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https://msp.org/agt/2018/18-2/p06.xhtml | #### Volume 18, issue 2 (2018)
Recent Issues
The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Moduli of formal $A$–modules under change of $A$
### Andrew Salch
Algebraic & Geometric Topology 18 (2018) 797–826
##### Abstract
We develop methods for computing the restriction map from the cohomology of the automorphism group of a height $dn$ formal group law (ie the height $dn$ Morava stabilizer group) to the cohomology of the automorphism group of an $A$–height $n$ formal $A$–module, where $A$ is the ring of integers in a degree $d$ field extension of ${ℚ}_{p}$. We then compute this map for the quadratic extensions of ${ℚ}_{p}$ and the height $2$ Morava stabilizer group at primes $p>3$. We show that the these automorphism groups of formal modules are closed subgroups of the Morava stabilizer groups, and we use local class field theory to identify the automorphism group of an $A$–height $1$–formal $A$–module with the ramified part of the abelianization of the absolute Galois group of $K$, yielding an action of $Gal\left({K}^{ab}∕{K}^{nr}\right)$ on the Lubin–Tate/Morava $E$–theory spectrum ${E}_{2}$ for each quadratic extension $K∕{ℚ}_{p}$. Finally, we run the associated descent spectral sequence to compute the $V\left(1\right)$–homotopy groups of the homotopy fixed-points of this action; one consequence is that, for each element in the $K\left(2\right)$–local homotopy groups of $V\left(1\right)$, either that element or an appropriate dual of it is detected in the Galois cohomology of the abelian closure of some quadratic extension of ${ℚ}_{p}$.
##### Keywords
formal groups, class field theory, stable homotopy groups, Lubin–Tate theory, formal modules, formal groups with complex multiplication, Morava stabilizer groups
##### Mathematical Subject Classification 2010
Primary: 11S31, 14L05, 55N22, 55P42, 55Q10 | 2018-03-22 21:25:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 23, "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": 0.8343228101730347, "perplexity": 606.6449271420038}, "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/1521257648003.58/warc/CC-MAIN-20180322205902-20180322225902-00402.warc.gz"} |
https://ltwork.net/how-has-it-felt-to-be-working-to-educate-the-public-about--5455051 | # How has it felt to be working to educate the public about human rights violations
###### Question:
How has it felt to be working to educate the public about human rights violations
### Help answer both questions and I’ll give you the brainless
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### Question 1 (1 point) question 1 unsaved ¿cuál palabra es el pronombre correcto para las palabras subrayadas?
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### If the measure of angle 2 is (5x+14) and angle 3 is (7x-14), what is the measure of angle 1 in degrees?
If the measure of angle 2 is (5x+14) and angle 3 is (7x-14), what is the measure of angle 1 in degrees? $If the measure of angle 2 is (5x+14) and angle 3 is (7x-14), what is the measure of angle 1 in degre$...
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### Potatoes cost £2 per kg.Carrots cost £3 per kg.Alfred buys p kg of potatoes and c kg of carrots.The total cost is
Potatoes cost £2 per kg. Carrots cost £3 per kg. Alfred buys p kg of potatoes and c kg of carrots. The total cost is £T. Write down a formula for T in terms of p and c....
### What are media executives, editors, or reporters called who open or close the gate on a particular story?
What are media executives, editors, or reporters called who open or close the gate on a particular story? a. gatekeepers c. social capitalists b. opinion leaders d. none of the above...
### For the feasibility region shown below, find the maximum value of the function p = 2x + 3y
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### Attempt 1 of 1 when compounds that are formed from ionic bonds decompose, the products are usually
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### Your soccer team has won 9 games out of 12 games. You lost 3 out of 12 games. What is the relative frequency of winning a game.
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### Nine friends share 12 pounds of pecans equally. how many pounds of pecans does each friend get?
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### If the circumference of a circle is 56.52 what is the area
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### Why is saint peter's basilica considered one of the holiest places of christianity?
Why is saint peter's basilica considered one of the holiest places of christianity?...
### The term 'Class A Accounting' as it is used by the researcher Christopher Nobes refers to: a) conservative accounting systems.
The term "Class A Accounting" as it is used by the researcher Christopher Nobes refers to: a) conservative accounting systems. b) the most efficient accounting systems. c) accounting systems that primarily serve external shareholders. d) accounting systems developed primarily for creditors and t...
### Office Hom x i (31) General (ELA Gr. x C Clever | Portal Practice Session - Intex G The pr /test/practice-session/9e1bc?FID=ca
Office Hom x i (31) General (ELA Gr. x C Clever | Portal Practice Session - Intex G The pr /test/practice-session/9e1bc?FID=ca 1d4880-bed2-4007-9773-8daaeac79501& amp;CFTOKEN=0&cratelD=9e1bc& ;packlb The United Nations is broken into five different groups--the General Assembly the Security Co...
### Unwritten rules that govern your social behavior on the field are called: a. sportsmanship b. fair play
Unwritten rules that govern your social behavior on the field are called: a. sportsmanship b. fair play c. being a decent individual d. all the above... | 2022-10-04 19:32:04 | {"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": 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": 0.17278076708316803, "perplexity": 4867.179603729584}, "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-2022-40/segments/1664030337524.47/warc/CC-MAIN-20221004184523-20221004214523-00397.warc.gz"} |
https://ncatlab.org/nlab/show/groupoid-principal+infinity-bundle | # nLab groupoid-principal infinity-bundle
Contents
### Context
#### Bundles
bundles
fiber bundles in physics
cohomology
# Contents
## Idea
The generalization of a $G$-principal ∞-bundle over an ∞-group $G$ as $G$ is generalized to a groupoid object in an (∞,1)-category.
## Definition
For $\mathbf{H}$ an (∞,1)-topos and $\mathcal{G}_\bullet \in Grp_\infty(\mathbf{H})$ a groupoid object in an (∞,1)-category, a $\mathcal{G}_\bullet$-principal $\infty$-bundle over $X$ is
• a morphism $P \to X$
• equipped with an anchor $a \colon P \to \mathcal{G}_0$ and a groupoid ∞-action of $\mathcal{G}_\bullet$ on $(P,a)$ over $X$;
• such that $P \to X \simeq (P//\mathcal{G})$ is the corresponding quotient map.
Last revised on January 5, 2018 at 05:12:53. See the history of this page for a list of all contributions to it. | 2021-08-03 07:10:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 14, "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": 0.8870913982391357, "perplexity": 2485.1995399525763}, "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/1627046154432.2/warc/CC-MAIN-20210803061431-20210803091431-00254.warc.gz"} |
https://www.physicsforums.com/threads/linear-algebra-dependent-or-independent.868739/ | # Linear Algebra- Dependent or independent
## Homework Statement
Let(v1, v2, v3) be three linearly independent vectors in a vector space V. Is the set {v1-v2, v2-v3, v3-v1} linearly dependent or independent?
## Homework Equations
Linearly independent is when c1v1+c2v2+...+ckvk=0
and c1=c2=...ck=0
## The Attempt at a Solution
c1(v1-v2)+ c2(v2-v3)+ c3(v3-v1)=0
c1-c3=0
-c1+c2=0
-c2+c3=0
therefore c1=c2=c3 and since c1, c2 and c3 are zero because for the first set of independent vectors I got c1v1+c2v2+c3v3=0 all c1=c2=c3=0,
which means this is the case for the second set and it must be linearly independent.
This is what i got but my answer key says the second set is linearly dependent. I'm having trouble seeing why.
Thanks for any help
Samy_A
Homework Helper
## Homework Statement
Let(v1, v2, v3) be three linearly independent vectors in a vector space V. Is the set {v1-v2, v2-v3, v3-v1} linearly dependent or independent?
## Homework Equations
Linearly independent is when c1v1+c2v2+...+ckvk=0
and c1=c2=...ck=0
## The Attempt at a Solution
c1(v1-v2)+ c2(v2-v3)+ c3(v3-v1)=0
c1-c3=0
-c1+c2=0
-c2+c3=0
therefore c1=c2=c3 and since c1, c2 and c3 are zero because for the first set of independent vectors I got c1v1+c2v2+c3v3=0 all c1=c2=c3=0,
which means this is the case for the second set and it must be linearly independent.
This is what i got but my answer key says the second set is linearly dependent. I'm having trouble seeing why.
Thanks for any help
Can you explain in detail how you concluded from c1=c2=c3 that c1, c2 and c3 are zero?
Can you explain in detail how you concluded from c1=c2=c3 that c1, c2 and c3 are zero?
from my set of equations i concluded that c1=c2=c3. So then I had made the assumption that c1=c2=c3 was zero because from the given set v1, v2, v3 being linearly indepedent, which would mean that c1v1+c2v2+c3v3=0 must have c1=c2=c3 from the definition of linear dependence. I assumed they were the same constants, is this wrong to assume?
Samy_A
Homework Helper
from my set of equations i concluded that c1=c2=c3. So then I had made the assumption that c1=c2=c3 was zero because from the given set v1, v2, v3 being linearly indepedent, which would mean that c1v1+c2v2+c3v3=0 must have c1=c2=c3 from the definition of linear dependence. I assumed they were the same constants, is this wrong to assume?
##v_1,v_2,v_3## being linearly independent means that if ##d_1v_1+d_2v_2+d_3v_3=0##, then ##d_1=0,d_2=0,d_3=0##.
There is no reason whatsoever to assume that the numbers ##c_1,c_2,c_3## that you chose for the set {##v_1-v_2, v_2-v_3, v_3-v_1##} must also work for ##v_1,v_2,v_3##.
but even still for my set of {v1-v2,v2-v1....} the c1=c2=c3 are all equall and I had set my equations to equal zero, then the only way this will be true is if they all equal zero, right?
Samy_A
Homework Helper
but even still for my set of {v1-v2,v2-v1....} the c1=c2=c3 are all equall and I had set my equations to equal zero, then the only way this will be true is if they all equal zero, right?
Why? All you found is that ##c_1=c_2=c_3##.
That seems sufficient to have ##c_1(v_1-v_2)+c_2(v_2-v_3)+c_3(v_3-v_1)=0##.
Ok, I'm seeing it clearer now. Thank you
Mark44
Mentor
##v_1,v_2,v_3## being linearly independent means that if ##d_1v_1+d_2v_2+d_3v_3=0##, then ##d_1=0,d_2=0,d_3=0##.
I would add that because the vectors are linearly independent, there can be no other solutions for the constants ##d_1, d_2,## and ##d_3##.
If the three vectors were linearly dependent, the equation ##d_1v_1+d_2v_2+d_3v_3=0## would have an infinite number of solutions for the constants, including ##d_1=0,d_2=0,d_3=0##. This is a fine point that often eludes new students of linear algebra.
MozAngeles | 2021-03-02 01:47:11 | {"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": 0.8187554478645325, "perplexity": 908.61696843076}, "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-2021-10/segments/1614178363211.17/warc/CC-MAIN-20210302003534-20210302033534-00121.warc.gz"} |
https://crypto.meta.stackexchange.com/questions/23/is-this-the-place-to-ask-about-crypto-algorithm-creation-new-techniques?noredirect=1 | For almost 7 years I've been working in algorithm creation for new encryption systems. I'll be the first to tell you that my goals are lofty and that it's no small task to make something worth using. With that in mind, is Crypto the place to ask about how implementations work or ask for clarifications on an existing algorithm's process?
Sample questions such as:
What attacks does this algorithm's technique defend against?
What is the benefit of this technique over this technique?
Some questions that may be on the edge of being subjective (but may need to be asked?) might include:
Is there an error in this implementation of this technique?
Will this optimization cause problems?
Basically any question that might include code. What's the limit on questions relating to new algorithm creation or techniques?
If there is a SE site where a such a question is on-topic, this is crypto.SE.
However, past experience (e.g. with Usenet group sci.crypt) shows that there is high potential for questions like "hey I do not know crypto but here is an algorithm [some sort of unreadable code in an obscure language] what do you think of it guys ?", or even "my new algorithm rocks, try to break it [followed by a sequence of a thousand digits]". The sample questions you cite are fine and on-topic, but I would argue for some clear and strict guidelines. We do not want people posting complete specification of their new marvelous cryptosystems, in particular if the specification consists in code in some programming language.
As a basic rule, the question shall be precise and narrow, like "how do I estimate the cost of linear cryptanalysis ?", and certainly not "is it secure ?".
• It's a fine line between acceptable and not. – Corey Ogburn Jul 13 '11 at 19:31
This is primarily a site for experts, so I would say that this is a perfect place for those type of questions.
However, everything needs to be taken on a case-by-case basis.
I agree with Thomas Pornin in general.
Plus, if any such questions are to be asked, I think people should be encouraged to use mathematical notation here instead of a sample code in any specific programming language. Even if the question is based on (to some extent) an implementation in any programming language... Or they should use pseudocode at least.
This site is not for computer engineers or programmers alone, since the core subject here is cryptography in general. I strongly believe the questions should be at least readable by a large portion of the users. | 2020-09-28 16:30:51 | {"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": 0.36885055899620056, "perplexity": 1010.8365270914541}, "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/1600401601278.97/warc/CC-MAIN-20200928135709-20200928165709-00435.warc.gz"} |
https://slicematrix.github.io/stock_market_anomalies.html | Detecting Stock Market Anomalies Part 1:¶
In trading as in life, it is often extremely valuable to determine whether or not the current environment is anomalous in some way. If things are acting "normal" we know our strategies can trade a certain way. For example, if we are in a normal trading environment we might employ a volatility shorting strategy. On the other hand, if we identify we are in an abnormally exciting market, it might behoove us to employ a strategy which does the exact opposite: seeking out opportunities for momentum based trading, for example. In that kind of market, shorting volatility could be very dangerous
SliceMatrix-IO offers a number of different options for detecting anomalies on both univariate and multivariate datasets. Today we will explore an anomaly detection algorithm called an Isolation Forest. This algorithm can be used on either univariate or multivariate datasets. It has one parameter, rate, which controls the target rate of anomaly detection. I.e. a rate equal to 0.2 will train the algorithm to detect anomalie in 1 out of 5 datapoints on average. The rate must be greater than 0 and less than 0.5
Since the Isolation Forest can handle multivariate data, it is ideal for detecting anomalies when you have multiple input features. In our case, our input features will be the daily trading volume for a list of ETF symbols. We will define this microcosm as our "market" although in practice we could potential make the universe much, much bigger
In [1]:
symbols = ['SPY', 'IWM', 'DIA', 'IEF', 'TLT', 'GLD', 'SLV', 'USO', 'XIV']
The goal of this algo is to determine when the trading volume for our list of symbols as a whole is in an anomalous state. This could mean, for example, that we are detecting a spike in trading volume. To do this, we begin by importing the SliceMatrix-IO Python client.
If you haven't installed the client yet, the easiest way is with pip:
pip install slicematrixIO
Now we can begin by creating the SliceMatrix-IO client. Make sure to substitute your own api key into the code.
Don't have a key yet? Get your api key here
In [2]:
from slicematrixIO import SliceMatrix
api_key = "insert your api key here"
sm = SliceMatrix(api_key)
Next let's import some useful Python modules such as Pandas, NumPy, and Pyplot
In [3]:
%matplotlib inline
import pandas as pd
#import pandas.io.data as web
from pandas_datareader import data as web
import datetime as dt
import numpy as np
import matplotlib.pyplot as plt
Grab trading volume data from Yahoo for our list of stocks using Pandas' Data-Reader
In [4]:
start = dt.datetime(2012, 1, 1)
end = dt.datetime(2017, 3, 6)
volume = []
closes = []
for symbol in symbols:
print symbol
vdata = web.DataReader(symbol, 'yahoo', start, end)
cdata = vdata[['Close']]
closes.append(cdata)
vdata = vdata[['Volume']]
volume.append(vdata)
volume = pd.concat(volume, axis = 1).dropna()
volume.columns = symbols
closes = pd.concat(closes, axis = 1).dropna()
closes.columns = symbols
SPY
IWM
DIA
IEF
TLT
GLD
SLV
USO
XIV
In [5]:
volume.head()
Out[5]:
SPY IWM DIA IEF TLT GLD SLV USO XIV
Date
2012-01-03 193697900 60504700 7175100 1297700 9076900 13385800 28140300 12369900 5366800
2012-01-04 127186500 34648500 7625200 1789000 8417100 11549700 18062600 13812800 6686900
2012-01-05 173895000 57274600 8678900 1311300 6465800 11621600 13858900 11799600 4373600
2012-01-06 148050000 45499800 7488600 998200 7348500 9790500 20679500 9760600 5765800
2012-01-09 99530200 52042400 5881800 379900 5582400 8771900 11638200 7509300 3306600
In [6]:
volume.plot(figsize=(12, 6))
plt.show()
The time series of volume is has siginificant spikes in trading volume accross our ETF universe. Some notable events include the October 2014 Treasury Flash Crash, August 2015's spike in volatility, as well as Donald Trump's election in late 2016. Note the relative quiet in the start of 2017...
While these events are obvious to the naked eye (well after the fact) what would be useful is the ability to automatically classify events based purely off the trading volume data, i.e. without the use of a human being. This is the goal of machine learning, and luckily this is exactly the kind of use case our algo, the Isolation Forest, was built to handle
We'll start by creating 3 anomaly detectors with increasing values to the rate parameter. Remember, this controls how many anomalies each detector will pick up
In [7]:
# isolation forest multivariate anomaly detector
iso_forest1 = sm.IsolationForest(dataset = volume, rate = 0.1) # want signal every 1 / 10 days on average
iso_forest2 = sm.IsolationForest(dataset = volume, rate = 0.2) # want signal every 1 / 5 days on average
iso_forest3 = sm.IsolationForest(dataset = volume, rate = 0.33) # want signal every 1 / 3 days on average
These three models are now training and ready to be used in the cloud.
Now let's get the anomaly scores (i.e. whether or not the trading day was anomalous) from each model. The Isolation Forest returns a score of 1 for normal days and -1 for anomalous trading activity
In [8]:
scores1 = iso_forest1.training_scores()
scores2 = iso_forest2.training_scores()
scores3 = iso_forest3.training_scores()
scores1 = pd.DataFrame(scores1, columns = ["scores"])
scores2 = pd.DataFrame(scores2, columns = ["scores"])
scores3 = pd.DataFrame(scores3, columns = ["scores"])
In [9]:
scores1.plot(ylim = (-2.0, 2.0))
Out[9]:
<matplotlib.axes._subplots.AxesSubplot at 0x7af9970>
In [10]:
print scores1.shape, volume.shape
(1301, 1) (1301, 9)
Let's make a function to visualize the 3 dectectors performance
In [11]:
import matplotlib.collections as collections
In [12]:
def draw_anomaly_plot(scores, volume, title, lw = 2):
fig, ax = plt.subplots(figsize=(12, 6))
ax.set_title(title)
ax.plot(scores.index.values, volume.sum(axis = 1), color='black')
ax.axhline(0, color='black', lw=2)
for i in range(0, scores.shape[0]):
score = scores.ix[i]
if score[0] < 0:
l = plt.axvline(x=i, color='red', alpha=0.25, lw = lw)
plt.show()
Now we can compare the three models and visualize how the rate parameter is affecting the probablity of detecting an anomaly
In [13]:
draw_anomaly_plot(scores1, volume, 'Market Volume Anomaly Detection (10%)')
In [14]:
draw_anomaly_plot(scores2, volume, 'Market Volume Anomaly Detection (20%)')
In [15]:
draw_anomaly_plot(scores3, volume, 'Market Volume Anomaly Detection (33%)')
We can see how the number of anomalies detected increases as we ratchet up the rate parameter.
In the models we created above, we used the entire dataset to train our Isolation Forests. In practice, we don't have access to information in the future (at least not with current technology) so we should introduce some reality into our model by splitting the dataset into two chunks: one for training the model (in-sample) and one for validating the model's performance (out-sample)
In [16]:
# split the dataset
volume_training = volume.ix[0:1200,:]
volume_testing = volume.ix[1201:,:]
In [17]:
iso_forest_live_model = sm.IsolationForest(dataset = volume_training, rate = 0.2)
This model is trained using only the volume_training dataframe. Now we can use this model to score the out of sample trading volume:
In [18]:
out_of_sample_scores = iso_forest_live_model.score(volume_testing.values.tolist())
In [19]:
out_of_sample_scores = pd.DataFrame(out_of_sample_scores, columns = ['scores'])
out_of_sample_scores.tail()
Out[19]:
scores
95 1
96 1
97 1
98 1
99 1
In [20]:
draw_anomaly_plot(out_of_sample_scores, volume_testing, 'Market Volume Anomaly Detection (Out of Sample)', lw = 7)
One of the strength's of using SliceMatrix-IO is that your models persist in the cloud after you train them, meaning you can load your models from any device anywhere on the planet with an internet connection.
For example, suppose we have one process which trains the models (e.g. using the code above) and another process which runs during live trading which does the anomaly scoring. Each model has an attribute called name which describes the unique id for that model:
In [21]:
print iso_forest_live_model.name
db51b214a67c
We can easily load this model in another process using the lazy load feature:
In [23]:
# in another process
iso_forest_live_model = sm.IsolationForest(name = "db51b214a67c")
# when we get a new data point we want to score...
iso_forest_live_model.score([[66650800, 30445200, 2580800, 2469300, 9460700, 10536000, 8681600, 13807500, 8518800]])
Out[23]:
[1]
This way you can use SliceMatrix-IO to easily and quickly create real time machine learning models for trading anywhere on the globe
Don't have a SliceMatrix-IO api key yet? Get your api key here
In [ ]: | 2018-07-17 16:50:27 | {"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": 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": 0.24655602872371674, "perplexity": 2811.1124327636758}, "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-2018-30/segments/1531676589757.30/warc/CC-MAIN-20180717164437-20180717184437-00105.warc.gz"} |
http://stackoverflow.com/questions/8333559/android-update-project-com-android-sdklib-internal-project-projectproperties-fai | # android update project com.android.sdklib.internal.project.projectproperties fails
I am trying to run the android update project command on a project i am working on.
After running the command i am presented with the following error. When i run this command on another project it works fine.
I have tried deleting the entire workspace and just checking everything out again and it still is not working.
VERSIONS
Hierarchy Viewer Version: 15.0.1.v201111031820-219398
Traceview Version: 15.0.1.v201111031820-219398
Dalvik Debug Monitor Service Version: 15.0.1.v201111031820-219398
Android Development ToolkitVersion: 15.0.1.v201111031820-219398
C:\Users\me\android-sdks\tools>android update project -p C:\Users\me\workspace\foo\bar\Framework
Updated local.properties
at com.android.sdklib.internal.project.ProjectProperties.parsePropertyFi
le(ProjectProperties.java:385)
perties.java:229)
at com.android.sdklib.internal.project.ProjectCreator.updateProject(Proj
ectCreator.java:605)
at com.android.sdkmanager.Main.updateProject(Main.java:693)
at com.android.sdkmanager.Main.doAction(Main.java:273)
at com.android.sdkmanager.Main.run(Main.java:119)
at com.android.sdkmanager.Main.main(Main.java:102)
C:\Users\me\android-sdks\tools>
-
Which version of the tools are you using? They made some changes to fix some bugs that may be related to this in r15. Also this blog article might help: pjeutr.com/node/3 – Charlie Collins Nov 30 '11 at 23:02
Versions posted. – prolink007 Dec 1 '11 at 16:04
@CharlieCollins Thanks for the help, i found my problem in the ant.properties file. – prolink007 Dec 1 '11 at 16:17
My ant.properties file was corrupted. There was some stuff in there that was not correct. I basically just cleared the ant.properties file and re-wrote some of the stuff there and it works fine now. | 2016-05-01 14:28:26 | {"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": 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": 0.39344024658203125, "perplexity": 3576.4991421645445}, "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-2016-18/segments/1461860116173.76/warc/CC-MAIN-20160428161516-00059-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://hdlbits.01xz.net/wiki/Gatesv | ## Gatesv
### From HDLBits
popcount3Previous
You are given a four-bit input vector in[3:0]. We want to know some relationships between each bit and its neighbour:
• out_both: Each bit of this output vector should indicate whether both the corresponding input bit and its neighbour to the left (higher index) are '1'. For example, out_both[2] should indicate if in[2] and in[3] are both 1. Since in[3] has no neighbour to the left, the answer is obvious so we don't need to know out_both[3].
• out_any: Each bit of this output vector should indicate whether any of the corresponding input bit and its neighbour to the right are '1'. For example, out_any[2] should indicate if either in[2] or in[1] are 1. Since in[0] has no neighbour to the right, the answer is obvious so we don't need to know out_any[0].
• out_different: Each bit of this output vector should indicate whether the corresponding input bit is different from its neighbour to the left. For example, out_different[2] should indicate if in[2] is different from in[3]. For this part, treat the vector as wrapping around, so in[3]'s neighbour to the left is in[0].
### Module Declaration
```module top_module(
input [3:0] in,
output [2:0] out_both,
output [3:1] out_any,
output [3:0] out_different );```
The both, any, and different outputs use two-input AND, OR, and XOR operations, respectively. Using vectors, this can be done in 3 assign statements. | 2021-06-22 01:57:13 | {"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": 0.8189089894294739, "perplexity": 1408.659560708747}, "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/1623488504969.64/warc/CC-MAIN-20210622002655-20210622032655-00376.warc.gz"} |
https://www.gamedev.net/forums/topic/564647-splitting-a-string-with-regex/ | • 10
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• 10
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# Splitting a string with regex
This topic is 2932 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
I am using Qt and trying to parse a simple INI file. I want to split each line up by commas, taking all characters that are in quotes as a string literal (i.e like C style strings). Here is are some examples of what my INI file contains:
1234, "text", "more text"
"textWithNoSpaces", "text with spaces, and even a comma"
I would like my parsing function to return an array of strings (QString) containing the text in and out of quotes, e.g:
s1 = "1234" s2 = "text" s3 = "more text" // Note that these quotes are not part of the string
s1 = "textWithNoSpaces" s2 = "text with spaces, and even a comma"
The problem is that Qt (rather surprisingly) does not have a simple substring function that takes a start and end index, like std::string's substr. What it does have, however, is a more powerful split function that takes a regular expression. So i would like to know how i can use regex to split each line by commas but preserve the commas withing quotes (and also trim any extra whitespace between separating commas). thanks in advance
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I've never used Qt before, but what you want it something similar to .NET's System.Text.RegularExpressions.Regex.Matches, which returns a collection of substrings which match against a regular expression (or emulate the functionality). Off the top of my head your regex might look something like this:
\w*((\"(.*?)\",?)|(([.^\"]*?),?))
But I'm no regex expert, so it could be completely wrong (can't even remember if '"' needs to be escaped), and it doesn't handle cases where you want to have escaped quotes be included as part of a token. However the basic idea is that you need to eat whitespace, try to match a quoted or unquoted string, and handle any special escaped characters you want to support. If you can iteratively find each matching substring, you're set.
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Zipster's regex looks pretty accurate, and if you're interested in learning more about regex this is a site I've used heavily in the past:
http://www.regular-expressions.info/
Although for your situation regex seems like a bit overkill. I've never used Qt before, but the first result of a search for "Qt substring" points me to a function called "mid" that is defined as:
"Returns a string that contains the len characters of this string, starting at position i."
which sounds exactly like what you were looking for.
QString::mid
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Thanks for the help Zipster and karwosts (karwosts, i almost missed your post, you posted it the second i hit the reply button [grin]).
@karwosts: The QString::mid function is exactly what i was initially looking for. Very poorly named, though, mid suggests that it finds the middle index or something.
I will have a look at that website, there is also extensive regex documentation with Qt (they have excellent documentation). I need to learn how to use regex better.
@Zipster: Thanks for the regex, it should get me started with it. I need to keep looking at the Qt docs to see if there is a function like that .NET one. The split function takes a regex as the string to split at (so in my case it would be the comma and whitespace). I'm not sure if i can tell it to split at a comma except if it's within some quotes. In other words, i think it would be better to try and match each string withing the separating commas, if that makes sense.
Anyway, i'll have a look at it tomorrow. If all else fails, i will just write my own little parser. Shouldn't be too hard.
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Fyi, i have found out how to get a list of matches using Qt, and have written regex to do so (partially thanks to the site karwosts posted):
\\s*((?:\"[^\"]*\")|(?:\\w|\\d)+)\\s*(,|$) The code gives the string to the regex object then asks it for the text it has matched. Then it moves the index along to find the next match, and loops until no more are found: QStringList parseLine(String line) { QStringList strings; String str; QRegExp rx("\\s*((?:\"[^\"]*\")|(?:\\w|\\d)+)\\s*(,|$)"); int pos = 0; while ((pos = rx.indexIn(line, pos)) != -1) { str = rx.cap(1); // Quotes are also matched, need to strip them if (str.startsWith('\"') && str.endsWith('\"')) str = str.mid(1, str.size()-2); strings << str; pos += rx.matchedLength(); } return strings;}
I guess in the end i could have just written a simple parser by looping through each character and checking for commas and quotes, but the regex solution is a lot neater and more robust. It may be slower, but i only need to parse the text once. | 2018-03-20 18:07:21 | {"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": 0.2339642345905304, "perplexity": 1640.7336280917257}, "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-20180320170119-20180320190119-00018.warc.gz"} |
https://zbmath.org/?q=an:0575.58030 | # zbMATH — the first resource for mathematics
The longitudinal index theorem for foliations. (English) Zbl 0575.58030
A topological formula for the analytical index of a differential operator D elliptic along the leaves of the foliation (V,F) is given. The index in the Atiyah-Singer theorem for families is an element of the $$K^ 0(B)=K_ 0(C(B))$$, where B is the basic space of the fibration. On the case of foliations the algebra C(B) is replaced by a canonically defined $$C^*$$-algebra $$C^*(V;F)$$ and $$ind(D)\in K_ 0(C^*(V;F))$$. The Kasparov K-bifunctor is a basic tool to prove the results of the paper.
Reviewer: V.Deundjak
##### MSC:
58J20 Index theory and related fixed-point theorems on manifolds 37C85 Dynamics induced by group actions other than $$\mathbb{Z}$$ and $$\mathbb{R}$$, and $$\mathbb{C}$$
Full Text:
##### References:
[1] M.F. Atiyah and I. Singer, The index of elliptic operators I, Ann. of Math., 87 (1968), 484-530. · Zbl 0164.24001 [2] - , The index of elliptic operators IV, Ami. of Math., 93 (1971), 119-1 38. [3] M.F. Atiyah, R. Bott and Shapiro, Clifford Modules, Topology, 3, suppl. 1 (1964), 3-38. · Zbl 0146.19001 [4] P. Baum, Cycles, Cocycles and K theory, to appear. [5] P. Baum and A. Connes, Geometric ^-theory for Lie groups and Foliations, preprint. [6] P. Baum and R. Douglas, K-holomology and index theory, Proceedings of A.M.S., 38. [6] L. Boutet de Montvel, A course on pseudodifferential operators and their applications, Duke Univ. Math. Series, II. · Zbl 0348.35002 [7] A. Connes, An analogue of the Thorn isomorphism, for crossed products of a C*- algebra by an action of R, Adv. in Math., 39 (1981). · Zbl 0461.46043 [8] , Sur la theorie non commutative de 1’integration, Lecture Notes in Math., 725, (1979), Springer, 19-143. [9] [11] A. Connes et G. Skandalis. Theoreme de 1’indice pour les feuilletages, C.R. Acad. Sci. Paris, 292 (1981), 871-876. · Zbl 0529.58030 [10] J. Dixmier, Les C*-algebres et lews representations 2eme edition, Paris Gauthier Villars, 1969. [11] 183-194. [12] J. Hayden and RJ. Plymen, On the invariant of Dixmier-Douady^r^nw/1. [13] M.W. Hirsh, Differential topology, Graduate texts in Math. 33, Springer Verlag, Berlin. [14] L. Hormander, On the index of pseudodifferential operators, Elliptische Differential- gleischungen Band II, Koll., Berlin, 1969. [15] G.G. Kasparov, Topological invariants of elliptic operators. I: /Chomology, Math. USSR Izv., 9 (1975), 751-792. · Zbl 0337.58006 [16] , Hilbert C*-modules: Theorems of Stinespring and Voiculescu, Journal of operator theory, 4 (1980). · Zbl 0456.46059 [17] , Operator K functor and extensions of C*-algebras, Izv. Akad. Nauk, S.S.S.R. ser. Mat., 44 (1980), 571-636. [18] , ^-theory, group C*-algebras and higher signatures (Conspectus), part 1-2, preprint. · Zbl 0957.58020 [19] J.M. Kister, Microbundles are bundles, Ann. of Math., 80 (1964), 190-199. · Zbl 0131.20602 [20] B. Lawson, Foliations, Bull. Am. Math. Soc., 80 (1974), 369-418. · Zbl 0293.57014 [21] J. Milnor, Microbundles I, Topology, 3, Suppl. 1 (1964), 53. [22] R.S. Palais, Seminar on the Atiyah-Singer index theorem, Annals of Math. Studies, 57 (1965). · Zbl 0202.23103 [23] I. Singer, Future extensions of index theory and elliptic operators, Prospects in Math., Annals, of Math. Studies, 70. · Zbl 0286.58011 [24] E. Winkelnkemper, The graph of a foliation, preprint. · Zbl 0526.53039
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2022-01-22 12:42:29 | {"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": 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": 0.7126345038414001, "perplexity": 3017.6311094990247}, "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/1642320303845.33/warc/CC-MAIN-20220122103819-20220122133819-00010.warc.gz"} |
https://www.acmicpc.net/problem/13094 | 시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
20 초 512 MB 0 0 0 0.000%
## 문제
In the headquarter building of ICPC (International Company of Plugs & Connectors), there are M light bulbs and they are controlled by N switches. Each light bulb can be turned on or off by exactly one switch. Each switch may control multiple light bulbs. When you operate a switch, all the light bulbs controlled by the switch change their states. You lost the table that recorded the correspondence between the switches and the light bulbs, and want to restore it.
You decided to restore the correspondence by the following procedure.
• At first, every switch is off and every light bulb is off.
• You operate some switches represented by S1.
• You check the states of the light bulbs represented by B1.
• You operate some switches represented by S2.
• You check the states of the light bulbs represented by B2.
• ...
• You operate some switches represented by SQ.
• You check the states of the light bulbs represented by BQ.
• After you operate some switches and check the states of the light bulbs, the states of the switches and the light bulbs are kept for next operations.
Can you restore the correspondence between the switches and the light bulbs using the information about the switches you have operated and the states of the light bulbs you have checked?
## 입력
The input consists of multiple datasets. The number of dataset is no more than 50 and the file size is no more than 10MB. Each dataset is formatted as follows.
N M Q
S1 B1
:
:
SQ BQ
The first line of each dataset contains three integers N (1≤N≤36), M (1≤M≤1,000), Q (0≤Q≤1,000), which denote the number of switches, the number of light bulbs and the number of operations respectively. The following Q lines describe the information about the switches you have operated and the states of the light bulbs you have checked. The i-th of them contains two strings Si and Bi of lengths N and M respectively. Each Si denotes the set of the switches you have operated: Sij is either 0 or 1, which denotes the j-th switch is not operated or operated respectively. Each Bi denotes the states of the light bulbs: Bij is either 0 or 1, which denotes the j-th light bulb is off or on respectively.
You can assume that there exists a correspondence between the switches and the light bulbs which is consistent with the given information.
The end of input is indicated by a line containing three zeros.
## 출력
For each dataset, output the correspondence between the switches and the light bulbs consisting of M numbers written in base-36. In the base-36 system for this problem, the values 0-9 and 10-35 are represented by the characters '0'-'9' and 'A'-'Z' respectively. The i-th character of the correspondence means the number of the switch controlling the i-th light bulb. If you cannot determine which switch controls the i-th light bulb, output '?' as the i-th character instead of the number of a switch.
## 예제 입력 1
3 10 3
000 0000000000
110 0000001111
101 1111111100
2 2 0
1 1 0
2 1 1
01 1
11 11 10
10000000000 10000000000
11000000000 01000000000
01100000000 00100000000
00110000000 00010000000
00011000000 00001000000
00001100000 00000100000
00000110000 00000010000
00000011000 00000001000
00000001100 00000000100
00000000110 00000000010
0 0 0
## 예제 출력 1
2222221100
??
0
1
0123456789A | 2018-08-18 00:39:03 | {"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": 0.27071237564086914, "perplexity": 1428.448895852775}, "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-2018-34/segments/1534221213247.0/warc/CC-MAIN-20180818001437-20180818021437-00266.warc.gz"} |
https://digital-library.theiet.org/content/books/10.1049/pbte086e_ch27 | http://iet.metastore.ingenta.com
1887
## Mobility enhancement for digital video broadcast networks via satellite
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The DVB-S2 standard has been optimised for provision of broadband multimedia services to geographically dispersed fixed satellite end-users under line-of-sight (LOS) channel condition. However, continuing growth in demand for mobile broadband services via satellite necessitates a detailed examination of the DVB-S2 technology to assess its suitability for application in the mobile satellite environment. The environment is affected by signal fading due to path blockage, multipath propagation and shadowing, Doppler shift which is expressed by the Rician channel K-factor parameter values. In this paper, a model was developed in MATLAB® to simulate transmission scenarios through a mobile satellite channel, in order to investigate the bit-error-rate (BER) performance of the 16-APSK and 32-APSK modulation formats for different coding rates. This modelling of higher modulation formats of the DVB-S2 standard until now, has not been addressed adequately in related literature. Moreover, the mobility effect over the BER performance is not well investigated in the literature especially for high modulation schemes. Results obtained by simulation indicate a significant degradation in the system's BER when compared to a line-of-sight channel condition. Which even becomes worse with added varying mobility scenarios. However, higher Rician channel K-factor values tend to improve the link quality closer to that of the AWGN. These results highlight a crucial need to develop improved receiver processing and new switching thresholds applicable to the mobile satellite environment that deliver improved link availability as well as enhanced data throughput for different mobility scenarios.
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Mobility enhancement for digital video broadcast networks via satellite, Page 1 of 2
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Please enter a valid email address | 2020-01-21 21:21:22 | {"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": 0.19508828222751617, "perplexity": 2883.6767526009476}, "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-2020-05/segments/1579250605075.24/warc/CC-MAIN-20200121192553-20200121221553-00222.warc.gz"} |
https://math.stackexchange.com/questions/840408/whether-or-not-x-1-x-n-are-independent-and-exchangeable | # Whether or not $X_1$,…,$X_n$ are independent and exchangeable
For some n = 1,2,..., let $Y_1$,...,$Y_{n+1}$ denote iid real-valued random variables.
Define $X_j$ = $Y_j$$Y_{j+1}, \hspace{10mm}j=1,...,n a) Are X_1,X_2,...,X_n independent? b) Are X_1,X_2,...,X_n exchangeable? Attempts: a) No. Counterexample: Let Y be a Bernoulli (0,1) distribution, with p = 1/2, where Y_1 = 0 and Y_2 = 1. Then X_1 = Y_1$$Y_{2}$
Now $E(Y_1*Y_2)%$ = $E(0*1)$ = $E(0)$ = 1/2
However, $E(Y_1)%$$E(Y_2)% = 1/2*1/2 = 1/4 Since E(Y_1*Y_2)% \neq E(Y_1)%$$E(Y_2)%$, the $X_i$'s are not independent.
b) Not sure.
• Your reasoning on a) is not valid; expressing $X_2$ in terms of $X_1$, $Y_1$, and $Y_3$ does not establish a dependence among $X_1$ and $X_2$ alone. – Dustan Levenstein Jun 20 '14 at 8:08
• Ok. Is the resulting product of two IID variables also IID? – statsguyz Jun 20 '14 at 8:09
• I don't actually know the solution; on gut intuition I suspect they're not exchangable in general, since the way the $Y_i$'s are linked together by the $X_i$'s is not symmetric up to permutation. – Dustan Levenstein Jun 20 '14 at 8:13
• Answers: a) Not in general (but this requires an explicit counterexample). b) Not in general (but this requires an explicit counterexample). Hint: Try Bernoulli {0,1}-valued random variables. – Did Jun 20 '14 at 8:15
Your reasoning on a) is not valid yet the good idea is there. Let's keep your example with the $X_{i}$'s being independant Bernouilli variables with $p=0.5$.
Then, $\mathbb{E} X_{1}X_{2} = \mathbb{E} Y_{1}Y_{2}^{2} Y_{3} = \mathbb{E}Y_{1} \mathbb{E}Y_{2}^{2} \mathbb{E}Y_{3}$ because of the independance of the $Y_{i}$s. Since $\mathbb{E}Y_{2}^{2} = p$, we have $\mathbb{E} X_{1}X_{2} = p^{3}$. On the other side, it is easy to see that $\mathbb{E}X_{i} = p^{2}$.
If $X_{1}$ and $X_{2}$ were independant, we should have $p^{3} = \mathbb{E} X_{1}X_{2} = \mathbb{E} X_{1} \mathbb{E}X_{2} = p^{4}$, which is not true.
What do you mean by "exchangeable variables ?" Here is my definition : $X_{1}, ... , X_{n}$ are exchangeable if, for every measurable function $f : \mathbb{R}^{n} \to \mathbb{R}_{+}$, and for every permutation $\sigma \in \mathfrak{S}_{n}$, we have : $$\mathbb{E}f(X_{\sigma(1)}, ..., X_{\sigma(n)}) = \mathbb{E}f(X_{1}, ..., X_{n}).$$
Let's try with $n=2$. We have $f(X_{1}, X_{2}) = f(Y_{1}Y_{2}, Y_{2}Y_{3}) = f \circ g (Y_{1}, Y_{2}, Y_{3})$, where we defined $g : \mathbb{R}^{3} \to \mathbb{R}^{2}$ by : $$g : (x,y,z) \to (xy,yz)$$
Then, $f \circ g$ is measurable and since $(Y_{1}, Y_{2}, Y_{3})$ is i.i.d., we have : $$\mathbb{E}f f(X_{1}, X_{2}) = \mathbb{E}f \circ g (Y_{1}, Y_{2}, Y_{3}) = \mathbb{E}f \circ g (Y_{3}, Y_{2}, Y_{1}) = \mathbb{E}f (Y_{3}Y_{2}, Y_{2}Y_{1}) = \mathbb{E}f(X_{2}, X_{1})$$
Therefore, $X_{1}$ and $X_{2}$ are exchangeable. I'm not sure the same result holds with $n > 2$, but you should try to adapt the proof (which might reveal tricky).
edit. Okay, here is a counterexample with $n=3$. Let's have $f(x,y,z) = xz$, nd $\sigma = (2,3,1)$. We have : $$\mathbb{E}f(X_{\sigma(1)}, X_{\sigma(2)}, X_{\sigma(3)}) = \mathbb{E}f(X_{2}, X_{3}, X_{1}) = \mathbb{E}Y_{2}Y_{3}Y_{1}Y_{2} = p^{3}$$
On the other side, we have : $$\mathbb{E}f(X_{1}, X_{2}, X_{3}) = \mathbb{E}Y_{1}Y_{2}Y_{3}Y_{4} = p^{4}$$
In conclusion, $X_{1}, X_{2}$ and $X_{3}$ are not exchangeable. The $n=2$ cas was deceptive ! | 2019-07-16 22:57:58 | {"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": 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": 0.9646281599998474, "perplexity": 313.1423842942791}, "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-2019-30/segments/1563195524972.66/warc/CC-MAIN-20190716221441-20190717003441-00114.warc.gz"} |
https://clashofclans.fandom.com/wiki/Giant_Skeleton | ## FANDOM
1,020 Pages
Not AvailableThis troop is not available in the current version.
"Big boned from early age, the Giant Skeleton was always destined to blow up more than just walls. His massive bomb damages everything around him after he is destroyed."
Level 1-8
• Summary
• The Giant Skeleton was a temporary troop that was available during the 2017 Halloween, along with Pumpkin Barbarian. They were made available again during the "Jack Skellingboom" event, along with the Ice Wizard, which lasted from 12/28/17 until 1/3/18. They were made available once again on Halloween 2018, along with Skeleton Barrel.
• They have high hitpoints and do massive damage upon death.
• Giant Skeletons prioritize defensive structures above all other targets, and will bypass all other types of enemy buildings and troops while any defenses remain on the battlefield. This is true even if they are under attack by enemy Clan Castle troops, heroes or Skeleton Trap skeletons. Note that like all troops that prioritize defenses, Giant Skeletons do not consider the Clan Castle to be a defense regardless of whether or not it contains enemy troops, but do consider the defending Grand Warden and the level 12 or 13 Town Hall (if its Giga Tesla or Giga Inferno has been triggered) to be defensive buildings.
Once all defenses are destroyed, Giant Skeletons become like any other troop with no preferred target; they will attack the nearest building to them regardless of type, and will turn and attack enemy units if they become aware of any nearby.
• Trivia
• You could have a maximum of 14 Giant Skeletons at one time in a complete set of fully upgraded Army Camps. On the battlefield, you could clone an additional 3 Giant Skeletons with three level 2 or higher Clone Spells.
• Similar to all other temporary troops, the Giant Skeleton cannot be donated through a Clan.
• Like all other temporary troops and spells, the Giant Skeleton can't be upgraded in the Laboratory. Instead, they depend on the player's Town Hall level.
• To calculate the health and damage statistics, two factors are considered: the base statistic and Town Hall multiplier.
• The base statistic for each Town Hall level equals the DPH and HP of certain levels of Giants.
• Each base statistic is multiplied by a fixed multiplier for each Town Hall level; the multiplier follows a roughly linear scale. For Town Hall level x, the multiplier is $(\lfloor 30 + (x-1)*70/11 \rfloor)/100$. Once the multiplier is applied, the statistic is rounded down to give the final statistic.
• Note that other statistics, such as training cost and death damage, are not multiplied by the multiplier.
• The Giant Skeleton is the third temporary troop that comes from Clash Royale, after Ice Wizard and Battle Ram. It's one of the two temporary troops from Clash Royale that prioritize defenses in Clash of Clans but doesn't only attack buildings in Clash Royale, the other is the Ice Wizard. The Giant Skeleton was added to clash royale on 4/1/2016 the date of the game's soft launch.
• The Giant Skeleton does equal damage as a Giant of the same level and has 2.5 times the Giant's hitpoints.
• Unlike his Clash Royale Counterpart, he attacks only defenses instead of everything.
• In the picture, he wears a brown Russian hat. But in the game, he wears a red one, resembling an opponent's Giant Skeleton troop in Clash Royale. The same situation applies to the Ice Wizard and Skeleton Barrel.
• The spawning sound and the attacking sound of Giant Skeleton is the same as the Giant.
Preferred Target Attack Type Housing Space Movement Speed Attack Speed Barracks Level Required Range
Defenses Melee (Ground Only) 20 12 2s 3 1 tile
Training Time of Giant Skeletons
1 Barracks 2 Barracks 3 Barracks 4 Barracks
2m 1m 40s 30s
Level* Damage per Second Damage per Attack Death Damage Hitpoints Training Cost Town Hall Level Required
1 7 14 800 360 250 2
2 11 22 1,000 504 750 3
3 18 36 1,200 686 1250 4
4 20 40 1,200 770 1250 5
5 29 58 1,400 1,037 1750 6
6 32 64 1,400 1,156 1750 7
7 45 90 1,600 1,628 2250 8
8 68 136 1,800 2,480 3000 9
9 87 174 2,000 3,132 3500 10
10 106 212 2,200 3,813 4000 11
11 114 228 2,200 4,100 4000 12
*The "level" here does not match up with the in-game levels. This is for purposes of clarity between different Town Hall levels, which have different statistics.
Home Village Army
Elixir Troops BarbarianArcherGiantGoblinWall BreakerBalloonWizardHealerDragonP.E.K.K.ABaby DragonMinerElectro DragonYeti (Yetimite)
Dark Elixir Troops MinionHog RiderValkyrieGolem (Golemite) • Witch (Skeleton) • Lava Hound (Lava Pup) • BowlerIce GolemHeadhunter
Super Troops Super BarbarianSuper ArcherSuper GiantSneaky GoblinSuper Wall BreakerInferno DragonSuper Witch (Big Boy)
Heroes Barbarian KingArcher QueenGrand WardenRoyal Champion
Elixir Spells Lightning SpellHealing SpellRage SpellJump SpellFreeze SpellClone Spell
Dark Spells Poison SpellEarthquake SpellHaste SpellSkeleton SpellBat Spell
Siege Machines Wall WreckerBattle BlimpStone SlammerSiege Barracks
Temporary Contents
Temporary Troops Ice WizardBattle RamPumpkin BarbarianGiant SkeletonSkeleton BarrelEl PrimoParty WizardRoyal Ghost
Temporary Spells Santa's SurpriseBirthday Boom
Temporary Traps Pumpkin BombSanta StrikeFreeze TrapShrink Trap
Other Temporary Contents The Waterfall
Community content is available under CC-BY-SA unless otherwise noted. | 2020-09-27 11:37:53 | {"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": 0.3008449971675873, "perplexity": 10508.340991638363}, "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/1600400274441.60/warc/CC-MAIN-20200927085848-20200927115848-00094.warc.gz"} |
https://math.stackexchange.com/questions/2120860/integral-of-product-of-two-error-complementary-functions-erfc | # Integral of product of two error complementary functions (erfc)
Could you please help me to show that the integral $$\int_0^{\infty} \mathrm{erfc}(ax) \, \mathrm{erfc}(bx)\, \mathrm{d}x$$ is equal to $$\frac{1}{ab\sqrt{\pi}} (a+b-\sqrt{a^2+b^2}),$$ where $$\mathrm{erfc}(y)=\frac{2}{\sqrt{\pi}} \int_y^{\infty} \exp(-t^2)\, \mathrm{d} t.$$ I have tried to expand the integral as $$\frac{4}{\pi }\int_0^{\infty} \int_{ax}^{\infty} \int_{bx}^{\infty} \exp(-t^2 -s^2) \, \mathrm{d}s \, \mathrm{d}t \, \mathrm{d} x$$ but I could not come up with the right change of variables. Any ideas on how to proceed? Thank you in advance!
• $s/ax=p, t/bx=q$ seems to be a good start – tired Jan 30 '17 at 13:25
• yep afterwards you can integrate one Gaussian followed by two elementary integrations..QED – tired Jan 30 '17 at 13:35
• As a general rule of thumb, functions that are defined by an integral can usually be integrated by parts. This is how the integral of $\ln{(x)}$ and $\arctan{(x)}$ and other such functions are derived. – David H Jan 30 '17 at 14:10
• Thank you guys for all your answers and suggestions, special thanks to Jack. – Mim Jan 30 '17 at 18:09
• You are welcome. – Did Apr 9 '17 at 16:18
At first, we may remove the useless extra parameter, then study $$I(a) = \int_{0}^{+\infty}\text{erfc}(ax)\,\text{erfc}(x)\,dx$$ through differentiation under the integral sign. Assuming $a>0$ we have $$I'(a) = \frac{1}{\sqrt{\pi}}\int_{0}^{+\infty}-2x e^{-a^2 x^2}\text{erfc}(x)\,dx \stackrel{pp}{=}\frac{1}{a^2\sqrt{\pi}}-\frac{2}{\pi a^2}\int_{0}^{+\infty}e^{-(a^2+1)x^2}\,dx$$ from which: $$I'(a) = \frac{1}{\sqrt{\pi}}\left(\frac{1}{a^2}-\frac{1}{a^2\sqrt{1+a^2}}\right)$$ and: $$I(a) = \frac{1}{\sqrt{\pi}}\left(\frac{\sqrt{1+a^2}-1}{a}\right).$$ Through a substitution, if $a,b>0$ we get: $$\int_{0}^{+\infty}\text{erfc}(ax)\,\text{erfc}(bx)\,dx = \color{red}{\frac{a+b-\sqrt{a^2+b^2}}{ab\sqrt{\pi}}}$$ as wanted.
That is, first note that, for every $x$, $$\mathrm{erfc}(x)=2P(X\geqslant \sqrt2 x)$$ where $X$ is standard normal hence, considering $(X,Y)$ i.i.d. standard normal and assuming that $a$ and $b$ are positive, one sees that the integral to be computed is $$I=4\int_0^\infty P(A_x)dx$$ where $$A_x:=[X\geqslant ax\sqrt2,Y\geqslant bx\sqrt2]$$ Now, $$(X,Y)=(R\cos\Theta,R\sin\Theta)$$ where $(R,\Theta)$ is independent, $\Theta$ is uniform on $(0,2\pi)$ and $R\geqslant0$ is such that $$P(R\geqslant r)=e^{-r^2/2}$$ for every $r\geqslant0$, hence $A_x\subset A_0=[\Theta\in(0,\pi/2)]$ and, on the event $A_0$, $$P(A_x\mid\Theta)=P(R\cos\Theta\geqslant ax\sqrt2,R\sin\Theta\geqslant bx\sqrt2\mid\Theta)=e^{-x^2u(\Theta)^2}$$ with $$u(\theta):=\max\left(\frac{a}{\cos\theta},\frac{b}{\sin\theta}\right)$$ Thus, still on $A_0$, $$\int_0^\infty P(A_x\mid\Theta)dx=\int_0^\infty e^{-x^2u^2(\Theta)}dx=\frac{\sqrt{\pi}}{2u(\Theta)}$$ This proves that $$\sqrt\pi I=4\sqrt\pi E\left(\int_0^\infty P(A_x\mid\Theta)dx\right)=2\pi E\left(\frac1{u(\Theta)}\mathbf 1_{A_0}\right)$$ that is, $$\sqrt\pi I=2\pi E\left(\min\left(\frac{\cos\Theta}a,\frac{\sin\Theta}b\right)\mathbf 1_{A_0}\right)$$ which is, using the distribution of $\Theta$, $$\sqrt\pi I=\int_0^{\pi/2}\min\left(\frac{\cos\theta}a,\frac{\sin\theta}b\right)d\theta=\frac1b\int_0^{\vartheta(a,b)}\sin\theta d\theta+\frac1a\int_{\vartheta(a,b)}^{\pi/2}\cos\theta d\theta$$ where the angle $\vartheta(a,b)$ in $(0,\pi/2)$ is uniquely defined by the condition that $$\tan\vartheta(a,b)=b/a$$ hence $$\sqrt\pi I=\frac{1-\cos\vartheta(a,b)}b+\frac{1-\sin\vartheta(a,b)}a$$ Finally, $$\cos\vartheta(a,b)=\frac{a}{\sqrt{a^2+b^2}}\qquad\sin\vartheta(a,b)=\frac{b}{\sqrt{a^2+b^2}}$$ hence $$I=\frac1{\sqrt{\pi}ab}\left(a-\frac{a^2}{\sqrt{a^2+b^2}}+b-\frac{b^2}{\sqrt{a^2+b^2}}\right)=\frac1{\sqrt{\pi}ab}\left(a+b-\sqrt{a^2+b^2}\right)$$ | 2019-05-20 15:00:39 | {"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": 0.9723445177078247, "perplexity": 118.54987209676915}, "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/1558232256040.41/warc/CC-MAIN-20190520142005-20190520164005-00333.warc.gz"} |
https://blog.tomrijnbeek.nl/technical/openal/openal-an-object-oriented-approach | OpenAL: an object-oriented approach
We have already discussed several topics related to OpenAL. This week we will investigate how we can structure the concepts of OpenAL to fit nicely with the object oriented paradigm, so we can write elegant C# code to play sounds and manage sound effects.
In this post we will quickly go over the three main concepts of OpenAL as discussed in my introduction post: listeners, sources, and buffers. In addition, we will also introduce a type for sound data, which comes in handy for sound effect management.
Helper
Whenever we use OpenAL, we are actually working with a library in a different language. If something goes wrong with executing code there, our program won’t crash. As a matter of fact, we have to explicitly ask OpenAL if there have been any errors. While many errors do not cause critical errors for our own application, they might cause unexpected behaviour, especially if different sound drivers get involved. If we do not check for errors regularly, it can be very difficult to trace back to the source of the error. For this reason, it is very helpful to check for errors after every OpenAL call, so we can be exactly sure where the error occurs. The following helper class will allow us to do that easily:
public class ALHelper
{
public static void Check()
{
ALError error;
if ((error = AL.GetError()) == ALError.NoError)
return;
// Fail silently for now.
Debug.Print(AL.GetErrorString(error));
}
public static void Call(Action function)
{
function();
ALHelper.Check();
}
public static TReturn Eval<TReturn>(Func<TReturn> function)
{
var val = function();
ALHelper.Check();
return val;
}
}
This is only a small portion of the class: we can define further overloads for the Call and Eval functions that allow us to send parameters. The most important part is the setup of this class: we have a Check method that checks for errors and does something with it. The Call and Eval functions are there to make our life easy, it allows us to call functions like so:
var handle = ALHelper.Eval(AL.GetSource)
This evaluates the expression, checks for OpenAL errors, and returns the result.
Sound data
With some helpers to get us on our way, let’s start with the simplest class: a wrapper for the data. While in essence the data consists of raw bytes. However, our data might be divided amongst multiple byte arrays, and the data is meaningless without also storing its format and sample rate. That’s why we can wrap it together nicely in a single class:
public class SoundBufferData
{
public IList<short[]> Buffers => this.buffers;
public ALFormat Format => this.format;
public int SampleRate => this.sampleRate;
public SoundBufferData(IList<short[]> buffers, ALFormat format, int sampleRate)
{
this.buffers = buffers;
this.format = format;
this.sampleRate = sampleRate;
}
}
This class is especially nice, because it can be completely constructed from the input files and then stored in the application memory until we need it.
Sound buffers
Before we can play any sound, we need to store it in a sound buffer. Storing sounds in a buffer consists of two steps: asking OpenAL to reserve the right amount of buffers and filling them. Let’s first set up a basic class that wraps the buffer handles for us:
public class SoundBuffer : IDisposable
{
public bool Disposed { get; private set; }
public SoundBuffer(int amount)
{
this.handles = ALHelper.Eval(AL.GenBuffers, amount);
}
public void Dispose()
{
if (this.Disposed)
return;
ALHelper.Call(AL.DeleteBuffers, this.handles);
this.Disposed = true;
}
static public implicit operator int[] (SoundBuffer buffer)
{
return buffer.handles;
}
}
The class itself has only very limited functionality: in the constructor we request the right amount from buffers from OpenAL and store them internally using an array. We also implement IDisposable to implement a method that releases the buffers once we are finished with them.
A nice addition, which I added based on an identical usage pattern from amulware.Graphics, is the implicit conversion to the handles. This means that in any OpenAL method that takes a set of buffer handles, the wrapper class can be passed as parameter (footnote: sadly the generic Call and Eval methods do not work as nicely, because the type parameters will be filled in wrongly).
Now that we have a class that manages our sound buffers, we want to actually be able to put some useful data in it. Since we also have a nice class that manages our data, we should make use of that. In the most basic form, these are the methods we will be needing:
private void fillBufferRaw(int index, short[] data, ALFormat format, int sampleRate)
{
if (index < 0 || index >= this.handles.Length)
throw new ArgumentOutOfRangeException(nameof(index));
ALHelper.Call(
() => AL.BufferData(this.handles[index], format, data, data.Length * sizeof (short), sampleRate));
}
public void FillBuffer(SoundBufferData data)
{
this.FillBuffer(0, data);
}
public void FillBuffer(int index, SoundBufferData data)
{
if (index < 0 || index >= this.handles.Length)
throw new ArgumentOutOfRangeException(nameof(index));
if (data.Buffers.Count > this.handles.Length)
throw new ArgumentException("This data does not fit in the buffer.", nameof(data));
for (int i = 0; i < data.Buffers.Count; i++)
this.fillBufferRaw((index + i) % this.handles.Length, data.Buffers[i], data.Format, data.SampleRate);
}
fillBufferRaw only forwards the fill buffer request to OpenAL. The remaining methods form a layer around it to allow us to use the SoundBufferData wrapper we wrote before.
