDS ADAPTATION OF FOOD CROPS UNDER CLIMATE CHANGE THREAT (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Agriculture is facing the disastrous effects of frequent drastic climate changes. Efforts have increased towards the implementation of inexpensive solutions for crop-yield prediction using publicly available data to prevent severe long-term problems like food scarcity and security, amongst others. Agricultural productiv- ity is intrinsic to the choice of plant species (i.e. cultivar) and represents oppor- tunity cost for farm managers. The currently used cultivars have been artificially selected for productivity at the expense of not being flexible to survive drastic cli- mate changes. Current state-of-the-art machine learning models have modelled holistically all agricultural counterparts (i.e. soil, management, weather, crop cul- tivars etc), albeit, oversimplifying some of the biological features of their culti- vars without taking advantage of their data properties. Specifically, these models oversimplify some biological features like the genotype making them irrelevant or depicting incomplete conclusions since not all of the information from the cul- tivar is incorporated. With the goal of creating new models that perform well on the yield prediction task in unstable weather conditions (e.g. under the effect of climate change), here the authors argue for the importance of incorporating additional biological features inferred from the genotype, like stability, and hy- pothesise that current state-of-the-art models for grain-yield prediction are blind to such features, and hence not applicable in such scenario.
Authors: Olivia Mendivil Ramos (Cold Spring Harbor Laboratory); Linda Petrini (Mila)
Agriculture, forestry and other land use
ICLR 2020 Hurricane Nowcasting with Irregular Time-step using Neural-ODE and Video Prediction (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Fast and accurate prediction of extreme climate events is critical especially in the recent globally warming environment. Considering recent advancements in deep neural networks, it is worthwhile to tackle this problem as data-driven spatio-temporal prediction using neural networks. However, a nontrivial challenge in practice lies in irregular time gaps between which climate observation data are collected due to sensor errors and other issues. This paper proposes an approach for spatio-temporal hurricane prediction that can address this issue of irregular time gaps in collected data with a simple but robust end-to-end model based on Neural Ordinary Differential Equation and video prediction model based on Retrospective Cycle-GAN.
Authors: Sunghyun Park (KAIST); Kangyeol Kim (KAIST); Sookyung Kim (Lawrence Livermore National Laboratory); Joonseok Lee (Google Research); Junsoo Lee (KAIST); Jiwoo Lee (Lawrence Livermore National Laboratory); Jaegul Choo (KAIST)
Extreme weather events Disaster prediction, management, and relief
ICLR 2020 Indigenous Knowledge Aware Drought Monitoring, Forecasting and Prediction Using Deep Learning Techniques (Proposals Track)
Abstract and authors: (click to expand)
Abstract: The general objective of this proposed research work is to design deep learning based hybrid comprehensive framework for drought monitoring, forecasting and prediction using scientific and indigenous knowledge as an integration of connectionist and symbolic AI. In Ethiopia, among all extreme climate events, drought is considered as the most complex phenomenon affecting the country and its impact is also high due to absence of locally grounded intelligent and explainable technology-oriented drought early warning and monitoring system. Thus, studying Ethiopic perspective of drought monitoring and prediction in line with continental and global climate change is vital for drought impact minimization and sustainable development of the country. Moreover, having technology assisted early protective, preventative action is also many times cheaper than the associated response to humanitarian crisis. Accordingly, this proposed work will have different expected outputs, including: drought risk identification, drought monitoring, drought preparedness, drought forecasting, drought mitigation, and post drought best practice recommendation models with interactive visualizations and explanations.
Authors: Kidane W Degefa (Haramaya University)
Disaster prediction, management, and relief Extreme weather events
ICLR 2020 TrueBranch: Metric Learning-based Verification of Forest Conservation Projects (Proposals Track) Best Proposal Award
Abstract and authors: (click to expand)
Abstract: International stakeholders increasingly invest in offsetting carbon emissions, for example, via issuing Payments for Ecosystem Services (PES) to forest conservation projects. Issuing trusted payments requires a transparent monitoring, reporting, and verification (MRV) process of the ecosystem services (e.g., carbon stored in forests). The current MRV process, however, is either too expensive (on-ground inspection of forest) or inaccurate (satellite). Recent works propose low-cost and accurate MRV via automatically determining forest carbon from drone imagery, collected by the landowners. The automation of MRV, however, opens up the possibility that landowners report untruthful drone imagery. To be robust against untruthful reporting, we propose TrueBranch, a metric learning-based algorithm that verifies the truthfulness of drone imagery from forest conservation projects. TrueBranch aims to detect untruthfully reported drone imagery by matching it with public satellite imagery. Preliminary results suggest that nominal distance metrics are not sufficient to reliably detect untruthfully reported imagery. TrueBranch leverages a method from metric learning to create a feature embedding in which truthfully and untruthfully collected imagery is easily distinguishable by distance thresholding.
Authors: Simona Santamaria (ETH Zurich); David Dao (ETH Zurich); Björn Lütjens (MIT); Ce Zhang (ETH)
Agriculture, forestry and other land use Carbon capture and sequestration Climate finance and economics Ecosystems and natural systems
ICLR 2020 Advancing Renewable Electricity Consumption With Reinforcement Learning (Proposals Track)
Abstract and authors: (click to expand)
Abstract: As the share of renewable energy sources in the present electric energy mix rises, their intermittence proves to be the biggest challenge to carbon free electricity generation. To address this challenge, we propose an electricity pricing agent, which sends price signals to the customers and contributes to shifting the customer demand to periods of high renewable energy generation. We propose an implementation of a pricing agent with a reinforcement learning approach where the environment is represented by the customers, the electricity generation utilities and the weather conditions.
Authors: Filip Tolovski (Fraunhofer Heinrich-Hertz-Institut)
Power and energy Data presentation and management Industry
ICLR 2020 Xingu: Explaining critical geospatial predictions in weak supervision for climate finance (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Monitoring, Reporting, and Verification (MRV) play a crucial key role in the decision-making of climate investors, policymakers and conservationists. Remote sensing is commonly used for MRV but practical solutions are constrained by a lack of labels to train machine learning-based downstream tasks. Recent work leverages weak supervision to alleviate the problem of labelled data scarcity. However, the definition of weak supervision signals is limited by the existence of millions of possible heuristic-based feature generation rules. Furthermore, these rules are often difficult to interpret for climate finance and underperform in critical data subsets. We propose Xingu, an interpretable MRV system to explain weak supervision rules using game-theoretic SHAP values for critical model predictions. Moreover, Xingu enables domain experts to collectively design and share labelling functions, thus curating a reusable knowledge base for weak supervision signals.
Authors: David Dao (ETH Zurich); Johannes Rausch (ETH Zurich); Ce Zhang (ETH); Iveta Rott (ETH Zurich)
Climate finance and economics Data presentation and management
ICLR 2020 Towards a unified standards for smart infrastructure datasets (Proposals Track)
Abstract and authors: (click to expand)
Abstract: Development of smart devices and smart home appliances allowed us to harness more data about energy patterns inside households, overtime this amount will increase. There are contributions published to address building datasets, working for objective of energy consumption optimization. Yet there are still factors if included could help in understanding problem better. This proposal tries to annotate missing features that if applied could help in a better understanding energy consumption in smart buildings impact on environment. Second, to have a unified standards that help different solutions to be compared properly.
Authors: Abdulrahman A Ahmed (Cairo University)
Buildings and cities Power and energy
ICLR 2020 MACHINE LEARNING APPLICATIONS THAT CAN HELP PASTORAL COMMUNITIES IN NORTHERN KENYA AND ELSEWHERE ADAPT TO CLIMATE CHANGE (Proposals Track)
Abstract and authors: (click to expand)
Abstract: I propose the use of Machine Learning techniques such as Active Learning(AL) and Transfer Learning(TL) to translate climate information and adaption technique from major Western and Asian languages to thousands of low resource languages in the developing world. Studies have shown that access to information can help people assess the magnitude of the climate change challenge, possible options and those feasible within the relevant context (Nyahunda & Tiri-vangasi, 2019) I endeavor to demonstrate that if this information was available in a language the locals can understand, it would result in local empowerment and as a result inspire action.