And with that, we have all the functionality of the sound buffers as well.
Source
The source is the most complex entity we will discuss today. Sources do not only have functionality, but also have a state: they can have a position and velocity, volume and pitch. Sources can also be played, paused, stopped, and rewinded, which means they have a playing state as well. This means that in addition to some methods, we will also have to give it some properties. Let’s not get ahead of ourselves and start with the basics again.
public class Source : IDisposable
{
public bool Disposed { get; private set; }
public Source()
{
this.handle = ALHelper.Eval(AL.GenSource);
}
public void Dispose()
{
if (this.Disposed)
return;
ALHelper.Call(AL.DeleteSource, this.handle);
this.Disposed = true;
}
#endregion
static public implicit operator int (Source source)
{
return source.handle;
}
}
The basics look pretty much identical to the SoundBuffer class, but instead of buffers we ask for a source, and since there will always be only one of them, we can do with a single integer handle, instead of an array of them.
Next we will be adding some controls to the source, since these are easy to implement.
public ALSourceState State => ALHelper.Eval(AL.GetSourceState, this.handle);
public void Play()
{
ALHelper.Call(AL.SourcePlay, this.handle);
}
public void Pause()
{
ALHelper.Call(AL.SourcePause, this.handle);
}
public void Stop()
{
ALHelper.Call(AL.SourceStop, this.handle);
}
public void Rewind()
{
ALHelper.Call(AL.SourceRewind, this.handle);
}
The four methods only forward the call to OpenAL. These forwarded calls in turn only change the state of the source, so that OpenAL knows what to do with them. We can retrieve the state again by using the AL.GetSourceState getter. In C# style, we write an accessor for this property.
A small detail we will have to add to our dispose method is stopping the source before disposing of it:
if (this.State != ALSourceState.Stopped)
this.Stop();
Right now we have a source we can create, play, and stop when we want, but it isn’t very useful yet until we can actually tell the source what buffers it should play. Sources play buffers according to a queue. Queueing buffers is easy enough:
private void queueBuffersRaw(int bufferLength, int[] bufferIDs)
{
ALHelper.Call(AL.SourceQueueBuffers, this.handle, bufferLength, bufferIDs);
}
public void QueueBuffer(SoundBuffer buffer)
{
var handles = (int[]) buffer;
this.queueBuffersRaw(handles.Length, handles);
}
We use the same pattern here as before: we have a method that forwards the call to the OpenAL, and then a wrapper method around it that allows us to use our own interface. Here we use an explicit conversion to an int[] to retrieve the actual handles of the buffers.
For our next task we require a bit more information: we also want to be able to unqueue buffers. This becomes important if we for example want to look at audio streaming: buffers we finished players can be removed from the front of the queue and we add new queues to the end of the queue to make sure we have sufficiently enough data to play from. OpenAL has accessors to get the amount of buffers currently processed and queued, so we will convert these into C# properties as well:
public int ProcessedBuffers
{
get
{
int processedBuffers;
AL.GetSource(this.handle, ALGetSourcei.BuffersProcessed, out processedBuffers);
ALHelper.Check();
return processedBuffers;
}
}
public int QueuedBuffers
{
get
{
int queuedBuffers;
AL.GetSource(this.handle, ALGetSourcei.BuffersQueued, out queuedBuffers);
ALHelper.Check();
return queuedBuffers;
}
}
public bool FinishedPlaying => this.ProcessedBuffers >= this.QueuedBuffers && !this.looping;
The FinishedPlaying property is an easy way to check if the source is still playing any sound. Our sound manager could then use that information to clean up the no longer necessary sources. Remark that the property includes a field (this.looping) we have not discussed yet, but we will come back to it later.
With these two properties we can implement methods that automatically unqueue any buffers finished playing, or just all the buffers if for some reason we want to start with a clean source.
public void UnqueueBuffers()
{
if (this.QueuedBuffers == 0)
return;
ALHelper.Call(() => AL.SourceUnqueueBuffers(this.handle, this.QueuedBuffers));
}
public void UnqueueProcessedBuffers()
{
ALHelper.Call(() => AL.SourceUnqueueBuffers(this.handle, this.ProcessedBuffers));
}
Due to the simplicity of these functions, we don’t have a raw unqueue method here.
Finally, we want to be able to influence the properties of a source. The pattern for each of the properties will be the same, so let’s look at the looping one, since we already saw that one before. The properties will look something like before:
private bool looping;
public bool Looping
{
get { return this.looping; }
set
{
ALHelper.Call(AL.Source, this.handle, ALSourceb.Looping, this.looping = value);
}
}
We use a backing field to easily retrieve the value. We could instead use the AL.GetSource method, but this is a small speedup which might be especially important if you access the properties every frame.
Properties in OpenAL use an enum with all possible properties. This means that the pattern for the other properties is very similar. For more examples of these properties, check the full source in the Github repository of my audio library.
Since we are using a backing field and not checking the actual source value, we have to be careful about setting the right value on first initialisation. Most importatly, we should set the volume and pitch to 1 in the constructor.
All of this together gives us the basic functionality of sources. Sources are easily the most complex entity in OpenAL and there are some advanced features we won’t touch upon here, since they are very rarely used.
Listener
The listener is a complicated entitie when it comes to OpenAL: OpenAL uses the single listener model. This means OpenAL can only work with one listener at a time. We could make use of a singleton pattern to force a single listener instance existing. While this would be a valid approach and stay true to the original design of OpenAL, I decided to choose a slightly different approach. The fact that only a single listener can be used in OpenAL is often seen as a limitation of OpenAL. The approach I took is pretty much identical to the pattern we used for the sound data: we use a class to store all the data, but it won’t be of any use, unless we put it in OpenAL somehow.
In this approach, we could even limit ourselves to using an IListener interface, since there is no additional logic required:
public interface IListener
{
Vector3 Position { get; }
Vector3 Velocity { get; }
float Gain { get; }
Vector3 Up { get; }
Vector3 At { get; }
}
In a 3D game, your player game object could be the listener. It is very likely that is has most of these properties already available to it, so using an interface makes using listeners very convenient.
Of course, the interface will have to be used to actually influence the results we are getting. We won’t go over it in this post, but this is where we would need an AudioManager. This manager could be responsible for updating the listener properties every frame, and we could even easily switch out listeners (let’s say we are an observer cycling through the players: this allows us to adapt the sound to that as well).
If the positioning of sounds is not important, which is almost always the case, unless you have some sort of first person 3D game, then the listener does not matter and we can use the default values as provided by OpenAL. Moreover, if we play stereo sound, the positional properties of every entity will be completely ignored. Hence, for most applications, the listener will be completely unnecessary.
Conclusion
We have stepped through the four main entities in OpenAL and wrote objects to represent all of them. While not implementing all the functionality – especially in sources there are many advanced features we did not touch upon – we now have a framework that we can use to access all OpenAL functionality, without having to use it’s procedural interface.
These classes provide an elegant basis for a more extensive audio library. The classes we have discussed have already been added to my audio library, and I will soon be using them to implement more advanced features. Progress on this can be found in the GitHub repository.
If you have any questions or comments, feel free to let me know, and I’ll see you next time. | 2017-06-26 22:17:09 | {"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": 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": 0.19065193831920624, "perplexity": 1610.501451950709}, "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-2017-26/segments/1498128320869.68/warc/CC-MAIN-20170626221252-20170627001252-00454.warc.gz"} |
https://nbviewer.ipython.org/github/qutip/qutip-notebooks/blob/master/examples/heom/heom-index.ipynb | Hierarchical Equation of Motion Examples¶
The "hierarchical equations of motion" (HEOM) method is a powerful numerical approach to solve the dynamics and steady-state of a quantum system coupled to a non-Markovian and non-perturbative environment. Originally developed in the context of physical chemistry, it has also been extended and applied to problems in solid-state physics, optics, single-molecule electronics, and biological physics.
QuTiP's implementation of the HEOM is described in detail in https://arxiv.org/abs/2010.10806.
This collection of examples from the paper illustrates how to use QuTiP's HEOM to model and investigate the dynamics of a variety of systems coupled to bosonic or fermionic baths.
Overview of the notebooks¶
In [ ]: | 2022-08-18 10:58:10 | {"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": 0.18837237358093262, "perplexity": 642.7468979132481}, "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-2022-33/segments/1659882573193.35/warc/CC-MAIN-20220818094131-20220818124131-00710.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/dcdss.20204i | # American Institute of Mathematical Sciences
April 2020, 13(4): ⅰ-ⅲ. doi: 10.3934/dcdss.20204i
## Dynamical systems and geometric mechanics: A special issue in Honor of Jürgen Scheurle
1 The University of Memphis, United States 2 Technische Universität München, Germany 3 RWTH Aachen, Germany
Published December 2019
Citation: Thomas Hagen, Andreas Johann, Hans-Peter Kruse, Florian Rupp, Sebastian Walcher. Dynamical systems and geometric mechanics: A special issue in Honor of Jürgen Scheurle. Discrete & Continuous Dynamical Systems - S, 2020, 13 (4) : ⅰ-ⅲ. doi: 10.3934/dcdss.20204i
[1] Xin Guo, Lei Shi. Preface of the special issue on analysis in data science: Methods and applications. Mathematical Foundations of Computing, 2020, 3 (4) : i-ii. doi: 10.3934/mfc.2020026 [2] Andrew D. Lewis. Erratum for "nonholonomic and constrained variational mechanics". Journal of Geometric Mechanics, 2020, 12 (4) : 671-675. doi: 10.3934/jgm.2020033 [3] Jiahao Qiu, Jianjie Zhao. Maximal factors of order $d$ of dynamical cubespaces. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 601-620. doi: 10.3934/dcds.2020278 [4] Fanni M. Sélley. A self-consistent dynamical system with multiple absolutely continuous invariant measures. Journal of Computational Dynamics, 2021, 8 (1) : 9-32. doi: 10.3934/jcd.2021002 [5] Meng Chen, Yong Hu, Matteo Penegini. On projective threefolds of general type with small positive geometric genus. Electronic Research Archive, , () : -. doi: 10.3934/era.2020117 [6] Feifei Cheng, Ji Li. Geometric singular perturbation analysis of Degasperis-Procesi equation with distributed delay. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 967-985. doi: 10.3934/dcds.2020305 [7] Bernard Bonnard, Jérémy Rouot. Geometric optimal techniques to control the muscular force response to functional electrical stimulation using a non-isometric force-fatigue model. Journal of Geometric Mechanics, 2020 doi: 10.3934/jgm.2020032 [8] Lingju Kong, Roger Nichols. On principal eigenvalues of biharmonic systems. Communications on Pure & Applied Analysis, 2021, 20 (1) : 1-15. doi: 10.3934/cpaa.2020254 [9] Peizhao Yu, Guoshan Zhang, Yi Zhang. Decoupling of cubic polynomial matrix systems. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 13-26. doi: 10.3934/naco.2020012 [10] Ilyasse Lamrani, Imad El Harraki, Ali Boutoulout, Fatima-Zahrae El Alaoui. Feedback stabilization of bilinear coupled hyperbolic systems. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020434 [11] Felix Finster, Jürg Fröhlich, Marco Oppio, Claudio F. Paganini. Causal fermion systems and the ETH approach to quantum theory. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020451 [12] Xiyou Cheng, Zhitao Zhang. Structure of positive solutions to a class of Schrödinger systems. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020461 [13] Simon Hochgerner. Symmetry actuated closed-loop Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 641-669. doi: 10.3934/jgm.2020030 [14] Javier Fernández, Cora Tori, Marcela Zuccalli. Lagrangian reduction of nonholonomic discrete mechanical systems by stages. Journal of Geometric Mechanics, 2020, 12 (4) : 607-639. doi: 10.3934/jgm.2020029 [15] Lingwei Ma, Zhenqiu Zhang. Monotonicity for fractional Laplacian systems in unbounded Lipschitz domains. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 537-552. doi: 10.3934/dcds.2020268 [16] Peter H. van der Kamp, D. I. McLaren, G. R. W. Quispel. Homogeneous darboux polynomials and generalising integrable ODE systems. Journal of Computational Dynamics, 2021, 8 (1) : 1-8. doi: 10.3934/jcd.2021001 [17] Yuri Fedorov, Božidar Jovanović. Continuous and discrete Neumann systems on Stiefel varieties as matrix generalizations of the Jacobi–Mumford systems. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020375 [18] João Marcos do Ó, Bruno Ribeiro, Bernhard Ruf. Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 277-296. doi: 10.3934/dcds.2020138 [19] Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020444 [20] Sergey Rashkovskiy. Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 563-583. doi: 10.3934/jgm.2020024
2019 Impact Factor: 1.233 | 2020-12-05 08:27:44 | {"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": 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": 0.4914408326148987, "perplexity": 14216.860334657373}, "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/1606141747323.98/warc/CC-MAIN-20201205074417-20201205104417-00633.warc.gz"} |
https://epo.wikitrans.net/Degrees_of_freedom_(statistics) | La ĉi-suba teksto estas aŭtomata traduko de la artikolo Degrees of freedom (statistics) article en la angla Vikipedio, farita per la sistemo GramTrans on 2017-12-22 12:09:59. Eventualaj ŝanĝoj en la angla originalo estos kaptitaj per regulaj retradukoj. Se vi volas enigi tiun artikolon en la originalan Esperanto-Vikipedion, vi povas uzi nian specialan redakt-interfacon. Rigardu la artikolon pri WikiTrans por trovi klarigojn pri kiel fari tion. Ankaŭ ekzistas speciala vortaro-interfaco por proponi aŭ kontroli terminojn.
En statistiko, la nombro da gradoj da libereco estas la nombro da valoroj en la fina kalkulo de statistiko kiuj estas liberaj varii.
La nombro da sendependaj manieroj preter kiu dinamika sistemo povas moviĝi, sen malobservado de ajna limo trudita sur ĝi, estas nomita pli sensenta de gradoj da libereco. En aliaj vortoj, la nombro da gradoj da libereco povas esti difinita kiel la mimimumnombro de sendependaj koordinatoj kiuj povas precizigi la pozicion de la sistemo tute.
Taksoj de statistikaj parametroj povas esti bazitaj sur malsamaj informkvantoj aŭ datenoj. La nombro da sendependaj informoj kiuj iras en la takson de parametro estas nomita la gradoj da libereco. Ĝenerale, la gradoj da libereco de takso de parametro estas egala al la nombro da sendependa dudekopo kiuj iras en la takson minus la nombro da parametroj utiligitaj kiel mezaj ŝtupoj en la takso de la parametro mem (ekz. la provaĵovarianco havas N − 1 gradoj da libereco, ĉar ĝi estas komputitaj de N hazarda dudekopo minus la nura 1 parametro taksita kiel meza paŝo, kio estas la provaĵmeznombro).
Matematike, gradoj da libereco estas la nombro da grandeco de la domajno de hazarda vektoro, aŭ esence la nombro da "liberaj" komponentoj (kiom multaj komponentoj devas esti konataj antaŭ ol la vektoro estas plene determinita).
La esprimo plejofte estas uzita en la kunteksto de liniaj modeloj ( linearregreso, analizo de varianco), kie certaj hazardaj vektoroj estas limigitaj por kuŝi en liniaj subspacoj, kaj la nombro da gradoj da libereco estas la dimensio de la subspaco. La gradoj da libereco ankaŭ estas ofte asociitaj kun la kvadratitaj longoj (aŭ "sumo de kvaranguloj" de la koordinatoj) de tiaj vektoroj, kaj la parametroj de ĥi-kvadratit kaj aliaj distribuoj kiuj ekestas en rilataj statistikaj testaj problemoj.
Dum enkondukaj lernolibroj povas lanĉi gradojn da libereco kiel distribuoparametroj aŭ tra hipoteztestado, estas la subesta geometrio kiu difinas gradojn da libereco, kaj estas kritika al bonorda kompreno de la koncepto. Walker (1940) [3] deklaris tion trafe kiel "la nombro da observaĵoj minus la nombro da necesaj rilatoj inter tiuj observaĵoj."
## Historio
Although the basic concept of degrees of freedom was recognized as early as 1821 in the work of astronomer and mathematician Carl Friedrich Gauss,[4] its modern definition and usage was first elaborated by English statistician William Sealy Gosset in his 1908 Biometrika article "The Probable Error of a Mean", published under the pen name "Student".[5] While Gosset did not actually use the term 'degrees of freedom', he explained the concept in the course of developing what became known as Student's t-distribution. The term itself was popularized by English statistician and biologist Ronald Fisher, beginning with his 1922 work on chi squares.[6]
## Notation
In equations, the typical symbol for degrees of freedom is ν (lowercase Greek letter nu). In text and tables, the abbreviation "d.f." is commonly used. R. A. Fisher used n to symbolize degrees of freedom but modern usage typically reserves n for sample size.
## Of random vectors
Geometrically, the degrees of freedom can be interpreted as the dimension of certain vector subspaces. As a starting point, suppose that we have a sample of independent normally distributed observations,
${\displaystyle X_{1},\dots ,X_{n}.\,}$
This can be represented as an n-dimensional random vector:
${\displaystyle {\begin{pmatrix}X_{1}\\vdots \X_{n}\end{pmatrix}}.}$
Since this random vector can lie anywhere in n-dimensional space, it has n degrees of freedom.
Now, let${\displaystyle {\bar {X}}}$be the sample mean. The random vector can be decomposed as the sum of the sample mean plus a vector of residuals:
${\displaystyle {\begin{pmatrix}X_{1}\\vdots \X_{n}\end{pmatrix}}={\bar {X}}{\begin{pmatrix}1\\vdots \1\end{pmatrix}}+{\begin{pmatrix}X_{1}-{\bar {X}}\\vdots \X_{n}-{\bar {X}}\end{pmatrix}}.}$
The first vector on the right-hand side is constrained to be a multiple of the vector of 1's, and the only free quantity is${\displaystyle {\bar {X}}}$. It therefore has 1 degree of freedom.
The second vector is constrained by the relation${\displaystyle \sum _{i=1}^{n}(X_{i}-{\bar {X}})=0}$. The first n − 1 components of this vector can be anything. However, once you know the first n − 1 components, the constraint tells you the value of the nth component. Therefore, this vector has n − 1 degrees of freedom.
Mathematically, the first vector is the orthogonal, or least-squares, projection of the data vector onto the subspace spanned by the vector of 1's. The 1 degree of freedom is the dimension of this subspace. The second residual vector is the least-squares projection onto the (n − 1)-dimensional orthogonal complement of this subspace, and has n − 1 degrees of freedom.
In statistical testing applications, often one isn't directly interested in the component vectors, but rather in their squared lengths. In the example above, the residual sum-of-squares is
${\displaystyle \sum _{i=1}^{n}(X_{i}-{\bar {X}})^{2}={\begin{Vmatrix}X_{1}-{\bar {X}}\\vdots \X_{n}-{\bar {X}}\end{Vmatrix}}^{2}.}$
If the data points${\displaystyle X_{i}}$are normally distributed with mean 0 and variance${\displaystyle \sigma ^{2}}$, then the residual sum of squares has a scaled chi-squared distribution (scaled by the factor${\displaystyle \sigma ^{2}}$), with n − 1 degrees of freedom. The degrees-of-freedom, here a parameter of the distribution, can still be interpreted as the dimension of an underlying vector subspace.
Likewise, the one-sample t-test statistic,
${\displaystyle {\frac {{\sqrt {n}}({\bar {X}}-\mu _{0})}{\sqrt {\sum \limits _{i=1}^{n}(X_{i}-{\bar {X}})^{2}/(n-1)}}}}$
follows a Student's t distribution with n − 1 degrees of freedom when the hypothesized mean${\displaystyle \mu _{0}}$is correct. Again, the degrees-of-freedom arises from the residual vector in the denominator.
### Of residuals
A common way to think of degrees of freedom is as the number of independent pieces of information available to estimate another piece of information. More concretely, the number of degrees of freedom is the number of independent observations in a sample of data that are available to estimate a parameter of the population from which that sample is drawn. For example, if we have two observations, when calculating the mean we have two independent observations; however, when calculating the variance, we have only one independent observation, since the two observations are equally distant from the mean.
In fitting statistical models to data, the vectors of residuals are constrained to lie in a space of smaller dimension than the number of components in the vector. That smaller dimension is the number of degrees of freedom for error.
Example
Perhaps the simplest example is this. Suppose
${\displaystyle X_{1},\dots ,X_{n}}$
are random variables each with expected value μ, and let
${\displaystyle {\overline {X}}_{n}={X_{1}+\cdots +X_{n} \over n}}$
be the "sample mean." Then the quantities
${\displaystyle X_{i}-{\overline {X}}_{n}\,}$
are residuals that may be considered estimates of the errors Xi − μ. The sum of the residuals (unlike the sum of the errors) is necessarily 0. If one knows the values of any n − 1 of the residuals, one can thus find the last one. That means they are constrained to lie in a space of dimension n − 1. One says that "there are n − 1 degrees of freedom for errors."
An example which is only slightly less simple is that of least squares estimation of a and b in the model
${\displaystyle Y_{i}=a+bx_{i}+e_{i}{\text{ for }}i=1,\dots ,n}$
where xi is given, but ei and hence Yi are random. Let${\displaystyle {\widehat {a}}}$and${\displaystyle {\widehat {b}}}$be the least-squares estimates of a and b. Then the residuals
${\displaystyle {\widehat {e}}_{i}=y_{i}-({\widehat {a}}+{\widehat {b}}x_{i})\,}$
are constrained to lie within the space defined by the two equations
${\displaystyle {\widehat {e}}_{1}+\cdots +{\widehat {e}}_{n}=0,\,}$
${\displaystyle x_{1}{\widehat {e}}_{1}+\cdots +x_{n}{\widehat {e}}_{n}=0.\,}$
One says that there are n − 2 degrees of freedom for error.
Notationally, the capital letter Y is used in specifying the model, while lower-case y in the definition of the residuals; that is because the former are hypothesized random variables and the latter are actual data.
We can generalise this to multiple regression involving p parameters and covariates (e.g. p − 1 predictors and one mean), in which case the cost in degrees of freedom of the fit is p.
## In linear models
The demonstration of the t and chi-squared distributions for one-sample problems above is the simplest example where degrees-of-freedom arise. However, similar geometry and vector decompositions underlie much of the theory of linear models, including linear regression and analysis of variance. An explicit example based on comparison of three means is presented here; the geometry of linear models is discussed in more complete detail by Christensen (2002).[7]
Suppose independent observations are made for three populations,${\displaystyle X_{1},\ldots ,X_{n}}$, ${\displaystyle Y_{1},\ldots ,Y_{n}}$and${\displaystyle Z_{1},\ldots ,Z_{n}}$. The restriction to three groups and equal sample sizes simplifies notation, but the ideas are easily generalized.
The observations can be decomposed as
{\displaystyle {\begin{aligned}X_{i}&={\bar {M}}+({\bar {X}}-{\bar {M}})+(X_{i}-{\bar {X}})\Y_{i}&={\bar {M}}+({\bar {Y}}-{\bar {M}})+(Y_{i}-{\bar {Y}})\Z_{i}&={\bar {M}}+({\bar {Z}}-{\bar {M}})+(Z_{i}-{\bar {Z}})\end{aligned}}}
where${\displaystyle {\bar {X}},{\bar {Y}},{\bar {Z}}}$are the means of the individual samples, and${\displaystyle {\bar {M}}=({\bar {X}}+{\bar {Y}}+{\bar {Z}})/3}$is the mean of all 3n observations. In vector notation this decomposition can be written as
${\displaystyle {\begin{pmatrix}X_{1}\\vdots \X_{n}\Y_{1}\\vdots \Y_{n}\Z_{1}\\vdots \Z_{n}\end{pmatrix}}={\bar {M}}{\begin{pmatrix}1\\vdots \1\1\\vdots \1\1\\vdots \1\end{pmatrix}}+{\begin{pmatrix}{\bar {X}}-{\bar {M}}\\vdots \{\bar {X}}-{\bar {M}}\{\bar {Y}}-{\bar {M}}\\vdots \{\bar {Y}}-{\bar {M}}\{\bar {Z}}-{\bar {M}}\\vdots \{\bar {Z}}-{\bar {M}}\end{pmatrix}}+{\begin{pmatrix}X_{1}-{\bar {X}}\\vdots \X_{n}-{\bar {X}}\Y_{1}-{\bar {Y}}\\vdots \Y_{n}-{\bar {Y}}\Z_{1}-{\bar {Z}}\\vdots \Z_{n}-{\bar {Z}}\end{pmatrix}}.}$
The observation vector, on the left-hand side, has 3n degrees of freedom. On the right-hand side, the first vector has one degree of freedom (or dimension) for the overall mean. The second vector depends on three random variables,${\displaystyle {\bar {X}}-{\bar {M}}}$, ${\displaystyle {\bar {Y}}-{\bar {M}}}$and${\displaystyle {\overline {Z}}-{\overline {M}}}$. However, these must sum to 0 and so are constrained; the vector therefore must lie in a 2-dimensional subspace, and has 2 degrees of freedom. The remaining 3n − 3 degrees of freedom are in the residual vector (made up of n − 1 degrees of freedom within each of the populations).
## In analysis of variance (ANOVA)
In statistical testing problems, one usually isn't interested in the component vectors themselves, but rather in their squared lengths, or Sum of Squares. The degrees of freedom associated with a sum-of-squares is the degrees-of-freedom of the corresponding component vectors.
The three-population example above is an example of one-way Analysis of Variance. The model, or treatment, sum-of-squares is the squared length of the second vector,
${\displaystyle {\text{SSTr}}=n({\bar {X}}-{\bar {M}})^{2}+n({\bar {Y}}-{\bar {M}})^{2}+n({\bar {Z}}-{\bar {M}})^{2}}$
with 2 degrees of freedom. The residual, or error, sum-of-squares is
${\displaystyle {\text{SSE}}=\sum _{i=1}^{n}(X_{i}-{\bar {X}})^{2}+\sum _{i=1}^{n}(Y_{i}-{\bar {Y}})^{2}+\sum _{i=1}^{n}(Z_{i}-{\bar {Z}})^{2}}$
with 3(n−1) degrees of freedom. Of course, introductory books on ANOVA usually state formulae without showing the vectors, but it is this underlying geometry that gives rise to SS formulae, and shows how to unambiguously determine the degrees of freedom in any given situation.
Under the null hypothesis of no difference between population means (and assuming that standard ANOVA regularity assumptions are satisfied) the sums of squares have scaled chi-squared distributions, with the corresponding degrees of freedom. The F-test statistic is the ratio, after scaling by the degrees of freedom. If there is no difference between population means this ratio follows an F distribution with 2 and 3n − 3 degrees of freedom.
In some complicated settings, such as unbalanced split-plot designs, the sums-of-squares no longer have scaled chi-squared distributions. Comparison of sum-of-squares with degrees-of-freedom is no longer meaningful, and software may report certain fractional 'degrees of freedom' in these cases. Such numbers have no genuine degrees-of-freedom interpretation, but are simply providing an approximate chi-squared distribution for the corresponding sum-of-squares. The details of such approximations are beyond the scope of this page.
## In probability distributions
Several commonly encountered statistical distributions (Student's t, Chi-Squared, F) have parameters that are commonly referred to as degrees of freedom. This terminology simply reflects that in many applications where these distributions occur, the parameter corresponds to the degrees of freedom of an underlying random vector, as in the preceding ANOVA example. Another simple example is: if${\displaystyle X_{i};i=1,\ldots ,n}$are independent normal${\displaystyle (\mu ,\sigma ^{2})}$random variables, the statistic
${\displaystyle {\frac {\sum \limits _{i=1}^{n}(X_{i}-{\bar {X}})^{2}}{\sigma ^{2}}}}$
follows a chi-squared distribution with n − 1 degrees of freedom. Here, the degrees of freedom arises from the residual sum-of-squares in the numerator, and in turn the n − 1 degrees of freedom of the underlying residual vector${\displaystyle \{X_{i}-{\bar {X}}\}}$.
In the application of these distributions to linear models, the degrees of freedom parameters can take only integer values. The underlying families of distributions allow fractional values for the degrees-of-freedom parameters, which can arise in more sophisticated uses. One set of examples is problems where chi-squared approximations based on effective degrees of freedom are used. In other applications, such as modelling heavy-tailed data, a t or F distribution may be used as an empirical model. In these cases, there is no particular degrees of freedom interpretation to the distribution parameters, even though the terminology may continue to be used.
## In nonparametric regression
Many non-standard regression methods, including ridge regression, linear smoothers, smoothing splines, and semiparametric regression are not based on ordinary least squares projections, but rather on regularized (generalized and/or penalized) least-squares, and so degrees of freedom defined in terms of dimensionality is generally not useful for these procedures. However, these procedures are still linear in the observations, and the fitted values of the regression can be expressed in the form
${\displaystyle {\hat {y}}=Hy,\,}$
where${\displaystyle {\hat {y}}}$is the vector of fitted values at each of the original covariate values from the fitted model, y is the original vector of responses, and H is the hat matrix or, more generally, smoother matrix.
For statistical inference, sums-of-squares can still be formed: the model sum-of-squares is${\displaystyle \|Hy\|^{2}}$; the residual sum-of-squares is${\displaystyle \|y-Hy\|^{2}}$. However, because H does not correspond to an ordinary least-squares fit (i.e. is not an orthogonal projection), these sums-of-squares no longer have (scaled, non-central) chi-squared distributions, and dimensionally defined degrees-of-freedom are not useful.
The effective degrees of freedom of the fit can be defined in various ways to implement goodness-of-fit tests, cross-validation, and other statistical inference procedures. Here one can distinguish between regression effective degrees of freedom and residual effective degrees of freedom.
### Regression effective degrees of freedom
For the regression effective degrees of freedom, appropriate definitions can include the trace of the hat matrix,[8] tr(H), the trace of the quadratic form of the hat matrix, tr(H'H), the form tr(2H - H H'), or the Satterthwaite approximation, tr(H'H)2/tr(H'HH'H). In the case of linear regression, the hat matrix H is X(X 'X)−1X ', and all these definitions reduce to the usual degrees of freedom. Notice that
${\displaystyle \operatorname {tr} (H)=\sum _{i}h_{ii}=\sum _{i}{\frac {\partial {\hat {y}}_{i}}{\partial y_{i}}},}$
the regression (not residual) degrees of freedom in linear models are "the sum of the sensitivities of the fitted values with respect to the observed response values",[9] i.e. the sum of leverage scores.
One way to help to conceptualize this is to consider a simple smoothing matrix like a Gaussian blur function. The Gaussian blur is an attempt to estimate the values of a smoothly varying function from otherwise noisy data. In contrast to a simple linear or polynomial fit, computing the effective degrees of freedom of the smoothing function is not straight-forward. In these cases, it is important to estimate the Degrees of Freedom permitted by the${\displaystyle H}$matrix so that the residual degrees of freedom can then be used to estimate statistical tests such as${\displaystyle \chi ^{2}}$.
### Residual effective degrees of freedom
There are corresponding definitions of residual effective degrees-of-freedom (redf), with H replaced by IH. For example, if the goal is to estimate error variance, the redf would be defined as tr((IH)'(IH)), and the unbiased estimate is (with${\displaystyle {\hat {r}}=y-Hy}$),
${\displaystyle {\hat {\sigma }}^{2}={\frac {\|{\hat {r}}\|^{2}}{{\hbox{tr}}\left((I-H)'(I-H)\right)}},}$
${\displaystyle {\hat {\sigma }}^{2}={\frac {\|{\hat {r}}\|^{2}}{n-\operatorname {tr} (2H-HH')}}={\frac {\|{\hat {r}}\|^{2}}{n-2\operatorname {tr} (H)+\operatorname {tr} (HH')}}}$
${\displaystyle {\hat {\sigma }}^{2}\approx {\frac {\|{\hat {r}}\|^{2}}{n-1.25\operatorname {tr} (H)+0.5}}.}$
The last approximation above[11] reduces the computational cost from O(n2) to only O(n). In general the numerator would be the objective function being minimized; e.g., if the hat matrix includes an observation covariance matrix, Σ, then${\displaystyle \|{\hat {r}}\|^{2}}$becomes${\displaystyle {\hat {r}}'\Sigma ^{-1}{\hat {r}}}$.
### General
Note that unlike in the original case, non-integer degrees of freedom are allowed, though the value must usually still be constrained between 0 and n.
Consider, as an example, the k-nearest neighbour smoother, which is the average of the k nearest measured values to the given point. Then, at each of the n measured points, the weight of the original value on the linear combination that makes up the predicted value is just 1/k. Thus, the trace of the hat matrix is n/k. Thus the smooth costs n/k effective degrees of freedom.
As another example, consider the existence of nearly duplicated observations. Naive application of classical formula, np, would lead to over-estimation of the residuals degree of freedom, as if each observation were independent. More realistically, though, the hat matrix H = X(X ' Σ−1X)−1X ' Σ−1 would involve an observation covariance matrix Σ indicating the non-zero correlation among observations. The more general formulation of effective degree of freedom would result in a more realistic estimate for, e.g., the error variance σ2, which in its turn scales the unknown parameters' a posteriori standard deviation; the degree of freedom will also affect the expansion factor necessary to produce an error ellipse for a given confidence level.
### Other formulations
Similar concepts are the equivalent degrees of freedom in non-parametric regression,[14] the degree of freedom of signal in atmospheric studies,[15][16] and the non-integer degree of freedom in geodesy.[17][18]
#### Alternative
The residual sum-of-squares${\displaystyle \|y-Hy\|^{2}}$has a generalized chi-squared distribution, and the theory associated with this distribution[19] provides an alternative route to the answers provided above.
## References
1. ^ "Degrees of Freedom". "Glossary of Statistical Terms". Animated Software. Retrieved 2008-08-21.
2. ^ Lane, David M. "Degrees of Freedom". HyperStat Online. Statistics Solutions. Retrieved 2008-08-21.
3. ^ Walker, H. M. (April 1940). "Degrees of Freedom". Journal of Educational Psychology. 31 (4): 253-269. doi:10.1037/h0054588.
4. ^ Walker, H. M. (April 1940). "Degrees of Freedom" (PDF). Journal of Educational Psychology. 31 (4): 253-269. doi:10.1037/h0054588.
5. ^ Student (March 1908). "The Probable Error of a Mean". Biometrika. 6 (1): 1-25. doi:10.2307/2331554. JSTOR 2331554.
6. ^ Fisher, R. A. (January 1922). "On the Interpretation of χ2 from Contingency Tables, and the Calculation of P". Journal of the Royal Statistical Society. 85 (1): 87-94. doi:10.2307/2340521. JSTOR 2340521.
7. ^ Christensen, Ronald (2002). Plane Answers to Complex Questions: The Theory of Linear Models (Third ed.). New York: Springer. ISBN 0-387-95361-2.
8. ^ Trevor Hastie, Robert Tibshirani, Jerome H. Friedman (2009), The elements of statistical learning: data mining, inference, and prediction, 2nd ed., 746 p. ISBN 978-0-387-84857-0, doi:10.1007/978-0-387-84858-7, [1] (eq.(5.16))
9. ^ Ye, J. (1998), "On Measuring and Correcting the Effects of Data Mining and Model Selection", Journal of the American Statistical Association, 93 (441), 120-131. JSTOR 2669609 (eq.(7))
10. ^ Clive Loader (1999), Local regression and likelihood, ISBN 978-0-387-98775-0, doi:10.1007/b98858, (eq.(2.18), p. 30)
11. ^ a b Trevor Hastie, Robert Tibshirani (1990), Generalized additive models, CRC Press, (p. 54) and (eq.(B.1), p. 305))
12. ^ Simon N. Wood (2006), Generalized additive models: an introduction with R, CRC Press, (eq.(4,14), p. 172)
13. ^ David Ruppert, M. P. Wand, R. J. Carroll (2003), Semiparametric Regression, Cambridge University Press (eq.(3.28), p. 82)
14. ^ Peter J. Green, B. W. Silverman (1994), Nonparametric regression and generalized linear models: a roughness penalty approach, CRC Press (eq.(3.15), p. 37)
15. ^ Clive D. Rodgers (2000), Inverse methods for atmospheric sounding: theory and practice, World Scientific (eq.(2.56), p. 31)
16. ^ Adrian Doicu, Thomas Trautmann, Franz Schreier (2010), Numerical Regularization for Atmospheric Inverse Problems, Springer (eq.(4.26), p. 114)
17. ^ D. Dong, T. A. Herring and R. W. King (1997), Estimating regional deformation from a combination of space and terrestrial geodetic data, J. Geodesy, 72 (4), 200-214, doi:10.1007/s001900050161 (eq.(27), p. 205)
18. ^ H. Theil (1963), "On the Use of Incomplete Prior Information in Regression Analysis", Journal of the American Statistical Association, 58 (302), 401-414 JSTOR 2283275 (eq.(5.19)-(5.20))
19. ^ Jones, D.A. (1983) "Statistical analysis of empirical models fitted by optimisation", Biometrika, 70 (1), 67-88
La ĉi-suba teksto estas la originala artikolo Grado de libereco el la Esperanto-Vikipedio, prenita de GramTrans 2014-01-03 04:03:02. Eblaj ŝanĝoj en la originalo estos kaptitaj per regulaj ĝisdatigoj.
Iu grado de libereco de fizika sistemo estas formala priskribo de sendependa parametro, kiu kontribuas al la stato de la sistemo. La aro da ĉiuj dimensioj de sistemo estas konata kiel faza spaco.
En meĥaniko, oni povas paroli pri geometria, kinematika libereca grado, kio signifas la moviĝemon de io.
En statistiko, la nombro da liberecaj gradoj estas, en la fina kalkulado, la nombro da valoroj, kiuj estas liberaj varii[1] [2].
## Referencoj
1. . Degrees of Freedom (Glosaro pri statistikaj terminoj) (angla) (Editoro: Animated Software) (elŝutita 21-a de aŭgusto 2008).
2. David M. Lane. Degrees of Freedom (HyperStat Online) (angla) (Editoro: Statistics Solutions (elŝutita 21-a de aŭgusto 2008)).
## Eksteraj ligiloj
##### Navigacio
Bonvole donacu por helpi al WikiTrans daŭrigi | 2018-12-11 23:33:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 51, "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": 0.9017900824546814, "perplexity": 3475.3654723544664}, "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-2018-51/segments/1544376823705.4/warc/CC-MAIN-20181211215732-20181212001232-00565.warc.gz"} |
https://gamedev.stackexchange.com/questions/60850/determining-axis-to-rotate-around | # Determining axis to rotate around
I'm trying to implement a free-look third person camera (using glm). I know that the general transformation is
newCameraPosition = translate(lookatPoint) * rotation(angle,axis) * translate(-lookatPoint);
So I need to find the axis to rotate around, with the constraint that I give the algorithm an axis in camera space to rotate around. Sounds confusing.
For example, let's take a camera that points up (0,1,0), is positioned in the XY plane at (-1,0,0) and is looking at the origin (0,0,0). So it is looking "along the x-axis".
Now I want to rotate the camera around the "camera-space-x-axis" (1,0,0). In words: The axis that "points to the right" when looking through the camera. Simply rotating around (1,0,0) doesn't work, since it will rotate the camera around the world-space x-axis. From the point of the camera however, the x-axis is in fact the z-axis in world space (0,0,1);
How do I go from the given camera-space axis to the world-space axis? I've tried just applying the inverse transform of the current camera transform to the given camera-space axis using
glm::vec3 rotateAxis = swizzle<X,Y,Z>(glm::inverse(GetCameraTransform()) * cameraSpaceAxis);
where cameraSpaceAxis.w = 0;
but that produces wrong results, e.g. if I give the algorithm the axis (1,0,0) to rotate around, continuously rotation around it in 1 degree steps just creates a wobbly circular motion around y and x axis;
• Just fyi I got lazy and just hardcoded it so you can only do pitch/yaw/roll changes one at a time (no arbitrary axes), and it works fine, but I'm leaving the question open because I'm interested in how this would be done. – TravisG Aug 15 '13 at 23:29 | 2019-10-15 14:23:34 | {"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": 0.31568026542663574, "perplexity": 1140.688548917422}, "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/1570986659097.10/warc/CC-MAIN-20191015131723-20191015155223-00520.warc.gz"} |
https://crypto.stackexchange.com/questions/38053/what-should-be-used-as-a-source-for-entropy | # What should be used as a source for entropy?
I have hardware based RNG which consists of TRNG and PRNG. TRNG is giving out 512 bit number which is being used as seed for PRNG. RNG is generating 160 bit random number using PRNG and reseeding is done after 2^20 numbers. I want to use hardware based RNG as entropy source. What should be used as source of entropy i.e. output of TRNG or PRNG ?
Thanks & Regards,
• As pure entropy source for a software (CS)PRNG? Always use the TRNG. – SEJPM Jul 29 '16 at 22:13
• For information-theoretical reasons, the roughly $160$ million bits obtained from the PRNG before reseeding still have a total entropy of at most $512$ bits. On the other hand, the TRNG should in theory yield a full bit of entropy per extracted bit. – yyyyyyy Jul 29 '16 at 23:17
• SEjPM & yyyyyyy , Thanks for your replies. @yyyyyyy , simplified formula for entropy (log2n) gives value of 7.32 for 160 bits and 9 for 512 bits. Will I be justified to claim 7.32 bit entropy if I decide to use output of RNG ? – user2363993 Jul 30 '16 at 0:05
• Why can't you just use the TRNG as the RNG without interposing a PRNG? The randomness is better that way... – Paul Uszak Sep 11 '16 at 21:55
Your calculation doesn't make sense. Think of what $n$ is in this formula! The entropy of a source with $n$ possible different equiprobable values is $\log_2(n)$. The entropy of a source that provides $k$ independent bits is $k$. If your source provided 512 independent bits then you would get 512 bits of entropy from it, but in practice physical sources have some amount of correlation that's hard to evaluate precisely, so you probably have much less. In any case, what matters with entropy is that it's sufficient to make the probability that a brute-force attack would succeed negligible. For this purpose, there is no meaningful difference between 160 bits and 512 bits. | 2019-08-23 04:48:57 | {"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": 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": 0.5970203876495361, "perplexity": 1030.3821225160164}, "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/1566027317847.79/warc/CC-MAIN-20190823041746-20190823063746-00021.warc.gz"} |
https://stats.stackexchange.com/questions/388586/confidence-interval-from-sample-quantiles | # Confidence interval from sample quantiles
## Context
I am running some stochastic simulations in R to determine appropriate sample sizes for a biological problem of interest to me.
My method iteratively generates "accumulation" curves which eventually tend to an asymptote. These curves are based on computing cumulative means.
## Specifics
I wish to compute a 95% confidence interval (CI) for the "true" endpoint ($$x$$-value) of these curves as they tend to the asymptote. Call this "true" endpoint $$\theta$$.
I have a 95% CI for the "true" $$y$$, call it ($$L$$, $$U$$), which is formed via taking the 2.5th and 97.5th percentiles of the resulting sample cumulative means.
The iterated function I am using is an estimator of $$\theta$$. This estimator takes the form:
$$\hat{\theta} = \frac{\hat{x}\hat{z}}{\hat{y}}$$
$$\hat{x}$$ is a sequence of the observed number of "types", and is a random variable on [1, 2, ..., $$m$$], with $$m$$ not known a priori.
$$\hat{z}$$ is a sequence of the observed number of unique "types", and is a discrete random variable on [1, 2, ..., $$n$$], with $$n$$ not known a priori.
Also, $$\hat{x} \geq \hat{z}$$, and consequently, $$m \geq n$$. Sensible guesses are made for the unknown $$m$$ and $$n$$.
It is known that $$\hat{y}$$ approaches $$\hat{z}$$ asymptotically, so that $$\hat{x}$$ approaches $$\hat{\theta}$$ in the limit sense. $$\hat{\theta}$$ can be thought of as the sample size required to observe all unique types.
## Issues
I compute a (likely crude) 95% CI for $$\theta$$ via ($$\frac{\hat{\theta}}{U}$$, $$\frac{\hat{\theta}}{L}$$).
I find a 95% CI for the "true" $$y$$ of ($$L$$, $$U$$) = (10, 13).
My estimate of $$\theta$$ is $$\hat{\theta}$$ = 440, with $$\hat{z}$$ = 18 giving a 95% CI for $$\theta$$ of ($$\frac{440(18)}{13}$$, $$\frac{440(18)}{10}$$) = (610, 792). Something is clearly amiss here... $$\hat{\theta}$$ should lie within the upper and lower limits of the CI, but it doesn't.
I'm beginning to doubt this approach for finding a CI.
## My Question
Any ideas on why my CI approach does not generate a sensible interval and potentially how I can easily obtain one from the given information?
The above situation is similar to the Coupon Collector Problem, as well as the Germain Tank Problem, but I found that neither corresponds to this problem exactly.
• I don't really follow the setup here, but there are potentially several issues to consider. One of the things you need to be very careful about is to avoid treating a succession of cumulative quantities as if they were independent. – Glen_b Jan 22 at 23:52
• Thanks. Yes, I suspect that covariance/correlation between observations will be of issue in deriving a meaningful CI around $\theta$. I guess my next question is how best to account for this. I've done some quick googling and searching of CV, but no solution immediately pops up. – compbiostats Jan 23 at 1:15
• A clearer understanding of the circumstances would be essential to coming up with a plausible model – Glen_b Jan 23 at 2:26
• I have edited my post that corrects the CI for $\theta$. I mistakingly left out the value of $z$, which is used in calculating the interval. I will add further details as to the nature of the variables and how they are generated. – compbiostats Jan 23 at 3:41
• Please see the updated post with further details. Please let me know if further clarification is needed. – compbiostats Jan 23 at 4:33 | 2019-08-22 05:26:09 | {"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": 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": 35, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7734687924385071, "perplexity": 394.2929811745652}, "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-2019-35/segments/1566027316783.70/warc/CC-MAIN-20190822042502-20190822064502-00498.warc.gz"} |
http://linlog.skepticats.com/entries/2010/12/Mercurial_hooks.php | ## Mercurial hooks
Last time I mentioned that I'd set up Mantis with a Subversion hook. Well, I've been rethinking the Subversion part.
I was listened to a back episode of Hanselminutes last week in which Scott was interviewing SourceGear's interviewing Eric Sink about DVCS and it was a very interesting conversation. Source control is one of those things you don't usually think about as a developer. You learn how to use a source control system that's "good enough", and after that, just sort of take it for granted. You certainly don't spend a lot of time jumping back and forth between systems and trying out the possibilities.
I really liked the way Eric explained distributed version control. As he pointed out, most of the arguments for DVCS that you hear seem pretty pointless, such as "There's no central server," or "You can commit on an airplane." Well...so what? Why wouldn't I want a central server - how else do you determine the authoritative repository? And honestly, who does important work on an airplane?
Instead, Eric framed the discussion in terms of flexibility. The flip-side of the above stupid arguments is actually pretty compelling. With DVCS, there's no central server, but that just means that your central server is determined by convention, not by the software, and it's much easier to set up "slave" repositories for remote sites. Likewise, while being able to commit on a plane is pointless, there's definite value in not needing to have a connection to the server to do core version control operations. Or, to put it another way, I may not code on a plane, but I do often code in coffee shops with slow WiFi connections.
So, in light of that, I decided to give Mercurial a try. According to Eric, it's fairly user-friendly, especially for Subversion users, and it's fairly Windows-friendly (it even has a TortoiseHg client, for whatever that's worth). So, since I was thinking of resurrecting LnBlog, I decided to use that as my test-case.
That leads me back into the Subversion hooks tie-in. Since I went to all the trouble of setting up an issue tracker and hooking it to SVN, I figured I'd do the same with Mercurial. Fortunately, it wasn't too bad once I figured out what I needed to do. I was able to fairly easily adapt the Powershell script I wrote for Subversion to work with Mercurial. In fact, the Mercurial version was actually shorter.
Actually adding a commit hook in Mercurial is pretty simple. You just add a line to your .hgrc file:
[hooks]commit = powershell \path\to\hg-commit-hook.ps1
It seems that Mercurial preserves the environment for hooks, so you don't seem to have to worry about absolute paths and such like you do in Subversion.
The changes to the script itself were fairly small. This wiki page had a few good examples that got me started. The two big things were the passing of data and generating the message to pass to Mantis. Mercurial actually passes data into hook scripts through environment variables rather than command-line parameters, which is nice in that you actually get meaningful variable names coming in. As for the message generation, Mercurial's log command allows you to specify a template for its output, including substitution variables and some simple formatting functions. The result is a nice, short script with only a couple of calls to hg:
[System.Reflection.Assembly]::LoadWithPartialName("System.Web") | Out-Null
$issue = hg log -vr$env:HG_NODE
# If we don't have an issue number, just exit.if ($issue -match "\b(?:bug|issue)\s*[#]{0,1}(\d+)\b") {$style_file = @'changeset = "Changeset {branches}{rev}:{node|short} by {author|person}, {date|date}\n{desc}\n{files}"file = " {file}\n"'@ Write-Output $style_file | Out-File -Encoding ASCII -Width 1000 hgstyle $data = hg log -vr $env:HG_NODE --style hgstyle rm hgstyle # Keep the cast to string from clobbering line breaks.$data = [String]::Join("n", $data)$postData = "secret=somePassword&message=" $postData += [System.Web.HttpUtility]::UrlEncode($data)
C:\Cygwin\bin\wget.exe -O req.out --post-data=\$postData http://yourhost.com/path/to/mantis/scripts/do_checkin.php rm req.out}
That's it - a measly two calls to Mercurial, including one to see if we even need to run the hook. By specifying the right template, we can get the entire message in one command. That template gives me something like this:
Changeset 70:cbdb625298ca by Peter Geer, Mon Dec 13 16:45:53 2010 -0500Got rid of unneeded requires now that we have an autoloader (issue #0000005). lib/article.php lib/creators.php`
Perhaps not quite as pretty as the Subversion version, but close enough for now. Perhaps if I feel like getting really fancy, I'll look at the Python API for Mercurial and try my hand at writing some in-process hook code.
Edit: Updated the script to put each of the listed file on a new, indented line.
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### Fun with remote execution policy
Thanks for the info. I was trying out your suggestions above when I encounter the message:
File C:\Temp\SamplePowershellScripts\Sample.ps1 cannot be loaded because the execution of scripts is disabled on this system. Please see "get-help about_signing" for more details.
I ran Set-ExecutionPolicy unrestricted and tried again, and the same error. If I navigate to the directory that contains my Powershell script, and run it within the Powershell command prompt, my script runs fine. But when I try to run the same script as a Mercurial commit script, it throws the error. Is there a trick for getting around this?
• Comment posted on Monday 12 Nov 2012 at 10:12am
• By Ryan
### That's odd
Strange. I'm not sure what's going on there. I actually don't use this method anymore (I ported my hook script to bash and moved it to the server), but I don't recall having to do anything special to get the Powershell script to run. My execution policy has always been set to RemoteSigned and it worked just fine.
The only thing I can think of that might be an issue is if the hook script is not being run as your user account. I believe that in Win7 the execution policy is per-user, so if the script runs as another account you would have to set the execution policy for that account too. I'm not sure if that's applicable to your situation, though. I just don't have any other brilliant suggestions.
### Try changing scope
Ryan - try
Set-ExecutionPolicy RemoteSigned -Scope LocalMachine
• Comment posted on Thursday 13 Dec 2012 at 11:06am
• By George Mauer | 2018-10-22 21:45:30 | {"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": 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": 0.4917471408843994, "perplexity": 1660.5641354710187}, "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-2018-43/segments/1539583515539.93/warc/CC-MAIN-20181022201445-20181022222945-00225.warc.gz"} |
https://aviation.stackexchange.com/questions/73654/does-high-density-altitude-affect-your-landing-speed | # Does high density altitude affect your landing speed?
The DPE asked me about high-density-altitude airports; he specifically asked me if I should add airspeed when I'm on landing approach to a high-density-altitude airport. My total understanding is that the ground roll and landing roll would be affected, as well as the climb, but I've never heard about landing speed being affected; I've been looking in books and researched on the web but I can't get a solid answer.
Your $$v_\mathrm{ref}$$ does not depend on density altitude since it is given in Indicated Airspeed, which already accounts for density effects. However, the True Airspeed and therefore also Groundspeed will be higher at a higher density altitude, resulting in more runway required to stop.
The Flight Safety Foundation has a nice summary of factors influencing $$v_\mathrm{ref}$$:
Factors Affecting the Final Approach Speed
The following airspeed corrections usually are not cummulative; only the highest airspeed correction should be added to VREF (unless otherwise stated in the AOM/QRH):
• Airspeed correction for wind;
• Airspeed correction for ice accretion;
• Airspeed correction for autothrottle speed mode or autoland; or,
• Airspeed correction for forecast turbulence/wind shear conditions.
Gross Weight
Because VREF is derived from the stall speed, the VREF value depends directly on aircraft gross weight.
The AOM/QRH usually provides VREF values as a function of gross weight in a table or graphical format for normal landings and for overweight landings.
(FSF ALAR Briefing Note 8.2 - The Final Approach Speed)
Altitude, Density Altitude or Pressure are not listed as factors affecting $$v_\mathrm{ref}$$. | 2021-11-29 06:11:47 | {"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": 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": 3, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47282177209854126, "perplexity": 4246.1752819334615}, "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/1637964358688.35/warc/CC-MAIN-20211129044311-20211129074311-00294.warc.gz"} |
https://mathhelpforum.com/threads/related-rates-with-parameters.143710/ | # Related rates with parameters
#### rcyoung3
I've been having trouble figuring this one out:
A particle moves in the xy plane with coordinates given by x=x(t) and y=y(t). If Theta denotes the angle between the positive x-axis and the line from the origin to the point (x,y). Find a formula for dTheta/dt in terms of x, y, dx/dt, and dy/dt. Evaluate this when x(t)=1+cos3t and y=sin3x
The main thing I'm having problems with is the initial set up. What sort of equation should I use? tan(theta)=x/y? theta=arctan(x/y)?
Thanks
#### CaptainBlack
MHF Hall of Fame
I've been having trouble figuring this one out:
A particle moves in the xy plane with coordinates given by x=x(t) and y=y(t). If Theta denotes the angle between the positive x-axis and the line from the origin to the point (x,y). Find a formula for dTheta/dt in terms of x, y, dx/dt, and dy/dt. Evaluate this when x(t)=1+cos3t and y=sin3x
The main thing I'm having problems with is the initial set up. What sort of equation should I use? tan(theta)=x/y? theta=arctan(x/y)?
Thanks
$$\displaystyle \tan(\theta)=\frac{y}{x}$$
CB
Similar Math Discussions Math Forum Date
Calculus
Calculus
Calculus
Calculus | 2019-11-15 02:03:44 | {"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": 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": 0.9063711762428284, "perplexity": 850.9837942062858}, "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-2019-47/segments/1573496668561.61/warc/CC-MAIN-20191115015509-20191115043509-00278.warc.gz"} |
http://openstudy.com/updates/4f071e27e4b075b56652caa0 | Here's the question you clicked on:
## Altair 4 years ago 1. Baileigh is using a piece of string to hang a painting on the wall. The back of the painting is diagrammed below. What is the length of the string? A. 52 cm B. 26 cm C. 68 cm D. 34 cm
• This Question is Closed
1. Altair
2. 2bornot2b
What is the dimension of the rectangular/painting
3. anonymous
4. Altair
24 cm 24 cm 10 cm 10 cm Note: Picture not drawn to scale.
5. 2bornot2b
the answer is 26, am I right?
6. Altair
idk if i knew will i ask for help??
7. 2bornot2b
thats the answer.
8. Altair
9. 2bornot2b
$\sqrt {27}$
10. Altair
11. 2bornot2b
$\sqrt {15}$
12. Altair
13. Altair
^^different question
14. 2bornot2b
?
15. Altair
the attach ment is different
16. 2bornot2b
So was my answer.
17. 2bornot2b
By the way, did you notice, I am actually ruining your life.
18. Altair
how?
19. 2bornot2b
By answering questions which I shouldn't. You don't have any idea, how simple those problems were, and you still couldn't solve them
20. Altair
lol idc i hate math
21. Altair
wats the answer
22. 2bornot2b
36
23. Altair
#### Ask your own question
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Privacy Policy | 2016-04-30 18:59:58 | {"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": 0.4634415805339813, "perplexity": 9370.721600269626}, "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-2016-18/segments/1461860112231.78/warc/CC-MAIN-20160428161512-00015-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://stats.stackexchange.com/questions/500211/how-to-show-that-normal-distribution-is-a-second-order-approximation-to-any-dist | # How to show that normal distribution is a second order approximation to any distribution around the mode?
How can I show that normal distribution is a second order approximation to any distribution around the mode?
• The Laplace approximation comes to mind : en.wikipedia.org/wiki/Laplace%27s_method Dec 10 '20 at 15:49
• Depending on what you mean by "second order approximation," the statement is false. If you are referring to density functions, then counterexamples include any distribution that does not have a differentiable density at its mode. If you are referring to CDFs, then counterexamples include all distributions of random variables that have nonzero probability of equaling their mode.
– whuber
Dec 10 '20 at 18:54
Consider an arbitrary probability distribution $$p(\theta)$$. We want to approximate the distribution around the mode $$\hat{\theta} = argmax \log p(\theta)$$. We perform a second order Taylor expansion around $$\hat{\theta}$$ in log space and we obtain $$\log p(\theta) = \log p(\hat{\theta}) + \frac{1}{2} (\theta-\hat{\theta})^T \underbrace{\left( \nabla \nabla^T \log p(\hat{\theta})\right)}_{=: \psi} (\theta-\hat{\theta}) + O(\theta^3)$$ Where $$\psi$$ is the hessian matrix. Note that the first order term disappears as we are at a maximum and hence the first derivative is zero there. This is very similar to a Gaussian pdf in normal space, in fact $$p(\theta) \approx p(\hat{\theta}) \cdot \exp(- \frac{1}{2}(\theta - \hat{\theta})^T(-\psi) (\theta - \hat{\theta}))$$
Then we can define the Laplace approximation $$q$$ of $$p$$ as $$q(\theta) = \mathcal{N}(\theta, \hat{\theta}, -\psi^{-1})$$ It should be clear that this is proportional to the second order Taylor expansion. May also note that the hessian at the mode is symmetric and negative definite, hence $$-\psi$$ is symmetric and positive definite.
• Should the LHS of your equation be $\log p(\theta)$ rather than $\log p(\delta)$? Dec 10 '20 at 16:30
• Yeah introducing the $\delta$ was unnecessary, changed it. Dec 10 '20 at 17:52 | 2021-10-19 20:54:33 | {"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": 10, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9361699223518372, "perplexity": 168.7210576607279}, "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/1634323585281.35/warc/CC-MAIN-20211019202148-20211019232148-00572.warc.gz"} |
https://archive.lib.msu.edu/crcmath/math/math/c/c624.htm | ## Continued Fraction Constant
A continued fraction with partial quotients which increase in Arithmetic Progression is
where is a Modified Bessel Function of the First Kind (Beeler et al. 1972, Item 99). A special case is
which has the value
(Lehmer 1973, Rabinowitz 1990).
See also e, Golden Mean, Modified Bessel Function of the First Kind, Pi, Rabbit Constant, Thue-Morse Constant
References
Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972.
Finch, S. Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/cntfrc/cntfrc.html
Guy, R. K. Review: The Mathematics of Plato's Academy.'' Amer. Math. Monthly 97, 440-443, 1990.
Lehmer, D. H. Continued Fractions Containing Arithmetic Progressions.'' Scripta Math. 29, 17-24, 1973.
Rabinowitz, S. Problem E3264. Asymptotic Estimates from Convergents of a Continued Fraction.'' Amer. Math. Monthly 97, 157-159, 1990. | 2021-12-09 01:49:21 | {"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": 0.7690564393997192, "perplexity": 4355.1996502588745}, "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-20211209000407-20211209030407-00388.warc.gz"} |
https://math.stackexchange.com/questions/908559/about-the-proof-of-the-heine-borel-theorem | # About the proof of the Heine-Borel Theorem
I'm self-studying from the book Understanding Analysis by Stephen Abbott, and I have a question about the prove of theorem 3.3.4 on page 84 (i.e. the Heine-Borel theorem).
To be more specific, let us assume $K \subseteq \mathbb{R}$ to be compact.$^1$ Then we would like to prove that this implies that $K$ is closed.$^2$ Stephen Abbott proceeds by considering a sequence $(x_n)$ with $x = \lim x_n$, where $(x_n)$ is contained in $K$. By definition of a compact set, the sequence $(x_n)$ has a convergent subsequence $(x_{n_k})$, and it follows from a well-known theorem$^3$ that $(x_{n_k})$ converges to the same limit $x$. Finally, the definition of a compact set requires that $x \in K$. Then according to Stephen Abbott, this proves that $K$ is closed.
But in his prove he has assumed that the sequence $(x_n)$ converges. What happens if $(x_n)$ does not converge? Then we can still have a subsequence that converges to a limit, right? If so, then I think his theorem is incomplete, or am I missing something?
$^1$ A set $K \subseteq \mathbb{R}$ is compact if every sequence in $K$ has a subsequence that converges to a limit that is also in $K$.
$^2$ A set $K \subseteq \mathbb{R}$ is closed if it contains its limit points.$^{2.1}$
$^{2.1}$ A point $x$ is a limit point of a set $K$ if every $\epsilon$-neighborhood $V_\epsilon (x)$ of $x$ intersects the set $K$ in some point other than $x$.
$^3$ Subsequences of a convergent sequence converge to the same limit as the original sequence.
• Just a note about terminology, technically your $^1$ is called sequentially compact. In general topological spaces this doesn't necessarily imply compact nor compact imply this. – DanZimm Aug 25 '14 at 11:54
• If u ve a sequence that does not converge then u dont have to show anything. – FWE Aug 25 '14 at 12:53
• @YonedaLemma could you please elaborate on that? Because that is exactly what I am confused about. – Hunter Aug 25 '14 at 12:56
• @YonedaLemma For the proof, his first assumption is that he is considers a sequence $(x_n)$ with $x= \lim x_n$. But what if we consider a sequence $(x'_n)$ that does not converge. As far as I know, we can still have a convergent subsequence $(x'_{n_k})$, but now we cannot use the theorem that "subsequences of a convergent sequence converge to the same limit as the original sequence", and so his prove breaks down. I must be missing something, but I don't see what it is. – Hunter Aug 25 '14 at 12:56
• $K$ is closed iff every convergent seq. in $K$ converges against a point in $K$. So u have to show: If $(x_n)$ is in $K$ and conv. against some $x$ then $x$ is in $K$. How: If $(x_n)$ is a seq. in $K$ that converges then because $K$ is compact, $(x_n)$ has a convergent subseq. with limit in $K$. By the theorem u mentioned the limit of the subsequent is identical to the limit of the original $(x_n)$ - so it must be in $K$ $\diamond$. (If for a proof u start with a seq. that does not conv. then u are just not about to prove that $K$ suffices the given definition of being a closed set). – FWE Aug 25 '14 at 13:03
Definition (Hausdorff space)
A topological space $X$ is called Hausdorff or $T_2$ space if and only iff every two points $x,y\in X$ have disjunct neighbourhoods $x\in O_x\subset x$ and $y\in O_y\subset X$.
Example (Metric spaces are Hausdorff)
Every metric space $M$ is (as a topological space) $T_2$ - for each $x, y\in M$ say $d:=d(x,y)$ is their distance, then the $\epsilon$-spheres around $x$ and $y$ with $\epsilon < \frac{d}{2}$ (f.i. open intervals with midpoint $x$ resp. $y$) are disjoint neighbourhoods of $x$ and $y$. Therefore especially $R$ is $T_2$ (since $R$ is a metric space).
Proposition (Compact subsets of $T_2$ spaces are closed)
Say $A\subset X$ where $X$ is a topological space that is Hausdorff (f.i. $R$).
If $A$ is compact then $A$ is closed.
Proof: Say $X$ is $T_2$ and $A\subset X$ is compact. We show that $A^c$ is open (and thereby $A$ is closed) by showing that any $y\in A^c$ has a neighbourhood $V_y\subset A^c$:
Say $y\in A^c$ arbitrary. Then for any $x\in A$ we have a neighbourhood $O_x$ of $x$ and a neighbourhood $V_y^x$ of $y$ that is disjoint to $O_x$ (since $X$ is $T_2$). So we have $$A\subset \bigcup_{x\in A}O_x$$ and $$\bigcup_{x\in A}O_x \cap\bigcap_{x\in A}V_y^x=\emptyset$$
and therefore $$\bigcap_{x\in A}V_y^x\subset A^c$$
Because $A$ is compact we can argue with finitely many $x\in A$. But then $V_y:=\bigcap_{x\in A}V_y^x$ is open - so altogether $V_y$ is an open neighbourhood of $y$ that is contained in $A^c$. $\diamond$
(For $X=R$ the $O_x$ and $V_y^x$ become open intervals in $R$ with midpoint $x$ resp. $y$. )
• Thanks for your answer. Unfortunately this is too advanced for the book I'm currently reading. The author has not defined what a topological space or a metric space is. (But don't delete the answer, because it might be useful for someone else.) – Hunter Aug 25 '14 at 13:02
• Yes I see - you are just confused about some simple point namely what to show for the proof. When besides the things the author shows u want also to show something else (f.i. for non converging sequences in $K$) then u are trying to do too much - see above comment. – FWE Aug 25 '14 at 13:11
• I think I understand it with your help. In order to prove that $K$ is closed, we must show that $K$ contains its limit points. A well-known theorem$^1$ tells us that every limit point $x$ of $K$ corresponds to some convergent sequence $(x_n)$ contained in $K$, that is, $x = \lim x_n$. Then he subsequently uses that to prove that $K$ is closed if $K$ is compact, as I have described above. --- $^1$ Theorem: A point $x$ is a limit point of a set $K$ if, and only if, $x = \lim x_n$ for some sequence $(x_n)$ contained in $K$ satisfying $x_n \neq x$ for all $n \in \mathbb{N}$. – Hunter Aug 25 '14 at 13:36
• Can you double check if the above is correct? – Hunter Aug 25 '14 at 13:36
• Not quite - a limit point of a set is a point that some sequence in that set converges to (usually that is taken as definition - not as well known theorem). A limit point of a set therefore corresponds not to a sequence in that set that converges to it but in general to any sequence in the set that converges to it. – FWE Aug 25 '14 at 13:42
I think you are not understanding what is going on. You need to prove that $K$ is closed, so you must prove that any point $x$ that is the limit of a sequence of pints $x_n \in K$ belongs to $K$. So you must assume that $x=\lim_n x_n$!
• Yeah, I am still confused because that is not the definition of a closed set, as far as I understand it. Is there a theorem that every sequence in a closed set must be convergent? – Hunter Aug 25 '14 at 11:07
• Such a theorem would be false... The author is using this definition of closedness: a set $C$ (in a metric space) is closed if $x \in C$ whenever $x=\lim_n x_n$ with $x_n \in C$ for every $n$. In other words, $C$ contains its cluster points. – Siminore Aug 25 '14 at 11:12
• I'm really sorry, but I'm still confused. For the proof, his first assumption is that he is considers a sequence $(x_n)$ with $x= \lim x_n$. But what if we consider a sequence $(x'_n)$ that does not converge. As far as I know, we can still have a convergent subsequence $(x'_{n_k})$, but now we cannot use the theorem that "subsequences of a convergent sequence converge to the same limit as the original sequence", and so his prove breaks down. I must be missing something, but I don't see what it is. – Hunter Aug 25 '14 at 12:55
• I think I understand it, but I'm not sure. In order to prove that $K$ is closed, we must show that $K$ contains its limit points. A well-known theorem$^1$ tells us that every limit point $x$ of $K$ corresponds to some convergent sequence $(x_n)$ contained in $K$, that is, $x = \lim x_n$. Then he subsequently uses that to prove that $K$ is closed if $K$ is compact, as I have described above. --- $^1$ Theorem: A point $x$ is a limit point of a set $K$ if, and only if, $x = \lim x_n$ for some sequence $(x_n)$ contained in $K$ satisfying $x_n \neq x$ for all $n \in \mathbb{N}$. – Hunter Aug 25 '14 at 13:37
• Yes, your last interpretation is fine. – Siminore Aug 25 '14 at 16:06 | 2019-08-23 05:27:43 | {"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": 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": 0.9602155089378357, "perplexity": 107.18572624762136}, "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-2019-35/segments/1566027317847.79/warc/CC-MAIN-20190823041746-20190823063746-00434.warc.gz"} |
https://puzzling.stackexchange.com/questions/101029/move-just-one-match/101038 | # Move just one match
Make a correct equation by just moving one matchstick!
This is the source. Spoiler--source reveals answer.
• You know the source reveal the answer, right? Aug 11, 2020 at 22:51
• @Voldemort'sWrath I didn't pay attention to it. I mean I didn't know. But I think that's the cheater's problem to look at it; not mine or non-cheaters. Aug 12, 2020 at 8:33
• @aminabuzz -- I mean, if you're revealing the answer in the question, it's not a great question, is it? Aug 12, 2020 at 13:26
• @Voldemort'sWrath It's better to provide a link if the question isn't your own creation Aug 12, 2020 at 13:36
Moving one:
From the '+' to make a '6' gives the true equation $$6-4=2$$
• Too small of an edit for me to suggest, but the numbers in the equation you wrote down are in the wrong order - not writing it here to prevent spoilers, but you need to swap 2 of the numbers around. Aug 12, 2020 at 14:11
• @crazyloonybin good spot! Thanks :) Aug 12, 2020 at 14:11
• No problem, the maths was still correct, but it was killing my OCD! Aug 12, 2020 at 14:13
I suppose you could do:
5-4≠2 as well, because it's true!
• That's an inequality, not an equation. Aug 11, 2020 at 22:17
• Whoops, I forgot about that Aug 12, 2020 at 10:05
• Alternately, almost the same, ≤ Aug 12, 2020 at 11:22
• @Ruadhan2300 I'm not sure you can really make a ≤ moving only 1 line, I guess you could add an angled line above an =, but that would be pretty far from the normal representation of that symbol.
– DBS
Aug 12, 2020 at 12:18
• I've seen it written with two parallel lines and one angled in the past, though I'll admit it's not the norm. I think it'd be understood anyway :) Aug 12, 2020 at 13:07 | 2022-05-26 09:13:11 | {"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": 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": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3535487651824951, "perplexity": 1271.522629858977}, "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-20220526065603-20220526095603-00717.warc.gz"} |
https://www.doubtnut.com/question-answer/if-the-equation-sin-2-x-k-sin-x-3-0-has-exactly-two-distinct-real-roots-in-0-pi-then-find-the-values-642550698 | # If the equation sin ^(2) x - k sin x - 3 = 0 has exactly two distinct real roots in [0, pi], then find the values of k .
Updated On: 17-04-2022
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Text Solution
Solution :
Let f(t) = t^(2) - kt - 3, where t = siin x. <br> Since equation has exactly two distinct real roots in [ 0, pi], f(t) = 0 must have exactly one root in (0, 1). <br> Now f(0) = -3 . <br> So., we must have f(1) = - k - 2 gt 0 <br> or k lt-2.
Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
Transcript
today question is if the equation X square minus x minus 3 equal to zero has exactly two distinct roots in 0 to find the value of this problem this is pathetic in sin x cos x and x belongs 2020-2021 we will belongs 2021 square - 3 - 3 + 2 is equal to be exactly two distinct real roots
dyskinetic will have at least one really between at least one year 2020 one day look like this when you can see at zero value is positive and at one value is Negative opposite Bank of opposite sign ok now I am going to do I am going to put 0 and 1 the value of opposite sign into 10 power minus 1 upon 1 minus A minus 3 to be lesson 3
and 8 - 11 - 3 - 2 X + 2 - 2 and 4 Students | 2022-05-21 02:55:55 | {"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": 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": 0.4078138768672943, "perplexity": 614.045370825157}, "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/1652662534773.36/warc/CC-MAIN-20220521014358-20220521044358-00247.warc.gz"} |
https://mathimages.swarthmore.edu/index.php?title=Modular_arithmetic&printable=yes | # Modular arithmetic
This is a Helper Page for:
Chryzodes
Markus-Lyapunov Fractals
Application of the Euclidean Algorithm
Modular Arithmetic is a system of arithmetic in which numbers 'wrap around' upon exceeding a maximum value, so that any arithmetic operation on a finite set of numbers remains within the set.
The most common everyday use of modular arithmetic is timekeeping. Using a standard 12-hour clock, adding 4 hours to a clock at 11:00 set the clock at 3:00, so 11+4 =3 on a clock.
Modular addition, using the analogy of clocks.
If we wrap around a number n, then numbers that are multiples of n away from each other are said to be congruent 'mod n'. On a clock the numbers wrap around every 12, so we say for example that $1 \equiv 13 \pmod{12}$. Note that if we wrap around every n, we start counting from zero, then when we reach the number n, we return to zero (the number n is not generally used, since it is the same as zero in this system).
We can extend this idea to allow numbers to wrap around at any number we choose. We could also say that $13 \equiv 27 \pmod{7}$ since 13 and 27 are a multiple of 7 apart from each other.
Example Solution $6 + 1 \pmod{15}$ Answer $1 + 1 \pmod{2}$ Answer $3 + 7 \pmod{6}$ Answer $2+21 \pmod{5}$ Answer
### References
Another explanation of modular arithmetic: http://mathworld.wolfram.com/ModularArithmetic.html | 2022-10-06 14:59:52 | {"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": 0, "mathjax_asciimath": 0, "img_math": 10, "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": 0.7674912214279175, "perplexity": 490.02061742995414}, "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-2022-40/segments/1664030337836.93/warc/CC-MAIN-20221006124156-20221006154156-00765.warc.gz"} |
https://hindimaintutorial.in/ideal-farm-codeforces-solution-theofanis-decided-to-visit-his-uncles-farm-there-are-ss-animals-and-nn-animal-pens-on-the-farm-for-utility-purpose-animal-pens-are-constructed-i/ | • # For Solution
Theofanis decided to visit his uncle’s farm. There are ss animals and nn animal pens on the farm. For utility purpose, animal pens are constructed in one row.
Uncle told Theofanis that a farm is lucky if you can distribute all animals in all pens in such a way that there are no empty pens and there is at least one continuous segment of pens that has exactly kk animals in total.
Moreover, a farm is ideal if it’s lucky for any distribution without empty pens.
Neither Theofanis nor his uncle knows if their farm is ideal or not. Can you help them to figure it out?
### Ideal Farm solution codeforces
The first line contains a single integer tt (1t1051≤t≤105) — the number of test cases.
The first and only line of each test case contains three integers ssnn, and kk (1s,n,k10181≤s,n,k≤1018nsn≤s).
### Ideal Farm solution codeforces
For each test case, print YES (case-insensitive), if the farm is ideal, or NO (case-insensitive) otherwise.
Example
input
Copy
4
1 1 1
1 1 2
100 50 200
56220 47258 14497
### Ideal Farm solution codeforces
Copy
YES
NO
NO
YES
Note
For the first and the second test case, the only possible combination is [1][1] so there always will be a subsegment with 11 animal but not with 22 animals. | 2022-06-27 20:38:09 | {"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": 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": 0.34010830521583557, "perplexity": 1522.0057490443976}, "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-2022-27/segments/1656103341778.23/warc/CC-MAIN-20220627195131-20220627225131-00629.warc.gz"} |
https://nbviewer.ipython.org/github/TarrySingh/Machine-Learning-Tutorials/blob/master/scipy/hypothesis.ipynb | Hypothesis Testing¶
Credits: Forked from CompStats by Allen Downey. License: Creative Commons Attribution 4.0 International.
In [1]:
from __future__ import print_function, division
import numpy
import scipy.stats
import matplotlib.pyplot as pyplot
from IPython.html.widgets import interact, fixed
from IPython.html import widgets
import first
# seed the random number generator so we all get the same results
numpy.random.seed(19)
# some nicer colors from http://colorbrewer2.org/
COLOR1 = '#7fc97f'
COLOR2 = '#beaed4'
COLOR3 = '#fdc086'
COLOR4 = '#ffff99'
COLOR5 = '#386cb0'
%matplotlib inline
Part One¶
As an example, let's look at differences between groups. The example I use in Think Stats is first babies compared with others. The first module provides code to read the data into three pandas Dataframes.
In [2]:
live, firsts, others = first.MakeFrames()
The apparent effect we're interested in is the difference in the means. Other examples might include a correlation between variables or a coefficient in a linear regression. The number that quantifies the size of the effect, whatever it is, is the "test statistic".
In [3]:
def TestStatistic(data):
group1, group2 = data
test_stat = abs(group1.mean() - group2.mean())
return test_stat
For the first example, I extract the pregnancy length for first babies and others. The results are pandas Series objects.
In [4]:
group1 = firsts.prglngth
group2 = others.prglngth
The actual difference in the means is 0.078 weeks, which is only 13 hours.
In [5]:
actual = TestStatistic((group1, group2))
actual
Out[5]:
0.078037266777549519
The null hypothesis is that there is no difference between the groups. We can model that by forming a pooled sample that includes first babies and others.
In [6]:
n, m = len(group1), len(group2)
pool = numpy.hstack((group1, group2))
Then we can simulate the null hypothesis by shuffling the pool and dividing it into two groups, using the same sizes as the actual sample.
In [7]:
def RunModel():
numpy.random.shuffle(pool)
data = pool[:n], pool[n:]
return data
The result of running the model is two NumPy arrays with the shuffled pregnancy lengths:
In [8]:
RunModel()
Out[8]:
(array([36, 40, 39, ..., 43, 42, 40]), array([43, 39, 32, ..., 37, 35, 41]))
Then we compute the same test statistic using the simulated data:
In [9]:
TestStatistic(RunModel())
Out[9]:
0.081758440969863955
If we run the model 1000 times and compute the test statistic, we can see how much the test statistic varies under the null hypothesis.
In [10]:
test_stats = numpy.array([TestStatistic(RunModel()) for i in range(1000)])
test_stats.shape
Out[10]:
(1000,)
Here's the sampling distribution of the test statistic under the null hypothesis, with the actual difference in means indicated by a gray line.
In [11]:
def VertLine(x):
"""Draws a vertical line at x."""
pyplot.plot([x, x], [0, 300], linewidth=3, color='0.8')
VertLine(actual)
pyplot.hist(test_stats, color=COLOR5)
pyplot.xlabel('difference in means')
pyplot.ylabel('count')
None
The p-value is the probability that the test statistic under the null hypothesis exceeds the actual value.
In [12]:
pvalue = sum(test_stats >= actual) / len(test_stats)
pvalue
Out[12]:
0.14999999999999999
In this case the result is about 15%, which means that even if there is no difference between the groups, it is plausible that we could see a sample difference as big as 0.078 weeks.
We conclude that the apparent effect might be due to chance, so we are not confident that it would appear in the general population, or in another sample from the same population.
Part Two¶
We can take the pieces from the previous section and organize them in a class that represents the structure of a hypothesis test.
In [13]:
class HypothesisTest(object):
"""Represents a hypothesis test."""
def __init__(self, data):
"""Initializes.
data: data in whatever form is relevant
"""
self.data = data
self.MakeModel()
self.actual = self.TestStatistic(data)
self.test_stats = None
def PValue(self, iters=1000):
"""Computes the distribution of the test statistic and p-value.
iters: number of iterations
returns: float p-value
"""
self.test_stats = numpy.array([self.TestStatistic(self.RunModel())
for _ in range(iters)])
count = sum(self.test_stats >= self.actual)
return count / iters
def MaxTestStat(self):
"""Returns the largest test statistic seen during simulations.
"""
return max(self.test_stats)
def PlotHist(self, label=None):
"""Draws a Cdf with vertical lines at the observed test stat.
"""
def VertLine(x):
"""Draws a vertical line at x."""
pyplot.plot([x, x], [0, max(ys)], linewidth=3, color='0.8')
ys, xs, patches = pyplot.hist(ht.test_stats, color=COLOR4)
VertLine(self.actual)
pyplot.xlabel('test statistic')
pyplot.ylabel('count')
def TestStatistic(self, data):
"""Computes the test statistic.
data: data in whatever form is relevant
"""
raise UnimplementedMethodException()
def MakeModel(self):
"""Build a model of the null hypothesis.
"""
pass
def RunModel(self):
"""Run the model of the null hypothesis.
returns: simulated data
"""
raise UnimplementedMethodException()
HypothesisTest is an abstract parent class that encodes the template. Child classes fill in the missing methods. For example, here's the test from the previous section.
In [14]:
class DiffMeansPermute(HypothesisTest):
"""Tests a difference in means by permutation."""
def TestStatistic(self, data):
"""Computes the test statistic.
data: data in whatever form is relevant
"""
group1, group2 = data
test_stat = abs(group1.mean() - group2.mean())
return test_stat
def MakeModel(self):
"""Build a model of the null hypothesis.
"""
group1, group2 = self.data
self.n, self.m = len(group1), len(group2)
self.pool = numpy.hstack((group1, group2))
def RunModel(self):
"""Run the model of the null hypothesis.
returns: simulated data
"""
numpy.random.shuffle(self.pool)
data = self.pool[:self.n], self.pool[self.n:]
return data
Now we can run the test by instantiating a DiffMeansPermute object:
In [15]:
data = (firsts.prglngth, others.prglngth)
ht = DiffMeansPermute(data)
p_value = ht.PValue(iters=1000)
print('\nmeans permute pregnancy length')
print('p-value =', p_value)
print('actual =', ht.actual)
print('ts max =', ht.MaxTestStat())
means permute pregnancy length
p-value = 0.16
actual = 0.0780372667775
ts max = 0.173695697482
And we can plot the sampling distribution of the test statistic under the null hypothesis.
In [16]:
ht.PlotHist()
As an exercise, write a class named DiffStdPermute that extends DiffMeansPermute and overrides TestStatistic to compute the difference in standard deviations. Is the difference in standard deviations statistically significant?
In [17]:
class DiffStdPermute(DiffMeansPermute):
"""Tests a difference in means by permutation."""
def TestStatistic(self, data):
"""Computes the test statistic.
data: data in whatever form is relevant
"""
group1, group2 = data
test_stat = abs(group1.std() - group2.std())
return test_stat
data = (firsts.prglngth, others.prglngth)
ht = DiffStdPermute(data)
p_value = ht.PValue(iters=1000)
print('\nstd permute pregnancy length')
print('p-value =', p_value)
print('actual =', ht.actual)
print('ts max =', ht.MaxTestStat())
std permute pregnancy length
p-value = 0.155
actual = 0.176049064229
ts max = 0.44299505029
Now let's run DiffMeansPermute again to see if there is a difference in birth weight between first babies and others.
In [18]:
data = (firsts.totalwgt_lb.dropna(), others.totalwgt_lb.dropna())
ht = DiffMeansPermute(data)
p_value = ht.PValue(iters=1000)
print('\nmeans permute birthweight')
print('p-value =', p_value)
print('actual =', ht.actual)
print('ts max =', ht.MaxTestStat())
means permute birthweight
p-value = 0.0
actual = 0.124761184535
ts max = 0.0917504268392
In this case, after 1000 attempts, we never see a sample difference as big as the observed difference, so we conclude that the apparent effect is unlikely under the null hypothesis. Under normal circumstances, we can also make the inference that the apparent effect is unlikely to be caused by random sampling.
One final note: in this case I would report that the p-value is less than 1/1000 or 0.001. I would not report that p=0, because the apparent effect is not impossible under the null hypothesis; just unlikely. | 2021-09-19 17:22:17 | {"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": 0.3931872248649597, "perplexity": 3945.5282959414317}, "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-2021-39/segments/1631780056892.13/warc/CC-MAIN-20210919160038-20210919190038-00365.warc.gz"} |
https://www.physicsforums.com/threads/wkb-approach-and-energies.135379/ | # WKB approach and energies
1. Oct 8, 2006
### Karlisbad
If we have a 1-dimensional problem so for big n "Energies" can be found in the form:
$$2 \int_{a}^{b}dx \sqrt (E_{n} - V(x) ) = (n+1/2) \hbar$$
where "a" and "b" are the turning points, then could we writte the equation for energies (where a>c>b using Mean-value theorem for integrals )
$$2 \sqrt (E_{n} - V(c) )(b-a) = (n+1/2) \hbar$$
for finite a,b,c ?
-Another question, when dealing with Semiclasical Quantum Gravity, do the "Energies" satisfy the same WKB constraint?, in particular if we define:
$$\pi _{ab}$$ as the "momenta" conjugate to the metric then the
"Energies" of quantum gravity for big n satisfy
$$\oint dV\pi _{ab}(x,y,z) = (n+1/2) \hbar$$ ?..
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Draft saved Draft deleted | 2017-11-22 07:49:41 | {"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": 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": 0.6243951320648193, "perplexity": 4513.35250826085}, "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-2017-47/segments/1510934806509.31/warc/CC-MAIN-20171122065449-20171122085449-00657.warc.gz"} |
http://databasefaq.com/index.php/tag/prediction | FAQ Database Discussion Community
## Generalized additive models for calibration
r,statistics,probability,prediction,calibration
I work on calibration of probabilities. I'm using a probability mapping approach called generalized additive models. The algorithm I wrote is: probMapping = function(x, y, datax, datay) { if(length(x) < length(y))stop("train smaller than test") if(length(datax) < length(datay))stop("train smaller than test") datax$prob = x # trainset: data and raw probabilities datay$prob...
## How to do prediction with weka
weka,k-means,prediction
i'm using weka to do some text mining, i'm a little bit confused so i'm here to ask how can i ( with a set of comments that are in a some way classified as: notes, status of work, not conformity, warning) predict if a new comment belong to a...
## Create a table from different data frames in R
r,table,prediction
With my data (2 variables, Xt and Yt), I performed a Linear model in R Commander, which is named as LinearModel.1 Then, I wanted to predict the values that Yt would acquire when using different values of Xt, as in their 95% of confidence limits. After the linear model was...
## R - How to get one “summary” prediction map instead for 5 when using 5-fold cross-validation in maxent model?
r,maps,prediction,cross-validation,maxent
I hope I have come to the right forum. I'm an ecologist making species distribution models using the maxent (version 3.3.3, http://www.cs.princeton.edu/~schapire/maxent/) function in R, through the dismo package. I have used the argument "replicates = 5" which tells maxent to do a 5-fold cross-validation. When running maxent from the...
## use Lenskit to predicate the book rating
java,plugins,prediction,collaborative-filtering,lenskit
I have a "csv " file which contains the user id, the book he/she has read, the rating for each book. I want to use Lenskit to predict a book rating for a user. For example, the user A has read 3 books,A,B,C, I want to predicate the rating for...
## R: Limit/Set values of predicted results from linear model
r,statistics,prediction,lm,predict
New to R. Looking to limit the range of values that can be predicted. df.Train <- data.frame(S=c(1,2,2,2,1),L=c(1,2,3,3,1),M=c(400,450,400,700,795),V=c(423,400,555,600,800),G=c(4,3.2,2,2.7,3.4), stringsAsFactors=FALSE) m.Train <- lm(G~S+L+M+V,data=df.Train) df.Test <- data.frame(S=c(1,2,1,2,1),L=c(1,2,3,1,1),M=c(400,450,500,800,795),V=c(423,475,555,600,555), stringsAsFactors=FALSE) round(predict(m.Train, df.Test, type="response"),digits=1) #seq(0,4,.1) #Predicted values should fall in this range I've experimented with the...
## Cannot generalize my Genetic Algorithm to new Data
statistics,genetic-algorithm,prediction,generalization
I've written a GA to model a handful of stocks (4) over a period of time (5 years). It's impressive how quickly the GA can find an optimal solution to the training data, but I am also aware that this is mainly due to it's tendency to over-fit in the...
## How to calculate PRESS and $R^2_{predicted}$ in Stata automatically
stata,prediction
So I have two models and I want to calculate these statistics. Is there any package to calculate them in Stata? PRESS statistic (wiki) And, if I am not mistaken. $$R^2_{predicted} = 1 - \frac{RESET}{ESS}$$. ...
## Machine learning predict text fields based on text fields
machine-learning,amazon,prediction,ibm-watson,predictionio
I am working on machine learning and prediction for about a month. I have tried IBM watson with bluemix, amazon machine learning and predictionIO. What I want to do is to predict a text field based on other fields. My csv file have four text fields named Question,Summary,Description,Answer and about...
## R prediction within an interval
r,machine-learning,glm,prediction,random-forest
quick question on prediction. The value I’m trying to predict is either 0 or 1 (it is set as numeric, not as a factor) so when I run my random forest: fit <- randomForest(PredictValue ~ <variables>, data=trainData, ntree=50) and predict: pred<-predict(fit, testData) all my predictions are between 0 and 1...
## SciKit-learn for data driven regression of oscillating data
python,time-series,scikit-learn,regression,prediction
Long time lurker first time poster. I have data that roughly follows a y=sin(time) distribution, but also depends on other variables than time. In terms of correlations, since the target y-variable oscillates there is almost zero statistical correlation with time, but y obviously depends very strongly on time. The goal... | 2017-11-20 17:21:20 | {"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": 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": 0.6289182901382446, "perplexity": 2721.033488034271}, "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/1510934806086.13/warc/CC-MAIN-20171120164823-20171120184823-00553.warc.gz"} |
https://physics.stackexchange.com/questions/109771/force-constant-of-metals-kohn-anomaly | # Force constant of metals - Kohn anomaly
In Introduction to Solid State Physics (Kittel), it assumed the force constant between plane $s$ and $s+p$ $C_p=A\frac{\sin pk_0a}{pa}$ in metals to represent a Kohn anomaly. It says such a form is expected in metals. But I have no idea why. Thinking of typical potential energy-distance curve with one inflection point, shouldn't $C_p$ has only one node? Why only metals have such shape of $C_p$ and thus Kohn anomaly?
I guess there are much complex quantum mechanical principles underlying the Kohn anomaly. Is it possible to explain the reason of that $C_p$ shape and Kohn anomaly in the classical manner? | 2019-08-18 13:01:59 | {"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": 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": 0.8020738959312439, "perplexity": 704.6507580264215}, "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/1566027313889.29/warc/CC-MAIN-20190818124516-20190818150516-00324.warc.gz"} |
http://www.mathjournals.org/jot/2013-069-001/2013-069-001-012.html | Previous issue · Next issue · Most recent issue · All issues
# Journal of Operator Theory
Volume 69, Issue 1, Winter 2013 pp. 233-256.
A family of non-cocycle conjugate $E_0$-semigroups obtained from boundary weight doubles
Authors Christopher Jankowski
Author institution: Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva, 84105 Israel
Summary: Let $\rho \in M_n(\C)^*$ and $\rho' \in M_{n'}(\C)^*$ be states, and define unital $q$-positive maps $\phi$ and $\psi$ by $\phi(A)=\rho(A)I_n$ and $\psi(D) = \rho'(D)I_{n'}$ for all $A \in M_n(\C)$ and $D \in M_{n'}(\C)$. We show that if $\nu$ and $\eta$ are type II Powers weights, then the boundary weight doubles $(\phi, \nu)$ and $(\psi, \eta)$ induce non-cocycle conjugate $E_0$-semigroups if $\rho$ and $\rho'$ have different eigenvalue lists. We then classify the $q$-corners and hyper maximal $q$-corners from $\phi$ to $\psi$, finding that if $\nu$ is a type II Powers weight of the form $\nu(\sqrt{I - \Lambda(1)} B \sqrt{I - \Lambda(1)})=(f,Bf)$, where $\Lambda(1) \in B(L^2(0, \infty))$ is the operator of multiplication by $\mathrm e^{-x}$, then the $E_0$-semigroups induced by $(\phi, \nu)$ and $(\psi, \nu)$ are cocycle conjugate if and only if $n=n'$ and $\phi$ and $\psi$ are conjugate.
DOI: http://dx.doi.org/10.7900/jot.2010oct06.1889
Keywords: $E_0$-semigroup, completely positive map, $q$-positive map
Contents Full-Text PDF | 2018-10-23 06:02:40 | {"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": 0.8327611088752747, "perplexity": 927.113157876255}, "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/1539583516071.83/warc/CC-MAIN-20181023044407-20181023065907-00451.warc.gz"} |
https://www.biostars.org/p/350699/ | mRNA / Protein Annotation questions - etiquette and consensus
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Entering edit mode
3.6 years ago
Biogeek ▴ 420
I am debating whether the following is good practice and could do with guidance/ consensus.
I have aligned mRNA-seq reads to a genome published approx. 3 years ago. From my understanding, they carried out a BlastP on the predicted proteins to annotate them with a function/ name. A lot where hypothetical/ no hit etc. Not much use.
1. Given that the proteins were predicted and annotated over 3 years ago, is it advisable to re-annotate these sequences to the most up to date UniprotKB release? I would assume this is common practice as people always want to be working with more / updated resources of information?..OR should I leave it up to the original authors of the genome to do this? What is generally accepted?
2. I have mRNA gene sequences as well as the original predicted proteins available in a .fasta file which I can use to re-annotate against UniprotKB (Swiss and Trembl). Does it matter if I choose to use mRNA over the predicted proteins as BlastX will search in all 6 coding frames anyway? Does BlastP on predicted proteins yield better results?
Thanks for the insight / consensus
Genome Out-dated Re-annotation blastx blastp • 777 views
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Has the genome been incorporated into NCBI or Ensembl? If yes, there should / could be a better annotation available, compared to the authors original annotation
0
Entering edit mode
h.mon, yes it's available on NCBI. In what way would it be 'better'?
Thanks for the insight.
0
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What is the species? Go to https://www.ncbi.nlm.nih.gov/ , then at the search box type the name of the species, select Genome database at the pull-down menu, and hit enter.
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3.6 years ago
excellent questions/remarks!
1) that is indeed what you would expect, but it rarely happens for several reasons. the original authors might not even care anymore (depending on their interest in that particular species). Usually people will use the 'official' version (== the one associated with the paper), partly because of not having to do the effort of doing it themself , partially because it can get confusing. Image you say that gene X has function Y (based on your update) but the official one still says Z , if people then look up gene X they will see function Z and not your function Y . Often these things are only updated when a new release of the genome is being presented, very rarely thus (unless it's a key/model species)
2) I would personally rely more on the proteins (blastP). with the mRNA (blastX) approach you might get spurious or 'second grade' hits due to matches on the non-protein frames. If a blastP does not give enough results you might consider blastX | 2022-07-06 19:10:18 | {"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": 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": 0.22599062323570251, "perplexity": 3039.084289921397}, "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-2022-27/segments/1656104676086.90/warc/CC-MAIN-20220706182237-20220706212237-00591.warc.gz"} |
https://tikz.dev/gd-algorithms-in-c | PGF/TikZ Manual
The TikZ and PGF Packages Manual for version 3.1.10
Graph Drawing
37Writing Graph Drawing Algorithms in C
by Till Tantau
In the present section we have a look at how graph drawing algorithms written in the C programming language (or in C++) can be used in the graph drawing framework.
Warning: Graph drawing algorithms written in C can be incredibly fast if you use the facilities of C correctly. However, C code is much less portable than Lua code in the sense that it has to be compiled for the specific platform used by the user and that it has to be linked dynamically during a run of the program. All of this in possible (and works, as demonstrated by the linking of the ogdf framework), but it is much harder to get right than writing Lua code.
Bottom line, you really should be using this method only if it is really necessary (namely, when Lua code is simply not fast enough).
In the following, I first explain how the link between and C code works, in general. Then, in the subsequent sections, we go over the different kinds of programming languages and frameworks for which there is direct support for such a link.
37.1How C and TeX Communicate¶
In order to use C code for graph drawing algorithms during a run of the program, there is no need to build a new version of . Rather, it is possible that C code is linked into the executable at runtime. This is made possible by the fact that Lua (which part of Lua$$\dots$$) is able to link C libraries at runtime – provided a strict regime of rules is adhered to:
• 1. When you say require in Lua, it will normally look for a .lua file; but it will also try to find a .so file (a shared C library) as a fallback.
• 2. If it finds such a shared library, Lua() will try to link this library dynamically at runtime.
• 3. Inside the library, there must be a function (called an entry point) with a special name (it must start with luaopen_ and it must otherwise be the path and name of the library with slashes replaced by underscores).
• 4. This function gets called by Lua, once. Its job is to setup the library so that it can be used by Lua. Mainly, this means that certain C functions get registered in such a way that Lua can call them.
• 5. At this point, control returns to Lua and, now, certain functions have become available on the Lua layer that, when called, actually invoke the C code of our linked library.
For each of the above points, there are some bells and whistles:
• 1. Lua looks at slightly inconvenient places for shared libraries: By default, (currently, 2013) it looks in a lib subdirectory of the directory containing the Lua executable. The logic behind is that the shared libraries depend on the specific architecture of the executable. Thus, unlike normal Lua files, the library needs to be installed “far away” from the actual package of which it is part.
• 2. Certain versions of Lua have a broken handling of filenames of libraries written in C. The TL2013 version of Lua, for instance, crashes when the filename of a shared library does not contain the complete path (while this works for normal file). Hopefully, this, too, will be fixed in future versions.
• 3. On certain platforms, the support for dynamic linking against Lua is broken since the symbol table of the Lua library has been stripped away. Hopefully, this will be fixed soon; in the meantime, a highly fragile workaround is to link in another copy of the Lua library.
• 4. The entry point that is called by Lua requires a certain signature (it takes a Lua state as its only parameter) and must return the number of objects it returns on the Lua stack.
• 5. The registration process of C functions is somewhat tricky and changes from Lua version to Lua version.
• 6. C functions that get called by Lua must follow all sorts of tricky rules in order to communicate with Lua correctly.
Despite the above obstacles, one can use graph drawing algorithms written in C inside Lua, in principle, as follows: One loads an appropriately prepared and located C library using require and this library uses commands like declare to register its own functions into the graph drawing system so that when the run method is called, a C functions gets called instead.
Unfortunately, the above approach is extremely tedious and error-prone and it is “no fun” to access Lua data structures (such as the syntactic digraph) from C. For this reason, I have written some libraries that encapsulate (as much as possible) of this communication between C and Lua. Indeed, when you use these libraries, you can focus entirely on the graph drawing issues and you will not even notice that your code “is talking to Lua”. (Except for the name of the entry point, which is fixed to start with luaopen_ and it is impossible to change this without disrupting a lot inside Lua’s module system).
There are libraries available for simplifying the communication between the graph drawing system and graph drawing algorithms written in
• • C, see Section 37.2,
• • C++, see Section 37.3,
• • Open Graph Drawing Framework, see Section 37.4.
37.2Writing Graph Drawing Algorithms in C¶
37.2.1The Hello World of Graph Drawing in C¶
As our first example, as always, the “hello world” of graph drawing simply places nodes on a circle. For this, we implement a function fast_hello_world in a file SimpleDemoC.c. It starts as follows:
As we can see, we first include a special header file of a rather small library that does all the hard work of translating between Lua and C for us (InterfaceFromC). These header files reside in the c subdirectory of the pgf package. Note that we do not have to include the headers of the Lua library; indeed, you do not need access to the source of Lua to use the interface headers. As a side effect, we will, however, have to write struct lua_State instead of the more common lua_State once in our code, namely in the declaration of the entry point; but that is the only downside.
The library InterfaceFromC declares the type pgfgd_SyntacticDigraph. In a moment, we will see that we can setup a key fast simple demo layout such that when this key is used on the display layer, the function fast_hello_world gets called. When it is called, the graph parameter will be a full representation of the to-be-laid-out graph. We can access the fields of the graph and even directly modify some of its fields (in particular, we can modify the pos fields of the vertices). Here is the complete code of the algorithm:
That is all that is needed; the C library will take care of both creating the graph object as all well as of deleting it and of copying back the computed values of the pos fields of the vertices.
Our next task is to setup the key fast simple demo layout. We can (and must) also do this from C, using the following code:
The function luaopen_pgf_gd_examples_c_SimpleDemoC is the function that will be called by Lua (we will come to that). More important for us, at the moment, is the declaration of the key: We use pgfgd_new_key to create a declaration record and then fill the different fields using appropriate function calls. In particular, the call pgfgd_key_algorithm allows us to link the key with a particular C function. The pgfgd_declare will then pass the whole declaration back to Lua, so the effect of the above is essentially the same as if you had written in Lua:
In our algorithm, in addition to the above key, we also use the fast simple demo radius key, which is a simple length key. This key, too, can be declared on the C layer:
We simply add this code to the startup function above.
Now it is time to compile and link the code. For this, you must, well, compile it, link it against the library InterfaceFromC, and build a shared library out of it. Also, you must place it somewhere where Lua will find it. You will find a Makefile that should be able to achieve all of this in the directory pgf/c/graphdrawing/pgf/gd/examples/c, where you will also find the code of the above example.
Now, all you need to do to use it is to write in Lua (after you have loaded the pgf.gd library, of course), would normally be the call
or in TikZ
This should cause Lua to find the shared library, load it, and then call the function in that library with the lengthy name (the name is always luaopen_ followed by the path and filename with slashes replaced by underscores).
Remark: Unfortunately, the above does not work with the Live 2013 versions of Lua due to a bugs that causes the “replace dots by slashes” to fail. For this reason, we currently need to rename our shared library file to
and then say
or in TikZ
In future versions of Lua, things should be “back to normal” in this regard. Also, the bug only concerns shared libraries; you can still create a normal Lua file with a nice name and place at a nice location and the only contents of this file is then the above require command.
Anyway, once we have loaded the shared library we can say:
37.2.2Documenting Algorithms Written in C¶
In our above example, we included a summary with the keys in the C code. It would be even better if we added a longer documentation and some examples that show how the key works; but this is a bit impracticable in C since multi-line strings are hard to write down in C. The trick is to use the documentation_in field of a key: It allows us to specify the name of a Lua file that should be loaded (using require) to install the missing documentation fields. As explained in Section 36.2.7, this Lua file may make good use the pgf.gd.doc package. Note, also, that for keys documented in this way the documentation can easily be included in this manual through the use of the \includedocumentationof command.
In our example, we would first add the following line twice in the C code (once for each key), assuming that the documentation resides in the file pgf/gd/doc/examples/SimpleDemoC.lua:
Note that since the documentation is a normal Lua file, it will be searched in the usual places Lua files are located (in the texmf trees) and not, like the C shared library, in the special lib subdirectory of the Lua binary.
Here are typical contents of the documentation file:
37.2.3The Interface From C¶
In the above example, we already saw some of the functions from the library InterfaceFromC that translated from Lua to C for us. For a complete list of all functions available, currently please see graphdrawing/c/pgf/gd/interface/c/InterfaceFromC.h directly.
Currently, the library provides C functions to directly access all aspects of the syntactic digraph and also of the graphs computed by the preprocessing of the layout pipeline. What is missing, however, is access to the tree of (sub)layouts and to collections. Hopefully, these will be added in the future.
37.3Writing Graph Drawing Algorithms in C++¶
Built on top of the C interface presented in the previous section, there is also a C++ interface available. It encapsulates as much of the C functions as possible in C++ classes. Thus, this interface is mostly there for convenience, it does not offer fundamentally new functionality.
37.3.1The Hello World of Graph Drawing in C++¶
Let us have a look at how our beloved hello world of graph drawing looks in C++. Although it is still possible to put graph drawing algorithms inside functions, it is more natural in C++ to turn them into methods of a class. Thus, we start the code of SimpleDemoCPlusPlus.c++ as follows:
As can be seen, we do not only include the interface from C++, but also that from C (since, currently, not all functionality of the C library is encapsulated in C++).
The interesting part is the struct FastLayout, which will contain our algorithm (you could just as well have used a class instead of a struct). It is derived from two classes: First, from a declarations class and, secondly, from a runner class. Both of them, just like everything else from the interface, reside in the namespace scripting. This name was chosen since the main purpose of the interface is to provide “scripting facilities” to C code through the use of Lua.
We are currently interested in the class runner. This class has a virtual function run that gets called when, on the Lua side, someone has selected the algorithm represented by the class. Thus, we place our algorithm in this method:
The run method has access to the member variable parameters, which contains all sorts of information concerning the to-be-drawn graph. In particular, the syntactic_digraph field gives us access to the syntactic digraph structure that was already available in the interface from plain C. However, we can also see that a template function like option allows us to access the graph’s option table in a simple way.
As for C code, our next task is to setup a key that, when used on the TikZ layer, will run our algorithm. For this, we can use an object derived from a declarations. In our example, the FastLayout is both derived from a runner (since it contains an algorithm) and also from declarations (since it also contains the code necessary for declaring this algorithm). If you prefer, you can split this into two classes. A declarations object must override the declare method. This method gets a script object as input, which is the “representation” of Lua inside the C++ code:
For each key that we wish to declare, we call the script’s declare method once. This method takes a key object as input, which can be configured through a sequence of calls to different member functions (like summary or algorithm). Most of these member functions are rather self-explaining; only algorithm is a bit trickier: It does not take a function as input, but rather an object of type runner and it will call the run method of this object whenever the algorithm is run.
Lastly, we also need to write the entry point:
Note that it is the job of the interface classes to free the passed declarations object. For this reason, you really need to call new and cannot pass the address of a temporary object.
As before, because of the bug in some Lua versions, to actually load the library at runtime, we need to rename it to
and then say
or in TikZ
We can now use it:
37.3.2The Interface From C++¶
The header graphdrawing/c/pgf/gd/interface/c/InterfaceFromC++.h contains, as the name suggest, the interface from C++. A complete documentation is still missing, but let us go over the main ideas:
Runners. Algorithms are represented by objects of type runner. An algorithm will overwrite the run method, as we saw in the example, and it should modify the parameters of the runner object.
In addition to the run method, there are also two more virtual methods, called bridge and unbrigde. The first is called before the run method is called and the second afterwards. The idea is that another framework, such as ogdf, can implement a new class ogdf_runner that overrides these two methods in order to transform the Lua/C representation of the input graph into an ogdf representation prior to the run method being called. The run method can then access additional member variables that store the graph representations in ogdf form (or another form, depending on the framework). The unbridge method allows the framework to translate back.
Although a runner object must be created for every algorithm, an algorithm can also reside in a function. The class function_runner is a simple wrapper that turns a function into such an object.
Keys. A key object is a temporary object that is passed to the declare method of a script. It represents the table that is passed to the Lua function declare. In order to make setting its field easy, for each field name there is a corresponding function (like summary) that takes the string that should be set to this field and returns the key object once more, so that we can chain calls.
The algorithm method gets a runner object as parameter and will store a pointer to this object inside Lua. Each time the algorithm is used, this object will be used to “run” the algorithm, that is, the methods prepare, bridge, run, and unbridge will be called in that order. Since the object is reused each time, only one object is needed; but this object may not be freed prematurely. Indeed, you will normally create the object using new once and will then never delete it.
A typical idiom you may find in the code is
This code is seen inside the declare method of objects that are both declarations and runners. They register “themselves” via the above code. Note, however, that this requires that the this pointer is not a temporary object. (The typing rules of C++ make it hard for this situation to happen, but it can be achieved.)
Reading options. Once options have been declared, your C++ algorithms will wish to read them back. For this, the parameters field of a runner object provides a number of templated methods:
• • The option_is_set method returns true if the passed option has been set and can be cast to the type of the template. So, option_is_set("node distance") will return true if the node distance key has been set for the graph as a whole (currently, there is no way to read the options of a vertex or an edge from C++, use the C methods instead).
• • The option function comes in two flavours: First, it takes a single option name and just returns the option’s value. If, however, the option has not been set or has another type, some sort of null value is returned. So, option("node distance") will return the configured node distance as a double. When an option has an initial value, this call will always return a sensible value.
The second flavour of option allows you to pass a reference to an object in which the option’s value should be stored and the function will return true if the option is set (and, thus, something was written into the reference). This is the “safest” way to access an option:
Caution must be taken for char* options: The returned string must be explicitly freed; it will be a copy of the string stored in the Lua table.
• • The configure_option method is used to set a member of an object based on the value of a certain option. For this, you must pass a pointer to a member function that sets the member. Here is an example:
If the option has not been set or does not have the correct type, the member function is not called.
Factories and modules. A Lua key is normally either a Boolean, a double, or a string. However, in C++, we may also sometimes wish Lua users to configure which C function is used to achieve something. One could do this using strings or numbers and then use search algorithms or a long switch, but this would neither be flexible nor elegant.
Instead, it is possible to store factories in Lua keys. A factory is a class derived from factory that implements the virtual function make. This function will return a new object of a template type. You can store such a factory in a key.
The make method of a parameters object allows you to invoke the factory stored in a key. (If no factory is stored in it, null is returned).
The configure_module method is akin to configure_option, only the result of applying the factory is passed to the member function of the class.
Scripts. A “script” is the abstraction of the communication between Lua and C++. From C++’s point of view, the script object offers different declare methods that allow us to “make objects and function scriptable” in the sense that they can then be called and configured from Lua. The script must be initialized with a Lua state and will be bound to that state (basically, the script only stores this single pointer).
When you call declare, you either pass a single key object (which is then declared on the Lua layer) or you pass a declarations object, whose virtual declare method is then called. The declarations objects are used to bundle several declarations into a single one.
37.4Writing Graph Drawing Algorithms Using OGDF¶
Built on top of the C++ interface, a small interface allows you to easily link algorithms written for the ogdf (Open Graph Drawing Framework) with graph drawing in Lua.
37.4.1The Hello World of Graph Drawing in OGDF – From Scratch¶
Note that the interface from ogdf resides in the ogdf folder, not in the interface folder.
Like in the plain C++ interface, we must now subclass the runner class and the declarations class. Also like the plain C++ interface, we can use multiple inheritance. The difference lies in the fact that we do not directly subclass form runner, but rather from ogdf_runner. This class implements the complicated “bridging” or “translation” process between the world of InterfaceFromC++ and ogdf:
As can be seen, in a subclass of ogdf_runner, the run method will have access to a member called graph and to another member called graph_attributes. These will have been setup with the graph from the Lua layer and, after the algorithm has run, the information stored in the x and y fields of the graph attributes and also the bend information of the edges will be written back automatically.
Next, we need to declare the algorithm. This is done as in the plain C++ interface:
Finally, we need the entry point, which is also “as usual”:
Yet again, we need to rename the resulting shared library and then say require on it. We can now use it:
37.4.2The Hello World of Graph Drawing in OGDF – Adapting Existing Classes¶
In the previous example we implemented a graph drawing algorithm using ogdf for use with Lua “from scratch”. In particular, the whole algorithm was contained in the run method of our main class. In practice, however, graph drawing algorithms are typically placed in classes that “know nothing about scripting”. For instance, our hello world of graph drawing might actually be implemented like this:
Now, what we actually want to do is to “make this class scriptable”. For this, we setup a new class whose run method will produce a new HelloWorldLayout, configure it, and then run it. Here is this run method:
Next, we need to write the declarations code. This is very similar to the “from scratch” version:
Two remarks are in order: First, it is customary to name the keys for the display system the same way as the classes. Second, the different configuration options of the algorithm are named with the class name followed by the option name. This makes it clear who, exactly, is being configured. However, these keys should then also get an alias field set, which will cause an automatic forwarding of the key to something more “user friendly” like just radius.
It remains to put the above methods in a “script” file. It is this file that, when compiled, must be linked at runtime against Lua.
37.4.3Documenting OGDF Algorithms¶
As explained in Section 37.2.2, we can add external documentation to algorithms written in C and, using the documentation_in method of the key class, we can use the exact same method to document ogdf algorithms.
I strongly recommend making use of this feature since, currently, the documentation of many ogdf classes is sketchy at best and using TikZ examples seems to be a good way of explaining the effect of the different parameters algorithms offer.
37.4.4The Interface From OGDF¶
The support for ogdf offered inside InterfaceFromOGDF.h is just the class ogdf_runner we saw already in the example. In addition, there is also a wrapper class ogdf_function_runner that allows you to wrap an algorithm implemented in a function that uses ogdf, but I expect this to be the case only rarely. | 2023-02-01 13:45:07 | {"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": 0.3529793918132782, "perplexity": 1089.653002993218}, "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-2023-06/segments/1674764499934.48/warc/CC-MAIN-20230201112816-20230201142816-00696.warc.gz"} |
http://en.wikiversity.org/wiki/Teletraffic_engineering/What_is_tariffing%3F | # Teletraffic engineering/What is tariffing?
Author: Moses Chisala
## What is Tariffing?
### Summary
This document is about tariffing as applied in the Telecommunications industrial. Several factors have been looked at; tariffing policy entities looking at the customer and what should be priced. Also components of tariffing or tariffs such as; Why are tariffs charged?, Components of tariffs, Special tariffs and Impact of tariffs on traffic.
### Definition
The word tariffing comes from the word tariff which means; tax, duty, due, fee, excise, levy or toll paid towards the use of a specific service. In the telecommunication environment it applies to the charging of telecommunication services that have been already used or prior to. Therefore, tariffing can be defined as the process of fixing a duty, fee or a price on the telecommunication services provided by the service provider and utilized by the end user (consumer) and the public policy regulating body acting as an overseer. The regulating body provides standards and guidelines to both the service provider and the end user. The standards and regulations imposed differ from one country to another.
Some of the elements affecting tariffing are:- Monopoly or competition; Pricing and Tariffs; Universal Service; Network interconnections and Abuse of Dominance.
Tariffing policy entities:
Customer
An end user customer uses one telecommunications network to initiate a communication to another customer of the same network or another. An 'interconnector' is a network operator that terminates a communication from a customer of another network operator to a customer of its network.
What Should Be Priced?
a. Rate Elements and Rate Structure
"Price elements and the structure of prices are intended to address two related issues: on the supply side, to ration scarce resources, and on the demand side, to change consumption behavior of end users.
The decision to make the next telephone call depends on the price of that incremental call, not the average price of all calls. The decision to talk for the next minute, once a call is placed, is based on the perceived price of that incremental minute. The decision to subscribe to a service is based on the perceived price of that incremental service. Each of these marginal decisions is performed by comparing the perceived price to the perceived benefit to be obtained. Customers often undertake these decisions with poor information, incomplete understanding, and only a vague notion of the actual price that will be charged. Time-of-day pricing is a crude form of peak load pricing, intended to cause users to change their behavior by shifting some of their calling to off-peak periods. Multi-part tariffs (fixed charge + usage-sensitive charge) can be used to segment the market according to user characteristics." [2]
The figure below shows a simple telecommunication network indicating the routing of the local call and long-distance call.
``` Simple Telecommunication Network
```
b. “Product” Definitions
"Fundamentally, the circuit switched telephone network is a time-sharing network. Telephone companies set different prices for different minutes of use, depending on the identity of the user, the distance of the call, and the time of day." [2]
The following componets also should be considered when looking at tariffing;
Why are tariffs charged?
Components of tariffs
Special tariffs
Impact of tariffs on traffic
Price-elasticity of demand
Elasticity of demand for new installations may be estimated taking into account the subjective price perception of potential customers. Price elasticity expresses the sensitivity of customers to the cost of the service. The elasticity parameter is calculated as the ratio of percentage change in demand (quantity sold per period) caused by a percentage change in price.
File:Price-elasticity of demand formula.PNG
#### Example
Example 1
If the average price for the new service that has been introduced in the network is R15 and the elasticity of revenue is 0.7. Asuming 4% drop in quantity demand.
Calculate
I. elasticity of quantity demand
II. the new price
Solutions
I.
$E_{RP} = 1 + E_{qp}$
0.7 = 1 + Eqp
Eqp = - 0.3
II.
Eqp = [(Q1/Qo) - 1]/[(P1/Po-1]
- 0.3 = [-0.04]/[15/Po-1]
Po = R13.24
#### Exercises
Question 1
A mobile network provider charging R2 per 1Mb data download has a subscriber base of 1.2 million for a period of six months. The subscriber base increases in five months to 1.6 million after the 64% reduction per download.
Calculate
I. the initial quantity demand
II. the relative Change in quantity demand
III. the relative change in price
IV. elasticity of quantity demand
V. elasticity of revenues
VI. comment on the answer in v.
### References
[1] INTERNATIONAL TELECOMMUNICATION UNION SERIES D SUPPLEMENT 3 (03/93)
[2] http://www.ingrimayne.com/econ/elasticity/Elastic1.html
[3] Steensrtup M., Routing in Communication Networks. Prentice Hall Inc, New Jersey, 1995
[4] Hanharan H., Integrated Digital Communications. School of Electrical and Information Engineering, University of the Witwatersrand, Johannesburg, 2006.
[5] [[[w:Tariffing|http://en.wikipedia.org/wiki/Tariffing]]]
[6] Kennedy I.G., Why is Network Planning Important?, Lecture Notes, ELEN5007 - Teletraffic Engineering, School of Electrical and Information Engineering, University of the Witwatersrand, 2005. | 2013-06-18 06:05:36 | {"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": 0, "img_math": 1, "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": 0.291192889213562, "perplexity": 3753.7707085563347}, "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-2013-20/segments/1368706961352/warc/CC-MAIN-20130516122241-00096-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://www.darwinproject.ac.uk/letter/DCP-LETT-2443.xml | DCP-LETT-2443
# From John Murray 1 April 1859
Albemarle St
Apl. 1. 1859
My dear Sir,
I hasten to thank you for your obliging letter of yesterday & for the interesting details regarding your work on Species contained in it.— On the strength of this information & my knowledge of your former publications,1 I can have no hesitation in swerving from my usual routine & in stating at once even without seeing the MS. that I shall be most happy to publish it for you on the same terms as those on which I publish for Sir Charles Lyell—viz—I will print an edition fixing the number of copies with your concurrence, according to what shall appear to me (on perusal of a part, at least, of the work) to be adviseable—& before publication, as soon as I can ascertain the cost of its production I will make you an offer amounting as nearly as I can ascertain to $\frac{2}{3}$ ds of the net proceeds of the edition—payable by note of hand at six months from the day of publication xxxxxxx2 I shall be quite willing to give the author 12 copies for himself & as many more as he may require at the trade price xxxxx
Yours very faithfully | (signed) John Murray. Charles Darwin Esq
## Footnotes
1
For CD’s earlier correspondence with John Murray concerning the publication of Journal of researches 2d ed., see Correspondence vol. 3. For CD’s other publications before April 1859, see Freeman 1977.