Authors: Jefferson Sankara (Lori Systems)
ICLR 2020 Nutrient demand, Risk and Climate change: Evidence from historical rice yield trials in India (Proposals Track)
Abstract and authors: (click to expand)
Abstract: We use data from historical agronomic fertilizer trials to identify the effect of climate change on the average rice yield and the yield variability in India. The contribution of this paper is three folds: firstly, it has a methodological contribution by modelling the input conditional yield densities using a stochastic production structure for a developing country like India. In doing so, it predicts and measure the effects of climate change on rice grown in tropical regions; secondly,it estimates the nutrient demand and its link with the climate change; thirdly, by modelling the yield uncertainty, it characterizes the risk and role for insurance as a tool for tackling climate change in the developing countries.
Authors: Sandip K Agarwal (IISER Bhopal)
Agriculture, forestry and other land use Climate policy
ICLR 2020 USING MACHINE LEARNING TO ANALYZE CLIMATE CHANGE TECHNOLOGY TRANSFER (CCTT) (Proposals Track)
Abstract and authors: (click to expand)
Abstract: The objective of the present paper is to review the climate change technology transfer. This research proposes a method for analysing CCTT using patent analysis and topic modelling. A collection of climate change mitigation related technology (CCMT) patents from patent databases would be used as input to group patents in several relevant topics for climate change mitigation using the topic exploration model in this research. The research questions we want to address are: how have the patenting activities changed over time in CCMT patents? And who are the technological leaders? The investigation of these questions can offer the technological landscape in climate change-related technologies at the international level. We propose a hybrid Latent Dirichlet Allocation (LDA) approach for topic modelling and identification of relationships between terms and topics related to CCMT, enabling better visualizations of underlying intellectual property dynamics. Further, we propose predictive modelling for CCTT and competitor analysis to identify and rank countries with a similar patent landscape. The projected results are expected to facilitate the transfer process associated with existing and emerging climate change technologies and improve technology cooperation between governments.
Authors: Shruti Kulkarni (Indian Institute of Science (IISc))
Climate finance and economics Data presentation and management Societal adaptation
ICLR 2020 Using ML to close the vocabulary gap in the context of environment and climate change in Chichewa (Proposals Track)
Abstract and authors: (click to expand)
Abstract: In the west, alienation from nature and deteriorating opportunities to experience it, have led educators to incorporate educational programs in schools, to bring pupils in contact with nature and to enhance their understanding of issues related to the environment and its protection. In Africa, and in Malawi, where most people engage in agriculture, and spend most of their time in the 'outdoors', alienation from nature is happening too, although in different ways. Large portion of the indigenous vocabulary and knowledge remains unknown or is slowly disappearing, and there is a need to build a glossary of terms regarding environment and climate change in the vernacular to improve the dialog regarding climate change and environmental protection.. We believe that ML has a role to play in closing the ‘vocabulary gap’ of terms and concepts regarding the environment and climate change that exists in Chichewa and other Malawian languages by helping to creating a visual dictionary of key terms used to describe the environment and explain the issues involved in climate change and their meaning. Chichewa is a descriptive language, one English term may be translated using several words. Thus, the task is not to detect just literal translations, but also translations by means of ‘descriptions’ and illustrations and thus extract correspondence between terms and definitions and to measure how appropriate a term is to convey the meaning intended. As part of this project, ML can be used to identify ‘loanword patterns’, which may be useful in understanding the transmission of cultural items.
Authors: Amelia Taylor (University of Malawi, The Polytechnic)
Ecosystems and natural systems Agriculture, forestry and other land use Climate and Earth science
NeurIPS 2019 Warm-Starting AC Optimal Power Flow with Graph Neural Networks (Papers Track)
Abstract and authors: (click to expand)
Abstract: Efficient control of power grids is important both for efficiently managing genera- tors and to prolong longevity of components. However, that problem is NP-hard and linear approximations are necessary. The deployment of machine learning methods is hampered by the need to guarantee solutions. We propose to use Graph Neural Networks (GNNs) to model a power grid and produce an initial solution used to warm-start the optimization. This allows us to achieve the best of both worlds: Fast convergence and guaranteed solutions. On a synthetic power grid modelling Texas, we achieve a mean speedup by a factor of 2.8. This allows us to dispense with linear approximation, leads to more efficient generator dispatch, and can potentially save hundreds of megatons of CO2 -equivalent.
Authors: Frederik Diehl (fortiss)
Power and energy
NeurIPS 2019 Quantifying Urban Canopy Cover with Deep Convolutional Neural Networks (Papers Track)
Abstract and authors: (click to expand)
Abstract: Urban canopy cover is important to mitigate the impact of climate change. Yet, existing quantification of urban greenery is either manual and not scalable, or use traditional computer vision methods that are inaccurate. We train deep convolutional neural networks (DCNNs) on datasets used for self-driving cars to estimate urban greenery instead, and find that our semantic segmentation and direct end-to-end estimation method are more accurate and scalable, reducing mean absolute error of estimating the Green View Index (GVI) metric from 10.1% to 4.67%. With the revised DCNN methods, the Treepedia project was able to scale and analyze canopy cover in 22 cities internationally, sparking interest and action in public policy and research fields.
Authors: Bill Cai (Massachusetts Institute of Technology); Xiaojiang Li (Temple University); Carlo Ratti (Massachusetts Institute of Technology )
Buildings and cities Agriculture, forestry and other land use
NeurIPS 2019 Using LSTMs for climate change assessment studies on droughts and floods (Papers Track)
Abstract and authors: (click to expand)
Abstract: Climate change affects occurrences of floods and droughts worldwide. However, predicting climate impacts over individual watersheds is difficult, primarily because accurate hydrological forecasts require models that are calibrated to past data. In this work we present a large-scale LSTM-based modeling approach that - by training on large data sets - learns a diversity of hydrological behaviors. Previous work shows that this model is more accurate than current state-of-the-art models, even when the LSTM-based approach operates out-of-sample and the latter in-sample. In this work, we show how this model can assess the sensitivity of the underlying systems with regard to extreme (high and low) flows in individual watersheds over the continental US.
Authors: Frederik Kratzert (LIT AI Lab, Institute for Machine Learning, Johannes Kepler University Linz, Austria); Daniel Klotz (LIT AI Lab, Institute for Machine Learning, Johannes Kepler University Linz, Austria); Johannes Brandstetter (LIT AI Lab, Institute for Machine Learning, Johannes Kepler University Linz, Austria); Pieter-Jan Hoedt (Johannes Kepler University Linz); Grey Nearing (Department of Geological Sciences, University of Alabama, Tuscaloosa, AL United States); Sepp Hochreiter (LIT AI Lab, Institute for Machine Learning, Johannes Kepler University Linz, Austria)
Climate and Earth science
NeurIPS 2019 Learning to Focus and Track Hurricanes (Papers Track)
Abstract and authors: (click to expand)
Abstract: This paper tackles the task of extreme climate event tracking. We propose a simple but robust end-to-end model based on multi-layered ConvLSTMs, suitable for climate event tracking. It first learns to imprint the location and the appearance of the target at the first frame in an auto-encoding fashion. Next, the learned feature is fed to the tracking module to track the target in subsequent time frames. To tackle the data shortage problem, we propose data augmentation based on conditional generative adversarial networks. Extensive experiments show that the proposed framework significantly improves tracking performance of a hurricane tracking task over several state-of-the-art methods.
Authors: Sookyung Kim (Lawrence Livermore National Laboratory); Sunghyun Park (Korea University); Sunghyo Chung (Kakao Corp.); Joonseok Lee (Google Research); Jaegul Choo (Korea University); Mr Prabhat (Lawrence Berkeley National Laboratory); Yunsung Lee (Korea University)
Extreme weather events Climate and Earth science
NeurIPS 2019 DeepWind: Weakly Supervised Localization of Wind Turbines in Satellite Imagery (Papers Track)
Abstract and authors: (click to expand)
Abstract: Wind energy is being adopted at an unprecedented rate. The locations of wind energy sources, however, are largely undocumented and expensive to curate manually, which significantly impedes their integration into power systems. Towards the goal of mapping global wind energy infrastructure, we develop deep learning models to automatically localize wind turbines in satellite imagery. Using only image-level supervision, we experiment with several different weakly supervised convolutional neural networks to detect the presence and locations of wind turbines. Our best model, which we call DeepWind, achieves an average precision of 0.866 on the test set. DeepWind demonstrates the potential of automated approaches for identifying wind turbine locations using satellite imagery, ultimately assisting with the management and adoption of wind energy worldwide.