2
The copyist inserted crosses in the places where the final text of the letter was to contain precise dates and figures. In the absence of the letter, there is no evidence to indicate what details were inserted.
## Letter details
Letter no.
DCP-LETT-2443
From
Murray, John (b)
To
Darwin, C. R.
Sent from
unstated
Source of text
National Library of Scotland (John Murray Archive) (Ms. 41913 p.32)
## Summary
On the strength of CD’s details about his work on species and his knowledge of CD’s former publications, JM offers to publish [Origin] without seeing the MS.
## Please cite as
Darwin Correspondence Project, “Letter no. 2443,” accessed on 4 May 2016, http://www.darwinproject.ac.uk/DCP-LETT-2443
letter | 2016-05-04 13:52:04 | {"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": 0.5396669507026672, "perplexity": 4335.027975081847}, "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-2016-18/segments/1461860123077.97/warc/CC-MAIN-20160428161523-00006-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://tex.stackexchange.com/questions/481966/too-much-space-between-section-and-text-in-a-twocolumn-document | # Too much space between section and text in a twocolumn document
I don't know why there is so much space between the section's title and the beginning of the text. I am using the same 'template' with class revtex4-1 for others documents and it works normally.
\documentclass[twocolumn,prl,nobalancelastpage,aps,10pt] {revtex4-1}
%\documentclass[rmp,preprint]{revtex4-1}
\usepackage[latin9]{inputenc}
\usepackage[english]{babel}
\usepackage{graphicx,bm,times}
\usepackage{subfig}
\graphicspath{ {C:/Varie/UNI/MANO/primosemestre/fraboni/esperimenti/RT/pictures/} }
\begin{document}
\title{Electrical resistance of Cu, Ni and Ge in the range $120K$ - $400K$}
\author{...}
\affiliation{...}
\begin{abstract}
We observed the temperature dependence of the electrical resistance of Cu, Ni and Ge in the range between $200K$ and $400K$. It resulted to be linear in the whole range for Cu and Ni. The one of the Ge exhibited this linear behaviour only up to $300K$ showing an exponential decay above. We also estimated the energy gap $E_g$ of Ge which resulted to be equal to $E_g=$
\end{abstract}
\date{\today}
\maketitle
\section{INTRODUCTION}
The aim of this study is to observe the dependence of the electrical resistance of two metals, Copper and Nickel, and of a doped semiconductor, the Germanium, as a function of the temperature. Furthermore our measurements allowed us to estimate the energy gap of the Germanium.
%The two metals showed a linear dependence while the semiconductor has two different behaviour. Through our measuments
\\
The starting point of our discussion are ...
• If I remove \maketitle the problem diseappears Mar 28 '19 at 19:13
• if the abstract's length is just one line it works well … what the hells is going on ? by the way there is a way to set this distance in any case ? Mar 28 '19 at 19:19
Let us first have a look on the corrected mwe of you to recreate the issue. Please see that I deleted some packages not needed for this issue and please see that package times is outdated. To get the issue I used your The starting point of our discussion are ... some more times, because with \blindtext I can not define the needed lines to show your issue.
I marked with <========= the relevant code:
\documentclass[twocolumn,prl,nobalancelastpage,aps,10pt] {revtex4-1}
%\documentclass[rmp,preprint]{revtex4-1}
\usepackage[latin9]{inputenc}
\usepackage[english]{babel}
\usepackage{times} % <======================================== outdated!
\usepackage{blindtext} % <============================ to add dummy text
\begin{document}
\title{Electrical resistance of Cu, Ni and Ge in the range $120K$ - $400K$}
\author{...}
\affiliation{...}
\begin{abstract}
We observed the temperature dependence of the electrical resistance of Cu, Ni and Ge in the range between $200K$ and $400K$. It resulted to be linear in the whole range for Cu and Ni. The one of the Ge exhibited this linear behaviour only up to $300K$ showing an exponential decay above. We also estimated the energy gap $E_g$ of Ge which resulted to be equal to $E_g=$
\end{abstract}
\date{\today}
\maketitle
\section{INTRODUCTION}
The aim of this study is to observe the dependence of the electrical resistance of two metals, Copper and Nickel, and of a doped semiconductor, the Germanium, as a function of the temperature. Furthermore our measurements allowed us to estimate the energy gap of the Germanium.
%The two metals showed a linear dependence while the semiconductor has two different behaviour. Through our measuments
\\
The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... % <====================
\blindtext % <==========================================================
\blindtext
\Blinddocument
\end{document}
The result is (see red arrows for the culprit):
The big white space results because LaTeX tries to fill the complete left column, because your class uses \flushbottom, that means the last line of the column has to be at the bottom of the column. You can use \raggedbottom instead to force not balanced colums.
MWE:
\documentclass[twocolumn,prl,nobalancelastpage,aps,10pt] {revtex4-1}
%\documentclass[rmp,preprint]{revtex4-1}
\usepackage[latin9]{inputenc}
\usepackage[english]{babel}
\usepackage{times} % <======================================== outdated!
\usepackage{blindtext} % <============================ to add dummy text
\raggedbottom % <=======================================================
\begin{document}
\title{Electrical resistance of Cu, Ni and Ge in the range $120K$ - $400K$}
\author{...}
\affiliation{...}
\begin{abstract}
We observed the temperature dependence of the electrical resistance of Cu, Ni and Ge in the range between $200K$ and $400K$. It resulted to be linear in the whole range for Cu and Ni. The one of the Ge exhibited this linear behaviour only up to $300K$ showing an exponential decay above. We also estimated the energy gap $E_g$ of Ge which resulted to be equal to $E_g=$
\end{abstract}
\date{\today}
\maketitle
\section{INTRODUCTION}
The aim of this study is to observe the dependence of the electrical resistance of two metals, Copper and Nickel, and of a doped semiconductor, the Germanium, as a function of the temperature. Furthermore our measurements allowed us to estimate the energy gap of the Germanium.
%The two metals showed a linear dependence while the semiconductor has two different behaviour. Through our measuments
\\
The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... % <====================
\blindtext % <==========================================================
\blindtext
\Blinddocument
\end{document}
Result:
Now the white space is at the bottom of the column.
If you do not like that you need to rephrase your text in first column to fit.
If you delete for example one sentence The starting point of our discussion are ... with commented \raggedbottom you have the following code
\documentclass[twocolumn,prl,nobalancelastpage,aps,10pt] {revtex4-1}
%\documentclass[rmp,preprint]{revtex4-1}
\usepackage[latin9]{inputenc}
\usepackage[english]{babel}
\usepackage{times} % <======================================== outdated!
\usepackage{blindtext} % <============================ to add dummy text
%\raggedbottom % <=======================================================
\begin{document}
\title{Electrical resistance of Cu, Ni and Ge in the range $120K$ - $400K$}
\author{...}
\affiliation{...}
\begin{abstract}
We observed the temperature dependence of the electrical resistance of Cu, Ni and Ge in the range between $200K$ and $400K$. It resulted to be linear in the whole range for Cu and Ni. The one of the Ge exhibited this linear behaviour only up to $300K$ showing an exponential decay above. We also estimated the energy gap $E_g$ of Ge which resulted to be equal to $E_g=$
\end{abstract}
\date{\today}
\maketitle
\section{INTRODUCTION}
The aim of this study is to observe the dependence of the electrical resistance of two metals, Copper and Nickel, and of a doped semiconductor, the Germanium, as a function of the temperature. Furthermore our measurements allowed us to estimate the energy gap of the Germanium.
%The two metals showed a linear dependence while the semiconductor has two different behaviour. Through our measuments
\\
The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... The starting point of our discussion are ... % <====================
\blindtext % <==========================================================
\blindtext
\Blinddocument
\end{document}
and the result:
Sometimes rephrasing is better than everything else ...
it is to wide for comment: i cant reproduce your problem. with your code, which i slightly change preamble (changes had not influence to xour problem) i obtain the following result:
off-topics: i suggest to use ˙mchempackage for writing chemical elements and formulas, andsiunitx for all values with units. see how is used in MWE below:
\documentclass[twocolumn,prl,nobalancelastpage,aps]{revtex4-1}
\usepackage{times}
\usepackage[version=4]{mhchem}
\usepackage{siunitx}
\usepackage{lipsum}
\begin{document}
\title{Electrical resistance of Cu, Ni and Ge in the range 120\,K to 400\,K}
\author{...}
\affiliation{...}
\begin{abstract}
We observed the temperature dependence of the electrical resistance of \ce{Cu}, \ce{Ni} and \ce{Ge} in the range between \SIrange{200}{400}{\kelvin}. It resulted to be linear in the whole range for \ce{Cu} and \ce{Ni}. The one of the Ge exhibited this linear behaviour only up to $300K$ showing an exponential decay above. We also estimated the energy gap $E_g$ of Ge which resulted to be equal to $E_g=?$.
\end{abstract}
\date{\today}
\maketitle
\section{INTRODUCTION}
The aim of this study is to observe the dependence of the electrical resistance of two metals, Copper and Nickel, and of a doped semiconductor, the Germanium, as a function of the temperature. Furthermore our measurements allowed us to estimate the energy gap of the Germanium.
\lipsum[1-3]
\section{The second section}
\lipsum[4-5]
\end{document}
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http://www.cs.utexas.edu/users/rvdg/laff/LAFF-On-PfHP/Week1-thinking-in-terms-of-vector-vector-operations.html | ## Section1.3Thinking in Terms of Vector-Vector Operations
### Unit1.3.1The Basic Linear Algebra Subprograms (BLAS)
Linear algebra operations are fundamental to computational science. In the 1970s, when vector supercomputers reigned supreme, it was recognized that if applications and software libraries are written in terms of a standardized interface to routines that implement operations with vectors, and vendors of computers provide high-performance instantiations for that interface, then applications would attain portable high performance across different computer platforms. This observation yielded the original Basic Linear Algebra Subprograms (BLAS) interface [3] for Fortran 77, which are now referred to as the level-1 BLAS. The interface was expanded in the 1980s to encompass matrix-vector operations (level-2 BLAS)~\cite{BLAS2} and matrix-matrix operations (level-3 BLAS) [1].
An overview of the BLAS and how they are used to achieve portable high performance is given in the Encyclopedia of Parallel Computing [5]. This article is somewhat out of date. In a later enrichment we will point you to the BLAS-like Library Instantiation Software (BLIS) [6], which is now a widely used open source framework for rapidly instantiating the BLAS and similar functionality.
Expressing code in terms of the BLAS has another benefit: the call to the routine hides the loop that otherwise implements the vector-vector operation and clearly reveals the operation being performed, thus improving readability of the code.
### Unit1.3.2Notation
In our discussions, we use capital letters for matrices ($A, B, C, \ldots$), lower case letters for vectors ($a, b, c, \ldots$), and lower case Greek letters for scalars ($\alpha, \beta, \gamma, \ldots$). Exceptions are integer scalars, for which we will use $i, j, k, m, n,$ and $p \text{.}$
Vectors in our universe are column vectors or, equivalently, $n \times 1$ matrices if the vector has $n$ components (size $n$). A row vector we view as a column vector that has been transposed. So, $x$ is a column vector and $x^T$ is a row vector.
In the subsequent discussion, we will want to expose the rows or columns of a matrix. If $X$ is an $m \times n$ matrix, then we expose its columns as
\begin{equation*} X = \left(\begin{array}{c | c | c | c} x_0 \amp x_1 \amp \cdots \amp x_{n-1} \end{array} \right) \end{equation*}
so that $x_j$ equals the column with index $j \text{.}$ We expose its rows as
\begin{equation*} X = \left(\begin{array}{c} \widetilde x_0^T \\ \widetilde x_1^T \\ \vdots \\ \widetilde x_{m-1}^T \end{array} \right) \end{equation*}
so that $\widetilde x_i^T$ equals the row with index $i \text{.}$ Here the $~^T$ indicates it is a row (a column vector that has been transposed). The tilde is added for clarity since $x_i^T$ would in this setting equal the column indexed with $i$ that has been transposed, rather than the row indexed with $i \text{.}$ When there isn't a cause for confusion, we will sometimes leave the $\widetilde ~$ off. We use the lower case letter that corresponds to the upper case letter used to denote the matrix, as an added visual clue that $x_j$ is a column of $X$ and $\widetilde x_i^T$ is a row of $X \text{.}$
We have already seen that the scalars that constitute the elements of a matrix or vector are denoted with the lower Greek letter that corresponds to the letter used for the matrix of vector:
\begin{equation*} X = \left( \begin{array}{c c c c} \chi_{0,0} \amp \chi_{0,1} \amp \cdots \amp \chi_{0,n-1} \\ \chi_{1,0} \amp \chi_{1,1} \amp \cdots \amp \chi_{1,n-1} \\ \vdots \amp \vdots \amp \amp \vdots \\ \chi_{m-1,0} \amp \chi_{m-1,1} \amp \cdots \amp \chi_{m-1,n-1} \end{array} \right) \quad {\rm and} \quad x = \left( \begin{array}{c c c c} \chi_0 \\ \chi_1 \\ \vdots \\ \chi_{m-1} \end{array} \right). \end{equation*}
If you look carefully, you will notice the difference between $x$ and $\chi \text{.}$ The latter is the lower case Greek letter "chi."
###### Remark1.3.1
Since this course will discuss the computation $C := A B + C \text{,}$ you will only need to remember the Greek letters $\alpha$ (alpha), $\beta$ (beta), and $\gamma$ (gamma).
### Unit1.3.3The dot product (inner product)
Given two vectors $x$ and $y$ of size $n$
\begin{equation*} x = \left( \begin{array}{c c c c} \chi_0 \\ \chi_1 \\ \vdots \\ \chi_{n-1} \end{array} \right) \quad {\rm and} \quad y = \left( \begin{array}{c c c c} \psi_0 \\ \psi_1 \\ \vdots \\ \psi_{n-1} \end{array} \right), \end{equation*}
their dot product is given by
\begin{equation*} x^T y = \sum_{i=0}^{n-1} \chi_i \psi_i. \end{equation*}
The notation $x^T y$ comes from the fact that the dot product also equals the result of multiplying $1 \times n$ matrix $x^T$ times $n \times 1$ matrix $y \text{.}$
A routine. coded in C, that computes $x^T y + \gamma$ where $x$ and $y$ are stored at location x with stride incx and location y with stride incy, respectively, and $\gamma$ is stored at location gamma is given by
#define chi( i ) x[ (i)*incx ] // map chi( i ) to array x
#define psi( i ) y[ (i)*incy ] // map psi( i ) to array y
void Dots( int n, double *x, int incx, double *y, int incy, double *gamma )
{
for ( int i=0; i<n; i++ )
*gamma += chi( i ) * psi( i );
}
in Assignments/Week1/C/Dots.c. Here stride refers to the number of items in memory between the stored components of the vector. For example, the stride when accessing a row of a matrix is lda when the matrix is stored in column-major order with leading dimension lda.
The BLAS include a function for computing the dot operation. Its calling sequence in Fortran, for double precision data, is
DDOT( N, X, INCX, Y, INCY )
where
• (input) N is an integer that equals the size of the vectors.
• (input) X is the address where $x$ is stored.
• (input) INCX is the stride in memory between entries of $x \text{.}$
• (input) Y is the address where $y$ is stored.
• (input) INCYnnnn is the stride in memory between entries of $y \text{.}$
The function returns the result as a scalar of type double precision. If the datatype were single precision, complex double precision, or complex single precision, then the first D is replaced by S, Z, or C, respectively.
To call the same routine in a code written in C, it is important to keep in mind that Fortran passes data by address. The call
Dots( n, x, incx, y, incy, &gamma );
which, recall, adds the result of the dot product to the value in gamma, translates to
gamma += ddot_( &n, x, &incx, y, &incy );
When one of the strides equals one, as in
Dots( n, x, 1, y, incy, &gamma );
one has to declare an integer variable (e.g, i_one) with value one and pass the address of that variable:
int i_one=1;
gamma += ddot_( &n, x, &i_one, y, &incy );
We will see examples of this later in this section.
In this course, we use the BLIS implementation of the BLAS as our library. This library also has its own (native) BLAS-like interface that we refer to as the BLIS Typed API. (BLIS is actually a framework for the rapid instantiation of BLAS-like functionality. It comes with four different interfaces to that functionality: The classic Fortran BLAS interface, the CBLAS interface for the C language (which is an interface that is rarely used), the BLIS Typed API with is reminiscent of the BLAS interface, but with added functionality and flexibility, and the BLIS object API, which which a Users' Guide can be found at https://github.com/flame/blis/blob/master/docs/BLISObjectAPI.md.) A Users' Guide for this interface can be found at https://github.com/flame/blis/blob/master/docs/BLISTypedAPI.md. There, we find the routine bli_ddotxv that computes $\gamma := \alpha x^T y + \beta \gamma \text{,}$ optionally conjugating the elements of the vectors. The call
Dots( n, x, incx, y, incy, &gamma );
translates to
double one=1.0;
bli_ddotxv( BLIS_NO_CONJUGATE, BLIS_NO_CONJUGATE,
n, &one, x, incx, y, incy, &one, &gamma );
The BLIS_NO_CONJUGATE is to indicate that the vectors are not to be conjugated. Those parameters are there for consistency with the complex versions of this routine (bli_zdotxv and bli_cdotxv).
### Unit1.3.4The IJP and JIP orderings
Let us return once again to the IJP ordering of the loops that compute matrix-matrix multiplication:
\begin{equation*} \begin{array}{l} {\bf for~} i := 0, \ldots , m-1 \\ ~~~ {\bf for~} j := 0, \ldots , n-1 \\ ~~~ ~~~ {\bf for~} p := 0, \ldots , k-1 \\ ~~~ ~~~ ~~~ \gamma_{i,j} := \alpha_{i,p} \beta_{p,j} + \gamma_{i,j} \\ ~~~ ~~~ {\bf end} \\ ~~~ {\bf end} \\ {\bf end} \end{array} \end{equation*}
This pseudo-code translates into the routine coded in C given in Figure 1.1.1.
Unit 1.3.2$C$$A$$B$
\begin{equation*} C = \left(\begin{array}{c | c | c | c} \gamma_{0,0} \amp \gamma_{0,1} \amp \cdots \amp \gamma_{0,n-1} \\ \hline \gamma_{1,0} \amp \gamma_{1,1} \amp \cdots \amp \gamma_{1,n-1} \\ \hline \vdots \amp \amp \vdots \\ \hline \gamma_{m-1,0} \amp \gamma_{m-1,1} \amp \cdots \amp \gamma_{m-1,n-1} \end{array} \right), \quad A = \left(\begin{array}{c} \widetilde a_0^T \\ \hline \widetilde a_1^T \\ \hline \vdots \\ \hline \widetilde a_{m-1}^T \end{array}\right), \quad \mbox{and } B = \left(\begin{array}{c | c | c | c} b_0 \amp b_1 \amp \cdots \amp b_{n-1} \end{array} \right). \end{equation*}
We then notice that
\begin{equation*} \begin{array}{l} \left(\begin{array}{c | c | c | c} \gamma_{0,0} \amp \gamma_{0,1} \amp \cdots \amp \gamma_{0,n-1} \\ \hline \gamma_{1,0} \amp \gamma_{1,1} \amp \cdots \amp \gamma_{1,n-1} \\ \hline \vdots \amp \vdots \amp \amp \vdots \\ \hline \gamma_{m-1,0} \amp \gamma_{m-1,1} \amp \cdots \amp \gamma_{m-1,n-1} \end{array} \right) \\ ~~~:= \left(\begin{array}{c} \widetilde a_0^T \\ \hline \widetilde a_1^T \\ \hline \vdots \\ \hline \widetilde a_{m-1}^T \end{array}\right)\left(\begin{array}{c | c | c | c} b_0 \amp b_1 \amp \cdots \amp b_{n-1} \end{array} \right) + \left(\begin{array}{c | c | c | c} \gamma_{0,0} \amp \gamma_{0,1} \amp \cdots \amp \gamma_{0,n-1} \\ \hline \gamma_{1,0} \amp \gamma_{1,1} \amp \cdots \amp \gamma_{1,n-1} \\ \hline \vdots \amp \vdots \amp \amp \vdots \\ \hline \gamma_{m-1,0} \amp \gamma_{m-1,1} \amp \cdots \amp \gamma_{m-1,n-1} \end{array} \right)\\ ~~~= \left(\begin{array}{c | c | c | c} \widetilde a_0^T b_0 + \gamma_{0,0} \amp \widetilde a_0^T b_1 + \gamma_{0,1} \amp \cdots \amp \widetilde a_0^T b_{n-1} + \gamma_{0,n-1} \\ \hline \widetilde a_1^T b_0 + \gamma_{1,0} \amp \widetilde a_1^T b_1 + \gamma_{1,1} \amp \cdots \amp \widetilde a_1^T b_{n-1} + \gamma_{1,n-1} \\ \hline \vdots \amp \vdots \amp \amp \vdots \\ \hline \widetilde a_{m-1}^T b_0 + \gamma_{m-1,0} \amp \widetilde a_{m-1}^T b_1 + \gamma_{m-1,1} \amp \cdots \amp \widetilde a_{m-1}^T b_{n-1} + \gamma_{m-1,n-1} \end{array} \right). \end{array} \end{equation*}
If this makes your head spin, you will want to quickly go through Weeks 3-5 of our MOOC titled "Linear Algebra: Foundations to Fontiers,.'' which is an introductory undergraduate course. It captures that the outer two loops visit all of the elements in $C \text{,}$ and the inner loop implements the dot product of the appropriate row of $A$ with the appropriate column of $B \text{:}$ $\gamma_{i,j} := \widetilde a_i^T b_j + \gamma_{i,j} \text{,}$ as illustrated by
\begin{equation*} \begin{array}{l} {\bf for~} i := 0, \ldots , m-1 \\ ~~~ {\bf for~} j := 0, \ldots , n-1 \\[0.15in] ~~~ ~~~ \left. \begin{array}{l} {\bf for~} p := 0, \ldots , k-1 \\ ~~~ ~~~ \gamma_{i,j} := \alpha_{i,p} \beta_{p,j} + \gamma_{i,j} \\ {\bf end} \end{array} \right\} ~~~\gamma_{i,j} := \widetilde a_i^T b_j + \gamma_{i,j} \\[0.2in] ~~~ {\bf end} \\ {\bf end} \end{array} \end{equation*}
which is, again, the IJP ordering of the loops.
###### Homework1.3.3
In directory Assignments/Week1/C copy file Assignments/Week1/C/Gemm_IJ_Dots.c into file Gemm_IJ_ddotxv.c. Replace the call to Dots to a call to the BLIS routine bli_bli_ddotxv, and compile and execute them with
make IJ_bli_ddotxv
View the resulting performance by making the necessary changes to the Live Script in Assignments/Week1/C/data/Plot_Inner_P.mlx. (Alternatively, use the script in Assignments/Week1/C/data/Plot_Inner_P_m.mlx.)
Obviously, one can equally well switch the order of the outer two loops, which just means that the elements of $C$ are computed a column at a time rather than a row at a time:
\begin{equation*} \begin{array}{l} {\bf for~} j := 0, \ldots , n-1 \\ ~~~ {\bf for~} i := 0, \ldots , m-1 \\[0.15in] ~~~ ~~~ \left. \begin{array}{l} {\bf for~} p := 0, \ldots , k-1 \\ ~~~ ~~~ \gamma_{i,j} := \alpha_{i,p} \beta_{p,j} + \gamma_{i,j} \\ {\bf end} \end{array} \right\} ~~~\gamma_{i,j} := \widetilde a_i^T b_j + \gamma_{i,j} \\[0.2in] ~~~ {\bf end} \\ {\bf end} \end{array} \end{equation*}
###### Homework1.3.4
Repeat the last exercises with the implementation in Assignments/Week1/C/Gemm_JIP.c. In other words, copy this file into files Gemm_JI_Dots.c, Gemm_JI_ddot.c, and Gemm_JI_bli_ddotxv.c. Make the necessary changes to these file, and compile and execute them with
make JI_Dots
make JI_ddot
make JI_bli_ddotxv
View the resulting performance with the Live Script in Assignments/Week1/C/data/Plot_Inner_P.mlx. (Alternatively, use the script in Assignments/Week1/C/data/Plot_Inner_P_m.mlx.)
In Figure~\ref{fig:IJP_JIP} we report the performance of the various implementations from the last homeworks. What we notice is that, at least when using Apple's clang compiler, not much difference results from hiding the inner-most loop in a subroutine.
### Unit1.3.5The axpy operations
Given a scalar, $\alpha \text{,}$ and two vectors, $x$ and $y \text{,}$ of size $n$ with elements
\begin{equation*} x = \left( \begin{array}{c c c c} \chi_0 \\ \chi_1 \\ \vdots \\ \chi_{n-1} \end{array} \right) \quad \mbox{and} \quad y = \left( \begin{array}{c c c c} \psi_0 \\ \psi_1 \\ \vdots \\ \psi_{n-1} \end{array} \right), \end{equation*}
\begin{equation*} y := \alpha x + y \end{equation*}
which in terms of the elements of the vectors equals
\begin{equation*} \left( \begin{array}{c c c c} \psi_0 \\ \psi_1 \\ \vdots \\ \psi_{n-1} \end{array} \right) := \alpha \left( \begin{array}{c c c c} \chi_0 \\ \chi_1 \\ \vdots \\ \chi_{n-1} \end{array} \right) + \left( \begin{array}{c c c c} \psi_0 \\ \psi_1 \\ \vdots \\ \psi_{n-1} \end{array} \right) = \left( \begin{array}{c c c c} \alpha \chi_0 + \psi_0 \\ \alpha \chi_1 + \psi_1 \\ \vdots \\ \alpha \chi_{n-1} + \psi_{n-1} \end{array} \right). \end{equation*}
The name axpy comes from the fact that in Fortran 77 only six characters and numbers could be used to designate the names of variables and functions. The operation $\alpha x + y$ can be read out loud as "scalar apha times x plus y" which yields the acronym axpy.
An outline for a routine that implements the axpy operation is given by
#define chi( i ) x[ (i)*incx ] // map chi( i ) to array x
#define psi( i ) y[ (i)*incy ] // map psi( i ) to array y
void Axpy( int n, double alpha, double *x, int incx, double *y, int incy )
{
for ( int i=0; i<n; i++ )
psi(i) +=
}
The BLAS include a function for computing the axpy operation. Its calling sequence in Fortran, for double precision data, is
DAXPY( N, ALPHA, X, INCX, Y, INCY )
where
• (input) N is the address of the integer that equals the size of the vectors.
• (input) ALPHA is the address where $\alpha$ is stored.
• (input) X is the address where $x$ is stored.
• (input) INCX is the address where the stride between entries of $x$ is stored.
• (input/output) Y is the address where $y$ is stored.
• (input) INCY is the address where the stride between entries of $y$ is stored.
It may appear strange that the addresses of N, ALPHA, INCX, and INCY are passed in. This is because Fortran passes parameters by address rather than value.) If the datatype were single precision, complex double precision, or complex single precision, then the first D is replaced by S, Z, or C, respectively.
In C, the call
Axpy( n, alpha, x, incx, y, incy );
translates to
daxpy_( &n, &alpha, x, &incx, y, &incy );
which links to the Fortran interface. Notice that the scalar parameters n, alpha, incx, and incy are passed "by address" because Fortran passes parameters to subroutines by address. We will see examples of its use later in this section.
The BLIS native routine for axpy is bli_dapyv. The call
Axpy( n, alpha, x, incx, y, incy );
translates to
bli_daxpyv( BLIS_NO_CONJUGATE, n, alpha, x, incx, y, incy );
The BLIS_NO_CONJUGATE is to indicate that vector $x$ is not to be conjugated. That parameter is there for consistency with the complex versions of this routine (bli_zaxpyv and bli_caxpyv).
In an implementation of the algorithm for computing $C := A B + C$ given by
\begin{equation*} \begin{array}{l} {\bf for~} i := 0, \ldots , m-1 \\ ~~~ {\bf for~} p := 0, \ldots , k-1 \\[0.05in] ~~~ ~~~ \left. \begin{array}{l} {\bf for~} j := 0, \ldots , n-1 \\ ~~~ ~~~ \gamma_{i,j} := \alpha_{i,p} \beta_{p,j} + \gamma_{i,j} \\ {\bf end} \end{array} \right\} ~~~ \widetilde c_i^T := \alpha_{i,p} \widetilde b_p^T + \widetilde c_i \\[0.1in] ~~~ {\bf end} \\ {\bf end} \end{array} \end{equation*}
and illustrated by
\begin{equation*} \begin{array}{rcl} \left(\begin{array}{c} \widetilde c_0^T \\ \hline \widetilde c_1^T \\ \hline \vdots \\ \hline \widetilde c_{m-1}^T \end{array}\right) := \left(\begin{array}{ccrcrcrcr} \widetilde c_0^T \amp+\amp \alpha_{0,0} \widehat b_0^T \amp+\amp \alpha_{0,1} \widehat b_1^T \amp+\amp \cdots \amp+\amp \alpha_{0,k-1} \widehat b_{k-1}^T \\ \hline \widetilde c_1^T \amp+\amp \alpha_{1,0} \widehat b_0^T \amp+\amp \alpha_{1,1} \widehat b_1^T \amp+\amp \cdots \amp+\amp \alpha_{1,k-1} \widehat b_{k-1}^T \\ \hline \amp\amp\amp\vdots\amp \\ \hline \widetilde c_{m-1}^T \amp+\amp \alpha_{m-1,0} \widehat b_0^T \amp+\amp \alpha_{m-1,1} \widehat b_1^T \amp+\amp \cdots \amp+\amp \alpha_{m-1,k-1} \widehat b_{k-1}^T \end{array}\right) \end{array} \end{equation*}
one can now replace the loop indexed by $j$ with a call to Axpy.
###### Homework1.3.6
Complete the following routine
#define alpha( i,j ) A[ (j)*ldA + i ] // map alpha( i,j ) to array A
#define beta( i,j ) B[ (j)*ldB + i ] // map beta( i,j ) to array B
#define gamma( i,j ) C[ (j)*ldC + i ] // map gamma( i,j ) to array C
void Axpy( int, double, double *, int, double *, int );
void MyGemm( int m, int n, int k, double *A, int ldA,
double *B, int ldB, double *C, int ldC )
{
for ( int i=0; i<m; i++ )
for ( int p=0; p<k; p++ )
Axpy( n, alpha( i,p ), &beta( p,0 ), ldB, &gamma( i,0 ), ldC );
}
You can find the partial implementation in Assignments/Week1/C/Gemm_IP_Axpy.c test the implementation with Live Script TestGemm_IP_Axpy.mlx.
### Unit1.3.6The IPJ and PIJ orderings
What we notice is that there are $3!$ ways of order the loops: Three choices for the outer loop, two for the second loop, and one choice for the final loop. Let's consider the IPJ ordering:
\begin{equation*} \begin{array}{l} {\bf for~} i := 0, \ldots , m-1 \\ ~~~ {\bf for~} p := 0, \ldots , k-1 \\ ~~~ ~~~ {\bf for~} j := 0, \ldots , n-1 \\ ~~~ ~~~ ~~~ \gamma_{i,j} := \alpha_{i,p} \beta_{p,j} + \gamma_{i,j} \\ ~~~ ~~~ {\bf end} \\ ~~~ {\bf end} \\ {\bf end} \end{array} \end{equation*}
One way to think of the above algorithm is to view matrix $C$ as its rows, matrix $A$ as its individual elements, and matrix $B$ as its rows:
\begin{equation*} C = \left(\begin{array}{c} \widetilde c_0^T \\ \hline \widetilde c_1^T \\ \hline \vdots \\ \hline \widetilde c_{m-1}^T \end{array}\right), \quad A = \left(\begin{array}{c | c | c | c} \alpha_{0,0} \amp \alpha_{0,1} \amp \cdots \amp \alpha_{0,k-1} \\ \hline \alpha_{1,0} \amp \alpha_{1,1} \amp \cdots \amp \alpha_{1,k-1} \\ \hline \vdots \amp \vdots\amp \amp \vdots \\ \hline \alpha_{m-1,0} \amp \alpha_{m-1,1} \amp \cdots \amp \alpha_{m-1,k-1} \end{array} \right), \quad \mbox{and} \quad B = \left(\begin{array}{c} \widetilde b_0^T \\ \hline \widetilde b_1^T \\ \hline \vdots \\ \hline \widetilde b_{k-1}^T \end{array}\right). \end{equation*}
We then notice that
\begin{equation*} \begin{array}{rcl} \left(\begin{array}{c} \widetilde c_0^T \\ \hline \widetilde c_1^T \\ \hline \vdots \\ \hline \widetilde c_{m-1}^T \end{array}\right) \amp:=\amp \left(\begin{array}{c | c | c | c} \alpha_{0,0} \amp \alpha_{0,1} \amp \cdots \amp \alpha_{0,k-1} \\ \hline \alpha_{1,0} \amp \alpha_{1,1} \amp \cdots \amp \alpha_{1,k-1} \\ \hline \vdots \amp \vdots \amp \amp \vdots \\ \hline \alpha_{m-1,0} \amp \alpha_{m-1,1} \amp \cdots \amp \alpha_{m-1,k-1} \end{array} \right) \left(\begin{array}{c} \widetilde b_0^T \\ \hline \widetilde b_1^T \\ \hline \vdots \\ \hline \widetilde b_{k-1}^T \end{array}\right) + \left(\begin{array}{c} \widetilde c_0^T \\ \hline \widetilde c_1^T \\ \hline \vdots \\ \hline \widetilde c_{m-1}^T \end{array}\right)\\ \amp=\amp \left(\begin{array}{ccrcrcrcr} \widetilde c_0^T \amp+\amp \alpha_{0,0} \widehat b_0^T \amp+\amp \alpha_{0,1} \widehat b_1^T \amp+\amp \cdots \amp+\amp \alpha_{0,k-1} \widehat b_{k-1}^T \\ \hline \widetilde c_1^T \amp+\amp \alpha_{1,0} \widehat b_0^T \amp+\amp \alpha_{1,1} \widehat b_1^T \amp+\amp \cdots \amp+\amp \alpha_{1,k-1} \widehat b_{k-1}^T \\ \hline \amp\amp\amp\vdots\amp \\ \hline \widetilde c_{m-1}^T \amp+\amp \alpha_{m-1,0} \widehat b_0^T \amp+\amp \alpha_{m-1,1} \widehat b_1^T \amp+\amp \cdots \amp+\amp \alpha_{m-1,k-1} \widehat b_{k-1}^T \end{array}\right). \end{array} \end{equation*}
This captures that the outer two loops visit all of the elements in $A \text{,}$ and the inner loop implements the updating of the $i$th row of $C$ by adding $\alpha_{i,p}$ times the $p$th row of $B$ to it, as captured by
\begin{equation*} \begin{array}{l} {\bf for~} i := 0, \ldots , m-1 \\ ~~~ {\bf for~} p := 0, \ldots , k-1 \\[0.15in] ~~~ ~~~ \left. \begin{array}{l} {\bf for~} j := 0, \ldots , n-1 \\ ~~~ ~~~ \gamma_{i,j} := \alpha_{i,p} \beta_{p,j} + \gamma_{i,j} \\ {\bf end} \end{array} \right\} ~~~ \widetilde c_i^T := \alpha_{i,p} \widetilde b_p^T + \widetilde c_i \\[0.2in] ~~~ {\bf end} \\ {\bf end} \end{array} \end{equation*}
###### Homework1.3.8
In directory Assignments/Week1/C copy file Assignments/Week1/ into file Gemm_IP_daxpy.c. Replace the inner-most loop with a call to the BLAS routine daxpy, and compile and execute them with
make IP_daxpy
View the resulting performance by making the necessary changes to the Live Script in Assignments/Week1/C/data/Plot_Inner_J.mlx. (Alternatively, use the script in Assignments/Week1/C/data/Plot_Inner_J_m.mlx.)
###### Homework1.3.9
In directory Assignments/Week1/C copy file Assignments/Week1/ into file Gemm_IP_bli_daxpyv.c, and compile and execute with
make IP_bli_daxpyv
Replace the inner-most loop with a call to the BLIS routine bli_daxpyv. View the resulting performance by making the necessary changes to the Live Script in Assignments/Week1/C/data/Plot_Inner_J.mlx. (Alternatively, use the script in Assignments/Week1/C/data/Plot_Inner_J_m.mlx.)
One can switch the order of the outer two loops to get
\begin{equation*} \begin{array}{l} {\bf for~} p := 0, \ldots , k-1 \\ ~~~ {\bf for~} i := 0, \ldots , m-1 \\[0.15in] ~~~ ~~~ \left. \begin{array}{l} {\bf for~} j := 0, \ldots , n-1 \\ ~~~ ~~~ \gamma_{i,j} := \alpha_{i,p} \beta_{p,j} + \gamma_{i,j} \\ {\bf end} \end{array} \right\} ~~~ \widetilde c_i^T := \alpha_{i,p} \widetilde b_p^T + \widetilde c_i^T \\[0.2in] ~~~ {\bf end} \\ {\bf end} \end{array} \end{equation*}
The outer loop in this second algorithm fixes the row of $B$ that is used to to update all rows of $C \text{,}$ using the appropriate element from $A$ to scale. In the first iteration of the outer loop ($p = 0$), the following computations occur:
In the second iteration of the outer loop ($p = 1$) it computes
and so forth.
###### Homework1.3.10
Repeat the last exercises with the implementation in Assignments/Week1/C/Gemm_PIJ.c. In other words, copy this file into files Gemm_PI_Axpy.c, Gemm_PI_daxpy.c, and Gemm_PI_bli_daxpyv.c. Make the necessary changes to these files, and compile and execute them with
make PI_Axpy
make PI_daxpy
make PI_bli_daxpyv
View the resulting performance with the Live Script in Assignments/Week1/C/data/Plot_Inner_J.mlx. (Alternatively, use the script in Assignments/Week1/C/data/Plot_Inner_J_m.mlx.)
### Unit1.3.7The JPI and PJI orderings
Let us consider the JPI ordering:
\begin{equation*} \begin{array}{l} {\bf for~} j := 0, \ldots , n-1 \\ ~~~ {\bf for~} p := 0, \ldots , k-1 \\ ~~~ ~~~ {\bf for~} i := 0, \ldots , m-1 \\ ~~~ ~~~ ~~~ \gamma_{i,j} := \alpha_{i,p} \beta_{p,j} + \gamma_{i,j} \\ ~~~ ~~~ {\bf end} \\ ~~~ {\bf end} \\ {\bf end} \end{array} \end{equation*}
Another way to think of the above algorithm is to view matrix $C$ as its columns, matrix $A$ as its columns, and matrix $B$ as its individual elements. Then
\begin{equation*} \begin{array}{l} \left(\begin{array}{c | c | c | c} c_0 \amp c_1 \amp \cdots \amp c_{n-1} \end{array}\right) := \\ ~~~ \left(\begin{array}{c | c | c | c} a_0 \amp a_1 \amp \cdots \amp a_{k-1} \end{array} \right) \left(\begin{array}{c | c | c | c} \beta_{0,0} \amp \beta_{0,1} \amp \cdots \amp \beta_{0,n-1} \\ \hline \beta_{1,0} \amp \beta_{1,1} \amp \cdots \amp \beta_{1,n-1} \\ \hline \vdots \amp \vdots\amp \amp \vdots \\ \hline \beta_{k-1,0} \amp \beta_{k-1,1} \amp \cdots \amp \beta_{k-1,n-1} \end{array} \right) + \left(\begin{array}{c | c | c | c} c_0 \amp c_1 \amp \cdots \amp c_{n-1} \end{array}\right) . \end{array} \end{equation*}
so that
\begin{equation*} \begin{array}{l} \left(\begin{array}{c | c | c | c} c_0 \amp c_1 \amp \cdots \amp c_{n-1} \end{array}\right) := \\ ~~~ \left(\begin{array}{c | c | c | c} c_0 + \beta_{0,0} a_0 + \beta_{1,0} a_1 + \cdots \amp c_1 + \beta_{0,1} a_0 + \beta_{1,1} a_1 + \cdots \amp \cdots \amp c_{n-1} + \beta_{0,n-1} a_0 + \beta_{1,n-1} a_1 + \cdots \end{array}\right) . \end{array} \end{equation*}
The algorithm captures this as
\begin{equation*} \begin{array}{l} {\bf for~} j := 0, \ldots , n-1 \\ ~~~ {\bf for~} p := 0, \ldots , k-1 \\[0.15in] ~~~ ~~~ \left. \begin{array}{l} {\bf for~} i := 0, \ldots , m-1 \\ ~~~ ~~~ \gamma_{i,j} := \alpha_{i,p} \beta_{p,j} + \gamma_{i,j} \\ {\bf end} \end{array} \right\} ~~~ c_j := \beta_{p,j} a_p + c_j \\[0.2in] ~~~ {\bf end} \\ {\bf end} \end{array} \end{equation*}
###### Homework1.3.11
In directory Assignments/Week1/C copy file Assignments/Week1/C/Gemm_JPI.c into file Gemm_JP_Axpy.c. Replace the inner-most loop with a call to Axpy, and compile and execute with
make JP_Axpy
View the resulting performance by making the necessary changes to the Live Script in Assignments/Week1/C/data/Plot_Inner_I.mlxdata/Plot_Inner_I.mlx. (Alternatively, use the script in Assignments/Week1/C/data/Plot_Inner_I_m.mlx.)
###### Homework1.3.12
In directory Assignments/Week1/C copy file Assignments/Week1/C/Gemm_JPI.c into file Gemm_JP_daxpy.c. Replace the inner-most loop with a call to the BLAS routine daxpy, and compile and execute with
make JP_daxpy
View the resulting performance by making the necessary changes to the Live Script in Assignments/Week1/C/data/Plot_Inner_I.mlx. (Alternatively, use the script in Assignments/Week1/C/data/Plot_Inner_I_m.mlx.)
###### Homework1.3.13
In directory Assignments/Week1/C copy file Assignments/Week1/C/Gemm_JPI.c into file Gemm_JP_bli_daxpyv.c. Replace the inner-most loop with a call to the BLIS routine bli_daxpyv, and compile and execute with
make JP_bli_daxpyv
View the resulting performance by making the necessary changes to the Live Script in Assignments/Week1/C/data/Plot_Inner_I.mlx. (Alternatively, use the script in Assignments/Week1/C/data/Plot_Inner_I_m.mlx.)
One can switch the order of the outer two loops to get
\begin{equation*} \begin{array}{l} {\bf for~} p := 0, \ldots , k-1 \\ ~~~ {\bf for~} j := 0, \ldots , n-1 \\[0.15in] ~~~ ~~~ \left. \begin{array}{l} {\bf for~} i := 0, \ldots , m-1 \\ ~~~ ~~~ \gamma_{i,j} := \alpha_{i,p} \beta_{p,j} + \gamma_{i,j} \\ {\bf end} \end{array} \right\} ~~~ c_j := \beta_{p,j} a_p + c_j \\[0.2in] ~~~ {\bf end} \\ {\bf end} \end{array} \end{equation*}
The outer loop in this algorithm fixes the column of $A$ that is used to to update all columns of $C \text{,}$ using the appropriate element from $B$ to scale. In the first iteration of the outer loop, the following computations occur:
In the second iteration of the outer loop it computes
and so forth.
###### Homework1.3.14
Repeat the last exercises with the implementation in Assignments/Week1/C/Gemm_PJI.c. In other words, copy this file into files Gemm_PJ_Axpy.c, Gemm_PJ_daxpy.c, and Gemm_PJ_bli_daxpyv.c. Then, make the necessary changes to these files, and compile and execute with
make PJ_Axpy
make PJ_daxpy
make PJ_bli_daxpyv
View the resulting performance by making the necessary changes to the Live Script in Assignments/Week1/C/data/Plot_Inner_I.mlx. (Alternatively, use the script in Assignments/Week1/C/data/Plot_Inner_I_m.mlx.)
The purpose of this section was mostly to help you think in terms of operations with vectors (the rows and columns of the matrices) when reasoning about, and implementing, the inner-most loop of the different algorithms for computing a matrix-matrix multiplication. On Robert's laptop, the performance is not much affected. For this reason, in the below exercise, we revisit the performance graphs for the different loop orderings from Section~\ref{sec:AllOrderings}.
### Unit1.3.8Discussion
###### Homework1.3.15
In Figure 1.3.3, the results of Homework 1.2.5 on Robert's laptop are again reported. What do the two loop orderings that result in the best performances have in common? You may want to use the following worksheet to answer this question:
Solution
They both have the loop indexed with $i$ as the inner-most loop and that loop computes with columns of $C$ and $A \text{.}$
###### Homework1.3.16
In Homework 1.3.15, why do they get better performance?
Solution
Matrices are stored with column major order, accessing contiguous data usually yields better performance, and data in columns are stored contiguously.
###### Homework1.3.17
In Homework 1.3.15, why does the implementation that gets the best performance outperform the one that gets the next to best performance?
Solution
The JPI loop ordering accesses columns of C and A in the inner loop. The column of C is read and written while the column of A is only read. The column of C is read and written while the column of A is only read. The JPI loop ordering keeps the column of C in cache memory which reduced the number of times it is read from and written to main memory.
###### Remark1.3.5
One thing that is obvious from all the exercises so far is that the gcc compiler doesn't do a very good job of automatically reordering loops to improve performance, at least not for the way we are writing the code. | 2019-01-22 05:56:45 | {"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": 1.0000040531158447, "perplexity": 4847.7578279614845}, "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-2019-04/segments/1547583829665.84/warc/CC-MAIN-20190122054634-20190122080634-00205.warc.gz"} |
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English Medium from Greek words trigonon ( three angles ) and metron ( measure ) and projects with! | 2021-06-22 08:50:04 | {"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": 0.4320359230041504, "perplexity": 2323.942124131145}, "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/1623488512243.88/warc/CC-MAIN-20210622063335-20210622093335-00248.warc.gz"} |
https://homework.cpm.org/cpm-homework/homework/category/CC/textbook/CCA/chapter/Ch10/lesson/10.3.2/problem/10-128 | Home > CCA > Chapter Ch10 > Lesson 10.3.2 > Problem10-128
10-128.
Multiple Choice: Which of the lines below is parallel to the line $5x−3y=11$? Homework Help ✎
1. $5x−3y=4$
1. $5x+3y=−2$
1. $3x−5y=11$
1. $3x+5y=−1$
Write each equation in $y=mx+b$ form, including the original equation.
Which one has the same slope as the original equation? | 2020-04-04 06:49:34 | {"extraction_info": {"found_math": true, "script_math_tex": 6, "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": 0.7242050170898438, "perplexity": 2004.4428945046911}, "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-2020-16/segments/1585370520039.50/warc/CC-MAIN-20200404042338-20200404072338-00429.warc.gz"} |
http://www.gamedev.net/topic/646105-another-neat-tool-ant-its-better-than-batch-files/ | • Create Account
# Another Neat Tool (ANT): It's better than batch files :)
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### #1AngleWyrm Members - Reputation: 551
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Posted 31 July 2013 - 11:48 PM
So there I was, just a hackin' and a codin' a mod for Minecraft in Eclipse. And at the end, there's a bunch of stuff to do: Run a couple special external tools, relocate a bunch of files into a new folder tree, and then zip them up, add comments to the zip file, and so on. And I had a pretty cool batch file to do all that. Then someone showed me ANT, and I'm sold.
Ant does all the stuff I was doing, but much more elegantly. The tool uses an xml file, usually called build.xml, and it looks like this:
<project>
<target>
<!-- do some stuff -->
</target>
<target>
<!-- do some other stuff -->
</target>
</project>
The build.xml that I made for my Minecraft modding endeavors looks like so:
Spoiler
It can do advanced stuff, like substituting a token string during a copy operation. Within my source files is @VERSION@, but when copied by the build.xml, that string gets replaced.
Edited by AngleWyrm, 31 July 2013 - 11:54 PM.
--"I'm not at home right now, but" = lights on, but no ones home | 2013-12-10 14:03:00 | {"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": 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": 0.20102865993976593, "perplexity": 4008.609712675933}, "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-2013-48/segments/1386164019989/warc/CC-MAIN-20131204133339-00099-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://www.nature.com/articles/s41598-018-30515-5?error=cookies_not_supported | ## Introduction
For decades, important advances in microbial ecology and many other fields, have been achieved thanks to the possibility of studying microbial communities by characterizing their genetic information. While the 16S rRNA gene has been widely accepted as a biological fingerprint for bacterial species, it presents some limitations. Many bacterial species have multiple 16S rRNA gene copies, leading to an artificial diversity overrepresentation1. Between some bacterial species, there are no significant differences in their 16S rRNA genes, but other genomic elements will confer them important features that will differentiate them as pathogens or harmless free-living organisms2,3. Other technical considerations regarding the characterization of the 16S rRNA gene, are primer and amplification biases4, chimera formation4,5 and other artifacts that make difficult the assessment of the real community structure, like the microheterogeneity of sequences between closely related strains, or the similarity of sequences between non-closely related species.
The use of high-throughput sequencing technologies has allowed the analysis of very complex environmental samples either by 16S rRNA gene amplification or Whole Metagenome Shotgun (WMS) sequencing which could retrieve the genomic information from all the organisms present in the sample. Also, bioinformatics tools have been redesigned to cope with the massive amount of data generated by high-throughput sequencing technologies. Advantages and limitations of sequencing strategies and metagenomic analysis software have been vastly described before4,6,7,8,9,10,11. However, the selection of sequencing or bioinformatic approaches for any project, remains a challenge due to several factors such as the constant change of sequencing technologies, database updating and rapid software development.
Arguably, the biggest challenge is the reduction of introduced biases in metagenomic studies. Sample handling and preservation12,13,14; DNA extraction technical issues15; sequencing technology artifacts6,10,16 and bioinformatic analysis limitations17 contribute to analysis biases.
To understand these problems and to elucidate the origin of different biases in a real sample, it is necessary to analyze the contribution of individual variables to a certain bias. These biases could be reflected either in an over- or underestimation of diversity depending on the sample handling variables and software parameters used in the sequences analysis. There are few reference datasets18,19,20 which can be used as a gold standard for every metagenomic project, allowing the control of different variables to evaluate tools impartially. Researchers have to select one of the many available tools or develop a new one to analyze their metagenomic data. Usually, even if a benchmark is performed comparing different tools, authors often use distinct metrics to evaluate the method performance. Also, benchmark results will vary if databases change or the software parameters or version change.
Here, we performed an objective comparison based on performance statistical measures of classification and error rate at different taxonomic levels. We used three in silico datasets for WMS and V3-V4 16S rRNA amplicon Illumina simulated reads, to evaluate eight different bioinformatic tools and seven public databases. We standardize the taxonomic annotation lineage by correcting all results based on the NCBI taxonomy database. Additionally, we report coverages and cut-off score values at different error rates for all tested methods.
Our goal is to contribute to standards and metric definition for metagenomic analysis through a standardized benchmark framework to constantly evaluate sequencing strategies, taxonomic profiling tools and databases.
## Materials and Methods
In this work, we chose a set of tools, used for taxonomic annotation of metagenomic samples, that could be installed in a local computer server. We used a 64 core/512 Gb of RAM PC server, using Ubuntu 16.04 Linux distribution, to perform all of the present work.
The performance of each program was evaluated with in silico sequences generated to simulate Illumina reads for whole metagenome shotgun (WMS) and amplicons from the V3-V4 variable region of 16S rRNA gene, in triplicate. We estimated, through error type and coverage calculation, the bias due to either the algorithm or the database used at different taxonomic levels from phylum to subspecies.
### In silico datasets for WMS and 16S rRNA profiling
Datasets for WMS analysis were obtained from the data published by Lindgreen et al.17 In order to obtain triplicate information, we choose the A1, A2 and A3 datasets which originally contained bacterial, archaea and eukarya genomes. However, in order to delimit our analysis, we removed eukaryotic genomes since the evaluated programs were not designed to evaluate eukaryotic information. Each dataset (A1, 673 genomes; A2, 678 genomes and A3, 674 genomes) had in silico simulated paired-end sequences of 100 bp length for each species genome. Lindgreen datasets also include divergent “shuffled” sequences from some species that are not supposed to be annotated (true negatives) and simulated reads with variable evolutionary distances generated by phylogenetic modelling to mimic nonexistent close relatives from Leptospira interrogans genome, which are expected to be classified somewhere on the Leptospira taxonomic lineage but not necessarily at genus or species levels. Sequences can be found at http://www.ucbioinformatics.org/metabenchmark.html.
To evaluate the performance of each program with amplicon datasets, we generated three amplicon libraries from V3-V4 variable regions of ribosomal 16S rRNA gene using the Grinder v0.5.4 software21. For in silico PCR we used primers S-D-Bact-0341-b-S-17 and S-D-Bact-0785-a-A-2122 and, as template, we extract the 16 S ribosomal sequences from the gbk files of the 840 bacterial genomes used by Lindgreen et al.17. Amplicon libraries shared the 90% of reference sequences and were constructed simulating 750,000 paired-end reads of 300 bp length using a linear abundance model and a per-base quality fixed in 30 Phred score. Additionally, we include in each library a set of 37,500 unclassifiable homemade shuffled sequences to assess as true negatives. The amplicons were rebuilt by Flash v1.2.1123 and extended fragments were used to perform the taxonomic annotation. Sequences are available at https://github.com/Ales-ibt/Metagenomic-benchmark.
### Taxonomic classification software
Four open source bioinformatic tools for WMS data24,25,26,27 and four different software for amplicon sequences28,29,30,31 were tested. In the particular case of Kraken and CLARK, specific databases based on k-mer spectra from RefSeq genomes were used. Uclust algorithm was used for clustering in QIIME pipeline as it is the default option. All methods based on ribosomal sequences annotation were tested using the main databases publicly available: Ribosomal Database Project (RDP) v11.532 available at https://rdp.cme.msu.edu/misc/resources.jsp; SILVA v12833 can be downloaded from https://www.arb-silva.de/no_cache/download/archive/release_128/; GreenGenes (GG) v13.534 from http://greengenes.secondgenome.com/downloads/database/13_5 as well as Metaxa2 database (MTX)31 that is included in the Metaxa2 software package. The database version could change if the program includes its own database with the software distribution as in the case of Parallel-meta. Specifications about the software tested are described in Supplementary Table 1.
### Software performance evaluation
To evaluate the different methods of analysis for both amplicons and WMS, we performed a binary classification test of TRUE or FALSE assignments per read comparing the taxid of the expected lineage against the taxid of the taxonomic annotation at every taxonomic level (domain, phylum, class, order, family, genus, species and subspecies). The TRUE ratings could be due to a correct taxonomic identification, i.e. a true positive annotation (TP); or a non-classification of a “shuffled” sequence, i.e. a true negative (TN). A FALSE classification means a misclassification that implies an erroneous annotation, i.e. a false positive (FP); or a non-classification at an specific taxonomic level, that means a false negative (FN). If we have a correct booked assignment up to family level, the table for this read looks like: TP, TP, TP, TP, TP, FN, FN, FN. However, in the case of a correct annotation to family level but erroneous genus level, we fill the table with TP, TP, TP, TP, TP, FP, FP, FP. Therefore, we are capable to differentiate between non-classification and misclassification at each taxonomic level. In the case of WMS data, the universe of classifiable sequences depends on the annotator approach (reads comparison with phylogenetic markers or k-mer spectra), The selection of the taxonomically informative sequences, depends on the extraction algorithm and is different for each method. Nevertheless, the above error definition works the same for amplicon and WMS data.
With this information, we built a confusion matrix from which we calculated performance statistical measures of classification such as sensitivity, specificity, and accuracy. Additionally, we used the Matthews Correlation Coefficient (MCC) as global description of the confusion matrices but weighing the compared classes (true or false positive and negatives). Values of MCC equal to zero, indicates that a tested combination generated results as good as obtaining them by random; a negative MCC score indicates results worse than obtaining them by random35. Formula used to calculate each descriptor are below:
$$\begin{array}{c}{\bf{E}}{\bf{P}}{\bf{Q}}\,({\bf{E}}{\bf{r}}{\bf{r}}{\bf{o}}{\bf{r}}\,{\bf{P}}{\bf{e}}{\bf{r}}\,{\bf{Q}}{\bf{u}}{\bf{e}}{\bf{r}}{\bf{y}})={\bf{F}}{\bf{P}}/{\bf{T}}{\bf{o}}{\bf{t}}{\bf{a}}{\bf{l}}\,{\bf{q}}{\bf{u}}{\bf{e}}{\bf{r}}{\bf{y}}\,{\bf{n}}{\bf{u}}{\bf{m}}{\bf{b}}{\bf{e}}{\bf{r}}\\ {\bf{C}}{\bf{o}}{\bf{v}}{\bf{e}}{\bf{r}}{\bf{a}}{\bf{g}}{\bf{e}}\,({\bf{C}}{\bf{o}}{\bf{v}})={\bf{T}}{\bf{P}}/{\bf{T}}{\bf{o}}{\bf{t}}{\bf{a}}{\bf{l}}\,{\bf{e}}{\bf{x}}{\bf{p}}{\bf{e}}{\bf{c}}{\bf{t}}{\bf{e}}{\bf{d}}\,{\bf{r}}{\bf{e}}{\bf{s}}{\bf{u}}{\bf{l}}{\bf{t}}{\bf{s}}\,{\bf{n}}{\bf{u}}{\bf{m}}{\bf{b}}{\bf{e}}{\bf{r}}\\ {\bf{S}}{\bf{e}}{\bf{n}}{\bf{s}}{\bf{i}}{\bf{t}}{\bf{i}}{\bf{v}}{\bf{i}}{\bf{t}}{\bf{y}}\,({\bf{a}}.{\bf{k}}.{\bf{a}}\,{\bf{T}}{\bf{r}}{\bf{u}}{\bf{e}}\,{\bf{P}}{\bf{o}}{\bf{s}}{\bf{i}}{\bf{t}}{\bf{i}}{\bf{v}}{\bf{e}}\,{\bf{R}}{\bf{a}}{\bf{t}}{\bf{e}}\,{\bf{o}}{\bf{r}}\,{\bf{R}}{\bf{e}}{\bf{c}}{\bf{a}}{\bf{l}}{\bf{l}})={\bf{T}}{\bf{P}}/({\bf{T}}{\bf{P}}+{\bf{F}}{\bf{N}})\\ {\bf{S}}{\bf{p}}{\bf{e}}{\bf{c}}{\bf{i}}{\bf{f}}{\bf{i}}{\bf{c}}{\bf{i}}{\bf{t}}{\bf{y}}\,({\bf{a}}.{\bf{k}}.{\bf{a}}\,{\bf{T}}{\bf{r}}{\bf{u}}{\bf{e}}\,{\bf{N}}{\bf{e}}{\bf{g}}{\bf{a}}{\bf{t}}{\bf{i}}{\bf{v}}{\bf{e}}\,{\bf{R}}{\bf{a}}{\bf{t}}{\bf{e}})={\bf{T}}{\bf{N}}/({\bf{T}}{\bf{N}}+{\bf{F}}{\bf{P}})\\ {\bf{A}}{\bf{c}}{\bf{c}}{\bf{u}}{\bf{r}}{\bf{a}}{\bf{c}}{\bf{y}}\,({\bf{A}}{\bf{C}}{\bf{C}})=({\bf{T}}{\bf{P}}+{\bf{T}}{\bf{N}})/({\bf{T}}{\bf{P}}+{\bf{F}}{\bf{P}}+{\bf{F}}{\bf{N}}+{\bf{T}}{\bf{N}})\\ {\bf{M}}{\bf{a}}{\bf{t}}{\bf{t}}{\bf{h}}{\bf{e}}{\bf{w}}{\bf{s}}\,{\bf{C}}{\bf{o}}{\bf{r}}{\bf{r}}{\bf{e}}{\bf{l}}{\bf{a}}{\bf{t}}{\bf{i}}{\bf{o}}{\bf{n}}\,{\bf{C}}{\bf{o}}{\bf{e}}{\bf{f}}{\bf{f}}{\bf{i}}{\bf{c}}{\bf{i}}{\bf{e}}{\bf{n}}{\bf{t}}\,({\bf{M}}{\bf{C}}{\bf{C}})\,=\\ \,({\bf{T}}{\bf{P}}\ast {\bf{T}}{\bf{N}})-({\bf{F}}{\bf{P}}\ast {\bf{F}}{\bf{N}})/{[({\bf{T}}{\bf{P}}+{\bf{F}}{\bf{P}})({\bf{T}}{\bf{P}}+{\bf{F}}{\bf{N}})({\bf{T}}{\bf{N}}+{\bf{F}}{\bf{P}})({\bf{T}}{\bf{N}}+{\bf{F}}{\bf{N}})]}^{{\bf{1}}/{\bf{2}}}\end{array}$$
### Coverage versus error per query plots generation
We generated coverage versus error or CVEs plots. Sequences assigned by each method were ordered from best to worst according to the respective reported score, then, we summed the number of false positives in the total number of queries to obtain the Error per query (EPQ) and we plotted it against the number of true positives divided by the total number of expected results (Coverage)36,37,38. The CVE plots for each taxonomic level were elaborated using the R software39. Such graphical representation allows visualizing directly the error accumulation as a function of the proportion of sequences annotated at each taxonomic level, without needing to observe the areas under the curve. Besides, it is possible to obtain the score cut-off value where each method reaches a given error value (see Supplementary Table 2).
Each method reports a particular assignment score. In the case of Kraken, we used the k-mers percentage of allocation with respect to the reference that the program assigns for each read, in order to establish a classification score for each assignment. CLARK reports a confidence score. The ranking for Parallel-Meta was the E-value, for Metaxa2 was the reliability score and for MetaPhlAn2 and MOCAT the alignment score was taken. In the particular case of SPINGO, we rank the similarity score in the output file and in the cases where the annotation was found as AMBIGUOUS, we extracted the lowest common ancestor (LCA) from the list of reported species. All plots are available at https://github.com/Ales-ibt/Metagenomic-benchmark
### Taxonomy lineage homogenization
In order to homogenize the assignments for each method and to determine the complete lineage adjusting to fill the eight basic ranks: domain, phylum, class, order, family, genus, species, and subspecies, we used the taxid according to NCBI Taxonomy database and we parsed the information by ETE 3 python library40. The process for obtaining an integrated matrix of all methods per sample required a set of scripts written in R, bash, perl and python, which are available at https://github.com/Ales-ibt/Metagenomic-benchmark
## Results
### Score equivalence by error rate using CVE plots
We evaluated eight different methods to determine the relation between sensitivity and specificity for each tool/database combination at eight taxonomic classification levels, using simulated data for either amplicons from 16S rRNA V3-V4 regions or Whole Metagenome Shotgun (WMS) reads. Some methods were combined with different databases but others only worked using their own database (see Materials and Methods). To compare results from different methods where each one uses a different score value, we used Coverage VS Error per query (CVE) plots (available from https://github.com/Ales-ibt/Metagenomic-benchmark) to visualize the error rate and coverage associated with different score values. A better method would depict a graph with a lower slope, meaning a higher coverage at a lower error rate.
To address the great volume of generated results, we presented them in subsections from an algorithm perspective. We evaluated tools by classifying them in BLAST-alignment and BLAST-independent based methods for 16S rRNA amplicon or Whole Metagenome Shotgun data. The cut-off score, coverage and standard deviation values for each method at 1%, 5% and 10% error rate at the eight different taxonomic classification levels, can be found in Supplementary Table 1.
### BLAST-alignment based methods using 16S rRNA amplicon sequencing
We evaluated a modified version of Parallel-meta v2.4.1 (Material and Methods) and Metaxa2 v2.1.1, in combination with four different databases. As mentioned, we generated the CVEs plots at eight taxonomic levels. To observe the performance of each tool/database combination, we summarize in Fig. 1A–C the coverage results only at 1,5 and 10% error cut-off values, for all taxonomic levels.
At higher taxonomic levels (domain and phylum), Parallel-meta and Metaxa2 combinations, reported the highest coverage (>95%) even at the lowest error rate (1%). In the case of Metaxa2-SILVA combination, the coverage dropped below 25% at phylum level being the lowest value of all method/database combinations and error rates (Fig. 1A–C). In a similar trend but with a less drastic drop, Parallel-meta-GG presented lower coverage values (<90%) at phylum level, at 1 and 5% error rate (Fig. 1A,B).
However, at intermediate taxonomic levels (class to family) the only method with coverage greater than 75% and a cumulative error equal or less than 1%, was Parallel-meta in combination with SILVA, RDP and MTX databases (Fig. 1A). Interestingly, at the genus rank, the only tool-database combination that presented over ~87% of expected coverage at 1% error rate, was Parallel-meta-MTX and for this combination, at species and subspecies levels, the coverage at 1% error was the highest among all combinations.
To evaluate further, other metrics such as accuracy and specificity were used to evaluate the performance of each combination (Fig. 2A,B). Parallel-meta-GG had the lowest accuracy, even at phylum level, in contrast to Parallel-meta-MTX which presented the highest accuracy at all taxonomic levels. At the genus rank, Parallel-meta-MTX reached an accuracy of 93% followed by Metaxa2-MTX with an accuracy of 86% (Fig. 2A).
In terms of specificity, all methods presented low values at different taxonomic levels. In general, methods based on local alignment algorithms (BLAST), had a high true positives rate but also a high false positive rate. The lowest specificity values were observed at the family level, where all methods had a high number of false positives. At genus, species and subspecies ranks, the true negative rate increased gradually (Fig. 2B), consistently with the accuracy drop at these same taxonomic levels (Fig. 2A).
### BLAST-independent based methods using 16S rRNA amplicon sequencing
We tested QIIME v1.9.1 and SPINGO v1.3 programs using the same datasets and database combinatorial design than described above. We found that SPINGO neither performed well with SILVA nor with GreenGenes databases, but in combination with MTX or RDP databases had a better performance (Fig. 1D–F).
The method with the lowest performance between phylum and family taxonomic levels was QIIME-SILVA, with coverage values from 30 to 45% at 1% of error rate (Fig. 1D). At the same error rate, only QIIME using either RDP or MTX databases, presented coverage values higher than 90% at domain, phylum and class taxonomic levels. Both SPINGO and QIIME in combination with GG database, presented the highest result variation among replicates. At family and genus levels, both SPINGO-RDP, QIIME-RDP and SPINGO-MTX combinations, performed very similarly maintaining coverages above ~75%. Finally, at the genus level, both methods underperformed when combined with GG and SILVA databases (Fig. 1D).
The method with the best performance at less stringent error cut-off values (5% and 10%) was QIIME-MTX at the family and genus levels. (Fig. 1E,F). However, at the species level, the accuracy of QIIME-MTX dropped to values under 50%, similar to SPINGO-RDP combination. In general, both methods lost accuracy in their predictions in combination with SILVA database and both tools presented the highest accuracy at genus level in combination with MTX database (Fig. 2C).
### BLAST-alignment based methods using Whole Metagenome Shotgun data
We evaluated the taxonomic annotation results by the same methods but using the extraction of 16S rRNA sequences from WMS data using Parallel-meta v2.4.1 and Metaxa2 v2.1.1. As depicted in the CVE plots and their summary in Fig. 3A–C, all combinations presented a drastic coverage droppage from class to family taxonomic levels at 1% of error rate. Some combinations like Metaxa2-SILVA, Metaxa2-RDP and Parallel-meta-GG had the lowest performance at any error rate (Fig. 3A–C). At higher error rates (5 and 10%) the methods reported the highest coverage values at class, order and family levels but only in combination with the MTX database (Fig. 3B,C).
Despite the observations in CVE plots, in terms of accuracy and specificity, all methods presented high values at all taxonomic levels (Fig. 4A,B). The difference between methods were observed in terms of sensitivity. The only method with the highest sensitivity from domain to species level was Parallel-meta-MTX. Actually, both methods combined with the MTX database and with GG showed results with a sensitivity >0.75 (up to family level). In contrast, the annotations of both methods in combination with the SILVA database, had the lowest sensitivity even at phylum level (Supplementary Fig. S3).
### BLAST-independent based methods using WMS data
Methods that do not rely solely on the taxonomic information from the 16S rRNA gene, are described in this section. Two of the most popular methods based on k-mer spectra comparison, Kraken v0.10.5-beta and CLARK v1.2.3.1, were used to annotate the WMS datasets. We also analyzed two annotation methods based on single copy marker genes (SCMG), MetaPhlAn2 and MOCAT. Each SCMG method can be used only with its own database; therefore, those results have no database combinations.
MetaPhlAn2 v2.2.0 and Kraken v1.3 reported the highest coverage until genus taxonomic level (75.5% and ~89.4%, respectively) at 1% of error rate. MOCAT showed a coverage drop to ~65% and ~11% at family and genus levels, respectively. We observed an interesting trend for CLARK results, which showed a constant coverage between 60–50% from domain to species taxonomic levels. At species level, CLARK had the highest coverage in comparison to all other methods at 1% of error rate (Fig. 3D).
Using more relaxed cut-off values of 5 and 10%, Kraken and MetaPhlAn2 coverage values at species level were improved. MOCAT showed a coverage value of ~98% up to family level, while CLARK remained with a constant coverage of ~60% from phylum to species (Fig. 3E,F). In general, at 10% error rate, all methods were capable of reporting coverage values above 80% until genus taxonomic level. At species level, MOCAT was the only method with a coverage drop below 30%, while the other methods kept values over 70%. K-mer based methods presented the highest coverage values until species taxonomic level at 5 and 10% of error rate. In terms of accuracy, Kraken and MOCAT performed better than CLARK and MetaPhlAn2 at all taxonomic levels (Fig. 4C). An abrupt accuracy decrease was observed in CLARK (below 25%) at subspecies levels.
The methods with lower false negative rate were MOCAT and Kraken, which maintained specificity values higher than 90% at all taxonomic levels. MetaPhlAn2 maintained values closer to 75% from phylum to genus taxonomic levels. The method with the lowest specificity was CLARK (Fig. 4D).
### Observed biases at phylum level and cut-off error filtering
Since we found that methods can present errors even at higher taxonomic levels such as phylum, we determined if the false positive and false negative (type I and II) errors were distributed evenly among different phyla or had a specific phyla distribution.
For ribosomal amplicon data results, all BLAST-alignment based methods reported very similar abundances at the phylum level without any remarkable biases (Fig. 5A). Metaxa2-SILVA and Parallel-meta-GG combinations presented different abundances than expected, the former presented false positive results referring to an unidentified_marine_bacterioplankton, while the latter had false positive results referring to Tenericutes and Thermotogae phyla (see Supplementary Table 2).
BLAST-independent methods showed a similar trend near to the expected abundance of the evaluated data. However, the SPINGO-SILVA combination overestimated the Firmicutes, Cyanobacteria, Bacteroidetes and Chlorobi phyla. This combination also underestimated the Proteobacteria phyla. The method with the greater bias at phyla taxonomic level was SPINGO in combination with GG, MTX and RDP databases according to MCC (Fig. 6A). These combinations presented false positive results distributed in up to 28 different phyla (collapsed in other phyla category in Fig. 5B), although in very low abundance.
In contrast to the results obtained in the taxonomic annotation of ribosomal amplicon sequences, other but more evident biases were observed in WMS data phyla abundances. In general, Metaxa2 and Parallel-meta in combination with most databases, showed a very similar trend and bias. The most evident errors occurred due to overestimation of the Proteobacteria, Actinobacteria, Bacteroidetes and Chlorobi phyla; and by an underestimation of the Acidobacteria, Firmicutes, Planctomycetes and Spirochaetes phyla. According to these observations, Metaxa2-SILVA combination presented the closest expected abundance of the Spirochaetes phylum but also the most abundant false-positive rate for the not expected phyla category (Fig. 5C). On the other hand, the method with the lowest false positive rate was Metaxa2-GG with only a few bad annotations to Tenericutes and Nistropinae phyla. The rest of the methods had from 0.01 to 0.1% of annotation to Other phyla category in total relative abundance, pointing to a variety of 23 different phyla.
We observed some opposite biases between BLAST-based and -independent methods, for a given phylum, while using WMS data. In the case of Proteobacteria and Acidobacteria phyla, their abundances were underestimated by most of the BLAST-independent methods (Fig. 5D), while BLAST-dependent methods (Fig. 5C) overestimated them. Other phyla like Firmicutes and Spirochaetes were underestimated by most methods using WMS data, but in different magnitude. On the other hand, when comparing k-mers spectra methods to those using single copy marker genes (SCMG) for taxonomic assignation, we observed in the later a greater tendency to overestimate Chloroflexi, Chlorobi, Verrucomicrobia, and Crenarchaeota phyla (Fig. 5D).
## Discussion
A well-known disadvantage of using 16S rRNA genes or its variables regions as phylogenetic marker is the similarity of sequences between non-closely related species41,42. Our datasets were constructed from reference genomes of isolated strains, so the presence of identical sequences from different organisms, could happen in real samples. After a clustering at 100% of identity, we observed that ~27–29% of the genomes had an identical V3-V4 region. Notably, the most of these clusters were formed from genomes of the same species (~16.5% of ~27–29%) or genera (~8.5%); and only a small proportion contained genomes from different families (~3.20%) or classes (~0.3%) (https://github.com/Ales-ibt/Metagenomic-benchmark/tree/master/datasets_16SrRNA/clustering). This means that the lack of resolution at species level of the V3-V4 variable regions of the 16S rRNA phylogenetic marker is a biological issue. The methods tested in this work could either classify these sequences correctly (TP), don’t classify it (FN) or classify them wrongly (FP).
On the one hand, there are those algorithms which classify at the lower taxonomic levels when they find ambiguity in upper levels, reporting the LCA (Metaxa2 or SPINGO). In this case, the methods compromise their sensitivity at genus, species or subspecies level. On the other hand, the methods that use one of the best alignment hits to classify ambiguities (as Parallel-meta), were affected in the specificity, since they risk reporting an incorrect assignment. The chance of a correct assignment at a given taxonomic level will decrease according to the number of identical sequences in the database.
The Parallel-meta-MTX combination presented the best results among BLAST-alignment based methods for 16S rRNA amplicon dataset analysis, overperforming the Metaxa2 algorithm. An important difference between Parallel-meta ad Metaxa2 is that the former use by default megablast settings (a bigger word size, different match/mismatch scores and gap penalties), while the latter use the default blastn settings. According to this, we expected an improvement in the Metaxa2 assignments using the megablast option. A mini-test revealed that performance statistical descriptors was almost identical, indicating that the differences observed between Parallel-meta and Metaxa2 are independent of the blast parameters and can be attributed completely to the algorithm (find the results and a detailed discussion in https://github.com/Ales-ibt/Metagenomic-benchmark/Metaxa2_blast_megablast.txt). Parallel-meta reports the best hit from the Blast search, while Metaxa2, among other things, performs a filter based on its reliability score.
Until class taxonomic level, Metaxa2 and Parallel-meta (both using MTX database) had a similar performance, but a notably difference was observed between order and genus levels. However, the sensitivity gap between these tools can be reduced at a cost of a higher error rate. Higher sensitivity tends to present a lower specificity and vice versa (Figs 1A–C and 2A,B) which is a well-known trade-off between those measures.
For BLAST-independent methods using amplicon data, QIIME performed better than SPINGO at almost every taxonomic level regardless the database combination. Notably, in terms of accuracy at species level, SPINGO-RDP performed better than any other method (Fig. 1D–F). This is consistent to the results reported by SPINGO authors, but based on MCC score values, the method had a poor performance (Fig. 6A). This is a good example of the convenience of using MCC values, which weight all four possible classes (TP, FP, TN, FN) in a confusion matrix.
The database effect was observed at different levels regardless the method. In terms of sensitivity, the MTX database had a positive effect in every method and taxonomic level, even at more stringent error rate cut-off (Fig. 1D–F). For specificity, QIIME-RDP was better at any combination and taxonomic level (Fig. 2D). However, MTX database increased the accuracy of Parallel-meta and QIIME at every taxonomic level (Fig. 2C). A foreseen problem of using the MTX database for taxonomic annotation is the lack of maintenance. Currently, it is a well curated database, but as far as we know remains static. Therefore, the sensitivity of any method will be affected unless new information is added to this database.
The QIIME algorithm has a clustering step where only a representative of each cluster is used for the taxonomic assignation, reducing the possible number of true positives and false negatives (higher specificity). Conversely, BLAST-alignment based methods annotate every sequence, increasing both true positive and false positive rates. However, the positive and negative rates could be controlled by using more strict cut-off values, improving the method performance (see Supplementary Table 2).
In the overall performance according to the MCC evaluation, we observed that QIIME-RDP is the best combination for results between superkingdom and class taxonomic levels. At order and family levels, QIIME-MTX gave better results (Fig. 6A). The Parallel-meta-MTX combination performed particularly better at genus and species levels. Also, SPINGO-MTX was the best combination at those taxonomic levels, confirming the positive effect of the MTX at lower taxonomic ranks. Interestingly, the popular GG database (set as default in the QIIME pipeline), did not improved the results of any evaluated method. Databases such as SILVA and GG in combination with any method, presented MCC values below 0.5 at all taxonomic ranks and at species and subspecies levels, they presented MCC negative values (Fig. 6A) indicating a performance worse than random assignment. In particular, SPINGO which relies on a k-mer spectra algorithm, was the most affected in combination with SILVA, probably due to misleading k-mer information. Smaller but highly curated databases such as RDP and MTX improved the overall performance of all methods at almost every taxonomic level, suggesting a positive effect related to the database size and curation refinement. However, at species and subspecies level, all methods presented MCC values close to zero (Fig. 6A), suggesting that annotations at these taxonomic levels is not reliable using 16S rRNA (V3-V4 regions) amplicon sequencing.
The datasets included a portion of shuffled sequences (Material and Methods) that increased the false positive rate in some method combinations, particularly for SPINGO. The use of a highly curated database such as MTX (~88,000 sequences) which is smaller than GG and RDP databases (~1 and 3 Million, respectively), resulted in a better annotation. This was clearly reflected not only on the coverage but the lower error rate observed in methods such as QIIME and Parallel-meta v2.4.1 (Fig. 6A).
We observed higher specificity and accuracy rates for all methods relying on 16S rRNA gene information extracted from WMS than from amplicon data. This trend is evident despite algorithm and technical differences between amplicon and WMS tool-database combinations (Figs 2A,B and 4A,B). We can relate the increase of specificity (and accuracy) to the availability of full 16S rRNA gene, represented by simulated short reads with a certain sequencing depth and abundance of each genome in the community. Its recovery is possible due to the use of Hidden Markov Models in the algorithms, which is a very sensitive method. For WMS data, the 16S rRNA gene represents a small fraction of the total data and it depicts the universe of assignable reads. On the other hand, for amplicon sequencing the higher sensitivity (Supplementary Figs 1 and 3), can be related to the genome representability in the amplicon dataset. Nevertheless, all methods showed better MCC values with WMS data than amplicon reads, with scores near to 0.25 (Fig. 6A,B).
Methods based on SCMG or k-mer spectra annotation presented the highest coverage at every taxonomic level. In particular, we observed that MetaPhlAn2 and Kraken had the highest coverage at any error rate or taxonomic level, except at species rank and 1% of error cut-off where CLARK showed the highest coverage (Fig. 3D). Kraken and MOCAT were the most accurate and specific methods, with small differences (at order and genus levels) (Fig. 4C,D). We observed again the classic trade-off between sensitivity and specificity for CLARK and MetaPhlAn2, specially at species and subspecies levels. However, MetaPhlAn2 performed very well at subspecies level, even better than the best BLAST-alignment based combination, Parallel-meta-MTX (Fig. 6B).
Interestingly, CLARK accuracy drop was due to taxonomic assignment errors involving shuffled sequences. This was not the case for Kraken, which can filter information by using a last common ancestor k-mer weighting assignment algorithm, reducing the false positive rate.
Databases created from reference genomes gave a better classification as seen with Kraken and single copy gene marker methods, when comparing to 16S rRNA marker gene databases (see Fig. 6B), especially when it is enriched in sequences of organisms that have not been properly characterized (i.e. SILVA). Moreover, the more genetic information, the more accurate the taxonomic classification is.
Several metagenomic studies report results and compare environments using high taxonomic levels such as phylum. However, in this study we report that abundance biases can be observed even at such high rank. BLAST-alignment based methods presented a higher bias when combined with large databases such as GG and SILVA but only for a few phyla. Regarding the BLAST-independent methods, SPINGO in combination with almost all databases, under or overestimated the abundance of 28 different phyla but in low rates. These errors represent a greater bias than observed for BLAST-based methods, which presented a higher proportion of false positives but distributed in only four different phyla (Fig. 5A and Supplementary Table 2). The QIIME and Parallel-meta methods in combination with MTX database did not assign any of the amplicon shuffled sequences which is reflected in all the tested metrics, presenting a very good balanced performance. Conversely, Metaxa2 and SPINGO assigned different numbers of shuffled sequences regardless the database used. Notably, most of these false positives were annotated with assignment scores lower than those for true positives, what making filtering easy.
The observed results from 16S rRNA assignment methods using WMS data, presented a more distributed bias among several phyla. It should be noted that in the tested datasets, Spirochaetes phylum contains information from an in silico modified Leptospira interrogans genome, where sequences from this non-existent relative were present. In particular, most of the method combinations assigned incorrectly those sequences to lower taxonomic levels except for Metaxa2-SILVA one. Nonetheless, Metaxa2-SILVA had the most abundant false-positive rate to not expected phyla (Fig. 5C), all of them pointing to an unidentified_marine_bacterioplankton. The main difference between SILVA and the rest of the databases is that it contains sequences from uncultured, poorly characterized bacteria, that increase the likelihood of reporting an erroneous hit, raising the false positive rates no matter the method.
Despite the presence of shuffled sequences, these data did not generate a significant bias for BLAST-alignment based methods.
A non-systematic bias was observed in the results generated from WMS data. The false positive rate was distributed randomly among a couple of phyla. However, CLARK presented a higher false positive rate distributed in several not expected phyla, resulting in a higher abundance bias (Fig. 5D). Our results differ from those reported by CLARK authors, although their datasets focused on other variables such as sequencing platform error rates and their metrics were calculated differently.
We observed methods presented different biases: 1) erroneous abundance assignment, where a few phyla were largely over or underrepresented or 2) erroneous richness assignment where several phyla were artificially reported. These two errors could impact the microbial diversity interpretation in any metagenomic project.
Most of the methods are not contemporary and have not been evaluated altogether using the same dataset and database, which increases the challenge to compare their performance. Also, databases have grown and suffered changes in the taxonomic annotation that can have a direct impact in the results of any project. Therefore, we have developed an eclectic benchmarking framework to compare objectively the selected tools.
For taxonomic annotation methods based on data from 16S rRNA sequencing, the latest publication corresponds to Parallel-meta 3 and Metaxa231,43 where the comparison to other tools was not extensive. While Metaxa2 authors explored the effect of databases and sequencing approaches (amplicons and WMS), Parallel-meta developers focused on the speed of their software. However, even if both methods performed better in comparison to QIIME at genus, species and subspecies levels, the datasets and evaluation criteria were different. Our results are consistent with the comparison made by the cited authors, but for classification at higher taxonomic levels, we observed that QIIME-RDP could be a better option (Table 1).
SPINGO is a novel method based on k-mer annotation designed to annotate sequences at genus or species level. If a query sequence contains a set of k-mers associated to more than one reference, the method labels it as AMBIGUOUS and reports a list of possible matches. Here, we manually curated the ambiguous results to report the LCA. Consistently with the results reported by Allard et al.30, we found that SPINGO-RDP was the method with the highest accuracy at the species level (Fig. 2C). Also, we found that this method presented the lowest specificity regardless the database combination (Fig. 2D). However, the AMBIGUOUS classification could be very convenient and easy to filter from the reported results. For our datasets, the taxonomic annotation for 25 to 35% of shuffled sequences were assigned as AMBIGUOUS but with a lower similarity score than for true positives. This indicates that the score similarity is a better criterion for filtering false positives than the AMBIGUOUS label. Only SPINGO-SILVA reported annotation for shuffled sequences with scores closer to true positives.
A recent comprehensive benchmark20 evaluated eleven tools and combinations between them, to classify WMS data. This study is probably the most extensive to date, where in addition to the performance of each tool, the synergy of their combinations was analyzed. However, other sequencing approaches like amplicon target sequencing or the use of different databases, were not considered. Here, we evaluated methods based on k-mer spectra annotation and found that our results were very similar to those obtained by Ounit et al.26 in terms of coverage (equivalent to precision in the cited work) and sensitivity at genus level. Consistently with our results, CLARK overperformed Kraken at subspecies taxonomic level, as observed in Fig. 4D. However, CLARK presented a higher false positive rate mainly because of the assignment of a large number of shuffled sequences with similar assignment scores to those of the true positives, which makes filtering impossible.
On the other hand, in agreement with Truong et al.27 results, we observed that MetaPhlAn2 annotated fewer false positives and false negatives than Kraken, but the latter presented higher accuracy and specificity until species level (Fig. 4C,D). Interestingly, at subspecies level MetaPhlAn2 overperformed Kraken in specificity as is shown in Fig. 4D.
As far as we know, our study is the first to benchmark MOCAT against other bioinformatics tools. Kultima et al.24 reports a high agreement between expected diversity and MOCAT annotations at genus level for real and simulated datasets. According to our results and based on MCC values, MOCAT is the best annotation method for class to species ranks (Table 1). Its higher specificity can be related to its very low false positive rate. Methods based on SCMG annotation presented better performance than any other evaluated method (Table 1). Even though their databases are smaller in size in comparison to either 16S rRNA or whole genome databases, the redundant information provided by several markers solve the lack of resolution or sensitivity for certain taxonomic groups.
## Conclusions
To the extent of our knowledge, this is the first study where several tools, developed in the last decade, are compared using a standard methodology with coverage, error rate and statistical measures of classification We can relate those metrics to scores and set a cut-off line for each method, seeking for higher sensitivity or specificity. Depending on the goals, sensitivity or specificity rates could have a different impact in metagenomic projects. Our results indicate that Parallel-meta-MTX combination is the best option for the analysis of the V3-V4 16S rRNA region at genus level, bearing in mind that at species and subspecies ranks, it will present higher error rate and lower sensitivity. Smaller but highly curated databases like RDP and MTX improved the results of tested methods in terms of sensitivity, specificity and accuracy. The standardization of taxonomic lineage is necessary to compare results, especially when the annotation was performed using different databases.
The overall performance of almost all methods using WMS data was better, but with an expected trade-off cost between sensitivity and specificity. High accuracy at low taxonomic levels could be convenient for a metagenomic project, especially if species or subspecies characterization is a relevant goal. However, is important to consider some problems for WMS sequencing approaches. Extraction of DNA at concentration and molecular weight from metagenomic samples, could be a challenge but necessary for amplification-free sequencing libraries. Also, if not all genomes present in the studied metagenomes were present in the reference database, which is the common case in environmental samples, the 16S-based methods would probably perform better than the WMS ones, as 16S rRNA databases are much extensive. However, several metagenomic studies are delivering hundreds or thousands of complete and draft bacterial genomes which will improve genome databases and WMS-based classification methods44,45,46,47. Finally, our work is delimited to bacterial and archaea taxonomy classification but in real life samples, the presence of eukaryotes could contribute to other misclassification problems that are not considered in our benchmark. These problems include the amplification and misclassification of ribosomal sequences belonging to mitochondrial or chloroplast genomes.
The results presented here could help other researchers to choose among the available tools, being aware of their advantages and disadvantages. Also, benchmarking of new tools could be done following our standard framework if the evaluated method reports a score for each assignment. Detailed information to benchmark, evaluate and choose the best of the tested tools, can be found at https://github.com/Ales-ibt/Metagenomic-benchmark. While this benchmark suite may be useful and available for reproducibility and implementation, is not free from the same problems of database dependence, manually defined criteria and software changes. Finally, we would like to highlight the importance of gold standards, recurrent evaluation of tools, databases curation and manual inspection of the taxonomic profiling results, for a better and more accurate microbial diversity description. | 2022-11-29 08:10:31 | {"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": 0.4432859718799591, "perplexity": 3806.225976823003}, "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/1669446710690.85/warc/CC-MAIN-20221129064123-20221129094123-00551.warc.gz"} |
https://www.shaalaa.com/concept-notes/concentration-of-a-solution_6272 | # Concentration of a Solution
#### definition
• Unsaturated solution: If the amount of solute contained in a solution is less than the saturation level, it is called an unsaturated solution. (till it is dissolving).
• Saturated solution: When no more solute can be dissolved in a solution at a given temperature, it is called a saturated solution.
• Solubility: The amount of the solute present in the saturated solution at this temperature is called its solubility.
# Concentration of a Solution:
• Take salt and dissolve it in water.
• After a time, it won’t be soluble.
• Heat it and try dissolving.
• It will dissolve!
• Try adding more and dissolve it.
From the about activity, the following can be inferred!
1. Unsaturated solution: If the amount of solute contained in a solution is less than the saturation level, it is called an unsaturated solution. (till it is dissolving).
2. Saturated solution: When no more solute can be dissolved in a solution at a given temperature, it is called a saturated solution.
3. Solubility: The amount of the solute present in the saturated solution at this temperature is called its solubility.
## How will you decide how concentrated the solution is?
Concentration of solution = " Amount of solute"/"Amount of solution" "or" "Amount of solute"/"Amount of solvent"
There are various ways of expressing the concentration of a solution
1. "Mass by mass percentage of a solution" = "Mass of solute"/"Mass of solution" xx 100
2. "Mass by volume percentage of a solution" = "Mass of solute"/"Volume of solution" xx 100.
#### Example
A solution contains 40 g of common salt in 320 g of water. Calculate the concentration in terms of mass by the mass percentage of the solution.
Mass of solute (salt) = 40 g
Mass of solvent (water) = 320 g
We know,
Mass of solution = Mass of solute + Mass of solvent
= 40 g + 320 g
= 360 g
Mass percentage of solution = "Mass of solute"/"Mass of solution" xx 100
= 40/360 xx 100
= 11.1%
#### Example
To make a saturated solution, 36 g of sodium chloride is dissolved in 100 g of water at 293 K. Find its concentration at this temperature.
Mass of solute (sodium chloride) = 36 g (Given)
Mass of solvent (water) = 100 g (Given)
Then, mass of solution = Mass of solute + Mass of solvent
= (36 + 100) g
= 136 g
Therefore, concentration (mass by mass percentage) of the solution
="Mmmmass of solute"/"Mass of solvent"xx100%
=36/136xx100%
= 26.47 %
If you would like to contribute notes or other learning material, please submit them using the button below.
### Shaalaa.com
Solubility of Solution [00:11:32]
S
0% | 2021-04-22 20:27:16 | {"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": 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": 0.36748841404914856, "perplexity": 3496.79467389485}, "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-2021-17/segments/1618039604430.92/warc/CC-MAIN-20210422191215-20210422221215-00538.warc.gz"} |
https://quantumcomputing.stackexchange.com/questions/2244/is-it-possible-to-calculate-the-absolute-value-of-a-permanent-using-boson-samp | # Is it possible to “calculate” the absolute value of a permanent using Boson Sampling?
In boson sampling, if we start with 1 photon in each of the first $M$ modes of an interferometer, the probability of detecting 1 photon in each output mode is: $|\textrm{Perm}(A)|^2$, where the columns and rows of $A$ are the first $M$ columns of the interferometer's unitary matrix $U$, and all of its rows.
This makes it look like for any unitary $U$, we can construct the appropriate interferometer, construct the matrix $A$, and calculate the absolute value of the permanent of $A$ by taking the square root of the probability of detecting one photon in each mode (which we get from the boson sampling experiment). Is this true, or is there some catch? People have told me that you can't actually get information about a permanent from boson sampling.
Also, what happens to the rest of the columns of $U$: How exactly is it that the experimental outcome only depends on the first $M$ columns of $U$ and all of its rows, but not at all on the other columns of $U$? Those columns of $U$ do not affect the outcome of the experiment in the first $M$ modes at all?
• Since you created photonics, please consider writing the tag-excerpt for it. Go here. Thank you. – Sanchayan Dutta Jul 5 '18 at 8:38
It appears to be true, up to a point. As I read Scott Aaronson's paper, it says that if you start with 1 photon in each of the first $M$ modes of an interferometer, and find the probability $P_S$ that a set $s_i$ photons is output in each mode $i\in\{1,\ldots, N\}$ where $\sum_is_i=M$, is $$P_s=\frac{|\text{Per(A)}|^2}{s_1!s_2!\ldots s_M!}.$$ So, indeed, if you take a particular instance where $s_i=0$ or 1 for every possible output, then, yes the probability is equal to the permanent of $A$, where $A$ is the first $M$ columns of $U$ and a specific subset of $M$ rows specified by the locations $s_i=1$. So, this is not quite as specified in the question: it is not all rows, but only some subset, so that $A$ is a square matrix, corresponding to the bits that the experiment "sees", i.e. the input rows and output rows. The photons never populate anything else, and so are blind to the other elements of the unitary matrix $U$.
This should be fairly obvious. Let's say I have some $3\times 3$ matrix $V$. If I start in some basis state $|0\rangle$ and find its product, $V|0\rangle$, then knowing that tells me very little about the outputs $V|1\rangle$ and $V|2\rangle$, aside from what can be said from the knowledge that $V$ is unitary, and hence columns and rows are orthonormal.
The issue that one must be careful of is the accuracy: you run this once and all you get is a single sample according to the probability distribution $P_s$. You run this a few times, and you start to build up information about the different probabilities. You run this enough times, and you can get an arbitrarily accurate answer, but how many is enough? There are two different ways that you can measure the error in an estimate of a value $p$. You can demand either an additive error $p\pm\epsilon$ or a multiplicative error, $p(1\pm\epsilon)$. Since we expect that a typical probability will be exponentially small in $n+m$, the multiplicative error demands far greater accuracy, which cannot be achieved efficiently via sampling. On the other hand, the additive error approximation can be achieved.
While a multiplicative error is what people usually want to calculate, the additive error can also be an interesting entity. For example, in the evaluation of the Jones polynomial.
Aaronson points us back further in time for where this connection between Boson sampling and the Permanent was first made:
It has been known since work by Caianiello in 1953 (if not earlier) that the amplitudes for $n$-boson processes can be written as the permanents of $n\times n$ matrices.
is to prove a connection between the ability of classical computers to solve the approximate BosonSampling problem and their ability to approximate the permanent
i.e. to understand the approximation problem associated with, e.g. finite sampling, and to describe the computational complexity consequences associated: that we believe such a thing is hard to evaluate classically.
• I'm not sure whether this is what you are saying, but it is not true that solving efficiently BosonSampling allows to efficiently estimate the permanents, which would imply that quantum computers are able to solve #P-hard problems. In other words, quantum computers can efficiently simulate the output of a boson sampler, but not efficiently compute its output probability distribution – glS Jun 6 '18 at 13:14
• @glS No, that's very much what I'm saying. The Aaronson paper is very careful to distinguish that issue, but it makes the computational complexity statement a lot messier, which is why I didn't state it. – DaftWullie Jun 6 '18 at 14:42
• @DaftWullie sorry, now I'm confused. Do we agree that boson sampling does not allow to efficiently estimate permanents? (see e.g. bottom of left column at pag 6 of arxiv.org/pdf/1406.6767.pdf) – glS Jun 6 '18 at 14:44
• @gls I agree that you cannot do it if you want an estimate of the permanent with some multiplicative error bound, which, admittedly, is the standard way of defining things (but since I carefully avoided defining anything...). If you’re willing to tolerate an additive error bound, then I believe you can do it. – DaftWullie Jun 6 '18 at 17:37
• "If I start in some basis state $|0\rangle$ and find its product, $V|0\rangle$, then knowing that tells me very little about the outputs $V|1\rangle$ and $V|2\rangle$", but every single element of $V$ is involved in giving you $V|0\rangle$. But for boson sampling, only the first $M$ columns are involved, isn't that amazing? – user1271772 Jun 6 '18 at 17:54
You cannot efficiently recover the absolute values of the amplitudes, but if you allow for arbitrary many samples, then you can estimate them to whatever degree of accuracy you like.
More specifically, if the input state is a single photon in each of the first $n$ modes, and one is willing to draw an arbitrary number of samples from the output, then it is in principle possible to estimate the permanent of $A$ to whatever degree of accuracy one likes, by counting the fraction of the times the $n$ input photons come out in the first $n$ different output ports. It is to be noted though that this does not really have much to do with BosonSampling, as the hardness result holds in the regime of the number of modes much larger than the number of photons, and it's about the efficiency of the sampling.
# BosonSampling
I'll try a very brief introduction to what boson sampling is, but it should be noted that I cannot possibly do a better job at this than Aaronson himself, so it's probably a good idea to have a look at the related blog posts of his (e.g. blog/?p=473 and blog/?p=1177), and links therein.
BosonSampling is a sampling problem. This can be a little bit confusing in that people are generally more used to think of problems having definite answers. A sampling problem is different in that the solution to the problem is a set of samples drawn from some probability distribution.
Indeed, the problem a boson sampler solves is that of sampling from a specific probability distribution. More specifically, sampling from the probability distribution of the possible outcome (many-boson) states.
Consider as a simple example a case with 2 photons in 4 modes, and let's say we fix the input state to be $(1,1,0,0)\equiv|1,1,0,0\rangle$ (that is, a single photon in each of the two first two input modes). Ignoring the output states with more than one photon in each mode, there are $\binom{4}{2}=6$ possible output two-photon states: $(1,1,0,0), (1,0,1,0), (1,0,0,1), (0,1,1,0), (0,1,0,1)$ and $(0,0,1,1)$. Let us denote for convenience with $o_i, i=1,.,6$ the $i$-th one (so, for example, $o_2=(1,0,1,0)$). Then, a possible solution to BosonSampling could be the series of outcomes: $$o_1, o_4, o_2, o_2, o_5.$$
To make an analogy to a maybe more familiar case, it's like saying that we want to sample from a Gaussian probability distribution. This means that we want to find a sequence of numbers which, if we draw enough of them and put them into a histogram, will produce something close to a Gaussian.
# Computing permanents
It turns out that the probability amplitude of a given input state $|\boldsymbol r\rangle$ to a given output state $|\boldsymbol s\rangle$ is (proportional to) the permanent of a suitable matrix built out of the unitary matrix characterizing the (single-boson) evolution.
More specifically, if $\boldsymbol R$ denotes the mode assignment list${}^{(1)}$ associated to $|\boldsymbol r\rangle$, $\boldsymbol S$ that of $|\boldsymbol s\rangle$, and $U$ is the unitary matrix describing the evolution, then the probability amplitude $\mathcal A(\boldsymbol r\to\boldsymbol s)$ of going from $|\boldsymbol r\rangle$ to $|\boldsymbol s\rangle$ is given by $$\mathcal A(\boldsymbol r\to\boldsymbol s) = \frac{1}{\sqrt{\boldsymbol r!\boldsymbol s!}} \operatorname{perm} U[\boldsymbol R|\boldsymbol S],$$ with $U[\boldsymbol R|\boldsymbol S]$ denoting the matrix built by taking from $U$ the rows specified by $\boldsymbol R$ and the columns specified by $\boldsymbol S$.
Thus, considering the fixed input state $|\boldsymbol r_0\rangle$, the probability distribution of the possible outcomes is given by the probabilities $$p_{\boldsymbol s} = \frac{1}{\boldsymbol r_0! \boldsymbol s!} \lvert \operatorname{perm}U[\boldsymbol R|\boldsymbol S] \rvert^2.$$
BosonSampling is the problem of drawing "points" according to this distribution.
This is not the same as computing the probabilities $p_s$, or even computing the permanents themselves. Indeed, computing the permanents of complex matrices is hard, and it is not expected even for quantum computers to be able to do it efficiently.
The gist of the matter is that sampling from a probability distribution is in general easier than computing the distribution itself. While a naive way to sample from a distribution is to compute the probabilities (if not already known) and use those to draw the points, there might be smarter ways to do it. A boson sampler is something that is able to draw points according to a specific probability distribution, even though the probabilities making up the distribution itself are not known (or better said, not efficiently computable).
Furthermore, while it may look like the ability to efficiently sample from a distribution should translate into the ability of efficiently estimating the underlying probabilities, this is not the case as soon as there are exponentially many possible outcomes. This is indeed the case of boson sampling with uniformly random unitaries (that is, the original setting of BosonSampling), in which there are $\binom{m}{n}$ possible $n$-boson in $m$-modes output states (again, neglecting states with more than one boson in some mode). For $m\gg n$, this number increases exponentially with $n$. This means that, in practice, you would need to draw an exponential number of samples to even have a decent chance of seeing a single outcome more than once, let alone estimate with any decent accuracy the probabilities themselves (it is important to note that this is not the core reason for the hardness though, as the exponential number of possible outcomes could be overcome with smarter methods).
In some particular cases, it is possible to efficiently estimate the permanent of matrices using a boson sampling set-up. This will only be feasible if one of the submatrices has a large (i.e. not exponentially small) permanent associated with it, so that the input-output pair associated with it will happen frequently enough for an estimate to be feasible in polynomial time. This is a very atypical situation, and will not arise if you draw unitaries at random. For a trivial example, consider matrices that are very close to identity - the event in which all photons come out in the same modes they came in will correspond to a permanent which can be estimated experimentally. Besides only being feasible for some particular matrices, a careful analysis of the statistical error incurred in evaluating permanents in this way shows that this is not more efficient than known classical algorithms for approximating permanents (technically, within a small additive error) ${}^{(2)}$.
# Columns involved
Let $U$ be the unitary describing the one-boson evolution. Then, basically by definition, the output amplitudes describing the evolution of a single photon entering in the $k$-th mode are in the $k$-th column of $U$.
The unitary describing the evolution of the many-boson states, however, is not actually $U$, but a bigger unitary, often denoted by $\varphi_n(U)$, whose elements are computed from permanents of matrices built out of $U$.
Informally speaking though, if the input state has photons in, say, the first $n$ modes, then naturally only the first $n$ columns of $U$ must be necessary (and sufficient) to describe the evolution, as the other columns will describe the evolution of photons entering in modes that we are not actually using.
(1) This is just another way to describe a many-boson state. Instead of characterizing the state as the list of occupation numbers for each mode (that is, number of bosons in first mode, number in second, etc.), we characterize the states by naming the mode occupied by each boson. So, for example, the state $(1, 0, 1, 0)$ can be equivalently written as $(1, 3)$, and these are two equivalent ways to say that there is one boson in the first and one boson in the third mode.
(2): S. Aaronson and T. Hance. "Generalizing and Derandomizing Gurvits's Approximation Algorithm for the Permanent". https://eccc.weizmann.ac.il/report/2012/170/
• I started with 1 photon in each input mode, and said we're looking at the probability of having 1 photon in each output mode, so that we could avoid all these more complicated general equations involving the permanent, which you provide. In fact if $M$ is the number of columns in $U$, we get that the probability of having 1 photon in each output mode is $|\textrm{Perm}(U)|^2$ from which we can easily get $|\textrm{Perm}(U)|$. If we let the experiment go on for long enough and get enough samples, can we not obtain an estimate for $|\textrm{Perm}(U)|$ ? – user1271772 Jun 6 '18 at 17:49
• In no part of the question did I mention "efficiency" or "sub-exponentially". I'm just interested to know whether or not it's possible to estimate $|\textrm{Perm}(U)|$ using boson sampling. – user1271772 Jun 6 '18 at 17:50
• @user1271772 I see. That's the standard way of talking about these things in this context so I might have automatically assumed you meant to talk about efficiency. If you don't care about the number of samples you have to draw then sure, you can compute the output probability distribution, and therefore the absolute values of the permanents, to whatever accuracy you like – glS Jun 6 '18 at 17:57
• @gIS, Aram Harrow once told me you cannot calculate Permanents using boson sampling, so I thought there was some "catch". The best classical algorithm for simulation of exact boson sampling is: $\mathcal{O}\left(m2^n + mn^2\right)$, for $n$ photons in $m$ output modes, what is the cost using the interferometer? – user1271772 Jun 6 '18 at 18:07
• @user1271772 I answered more specifically your first point in the edit. I guess I got confused because the setting you are mentioning does not seem to have really much to do with boson sampling, but is more generally about the dynamics of indistinguishable bosons through an interferometer – glS Jun 6 '18 at 18:30 | 2019-09-19 17:28:51 | {"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": 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": 0.8505818843841553, "perplexity": 255.27821371981122}, "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/1568514573561.45/warc/CC-MAIN-20190919163337-20190919185337-00224.warc.gz"} |
https://testbook.com/question-answer/what-is-the-value-ofrm-displaystyle-lim--5f9fe71718dc2a1bcbcf9d07 | # What is the value of $$\rm \displaystyle \lim_{x \to 0} {x^2}{e^{\sin \left( {\tfrac{1}{x}} \right)}}$$?
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## Detailed Solution
Concept:
The Squeeze Theorem (The Sandwich Theorem): is used on a function where it will be almost impossible to differentiate.
• The squeeze theorem states that if we define functions such that h(x) ≤ f(x) ≤ g(x) and if $$\rm \displaystyle \lim_{x \to a}h(x) = \lim_{x \to a}g(x) = L$$, then $$\rm \displaystyle \lim_{x \to a}f(x) = L$$.
Calculation:
We know that -1 ≤ sin θ ≤ 1.
⇒ -1 ≤ $$\rm \sin \left(\dfrac1x\right)$$ ≤ 1
Since, ex is a strictly increasing function for all real values of x, we can say that:
⇒ e-1 ≤ $$\rm e^{\sin \left(\tfrac1x\right)}$$ ≤ e1
Also, since x2 ≥ 0, we can say that:
⇒ x2e-1 ≤ $$\rm x^2e^{\sin \left(\tfrac1x\right)}$$ ≤ x2e1
⇒ $$\rm \dfrac{x^2}{e}\leq x^2e^{\sin \left(\tfrac1x\right)}\leq x^2e$$
So, we can consider h(x) = $$\rm \dfrac{x^2}{e}$$, f(x) = $$\rm \displaystyle \lim_{x \to 0} {x^2}{e^{\sin \left( {\tfrac{1}{x}} \right)}}$$ and g(x) = x2e.
Now, $$\rm \displaystyle \lim_{x \to 0}h(x) = \lim_{x \to 0}\dfrac{x^2}{e}=0$$.
And $$\rm \displaystyle \lim_{x \to 0}g(x) = \lim_{x \to 0}x^2e=0$$.
Since, $$\rm \displaystyle \lim_{x \to 0}h(x) =\lim_{x \to 0}g(x) =0$$, we must have $$\rm \displaystyle \lim_{x \to 0}f(x) =0$$.
Hence, $$\rm \displaystyle \lim_{x \to 0} {x^2}{e^{\sin \left( {\tfrac{1}{x}} \right)}}=0$$. | 2021-10-21 02:55:48 | {"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": 0.780620276927948, "perplexity": 1474.461602668751}, "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/1634323585380.70/warc/CC-MAIN-20211021005314-20211021035314-00640.warc.gz"} |
https://naml.us/post/plates/ | # Plates
Here’s a combinatorial problem I found recently: given a 100 story building and two identical plates, what is the worst case number of drops required to determine the lower floor from which the plates break when dropped (if a plate drops and does not break, it is undamaged). The answer is 14, which I’ll state without proof.
In the interest of completely useless generalization, we can ask what happens if we add more plates. Specifically, what is the cost $C(s)$ to analyze an $s$ story building if we can buy as many plates as we like? Say each plate costs as much as one drop.
First we need to figure out how many drops it takes for a given number of plates, or (roughly) equivalently the number of floors we can analyze for a given number of plates and drops. If we count the zeroth story as a floor to make the formulas slightly prettier, the answer is that $n$ drops and $k$ plates can analyze a building with $S(n,k)$ floors, where $$S(n,k) = \binom{n}{0} + \binom{n}{1} + \cdots + \binom{n}{k} = \sum_{p \le k} \binom{n}{k}$$ (This can be proved by induction on the number of plates.) Thus, $S(n,k)$ is the number of subsets of [1..n] with at most $k$ elements, which turns out to have no closed form expression (Graham et al.). Therefore, we’ll have to settle for asymptotics. The best estimates I could find are given in Worsch 1994. Since they details vary depending on the relative growth of $n$ and $k$, we first need a rough idea of the growth rate of $n / k$.
For a building of $s$ floors, brute force binary search requires $n = k = \lg s + 1$, so $C(s) \lt 2 + 2 \lg s$ and $n, k \le n + k = C(s) \lt 2 \lg s$. Since at least $\lg s$ tests are required regardless of the number of plates, we have $\lg s \le n \lt 2 + 2 \lg s$. Lacking an obvious lower bound for $k$, I’ll assume for the moment that $k = \Theta(\lg s) = \Theta(n)$. Numerical evidence indicates that $n/k$ is in fact between 2 and 3.