Authors: Sharon Zhou (Stanford University); Jeremy Irvin (Stanford); Zhecheng Wang (Stanford University); Ram Rajagopal (Stanford University); Andrew Ng (Stanford U.); Eva Zhang (Stanford University); Will Deaderick (Stanford University); Jabs Aljubran (Stanford University)
Power and energy
NeurIPS 2019 Streamflow Prediction with Limited Spatially-Distributed Input Data (Papers Track)
Abstract and authors: (click to expand)
Abstract: Climate change causes more frequent and extreme weather phenomena across the globe. Accurate streamflow prediction allows for proactive and mitigative action in some of these events. As a first step towards models that predict streamflow in watersheds for which we lack ground truth measurements, we explore models that work on spatially-distributed input data. In such a scenario, input variables are more difficult to acquire, and thus models have access to limited training data. We present a case study focusing on Lake Erie, where we find that tree-based models can yield more accurate predictions than both neural and physically-based models.
Authors: Martin Gauch (University of Waterloo); Juliane Mai (University of Waterloo); Shervan Gharari (University of Saskatchewan); Jimmy Lin (University of Waterloo)
Climate and Earth science Disaster prediction, management, and relief Extreme weather events
NeurIPS 2019 Establishing an Evaluation Metric to Quantify Climate Change Image Realism (Papers Track)
Abstract and authors: (click to expand)
Abstract: With success on controlled tasks, generative models are being increasingly applied to humanitarian applications. In this paper, we focus on the evaluation of a conditional generative model that illustrates the consequences of climate change-induced flooding to encourage public interest and awareness on the issue. Because metrics for comparing the realism of different modes in a conditional generative model do not exist, we propose several automated and human-based methods for evaluation. To do this, we adapt several existing metrics, and assess the automated metrics against gold standard human evaluation. We find that using Frechet Inception Distance (FID) with embeddings from an intermediary Inception-V3 layer that precedes the auxiliary classifier produces results most correlated with human realism. While insufficient alone to establish a human-correlated automatic evaluation metric, we believe this work begins to bridge the gap between human and automated generative evaluation procedures.
Authors: Sharon Zhou (Stanford University); Sasha Luccioni (Mila); Gautier Cosne (Mila); Michael Bernstein (Stanford University); Yoshua Bengio (Mila)
Data presentation and management Societal adaptation
NeurIPS 2019 Energy Usage Reports: Environmental awareness as part of algorithmic accountability (Papers Track)
Abstract and authors: (click to expand)
Abstract: The carbon footprint of algorithms must be measured and transparently reported so computer scientists can take an honest and active role in environmental sustainability. In this paper, we take analyses usually applied at the industrial level and make them accessible for individual computer science researchers with an easy-to-use Python package. Localizing to the energy mixture of the electrical power grid, we make the conversion from energy usage to CO2 emissions, in addition to contextualizing these results with more human-understandable benchmarks such as automobile miles driven. We also include comparisons with energy mixtures employed in electrical grids around the world. We propose including these automatically-generated Energy Usage Reports as part of standard algorithmic accountability practices, and demonstrate the use of these reports as part of model-choice in a machine learning context.
Authors: Kadan Lottick (Haverford College); Silvia Susai (Haverford College); Sorelle Friedler (Haverford College); Jonathan Wilson (Haverford College)
Environmental impacts of computing
NeurIPS 2019 Natural Language Generation for Operations and Maintenance in Wind Turbines (Papers Track)
Abstract and authors: (click to expand)
Abstract: Wind energy is one of the fastest-growing sustainable energy sources in the world but relies crucially on efficient and effective operations and maintenance to generate sufficient amounts of energy and reduce downtime of wind turbines and associated costs. Machine learning has been applied to predict faults in wind turbines, but these predictions have not been supported by suggestions on how to avert and fix occurring errors. In this paper, we present a data-to-text generation system utilising transformers to produce event descriptions of turbine faults from SCADA data capturing the operational status of turbines, and proposing maintenance strategies. Experiments show that our model learns reasonable feature representations that correspond to expert judgements. We anticipate that in making a contribution to the reliability of wind energy, we can encourage more organisations to switch to sustainable energy sources and help combat climate change.
Authors: Joyjit Chatterjee (University of Hull); Nina Dethlefs (University of Hull)
Power and energy Ecosystems and natural systems
NeurIPS 2019 Make Thunderbolts Less Frightening — Predicting Extreme Weather Using Deep Learning (Papers Track)
Abstract and authors: (click to expand)
Abstract: Forecasting severe weather conditions is still a very challenging and computationally expensive task due to the enormous amount of data and the complexity of the underlying physics. Machine learning approaches and especially deep learning have however shown huge improvements in many research areas dealing with large datasets in recent years. In this work, we tackle one specific sub-problem of weather forecasting, namely the prediction of thunderstorms and lightning. We propose the use of a convolutional neural network architecture inspired by UNet++ and ResNet to predict thunderstorms as a binary classification problem based on satellite images and lightnings recorded in the past. We achieve a probability of detection of more than 94% for lightnings within the next 15 minutes while at the same time minimizing the false alarm ratio compared to previous approaches.
Authors: Christian Schön (Saarland Informatics Campus); Jens Dittrich (Saarland University)
Extreme weather events Climate and Earth science
NeurIPS 2019 Cumulo: A Dataset for Learning Cloud Classes (Papers Track) Best Paper Award
Abstract and authors: (click to expand)
Abstract: One of the greatest sources of uncertainty in future climate projections comes from limitations in modelling clouds and in understanding how different cloud types interact with the climate system. A key first step in reducing this uncertainty is to accurately classify cloud types at high spatial and temporal resolution. In this paper, we introduce Cumulo, a benchmark dataset for training and evaluating global cloud classification models. It consists of one year of 1km resolution MODIS hyperspectral imagery merged with pixel-width `tracks' of CloudSat cloud labels. Bringing these complementary datasets together is a crucial first step, enabling the Machine-Learning community to develop innovative new techniques which could greatly benefit the climate community. To showcase Cumulo, we provide baseline performance analysis using an invertible flow generative model (IResNet), which further allows us to discover new sub-classes for a given cloud class by exploring the latent space.
Authors: Valentina Zantedeschi (Jean Monnet University); Fabrizio Falasca (Georgia Institute of Technology); Alyson Douglas (University of Wisconsin Madison); Richard Strange (University of Oxford); Matt Kusner (University College London); Duncan Watson-Parris (University of Oxford)
Climate and Earth science Data presentation and management
NeurIPS 2019 Targeting Buildings for Energy Retrofit Using Recurrent Neural Networks with Multivariate Time Series (Papers Track)
Abstract and authors: (click to expand)
Abstract: The existing building stock accounts for over 30% of global carbon emissions and energy demand. Effective building retrofits are therefore vital in reducing global emissions. Current methods for building energy assessment typically rely on walk-throughs, surveys or the collection of in-situ measurements, none of which are scalable or cost effective. Supervised machine learning methods have the potential to overcome these issues, but their application to retrofit analysis has been limited. This paper serves as a novel showcase for how multivariate time series analysis with Gated Recurrent Units can be applied to targeted retrofit analysis via two case studies: (1) classification of building heating system type and (2) prediction of building envelope thermal properties.
Authors: Gaby Baasch (University of Victoria)
Buildings and cities
NeurIPS 2019 Coupling Oceanic Observation Systems to Study Mesoscale Ocean Dynamics (Papers Track)
Abstract and authors: (click to expand)
Abstract: Understanding local currents in the North Atlantic region of the ocean is a key part of modelling heat transfer and global climate patterns. Satellites provide a surface signature of the temperature of the ocean with a high horizontal resolution while in situ autonomous probes supply high vertical resolution, but horizontally sparse, knowledge of the ocean interior thermal structure. The objective of this paper is to develop a methodology to combine these complementary ocean observing systems measurements to obtain a three-dimensional time series of ocean temperatures with high horizontal and vertical resolution. Within an observation-driven framework, we investigate the extent to which mesoscale ocean dynamics in the North Atlantic region may be decomposed into a mixture of dynamical modes, characterized by different local regressions between Sea Surface Temperature (SST), Sea Level Anomalies (SLA) and Vertical Temperature fields. Ultimately we propose a Latent-class regression method to improve prediction of vertical ocean temperature.
Authors: Gautier Cosne (Mila); Pierre Tandeo (IMT-Atlantique); Guillaume Maze (Ifremer)
Climate and Earth science Data presentation and management
NeurIPS 2019 Background noise trends and the detection of calving events in a glacial fjord (Papers Track)
Abstract and authors: (click to expand)
Abstract: Predicting future sea levels depends on accurately estimating the rate at which ice sheets deliver fresh water and ice to the oceans, and projecting rates of iceberg calving will be improved with more observations of calving events. The background noise environment in a glacial fjord was measured and the data were analyzed. This paper includes an analysis of methods useful for evaluating background noise. It explores the utility of spectral probability density in evaluating background noise characteristics in the frequency domain, models probability density functions of spectral levels and introduces a parameter $$\sigma_T$$ that quantifies the character of noise in frequency bands of interest. It also explores the utility of k-medoids clustering as a pre-sorting method to inform the selection of features on which to base the training of more complex algorithms.