In the case where $n/k$ is a constant of at least 2, Worsch 1994 gives $$S(n,k) = (C(x) + O(1))^n \approx C(x)^n$$ where $$C(n/k) = C(x) = x^\frac{1}{x} \left(\frac{x}{x-1}\right)^\frac{x-1}{x}$$ We can now use this approximation to find the optimal ratio $x$ by optimizing $n+k$ subject to $S = s$. For convenience, let $D(x) = C’(x)/C(x)$ be the logarithmic derivative of $C$. Applying Lagrange multipliers, we have \begin{aligned} E =~& n + k - \lambda (C\left(\frac{n}{k}\right)^n - s) \\ \frac{\partial E}{\partial n} =~& 1 - \lambda \left( n C^{n-1} C D \frac{1}{k} + C^n \log C \right) \\ =~& 1 - \lambda C^n \left(D x + \log C\right) \\ \frac{\partial E}{\partial k} =~& 1 - \lambda n C^{n-1} C D \frac{n}{k^2} \\ =& 1 - \lambda C^n D x^2 \end{aligned} Equating derivatives to zero and solving gives $\log C + Dx + Dx^2 = 0$. Filling in the details, \begin{aligned} \log C =~& \frac{1}{x} \log x + \frac{x-1}{x} \log \frac{x}{x-1} \\ =~& \log x + \frac{1}{x} log (x-1) - \log (x-1) \\ D =~& \frac{C’}{C} = \frac{1}{x} - \frac{1}{x^2} \log (x-1) + \frac{1}{x(x-1)} - \frac{1}{x-1} \\ =~& -\frac{1}{x^2} \log (x-1) \\ \log C + Dx+Dx^2 =~& \log x + \frac{1}{x} log (x-1) - \log (x-1) - \frac{1}{x} \log (x-1) - \log (x-1) \\ =~& \log x - 2 \log (x-1) = 0 \\ \log x =~& 2 \log (x-1) \\ x =~& (x-1)^2 \\ 0 =~& x^2 - 3x + 1 \\ x =~& \frac{3 + \sqrt{5}}{2} \end{aligned} Thus, $n \approx 2.62 k$, $S(n, n / 2.62) \approx 1.94^n$, and $C(s) \approx (1 + 1/x) \log s / \log x \approx 1.44 \lg s$. | 2019-02-17 10:18:23 | {"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": 0.9999316930770874, "perplexity": 540.5608429601072}, "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-2019-09/segments/1550247481832.13/warc/CC-MAIN-20190217091542-20190217113542-00392.warc.gz"} |
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My goal is to show a custom Bayesian Model class that implements the sklearn API. Truncated Poisson Distributions in PyMC3. shape) c = pymc3. By voting up you can indicate which examples are most useful and appropriate. However, PyMC3 allows us to define the probabilistic model, which combines the encoder and decoder, in the way by which other general probabilistic models (e. , generalized linear models), rather than directly implementing of Monte Carlo sampling and the loss function as done in the Keras example. Since all of the applications of MRP I have found online involve R ’s lme4 package or Stan , I also thought this was a good opportunity to illustrate MRP in Python with PyMC3. Example Neural Network with PyMC3; Linear Regression Function Matrices Neural Diagram LinReg 3 Ways Logistic Regression Function Matrices Neural Diagram LogReg 3 Ways Deep Neural Networks Function Matrices Neural Diagram DeepNets 3 Ways Going Bayesian. Categorical ('c', p, observed = data, shape = 1) return model. Examples based on real world datasets¶ Applications to real world problems with some medium sized datasets or interactive user interface. My preferred PPL is PYMC3 and offers a choice of both MCMC and VI algorithms for inferring models in Bayesian data analysis. PyMC is used for Bayesian modeling in a variety of fields. We propose Edward, a Turing-complete probabilistic programming language. With the help of Python and PyMC3 you will learn to implement, check and expand Bayesian models to solve data analysis problems. It explores how a sklearn-familiar data scientist would build a PyMC3 model. It can either put the constant into the a values, or into the intercept, and either way is pretty much fine. Coin toss with PyMC3; In this example we'll look at Minnesota, a state that contains 85 county's in which different measurements are taken, ranging from. Bayesian machine learning (read 'Bayesian. We use the non-trivial embedding for many non-trivial inference problems. Survival analysis studies the distribution of the time to an event. 3Comparing scitkit-learn, PyMC3, and PyMC3 Models Using the mapping above, this library creates easy to use PyMC3 models. PyMC3 port of the book "Statistical Rethinking A Bayesian Course with Examples in R and Stan" by Richard McElreath PyMC3 port of the book "Bayesian Cognitive Modeling" by Michael Lee and EJ Wagenmakers : Focused on using Bayesian statistics in cognitive modeling. Part 1 is here. this can explain why someone running this demo could have a problem with the first but not second example. Tue, Oct 24, 2017, 6:30 PM: Probabilistic programming are a family of programming languages where a probabilistic model can be specified, in order to do inference over unknown variables. find_MAP # draw 2000 posterior samples trace = pymc3. Its flexibility and extensibility make it applicable to a large suite of problems. Stay ahead with the world's most comprehensive technology and business learning platform. His great book provides us some introductory examples to Bayesian Methods and is done using Allen's own l. Imagine we have a dataframe with each row being observations and three columns: Team 1 ID, Team 2 ID, Winner where the last column contains the winning team ID. 2 , 'late_slope' :. max + 1 a = np. Categorical taken from open source projects. Generate Synthetic Data; Fit a model with PyMC3; Fit a model with PyMC3 Models; Advanced; Examples; API. For example, zero-truncated Poisson distributions can be used to model counts that are constrained to be non-negative. Active 2 years, 7 months ago. modelcontext (model) ¶ return the given model or try to find it in the context if there was none supplied. 2033011196250568e-16, array([ 0. For example, the generated quantities section can be used to com - pute PPCs and evaluate losses. Both have built-in implementations of PPCs and explicit documenta - tion to do model evaluation and comparison. (For example, if factor 1 generated proto-columns A and B, and factor 2 generated proto-columns C and D, then our final columns are A * C, B * C, A * D, B * D. zeros(5), scale=1. shape¶ Tuple of array dimensions. 158 ) or at thresholds ( 0. py:384: FutureWarning: Conversion of the second argument of issubdtype from float to np. We first introduce Bayesian inference and then give several examples of using PyMC 3 to show off the ease of model building and model fitting even for difficult models. In the next few sections we will use PyMC3 to formulate and utilise a Bayesian linear regression model. (for example, saying that all but what I have learnt from using Pyro and PyMC3, the training process is really long and it. PyMC3 is alpha software that is intended to improve on PyMC2 in the following ways (from GitHub page): Intuitive model specification syntax, for example, x ~ N(0,1) translates to x = Normal(0,1) Powerful sampling algorithms such as Hamiltonian Monte Carlo. This is implemented through Markov Chain Monte Carlo (or a more efficient variant called the No-U-Turn Sampler) in PyMC3. This notebook contains the code required to conduct a Bayesian data analysis on data collected from a set of multiple-lot online auction events executed in Europen markets, over the course of a year. Alternatively, 'advi', in which case the model will be fitted using automatic differentiation variational inference as implemented in PyMC3. Mathematical Background. In this post, we discuss probabilistic programming languages on the example of ordered logistic regression. Simple trick: * If your problems has words like "or", "either", "atleast" or their synonyms, you need to 'ADD' favorable cases & hence the probabilities. This is no small task for a beginner in bayesian statistics and takes some getting used to. PyMC3 port of the book “Statistical Rethinking A Bayesian Course with Examples in R and Stan” by Richard McElreath. Arrows point from parent to child and display the label that the child assigns to the parent. find_map (bool): whether or not to use the maximum a posteriori estimate as a starting point; passed directly to PyMC3. I will assume that you know what a Gaussian distribution and Gamma dis. Generate Synthetic Data; Fit a model with PyMC3; Fit a model with PyMC3 Models; Advanced; Examples; API. Style and approach Bayes algorithms are widely used in statistics, machine learning, artificial intelligence, and data mining. PyMC in Scientific Research. Mathematical Background. This guide will show you how compare this statistic using Bayesian estimation instead, giving you nice and interpretable results. Tutorial¶ This tutorial will guide you through a typical PyMC application. PyMC provides three objects that fit models: MCMC, which coordinates Markov chain Monte Carlo algorithms. Here are the examples of the python api pymc3. we got a distribution of plausible values. Detailed notes about distributions, sampling methods and other PyMC3 functions are. Marginal in the example, but the same works for other implementations. Bayesian Data Analysis with Python and PyMC3. PyMC in Scientific Research. The sampling algorithm used is NUTS, in which parameters are tuned automatically. In [455]: with model : # Initial values for stochastic nodes start = { 'early_intercept' :. Gaussian Process Regression. GitHub Gist: instantly share code, notes, and snippets. Simple trick: * If your problems has words like "or", "either", "atleast" or their synonyms, you need to 'ADD' favorable cases & hence the probabilities. This is implemented through Markov Chain Monte Carlo (or a more efficient variant called the No-U-Turn Sampler) in PyMC3. I was working a little on my own in trying to implement the NUTS algo, and I have been doing this mostly by looking at the old matlab implementation, some of twiecki’s code in pymc3, and the paper itself. This blog post is based on the paper reading of A Tutorial on Bridge Sampling, which gives an excellent review of the computation of marginal likelihood, and also an introduction of Bridge sampling. Check out the getting started guide, or interact with live examples using Binder!. , generalized linear models), rather than directly implementing of Monte Carlo sampling and the loss function as done in the Keras example. Review from lecture Introduction to pymc3 Inference and Representation Rachel Hodos New York University Lab 2, September 9, 2015 Rachel Hodos Lab 2: Inference and Representation. Long-time readers of Healthy Algorithms might remember my obsession with PyMC2 from my DisMod days nearly ten years ago, but for those of you joining us more recently… there is a great way to build Bayesian statistical models with Python, and it is the PyMC package. Its applications span many fields across medicine, biology, engineering, and social science. The two discuss how Bayesian Inference works, how it’s used in Probabilistic Programming. A minimal reproducable example of poisson regression to predict counts using dummy data. 01/13/2017 ∙ by Dustin Tran, et al. 1 , 'early_slope' :. Variational Inference. PyMC3 is a new open source Probabilistic Programming framework written in Python that uses Theano to compute gradients via automatic differentiation as well as compile probabilistic programs on. The code behind these examples is small and accessible to most Python developers, even if they don't have much HTML experience. Decorator for reusable models in PyMC3. dtype(float). By the way, this is an implementation of the constrained Probabilistic Matrix Factorization (equation 7 in the paper by Salakhutdinov and Mnih). pylabtools import figsize from IPython. So, getting into PyMC3 a lot more and working through examples, I found I cannot implement in an up-to-date form an example from Cameron Davidson-Pilon's Bayesian Methods for Hackers, specifically the Price is Right example, in the library's current version. There is a really cool library called pymc3. ArviZ, a Python library that works hand-in-hand with PyMC3 and can help us interpret and visualize posterior distributions. The Truncated Poisson is a discrete probability distribution that is arbitrarily truncated to be greater than some minimum value k. In this post i am going to tell you about pickle. Examples of random walk Monte Carlo methods include the following: Metropolis–Hastings algorithm: This method generates a Markov chain using a proposal density for new steps and a method for rejecting some of the proposed moves. Installation. John Salvatier, Thomas V. This article elaborates on the foundations for symbolic mathematics in Theano and PyMC3; specifically, its current state, some challenges, and potential improvements. I have uploaded a sample data set or sensor readings. Alas, I have not been able to find any examples of how either idea may work. iterable: an iterable containing the sorted y elements. PyMC3 and Edward offer a productive out-of-the-box experience for model evaluation. 3 explained how we can parametrize our variables no longer works. Expert in Bayesian Machine Learning and Data Science. import pymc3 def create_model (data): with pymc3. There are hundreds of textbooks, research papers. Created using Sphinx 1. get_values ('theta'), observed_data. Thanks for the example! Great for novices like myself to work through. By the way, this is an implementation of the constrained Probabilistic Matrix Factorization (equation 7 in the paper by Salakhutdinov and Mnih). I had sent a link introducing Pyro to the lab chat, and the PI wondered about differences and limitations compared to PyMC3, the ‘classic’ tool for statistical modelling in Python. 70) Example to perform linear mixed effects regression in a Bayesian setting using the PyMc3 framework (on bitbucket) 71) Example of linear mixed effects regression in a Bayesian setting (probabilistic programming) using the rstanarm framework (on bitbucket) 72) Simple example of regression and decision tree in R (on bitbucket). modelcontext (model) ¶ return the given model or try to find it in the context if there was none supplied. pymc3 uses fancier sampling approaches (my last post on Gibbs sampling is another fancy sampling approach!) This is going to be a common theme in this post: The Gaussian linear regression model I'm using in these posts is a small Gaussian model, which is easy to work with and has a closed-form for its posterior. We will also look into mixture models and clustering data, and we will finish with advanced topics like non-parametrics models and Gaussian processes. Pythonで使えるフリーなMCMCサンプラーの一つにPyMC3というものがあります．先日．「PyMC3になってPyMC2より速くなったかも…」とか「Stanは離散パラメータが…」とかいう話をスタバで隣に座った女子高生がしていた（ような気. It might be slightly out of date (but also you can make a pull request or two here!) GitHub pymc-devs/resources. I teach users a practical, effective workflow for applying Bayesian statistics using MCMC via PyMC3 (and other libraries) using real-world examples. We measure the effect of protected variables, which should not influence decision making, on the output. PyMC3 is a Python package for doing MCMC using a variety of samplers, including Metropolis, Slice and Hamiltonian Monte Carlo. For example, I had a model using a GaussianRandomWalk variable and I wanted to generate predictions into the future. PyMC provides three objects that fit models: MCMC, which coordinates Markov chain Monte Carlo algorithms. Currently, the following models have been implemented: Linear Regression; Hierarchical Logistic Regression. Example Neural Network with PyMC3; Linear Regression Function Matrices Neural Diagram LinReg 3 Ways Logistic Regression Function Matrices Neural Diagram LogReg 3 Ways Deep Neural Networks Function Matrices Neural Diagram DeepNets 3 Ways Going Bayesian. MAP estimate. > I couldn’t find examples in either Edward or PyMC3 that make non-trivial use of the embedding in Python. The gradient of func. For example, if we wish to define a particular variable as having a normal prior, we can specify that using an instance of the Normal class. The main benefit of these methods is uncertainty quantification. py: Deprecated nuts_kwargs and step_kwargs: Dec 27, 2018: baseball. linear regression –the Bayesian way 04. PyMC3 on the other hand was made with Python user specifically in mind. Instead, it adds the pm. custom Distribution in PymC3 specific example. MNIST classfification using multinomial logistic + L1¶ Here we fit a multinomial logistic regression with L1 penalty on a subset of the MNIST digits classification task. By the way, this is an implementation of the constrained Probabilistic Matrix Factorization (equation 7 in the paper by Salakhutdinov and Mnih). In future, it will be treated as np. We can also look at probability intervals (there's a 0. I’m a Data Scientist and Entrepreneur. Python numpy. C:\Users\JIMSJOO\Anaconda3\envs\bayes\lib\site-packages\pymc3\model. Index; Module Index; Search Page; Table Of Contents. Thankssample-data-pmprophet. The array may be recreated, a = np. Long-time readers of Healthy Algorithms might remember my obsession with PyMC2 from my DisMod days nearly ten years ago, but for those of you joining us more recently… there is a great way to build Bayesian statistical models with Python, and it is the PyMC package. This blog post is based on the paper reading of A Tutorial on Bridge Sampling, which gives an excellent review of the computation of marginal likelihood, and also an introduction of Bridge sampling. menting model evaluation. py: disaster_model_theano_op. PyMC3’s step methods submodule contains the following samplers: NUTS, Metropolis, Slice, HamiltonianMC, and BinaryMetropolis. PyMC3 Models Documentation, Release 1. Bayesian machine learning (read 'Bayesian. Indeed, your whole company is structured around two main teams — the China Team and the Canada Team — making every experiment politically contentious, as executives from each try to one-up each. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. 70) Example to perform linear mixed effects regression in a Bayesian setting using the PyMc3 framework (on bitbucket) 71) Example of linear mixed effects regression in a Bayesian setting (probabilistic programming) using the rstanarm framework (on bitbucket) 72) Simple example of regression and decision tree in R (on bitbucket). We don't do so in tutorials in order to make the parameterizations explicit. display import Image from matplotlib import pyplot as plt from matplotlib import rc #rc("font", family="serif", size=16) % matplotlib inline. , 2010; Bastien et al. A PyMC3 implementation of the algorithms from: Validating Bayesian Inference Algorithms with Simulation-Based Calibration (Talts, Betancourt, Simpson, Vehtari, Gelman). Function to minimise. Compared to the. PyMC3 is a Python-based statistical modeling tool for Bayesian statistical modeling and Probabilistic Machine Learning which focuses on advanced Markov chain Monte Carlo and variational fitting algorithms. allow the random walk variable to diverge), I just wanted to use a fixed value of the coefficient corresponding to the last inferred value. A common appli. Bayesian Survival analysis with PyMC3 Raw. Instead, we have a control parameter $$\alpha$$ which lets us allocate the variance between the hidden Brownian motion and the noise. Survival analysis studies the distribution of the time to an event. Using PyMC3 » Introduction to Python which has 85 counties with 2 to 116 measurements per county. 7 that supersede 3. Currently, pymc 's stable release (2. Probabilistic Programming in Python with PyMC3 John Salvatier @johnsalvatier Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. See Probabilistic Programming in Python using PyMC for a description. 88476599, -0. Key Idea: Learn probability density over parameter space. Filters out variables not in the model. The sampling algorithm used is NUTS, in which parameters are tuned automatically. We use the non-trivial embedding for many non-trivial inference problems. This model employs several new distributions: the Exponential distribution for the and priors, the Student-T (StudentT) distribution for distribution of returns, and the GaussianRandomWalk for the prior for the. This tutorial is intended for analysts, data scientists and machine learning practitioners. In the original pymc, I can use numpy. This is the 3rd blog post on the topic of Bayesian modeling in PyMC3, see here for the previous two:. To get a range of estimates, we use Bayesian inference by constructing a model of the situation and then sampling from the posterior to approximate the posterior. Probabilistic Programming in Python. Of course for real examples we do not know the true value of the parameters, that's the whole point of doing inferences in the first place. Introduction to PyMC3 models¶. custom Distribution in PymC3 specific example. This is no small task for a beginner in bayesian statistics and takes some getting used to. If you continue browsing the site, you agree to the use of cookies on this website. As we can see from this example we did not get a single number for. However, I think I'm misunderstanding how the Categorical distribution is meant to be used in PyMC. Containers, like variables, have an attribute called value. This model employs several new distributions: the Exponential distribution for the and priors, the Student-T (StudentT) distribution for distribution of returns, and the GaussianRandomWalk for the prior for the. Abstract: If you can write a basic model in Python's scikit-learn library, you can make the leap to Bayesian inference with PyMC3, a user-friendly intro to probabilistic programming in Python! The only requisite background for this workshop is minimal familiarity with Python, preferably with some exposure to building a model in sklearn. Poisson taken from open source projects. For example, CPython 2. To learn more about PyMC, please refer to the online user's guide. I am using PyMC3, an awesome library Do check the documentation for some fascinating tutorials and examples. Introduction to Probabilistic Programming 02. Stay ahead with the world's most comprehensive technology and business learning platform. Check out the getting started guide, or interact with live examples using Binder!. Get the latest release of 3. This post will show how to fit a simple multivariate normal model using pymc3 with an normal-LKJ prior. In a good fit, the density estimates across chains should be similar. 7 that supersede 3. Without being an expert, PyMC3 is a full inference package. We also encourage you to check out other modelling libraries written in Python including pymc3, edward and statsmodels. We use the non-trivial embedding for many non-trivial inference problems. You can see below a code example. Probabilistic Programming in Python. For example, I had a model using a GaussianRandomWalk variable and I wanted to generate predictions into the future. Mathematically, these are not trivial concepts and might require a bit time and patience to understand. Point (*args, **kwargs) ¶ Build a point. We first introduce Bayesian inference and then give several examples of using PyMC 3 to show off the ease of model building and model fitting even for difficult models. The first block fits the GP prior. ArviZ I helped create ArviZ, a Python package for exploratory analysis of Bayesian models that is compatible with PyStan , PyMC3 , emcee , Pyro , and TensorFlow probability. We have two mean values, one on each side of the changepoint. Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. The Erlang distribution is just a special case of the Gamma distribution: a Gamma random variable is also an Erlang random variable when it can be written as a sum of exponential random variables. Probabilistic Programming in Python. Motivating example. PyMC3 and Edward offer a productive out-of-the-box experience for model evaluation. But most of the examples on using the library are in Jupyter notebooks. ones (k) p = pymc3. Pythonで使えるフリーなMCMCサンプラーの一つにPyMC3というものがあります．先日．「PyMC3になってPyMC2より速くなったかも…」とか「Stanは離散パラメータが…」とかいう話をスタバで隣に座った女子高生がしていた（ような気. 0, pgtol=1e-05, epsilon=1e-08, iprint=-1, maxfun=15000, maxiter=15000, disp=None, callback=None, maxls=20)¶. Filters out variables not in the model. For example, I had a model using a GaussianRandomWalk variable and I wanted to generate predictions into the future. When the units of a measurement scale are meaningful in their own right, then the difference between means is a good and easily interpretable measure of effect size. Filters out variables not in the model. fmin_l_bfgs_b(func, x0, fprime=None, args=(), approx_grad=0, bounds=None, m=10, factr=10000000. Bayesian Linear Regression with PyMC3. This project took around 2000 lines of query (Query example can be provided). PyMC (currently at PyMC3, with PyMC4 in the works) "PyMC3 is a Python package for Bayesian statistical modeling and probabilistic machine learning which focuses on advanced Markov chain Monte Carlo and variational fitting algorithms. PyMC3 はまだ alpha 版ですし、ドキュメントもあまり整備されてないのでちょっと大変ですが、これからも頑張ってみようと思います。 あと、一応続きます。. I had some trouble figuring it out on my own, so I tried the example model that was provided in the book (page 236, figure 9. Probabilistic Programming in Python with PyMC3 John Salvatier @johnsalvatier Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. we got a distribution of plausible values. So that our PyMC3 example is somewhat comparable to their example, we use the stretch of data from before 2004 as the "training" set. The GitHub site also has many examples and links for further exploration. If we would like to reduce the dimensionality, the question remains whether to eliminate (and thus ) or (and thus ). MCMC algorithms are available in several Python libraries, including PyMC3. It's natural to think about the job of the likelihood function in this direction: given a fixed value of model parameters, what i. Python and in particular the powerful library called PyMC3. Check out the getting started guide, or interact with live examples using Binder!. However, PyMC3 lacks the steps between creating a model and reusing it with new data in production. *FREE* shipping on qualifying offers. Probabilistic programming in Python: Pyro versus PyMC3 Thu, Jun 28, 2018. PyMC3 implements several standard sampling algorithms, such as adaptive Metropolis-Hastings and adaptive slice sampling, but PyMC3’s most capable step method is the No-U-Turn Sampler. py: Replaced njobs with chains through all tests and examples: Feb 1, 2018. Other goals and/or different models. I had sent a link introducing Pyro to the lab chat, and the PI wondered about differences and limitations compared to PyMC3, the ‘classic’ tool for statistical modelling in Python. Uses same args as dict() does. io/`_ provides a nice interface for Markov-Chain Monte Carlo. Pythonで使えるフリーなMCMCサンプラーの一つにPyMC3というものがあります．先日．「PyMC3になってPyMC2より速くなったかも…」とか「Stanは離散パラメータが…」とかいう話をスタバで隣に座った女子高生がしていた（ような気. Topic models For example, a document containing words like “dog”, “cat” or “rat” likely has a different underlying topic than a document containing words like “CPU”, “GPU” or “RAM”. Transformed prior variables; Prior variables; Variables in likelihood; Under the hood; Theano; Specifying sampler (step) and multiple chains; Samplers available. Probabilistic programming allows a user to specify a Bayesian model in code and perform inference on that model in the presence of observed data. What would you like to do? Embed. For example, fully conditional models may require an enormous amount of data to cover all possible cases, and probabilities may be intractable to calculate in practice. Installing pymc3 on Windows machines PyMC3 is a python package for estimating statistical models in python. PyMC3 has been used to solve inference problems in several scientific domains, including astronomy, molecular biology, crystallography, chemistry, ecology and psychology. Being a computer scientist, I like to see “Hello, world!” examples of programming languages. Instead, we are interested in giving an overview of the basic mathematical consepts combinded with examples (writen in Python code) which should make clear why Monte Carlo simulations are useful in Bayesian modeling. This post in particular focuses on Jupyter's ability to add HTML output to any object. For example, with few data points our uncertainty in $\beta$ will be very high and we'd be getting very wide posteriors. Bayesian Neural Network in PyMC3. It is actually a general framework which includes as special cases the very first and simpler MCMC. The actual work of updating stochastic variables conditional on the rest of the model is done by StepMethod objects, which are described in this chapter. (Part 2) Posted on November 20, 2016 Written by The Cthaeh 5 Comments In the first part of this post , I gave the basic intuition behind Bayesian belief networks (or just Bayesian networks ) — what they are, what they’re used for, and how information is exchanged between their nodes. py: disaster_model_theano_op. In the previous example we were able to deduce the stationary distribution of the Markov chain by looking at the samples generated from the chain after the burn in period. July 2, 2018 From my student Rui Wang, PhD in Physics and MS in Biostatistics. For example, a study conducted by Holbrook, Crowther, Lotter, Cheng and King in 2000 investigated the effectiveness of benzodiazepine for the treatment of insomnia. 0 The question marks represent things that don’t exist in the two libraries on their own. 0 of the textbook to PyMC3 which I think would be helpful if you go down this path. MCMC algorithms are available in several Python libraries, including PyMC3. Also, we are not going to dive deep into PyMC3 as all the details can be found in the documentation. See Probabilistic Programming in Python using PyMC for a description. 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http://rafbis.it/qowu/ggplot-map.html | ## Ggplot Map
ggplot is a Python implementation of the grammar of graphics. You just have to provide the data, tell this tool the way to map variables to aesthetics and the right graphical primitives to use. When you call ggplot, you provide a data source, usually a data frame, then ask ggplot to map different variables in our data source to different aesthetics, like position of the x or y-axes or color of our points or bars. Use geom_polygon() to visualize the data points. The topic of inset maps has gained attention and recently Enrico Spinielli asked inset maps could be created for data in unusual coordinate systems: Speaking of insets, do you know of any ggplot2 examples with an. kriged1 and lzn. x and y are what we used in our first ggplot + geom_line() function call to map the variables age and circumference to x-axis and y-axis values. Bar Charts on A Map Bar Charts by ggplot2. To begin with, I am using below libraries ggplot has no special syntax for heatmap, it uses combination of geom_title and scale_fill_gradient to plot heatmap. Polygons from a reference map Source: R/geom-map. But I still need to have the state boundaries come through on the map, but I can't figure it out. It would be informative to add finer administrative information on top of the previous map, starting with state borders and names. Reading time ~1 minute At times it is convenient to draw a frequency bar plot; at times we prefer not the bare frequencies but the proportions or the percentages per category. For this exercise we are going to use plotnine which is a Python implementation of the The Grammar of Graphics, inspired by the interface of the ggplot2. A good general-purpose solution is to just use the colorblind-friendly palette below. The different color systems available in R are described at this link : colors in R. We are used to seeing similar maps produced with conventional GIS platforms or software such as Processing but I hadn't yet seen one from the R community (feel free to suggest some in the comments). It inherits x = displ from ggplot() but specifies its own mapping for y = cty. This page provides help for adding titles, legends and axis labels. This grammar, based on the Grammar of Graphics (Wilkinson, 2005), is composed of a set. For users wishing to create a good map without too much thought I would recommend this worksheet. A good general-purpose solution is to just use the colorblind-friendly palette below. ; Inspect the structure of usa. At least 3 variables are needed per observation: x: position on the X axis. It includes four major new features: Subtitles and captions. color and fill. In the following examples, I'll show you how to modify the axes of such ggplots. To arrange multiple ggplot2 graphs on the same page, the standard R functions - par() and layout() - cannot be used. Figure 3: Heatmap with Manual Color Range in Base R. (If you know NYC, you know that the map is distorted — don't worry we will fix this in the last step). John Tukey. One of the oldest and most popular is matplotlib - it forms the foundation for many other Python plotting libraries. Fehler beim Laden des Minibildes. R code for a ggplot2 map of Europe. ggplot2 maps with insets. Here is the first 10 rows of the dataset I am using:. Posts about ggplot2 written by Gina. A popular package for graphics is the ggplot2 package of the tidyverse and in this example I'll show you how to create a heatmap with ggplot2. x1,y=coords. 1 tmap basics. The mapdata package contains a few more, higher-resolution outlines. plotnine is a Python package allowing you to use ggplot2-like code that is implementing the grammar of graphics. GitHub Gist: instantly share code, notes, and snippets. arrange() and arrangeGrob() to arrange multiple ggplots on one page; marrangeGrob() for arranging multiple ggplots over multiple pages. • CC BY RStudio • [email protected] In the second plot, geom_point() inherits only data but not all the mapping. This is done via the aes() argument. There is a wealth of information on the philosophy of ggplot2, how to get started with ggplot2, and how to customize the smallest elements of a graphic using ggplot2 — but it's all. Dieses wurde entwickelt, um geographische. The example uses two CSV files, cities-coords. To create a heatmap, we'll use the built-in R dataset mtcars. Thank you very much for this guide! It was very useful and I've learned a lot! ggplot2 is a powerful graphic package and with thematic map (and not google) possibilities are endless! Thx again! 😉. As I was learning I realized information about creating maps in ggplot is scattered over the internet. WIth ggiraph, you can take an existing ggplot2 bar chart. The different color systems available in R are described at this link : colors in R. View source: R/ggsurv. After you've told ggplot() what data to use in R, the next step is to tell it how your data corresponds to visual elements of your plot. This article provide many examples for creating a ggplot map. We need to tell the function which shapefile we want to use, but also the longitude and latitude columns, and which column contains the regions. It provides a more programmatic interface for specifying what variables to plot, how they are displayed, and general visual properties. We need to change the color palette, improve the legend, use a log scale transformation for the colorscale, change background and add titles and explanation. In one recent project I needed to draw several maps and visualize different kinds of geographical data on it. Also, per Joachim's suggestion, I put a box around the blown up area of the map. In this particular example, we're going to create a world map showing the points of Beijing and Shanghai, both cities in China. rayshader is an open source package for producing 2D and 3D data visualizations in R. In most cases, when you map categorical data to an aesthetic like color, you are also defining sub-groupings of the data, and ggplot2 will draw a lines, calculate statistics, etc. color and fill. The downside is that:. By simply tinkering with the xlim and ylim arguments of the plot function we can limit the display to just Europe. plotnine is a Python package allowing you to use ggplot2-like code that is implementing the grammar of graphics. To display data values, map variables. We then loop over each row of the annotations data frame and add each annotation ( geom_curve() and geom_text() calls) to the map object one by one. You can see the default ggplot color gradient below. 고정 종횡비 고정. Um die Funktionalität zu erweitern, kann zusätzlich das Paket ggspatial genutzt werden. geom_map takes care of the left join of the map with the data. Preparing the data. Finally, in Section $$4$$ I combine all of these pieces together to create the final. This involves a separation between the input data and the aesthetics (how data are visualised): each input dataset can be 'mapped' in a range of different ways including location on the map (defined by data's geometry), color, and other visual variables. Learning Objectives. In this course, Mike Chapple shows how to work with ggplot2 to create basic visualizations, how to beautify those visualizations by applying different aesthetics, and how to visualize data with maps. However, my code using ggsave or tiff() with. However, the layer after that, geom_smooth() inherits everything from ggplot(). ggplot2 is a system for declaratively creating graphics, based on The Grammar of Graphics. Easily turn data from the maps package in to a data frame suitable for plotting with ggplot2. This mapping between data and visual aesthetics is the second element of a ggplot2 layer. The map frame has to contain a variable region or id. To begin with, I am using below libraries ggplot has no special syntax for heatmap, it uses combination of geom_title and scale_fill_gradient to plot heatmap. kriged1) Formal class 'SpatialPointsDataFrame' [package "sp"] with 5 slots. ggplot(data=gapminder, aes(x=lifeExp)) + geom_density(size=1. global <- map_data("world") #World longitude and latitude data View(global) #view the data and notice the column of long, lat, and group gg1 <- ggplot() + geom_polygon(data = global, aes(x=long, y. We are used to seeing similar maps produced with conventional GIS platforms or software such as Processing but I hadn't yet seen one from the R community (feel free to suggest some in the comments). x2,col=type), data=tmp) 51. p <- ggmap (get_googlemap (center = c (lon = -122. This is called a sequential color scale, because it maps data sequentially from one color to another color. The call to ggplot and aes sets up the basics of how we are going to represent the various columns of the data frame. colour maps to the colors of lines and points, while fill maps to the color of area fills. , add geoms - graphical representation of the data in the plot (points, lines, bars). However, the following R. map_id, alpha, color, fill, linetype, size Maps AB C Basics Build a graph with qplot() or ggplot() ggplot2 is based on the grammar of graphics, the idea that you can build every graph from the same few components: a data set, a set of geoms—visual marks that represent data points, and a coordinate system. Customized choropleth map with R and ggplot2 There is a bit of work to do to get a descent figure. I used the geocode() function to get the coordinates of these places and qmap() to get the maps. This R package makes it easy to integrate and control Leaflet maps in R. With ggplot2, it's easy to: • produce handsome, publication-quality plots with automatic legends created from the plot specification • superimpose multiple layers (points, lines, maps, tiles, box plots) from different data sources with automatically adjusted common scales. In ggmap: Spatial Visualization with ggplot2. Once you have downloaded that, unzip it and put the whole inputs directory in the current working directory where you are. Dieses wurde entwickelt, um geographische. Both codes shown in. When I attended usrR! 2012 last month, there was an interesting presentation by Dr. : "red") or by hexadecimal code (e. However, I came across a post of Bob Rudis where he proposes coord_proj() which should do what coord_map does but using proj4::project instead of mapproject. The ggplot data should be in data. This example demonstrates the "ggplot" style, which adjusts the style to emulate ggplot (a popular plotting package for R). Before you get started, read the page on the basics of plotting with ggplot and install the package ggplot2. At the intersection of each category we'll draw a box, except here we call it a tile, using the geom_tile() layer. Of course, it is straightforward to edit the color scheme for one given plot. R package to add north symbols and scale bars to maps created with ggplot or ggmap View on GitHub. Density map of crime in Houston, TX made in ggmap (David Kahle) ggmap is a powerful package for visualizing spatial data and models. The goal of this article is to describe how to change the color of a graph generated using R software and ggplot2 package. The map object we get from OSM is not directly in the format for ggplot2, we should then apply autoplot function. Take a pill for a headache and immerse yourself in a world ruled by command lines with obscure syntax; but if you commit yourself to learn, an unbelievable power will raise from. Now, this is a complete and full fledged tutorial. Note that this example is based on a density plot. It seems as though there are no limits to what can be done with ggplot2. In this course, Mike Chapple shows how to work with ggplot2 to create basic visualizations, how to beautify those visualizations by applying different aesthetics, and how to visualize data with maps. 608013), zoom = 11. 7) of our open source book Geocomputation with R. ggplot style sheet¶. We need to change the color palette, improve the legend, use a log scale transformation for the colorscale, change background and add titles and explanation. Files for ggplot, version 0. Description. Published on October 29, 2016 at 4:48 pm; Updated on April 28, 2017 at 6:27 pm; 5,178 reads. Chapter 9 Plotting "Spatial" Data with ggplot. We are then adding a classic ggplot layer (geom_point) to plot all of the rows in our i2 data set. Set up your map in ggplot. Next Page. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. We then plot that using ggplot2 with the following line: ggplot() + geom_polygon( data=fifty_states, aes(x=long, y=lat, group = group),color="white", fill="grey10" ) You should see the following in the Plots pane of R Studio: Fine, if a bit ugly. The imported packages are kept to an absolute. In the following examples, I'll show you how to modify the axes of such ggplots. ggplot is a powerful tool for making custom maps. Simple data mining and plotting data on a map with ggplot2. Using ggplot to plot pie charts on a geographical map Posted on October 25, 2018 July 30, 2019 by Marriane Makahiya In this post, we would go through the steps to plot pie charts on a world map, just like the one below. Compared to base graphics, ggplot2. In this case we got a map of the whole world. Set up your map in ggplot. 8 thoughts on " Creating a large scale map using ggplot2: a step by step guide. With coord_map all elements of the graphic have to be projected which is not the case here. x - (required) x coordinate of the text label ; y - (required) y coordinate of the text label ; label - (required) the text for the label ; size - (default: 5) size of the font ; colour - (default: "black") the color of the text label. At the intersection of each category we'll draw a box, except here we call it a tile, using the geom_tile() layer. The map frame has to contain a variable region or id. geom_map takes care of the left join of the map with the data. I found the combination of R/ggplot/maps package extremely flexible and powerful, and produce nice looking map based visualizations. R's ggplot2 package is a well-known tool for producing beautiful static data visualizations that you can include in a printed report. Once you successfully import that data into R, ggplot2 works with simple features data frames to easily generate geospatial visualizations using all the. txt) or view presentation slides online. I was also interested in how to plot this information geographically on a map of Sweden and represent the number of individuals by the size of a circle over the corresponding city. aes defines the "aesthetics", which is how columns of the data frame map to graphical attributes such as x and y position, color, size, etc. Then I plot the chapters choosing. In addition to maps, rayshader also allows the user to translate ggplot2 objects into beautiful 3D data. name/knitr/options#chunk_options opts_chunk$set(comment = "", error= TRUE, warning = FALSE. This can be done using functions from the cowplot package. It accepts any object that can be coerced to the network class, including adjacency or incidence matrices, edge lists, or one-mode igraph network objects. filippoolioso. functions for quick map plotting (c. While qplot provides a quick plot with less flexibility, ggplot supports layered graphics and provides control over each and every aesthetic of the graph. Key R functions and packages: We'll use the viridis package to set the color palette. ; Construct a ggplot, step by step: Use usa as the data layer. You only need to supply mapping if there isn't a mapping defined for the plot. , add geoms - graphical representation of the data in the plot (points, lines, bars). Of course, it is straightforward to edit the color scheme for one given plot. To create a heatmap, we'll use the built-in R dataset mtcars. This is the most basic heatmap you can build with R and ggplot2, using the geom_tile () function. Ggplot Circle Plot. In one recent project I needed to draw several maps and visualize different kinds of geographical data on it. This coordinate system provides the full range of map projections available in. We then loop over each row of the annotations data frame and add each annotation ( geom_curve() and geom_text() calls) to the map object one by one. Along the way, we will create a Hospital Density Map for Scotland as the one below: Before We Start. ggplot2 is a system for declaratively creating graphics, based on The Grammar of Graphics. There is a wealth of information on the philosophy of ggplot2, how to get started with ggplot2, and how to customize the smallest elements of a graphic using ggplot2 — but it's all. I created a density plot using ggplot's stat_density_2d and I am trying to overlay this on top of a map which is a shapefile read and loaded to function in ggplot. Concise tutorial on how to use R Studio and ggplot2 package to create quick plots. In ggplot2, guides are produced automatically based on the layers in your plot. The map frame has to contain a variable region or id. It also includes as numerous bug fixes and minor improvements, as described in the release notes. We then plot that using ggplot2 with the following line: ggplot() + geom_polygon( data=fifty_states, aes(x=long, y=lat, group = group),color="white", fill="grey10" ) You should see the following in the Plots pane of R Studio: Fine, if a bit ugly. An alternative for ggplot maps is to use geom_map. ", exact = FALSE, ) Arguments. If you're coming from base graphics, some of the syntax may appear intimidating, but's it's all part of the "grammar of graphics" after which ggplot2 is modeled. An alternative for ggplot maps is to use geom_map. A pie chart is considered as a circular statistical graph, which is divided into slices to illustrate numerical proportion. Es wird hauptsächlich in Verbindung mit normalen Daten verwendet, kann aber auch zur Darstellung von geographischen Daten benutzt werden. By simply tinkering with the xlim and ylim arguments of the plot function we can limit the display to just Europe. This is done via the aes() argument. I will show you the ggplot2 approach and how it avoids the problems inherent in other approaches. Using ggplot to plot pie charts on a geographical map Posted on October 25, 2018 July 30, 2019 by Marriane Makahiya In this post, we would go through the steps to plot pie charts on a world map, just like the one below. they are very helpful during seeking/comparing missing values in time series or checking cross-correlations for large number of financial instruments. The topic of inset maps has gained attention and recently Enrico Spinielli asked inset maps could be created for data in unusual coordinate systems: Speaking of insets, do you know of any ggplot2 examples with an. Here is a short tutorial, monospace font indicates the code you need to run in R. How I use shapefiles in R with ggplot2 and RGDAL. Another example of this is the use of maps in presenting data. ; Map long and lat onto the x and y aesthetics, respectively. Therefore we need some way to translate the maps data into a data frame format the ggplot can use. The examples below documents ggmap syntax, starting with Google basemaps as examples. they are very helpful during seeking/comparing missing values in time series or checking cross-correlations for large number of financial instruments. You provide the data, tell ggplot2 how to map variables to aesthetics, what graphical primitives to use, and it takes care of the details. It includes four major new features: Subtitles and captions. Since I myself currently live in the city of Freiburg in the south of Germany, we will create the tutorial using this city. In this particular example, we're going to create a world map showing the points of Beijing and Shanghai, both cities in China. In the latter section of the post I go over options for saving the resulting plots, either together in a single document, separately, or by creating combined plots. ggplot2 also makes it easy to make much more complicated data visualizations, like geospatial maps: There's also a lot that you can do to format a chart. The imported packages are kept to an absolute. But the reason I use them. Other types of maps, like dot maps, can also be generated using ggplot. First we use the get_map() command from ggmap to pull down the basemap. These settings were shamelessly stolen from (with permission). mature spreading gif pic compilation music xxx. Now, this is a complete and full fledged tutorial. It combines the advantages of both base and lattice graphics: conditioning and shared axes are handled automatically, and you can still build up a plot step by step from multiple data sources. You can see the default ggplot color gradient below. GitHub Gist: instantly share code, notes, and snippets. We need to change the color palette, improve the legend, use a log scale transformation for the colorscale, change background and add titles and explanation. Here I will show how to add small graphical information to maps – just like putting a stamp on an envelope. It includes four major new features: Subtitles and captions. But in this tutorial, you take this a step further, and make a map that shows population by longitude and latitude at the country level. These two data sets will be used to generate the graphs below. Origianlly based on Leland Wilkinson's The Grammar of Graphics, ggplot2 allows you to create graphs that represent both univariate and multivariate numerical and categorical data in a. If it is made with R ggplot package functions geom_histogram () or geom_bar () then bar chart may look like this: The elegance of ggplot functions realizes in simple yet compact expression of visualization formula while hiding many options assumed by default. The base R function to calculate the box plot limits is boxplot. Make some simple maps using ggplot() Now we can create the maps in the same way we make non-geographic charts in ggplot. txt) or view presentation slides online. To do so we need the packages png and grid [crayon-5ea8f421dd5cc907440222/] Btw, this is just a cool and fast way to import different packages …. 608013), zoom = 11. He likes maps, ggplot and a good story. (Gio did most of the hard work of data munging and modeling though!) Figured I would detail the process here for some notes. However, I came across a post of Bob Rudis where he proposes coord_proj() which should do what coord_map does but using proj4::project instead of mapproject. name/knitr/options#chunk_options opts_chunk$set(comment = "", error= TRUE, warning = FALSE. : "red") or by hexadecimal code (e. The ggnet2 function is a visualization function to plot network objects as ggplot2 objects. In the remainder of this section I initialize the $$\text{R}$$ code I use in the analysis below. It would be informative to add finer administrative information on top of the previous map, starting with state borders and names. great tits, warp speed. It is a package built over ggmap2 and helps us map spatial data over online maps like Google maps or Open Street Maps. In the following examples, I'll show you how to modify the axes of such ggplots. Now, instead of qplot, we need to use ggplot. In addition, rgeos and maptools removed, not needed. Shapefiles in R with ggplot2 & rgdal 2018/09/04. Plotting the map using ggplot2 The goal is to produce a map where each chapter is plotted according to its location, with the point's size indicating the amount of Twitter followers. There is no alternative to this - ggplot2. ggplot2: axis manipulation and themes ## knitr configuration: http://yihui. However, you will have to convert your data from spatial (sp) objects to data. Subplots in maps with ggplot2 Following the surprising success of my latest post , I decided to show yet another use case of the handy ggplot2::annotation_custom(). Making Maps with GGPLOT. To begin with, I am using below libraries ggplot has no special syntax for heatmap, it uses combination of geom_title and scale_fill_gradient to plot heatmap. So here I combine all that knowledge. Example: Creating a Heatmap in R. It is not specifically geared towards mapping, but one can generate great maps. Take a look at the documentation using ?map_data to see other options. 7) of our open source book Geocomputation with R. The arc length represents the angle of pie chart. Although R does provide built-in plotting functions, the ggplot2 library implements the Grammar. I'll also add black borders and make sure that the map is plotted using the right scale. You just have to provide the data, tell this tool the way to map variables to aesthetics and the right graphical primitives to use. This base map will then be extended with different map elements, as well as zoomed in to an area of interest. Guest blog by Michael Grogan. Include maps in ggplot graphs, overlay data on maps, and learn how to realize complex matrix scatterplots; About : ggplot2 is one of the most sophisticated and advanced packages of R and its use is constantly growing in the community of R programmers. Now we can use ggplot2 to plot the polygons, and fill them with a gradient based on the number of dogs. March 17, 2015 Type Package Title An Implementation of the Grammar of Graphics Version 1. ggplots are almost entirely customisable. This make it difficult if we want to produce a map like the above screenshot, which was posted by Tyler Rinker, the author of R package pacman. It would be informative to add finer administrative information on top of the previous map, starting with state borders and names. The different color systems available in R are described at this link : colors in R. In this map we are simply creating the ggmap object called p which contains a Google map of Seattle. Simple data mining and plotting data on a map with ggplot2. These settings were shamelessly stolen from (with permission). The component of a scale that you’re most likely to want to modify is the guide, the axis or legend associated with the scale. Use geom_polygon() to visualize the data points. It provides a more programmatic interface for specifying what variables to plot, how they are displayed, and general visual properties. Example 2: Create Heatmap with geom_tile Function [ggplot2 Package] As already mentioned in the beginning of this page, many R packages are providing functions for the creation of heatmaps in R. unit = "km") On the example above, I call the « scaleBar » function, and I specify some values for the arguments. Marcin Kierczak ggplot2 and maps. Guides allow you to read observations from the plot and map them back to their original values. Setting up a data frame for visualization. Inset maps enable multiple places to be shown in the same geographic data visualisation, as described in the Inset maps section (8. As stated in the title, I'm trying to create a continuous scale with distinct color and value breaks within the ggplot2 package in R. How to add a background image to ggplot2 graphs. Now it is just the center of the states (mean(lon), min(lat)). ggplot2 also makes it easy to make much more complicated data visualizations, like geospatial maps: There's also a lot that you can do to format a chart. A couple of people have asked for some code to help them on their way with map making in R, so here is a simple snippet of code I used to make a. In my continued playing around with ggplot I wanted to create a chart showing the cumulative growth of the number of members of the Neo4j London meetup group. Nonetheless, you may encounter a case in which you really do want to use one. Find more Do More With R. # map the counties ggplot() + geom_polygon(data=counties, aes(x=long, y=lat, group=group)) How about the points. 7) of our open source book Geocomputation with R. Graphics with ggplot2. In this particular example, we're going to create a world map showing the points of Beijing and Shanghai, both cities in China. data A data frame. This can be done using functions from the cowplot package. Make some simple maps using ggplot() Now we can create the maps in the same way we make non-geographic charts in ggplot. # Using the ggplot2 function coord_map will make things look better and it will also let you change # the projection. Making a data frame from map outlines. is more verbose for simple / canned graphics; is less verbose for complex / custom graphics; does not have methods (data should always be in a data. When I attended usrR! 2012 last month, there was an interesting presentation by Dr. The elements of the two files are linked by their offsets in the file: the first geometric feature (offset 0 in the shp) has its attributes in the first attribute tuple (offset 0 in the dbf file). frame(state = tolower(rownames(USArrests)), USArrests) library(reshape2) # for melt crimesm - melt(crimes, id = 1) library. Preparing the data. So I created a theme (theme_map). In this seventh episode of Do More with R, learn how to create maps in R—it's easier than you think, thanks to new and updated packages like sf, tmap, and ggplot2. ggplot generates legends only when you create an aesthetic mapping inside aes. Also, per Joachim's suggestion, I put a box around the blown up area of the map. Both codes shown in. In this lesson you will create the same maps, however instead you will use ggplot(). In the previous lesson, you used base plot() to create a map of vector data - your roads data - in R. Posts about ggplot2 written by Gina. Inset maps enable multiple places to be shown in the same geographic data visualisation, as described in the Inset maps section (8. After all these, ggplot2 takes care of all other details. pred: num [1:9962] 9. colour maps to the colors of lines and points, while fill maps to the color of area fills. Hadley Wickham's R package ggplot2 was created based upon Wilkinson's writings. Using Maps in ggplot2. This is called a sequential color scale, because it maps data sequentially from one color to another color. While qplot provides a quick plot with less flexibility, ggplot supports layered graphics and provides control over each and every aesthetic of the graph. ggplot2 - Pie Charts. To get all the innards of a ggplot you can use the functions. R source library(ggplot2) crimes - data. Draw the map without attributes. This is about plotting reference maps from shapefiles using ggplot2. We then loop over each row of the annotations data frame and add each annotation ( geom_curve() and geom_text() calls) to the map object one by one. Default statistic: stat_identity Default position adjustment: position_identity. 7) of our open source book Geocomputation with R. You only need to supply mapping if there isn't a mapping defined for the plot. After all these, ggplot2 takes care of all other details. global <- map_data("world") #World longitude and latitude data View(global) #view the data and notice the column of long, lat, and group gg1 <- ggplot() + geom_polygon(data = global, aes(x=long, y. separately for every sub-grouping of the data. ; Inspect the structure of usa. 000) result in very interesting drawings. My setup is Mac OS 10. 3 MB) File type Egg Python version 2. This is called a sequential color scale, because it maps data sequentially from one color to another color. Using the same data as in the previous exercise, build a static map quickly and easily using ggmap. A couple of people have asked for some code to help them on their way with map making in R, so here is a simple snippet of code I used to make a. Hacking maps with ggplot2 This is a very short post on mapping with ggplot2. Both codes shown in. You provide the data, tell ggplot2 how to map variables to aesthetics, what graphical primitives to use, and it takes care of the details. Using map_data and build from scratch. ggplots are almost entirely customisable. When we map a continuous variable to a color scale, we map the values for that variable to a color gradient. If qplot is an integral part of ggplot2, then the ggplot command is a super component of the ggplot2 package. ##1) Create a map with all of the crime locations plotted. Guest blog by Michael Grogan. rayshader is an open source package for producing 2D and 3D data visualizations in R. In particular, ggplot cannot work with a vector by itself. Make some simple maps using ggplot() Now we can create the maps in the same way we make non-geographic charts in ggplot. Recently, I was attempting to layer plots created using ggplot onto a map. This article provide many examples for creating a ggplot map. Hey everybody, this is just a short post but I found it very useful. This is the most basic heatmap you can build with R and ggplot2, using the geom_tile () function. Typically the problem can be decomposed into two problems: using one data source to draw a map, and adding metadata from another information source to the map. It would be informative to add finer administrative information on top of the previous map, starting with state borders and names. In the first plot, geom_point() inherits the same data and mapping from ggplot(). Luckily, they're fairly straightforward to produce in ggplot2. You provide the data, tell ggplot2 how to map variables to aesthetics, what graphical primitives to use, and it takes care of the details. An alternative for ggplot maps is to use geom_map. Create a data frame of map data Source: R/fortify-map. Take a look at the documentation using ?map_data to see other options. Data Visualization with ggplot2 : : CHEAT SHEET ggplot2 is based on the grammar of graphics, the idea that you can build every graph from the same components: a data set, a coordinate system, and geoms—visual marks that represent data points. Making maps with R; Create maps with the maptools package; Maps with R; Maps with R; Cartographie avec R; CRAN Task View: Analysis of Spatial Data; Visualisation with R; introduction-spatial-data-ggplot2/. The Complete ggplot2 Tutorial - Part1 | Introduction To ggplot2 (Full R code) Previously we saw a brief tutorial of making charts with ggplot2 package. This is called a sequential color scale, because it maps data sequentially from one color to another color. Some features: - Uses multiple map tiles stitched together to create high quality images. The maps package comes with a plotting function, but, we will opt to use ggplot2 to plot the maps in the maps package. Python has a number of powerful plotting libraries to choose from. 3) If you want, you can also add a histogram later. Set up your map in ggplot. Include maps in ggplot graphs, overlay data on maps, and learn how to realize complex matrix scatterplots; About : ggplot2 is one of the most sophisticated and advanced packages of R and its use is constantly growing in the community of R programmers. ggplot2 ist eines der am häufigsten benutzten Pakete zur Datenvisualisierung in R. Guides allow you to read observations from the plot and map them back to their original values. Often you will find your self grabbing data sets from some site, scraping, data cleaning and reshaping, and graphing. ggplot(df, aes(x = lon, y = lat)) + coord_quickmap() + geom_point() In addition, the ggmap package offers some functionality to plot the data on maps. Nonetheless, you may encounter a case in which you really do want to use one. Scale bar and North arrow on a ggplot2 map using R 10 November 2013 IT , Maps , Pense-bête ggplot2 , legend , Map , north arrow , R , scale bar Ewen Gallic After some research on the Internet, I gave up trying to find an R function to add a scale bar and a North arrow on a map, using ggplot(). I found the combination of R/ggplot/maps package extremely flexible and powerful, and produce nice looking map based visualizations. We were doing some exploratory data analysis on some attacker data at work and one of the things I was interested is what were "working hours" by country. The two things we can do are: setting a static color for our entire graph; mapping a variable to a color so each level of the variable is a different color in our graph; In the earlier examples, we used a static color (red) to modify all of the points and bars in the two graphs that we created. Parameters. In this post I'll show you to use the gganimate package from David Robinson to create animations from ggplot2 plots. R - Heat maps with ggplot2 Heat maps are a very useful graphical tool to better understand or present data stored in matrix in more accessible form. 8 Common ggplot issues. Introduction. These visual caracteristics are known as aesthetics (or aes) and include:. Note that if you, the student, wish to run all the code yourself, you should download the inputs directory as a zipped file by going here with a web browser and then clicking the big "Download" button on the right. Hotwife XXX - Lena Anderson Enjoys Wine And Cock Time. The overall appearance can be edited by changing the overall appearance and the colours and symbols used. In the previous lesson, you used base plot() to create a map of vector data - your roads data - in R. Could fine-tune the location of states'label as I did in the China map later. ggplot2 VS Base Graphics. A color can be specified either by name (e. Export plots for use outside of the R environment. Note that if you, the student, wish to run all the code yourself, you should download the inputs directory as a zipped file by going here with a web browser and then clicking the big "Download" button on the right. However, the layer after that, geom_smooth() inherits everything from ggplot(). Advertisements. y: position on the Y axis. plotnine is a Python package allowing you to use ggplot2-like code that is implementing the grammar of graphics. PlotSnow’sdata london + geom_point(mapping= aes(x=coords. You will also learn how to create a choropleth map, in which areas are patterned in proportion to a given variable values being displayed on the map, such as population life expectancy or density. Learning Objectives. Of course, it is straightforward to edit the color scheme for one given plot. When I attended usrR! 2012 last month, there was an interesting presentation by Dr. In this blog, we will create a heat-map choropleth creating US county level map using the data from the previous blog. However, I came across a post of Bob Rudis where he proposes coord_proj() which should do what coord_map does but using proj4::project instead of mapproject. However, the following R. These two data sets will be used to generate the graphs below. If qplot is an integral part of ggplot2, then the ggplot command is a super component of the ggplot2 package. In order to make a reproducible example that would be appropriate I need to link to the data set since the dput is so large. To display data values, map variables. The default colors in ggplot2 can be difficult to distinguish from one another because they have equal luminance. ggplot2 is a system for declaratively creating graphics, based on The Grammar of Graphics. In a recent working paper I made a hexbin map all in R. The basic solution is to use the gridExtra R package, which comes with the following functions:. You probably need. Package ggplot2. When we map a continuous variable to a color scale, we map the values for that variable to a color gradient. Next, we call up the state boundaries data using data("fifty_states"). The call to ggplot and aes sets up the basics of how we are going to represent the various columns of the data frame. Of course, it is straightforward to edit the color scheme for one given plot. We begin by specifying two categorical variables for the x and y aesthetics. Python has a number of powerful plotting libraries to choose from. frame s to use ggplot. Let us see how to Save the plots drawn by R ggplot using R ggsave function, and the. I wanted to achieve the effect of the glow from space, so used dark background tones (I made a black fill for the countries and dark gray fill for seas and oceans). kriged1) Formal class 'SpatialPointsDataFrame' [package "sp"] with 5 slots. This is a little more complicated to get right, because historams are computed differently and need some additional arguments. In the previous lesson, you used base plot() to create a map of vector data - your roads data - in R. The different color systems available in R are described at this link : colors in R. Afterwards, we can use all the power of ggplot2 to include points, labels, paths, etc. However, my code using ggsave or tiff() with. Recently, I wondered whether there is a way to draw a fish shape using a mathematical function. A couple of people have asked for some code to help them on their way with map making in R, so here is a simple snippet of code I used to make a. However, I came across a post of Bob Rudis where he proposes coord_proj() which should do what coord_map does but using proj4::project instead of mapproject. This involves a separation between the input data and the aesthetics (how data are visualised): each input dataset can be ‘mapped’ in a range of different ways including location on the map (defined by data’s geometry), color, and other visual variables. ; Inspect the structure of usa. There are cartodb and mapbox which are great for creating server-"baked" tilesets, leaflet and d3. You probably…. However, the layer after that, geom_smooth() inherits everything from ggplot(). We need to change the color palette, improve the legend, use a log scale transformation for the colorscale, change background and add titles and explanation. ggplot2 implements the grammar of graphics, a coherent system for describing and building graphs. Mapping with ggplot: Create a nice choropleth map in R This post shows how to use ggplot to map a choropleth map from shapefiles, as well as change legend attributes and scale, color, and titles, and finally export the map into an image file. The map contains three layers: buildings, water and the. 0 integration. The above map (and this one) was produced using R and ggplot2 and serve to demonstrate just how sophisticated R visualisations can be. There is a one-to-one relationship. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. We are then adding a classic ggplot layer (geom_point) to plot all of the rows in our i2 data set. Now, instead of qplot, we need to use ggplot. The package "maps" contains geographical information very useful for producing maps, and it's fairly easy to use this to make plots in ggplot2. The call to ggplot and aes sets up the basics of how we are going to represent the various columns of the data frame. If specified and inherit. Fehler beim Laden des Minibildes. Nonetheless, you may encounter a case in which you really do want to use one. It is not specifically geared towards mapping, but one can generate great maps. There is a one-to-one relationship. The simple graph has brought more information to the data analyst's mind than any other device. The call to ggplot and aes sets up the basics of how we are going to represent the various columns of the data frame. Easily turn data from the maps package in to a data frame suitable for plotting with ggplot2. Since I haven't worked very much with maps in ggplot2 yet, I had to find some good blogposts online first. To do so we need the packages png and grid [crayon-5ea8f421dd5cc907440222/] Btw, this is just a cool and fast way to import different packages …. Customized choropleth map with R and ggplot2 There is a bit of work to do to get a descent figure. geom_map requires specifying plot limits in some way, such as with expand_limits. The base R function to calculate the box plot limits is boxplot. So I created a theme (theme_map). The latter is superimposed on p1, then the former is flipped horizontally and added to the right side of it. The map frame has to contain a variable region or id. May 23, 2019, 4:06am #1. The default colors in ggplot2 can be difficult to distinguish from one another because they have equal luminance. Here is a short tutorial, monospace font indicates the code you need to run in R. But apart from that: nothing fancy such as ggmap or the like. x - (required) x coordinate of the text label ; y - (required) y coordinate of the text label ; label - (required) the text for the label ; size - (default: 5) size of the font ; colour - (default: "black") the color of the text label. The ggplot data should be in data. To arrange multiple ggplot2 graphs on the same page, the standard R functions - par() and layout() - cannot be used. David Kahle about the package ggmap. As stated in the title, I'm trying to create a continuous scale with distinct color and value breaks within the ggplot2 package in R. 7) of our open source book Geocomputation with R. Using Maps in ggplot2. fill: the numeric value that will be translated in a color. World maps that show population by longitude and latitude are almost like a meme in cartography and data visualization. After all these, ggplot2 takes care of all other details. Subplots in maps with ggplot2 Following the surprising success of my latest post , I decided to show yet another use case of the handy ggplot2::annotation_custom(). It accepts any object that can be coerced to the network class, including adjacency or incidence matrices, edge lists, or one-mode igraph network objects. For this example we take data from the maps package using ggplot2::map_data(). 608013), zoom = 11. In the second plot, geom_point() inherits only data but not all the mapping. It's used by websites ranging from The New York Times and The Washington Post to GitHub and Flickr, as well as GIS specialists like OpenStreetMap, Mapbox, and CartoDB. ##1) Create a map with all of the crime locations plotted. R package to add north symbols and scale bars to maps created with ggplot or ggmap View on GitHub. Afterwards, we can use all the power of ggplot2 to include points, labels, paths, etc. The R ggplot2 package is useful to plot different types of charts and graphs, but it is also essential to save those charts. In your case, that would mean stacking the dv and sim columns and adding an additional column that marks whether a value came from dv or sim. Making maps with R; Create maps with the maptools package; Maps with R; Maps with R; Cartographie avec R; CRAN Task View: Analysis of Spatial Data; Visualisation with R; introduction-spatial-data-ggplot2/. The ggplot() syntax is different from the previous as a plot is built up by adding components with a +. Introduction. Then, we experimented with using color and linetype to map the Tree variable to different colored lines or linetypes. In particular, I’ve started to use the ‘ggplot2’ to create what I think are exceptionally good-looking maps (no offense to ArcMap, but something about ‘ggplot2’ maps are just so crisp). In the second plot, geom_point() inherits only data but not all the mapping. John Tukey. May 23, 2019, 4:06am #1. Hey everybody, this is just a short post but I found it very useful. Another key parameter is the coord_equal() coordinate modification: since we're dealing with map data, if the scaling of the x and y axis are not the same the map. The ggnet2 function is a visualization function to plot network objects as ggplot2 objects. There are cartodb and mapbox which are great for creating server-"baked" tilesets, leaflet and d3. Introduction Last week I was playing with creating maps using R and GGPLOT2. If you're lucky, you can work with geographic data that is pre-formatted and available in packages. Um die Funktionalität zu erweitern, kann zusätzlich das Paket ggspatial genutzt werden. This coordinate system provides the full range of map projections available in. When I attended usrR! 2012 last month, there was an interesting presentation by Dr. It includes four major new features: Subtitles and captions. If specified and inherit. Chapter 9 Plotting "Spatial" Data with ggplot. ggplot2-cheatsheet-2. We need to distinguish between two different ways of modifying colors in a ggplot graph. Heat maps are a very useful graphical tool to better understand or present data stored in matrix in more accessible form. I'll also add black borders and make sure that the map is plotted using the right scale. OpenStreetMap is a new package that accesses raster open street maps from Mapnik, and satellite imagery from Bing. Hello I'm just wondering whether anyone would be able to help me. mature spreading gif pic compilation music xxx. To do so we need the packages png and grid [crayon-5ea8f421dd5cc907440222/] Btw, this is just a cool and fast way to import different packages …. y: position on the Y axis. In this seventh episode of Do More with R, learn how to create maps in R—it's easier than you think, thanks to new and updated packages like sf, tmap, and ggplot2. MikeFliss&SaraLevintow! 2. Example: Creating a Heatmap in R. Description. With ggplot2, it's easy to: • produce handsome, publication-quality plots with automatic legends created from the plot specification • superimpose multiple layers (points, lines, maps, tiles, box plots) from different data sources with automatically adjusted common scales. 8 Common ggplot issues. However, I came across a post of Bob Rudis where he proposes coord_proj() which should do what coord_map does but using proj4::project instead of mapproject. We recommend you read our Getting Started guide for the latest installation or upgrade instructions, then move on to our Plotly Fundamentals tutorials or dive straight in to some Basic Charts tutorials. Setting up a data frame for visualization. In the ToC below the article you can find out references to the previous article and the project's goal. Creating a map using ggplot2 and rworldmap. In ggplot2, guides are produced automatically based on the layers in your plot. See Axes (ggplot2) for information on how to modify the axis labels. The majority of this work was carried out by Thomas Pederson, who I was lucky to have as my "ggplot2 intern. Like ggplot2, tmap is based on the idea of a ‘grammar of graphics’ (Wilkinson and Wills 2005). 3 Choropleth mapping with ggplot2. MikeFliss&SaraLevintow! 2. Speaking of insets, do you know of any ggplot2 examples with an. Create a histogram of the lengths of the rivers. Of course, you need the usual suspects such as rgdal and rgeos when dealing with geodata, and raster for the relief. We will be using a base with all data information and a geometric object which defines the type of plot. The resolution argument is quite self-explanatory and you can see from the resulting map that "low" is actually a more than acceptable resolution. Inspired by his tutorial, I decided to create a worldmap of my own, the R code for which you may find below. You can see the default ggplot color gradient below. frame, SpatialPolygonsDataFrameどちらでもおk ggplot + geom_polygon (data = map, aes (x = long, y = lat, group = id)) {ggplot2} を使って描画させる場合は、SpatialPolygonsDataFrameをdata. Chapter 9 Plotting "Spatial" Data with ggplot. ggmap builds on ggplot and allows to pull in tiled basemaps from different services, like Google Maps, OpenStreetMaps, or Stamen Maps 15. In this post I show an example of how to automate the process of making many exploratory plots in ggplot2 with multiple continuous response and explanatory variables. they are very helpful during seeking/comparing missing values in time series or checking cross-correlations for large number of financial instruments. Perhaps the simplest approach to drawing maps is to use geom_polygon() to draw boundaries for different regions. How to change the number of breaks on a datetime axis with R and ggplot2 May 6, 2. Then, we experimented with using color and linetype to map the Tree variable to different colored lines or linetypes. points, lines, polygons). ggplot is a powerful tool for making custom maps. In Section $$3$$ I download a satellite map of Los Angeles, CA from Google Maps. Posts about ggplot2 written by Gina. As always, first prepare the data that will be used for generating the graph. Plotting maps from shapefiles with attributes using ggplot; by Huanfa Chen; Last updated almost 3 years ago Hide Comments (-) Share Hide Toolbars. Introduction to R View on GitHub. If specified and inherit. Aug 22, 2012. Graphics with ggplot2. Let’s load that into a dataframe. The map contains three layers: buildings, water and the. Create a data frame of map data Source: R/fortify-map. R source library(ggplot2) crimes - data. Well, almost. Another example of this is the use of maps in presenting data. geom_sf in ggplot2 How to use geom_sf with Plotly. Thanks to the post of Pascal Mickelson and Scott Chamberlain which gave users like me a guide on how to create inset map in R using ggplot2. ## position_identityMarcin Kierczak ggplot2 and maps. It inherits x = displ from ggplot() but specifies its own mapping for y = cty. With ggplot2, it's easy to: • produce handsome, publication-quality plots with automatic legends created from the plot specification • superimpose multiple layers (points, lines, maps, tiles, box plots) from different data sources with automatically adjusted common scales. Many thanks especially to Dominic Royé for his detailed blog article which I used as an orientation for this tutorial. This tutorial will introduce you to the popular R package ggplot2, its underlying grammar of graphics, and show you how to create stylish and simple graphs quickly. If you’re lucky, you can work with geographic data that is pre-formatted and available in packages. My setup is Mac OS 10. ggplot2 also makes it easy to make much more complicated data visualizations, like geospatial maps: There's also a lot that you can do to format a chart. Inset maps enable multiple places to be shown in the same geographic data visualisation, as described in the Inset maps section (8. It is more complicated to place a bar chart than plot just a bubble on certain spot. The majority of this work was carried out by Thomas Pederson, who I was lucky to have as my "ggplot2 intern. After you've told ggplot() what data to use in R, the next step is to tell it how your data corresponds to visual elements of your plot. You can see the default ggplot color gradient below. ggplot includes quite a few map objects built in, one of which is “state”. Unlike raster image maps, vector maps require you to obtain spatial data files which contain detailed information necessary to draw all the components of a map (e. R has several systems for making graphs, but ggplot2 is one of the most elegant and most versatile. The ggsn package improves the GIS capabilities of R, making possible to add 18 different north symbols and scale bars in kilometers, meters, nautical miles, or statue miles, to maps in geographic or metric coordinates created with ggplot or ggmap. Thankfully, this new version of ggplot2 introduces that support! Currently all maps in the choroplethr ecosystem are stored as ggplot2 “fortified” dataframes. Plotting geospatial data is a common visualisation task, and one that requires specialised tools. This is the most basic heatmap you can build with R and ggplot2, using the geom_tile () function. | 2020-09-22 00:44:41 | {"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": 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": 0.29737940430641174, "perplexity": 1986.565540622149}, "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/1600400202686.56/warc/CC-MAIN-20200922000730-20200922030730-00018.warc.gz"} |
https://math.stackexchange.com/questions/1730911/why-werent-continuous-functions-defined-as-darboux-functions | # Why weren't continuous functions defined as Darboux functions?
When we were in primary school, teachers showed us graphs of 'continuous' functions and said something like
"Continuous functions are those you can draw without lifting your pen"
With this in mind I remember thinking (something along the lines of)
"Oh, that must mean that if the function takes two values $f(y)<f(z)$ then for every $c$ between $f(y), f(z)$ there must be some $x\, (y<x<z)$ such that $f(x)=c$"
And that's what I thought a continuous function was. But then the $\epsilon$-$\delta$ definition appeared, which put a more restrictive condition on what a continuous function was.
So, my question is, given the fact that Darboux functions "seem continuous" (in some subjective sense, I guess), why wasn't this used as the definition of continuity? More generally, how did today's (analytical) definition of continuity appear?
• Somebody did propose that as the definition of continuity. I don't remember exactly who, maybe Maxwell. It turned out not to work. – Giuseppe Negro Apr 6 '16 at 19:10
• May I ask why the downvote? – YoTengoUnLCD Apr 6 '16 at 19:15
• @DavidMitra Yup, I know. My question has nothing to do with that (I even said that in the part of the "more restrictive condition $[\dots]$"). What I'm asking is why wasn't the term "Continuous function" used for "Darboux function". – YoTengoUnLCD Apr 6 '16 at 19:17
• I suspect you meant to write: "Oh, that must mean that if the function takes $2$ values $f(y)<f(z)$ then for every $c$ between $f(y)$ and $f(z)$, there must be some $x$ between $y$ and $z$ such that $f(x)=c$". Or maybe you're just reflecting accurately the troubles you had with with quantifier order when you were in primary school. :0) – Alex Kruckman Apr 6 '16 at 20:59
• "Continuous functions are those you can draw without lifting your pen" is FALSE unless you require first that the domain is an interval in $\mathbb R$. For example $x\mapsto 1/x$ of $x\mapsto {\tan x}$ or $x\mapsto 1/{\sin x}$ are continuous, but their domains are not intervals, so their graphs consist of separate components and can not be drawn without lifting a pen. (They can not be drawn at all because they are infinite, but that's another story.) – CiaPan Apr 7 '16 at 10:27
You can't actually draw many Darboux functions without lifting your pen from paper. The extreme example is the Conway base 13 function, which takes every value in every interval and hence is a Darboux function. You can't however begin to even imagine what this function looks like, let alone draw it with a pen.
So you may want to require the function to be bounded. However this still fails, since you can get functions like,
$$f(x) = \begin{cases} \sin (1/x), & \text{if } x \neq 0 \\ 0 & \text{if } x = 0 \end{cases}$$
Which again, you can't draw. So one idea may be to require functions $f:[a,b] \rightarrow \Bbb R$ to be of bounded variation, meaning that,
$$\sup\left\{\sum_{i=1}^n |f(x_i)-f(x_{i-1})| \;\middle|\; a=x_0<x_1<\dots<x_n \right\} < \infty$$
Intuitively, this 'measures' the graph of the line $\{(x,f(x)) \mid x \in [a,b] \}$ and requires it to be finite. Then we intuitively should get a finite length curve which we can actually draw without lifting your pen.
It turns out however, that Darboux functions which have bounded variations are actually continuous. So in attempt to define continuity in a more intuitive way, we have found a more restrictive definition.
Even worse, this still isn't enough. One can show that the function,
$$f(x) = \begin{cases} x^3\sin (1/x), & \text{if } x \neq 0 \\ 0 & \text{if } x = 0 \end{cases}$$
is continuous and has bounded variation, but you can't really draw it. Note this function is also differentiable and has continuous first derivative. I'll spare you the details, but using similar ideas we can also construct infinitely differentiable functions of bounded variation, which you can't draw on paper.
From this, I think you can see why we don't try to model continuity off the intuitive definition. Instead, we adopt the usual definition because it's a much more useful and interesting class of functions to work with.
• Why can't $x^3\sin (1/x)$ be drawn? – Navin Apr 7 '16 at 4:31
• @Navin There's a bit of ambiguity here in terms of what can be drawn, but because $x^3\sin(1/x)$ has infinitely many local maxima and minima near 0, I would argue you can't draw all of them (even though they do become arbitrarily small). – ktoi Apr 7 '16 at 6:00
• I will add that functions with all real values in every open interval have been mentioned in several other posts on this site. See, for example, the links given here. – Martin Sleziak Apr 7 '16 at 7:44
• Another possible example of a continuous function that, in some sense "can't be drawn" is $$x \in (0,1/\pi) \mapsto \sin\left(\frac{1}{x}\right).$$ The problem, really, is that it takes an infinite amount of ink and/or time to actually draw it. – goblin Apr 8 '16 at 13:38
The Darboux definition does not correspond very well with our intuition about continuity. For example, the Conway function takes on every value in every interval, and is therefore Darboux. However it is not continuous, and I don't think we want it to be continuous, because it certainly doesn't agree with your teacher's definition of drawing without lifting your pencil.
The $\varepsilon$-$\delta$ definition is rigged so that if $f : X \rightarrow Y$ is a function between metric spaces, then the following are equivalent:
1. $f$ is $\varepsilon$-$\delta$ continuous
2. $f$ preserves the "converges to" relation; meaning that from $x \rightarrow x_\infty$ we can deduce $f(x) \rightarrow f(x_\infty)$.
I think that Condition 2 is closer to what we really use in practice, e.g. we often want to commute $\frac{d}{dx}$ across an infinite summation, or change the order of integration, etc. So as a general rule, I think that when we're thinking about continuity, we should keep in mind its mathematical purpose, namely, the preservation of limits.
Taking this philosophy to its logical conclusion, convergence spaces are a very very natural structure to study. Modulo certain largely irrelevant size issues, the idea is basically that:
• a convergence space is a set $X$ together with a distinguished collection of ordered pairs $(x,x_\infty)$ where $x$ is a net in $X$ and $x_\infty$ is an element of $X$. The idea is that $(x,x_\infty)$ is in this collection iff $x$ converges to $x_\infty$; we write $x \rightarrow x_\infty$. Certain axioms are imposed.
• a morphism of convergence spaces is a continuous function, i.e. a function $f : X \rightarrow Y$ such that for all nets $x$ in $X$ and all elements $x_\infty$ in $X$, we have $$(x \rightarrow x_\infty) \rightarrow (f(x) \rightarrow f(x_\infty))$$
It was this viewpoint (namely, that a continuous function is, by definition, a morphism of convergence spaces) that allowed me to finally make peace with the $\varepsilon$-$\delta$ definition of continuity for mappings between metric spaces.
By the way, the category $\mathbf{Conv}$ of convergence spaces is better-behaved categorially than the category of topological spaces $\mathbf{Top}$; in particular, $\mathbf{Conv}$ is Cartesian closed, while $\mathbf{Top}$ famously isn't. Its almost as if category theory is trying to tell us that convergence is secretly the correct way of thinking about continuity (cue X-Files theme music).
I want to focus on your question "why wasn't this used as the definition of continuity?" In other words, you're asking why we don't interpret continuity to mean "having the intermediate value property."
One answer that hasn't been mentioned yet is that continuity can be a purely local phenomenon. That is, it makes sense to ask whether a function is continuous or discontinuous at a point. By contrast, one cannot ask whether a function possesses the intermediate value property at a point. My understanding is that in the early history of analysis, the local and global aspects of continuity often weren't carefully distinguished -- or rather, they weren't even recognized as different. This is why, for example, many could confuse continuity and uniform continuity. The latter is a strictly global phenomenon, too: it does not make sense to ask whether a function is uniformly continuous at a point. But as it became clear that continuity could be interpreted as a pointwise phenomenon, these different shades of regularity -- local versus global -- came into view. | 2019-05-23 03:28:24 | {"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": 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": 0.8735066056251526, "perplexity": 273.0615746016829}, "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/1558232257002.33/warc/CC-MAIN-20190523023545-20190523045545-00429.warc.gz"} |
https://email.esm.psu.edu/pipermail/macosx-tex/2012-July/049649.html | [OS X TeX] Re: "Runaway argument?" error in figure caption
John B. Thoo jthoo at yccd.edu
Tue Jul 17 19:34:17 EDT 2012
Thanks to Z[bigniew] N, Manfred B, and Alan M for their replies. Below are my results following their suggestions.
On Jul 17, 2012, at 12:00 PM, <macosx-tex-request at email.esm.psu.edu> wrote:
> Date: Tue, 17 Jul 2012 14:10:40 +0000
> From: "Nitecki, Zbigniew H." <Zbigniew.Nitecki at tufts.edu>
>
> Your "begin" and "end" don't match (\begin{smalltrix}.\end{small matrix})
Oops ... that was a typo, but thankfully not inside the code. :-) Thanks.
> Date: Tue, 17 Jul 2012 17:52:59 +0300
> From: Manfred Braun <manfred.braun at uni-due.de>
>
> Within a caption the use of commands and environments is restricted. Commands must be "protected". A possible solution is as follows: Define, for instance,
>
> \newcommand\mymatrix{ \left[ \begin{smallmatrix} 3 \\ 4 \end{smallmatrix} \right] }
>
> in the preamble. Then replace your caption by
>
> \caption{It is useful to picture vectors as arrows, although this may not be a literal representation of vectors. Here we identify the vector $\vec{u} = \protect\mymatrix$ in $\R{2}$ represented as an arrow with the point $(3,4)$ in the $xy$ plane.}
>
> This should work. Important is to include the \protect command. It prevents the immediate expansion of the subsequent \mymatrix command, the expansion is postponed until the caption is typeset.
Yes, that worked! :-) Thanks.
> Date: Tue, 17 Jul 2012 11:46:37 -0400
> From: "Alan Munn" <amunn at gmx.com>
>
> A possible solution is as follows: Define, for instance, \newcommand\mymatrix{ \left[ \begin{smallmatrix} 3 \\ 4 \end{smallmatrix} \right] } in the preamble. Then replace your caption by \caption{It is useful to picture vectors as arrows, although this may not be a literal representation of vectors. Here we identify the vector $\vec{u} = \protect\mymatrix$ in $\R{2}$ represented as an arrow with the point $(3,4)$ in the $xy$ plane.} This should work.
>
> [...snip, snip...]
>
> Alternatively, you can load the caption package and provide an alternative title for the caption to be used in the list of figures:
>
> \usepackage{caption}
>
> \begin{figure}
> ...
> \captionsetup{singlelinecheck=off}
> \caption[stuff for list of figures]{stuff for the actual caption}
> \end{figure}
I tried that
\captionsetup{singlelinecheck=off}
\caption{It is useful to picture vectors as arrows, although this may not be a literal representation of vectors. Here we identify the vector $\vec{u} = \left[\begin{smallmatrix} 3 \\ 4 \end{smallmatrix}\right]$ in $\R{2}$ represented as an arrow with the point $(3,4)$ in 2-dimensional Euclidean space, that is, in the $xy$ plane.}
but still got the error
[5]
! Argument of \@caption has an extra }.
<inserted text>
\par
l.178 ...idean space, that is, in the $xy$ plane.}
?
Runaway argument?
\@captype {\def \@currenvir {smallmatrix}\edef \@currenvline {\on at line \ETC.
! Paragraph ended before \@caption was complete.
\par
l.178 ...idean space, that is, in the $xy$ plane.}
?
[6]
But now I know about the caption package. :-) Thanks.
---John.
>> Date: Tue, 17 Jul 2012 06:38:25 -0700
>> From: "John B. Thoo" <jthoo at yccd.edu>
>> Subject: [OS X TeX] "Runaway argument?" error in figure caption
>>
>> Hi, everyone. I apologize that this is not a Mac-specific question, but rather a general LaTeX question; however, I don't know whom else to ask.
>>
>> This code
>>
>> \begin{figure}
>> \begin{tikzpicture}
>> \pgftransformscale{0.75}
>> %% axes
>> \draw[help lines,lightgray] (-1,-1) grid (5,5);
>> \draw[thin] (-1,0) -- (5,0) node[anchor=north]{$x$};
>> \draw[thin] (0,-1) -- (0,5) node[anchor=west]{$y$};
>> %% u and (u1,u2)
>> \draw[thick,-latex] (0,0) -- (3,4);
>> \draw (1.6,2) node[anchor=west]{$\vec{u} = \left[\begin{array}{c} 3 \\ 4 \end{array}\right]$};
>> \fill (3,4) circle (0.08) node[anchor=west]{$(3,4)$};
>> \end{tikzpicture}
>> \caption{It is useful to picture vectors as arrows, although this may not be a literal representation of vectors. Here we identify the vector $\vec{u} = \left[\begin{smallmatrix} 3 \\ 4 \end{smallmatrix}\right]$ in $\R{2}$ represented as an arrow with the point $(3,4)$ in the $xy$ plane.}
>> \label{fig.syslineqns:vectorasarrow}
>> \end{figure}
>>
>> produces this error
>>
>> [5]
>> ! Argument of \@caption has an extra }.
>> <inserted text>
>> \par
>> l.177 ...ith the point $(3,4)$ in the $xy$ plane.}
>>
>> ?
>> Runaway argument?
>> \@captype {\def \@currenvir {smallmatrix}\edef \@currenvline {\on at line \ETC.
>> ! Paragraph ended before \@caption was complete.
>> \par
>> l.177 ...ith the point $(3,4)$ in the $xy$ plane.}
>>
>> ?
>>
>> Overfull \hbox (73.62pt too wide) in paragraph at lines 217--249
>> []$[]$
>> [6] [7]
>>
>>
>> The figure and caption appear to typeset OK, though. I think the error is because of the \begin{smalltrix}...\end{smallmatrix}, but I don't know how to fix it.
>>
>> Any suggestions? I am using TeX-Live 2009 that I typeset using pdflatex in an xterm window and view using Preview. My OS is Lion.
>>
>> Thanks very much.
>>
>> ---John.
-----------------------------------------------------------------------
"Ten thousand difficulties do not make one doubt.... A man may be annoyed that he cannot work out a mathematical problem ... without doubting that it admits an answer."
---John Henry Newman [_Apologia_, p. 239 in Project Gutenberg's
<http://www.gutenberg.org/ebooks/22088>] | 2018-11-20 15:39:03 | {"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": 0.9960296750068665, "perplexity": 6566.7650349990345}, "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-2018-47/segments/1542039746465.88/warc/CC-MAIN-20181120150950-20181120172158-00052.warc.gz"} |
https://stats.stackexchange.com/questions/linked/10419 | 19k views
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https://www.coursehero.com/file/8656864/exam2practicesolutions/ | # exam2practicesolutions - Math 2260 Exam#2 Practice Problem...
• Notes
• CorporalStarOkapi4323
• 13
This preview shows page 1 - 4 out of 13 pages.
Math 2260 Exam #2 Practice Problem Solutions 1. Evaluate Z tan 3 ( x ) dx.
2. Integrate Z sin 4 (2 x ) dx.
1
3. Integrate Z x 2 - 25 x dx.
4. Evaluate Z e 1 x (ln x ) 3 dx.
2
5. Suppose a 20 foot chain which weighs 5 pounds per foot is coiled on the ground. One end of the chain is attached to a small crane. How much work does it take to lift this end 20 feet off the ground, so that the chain is fully extended in the air? | 2021-12-09 01:27:41 | {"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": 0.8503920435905457, "perplexity": 2148.285600428806}, "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-20211209000407-20211209030407-00440.warc.gz"} |
https://programs.team/apio2012-and-luogu-p1552-dispatch.html | # "APIO2012" and "Luogu P1552" dispatch
### Description
In this gang, there is a ninja called Master. Except Master, every Ninja has only one superior. In order to keep secrets and enhance the leadership of ninjas, all instructions related to their work are always sent by their superiors to their direct subordinates, and are not allowed to be sent by other means.
Now you need to recruit a group of ninjas and send them to customers. You need to pay a certain salary for each dispatched ninja, and make the total salary not exceed your budget. In addition, in order to send instructions, you need to select a ninja as the manager. The manager is required to send instructions to all dispatched ninjas. When sending instructions, any Ninja (whether dispatched or not) can be used as the messenger. The manager may or may not be assigned. Of course, if the manager is not dismissed, you don't have to pay the manager's salary.
Your goal is to maximize customer satisfaction within your budget. Here, customer satisfaction is defined as the total number of dispatched ninjas multiplied by the leadership level of the manager, and the leadership level of each Ninja is also certain.
Write a program to give the superior \ (b\u i\), salary \ (c\u i\), leadership \ (l\u i\), and the total salary budget paid to the Ninjas \ (M\), and output the maximum value of customer satisfaction when the above requirements are met within the budget.
### Hint
• $$1 ≤ n ≤ 10^5$$ number of ninjas;
• $$1 ≤ m ≤ 10^9$$ total salary budget;
• $$0 ≤ b_i < i$$ the number of Ninja's superior;
• $$1 ≤ C_i ≤ M$$ Ninja's salary;
• $$1 ≤ l\u I ≤ 10^9$$ Ninja leadership level.
• For the data of the previous \ (30\%\), \ (n ≤ 3\times 10^3\).
### Solution
Obviously, the working relationship of Ninja forms a tree structure.
Then the problem can be formalized as follows: select as many nodes as possible in each subtree so that the total cost of these nodes does not exceed \ (m\). Finally, merge the answers of all subtrees.
It is not difficult to think of starting from the leaf node and maintaining the Ninja set with an appropriate data structure.
Whenever a point is reached, first merge the current set to the superior, and adjust the superior set so that the Ninja cost no more than \ (m\) and the set is as large as possible.
We greedily think that as long as we pop up the Ninjas that cost a lot each time, because the answer only involves the leadership of the roots and the number of ninjas.
After one point is completed, you can directly use your superior to update the answer.
For collection maintenance, we need an appropriate data structure that supports deletion of maximum values and efficient consolidation. Here, select the left leaning tree.
As for the complexity, since each Ninja will only pop up once, the time complexity is \ (O(n\log n) \).
### Code
#include <algorithm>
#include <iostream>
using namespace std;
const int N = 1e5 + 5;
struct ninja {
} nj[N];
int n, m;
struct ltNode {
int ch[2], val, dist, rt;
} t[N];
#define lc t[x].ch[0]
#define rc t[x].ch[1]
int merge(int x, int y) {
if (!x || !y) return x | y;
if (t[x].val < t[y].val) swap(x, y);
rc = merge(rc, y);
if (t[lc].dist < t[rc].dist) swap(lc, rc);
t[x].rt = t[lc].rt = t[rc].rt = x;
t[x].dist = t[rc].dist + 1;
return x;
}
int findrt(int x) {
return x == t[x].rt ? x : t[x].rt = findrt(t[x].rt);
}
struct LefTr {
int root;
int size;
long long sum;
inline void join(LefTr t) {
size += t.size, sum += t.sum;
root = merge(root, t.root);
}
inline void pop() {
sum -= t[root].val;
root = merge(t[root].ch[0], t[root].ch[1]);
--size;
}
} lt[N];
void init() {
for (register int i = 1; i <= n; i++) {
lt[i].root = t[i].rt = i;
lt[i].size = 1;
lt[i].sum = t[i].val = nj[i].cost;
}
}
signed main() {
ios::sync_with_stdio(false);
cin >> n >> m;
for (register int i = 1; i <= n; i++)
cin >> nj[i].fa >> nj[i].cost >> nj[i].lead;
init();
long long ans = 0ll;
for (register int i = 1; i <= n; i++)
ans = max(ans, nj[i].lead * 1LL);
for (register int i = n; i > 1; i--) {
int f = nj[i].fa;
lt[f].join(lt[i]);
while (lt[f].sum > m) lt[f].pop();
ans = max(ans, lt[f].size * 1LL * nj[f].lead);
}
cout << ans << endl;
return 0;
}
Tags: data structure
Posted by Penelope on Tue, 31 May 2022 12:43:21 +0530 | 2022-09-29 14:29:56 | {"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": 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": 0.1725982129573822, "perplexity": 6359.395839987228}, "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-2022-40/segments/1664030335355.2/warc/CC-MAIN-20220929131813-20220929161813-00798.warc.gz"} |
https://www.gamedev.net/forums/topic/286068-new-sdl-game-now-with-online-highscores/ | # New SDL Game (Now With Online HighScores!)
This topic is 4757 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
RBlocks - Direct Download It's a horribly done Tetris clone. Please tell me if you find any bugs (there are probably millions). Oh, thank you goes to IFooBar for the graphics and coldacid for the... the... something. I plan on putting in a background image as well as a highscore system. Would you guys mind testing that as well?
Controls
--------
Arrows - Move
Up - Rotate
Space - Insta-Down
[Edited by - Rob Loach on December 7, 2004 3:28:25 PM]
##### Share on other sites
The only real problem I found atm is that the blocks are not randomly generated enough. I found myself getting the same blocks 3 or 4 times in a row.
##### Share on other sites
nice job. the only other problem (besides the one mentioned above) was that the app didn't close (or do anything) when the window close (X) was clicked. besides that, it was good. i liked the texture on the blocks; solid + shiny gets annoying quickly.
cheers.
##### Share on other sites
that's a great start! now you need some scoring.. :-) you could do some little animated effects in the background too, or even on the blocks.
did anyone ever play xixit or chain reaction? They were two great tetris clones with some really spiffy graphics and music (almost entirely done by demo sceners. the game itself was done by tran, of pmode fame).
cheers
sam
##### Share on other sites
Very good, my only niggle is that in the original game, there was no collision with the top of the board during a rotation. You can't instantly rotate certian pieces(like the long piece) when they appear, you have to wait two clicks before you can rotate it.
Besides that, nice.
##### Share on other sites
Well, I guess my problem sort of qualifies as a bug :) I managed to get the left leaner block, get this, 13 times in a row! Perhaps you need to work on the randomization a tiny bit? :D Other then that, it worked pretty well.
##### Share on other sites
just a thought...
shouldn't this be in "Your Announcements"
##### Share on other sites
I like it but when pressing space te block should go faster not just going to the bottom immediately. And you should be able to hold the button instead of pressing down alot of times to let the block go faster to the bottom like you need to do with the down arror key.
Good job, and good luck wih further programming,
Rob
##### Share on other sites
Quote:
Original post by DigitalChaosshouldn't this be in "Your Announcements"
I just needed initial testers and some quick feedback. But, I'll ask someone to move it to the Alternative Game Library thread....
Quote:
Original post by SirLuthorWell, I guess my problem sort of qualifies as a bug :) I managed to get the left leaner block, get this, 13 times in a row! Perhaps you need to work on the randomization a tiny bit? :D Other then that, it worked pretty well.
Imagine the odds [smile]. I'll rework my random number generator.
Quote:
Original post by BinomineVery good, my only niggle is that in the original game, there was no collision with the top of the board during a rotation. You can't instantly rotate certian pieces(like the long piece) when they appear, you have to wait two clicks before you can rotate it.
Good point, I'll implement that, somehow.
Quote:
Original post by stormrunnernice job. the only other problem (besides the one mentioned above) was that the app didn't close (or do anything) when the window close (X) was clicked.
Haha, that's weird.
Thanks alot for testing it you guys. I'll try to implement everything. A new version should be up sometime. Mind testing that one too? [smile]
[Edited by - Rob Loach on December 2, 2004 8:19:51 AM]
##### Share on other sites
Quote:
Imagine the odds [smile]. I'll rework my random number generator.
Indeed :D There are what, 7 blocks? And so there is a 1/7 chance of getting it once [grin] So 13 times is... 1/96889010407. Not a large number! [oh] You may want to, instead of randomly generating a tile each time, have a set stack of, say, 20 of each tile, that gets randomized before each game, and shoved into a stack, which is just drawn off of, as needed. That would, methinks, give a more rounded outcome!
Quote:
Thanks alot for testing it you guys. I'll try to implement everything. A new version should be up sometime. Mind testing that one too? [smile]
As someone has probably said at least once in history, there is no such thing as 'too many tetris games'! Rest assured, you make it, and people will come!
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looking good dude.
a few things,
-i had to tap the down arrow to make the block move down. sometimes i want that block to fly downwards, and it gets anonying to have to repeteadly tap it
-i noticed clicking the "X" on the window didnt close the game. you can do this by just checking for an SDL_QUIT event from the message pump.
##### Share on other sites
I fixed a bunch of the bugs as well as added a bunch of new stuff. Check it out: Goodness!
[Edited by - Rob Loach on December 6, 2004 11:50:52 AM]
##### Share on other sites
I would second graveyard filla's reply about being able to hold down the Down key to make the blocks move down faster.
I downloaded the new version, and when I clicked the close box, I received the following error:
"Instruction at "0x77f83aed" refrenced memory at "0x00000003". The memory could not be "written"."
Sounds like a bad pointer reference to me.
My Machine: WinXP Pro, 1.4Ghz Pentium M, 512 MB Ram, Intel Integrated Graphics Card.
Besides that I would say the game is pretty good.
If you do want to add more, I would try incorportating SDL_mixer to add some sound.
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Hey looking good!
I made you some new block sets just for the hell of it. They're here. Just rename them to blocks.bmp (for anyone else who wants to try them) and they should work. They're no works of art, but they're something a bit different :-)
Greetings to whoever I got the original textures from (they were originally quite a lot bigger; I resized them and added borders and generally fiddled with them a bit).
cheers
sam
##### Share on other sites
v0.2
Tap space VERY fast and the game box PILES up.
You continue to gain points, and don't get a gameover
Also suggest a GAMEOVER screen and Highscores Table
Finally, if you lower a block a then want to move it into an alcove, it locks:
+- -+ +- +| |+----+
falls to
+- +-+| -+ |+----+
in normal tetris, before the piece locks, hold left and it moves to:
+-+- +|-+ |+----+
If you understand, please include that in v0.3
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I second the last poster - the "sliding" mechanism is what separates the Tetris wannabees from the experts!
In addition the score should decrease as the block drops so the player is punished for taking too long. Also you can punish the player for doing too many rotations. That way skilled players can build up points by dropping quickly.
Also you don't seem to be using key repeats which means the player constantly has to press and release buttons to move and rotate. This gets tiring quickly.
Tetris isn't quite as simple as it seems ;-)
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Quote:
Original post by wyrzyI would second graveyard filla's reply about being able to hold down the Down key to make the blocks move down faster.
It's on my to-do list [smile].
Quote:
Original post by wyrzyI downloaded the new version, and when I clicked the close box, I received the following error:"Instruction at "0x77f83aed" refrenced memory at "0x00000003". The memory could not be "written"."Sounds like a bad pointer reference to me.My Machine: WinXP Pro, 1.4Ghz Pentium M, 512 MB Ram, Intel Integrated Graphics Card.
Weird... I'll have to check it out.
Quote:
Original post by wyrzyIf you do want to add more, I would try incorportating SDL_mixer to add some sound.
Planned for when I'm done gameplay [smile].
Quote:
Original post by izzoI made you some new block sets just for the hell of it. They're here. Just rename them to blocks.bmp (for anyone else who wants to try them) and they should work. They're no works of art, but they're something a bit different :-)
Hey, that's a lot, you mind if I include those in the release? You'll of course get on the Thank You list [smile].
Quote:
Original post by ZeophliteTap space VERY fast and the game box PILES up.You continue to gain points, and don't get a gameover
Hmmm, strange. It's on my to do list.
Quote:
Original post by ZeophliteFinally, if you lower a block a then want to move it into an alcove, it locks:
Really? It doesn't for me:
In that screenshot, I just moved the blue piece under the green one. Or am I missing something here?
Quote:
Original post by Captain LogicIn addition the score should decrease as the block drops so the player is punished for taking too long. Also you can punish the player for doing too many rotations. That way skilled players can build up points by dropping quickly.
Great ideas. I'll see what I can do. Have the score go up when they speed the block down instead of just go up all the time.... Punish too many rotations is an awesome idea. Any more?
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Quote:
Original post by Rob LoachHey, that's a lot, you mind if I include those in the release? You'll of course get on the Thank You list [smile].
No worries, go for it! You might want to adjust the block which is used as the border coz a couple of those that I did make the border really obviously repetitive.
cheers
sam
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Quote:
Original post by izzo
Quote:
Original post by Rob LoachHey, that's a lot, you mind if I include those in the release? You'll of course get on the Thank You list [smile].
No worries, go for it! You might want to adjust the block which is used as the border coz a couple of those that I did make the border really obviously repetitive.
I'll include them as "Extra Blocks" that you can download seperatly. How does "Sam's Block Package" sound? [smile]
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Heh sounds good :)
Have you played Xixit or Chain Reaction? They are two old Sega Columns-style DOS games with some really cool block sets. Some of them are animated; I reckon some animated block sets would be a cool future addition to your game. Also they have some block sets which aren't all square (as in they are sort of blobby objects that fit into their tile size). Do you handle transparent images? I was going to have a go at doing some that weren't just plain blocks but my pixel pushing skills aren't that great :)
sam
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Planned for next release is online highscores. Any comments?
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Yes, the Tetris clone has online highscores. Just play it and then upload the score.dat inside the game directory. Do it, you must.
[Edited by - Rob Loach on December 7, 2004 6:29:18 PM]
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Not bad =) Only real problem is that it crashes on exit. Also, the rotation of the pieces doesn't seem as intuitive as the original. They don't seem to move exactly as I expect them to.
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Hey nice work, many improvements from the first release :). However there is a logic error - I dont know if you meant it to be intentional or not - you gain score by pressing the down key or space bar - yes I can see how this promotes faster thinking, but usually you only get points per line cleared. Just something that stood out to me.
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Also for pure asthetic looks, the transparency is not being set for the "New Game" image, you can see the black around it and mabey for the exit game. I'd suggest setting transparency for those colors to (1,1,1) since that is the color of your transparency.
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This topic is 4757 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. | 2017-12-17 08:23:36 | {"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": 0.20346076786518097, "perplexity": 3000.1719276290405}, "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-2017-51/segments/1512948594665.87/warc/CC-MAIN-20171217074303-20171217100303-00664.warc.gz"} |
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Zbl 1187.90286
Huang, Nan Jing; Li, Jun; Thompson, H.B.
Stability for parametric implicit vector equilibrium problems.
(English)
[J] Math. Comput. Modelling 43, No. 11-12, 1267-1274 (2006). ISSN 0895-7177
Summary: We consider a class of parametric implicit vector equilibrium problems in Hausdorff topological vector spaces where a mapping $f$ and a set $K$ are perturbed by parameters $\epsilon$ and $\lambda$, respectively. We establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution set mapping $S\colon\Lambda_1\times\Lambda_2\to 2^X$ for such parametric implicit vector equilibrium problems.
MSC 2000:
*90C33 Complementarity problems
90C31 Sensitivity, etc.
Keywords: parametric implicit vector equilibrium problems; upper semicontinuity; lower semicontinuity; $C$-convex; solution set mapping
Highlights
Master Server | 2013-06-19 06:08:49 | {"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": 0.7618362307548523, "perplexity": 7305.575435354686}, "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-2013-20/segments/1368708142388/warc/CC-MAIN-20130516124222-00067-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://optimization-online.org/2020/09/8000/ | # On complexity and convergence of high-order coordinate descent algorithms
Coordinate descent methods with high-order regularized models for box-constrained minimization are introduced. High-order stationarity asymptotic convergence and first-order stationarity worst-case evaluation complexity bounds are established. The computer work that is necessary for obtaining first-order $\varepsilon$-stationarity with respect to the variables of each coordinate-descent block is $O(\varepsilon^{-(p+1)/p})$ whereas the computer work for getting first-order $\varepsilon$-stationarity with respect to all the variables simultaneously is $O(\varepsilon^{-(p+1)})$. Numerical examples involving multidimensional scaling problems are presented. The numerical performance of the methods is enhanced by means of coordinate-descent strategies for choosing initial points. | 2022-12-06 10:43:46 | {"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": 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": 0.8264321684837341, "perplexity": 1064.6338879616742}, "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/1669446711077.50/warc/CC-MAIN-20221206092907-20221206122907-00206.warc.gz"} |
https://zbmath.org/?q=an:0273.42013 | ## On convergence of orthogonal series of Bessel functions.(English)Zbl 0273.42013
### MSC:
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 33C10 Bessel and Airy functions, cylinder functions, $${}_0F_1$$ 34L99 Ordinary differential operators 41A30 Approximation by other special function classes
Full Text:
### References:
[1] Benedek A. and Panzone R. , On mean convergence of Fourier-Bessel series of negative order , Studies in App. Math. Vol. 4 n^\circ 3 , ( 1971 ), 281 - 292 . MR 310535 | Zbl 0218.42012 · Zbl 0218.42012 [2] Benedek A. and Panzone R. , Mean convergence of Bessel and Dini series, Notices AMS , 18 , n0 6 , ( 1971 ), p. 951 (to appear Rev. UMA, vol. 26 , ( 1972 ))- [3] Muckenhoupt B. , Mean convergence of Hermite and Laguerre series, II , TAMS , 147 , ( 1970 ), 433 - 460 . MR 256051 | Zbl 0191.07602 · Zbl 0191.07602 [3] Titchmarsh , E.C. , Eigenfunction expansions I , Oxford , ( 1962 ). · Zbl 0099.05201 [4] Watson , G.N. , A treatise on the theory of Bessel functions , Cambridge , ( 1952 ). Zbl 0174.36202 · Zbl 0174.36202 [5] Wing , G.M. , The mean convergence of orthogonal series , Amer. J. of Math. , LXXII , ( 1950 ), 792 - 808 . MR 37923 | Zbl 0041.38515 · Zbl 0041.38515
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2022-05-19 08:42:23 | {"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": 0.9414042830467224, "perplexity": 3235.832567499277}, "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/1652662526009.35/warc/CC-MAIN-20220519074217-20220519104217-00543.warc.gz"} |
http://mathhelpforum.com/geometry/227752-curved-surface-area.html | # Math Help - Curved surface area
1. ## Curved surface area
I have the answers but i m unable to work it out
2. ## Re: Curved surface area
Originally Posted by haftakhan
I have the answers but i m unable to work it out
Hello,
the area in question is a rectangle with the length of 9.5 m and the width of a quarter perimeter of a circle with radius r = 0.8 m.
Therefore:
$A = 9.5\ m \cdot \frac14 \cdot 2 \cdot \pi \cdot 0.8 \ m \approx 11.94\ m^2$
3. ## Re: Curved surface area
What earboth calculated was the curved surface area of the cylinder, the area of contact with the ends of the cylinder must be added to this.
To find that area split the circle cross section up into three parts. 1. The area of contact, 2. The right angled triangle shown in the diagram, 3. The remainder of the circle which is 270 degrees around the centre.
4. ## Re: Curved surface area
Originally Posted by Shakarri
What earboth calculated was the curved surface area of the cylinder, the area of contact with the ends of the cylinder must be added to this.
To find that area split the circle cross section up into three parts. 1. The area of contact, 2. The right angled triangle shown in the diagram, 3. The remainder of the circle which is 270 degrees around the centre.
Hello,
thanks for pointing out that I forgot to calculate the front and rear part of the cross-sections. But: In this case the complete area of the cross-sections, which have contact to the oil, can be calculated as a half circle minus a half square:
$A_{complete}= \underbrace{9.5\ m \cdot \frac14 \cdot 2 \cdot \pi \cdot 0.8 \ m }_{\text{curved surface area}}+ \underbrace{\frac12 \cdot \pi \cdot 0.8^2}_{\text{half circle}} - \overbrace{\frac12 \cdot \frac12 \cdot 1.6^2}^{\text{half square, diameter as diagonal}} \approx 12.3\ m^2$ | 2015-06-02 04:29:21 | {"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": 0, "img_math": 0, "codecogs_latex": 2, "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": 0.7442019581794739, "perplexity": 473.70994497271636}, "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/1433195035316.21/warc/CC-MAIN-20150601214355-00092-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://conwaylife.com/forums/viewtopic.php?f=7&t=2036&p=49830 | For general discussion about Conway's Game of Life.
muzik
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### Re: Thread for basic questions
Apple Bottom wrote:
gameoflifemaniac wrote:Related: how many two-state black-white reversal rules are there (rules like Day & Night)?
Rules that are their own black/white reversal? According to the wiki, 512.
Didn't there used to be a list of said self-complementary rules on the wiki?
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Apple Bottom
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### Re: Thread for basic questions
muzik wrote:Didn't there used to be a list of said self-complementary rules on the wiki?
Yes. (It's in my userspace because I didn't consider the list sufficiently interesting to warrant a Main namespace article.)
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muzik
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### Re: Thread for basic questions
Is there a list (anywhere) that lists the rules where 2x2 blocks simulate other CA using the margolus neighbourhood?
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Apple Bottom
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### Re: Thread for basic questions
muzik wrote:Is there a list (anywhere) that lists the rules where 2x2 blocks simulate other CA using the margolus neighbourhood?
Not to my (very limited) knowledge, but David Eppstein notes such simulations on his glider page, e.g. here.
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muzik
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### Re: Thread for basic questions
This is the only other rule I know of with this property:
Code: Select all
x = 2, y = 2, rule = B1246/S012348
2o$2o! Code: Select all x = 4, y = 4, rule = B1246/S012348 4o$4o$2b2o$2b2o!
Can it be proved that every single such rule can be simulated with a totalistic or non-totalistic rule, given that the 2x2 sections are shrunk down to 1x1 and only every second generation is considered?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
Apple Bottom
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### Re: Thread for basic questions
muzik wrote:This is the only other rule I know of with this property
Here's a few examples from Eppstein's page (this list is probably not exhaustive):
B3/S15
B3/S25
B347/S045
B35678/S5678
B3568/S2567
B36/S1258
B368/S25
B38/S125
B38/S15
B38/S25
B38/S5
How many different Margolus neighborhood CAs are there? Try to enumerate them, and see if you can compute the total number.
What constraints do the B/S conditions of rules that simulate these CAs satisfy? How many such rules are there?
When you have two identical numbers, i.e. "there are x different Margolus neighborhood CAs, and there are also x different ules satisfying the constraints I have worked out", can you show that each such CA is simulated by one of these rules, and vice versa?
Can you come up with a way to "convert" a rule to its equivalent Margolus neighborhood CA, or to "convert" a Margolus neighborhood CA to its equivalent rule?
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muzik
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### Re: Thread for basic questions
Are there any ways to play and display RLEs and patterns on the wiki just like on the forums with the code boxes?
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Bullet51
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### Re: Thread for basic questions
Given a pattern P and a number k, is the problem of synthesizing P in k gliders decidable?
A stronger version:
Is it possible to enumerate all K-glider collisions? (K is the largest number such that there is something synthesizable by K+1 gliders but not synthesizable by K gliders)
Still drifting.
dvgrn
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### Re: Thread for basic questions
muzik wrote:Are there any ways to play and display RLEs and patterns on the wiki just like on the forums with the code boxes?
Check out LifeViewer Build 233 (Tiki bar link). This is a work in progress, but it seems very promising so far.
If you have ideas for what should be possible, or shouldn't be possible, starting from a wiki RLE snippet, please go ahead and add it to that discussion!
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### Re: Thread for basic questions
Bullet51 wrote:Given a pattern P and a number k, is the problem of synthesizing P in k gliders decidable?
I guess the problem may not be provably undecidable for small k, but nobody is going to be able to prove that it's decidable either, even for k=4. We can't enumerate 4-glider collisions reliably, and until we can there's not much point in looking at k>4 cases.
(Someone please correct me if I'm wrong. I usually am, about things like decidability questions.)
Here's an example of why 4-glider enumeration is a nearly neverending process. Take a 3-glider synthesis of a switch engine -- not the recently-discovered "clean" synthesis, but one of simsim314's messy ones where the switch engine doesn't self-destruct. Now figure out where you can safely stop colliding one more glider into that switch engine. As long as you can produce a big messy explosion that interacts with the entire length of the switch engine's debris, you might get something different by waiting longer to send in that glider.
Bullet51 wrote:A stronger version:
Is it possible to enumerate all K-glider collisions? (K is the largest number such that there is something synthesizable by K+1 gliders but not synthesizable by K gliders)
See the "Argh, kickbacks" section of this message:
dvgrn wrote:From the point of view of 4G collisions, that's actually not good enough. A fourth glider could hit a piece of junk, or the last dying spark from let's say the 2-glider-mess reaction, and prolong it for long enough that a very long-delayed kickback glider might do something unique.
Even in the 4-glider case, there's no way to prove that one of those long-delayed kickbacks might not hit the Prolonged 2-Glider Mess and improbably turn it into Pattern P.*
-- Yes, we know that that's too improbable to happen in almost any conceivable case... but we also know how to make arbitrarily high-population "diehard seeds" that are statistically indistinguishable from Prolonged 2-Glider Mess ash. It doesn't seem to me a valid proof will ever be able to find its way around that problem.
-------------------------------
* Well, okay, Pattern P plus N output gliders. But you could shoot those down, making a synthesis of P with 4+N gliders. That doesn't seem to make very much difference to the basic problem.
toroidalet
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### Re: Thread for basic questions
dvgrn wrote:Here's an example of why 4-glider enumeration is a nearly neverending process. Take a 3-glider synthesis of a switch engine -- not the recently-discovered "clean" synthesis, but one of simsim314's messy ones where the switch engine doesn't self-destruct. Now figure out where you can safely stop colliding one more glider into that switch engine. As long as you can produce a big messy explosion that interacts with the entire length of the switch engine's debris, you might get something different by waiting longer to send in that glider.
But this only proves that a depth-first search fails. A breadth-first search (although slower) will not end up fixated on the SE+G explosions.
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."
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dvgrn
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### Re: Thread for basic questions
toroidalet wrote:
dvgrn wrote:Here's an example of why 4-glider enumeration is a nearly neverending process. Take a 3-glider synthesis of a switch engine -- not the recently-discovered "clean" synthesis, but one of simsim314's messy ones where the switch engine doesn't self-destruct. Now figure out where you can safely stop colliding one more glider into that switch engine. As long as you can produce a big messy explosion that interacts with the entire length of the switch engine's debris, you might get something different by waiting longer to send in that glider.
But this only proves that a depth-first search fails. A breadth-first search (although slower) will not end up fixated on the SE+G explosions.
If you can prove that none of the SE+G explosions produces Pattern P, then maybe breadth-first vs. depth-first could make a difference somehow... though I'm not quite sure how: if it's a complete enumeration, then you'll have to get to all the same cases eventually, either way.
Maybe you can prove that about SE+G, for some target P anyway, if there are unwanted output gliders. Unfortunately you'll also have to be able to prove something similar for all possible Two Interacting Two-Glider-Messes, and for any of the gazillion three-glider methuselahs with a fourth glider added at any point... and so forth and so on.
For any long-lived 3G crash that _doesn't_ produce output gliders or spaceships, how do you prove that it can't be made to settle into your target Pattern P, without trying every possible glider you can hit the active reaction with before it settles? That should give some sense of the size of the problem, and that's just for k=4.
For most P, we know immediately that it's so unlikely that there's no point in bothering to check... but a positive answer to the question would require a provably correct algorithm, not a common-sense statistical argument that's likely to have occasional incredibly rare exceptions.
Here's a related opinion about proofs involving 4-glider and k-glider collisions, from someone with much more respectable mathematical credentials than mine...!
calcyman wrote:Corollary: producing a complete list of constructions with k gliders is, at least morally, impossible.
Maybe 3-glider collisions can be fully classified (I'm imagining tens of thousands of individual cases together with a few hundred infinite families), but I doubt anyone could ever manage an exhaustive classification of all possible 4-glider collisions.
In particular, I doubt anyone could ever prove the falsity of the following claim:
"There is a 4-glider synthesis of the Caterpillar."
toroidalet
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### Re: Thread for basic questions
Is there any way to join 2 streams of ants?
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drc
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### Re: Thread for basic questions
How are oscillator orders determined? Like this? It seems to have a pattern but I can't figure it out.
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wildmyron
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### Re: Thread for basic questions
drc wrote:How are oscillator orders determined? Like this? It seems to have a pattern but I can't figure it out.
The comparison method is detailed on the site. This comparison method is used to determine the standard form of objects in Small Object Format.
toroidalet wrote:Is there any way to join 2 streams of ants?
I don't understand what you mean. Can you show what the input and output of the joining process should look like?
The latest version of the 5S Project contains over 221,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki.
muzik
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### Re: Thread for basic questions
How many non-totalistic CA are there?
Also, would I be correct in saying that there are 2^512 non-isotopic CA?
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### Re: Thread for basic questions
muzik wrote:... would I be correct in saying that there are 2^512 non-isotopic CA?
No. There are 2^512 2-state CA with moore neighbourhoods, but note that this is a superset of the set of all isotropic 2-state CA with moore neighbourhoods. To get the amount of non-isotropic CA you'd have to subtract one from the other.
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### Re: Thread for basic questions
muzik wrote:How many non-totalistic CA are there?
Come on, that's high school-level mathematics. It would likely have taken you less time to figure out the answer yourself than to write this post.
Also, would I be correct in saying that there are 2^512 non-isotopic CA?
No, because there's no agreed-on definition of "non-isotopic". ("Non-isotRopic", on the other hand...)
blah wrote:No. There are 2^512 2-state CA with moore neighbourhoods, but note that this is a superset of the set of all isotropic 2-state CA with moore neighbourhoods. To get the amount of non-isotropic CA you'd have to subtract one from the other.
More precisely still, that's 2-state CAs defined on ℤ² using the range-1 Moore neighborhood.
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muzik
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### Re: Thread for basic questions
Apple Bottom wrote:
muzik wrote:How many non-totalistic CA are there?
Come on, that's high school-level mathematics. It would likely have taken you less time to figure out the answer yourself than to write this post.
So since there's 51 different birth conditions, that would be 2^51. Am I making any mistakes here?
Apple Bottom wrote:
Also, would I be correct in saying that there are 2^512 non-isotopic CA?
No, because there's no agreed-on definition of "non-isotopic". ("Non-isotRopic", on the other hand...)
The next time you see autocorrect, give it a massive slap across the face. Preferably with a cactus.
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
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### Re: Thread for basic questions
muzik wrote:So since there's 51 different birth conditions, that would be 2^51. Am I making any mistakes here?
Yes: you're not counting survival conditions.
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muzik
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### Re: Thread for basic questions
Apple Bottom wrote:
muzik wrote:So since there's 51 different birth conditions, that would be 2^51. Am I making any mistakes here?
Yes: you're not counting survival conditions.
Right, so that would make it 2^102.
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### Re: Thread for basic questions
muzik wrote:How many non-totalistic CA are there?
Also, would I be correct in saying that there are 2^512 non-isotopic CA?
2^64. Since every transition can have 8 different orientations (rotation and reflection), there are 2^64 non-totalistic rules, because 512 divided by 8 is 64.
One big dirty Oro. Yeeeeeeeeee...
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### Re: Thread for basic questions
gameoflifemaniac wrote:
muzik wrote:How many non-totalistic CA are there?
Also, would I be correct in saying that there are 2^512 non-isotopic CA?
2^64. Since every transition can have 8 different orientations (rotation and reflection), there are 2^64 non-totalistic rules, because 512 divided by 8 is 64.
Yes, but now you're back to calculating isotropic rules, aren't you? The question was (supposed to be) about non-isotropic rules. Also, some transitions are twofold or fourfold rotationally symmetric, or mirror symmetric, so you can't really just divide like that, you end up with much too small a number. 2^102 is pretty clearly right for isotropic rules, isn't it? That accounts for all the isotropic rule strings that you could possibly generate.
-- This is the problem with the term "non-totalistic". People have been using it to mean "isotropic non-totalistic", but that's not really what it means. If you pick a MAP rule at random, it's definitely not going to be totalistic, probability near zero -- but it's also very very unlikely to be isotropic. Those near-2^512 rules are the full set of (mostly kinda boring) non-totalistic rules.
When these new rule types first started showing up on LifeViewer, I tried to be careful to use "totalistic", "isotropic non-totalistic", "anisotropic non-totalistic" as the three categories, in hopes that people would pick those terms up. But I have to admit those last two are pretty horrible terms.
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### Re: Thread for basic questions
gameoflifemaniac wrote:
muzik wrote:How many non-totalistic CA are there?
Also, would I be correct in saying that there are 2^512 non-isotopic CA?
2^64. Since every transition can have 8 different orientations (rotation and reflection), there are 2^64 non-totalistic rules, because 512 divided by 8 is 64.
That same reasoning would lead you to believe that there are 3^(3^9/8) such 3-state rules, which is nonsensical since that number isn't an integer.
What do you do with ill crystallographers? Take them to the mono-clinic!
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### Re: Thread for basic questions
There should be 2^102 isotropic rules in total, 2^101 essentially distinct because every rule has either an ON/OFF dual rule or an ON-OFF-symmetric/strobing dual rule. There should be 2^512 - 2^102 non-isotropic rules, but the number of essentially distinct ones is harder to calculate due to rotations/reflections.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)
$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$
http://conwaylife.com/wiki/A_for_all
Aidan F. Pierce | 2019-10-15 10:50:50 | {"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": 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": 0.682747483253479, "perplexity": 3471.8315901838487}, "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/1570986658566.9/warc/CC-MAIN-20191015104838-20191015132338-00050.warc.gz"} |
https://www.nature.com/articles/s41598-021-04409-y?error=cookies_not_supported | ## Introduction
Humankind and the environment are highly dependent on the type of energy consumed. Environmental pollution from traditional fuel sources has caused the world to develop renewable energy sources such as supercapacitors (SC), batteries, and hybrid systems1,2,3,4,5. Although they differ from each other both in function and in the application, SCs surpass batteries in energy density and capacity6,7. These characteristics have been achieved through multicomponent use of nano-materials with a controlled structure8,9,10.
One way to increase the electrode material's capacity is to use carbon materials as a matrix for charge accumulation via an electrochemical double layer11,12. Thus, adding specific functionalities in the carbonaceous system to create preeminent composites for electrode system withdraws considerable attention in the development of energy storage devices13.
Choi et al. reported that MOFs could be integrated into supercapacitor SC devices due to metal oxide and organic constituents. Their results showed that MOFs could provide sufficiently high capacitance and durability for SC electrodes14. Although MOFs have lower electrical conductivity than carbon-based materials, they can be used as components of graphite carbon materials to make active electrode materials of SCs15. MOFs are attractive candidates to meet the requirements of the following generation energy storage technologies. They can easily combine carbon-based materials to form the high-working performance composite applied for SCs’ electrodes. The strategies of combining MOFs and other carbon-based materials with conducting polymers can help increase the energy storage capacitance16,17,18.
In the previous study, we synthesized the rGO and Zn-MOF composites combined with PANI in different forms19. As a result of the study, we found that rGO/Zn-MOF aerogel exhibits much better electrochemical performance after in-situ modification with PANI.
In this study, the electrodes for SCs were fabricated in hybrid composites made of rGO, MOFs based on Mn or Cu, and PANI. The structure of electrodes obtained is depicted in Fig. 1. The MOFs can enhance electrolyte ions' adsorption/desorption behaviors during EDLC charging/discharging of SCs and give potential opportunities in turning their electronic and electrochemical properties via modifying their metal center and organic linkers17. The changes in organic linkers may lead to a shift in their crystalline structures and electrochemical properties6. MOF powders can serve as a stable and underlying conductive network with high electrical conductivity and improved cycling stability in hydrogel materials20. Based on the previous results, we propose MOF synthesis using different metal ions. Hence, it can enhance electrolyte ions' adsorption/desorption behaviors during EDLC charging/discharging of SCs. The MOFs give potential opportunities in turning their electronic and electrochemical properties via modifying their metal center and organic linkers17. The idea of this study is aiming at the structure of MOF based on Cu2+, and Mn2+ developed from our previous study.
## Experimental
### Materials
Synthetic graphite powder (< 20 μm), potassium permanganate (KMnO4 ≥ 99.0%), ammonium persulfate ((NH4)2S2O8, ≥ 98.0%), aniline, Manganese (II) chloride tetrahydrate (MnCl4·4H2O), Copper (II) nitrate trihydrate (Cu(NO3)2·3H2O), terephthalic acid (H2BDC, 98%), N,N′-dimethylformamide and perchloric acid (HClO4, 70%) were products of Sigma-Aldrich. Sulfuric acid (96%), hydrogen peroxide solution (30%), and all solvents were purchased from local companies PENTA and VWR Chemicals. All chemicals were used without any further purification.
### GO preparation
Graphene oxide (GO) was prepared according to the modified Hummers’ method. Firstly, a four-neck flask containing 3 g of graphite powders and 3 g of KNO3 were put in an ice bath. Then, 150 mL H2SO4 (96%) was slowly added to the flask, and the suspension was stirred for 15 min. Next, 18 g of KMnO4 was slowly added to the mixture under continuous stirring. The mixture was then stirred at 35 °C for 1 h. After that, the suspension was put into an ice bath, and 200 mL of deionized (DI) water was dropped slowly into the mixture to reach room temperature. An additional 100 mL of DI water was added before the mixture was re-heated to 90 °C. Then, 40 mL of hydrogen peroxide (30%) was slowly poured into the mixture and stirred for 30 min. Subsequently, the mixture was cooled down to room temperature, washed with DI water, and centrifuged until its pH was approximately neutral. The generated GO suspension was kept in cold conditions for further experiments.
### Synthesis of Mn-MOF and Cu-MOF
Mn-MOFs were synthesized following a typical procedure described previously with modification21. In brief, MnCl2·4H2O (1.187 g, 6 mmol) and H2BDC (0.199 g, 1.2 mmol) were dissolved in 15 mL of dimethylformamide (DMF). The mixture was stirred and sonicated until complete dissolution. The mixture was then transferred into a Teflon-lined stainless-steel autoclave, heated up to 120 °C for 20 h then cooled to room temperature. The crystallites were collected and washed several times with methanol and DMF before being centrifugated at 4000 rpm for 30 min. The obtained residue was activated by removing the solvent under vacuum at 100 °C over 12 h to produce Manganese-1,4-Benzenedicarboxylate (Mn-BDC). The preparation of Copper-1,4-benzenedicarboxylate (Cu-BDC) followed the same procedure, but Cu(NO3)2·3H2O (1.45 g, 6 mmol) was used instead of MnCl2.4H2O.
### Synthesis of rGO-MOF composites
Two different composites were prepared. Accordingly, rGO/Mn-MOF aerogel (M1) was synthesized using a one-step hydrothermal co-assembly method22. A mixture of 0.02 g Mn-MOF and 5.589 g GO suspension (17.89 mg/mL) was sonicated for 60 min. The content was then transferred to an autoclave, heated to 160 °C for 5 h, and then cooled to room temperature. The hybrid hydrogel was collected, washed several times with DI water, and kept in 10 mL of DI water. A similar procedure was applied in preparing rGO/Cu-MOF (M2), but 0.02 g Cu-MOF was used instead of Mn-MOF. All hybrid composites were freeze-dried to obtain M1 and M2 composites.
### Modification of rGO-MOF composites by PANI
Both rGO-MOF composites supported with PANI, M1, and M2 were modified via in-situ polymerization of aniline23. To this end, a piece of synthesized graphene hydrogel was immersed in 50 mL of DI water in a 100 mL beaker. Then 1.5 mL of aniline was added. Hence, the solution was kept for 2 h at room temperature before the hydrogel piece was taken out. This step was repeated before a piece of hydrogel was immersed in a 50 mL solution of perchloric acid (6.8%) for 18 h. After that, the sample obtained was immersed in perchloric acid solution (9.2%, 22 mL) and kept at 0 °C for 1 h. Then, the ammonium persulfate (17.5 mM, 10 mL) solution was dropped slowly into a perchloric acid solution under continuous stirring. After that, the solution was kept stabilized at 0 °C for 24 h to polymerize. The samples were taken out and were rinsed with DI water and then freeze-dried to obtain rGO/Mn-MOF@PANI (M1P) and rGO/Cu-MOF@PANI (M2P).
### Characterization techniques
We conducted the characterizations using the methods of our previous studies19,22. Mn-MOF and Cu-MOF's crystal structures were analyzed via X-ray powder diffraction (XRD) patterns employing a Cu–Kα radiation source from a D8 Advance Brucker powder diffractometer. The chemical composition was identified by ATR-FTIR spectroscopy by using Nicolet iS10 (Thermo Scientific) equipped with an ATR sampling accessory with a Ge crystal plate. The pore morphologies were characterized by a NANOSEM 450 (FEI, USA) scanning electron microscope (SEM) operated at 5 kV under 90 Pa pressure. The prepared samples were also investigated by transmission electron microscopy (TEM) employing the JEOL JEM-2100 electron microscope (JEOL, Japan) operated at 160 kV accelerating voltage. The samples were ultrasonically dispersed in water (0.5 wt%), drop-cast onto formvar coated 300 mesh copper grids, and gently dried.
The determination of C, H, N was conducted by the FLASH method. The content of elements in the samples was determined by the EDX-XRF method (Energy ray dispersion spectroscopy—X-ray fluorescence), which was based on the elemental analysis of X-ray diffraction (energy) materials. Each element has a different X-ray energy radiation by type and quantum of X-ray. Radiation was determined by the type and amounts of elements in the sample.
To analyze the chemical composition and binding energy of the composites obtained, X-ray Photoelectron Spectroscopy (XPS) was applied. The measurements were carried out by using the photoelectron spectrometer Hermo Scientific K-Alpha XPS system (Thermo Fisher Scientific) with a monochromatic Al Kα source, pass energies of 200 eV (step size 1.0 eV) and 30 eV (step size 0.1 eV) for the survey and high-resolution spectra, respectively.
To further identify Mn and Cu's components, we used the EDX method to determine them. The content of elements in the samples was determined by EDX-XRF method (Energy ray dispersion spectroscopy—X ray fluorescence), which is based on elemental analysis of X-ray diffraction (energy) materials. Each element has a different X-ray energy radiation by type and quantum of X-ray. Radiation is determined by the type and amount of elements in the sample. The method is suitable for determining elemental representation in matrices in powder, liquid, and solid form; it is a non-destructive method (the study of material surfaces). The amount of elements analyzed is evaluated in weight percent (% m/m). Powered samples in special cups were placed inside the instrument at the appropriate sample to the autosampler. The content of the elements was determined using an Energy Dispersive X-ray Spectrometer (Thermo Scientific, ARL Quant X). The samples were analyzed in a specially selected method: any sample Helium in Quant program.
### Fabrication of working electrodes and their electrochemical testing
The electrochemical test was performed following our previous studies19,22. A slurry containing the crushed composite using a solution of PTFE (10% of total mass) in 1 mL of ethanol was prepared. Hence, the slurry was coated as a circle of 0.25 cm radius on a titanium mesh and then compressed. The as-prepared electrodes' electrochemical performance was investigated using cyclic voltammetry (CV), galvanostatic charge–discharge tests, and electrochemical impedance spectroscopy (EIS) techniques on a potentiostat Autolab PGSTAT-128 N at room temperature.