Authors: Dara Farrell (Graduate of University of Washington)
Climate and Earth science
NeurIPS 2019 Reducing Inefficiency in Carbon Auctions with Imperfect Competition (Papers Track) | 2022-12-04 16:03:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3987732231616974, "perplexity": 5148.4052852238065}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710974.36/warc/CC-MAIN-20221204140455-20221204170455-00542.warc.gz"} |
http://gis.stackexchange.com/questions/37464/migrate-python-scripts-from-9-3-to-arcgis10/37465 | Migrate python scripts from 9.3 to Arcgis10
What changes are needed to migrate scripts from the ArcGis 9.x environment/gp-object to the ArcGis 10/arcpy environment?
Can anyone provide a good overview what the changes are?
Can someone share pitfalls etc from their own experience?
-
GeoChalkboard can give you a good overview of the changes!
Here's the list, but check it out for more detail:
1. Replace the import statement
2. Replace all gp. with arcpy.
3. Check your capitalization.
4. The result tool is different.
5. Replace any del gp statements.
6. The overwrite tool is different.
7. Import the env module from arcpy.
8. List item
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Thanks Roy. Good resource there! – LarsVegas Oct 24 '12 at 14:15
One little comment: 2. Replace all gp. with arcpy isn't really needed if you assign your import to gp, lik so: import arcpy gp = arcpy. Which also makes 5. obsolete, as well. – LarsVegas Oct 26 '12 at 8:45 | 2015-01-27 14:38:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26869073510169983, "perplexity": 12592.654557709855}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422121981339.16/warc/CC-MAIN-20150124175301-00190-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://quantumcomputing.stackexchange.com/questions/3947/advantage-of-hadamard-gate-over-rotation-about-the-x-axis-for-creating-superposi?noredirect=1 | When I look at most circuits (admittedly small sample as I'm a beginner), the Hadamard gate is used a lot to prepare a superposition from say the $\mid0\rangle$ state.
But upon a little reflection, we can prepare a superposition using a $\dfrac{\pi}{2}$ rotation about the X axis.
I do know that a successive application of the Hadamard gate yields the initial state back (for any state).
If we have one of $\mid0\rangle$ or $\mid1\rangle$, we can recover them using a succession of said rotation followed by a NOT gate (Pauli-X).
So why is the Hadamard gate preferred to create superpositions when it uses more gates (rotation about Z then rotation about X then rotation about Z again)?
If it is because the Hadamard gate allows recovery of any initial state, why is that property so important? (Even when not actually used when I look at the examples I see.)
• Why are you talking about $\pi/2$ rotations about the $X$ basis? What you want is a $\pi/2$ rotation about the $Y$ axis, which indeed acts almost like a Hadamard, as it also maps between X and Z eigenstates. Aug 6, 2018 at 9:53
• @NorbertSchuch Thank you. I just checked and it you are right. Do you mind writing an answer where you talk about the comparison between Hadamard and $\frac{\pi}{2}$ rotation about $Y$? Aug 6, 2018 at 14:52
• I don't see how this would make sense. On the one hand, this is not the question. On the other hand, take the answer of DaftWullie and strip the part about $\sqrt{X}$ not being real, and you probably get what I would write. Aug 6, 2018 at 22:18
It's mostly about simplicity and adopted convention. In the end, this is basically the same question as "why should I pick a universal set of gates A rather than a universal set B?" (see here). Experimentalists would pick the universal set they have available. Theorists just pick something that they like to work with, and eventually a convention is adopted. But it doesn't matter which convention they adopt because any universal set is easily converted into any other universal set, and it is (or should be) understood that the quantum circuits describing algorithms are not what you actually want to run on a quantum computer: you need to recompile them for the available gate set and optimise based on the available architecture (and this process is unique to each architecture).
You could use operations such as $\sqrt{X}$, but they are a little bit more fiddly because of all the imaginary numbers that appear. Or there's $\sqrt{Y}$ which gives an even more direct comparison to $H$, avoiding imaginary numbers.
One of the main purposes of $H$ in a quantum circuit is to prepare uniform superpositions: $H|0\rangle=(|0\rangle+|1\rangle)/\sqrt{2}$. But $\sqrt{Y}$ also does this: $\sqrt{Y}|1\rangle=(|0\rangle+|1\rangle)/\sqrt{2}$. When you start combining multiple Hadamards on unknown input states (i.e. the Hadamard transform), it has a particularly convenient structure $$H^{\otimes n}=\frac{1}{\sqrt{2^n}}\sum_{x,y\in\{0,1\}^n}(-1)^{x\cdot y}|x\rangle\langle y|.$$
The Hadamard gives you some very nice inter-relations (reflecting basis changes between pairs of mutually unbiased bases), $$HZH=X\qquad HXH=Z \qquad HYH=-Y.$$ It also enables relations between controlled-not and controlled phase, and between controlled-not in two different directions (swapping control and target). There are similar relations for $\sqrt{Y}$: $$\sqrt{Y}Z\sqrt{Y}^\dagger=YZ=iX \qquad \sqrt{Y}X\sqrt{Y}^\dagger=YX=-iZ\qquad \sqrt{Y}Y\sqrt{Y}^\dagger=Y$$ Part of this looking (slightly) nicer is because, as stated in the question, $H^2=\mathbb{I}$.
One way that many courses introduce the basic idea of quantum computation, and interference, is to use the Mach-Zehnder interferometer. This consists of two beam splitters which, mathematically, should be described by $\sqrt{X}$ (or $\sqrt{Y}$ would do). Indeed, this is important for a first demonstration because of course these operations are "square root of not", which you can prove is logically impossible classically. However, once that initial introduction is over, theorists will often substitute the beam splitter operation for Hadamard, just because it makes everything slightly easier.
• I see. And coming from computer science, I'm always looking at what is optimal ($i.e.$ minimum number of gates) so I was wondering what the hell are physicists are up to. Thanks for your answer. Aug 6, 2018 at 7:19
• @DaftWullie It would be more fair to compare to $\sqrt{Y}$, which is real and accomplishes the same effect as $H$ on the computational basis. (I agree that's not what the OP asked.) Aug 6, 2018 at 9:35
• @NorbertSchuch I considered that while writing the answer, but was concerned that it only confused the issue more because there's even less to pick between them. Aug 6, 2018 at 9:54
• Fair point. But then again, the case where there's least to pick between them is where the "real" differences between pi/2 rotations and Hadamard become most clear. Aug 6, 2018 at 10:07
• more than the imaginary numbers in the matrix, I would argue that what is nice about $H$ is the simplicity of its spectrum. $H$ is the gate that switches between the eigenbases of $Z$ and $X$. The matrix that does the same between, say, $X$ and $Y$, contains imaginary numbers but arguably works exactly the same, provided we use eigenbases of $X$ and $Y$ as "standard" instead of those of $Z$ and $X$ as it's commonly done. In other words, what is "simple" about $H$ (or one thing that is) is the fact that it represents a change of basis between two mutually unbiased bases.
– glS
Aug 6, 2018 at 10:07
I think the major advantages of the Hadamard gate are "usability" stuff, as opposed to fundamental mathematical stuff. It's just easier to remember and simpler to apply.
1. The Hadamard gate's marix is real and symmetric. Makes it easy to remember.
2. Hadamard is its own inverse. Makes it easy to optimize in circuits. Any two Hs that meet cancel out; whereas $\sqrt{X}$ tends to meet $\sqrt{X}$ as often as $\sqrt{X}^{-1}$ leaving behind $X$ operations.
3. Hadamard's effect on operators is easy to remember: swap X for Z. Whereas for $\sqrt{X}$ style operations you need to remember a right hand rule. If you pass a hadamard over a CZ, it turns into a CNOT. If you pass a $\sqrt{Y}$ over a CZ, whether you get a CNOT or a CNOT+Z depends on whether you went left-to-right or right-to-left.
4. In the surface code you need twist defects or distilled states to do $\sqrt{X}$ gates. Hadamard operations need neither (though the twists are more efficient...).
5. The Hadamard is unique. There are two values $M$ such that $M^2 = X$, and so you need an agreed upon convention for which one $\sqrt{X}$ is.
PS: it would be better to compare a Hadamard to a 90 degree rotation about the Y axis, not the X axis, because the Hadamard operation is equivalent $\sqrt{Y}$ up to Pauli operations ($H \propto Z \cdot \sqrt{Y}$).
Any Hermitian quantum gate $U$ is "self-recovering". This is because $U$ is unitary, and $$UU^{\dagger}=U^{\dagger}U=I$$ If $U$ is also Hermitian, then $U=U^{\dagger}$ and $$UU=I$$
Hadamard gate prepares $\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ superposition from $|0\rangle$ state. If you need this superposition, you use Hadamard. If you need a different superposition, $\alpha|0\rangle + \beta|1\rangle$ with some $\alpha$ and $\beta$, you need a different gate or a sequence of gates; Hadamard gate has no advantage here.
• You certainly answer the question and thanks for that. Though would you mind elaborating why one would specifically need $\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ over say $\frac{1}{\sqrt{2}}(|0\rangle - i |1\rangle)$? I believe elaborating on that will shed more light to aid my understanding. Aug 6, 2018 at 7:12
• @NtwaliB. Suppose you need just a superposition with 50% chances being $|0\rangle$ and 50% chances being $|1\rangle$; both $\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ and $\frac{1}{\sqrt{2}}(|0\rangle - i |1\rangle)$ are equally good for you, but what would you choose? Aug 6, 2018 at 7:19
• I would choose the one that makes the computer do the least amount of work. If a Hadamard gate is implemented in terms of rotations, I will use a rotation about X as it saves me the use of two additional gates. If Hadamard is a native gate, I will use Hadamard since most people are used to it. Note: Hadamard generates $\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ while $R_x(\frac{\pi}{2})$ generates $\frac{1}{\sqrt{2}}(|0\rangle - i|1\rangle)$ Aug 6, 2018 at 7:24
• @kludg Why would $U=U^\dagger$ for real $U$?? This is completely wrong. Try e.g. [1 -1;1 1] (normalized) - a pi/2 rotation about Y - which doesn't square to the identity. (Indeed, a Y rotation by pi/2 prepares the same superpositions as H starting from the computational basis.) Aug 6, 2018 at 9:31
• @kludg this is not true as written. Did you mean to write hermitian instead of real?
– glS
Aug 6, 2018 at 9:32 | 2022-10-07 21:23:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7884351015090942, "perplexity": 521.0912820156198}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030338280.51/warc/CC-MAIN-20221007210452-20221008000452-00226.warc.gz"} |
http://www.calculatorsoup.com/calculators/financial/future-value-investment-calculator.php | # Future Value of a Lump Sum Investment Calculator
Present Value (PV) $Number of Periods (t) Interest Rate per Period (R) % Compounding per Period (m) Answer: Future Value (FV) of the Present Sum$ 25,327.86 Future Value Interest Factor (FVIF) = 1.68852
## Calculator Use
Calculate the future value of a present value lump sum investment, or a one time investment, based on a constant interest rate per period and compounding. To include an annuity use a comprehensive future value calculation.
Period
commonly a period will be a year but it can be any time interval you want as long as all inputs are consistent.
Investment (PV)
is the present value or principal amount to be invested.
Interest Rate (R)
is the annual nominal interest rate or "stated rate" in percent. r = R/100, the interest rate in decimal
Number of Periods (t)
commonly this will be number of years but periods can be any time unit. Enter whole numbers or use decimals for partial periods such as months for example, 7.5 years is 7 yr 6 mo.
Compounding (m)
is the number of times compounding occurs per period. If a period is a year then annually=1, quarterly=4, monthly=12, daily = 365, etc.
Continuous Compounding
is when the frequency of compounding (m) is increased up to infinity. Enter c, C or Continuous for m.
Interest Rate (i)
i = (r/m); interest rate per compounding period.
Total Number of Periods (n)
n = mt; is the total number of compounding periods for the life of the investment.
Future Value (FV)
the calculated future value of our investment
FVIF
Future Value Interest Factor that accounts for your input Number of Periods, Interest Rate and Compounding Frequency and can now be applied to other present value amounts to find the future value under the same conditions.
## Future Value Formula for a Present Value:
$FV = PV\left(1+\frac{r}{m}\right)^{mt}$
where r=R/100 and is generally applied with r as the yearly interest rate, t the number of years and m the number of compounding intervals per year. Although, we can think of r as a rate per period, t the number of periods and m the compounding intervals per period where a period is any interval of time. We can reduce this to the more general
$FV = PV(1+i)^n$
where i=r/m and n=mt with i the rate per compounding period and n the number of compounding periods.
When m approaches infinity, m → ∞ (continuous compounding)
$FV = PVe^{rt}$
Future Value Formula Derivations
Example Future Value Calculations for a Lump Sum Investment:
You put $10,000 into an ivestment account earning 6.25% per year compounded monthly. You want to know the value of your investment in 2 years or, the future value of your account. • Investment (pv) =$10,000
• Interest Rate (R) = 6.25%
• Number of Periods (years) (t) = 2
• Compounding per Period (per year) (m) = 12
$FV = \10,000(1+0.0625/12)^{12\times2}= \11,327.81$
Cite this content, page or calculator as:
Furey, Edward "Future Value of an Investment Calculator" From http://www.CalculatorSoup.com - Online Calculator Resource. | 2016-09-25 03:44:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.304759681224823, "perplexity": 2687.4352098739682}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738659833.43/warc/CC-MAIN-20160924173739-00285-ip-10-143-35-109.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/240827/find-parametric-varable-in-terms-of-the-distance-from-a-point-to-a-line | # find parametric varable in terms of the distance from a point to a line
I have two lines defined by a point and a vector:
• $Q(s) = A + s\vec{v}$
• $P(t) = B + t\vec{u}$
Suppose distance d is given
I want to know $s$ and $t$ for points $P$ and $Q$ in terms of $d$. $d$ is perpendicular to $line(B, \vec{u})$
so I found out (wikipedia):
\begin{aligned} d & = ||(B - Q) - ((B - Q).\vec{u})\vec{u}|| \\ & = ||(B - A - s\vec{v}) - ((B - A - s\vec{v})\cdot\vec{u})\vec{u}|| \\ & = ||(\vec{w} - s\vec{v}) - ((\vec{w} - s\vec{v})\cdot\vec{u})\vec{u} || \end{aligned}
Can somebody explain the algebra to write $s$ in terms of $d$
$$s = f(d) = \dots$$
-
I wouldn't solve the problem that way, but anyway, your expression can be written as $d=\|[\vec{w} - (\vec{w}\cdot\vec{u})u] - s[\vec{v} - (\vec{v}\cdot\vec{u})u]\|=\|\vec{p}+s\vec{q}\|$ (say). Now, suppose $\vec{q}=a\vec{p}+b\vec{r}$ for some numbers $a,b$ and some $\vec{r}\perp\vec{p}$. Then $d=\|(1+sa)\vec{p}+sb\vec{r}\|$. As $\vec{p}\perp\vec{r}$, we get $d^2=(1+sa)^2\|\vec{p}\|^2+s^2b^2\|\vec{r}\|^2$. Solving this quadratic equation, you get $s$. Now, to find $a,b$ and $\vec{r}$, you may use Gram-Schmidt orthogonalization. – user1551 Nov 20 '12 at 5:32
How would you solve it then? I want to apply it to the following situation: point $A$ is a ball with radius $d$ travelling a distance $\vec{v}$. It may hit a wall $(B, \vec{u})$. I want to calculate whether and where in its trajectory it hits the wall as well as the point of collision on the wall. – Jan Nov 20 '12 at 8:53
The problem can be solved in another way. Let $F$ be the foot of perpendicular drawn from $A$ to the line $BP$. Then $$\vec{AF} = \vec{w} - \frac{\vec{w}\cdot\vec{u}}{\|\vec{u}\|^2}\vec{u}.$$ Let $R=A+\lambda\vec{v}$ be the point where the line extending $QA$ meets the line extending $PB$. Then $\vec{AF} \perp \vec{RF} (=\vec{RA}+\vec{AF})$. Hence $$\vec{AF}\cdot(-\lambda\vec{v}+\vec{AF})=0.$$ Solve it to get $\lambda$. Then, by similarity of triangles, we have $$\frac{d}{\|\vec{AF}\|} = \frac{\|\vec{RQ}\|}{\|\vec{RA}\|} \equiv \frac{\lambda-s}{\lambda},\\$$ So you may solve for $s$. Finally, $t$ can be solved by observing that: $$t\vec{u} = \vec{BP} = \textrm{ projection of } \vec{BQ} \textrm{ along } \vec{u} =\left[(s\vec{v}-\vec{w})\cdot\frac{\vec{u}}{\|\vec{u}\|}\right]\frac{\vec{u}}{\|\vec{u}\|}.$$ | 2015-09-04 15:01:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9755306243896484, "perplexity": 155.21541197722624}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645353863.81/warc/CC-MAIN-20150827031553-00081-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://nbviewer.ipython.org/github/gpeyre/numerical-tours/blob/NtToolBox_12/python/optimaltransp_5_entropic.ipynb | # Entropic Regularization of Optimal Transport¶
In [1]:
from __future__ import division
import numpy as np
import scipy as scp
import pylab as pyl
import matplotlib.pyplot as plt
from nt_toolbox.general import *
from nt_toolbox.signal import *
import warnings
warnings.filterwarnings('ignore')
%matplotlib inline
## Entropic Regularization of Optimal Transport¶
We consider two input histograms $p,q \in \Si_N$, where we denote the simplex in $\RR^N$ $$\Si_{N} \eqdef \enscond{ p \in (\RR^+)^N }{ \sum_i p_i = 1 }.$$ We consider the following discrete regularized transport $$W_\ga(p,q) \eqdef \umin{\pi \in \Pi(p,q)} \dotp{C}{\pi} - \ga E(\pi).$$ where the polytope of coupling is defined as $$\Pi(p,q) \eqdef \enscond{\pi \in (\RR^+)^{N \times N}}{ \pi \ones = p, \pi^T \ones = q },$$ where $\ones \eqdef (1,\ldots,1)^T \in \RR^N$, and for $\pi \in (\RR^+)^{N \times N}$, we define its entropy as $$E(\pi) \eqdef - \sum_{i,j} \pi_{i,j} ( \log(\pi_{i,j}) - 1).$$
When $\ga=0$ one recovers the classical (discrete) optimal transport. We refer to the monograph Villani for more details about OT. The idea of regularizing transport to allows for faster computation is introduced in Cuturi.
Here the matrix $C \in (\RR^+)^{N \times N}$ defines the ground cost, i.e. $C_{i,j}$ is the cost of moving mass from a bin indexed by $i$ to a bin indexed by $j$.
The regularized transportation problem can be re-written as a projection $$W_\ga(p,q) = \ga \umin{\pi \in \Pi(p,q)} \KLdiv{\pi}{\xi} \qwhereq \xi_{i,j} = e^{ -\frac{C_{i,j}}{\ga} }$$ of $\xi$ according to the Kullback-Leibler divergence. The Kullback-Leibler divergence between $\pi, \xi \in (\RR^+)^P$ is $$\KLdiv{\pi}{\xi} = \sum_{i,j} \pi_{i,j} \pa{ \log\pa{ \frac{\pi_{i,j}}{\xi_{i,j}} } - 1}.$$
This interpretation of regularized transport as a KL projection and its numerical applications are detailed in BenamouEtAl.
Given a convex set $\Cc \subset \RR^N$, the projection according to the Kullback-Leiber divergence is defined as $$\KLproj_\Cc(\xi) = \uargmin{ \pi \in \Cc } \KLdiv{\pi}{\xi}.$$
## Iterative Bregman Projection Algorithm¶
Given affine constraint sets $(\Cc_1,\ldots,\Cc_K)$, we aim at computing $$\KLproj_\Cc(\xi) \qwhereq \Cc = \Cc_1 \cap \ldots \cap \Cc_K.$$
This can be achieved, starting by $\pi_0=\xi$, by iterating $$\forall \ell \geq 0, \quad \pi_{\ell+1} = \KLproj_{\Cc_\ell}(\pi_\ell),$$ where the index of the constraints should be understood modulo $K$, i.e. we set $\Cc_{\ell+K}=\Cc_\ell$.
One can indeed show that $\pi_\ell \rightarrow \KLproj_\Cc(\bar \pi)$. We refer to BauschkeLewis for more details about this algorithm and its extension to compute the projection on the intersection of convex sets (Dikstra algorithm).
## Iterative Projection for Regularized Transport aka Sinkhorn's Algorithm¶
We can re-cast the regularized optimal transport problem within this framework by introducing $$\Cc_1 \eqdef \enscond{\pi \in (\RR^+)^{N \times N} }{\pi \ones = p} \qandq \Cc_2 \eqdef \enscond{\pi \in (\RR^+)^{N \times N} }{\pi^T \ones = q}.$$
The KL projection on $\Cc_1$ sets are easily computed by divisive normalization of rows. Indeed, denoting $\pi = \KLproj_{\Cc_1}(\bar \pi)$, one has $$\forall (i,j), \quad \pi_{i,j} = \frac{ p_i \bar\pi_{i,j} }{ \sum_{s} \bar\pi_{i,s} }$$ and similarely for $\KLproj_{\Cc_1}(\bar \pi)$ by replacing rows by colums.
A fundamental remark is that, if $\bar\pi = \diag(a) \xi \diag(b)$ (a so-called diagonal scaling of the kernel $\xi$), then one has $$\KLproj_{\Cc_1}(\bar \pi) = \diag(\tilde a) \xi \diag(b) \qandq \KLproj_{\Cc_2}(\bar \pi) = \diag(a) \xi \diag(\tilde b)$$ where the new scaling reads $$\tilde a = \frac{p}{\xi(b)} \qandq \tilde b = \frac{q}{\xi^T(a)}$$ where $\frac{\cdot}{\cdot}$ is entry-wise division.
This means that the iterates of Bregman iterative projections, starting with $a_0 \eqdef \ones$ always have the form $\pi_\ell = \diag(a_\ell) \xi \diag(b_\ell)$ and these diagonal scaling weights are updated as follow $$a_{\ell+1} \eqdef \frac{p}{\xi(b_\ell)} \qandq b_{\ell+1} \eqdef \frac{q}{\xi^T(a_{\ell+1})}.$$ This algorithm is in fact the well known Sinkhorn algorithm Sinkhorn.
## Transport Between Point Clouds¶
We first test the method for two input measures that are uniform measures (i.e. constant histograms) supported on two point clouds (that do not necessarily have the same size).
We thus first load two points clouds $x=(x_i)_{i=1}^{N_1}, y=(y_i)_{i=1}^{N_2},$ where $x_i, y_i \in \RR^2$.
Number of points in each cloud.
In [2]:
N = [300,200]
Dimension of the clouds.
In [3]:
d = 2
Point cloud $x$, of $N_1$ points inside a square.
In [4]:
from numpy import random
x = random.rand(2,N[0])-.5
Point cloud $y$, of $N_2$ points inside an anulus.
In [5]:
theta = 2*np.pi*random.rand(1,N[1])
r = .8 + .2*random.rand(1,N[1])
y = np.vstack((np.cos(theta)*r,np.sin(theta)*r))
Shortcut for displaying point clouds.
In [6]:
plotp = lambda x,col: plt.scatter(x[0,:], x[1,:], s=200, edgecolors="k", c=col, linewidths=2)
Display of the two clouds.
In [7]:
plt.figure(figsize=(10,10))
plotp(x, 'b')
plotp(y, 'r')
plt.axis("off")
plt.xlim(np.min(y[0,:])-.1,np.max(y[0,:])+.1)
plt.ylim(np.min(y[1,:])-.1,np.max(y[1,:])+.1)
plt.show()
Cost matrix $C_{i,j} = \norm{x_i-y_j}^2$.
In [8]:
x2 = np.sum(x**2,0)
y2 = np.sum(y**2,0)
C = np.tile(y2,(N[0],1)) + np.tile(x2[:,np.newaxis],(1,N[1])) - 2*np.dot(np.transpose(x),y)
Target histograms, here uniform histograms.
In [9]:
p = np.ones(N[0])/N[0]
q = np.ones(N[1])/N[1]
Regularization strength $\ga$.
In [10]:
gamma = .01;
Gibbs Kernel.
In [11]:
xi = np.exp(-C/gamma)
Initialization of $b_0=\ones_{N_2}$ ($a_0$ does not need to be initialized).
In [12]:
b = np.ones(N[1])
One sinkhorn iterations.
In [13]:
a = p/(np.dot(xi,b))
b = q /(np.dot(np.transpose(xi),a))
Exercise 1
Implement Sinkhorn algorithm. Display the evolution of the constraints satisfaction errors $\norm{ \pi \ones - p }, \norm{ \pi^T \ones - q }$ (you need to think about how to compute these residuals from $(a,b)$ alone). isplay the violation of constraint error in log-plot.
In [14]:
run -i nt_solutions/optimaltransp_5_entropic/exo1
In [15]:
# Insert your code here.
Compute the final matrix.
In [16]:
Pi = np.dot(np.dot(np.diag(a),xi),np.diag(b))
Display it.
In [17]:
plt.figure(figsize=(5,5))
imageplot(Pi)
Exercise 2
Display the regularized transport solution for various values of $\gamma$. For a too small value of $\gamma$, what do you observe ?
In [18]:
run -i nt_solutions/optimaltransp_5_entropic/exo2
In [19]:
# Insert your code here.
Compute the obtained optimal $\pi$.
In [20]:
Pi = np.dot(np.dot(np.diag(a),xi),np.diag(b))
Keep only the highest entries of the coupling matrix, and use them to draw a map between the two clouds. First we draw "strong" connexions, i.e. linkds $(i,j)$ corresponding to large values of $\pi_{i,j}$. We then draw weaker connexions.
In [21]:
plt.figure(figsize=(10,10))
plotp(x, 'b')
plotp(y, 'r')
A = Pi * (Pi > np.min(1./np.asarray(N))*.7)
i,j = np.where(A != 0)
plt.plot([x[0,i],y[0,j]],[x[1,i],y[1,j]],'k',lw = 2)
A = Pi * (Pi > np.min(1./np.asarray(N))*.3)
i,j = np.where(A != 0)
plt.plot([x[0,i],y[0,j]],[x[1,i],y[1,j]],'k:',lw = 1)
plt.axis("off")
plt.xlim(np.min(y[0,:])-.1,np.max(y[0,:])+.1)
plt.ylim(np.min(y[1,:])-.1,np.max(y[1,:])+.1)
plt.show()
## Transport Between Histograms¶
We now consider a different setup, where the histogram values $p,q$ are not uniform, but the measures are defined on a uniform grid $x_i=y_i=i/N$. They are thue often refered to as "histograms".
Size $N$ of the histograms.
In [22]:
N = 200
We use here a 1-D square Euclidean metric.
In [23]:
t = np.arange(0,N)/N
Define the histogram $p,q$ as translated Gaussians.
In [24]:
Gaussian = lambda t0,sigma: np.exp(-(t-t0)**2/(2*sigma**2))
normalize = lambda p: p/np.sum(p)
sigma = .06;
p = Gaussian(.25,sigma)
q = Gaussian(.8,sigma)
Add some minimal mass and normalize.
In [25]:
vmin = .02;
p = normalize( p+np.max(p)*vmin)
q = normalize( q+np.max(q)*vmin)
Display the histograms.
In [26]:
plt.figure(figsize = (10,7))
plt.subplot(2, 1, 1)
plt.bar(t, p, width = 1/len(t), color = "darkblue")
plt.subplot(2, 1, 2)
plt.bar(t, q, width = 1/len(t), color = "darkblue")
plt.show()
Regularization strength $\ga$.
In [27]:
gamma = (.03)**2
The Gibbs kernel is a Gaussian convolution, $$\xi_{i,j} = e^{ -(i/N-j/N)^2/\gamma }.$$
In [28]:
[Y,X] = np.meshgrid(t,t)
xi = np.exp(-(X-Y)**2/gamma)
Initialization of $b_0=\ones_{N}$.
In [29]:
b = np.ones(N)
One sinkhorn iteration.
In [30]:
a = p/(np.dot(xi,b))
b = q /(np.dot(np.transpose(xi),a))
Exercise 3
Implement Sinkhorn algorithm. Display the evolution of the constraints satisfaction errors $\norm{ \pi \ones - p }, \norm{ \pi^T \ones - q }$. You need to think how to compute it from $(a,b)$. Display the violation of constraint error in log-plot.
In [31]:
run -i nt_solutions/optimaltransp_5_entropic/exo3
In [32]:
# Insert your code here.
Display the coupling. Use a log domain plot to better vizualize it.
In [33]:
Pi = np.dot(np.dot(np.diag(a),xi),np.diag(b))
plt.figure(figsize=(5,5))
imageplot(np.log(Pi+1e-5))
One can compute an approximation of the transport plan between the two measure by computing the so-called barycentric projection map $$t_i \in [0,1] \longmapsto s_j \eqdef \frac{\sum_{j} \pi_{i,j} t_j }{ \sum_{j} \pi_{i,j} } = \frac{ [a \odot \xi(b \odot t)]_j }{ p_i }.$$ where $\odot$ and $\frac{\cdot}{\cdot}$ are the enry-wise multiplication and division.
This computation can thus be done using only multiplication with the kernel $\xi$.
In [34]:
s = np.dot(xi,b*t)*a/p
Display the transport map, super-imposed over the coupling.
In [35]:
plt.figure(figsize=(5,5))
imageplot(np.log(Pi+1e-5))
plt.plot(s*N,t*N, 'r', linewidth=3)
plt.xlim(0,N)
plt.ylim(N,0)
plt.show()
## Wasserstein Barycenters¶
Instead of computing transport, we now turn to the problem of computing barycenter of measures. A barycenter $q$ solves $$\umin{q} \sum_{k=1}^K W_\ga(p_k,q)$$ where $\la_k$ are positive weights with $\sum_k \la_k=1$. This follows the definition of barycenters proposed in AguehCarlier.
With of the histograms.
In [36]:
N = 70
Load input histograms $(p_k)_{k=1}^K$.
In [37]:
names = ['disk','twodisks','letter-x','letter-z']
vmin = .05
P = np.zeros([N,N,len(names)])
for i in range(len(names)):
p = load_image("nt_toolbox/data/" + names[i] + ".bmp",N)
p = normalize(rescale(p)+vmin)
P[:,:,i] = p
K = len(names)
Display the input histograms.
In [38]:
plt.figure(figsize=(5,5))
for i in range(K):
imageplot(P[:,:,i], '',[2,2,i+1])
In this specific case, the kernel $\xi$ associated with the squared Euclidean norm is a convolution with a Gaussian filter $$\xi_{i,j} = e^{ -\norm{i/N-j/N}^2/\gamma }$$ where here $(i,j)$ are 2-D indexes.
The multiplication against the kernel $\xi(a_\ell)$ can now be computed efficiently, using fast convolution methods. This crucial points was exploited and generalized in SolomonEtAl to design fast optimal transport algorithm.
Regularization strength $\ga$.
In [39]:
gamma = (.04)**2
Define the $\xi$ kernel. We use here the fact that the convolution is separable to implement it using only 1-D convolution, which further speeds up computations.
In [40]:
from scipy import signal
from nt_toolbox.perform_blurring import perform_convolution
n = 41 # width of the convolution kernel
t = np.linspace(-n/(2*N),n/(2*N),n)
g = np.exp(-t**2/gamma)[:,np.newaxis]
g2 = np.dot(g,np.transpose(g))
xi = lambda x: np.transpose(signal.convolve2d(np.transpose(signal.convolve2d(x, g,mode="same")),g,mode="same"))
Display the application of the $\xi$ kernel on one of the input histogram.
In [41]:
plt.figure(figsize=(10,5))
imageplot(P[:,:,0],'',[1,2,1])
imageplot(xi(P[:,:,0]),'',[1,2,2])
Weights for isobarycenter.
In [42]:
lambd = np.ones(K)/K
It is shown in BenamouEtAl that the problem of Barycenter computation boilds down to optimizing over couplings $(\pi_k)_k$, and that this can be achieved using iterative Bregman projection that defines iterates $(\pi_{k,\ell})_k$. These iterates can be written using diagonal scalings $\pi_{k,\ell} \eqdef \diag(a_{k,\ell}) \xi \diag(b_{k,\ell}).$
Initialize the scaling factors.
In [43]:
b = np.ones([N,N,K])
a = np.copy(b)
The first step of the Bregman projection method corresponds to the projection on the fixed marginals constraints $\pi_k \ones=p_k$. This is achieved by updating $$\forall k=1,\ldots,K, \quad a_{k,\ell+1} = \frac{p_k}{ \xi( b_{k,\ell} ) }.$$
In [44]:
for k in range(K):
a[:,:,k] = P[:,:,k]/xi(b[:,:,k])
The second step of the Bregman projection method corresponds to the projection on the equal marginals constraints $\forall k, \pi_k^T \ones=q$. This is achieved by first computing the target barycenter using a geometric means $$\log(q_\ell) \eqdef \sum_k \lambda_k \log( b_{k,\ell} \odot \xi( a_{k,\ell} ) ).$$
In [45]:
q = np.zeros(N)
for k in range(K):
q = q + lambd[k] * np.log(np.maximum(1e-19*np.ones(len(b[:,:,k])), b[:,:,k]*xi(a[:,:,k])))
q = np.exp(q)
And then one can update the other maginals to be equal to this barycenter at step $\ell$. $$\forall k=1,\ldots,K, \quad b_{k,\ell+1} \eqdef \frac{q_\ell}{ \xi(a_{k,\ell+1}) }.$$
In [46]:
for k in range(K):
b[:,:,k] = q/xi(a[:,:,k])
Exercise 4
Implement the iterative algorithm to compute the iso-barycenter of the measures. Plot the decay of the error $\sum_k \norm{\pi_k \ones - p_k}$.
In [47]:
run -i nt_solutions/optimaltransp_5_entropic/exo4
In [48]:
# Insert your code here.
Display the barycenter.
In [ ]:
plt.figure(figsize=(5,5))
imageplot(q)
Exercise 5
Compute barycenters for varying weights $\la$ corresponding to a bilinear interpolation inside a square.
In [ ]:
run -i nt_solutions/optimaltransp_5_entropic/exo5
In [ ]:
# Insert your code here.
## Bibliography¶
• [Villani] C. Villani, (2009). Optimal transport: old and new, volume 338. Springer Verlag.
• [Cuturi] M. Cuturi, (2013). Sinkhorn distances: Lightspeed computation of optimal transport. In Burges, C. J. C., Bottou, L., Ghahramani, Z., and Weinberger, K. Q., editors, Proc. NIPS, pages 2292-2300.
• [AguehCarlier] M. Agueh, and G Carlier, (2011). Barycenters in the Wasserstein space. SIAM J. on Mathematical Analysis, 43(2):904-924.
• [CuturiDoucet] M. Cuturi and A. Doucet (2014). Fast computation of wasserstein barycenters. In Proc. ICML.
• [BauschkeLewis] H. H. Bauschke and A. S. Lewis. Dykstra's algorithm with Bregman projections: a convergence proof. Optimization, 48(4):409-427, 2000.
• [Sinkhorn] R. Sinkhorn. A relationship between arbitrary positive matrices and doubly stochastic matrices. Ann. Math. Statist., 35:876-879, 1964.
• [SolomonEtAl] J. Solomon, F. de Goes, G. Peyr , M. Cuturi, A. Butscher, A. Nguyen, T. Du, and L. Guibas. Convolutional Wasserstein distances: Efficient optimal transportation on geometric domains. Transaction on Graphics, Proc. SIGGRAPH, 2015.
• [BenamouEtAl] J-D. Benamou, G. Carlier, M. Cuturi, L. Nenna, G. Peyr . Iterative Bregman Projections for Regularized Transportation Problems. SIAM Journal on Scientific Computing, 37(2), pp. A1111-A1138, 2015. | 2022-08-08 06:42:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8659385442733765, "perplexity": 1768.5145409767383}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570767.11/warc/CC-MAIN-20220808061828-20220808091828-00122.warc.gz"} |
https://www.storyofmathematics.com/glossary/yard/ | # Yard|Definition & Meaning
## Definition
Yard, denoted by yd, is the unit of length that equals 3 feet (36 inches) or 0.9144 meters. Equivalently, a distance of 1 mile equals 1760 yards.
Usually, the yard is a part of the imperial system that the United States still adopts to express distance units in feet, inches, and yards. Furthermore, other imperial units, such as pounds, miles, etc., are also used to indicate their respective quantities.
The yard is frequently used to measure distances in sports and other physical activities, as well as in construction and real estate.
In the textile business, it is also used to measure the length of cloth or other materials. The term yard is also used in nautical measures. It is the unit of length used to measure the length of a ship or the depth of water in a harbor or channel in this context.
Figure 1: Conversion of Yard to meters and centimeters in SI Units
Furthermore, yards are frequently used in landscaping to gauge the size of lawns, gardens, and other outdoor spaces. For instance, a landscaper may use yards to calculate how much sod is required to cover a certain patch of lawn or how much mulch or other materials are required to cover a garden bed. Yards may also determine a property’s size and how the landscaping will be laid out.
## Imperial System and Its Usage
The Imperial system, often known as the British system or imperial units, is a measuring system that was widely used in the United Kingdom and its former colonies, including the United States. The Imperial system contains the length (inches, feet, yards, and miles), weight (ounces, pounds, and tonnes), and volume units (fluid ounces, pints, quarts, and gallons).
Furthermore, Temperature (Fahrenheit), energy (British thermal units), and pressure are also included in the Imperial system (pounds per square inch). Although used widely before, nowadays, the metric system is used instead throughout most of the globe, including the United States.
Figure 2: Imperial Units and their equivalent in SI Units.
The Imperial System was first established in the United Kingdom in the 18th and 19th centuries and was standardized in its colonies, such as the United States. It was widely used throughout the 19th and 20th centuries but later on, lost its usage at the end of the 20th century.
The usage of scientific improvements and occurrences of technological advances changed the whole retrospective around the quantities and their measurement, and thus, the metric system was considered to be a more logical and consistent system of measurement of units. Thus, the world shifted to the SI Unit system.
Nowadays, the SI Unit is the mainstream way of measurement of quantities. However, the imperial system is still widely used in measurements in everyday life, such as road distances, body temperatures, cooking quantities, and industries.
## Importance and Uses of Yard in Practical Applications
The yard is a pretty commonly used unit of measurement of distance in the US, and many landscaping or distances are related to sports, real estate, textile and clothing, and food and agriculture. Furthermore, It is also an important tool of measurement for construction works, with the dimensions of the rooms and lots measured in yards and feet.
Similar to how the size of a house or the area of a plot of land can be described, the yard is frequently employed in real estate. Because of this, it is simple for purchasers to comprehend a property’s dimensions.
The unit yard is used in landscaping to determine the size of lawns and gardens as well as the number of materials required for projects. This enables both experts and individuals to plan and carry out landscaping tasks precisely.
The yard is also used in the textile and apparel industries to measure materials or clothing and ensure that garment measurements are precise.
Moreover, yards are a common unit of measurement in sports for field or track events like the long jump and the 100-yard race. This makes it possible to quantify sports performance precisely and consistently.
Additionally, these are also used in agriculture and fishing to measure the length of a fishing net or the size of an agricultural plot. This enables precise yield computation and resource management.
## Examples Explaining the Usage of Yard and Imperial System in Measurements
A property dealer bought land for \$0.5 Per Yard2. The land was 25 meters long and 50 meters wide. Find the area of the land in the unit, yard, and, subsequently, the cost of the land that the property dealer has bought. ### Solution First of all, we require to convert the metric units into imperial units, that is, meters to yards. To convert meters to yards, we follow the following conversion: 1 metre = 1.09361 yards 25 meters = (1.09361 x 25) yards 25 meters = 27.34 yard 50 meters = (1.09361 x 50) yards 50 meters = 54.681 yards So the land is 27.34 yards long and 54.681 yards wide. Thus the area of the land is equal to the following: Area of land = 54.681 x 27.34 Area of land = 1494.98 yard2 Thus the Area that the property dealer bought was 1494.98 sq yards, and its cost can be calculated as below: Cost of land = 0.5 USD/sq yard x 1494.98 sq yards Cost of land = 747.5 USD. Hence, the cost of the land for the property dealer is \$747.5.
Figure 3: Illustration showing the parameters of the land bought by the property dealer
A salesman is selling linen for \$25/yard to a clothing shop. The dealer of the clothing shop buys 10 meters of linen from the salesman. Find the cost of the linen for the dealer. ### Solution Similarly to Example 1, we have to convert the metric units to imperial units. Length of Linen bought = 10 meters x 1.09361 yards Length of Linen bought = 10.9361 yards Now, the cost of linen can be calculated by the following steps: Cost of Linen = 10.9361 yards x \$25/Yard
Cost of Linen = \$273.4025 Hence, the final cost of linen bought by the dealer is \$273.4025.
All the above figures are drawn using GeoGebra. | 2023-03-21 23:41:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4381881058216095, "perplexity": 1777.6402140028583}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943747.51/warc/CC-MAIN-20230321225117-20230322015117-00239.warc.gz"} |