Electrochemical measurements were performed in a three-electrode cell using a working electrode, a platinum wire with a high area dimension electrode, and an Ag/AgCl reference electrode. The measurements were carried out in an aqueous solution of two different electrolytes of 1 M H2SO4 at room temperature.
The prepared materials' cycling stability was measured in a two-electrode system by BioLogic battery cyclers (BCS-810) at a current density of 1 A/g for 5000 times. In the two-electrode system, the two same electrodes were compressed in a Swagelok cell and separated by a piece of supercapacitor separator (NKK-MPF30AC).
## Results and discussion
This study also used the 3D carbon-based materials (CBM) synthesized from 2D graphene oxide. The 3D substrate materials have higher porosity and specific surface areas. However, they also have the drawbacks of low conductivity and poor hydrophilic13. Due to the sp2 hybridization inside the structure, 2D CBMs have better electrochemical properties and good electrical conductivity and can be widely composed with CPs in widespread application in SCs. However, the 2D CBMs can accumulate easily, such as GO, during the synthesis processes13.
Furthermore, during the working process in the ambient conditions, the layer made of 2D CBMs can be easy peeled off from the electrode surfaces. However, their composites may help to hinder and diminish the self-strip phenomenons. To increase the working performance of the supercapacitor electrode materials, MOFs were used. MOF powders can serve as a stable and underlying conductive network with high electrical conductivity and improved cycling stability. Such composite materials can help to prepare the next generation of electrochemical energy harvesting and storage devices with long cycle life20. Changing the porosity of MOFs required different synthesis conditions. Every changing factor will lead to a difference in the morphology of the MOFs.
Our composites were made of the rGO matrix connecting the other components inside its structure. Moreover, during the polymerization process, the matrix absorbed aniline inside the solution by its porous structure. The composites have the scaffold of rGO sheets on which PANI and MOFs adhered. In contrast to the rGO matrix, MOF has a crystalline structure. Their surface is smooth, as can be seen from the SEM picture, and aniline cannot attach. If we synthesize MOF@PANI using the same process applied for M1P and M2P, PANI will be synthesized separately from the structure of MOF during the polymerization process. It means that there is no composite MOF@PANI can be made. We can only get the two different compounds PANI and MOF separately after the reaction. Hence, the MOF only cannot form the electrode materials because of their smooth surface. In the previous study, we attempted to make the electrode containing the MOF only. However, the fabrication is not stable, and the electrode will be destroyed after drying.
The purpose of this study is the application of rGO composite as electrode materials. As we mentioned in the introduction part, this study focused on improving the operating performance of rGO and MOF further investigating our previous study. rGO is well known as the typical materials for SC; however, they also contain drawbacks such as low specific surface areas. The addition of rGO and PANI to the composite aims to improve the electrochemical properties of the electrode’s materials. Their application as SC electrode materials can be found in the litteratures4,24.
Our group had published a paper related to the effect of the concentration of aniline or pyrrole25. We reported that the aniline or pyrrole monomer concentrations (3% and 6%) did not affect the polymers' products. According to those results, we chose the standard concentration 3% of monomer solution in this study. The relative amounts of rGO: MOF chosen in this study were optimized from our previous publication. We did optimizations and found in the composite, if the amount of MOFs increases after the hydrothermal reaction, the large amount of MOF powders would be superfluous and precipitated inside the solution. Hence, the amount of MOF inside the composite cannot be predicted precisely.
### XRD and FTIR characterizations
The MOFs materials were analyzed by different methods to identify their structural and chemical features. Characteristic XRD peaks were found at 10.2°, 12.1°, and 24.9° for Cu-BDC (MOF) and 10.1°, 14.7°, and 24.5° for Mn-MOF (Fig. 2a). The observed XRD spectra are in good agreement with the simulated one (black line). The XRD pattern of Cu-MOF was compared with the Cu-BDC XRD simulated in the literature reported by Silva et al.26. The diffraction patterns of Mn-BDC are consistent with the simulated XRD pattern and compared with the literature (monoclinic crystalline framework patterns of MnO6with octahedral geometry, Mn3(1,4-BDC)3(m-DMF)2)27. Hence, XRD spectra was also compared with the simulated Mn-BDC (MOF) XRD reported by Asghar et al.28. It can indicate that the Mn-BDC (MOF) and Cu-BDC (MOF) were successfully synthesized. According to previous studies, the XRD data suggest that solvothermal synthesized Mn/Cu-MOFs contain diamond-shaped channels22,29,30. Besides, the crystalline structure of Mn-MOF detected via XRD depends on the solvent inside the structure. The Mn-MOF structure was changed during the heating vacuum process while DMF molecules were removed from the skeleton structure. It changed the 3D crystalline dimension distance inside the Mn-MOFs after the thermal activation. As a consequence, the Mn-BDC (MOF) diffraction peaks were attenuated31.
The XRD spectra of all composites are shown in Fig. 2c. After the hydrothermal reaction, the XRD spectra of Mn-MOF in M1 and M1P showed the most substantial peak at 29.5°. Due to the attenuation of Mn-MOF, their peaks were covered. However, the peaks at 9.2° showed that the existence of Mn-MOF in the composites. In contrast, M2 and M2P show high crystallinity in their XRD spectra. Those spectra showed the stability of the crystalline structure of MOFs in the composites after the synthesis processes.
The Fourier transforms infrared (FTIR) spectra of Mn/Cu-MOF’s are shown in Fig. 2b. As observed, the signal at 3362 cm−1 displays the –OH stretching; the peak at 1588 cm−1 relates to the asymmetric vibration of –COO. The asymmetric and symmetric stretch of carboxylate groups corresponds to the peak at 1392 cm−1. The peaks at 1159 cm−1, 1107 cm−1, and 1019 cm−1 correspond to C–C vibration. Those results also confirmed that Mn/Cu-MOFs were successfully synthesized via hydrothermal reaction.
Figure 3a displays the IR spectra of composites. The composites were formed after the reduction of GO to make rGO sheets via hydrothermal reaction. After the hydrothermal reaction, the GO is reduced to rGO. Hence, carbonyl groups (C=O) are reduced to methylene (–CH2–). The peaks at 2983 and 2901 cm−1 in all spectra show the symmetric and asymmetric stretching vibration of –CH2–, respectively32. The stretching vibration of the C=C plate of samples depicts the peak at 1580 cm−1. The sp2 carbon stretching vibration peaks of C=O due to the carboxylic group site at the edge of GO are displayed at 1714 cm−1. At 1565 cm−1, the strong peaks represent the aromatic C=C in-plane vibrations in the rGO sheet. Hence the peaks at 1203 and 1095 cm−1 displayed the C–O stretching vibrations and the carbonyl groups leftover after reduction33,34. Due to the resemblance in the aromatic structure, the FT-IR spectra of those composites appeared similar to each other. However, in M1P and M2P, the band at 1232–1289 cm−1 can be assigned to the π-electron delocalization induced in the polymer through protonation or C–N–C stretching vibration. Furthermore, the peak at 1232 can show the C–N+ stretching vibration in the polaron structure. Those peaks can confirm the existence of PANI inside the composite. Each sample was analyzed three times (RDS: ± 001289–000112). The averaged values from three parallel measurements of the individual samples are already shown in the table. Values of elements are given in percent by weight (% m/m).
### XPS study
X-ray photoelectron spectroscopy (XPS) was applied to characterize further the chemical composition, the oxidation state of elements, and functional groups. According to results obtained, rGO/Cu MOF sample exhibited typical peaks for the organic frameworks (C1s, O1s, and N1s signals) and Cu2p3/2 signal centered at ca 934.4 eV corresponding to Cu2+ species (Fig. 3b). The oxidation state of copper also confirms the satellite feature at ca 937–946 eV typical for Cu2+ state (Fig. S2a). Similarly, manganese depicted a satellite feature at ca 646 eV confirming the Mn2+ state (Fig. S2c). The presence of C1s signal confirms the presence of rGO at ca 284.1 eV corresponding to sp2 carbon and satellite feature (π–π*) and ca 290.6 eV attributed to delocalized conductive π electrons. The other C1s signals, namely sp3 (284.6 eV), C–O (285.9 eV), C=O (287.40 eV), and OC=O (288.60 eV), could be attributed to the organic frameworks and some oxidation on the surface. After coating by PANI, the signal of C1s changed only slightly, more likely due to the low PANI concentration in the composite, which is related to the coating thickness (Fig. S3). The thin PANI coating indicates the minimal increase of nitrogen content, which could serve as a marker for PANI coating. In the case of complete coverage with the thick PANI layer, the ratio N/C should be close to 1/635. This is not the case indicating a thin layer coating by PANI. Typical signals of N1s were detected at ca 399.3 eV that corresponds to –NH– and N1s. The signal at ca 401.2 eV corresponds to –N+ species indicating that PANI is in the form of emeraldine salt (Fig. S4). The presence of the ClO4 (Cl2p) anion was detected in the spectrum at 207.2 eV, which can be explained by using an HClO4 solution to polymerize aniline36,37,38. Those results confirmed the successful synthesis of composites made of Mn/Cu-MOFs, rGO, and PANI.
### Elemental analysis
After the in-situ polymerization of aniline on rGO/Mn-MOF (M1) and rGO/Cu-MOF (M2) to make rGO/Mn-MOF@PANI (M1P) and rGO/Cu-MOF@PANI (M2P), the elemental analysis was carried out to find the different elements and their distribution in the composites before and after the reaction. The results obtained are shown in Table 1. As can be seen from the table, C, H, and N are the main components of samples. During the oxidization via modified Hummer’s method, KNO3 was reacted with graphite to transfer it to GO, which led to the N atom's existence in M1 and M2. After being supported with PANI, the percentage of N in the composites was increased. Among other things, M2P contains a higher concentration of N than M1P. Those increases of N% showed that PANI was supported on the structure of M1 and M2. Moreover, the difference in N percentage change of M2P was higher than M1P. It can be explained due to the catalytical properties of copper during the reaction. Copper compounds were reported to be an efficient catalyst for PANI, and it may lead to a higher amount of PANI being formed inside the M2P39,40.
The chemical compositions of the sample metal components were further determined using EDX-XRF (Detailed information is shown in Table 2). The materials will be calculated to determine the metal component percentages in the composites. It can prove that after the polymerization process, the Mn/Cu-MOFs remained stable in the composite. Furthermore, the existence of Cl can also verify the existence of PANI. During the polymerization process in HClO4, Cl was captured on the polymer chains, leading to its percentage appearance.
The pristine MOFs powders have low conductivity (10–12–10–14 S cm−1)41,42. Hence, the samples’ conductivities were tested to decipher the improvement of PANI on the composites. The resulting composite of M2 contained Cu-MOF showed higher electrical conductivities (4 × 10–2 S cm−1) than the composite of M1 (3.3 × 10–2 S cm−1). Hence, after being supported with PANI, the composite's conductivities were increased to 2.8 × 10–1 S cm−1 (M1P) and 3.7 × 10–1 S cm−1 (M2P). The graphite sheets of the composite after the polymerization processes contained PANI on their surface tightly. Additionally, the conductivity of the composite could be increased due to the intact contact of PANI on the rGO/MOF conducting surface.
### Morphology characterizations
Figure S1 shows the SEM images of the synthesized Mn/Cu-MOFs. The prepared MOFs particles appeared to have regular and ordered structures, confirming the synthesis process's success. The SEM image of Mn-MOF particles received (Fig. S1) showed the uniform with microcrystals structures.
Figure 4 shows the morphology of composites M1, M2, M1P, and M2P obtained via hydrothermal reaction in the autoclave. After being synthesized via the hydrothermal reaction, GO was reduced to rGO, forming the carbon graphene sheet. Those sheets contain the hydrophobic basal plane and the hydrophilic edge, which can be seen in Fig. 4. During the sheet forming reaction, Mn/Cu-MOF was captured inside the structures of those composites. According to the TEM images, MOFs particles are located inside the structures of M1 and M2 (Fig. 4e,f). Figure 4 also shows the composites' highly porous structure, facilitating access to electrolyte ions, enhancing interaction with the material surface, and activating electrochemical reactions22. The morphology of M1P and M2P changes markedly after their modification with PANI: PANI is distributed on or intercalates between the surfaces of rGO sheets and the MOF particles (Fig. 4g,h). Thus, PANI's addition into the composites may enhance the pseudo-capacitance of M1P and M2P, hence leading to their higher electrochemical performance.
### Electrochemical characterizations
To understand the operating performance of electrode materials, we compressed the composites' slurry on the titanium mess and analyzed their electrochemical properties. (details are in supplementary information). The SC electrode characteristics are generally measured and deciphered using the cyclic voltammetry (CV) analysis. Figure 5 compared the electrochemical properties of the electrodes made of those composites. We used the typical tree-electrode system to CV test in a fixed potential window of − 0.2 to 0.8 V using 1 M H2SO4 as the electrolyte43. The samples showed that the response currents of M1 and M2 exhibited redox peaks caused by the electrode materials and carbon’s faradic reactions. They can be expressed as follows:
$${\text{M}}\left( {{\text{C}}_{{8}} {\text{H}}_{{4}} {\text{O}}_{{4}} } \right)\left( {{\text{H}}_{{2}} {\text{O}}} \right)_{{2}} + {\text{C}}^{ + } + {\text{e}}^{ - } \leftrightarrow {\text{MC}}\left( {{\text{C}}_{{8}} {\text{H}}_{{4}} {\text{O}}_{{4}} } \right)\left( {{\text{H}}_{{2}} {\text{O}}} \right)_{{2}}$$
(1)
where M denotes the metal ion of Mn and Cu from the MOFs compound44. The CV spectra of samples at different scan rates from 10 to 100 mV s−1 can be found in Fig. S5. Notably, the electrodes made of M1P and M2P showed higher current density than M1 and M2, indicating that their capacitances were enhanced. We can see two pairs of the redox peaks showed in the CV curves of M1P and M2P, which are related to the surface reactions of PANI among the reduced state, the partially oxidized state, and the complete oxidation states, respectively45. The appearance of those redox peaks could be explained through the insertion and desertion of SO42− ions (doping) in PANI according to Eq. (2):
$$\left( {{\text{PANI}}} \right)_{n} + ny \; {\text{SO}}_{{4}}^{{{2} - }} \to \left[ {{\text{PANI}}^{{{\text{y}} + }} {\text{SO}}_{{4}}^{{{2} - }} } \right] + ny\;{\text{e}}^{ - }$$
(2)
where y is the doping degree, defined as the ratio between the number of charges in the polymer and the number of monomer units46. Additionally, PANI has a good conductivity property. During the working process, under the current flow, PANI can be easily converted between various oxidation states such as emeraldine, leucoemeraldine, and pernigraniline. The spectra of M1P and M2P showed two pairs of redox peaks related to the activity in acidic aqueous electrolytes. The first anodic peaks can be associated with doping of SO42− anions related to the conversion of leucoemeraldine form of PANI to emeraldine salt (C1/A1). The next peak signifies the transition of emeraldine to a fully oxidized pernigraniline state (C2/A2)47. The reaction mechanism of PANI salts was displayed in Fig. 1.
The explanation of specific capacitance improvements when supported with PANI into the composite structures was also displayed by the galvanostatic charge–discharge (GCD) curves. Figure 5b showed that all composites exhibited the triangle shapes when they were tested at the current densities of 0.5 A/g, which implies good electrochemical reversibility48. The specific capacitance value was calculated as follows:
$${C}_{s}= \frac{I.\Delta t}{m. \Delta V}$$
(3)
where I denotes the applied current (A), Δt is the time taken for the discharge, m is the mass of active electrode material, and ΔV is the discharge potential22.
The GCD curves of M1 and M2 showed that the Mn-MOF composite has a longer discharging time than the composite of Cu-MOF, which can cause a higher specific capacitance of M1 than M2. This phenomenon can be explained due to the higher numbers of different oxidation states of Mn ions. During the charge/discharge process, Mn4+ can be formed. They can facilitate the bulk redox reactions, enhancing the operating performance when used as a supercapacitor48. To understand the composites' electrochemical properties, we conducted the GCD tests of those electrodes in different scan rates from 0.5 to 5 A/g (Fig. S6). The capacitances of electrodes made of those composites decrease when the current densities increased (Fig. 5c).
It can be explained by ions' faradic reaction between the electrolyte and the electrode materials during the scanning process. At the high scanning rates, the electrolyte ions’ accessibility to the electrode materials' surface decreased. Indeed, it is proven that the capacitance of the electrode materials depends on their structure and morphologies49. The porous structure of the samples is beneficial for ionic conductivity, while the components of the composites can improve the ion transportability of electrodes.
Moreover, porous bridges inside the electrode allow it to overcome the limitations on both intercalation and adsorption of charged ions. The porous structure also increased the possibility of the interaction between those ions, which led to a better opportunity for reactions49. Considering these reasons, we can assume that an increase influenced the electrolyte ion's diffusion into the electrode matrix in the sweep rate. The electrolyte ions did not interact with the electrodes for a long time and could not reach deep pores. Consequently, this led to a decrease in the specific capacity of the composites.
However, as we described before, Cu-MOF catalyzed in-situ aniline polymerization during the polymerization process, leading to higher PANI in M2P than M1P. PANI is generally considered to enhance the electrochemical performance of carbon-rich due to its high pseudo-capacitance45. The M1P and M2P composites showed their specific capacitance of 225.8 and 276.6 F/g at 0.5 A/g, respectively, while the values of M1 and M2 are 163.2 and 135.2 F/g. It can be explained by a higher PANI amount inside M2P than in M1P and better distribution of PANI inside of MP2, which demonstrated pseudo-capacitance improvement of M2P. The specific capacitance enhancement of M1P and M2P at high current densities can also be attributed to the synergetic effect of pseudo-capacitance and EDLC between PANI and the Mn/Cu-MOFs particles inside the structure. The MOFs usage in the electrochemical application can provide good EDLC properties when they were combined with rGO15. At the same time, PANI, being a conductive polymer, can promote electrical contacts between structures within M1P and M2P. It can facilitate diffusion contact between electrolyte ions during scanning, causing high pseudo-capacitance results of those materials31. Consequently, the combination of PANI and MOFs particles consequently helps to increase the specific capacitance results at high scan rates.
Next, we conducted electrochemical impedance studies (EIS) to decipher the ion transport mechanism. The positive of the improvement of the materials can be identified via the EIS results. Figure 5d shows that the composites' Nyquist plots have the semicircles in the high and mid-frequency regions from the real axis, most likely due to the charge transfer resistance (Rct) between the electrode and electrolyte interfaces50. The values of Rct can be determined from the radius of the semicircles. Comparing with the Rct values for M1 (9.86 Ω) and M2 (10.83 Ω), the lower Rct values of M1P (4.74 Ω) and M2P (4.53 Ω) suggest the ideal capacitive behavior due to the better ion diffusion path which can facilitate the diffusion rate when PANI was supported to the composites51. The oblique line’s slope in low-frequency regions relates to the ions diffusion rate in the electrolyte. Figure 5d shows that the composites of M1P and M2P exhibited a more straight-line long imaginary axis compared to M1 and M2, which can indicate that lower diffusion resistance of the electrolyte ions in their working process52.
Although MOFs are novel developed porous materials that can be easily adjusted by altering their bridging organic ligands, the poor conductivity has always been the notable hindrance to promoting the electrochemical performance of most MOFs applied on SCs. However, due to their excellent specific surface areas and easily adjustable pore environments, MOFs still have many potential opportunities to improve their working performance. Furthermore, according to their metal and carbon sources, MOFs can have various morphologies, which can facilitate their cooperation with conducting polymer to fabricate the high working performance composite materials17. The specific capacitance of this study and other composite materials for supercapacitor electrodes are compared and shown in Table S1. Compared to the published results, rGO, Mn/Cu-MOF, and PANI composites showed excellent specific capacitances at 0.5 A/g. The high working performance of those composite materials is mainly attributed to PANI's pseudocapacitance and the combination of rGO and Mn/Cu-MOF. In our previous study, the specific capacitance of rGO/Zn-MOF@PANI at 0.5 A/g was 253.35 F/g. The electrode materials derived from rGO, MOFs, and PANI composite may present ideal porous structures for ease-diffusion of electrolyte ions. The results shown in Table S1 also exhibit the change of the specific capacitances at the same testing conditions related to the structure of metal ions inside MOFs’ structures.
### Cyclic stabilities
To study the retentions of composites, we tested the two-electrode symmetrical SC. Figure 6 shows the samples' cycling stability performance at the applied current density of 1 A/g for 5000 cycles. The composite of M1 and M2, which contain only Mn/Cu-MOF and rGO, shows good cycle stability with capacitance retention of approximately 92%. However, M1P and M2P retentions show a visible decrease for the first 1500 cycles due to PANI degradation during the charge/discharge process53. Then, the retention ability is stabilized at the capacitance retentions of 82.69% and 79.42% for M2P and M1P, respectively. The better retention of M2P to M1P can be attributed to the former’s higher PANI percentage contained inside.
The stabilities of the composites were further confirmed by applying the potential scan rate at 10 mV s−1 for M1, M2, M1P, and M2P electrodes (Fig. S7a). There are slight changes in the shapes of the cyclic voltammogram of the electrode’s materials. The significant changes of M1P may be due to the deformation of the PANI composite on the surface. Two peaks appeared on the curve of M2P show that the redox reaction of PANI converted between various oxidation states such as emeraldine, leucoemeraldine, and pernigraniline. The charge–discharge plots of the composites also show their high capacitance retentions after 5000 cycles of stability tests (Fig. S8). After stability tests, the capacitive behavior of composites was shifted and can be seen via the semicircle of Rct in Fig. S7c. The reduced Rct of M2P showed a better ion diffusion rate inside the composite structure51. Hence, the oblique line’s slope in low-frequency regions relates to the ions diffusion rate of M1P was shifted and show the diffusion of the ions inside the composite now decreased. It also explained the Rct increase of M1P52. The excellent stability of M2P may be due to the catalytical phenomenon of Cu-MOF on the in-situ growth of PANI on rGO sheets. The amount and stable PANI synthesized in M2P can facilitate efficient electron transfer. Hence, it can help PANI prevent structural degradation and deformation.
Figures S9 and Fig. S10 displayed the surface morphologies of the electrodes materials before and after stability tests, respectively. As we can see in Fig. S9, after the electrodes fabrications process, PTFE polymers appeared and covered the surface of the rGO matrices of the composites. PTFE plays the binder's role, which can help the composites to maintain their structure on the titanium meshes. However, due to the coverage, the other components cannot be seen clearly via the SEM images of the surface. After 5000 cycles, the amounts of PTFE on the surfaces were reduced (Fig. S10). Hence, the IR spectra of the electrode’s materials shown in Fig. S11 proved the existence of the components on the structure before and after 5000 cycles tests. Due to the addition of PTFE, the C-F asymmetric stretching peaks at 1151.29 cm−1 and symmetric stretching peaks at 1209.15 cm−1 appeared on every sample54. The spectra of all samples did not show the change before and after the stability tests. The high-intensity peaks at 1588 cm−1 related to the asymmetric vibration of –COO groups that confirmed that Mn/Cu-MOFs have remained inside the composites after the stability test.
Although PANI is a promising material, it still has drawbacks that can restrain its application on SCs. As mentioned in the paper, PANI showed substantial degradation during the doping/undoing process, limiting the stability of SC for long cycles use6. Furthermore, during the charge/discharge cycle process, the electronic conductivity of PANI tends to decrease due to the change of their molecular structures while the faradaic reactions are conducted on the surface of the PANI chains55. The number of charges can be stored or released when a PANI molecule switches between the highly and poorly conducting state via the electrochemical redox reactions. After a certain number of working cycles, PANI will be degraded. Hence, it leads to decreased electrical current carrying capacity and storage capacitance of applied SCs56.
The combination of PANI with other materials to form the composites in this study aims to solve those problems mentioned. The choice of the constituents of composites will cause an effect on their conductivity, surface areas, chemical endurance, and mechanical durability of SCs’ electrodes. Those characteristics of electrodes will directly influence the capacitance of an SC. Both capacitance and stability are vital for the working of SC. An SC has high specific capacitance but cannot work for a long time, or a stable SC can keep their retention for an extended period, but low specific capacitance; neither of their application is limited. There is no priority in this matter. Our group is doing our best to optimize the SC by combining two vital factors.
In this study, there are only two kinds of MOF components composited with PANI. The obtained results can show the improvement in the specific capacitance of SCs after conjugating the composite with PANI. To increase the electrochemical performance and make the tuning conclusion, more samples should be prepared to show the scientific evidence. The treatment of the MOF materials or the composite after synthesizing can make the working performance change.
## Conclusion
In summary, composites made of rGO, Mn/Cu-MOF were fabricated and supported with PANI to be used as electrode materials for SCs. It was found that composite containing Cu-MOF acts as a catalyst for aniline polymerization, which leads to a higher concentration of PANI, thus improving the working performance of the electrode. This study agrees well with reported literature results that the introduction of PANI into the composites increases the pseudo-capacitance, thus enhancing the electrode materials' working performance. Besides it, composites also exhibited cycle stability. The results obtained confirm the high potential of materials based on MOFs, rGO, and conductive polymers as components of electrode materials for SCs. | 2023-02-02 22:08:55 | {"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": 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": 0.5590105652809143, "perplexity": 4081.8521850271777}, "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/1674764500041.18/warc/CC-MAIN-20230202200542-20230202230542-00608.warc.gz"} |
https://www.drmaciver.com/2013/03/another-new-hypothesis-feature-flags/ | # Another new hypothesis feature: flags
This has the virtue of being the first hypothesis feature that isn’t blatantly stolen, excuse me, “ported”, from Scalacheck.
Instead it’s blatantly stolen from a post by John Regehr about Csmith.
Update: John Regehr pointed out in the comments that I was misattributing this idea to him, and it was in fact due to Alex Groce.
What’s the idea?
The idea is basically to change the distribution of the search inputs. Rather than exploring the whole space more or less uniformly at each size, each probe into the space is more focused. This produces examples which are in some sense more “interesting”.
How does this work?
The idea is that in any given run of the producers we have a set of flags which may be turned on and off. Let me show an example:
@produces(int) def produce_int(self,size): p = 1.0 / (size + 1) n = int(log(random()) / log(1 - p)) if self.is_flag_enabled("allow_negative_numbers", size): if random() <= 0.5: n = -n return n
So on some runs we will be allowed to produce negative numbers, on some we won’t.
This means that we can, for example, produce very long lists of only positive integers because negative integers were turned off for this run. Previously a list would be all-positive with probability $$2^{-n}$$ (where $$n$$ is the length of the list), so for example the following would have been unfalsifiable:
from hypothesis import assume, falsify def long_lists_contain_negative_elements(xs): assume(len(xs) >= 50) assert any((a < 0 for a in xs)) return True falsify(long_lists_contain_negative_elements, [int])
But with the new flag based code it’s easy to falsify.
The example that actually motivated this was the stateful testing one in the previous post. If we add a “clear” operation to it and allow that as a test step then we become unable to find falsifying examples because the clear step stomps on things too regularly to ever generate long enough examples.
This is also illustrative of why this is useful in general: Bugs will typically be exhibited by the interaction of one or two features. When we’re looking at all the features we may not exercise the interaction of those two enough to actually test them properly, but when we selectively disable features we can study pairwise interactions much more thoroughly.
Currently the way this is implemented internally is quite gross. I wouldn’t look at it if I were you. I’m mostly focused on hypothesis externals right now, and will think about how to better redesign its insides at a later date.
Update: This feature has been temporarily removed due to me being really unhappy with the implementation and it getting in the way of some internals I’m refactoring at the moment. It will be back before the next released version of hypothesis.
This entry was posted in Hypothesis, Uncategorized on by .
## 3 thoughts on “Another new hypothesis feature: flags”
1. david Post author
Yeah, but right now it’s gross in a way that probably makes it harder to use and modify than it should be rather than just algorithmically gross. :-)
One thing you might find interesting by the way is the way this feature interacts with the search strategy.
When searching, hypothesis has a “size” parameter that roughly controls the complexity of the search space (it’s ad-hoc and unspecified exactly what this means and is interpreted differently for different types, but basically low size parameters should produce a distribution which is tightly clustered around some point). When searching we start the size parameter low, then raise it until we find a counterexample, then lower it until we stop finding counterexamples.
This size parameter also controls the number of flags that are turned on: At low size parameters most are turned off, at high size parameters most are turned on. | 2022-09-26 10:26:10 | {"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": 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": 0.5857111811637878, "perplexity": 1129.8891927973605}, "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-2022-40/segments/1664030334855.91/warc/CC-MAIN-20220926082131-20220926112131-00116.warc.gz"} |
https://testbook.com/question-answer/a-lossless-matching-circuit-is-shown-in-the-figure--600a901ec011aad185ade8e1 | A lossless matching circuit is shown in the figureThe values satisfying the matching condition are:
Free Practice With Testbook Mock Tests
Options:
1. XS1 = -j25.1, XP = +j100, XS2 = -j50
2. XS1 = +j25.1, XP = -j100, XS2 = -j50
3. XS1 = -j25.1, XP = -j100, XS2 = -j50
4. XS1 = +j25.1, XP = +j100, XS2 = +j100
Correct Answer: Option 1 (Solution Below)
This question was previously asked in
ISRO Scientist EC 2012 Official Paper
Solution:
Concept:
Matching Network:
It is also called an impedance transformer is used to create matched impedance between a source and load. Between a power amplifier and antenna. For matching,
Solution:
Given ZS = 50 Ω
Choose option (a)
Let $$50 = {X_{{S_2}}} + \frac{{{X_P}\left( { - 125.0 + 125.1 + 100} \right)}}{{\left( {{X_P} + 125.1 - 125.1 + 100} \right)}}$$
$$50 = {X_{{S_2}}} + \frac{{{X_P} \times 100}}{{{X_P} + 100}}$$
Put XP = j 100
$$50 = {X_{{S_2}}} + \frac{{j \times 100 \times 100}}{{j100 + 100}}$$
$$50 = {X_{{S_2}}} + \frac{{j100}}{{j + 1}}$$
$${X_{{S_2}}} = 50 - \frac{{j100}}{{j + 1}} = \frac{{50j + 50 - j100}}{{j + 1}} = \frac{{ - j50 + 50}}{{j + 1}} = - j50$$
So $${X_{{s_1}}} = - j25.1,$$ XP = j100, $${X_{{S_2}}} = - j50$$
Correct choice is option (a)
$${\rm{\Gamma }} = \frac{{{Z_L} - {Z_0}}}{{{Z_L} + {Z_0}}}$$ | 2021-07-26 23:43:22 | {"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": 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": 0.670845627784729, "perplexity": 14676.776188729273}, "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-2021-31/segments/1627046152156.49/warc/CC-MAIN-20210726215020-20210727005020-00274.warc.gz"} |
https://motls.blogspot.com/2019/05/only-courts-and-god-should-punish.html | ## Wednesday, May 08, 2019 ... //
### Only courts and God should punish people for crimes
Lessons from an ice-hockey player's suicide
Right-wing journalist Laura Loomer has been banned from 190 websites including Lyft and Uber – concerning these two, she was dissatisfied with the absence of non-Muslim drivers and the companies were dissatisfied with her dissatisfaction! When Facebook and its subsidiary Instagram banned her last week, this journalism alumni – a brave Valedictorian from a not so prominent college – lost 90% of income and the sort of career she's been building for some five years. She started to suggest that she was thinking about suicide.
Many people love to blame suicides on psychological problems but in many contexts, there are very objective reasons why someone could make such a final decision. And with certain sufficiently serious objective problems (serious diseases are the most obvious ones), even people with rock-solid psychology could almost rationally decide that suicide is the best option. We may approach this issue using the probability calculus.
OK, yesterday, on May 7th, Czech ice-hockey fans were shocked by the news that Adam Svoboda (*1978) hanged himself. He's been a goaltender in the Czech national team (who won e.g. the 2005 World Championship – although as the third goalman, he was mainly the entertainer of the team) and about 14 additional municipal (Czech, European, and Kazakh) clubs. Those included HC Škoda Pilsen in my hometown. Six years ago, we would root for him – and with him (and Marek Mazanec and Tuukka Rask) as the goalie, Pilsen won its only historical championship in 2012/2013. Svoboda also won the championship with Slavia Prague in 2008.
The statistics is enough to indicate he was an extremely good goaltender. He wasn't necessarily in the Dominik Hašek category but almost certainly in the next one.
Svoboda retired two years ago and became a coach in Pardubice (the town of gingerbread, Semtex, and horse races) plus an assistant coach in the national team.
In 2010, he underwent a surgery of the brain to remove a blood clot. As we know, this event was nothing compared to an event that fatally influenced his life in this year. The key reason for his suicide looks obvious in this case. In early 2019, he caused a car accident with his Volvo XC90. No deaths or serious injuries occurred but there was a legal problem: he was driving with 0.18% of ethanol in his blood. It's a lot. He drove on the wrong side of the road.
When some alcohol is tolerated, it's about 0.05%. About 0.5% is said to be fatal for men (0.4% for women) but in 2013, a Pole was found in Tarnowska Wola with 1.374% and he survived. The record, 1.48%, was measured in Poznan in 1995.
Svoboda's alcohol content was just 13% of the 2013 Pole's but it was still a lot. But without "positive feedbacks", nothing much would happen outside his driving license (which he almost certainly lost, at least for years) and a risk of up to 3 years in jail. The real problem were the feedbacks. He was spectacularly fired as a coach in Pardubice and the national team – although he was later readmitted as a personal coach in Pardubice or something like that. But I think it was clear that his status and income dramatically dropped.
Only when he's dead now, you may hear the people who point out he was an athlete with exceptional character. A few months ago, those who just screamed "punish him" were much more visible.
OK, I just think that these out-of-court punishment for the illegal driving and similar sins are simply wrong and counterproductive for the society.
So far, a similar comment of mine is the most upvoted one under an article about the tragic death but you can see that the opposition to my opinion is substantial, too.
My calculation notices that he has actually caused damages that are only comparable to thousands of dollars. However, it made his suicide likely – perhaps 10% – and his life was worth millions of dollars. It is not popular to convert lives to money but the insurance companies have to do such things and you may compare his life's worth with the lifetime earnings, too. The latter comparison has a logic: a primary purpose of the money is to allow the owner to survive!
Millions of dollars are clearly greater than thousands of dollars. But even if you calculate the mean value and multiply millions of dollars by 10%, you get hundreds of thousands of dollars. Adam Svoboda was still clearly overpunished – I think that by some two orders of magnitude. This just shouldn't happen. And perhaps people who push others to existential problems or suicide should be punished when something bad happens.
The people on the other side claim that as a famous goaltender or coach, he was "elite" or a "role model" so he should be more punished for driving under the influence of alcohol (and other things) than the "ordinary people". I totally disagree with these claims. The constitution says that people are equal in front of the law. The selective punishment of the successful people is wrong, wrong, wrong. It is unjust and it is also bad for the society because it really discourages success! And I find it obvious that the actual main driver behind the efforts to overpunish the successful people is nothing else than jealousy.
The elite or successful people belong to this group because they could and they did something extraordinary enough – something that may be measured meritocratically and usually has nothing to do with morality. It doesn't mean or shouldn't mean that they face some extra universal disadvantages or punishments, that they have some extra duties. In particular, it's wrong to expect that a goaltender is a moral role model – and it's wrong to "demand" it, too. And at the end, I believe that in reality, athletes' morality doesn't differ from the average people much. Why should goaltenders be the moral elite? What about teachers at universities, high schools, basic schools? Interpreters? Truck drivers? Children's coaches with ponies in amusement parks? Pilots? Hairdressers? Ticket inspectors? Plastic surgeons? Managers? Comedians? Most occupations work with other people in one way or another. Does it make any sense to "demand" that they avoid even smaller sins or violations of the law?
There are many similar campaigns and whole ideologies that are directed against the successful people – that want to make their lives harder. Larry Summers wasn't allowed to speak about women in science because he was considered a powerful man – the president of Harvard University. Why should exactly a man with this job be stripped of his basic civic rights? If something, people like presidents of universities should have more freedom, not less freedom, to talk about similar crucial things.
On a more mundane level, I still remember my shock when I was told 15 years that as a house master in some undergraduate dormitories, I couldn't have dated students. What? Every homeless guy may date Harvard students. Why should a house master be forbidden to do such things? Are his or her genes so terrible that the society has to frantically defend its gene fund from such segments of DNA? And why would the universities hire such people if they believe that they're genetic trash? You know, with such restrictions and many others, do you really want to be a university professor? Isn't it sane to prefer to be homeless, living in fresh air – occasionally enriched with some scent of the trash bins where good stuff sometimes waits for you?
As a person who loves freedom, I would choose the latter. But even the people who don't give a damn about freedom must understand that these selective restrictions and punishments against the successful may influence some people's priorities.
It took some time and experience for the political systems and Parliaments to refine our legal systems so that the punishments for various crimes and violations of the law are approximately adequate – they sufficiently discourage people from doing undesirable things (and compensate the victims) while they allow the people to keep on living despite minor sins that everyone can make. But the "positive feedbacks", various out-of-court punishments that hockey clubs, universities, and tons of other places declare against the "sinners", are just circumventing the legal system.
These extra punishments are destabilizing because they circumvent the lawmakers' careful decisions about the right amount of punishment for "sins"; they're unjust because they break the equality of the people under the law; and since they mostly target the successful people, they're regressive because they discourage people from being successful.
If some sin – like driving under the influence – has nothing to do with your relationship to the sinner, please leave the punishment for the sins to police, courts... and God (I mean the probabilistic laws of quantum mechanics). | 2019-05-25 12:52:25 | {"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": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2531597912311554, "perplexity": 3112.5670114949594}, "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/1558232258058.61/warc/CC-MAIN-20190525124751-20190525150751-00089.warc.gz"} |
https://github.com/eugenio-valdano/threshold | # eugenio-valdano/threshold
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Python
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# Computing the Epidemic Threshold on Temporal Networks
Provides Python tools for computing the epidemic threshold on temporal network, as explained in paper
Analytical Computation of The Epidemic Threshold on Temporal Networks
Valdano E, Ferreri L, Poletto C, Colizza V, Phys Rev X 5, 021005 2015.
When you use this code, please cite the above reference.
## Content
• test_system.py checks if your system has all the needed libraries.
• threshold.py main module.
• threshold_util.py additional methods for network handling.
## Required external modules
• numpy
• scipy
• networkx
• pandas (for threshold_util.py)
Run test_system.py to check if you have everything you need.
# Overview
The package consists of two objects: the class tnet for uploading and managing the temporal network, and the class threshold, for the actual computation of the threshold.
## import
The directory containing threshold.py must be in your Python search path. You can temporarily add it using
from sys import path
path.append('<dir to threshold.py>')
Then actually import the module as, for instance,
import threshold as thr # main module
import threshold_util as thu # additional utils
## tnet: manage your temporal network
Class tnet is able to load a temporal network given in different formats:
• path to a text file containing the whole edge list. First two columns represent edges' origin and destination, while last column is the time stamp. Time stamps are assumed to be integers from 0. If there are more than 3 columns, then 3rd column is interpreted as edge weight. Further columns between the 3rd and the last (time) are disregarded. Default separator is \t; different separators (e.g. separator=',') can be input via the optional keyword separator in the tnet constructor. By default the edge list is assumed undirected; this can be changed via the optional keyword directed in the tnet constructor.
• (Python) list of networkx Graph or DiGraph objects. If the network is weighted, weights must be assigned to edges as weight keywords.
The network can then be loaded in class tnet as follows:
R = thr.tnet(my_network)
### Arguments for tnet, with their default values
• my_network: where to look for the network, according to supported formats (see above);
• period = None: set period like this, if only a part of the network is to be used, up to period T (less than the one inferred from time stamps);
• dtype = 'float128': the bit length of the used float. 'float128' is the default because it is often needed. Every string that is not 'float64' is interpreted as 'float128'.
##### other optional keywords
• directed: it may be used when loading from text file. If directed=True, then the edge list is assumed to be directed. If not specified, treated as directed=False. When loading from a list of networkx graphs, it inherits from them the fact of being (un)directed.
• attributes=None: with this keyword you can provide a dictionary for assigning node attributes. Imagine your nodes are people, you could set attributes={'id1':'male','id2':'female'}. The dictionary does not have to be exhaustive. Nodes without attribute are allowed.
• separator: it may be used when loading from text file, to specify the separator. If not specified, treated as separator='\t'.
### Attributes
name description
N number of nodes.
T period. You can manually reduce it. It will drop the time steps in excess from the end.
weighted True/False
lG list of networkx graphs
lA list of adjacency matrices in scipy.sparse.csr_matrix format
attributes node attributes
nodelist list of nodes
## threshold: compute the threshold
Intstantiate a threshold object like this:
myth = th.threshold(X)
Where X can be either a tnet object or a list of adjacency matrices in scipy.sparse.csr_matrix. Additional optional arguments are
##### related to power method:
• eval_max=20000: maximum number of eigenvalue evaluations.
• tol=1e-6 : tolerance for power method convergence.
• store=10 : number of eigenvector(value) values to use to check convergence.
• convergence_on_eigenvector=True. If True uses the algorithm that checks convergence on the L1 norm of the principal eigenvector (probably more accurate). If False, checks the convergence of the eigenvalue estimate itself.
##### related to the temporal network:
• weighted=None. You have to specify it when you provide a list of adjacency matrices instead of a tnet object. You can specify it also with a tnet object if you want to override the .weighted attribute of the tnet object. If the network itself is weighted, you still can set weighted=False here. It simply means it multiplies transmissibility directly to the adjacency matrices. To know more about weights, read this article. weighted=False is more time-efficient than weighted=True.
• attributes=None. It is ignored when X is a tnet object, as it will inherit the attributes from X. When X is a list of matrices, you can use this to provide a list of length N containing the attribute of each node. If you do not wish to set an attribute for node i, put None in the list at place i.
You can access and edit eval_max, tol, store and weighted as class attributes.
The class has also the attribute convergente_on which is either eigenvector or eigenvalue. You can access it and edit it.
For instance:
myth.tol = 1e-5
myth.convergence_on = 'eigenvalue'
The class has the attribute lA which is the list of adjacency matrices. You can access it and set it safely.
Finally, the attribute avg_k returns the average (weighted) degree of the network, i.e., \frac{\sum_{t=1}^T\sum_{i,j}A_{t,ij}}{NT}
### compute method
This carries out the actual computation of the threshold.
x = th.compute(mu, vmin=1e-3, vmax=1, maxiter=50, root_finder='brentq', **kwargs)
• mu is the only compulsory argument. It can be either a single value (recovery probability) or a dictionary having a recovery probability for every attribute: {'attr 1': 0.1, 'attr 2': 0.3, 'default':0.6}. It must always have a 'default' value, which will be assigned to nodes with no attribute.
• vmin and vmax are the boundaries of the intervals in which to look for the threshold.
• maxiter is the maximum number of iterations of the root finding algorithm.
• root_finder can be either 'brentq' or 'bisect', referring to the functions in scipy.optimize. For further details see, for instance, scipy documentation.
• Other keyword arguments are directly sent to the root finding scipy function (e.g. xtol and rtol).
## threshold_util
This module contains two functions: DataFrame_to_lG and DataFrame_to_lA. They turn a pandas.DataFrame object into a list of networkx graphs or scipy.sparse CSR matrix. The former is a suitable input for threshold.tnet, the latter for threshold.threshold.
### DataFrame_to_lG
lG = thu.DataFrame_to_lG(df, directed=False, weight=None, source='source', target='target', time='time')
• df is a pandas.DataFrame.
• directed bool variable about (un)directedness.
• source name of the column of source nodes.
• target name of the column of target nodes.
• time name of the column with timestamps.
• weight can be None (unweighted network) or a string with the name of the column to be interpreted as weights.
It returns a list of networkx Graph or DiGraph objects.
### DataFrame_to_lA
Assumes node id's are integers from 0 to N-1, where N is the number of nodes.
lA = thu.DataFrame_to_lA(df, directed=False, source='source', target='target', time='time', weight='weight', dtype=np.float128, force_beg=None, force_end=None)
• df is a pandas.DataFrame.
• directed bool variable about (un)directedness.
• source name of the column of source nodes.
• target name of the column of target nodes.
• time name of the column with timestamps.
• weight can be None (unweighted network) or a string with the name of the column to be interpreted as weights.
• force_beg if not None, will discard all timesteps smaller than this.
• force_end if not None, will discard all timesteps larger than this. | 2017-03-01 20:55:14 | {"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": 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": 0.27434423565864563, "perplexity": 3820.376919464102}, "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-2017-09/segments/1487501174276.22/warc/CC-MAIN-20170219104614-00131-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/4429526/intuition-for-finding-a-group-g-such-that-g-cong-mathrmautg | Intuition for finding a group $G$ such that $G \cong \mathrm{Aut}(G)$
I'm trying to find a group such that the map $$G \to \mathrm{Aut}(G)$$ sending $$a$$ to the the conjugation map $$\phi_a (x) = axa^{-1}$$ is an isomorphism.
I know that $$G = S_3$$ works and I know how to prove it, but I don't understand how I would find this if I didn't know it to be true. I don't know if the key is to specify a group by its generators, because I know the proof for $$S_3$$ boils down to automorphisms preserving the order of elements and therefore being uniquely determine by the permutation of the transpositions.
Could someone give me some insight into how one would think to try, say, $$S_3$$? If there is another natural group (other than the trivial group, of course) I'd be very interested in seeing how someone might come up with one.
• You might be interested by this related question. Apr 17, 2022 at 7:46
There are two properties which jointly guarantee that $$G\to \operatorname{Aut}(G)$$ is an isomorphism:
• to get injectivity, $$G$$ should have a trivial center, as $$Z(G)$$ is exactly the kernel of the canonical map $$G\to \operatorname{Aut}(G)$$;
• to get surjectivity, $$G$$ should not have (non-trivial) outer automorphisms (this is basically the definition of an outer automorphism, it is an automorphism not in the image of this canonical map $$G\to \operatorname{Aut}(G)$$).
One can define the group of outer automorphisms $$\operatorname{Out}(G) = \operatorname{Aut}(G)/G$$ (so this is the cokernel of the map $$G\to \operatorname{Aut}(G)$$). Be careful that the name is slightly misleading: the set of outer automorphisms consists of all automorphism which are not inner (so not in the image of $$G\to \operatorname{Aut}(G)$$), so it is a subset of $$\operatorname{Aut}(G)$$ (and does not form a group), but the group of outer automorphisms is a quotient of $$\operatorname{Aut}(G)$$.
Then what you want is that $$Z(G)$$ and $$\operatorname{Out}(G)$$ are both trivial. Usually $$Z(G)$$ is easy to understand and compute, and for instance it is a very easy exercise to show that $$Z(S_n)$$ is trivial for all $$n$$ except $$n=2$$. On the other hand, $$\operatorname{Out}(G)$$ tends to be trickier to compute, and requires a finer understanding of $$G$$. For instance, it is a standard fact that $$\operatorname{Out}(S_n)$$ is trivial for all $$n$$ except $$n=6$$, but it is far less easy to prove, and the fact that there is an exception for $$n=6$$ (one of my favourite factoids about all of mathematics) should convince you that something tricky is going on.
So my point is that the crux of finding complete groups (groups such that $$G\to \operatorname{Aut}(G)$$ is an isomorphism) is to find groups with trivial outer automorphism group, and that just requires a detailed study of the group in question.
There are certain classes of groups that are guaranteed to be complete. For example, if $$G$$ is the automorphism group of a non-abelian simple group, then it is complete. An even deeper result is that if you start with a finite group $$G_0$$ such that $$Z(G_0)$$ is trivial, and define inductively $$G_{n+1}=\operatorname{Aut}(G_n)$$, then for $$n$$ large enough $$G_n$$ is complete. But that is difficult.
• But isn't $${\rm Out}(G)\cong {\rm Aut}(G)/{\rm Inn}(G)?$$ Apr 17, 2022 at 11:24
• Sure, that might be a clearer way of writing it. I don't think $\operatorname{Aut}(G)/G$ is truly ambiguous since there is a clear canonical map $G\to \operatorname{Aut}(G)$, but it is true that it could be confused to mean that $G$ is actually a subgroup of $\operatorname{Aut}(G)$. Apr 17, 2022 at 11:42 | 2023-03-29 09:30:09 | {"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": 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": 36, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9402406811714172, "perplexity": 86.52035267336298}, "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/1679296948965.80/warc/CC-MAIN-20230329085436-20230329115436-00264.warc.gz"} |
https://read.somethingorotherwhatever.com/entry/GdelforGoldilocksARigorousStreamlinedProofofavariantofGdelsFirstIncompletenessTheorem | # Gödel for Goldilocks: A Rigorous, Streamlined Proof of (a variant of) Gödel's First Incompleteness Theorem
• Published in 2014
In the collection
Most discussions of G\"odel's theorems fall into one of two types: either they emphasize perceived philosophical, cultural "meanings" of the theorems, and perhaps sketch some of the ideas of the proofs, usually relating G\"odel's proofs to riddles and paradoxes, but do not attempt to present rigorous, complete proofs; or they do present rigorous proofs, but in the traditional style of mathematical logic, with all of its heavy notation and difficult definitions, and technical issues which reflect G\"odel's original approach and broader logical issues. Many non-specialists are frustrated by these two extreme types of expositions and want a complete, rigorous proof that they can understand. Such an exposition is possible, because many people have realized that variants of G\"odel's first incompleteness theorem can be rigorously proved by a simpler middle approach, avoiding philosophical discussions and hand-waiving at one extreme; and also avoiding the heavy machinery of traditional mathematical logic, and many of the harder detail's of G\"odel's original proof, at the other extreme. This is the just-right Goldilocks approach. In this exposition we give a short, self-contained Goldilocks exposition of G\"odel's first theorem, aimed at a broad, undergraduate audience.
### BibTeX entry
@article{GdelforGoldilocksARigorousStreamlinedProofofavariantofGdelsFirstIncompletenessTheorem,
title = {G{\"{o}}del for Goldilocks: A Rigorous, Streamlined Proof of (a variant of) G{\"{o}}del's First Incompleteness Theorem},
abstract = {Most discussions of G\"odel's theorems fall into one of two types: either
they emphasize perceived philosophical, cultural "meanings" of the theorems,
and perhaps sketch some of the ideas of the proofs, usually relating G\"odel's
proofs to riddles and paradoxes, but do not attempt to present rigorous,
complete proofs; or they do present rigorous proofs, but in the traditional
style of mathematical logic, with all of its heavy notation and difficult
definitions, and technical issues which reflect G\"odel's original approach and
broader logical issues. Many non-specialists are frustrated by these two
extreme types of expositions and want a complete, rigorous proof that they can
understand. Such an exposition is possible, because many people have realized
that variants of G\"odel's first incompleteness theorem can be rigorously
proved by a simpler middle approach, avoiding philosophical discussions and
hand-waiving at one extreme; and also avoiding the heavy machinery of
traditional mathematical logic, and many of the harder detail's of G\"odel's
original proof, at the other extreme. This is the just-right Goldilocks
approach. In this exposition we give a short, self-contained Goldilocks
} | 2021-05-11 10:51:00 | {"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": 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": 0.6557254195213318, "perplexity": 2361.5417002214012}, "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-2021-21/segments/1620243991982.8/warc/CC-MAIN-20210511092245-20210511122245-00397.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Aromano.vittorio | # zbMATH — the first resource for mathematics
## Romano, Vittorio
Compute Distance To:
Author ID: romano.vittorio Published as: Romano, V.; Romano, Vittorio External Links: ORCID
Documents Indexed: 92 Publications since 1994, including 2 Books Reviewing Activity: 24 Reviews
all top 5
#### Co-Authors
10 single-authored 22 Mascali, Giovanni 10 Anile, Angelo Marcello 10 Blokhin, Aleksandr Mikhaĭlovich 6 Bushmanov, R. S. 6 Camiola, Vito Dario 5 Torrisi, Mariano 4 Alì, Giuseppe 4 Larosa, Salvatore 4 Sellier, Jean Michel 3 Junk, Michael 3 Majorana, Armando 3 Nastasi, Giovanni 2 Bonanno, Alfio 2 Bushmanova, A. S. 2 Coco, Marco 2 La Magna, Antonino 2 Liotta, Salvatore Fabio 2 Nicosia, Giuseppe 2 Rusakov, Alexandr 2 Torcasio, Rosa Claudia 2 Tracinà, Rita 2 Trakhinin, Yuri L. 2 Zwierz, Marcin 1 Beneduci, Roberto 1 Camiola, D. 1 Capasso, Vincenzo 1 Deretzis, I. 1 Luca, Liliana 1 Nicosia, Guiseppe 1 Nikiforakis, Nikolaos 1 Palagachev, Dian K. 1 Patanè, Andrea 1 Pavón, Diego 1 Rotundo, Nella 1 Rudometova, A. S. 1 Santoro, Andrea 1 Stracquadanio, Giovanni
all top 5
#### Serials
6 Continuum Mechanics and Thermodynamics 4 Journal of Computational Physics 4 Journal of Mathematical Physics 4 SIAM Journal on Applied Mathematics 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Mathematical and Computer Modelling 2 Journal of Mathematical Analysis and Applications 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Ricerche di Matematica 2 COMPEL 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Journal of Physics A: Mathematical and General 2 Annales de l’Institut Henri Poincaré. Physique Théorique 2 Vychislitel’nye Tekhnologii 2 Communications in Nonlinear Science and Numerical Simulation 2 Mathematics in Industry 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal of Engineering Science 1 Journal of Statistical Physics 1 Mathematical Methods in the Applied Sciences 1 Wave Motion 1 Meccanica 1 SIAM Journal on Numerical Analysis 1 Acta Applicandae Mathematicae 1 European Journal of Applied Mathematics 1 Journal of Global Optimization 1 Annals of Physics 1 Communications in Applied Analysis 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Journal of Physics A: Mathematical and Theoretical 1 Communications in Applied and Industrial Mathematics
all top 5
#### Fields
69 Statistical mechanics, structure of matter (82-XX) 39 Partial differential equations (35-XX) 32 Fluid mechanics (76-XX) 23 Optics, electromagnetic theory (78-XX) 16 Numerical analysis (65-XX) 7 Classical thermodynamics, heat transfer (80-XX) 4 Relativity and gravitational theory (83-XX) 3 Quantum theory (81-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of deformable solids (74-XX) 2 Astronomy and astrophysics (85-XX) 1 General and overarching topics; collections (00-XX) 1 Ordinary differential equations (34-XX) 1 Differential geometry (53-XX) 1 Operations research, mathematical programming (90-XX)
#### Citations contained in zbMATH Open
59 Publications have been cited 456 times in 157 Documents Cited by Year
Non parabolic band transport in semiconductors: closure of the moment equations. Zbl 1080.82584
Anile, Angelo Marcello; Romano, Vittorio
1999
Central schemes for balance laws of relaxation type. Zbl 0982.65093
Liotta, Salvatore Fabio; Romano, Vittorio; Russo, Giovanni
2000
Non-parabolic band transport in semiconductors: Closure of the production terms in the moment equations. Zbl 0962.82085
Romano, Vittorio
2000
Extended hydrodynamical model of carrier transport in semiconductors. Zbl 0966.35076
Anile, Angelo Marcello; Romano, Vittorio; Russo, Giovanni
2000
Non-parabolic band hydrodynamical model of silicon semiconductors and simulation of electron devices. Zbl 0981.35040
Romano, Vittorio
2001
2D numerical simulation of the MEP energy-transport model with a finite difference scheme. Zbl 1216.82035
Romano, V.
2007
Recent developments in hydrodynamical modeling of semiconductors. Zbl 1036.82027
Anile, A. M.; Mascali, G.; Romano, V.
2003
2D simulation of a silicon MESFET with a nonparabolic hydrodynamical model based on the maximum entropy principle. Zbl 0995.82525
Romano, Vittorio
2002
Hydrodynamical modeling of charge carrier transport in semiconductors. Zbl 1082.82010
Anile, Angelo Marcello; Romano, Vittorio
2000
Numerical solution for hydrodynamical models of semiconductors. Zbl 1012.82027
Romano, Vittorio; Russo, Giovanni
2000
Numerical simulation of a double-gate MOSFET with a subband model for semiconductors based on the maximum entropy principle. Zbl 1263.82061
Camiola, Vito Dario; Mascali, Giovanni; Romano, Vittorio
2012
A hydrodynamical model for holes in silicon semiconductors: the case of non-parabolic warped bands. Zbl 1211.82062
Mascali, Giovanni; Romano, Vittorio
2011
Exact maximum entropy closure of the hydrodynamical model for si semiconductors: the 8-moment case. Zbl 1197.82118
La Rosa, Salvatore; Mascali, Giovanni; Romano, Vittorio
2009
Electron-phonon hydrodynamical model for semiconductors. Zbl 1339.82018
Romano, V.; Zwierz, M.
2010
Linear asymptotic stability of the equilibrium state for the 2-D MEP hydrodynamical model of charge transport in semiconductors. Zbl 1105.35015
Blokhin, A. M.; Bushmanov, R. S.; Rudometova, A. S.; Romano, V.
2006
Application of weak equivalence transformations to a group analysis of a drift-diffusion model. Zbl 0947.35009
Romano, Vittorio; Torrisi, Mariano
1999
Hydrodynamical model of charge transport in GaAs based on the maximum entropy principle. Zbl 1029.82045
Mascali, Giovanni; Romano, Vittorio
2002
A non parabolic hydrodynamical subband model for semiconductors based on the maximum entropy principle. Zbl 1255.82064
Mascali, Giovanni; Romano, Vittorio
2012
DSMC method consistent with the Pauli exclusion principle and comparison with deterministic solutions for charge transport in graphene. Zbl 1349.82114
Romano, Vittorio; Majorana, Armando; Coco, Marco
2015
Hydrodynamical model for charge transport in graphene. Zbl 1310.82052
Camiola, V. D.; Romano, V.
2014
Nonlinear asymptotic stability of the equilibrium state for the MEP model of charge transport in semiconductors. Zbl 1109.35108
Blokhin, A. M.; Bushmanov, R. S.; Romano, V.
2006
Charge transport in graphene including thermal effects. Zbl 1371.82144
Mascali, Giovanni; Romano, Vittorio
2017
2d numerical simulations of an electron-phonon hydrodynamical model based on the maximum entropy principle. Zbl 1231.78043
Romano, Vittorio; Rusakov, Alexander
2010
Simulation of a double-gate MOSFET by a non-parabolic energy-transport subband model for semiconductors based on the maximum entropy principle. Zbl 1297.81176
Camiola, Vito Dario; Mascali, Giovanni; Romano, Vittorio
2013
A hydrodynamic model for covalent semiconductors with applications to GaN and SiC. Zbl 1254.82041
Alì, Giuseppe; Mascali, Giovanni; Romano, Vittorio; Torcasio, Rosa Claudia
2012
Simulation of Gunn oscillations with a non-parabolic hydrodynamical model based on the maximum entropy principle. Zbl 1071.78031
Mascali, Giovanni; Romano, Vittorio
2005
Asymptotic stability of the equilibrium state for the hydrodynamical model of charge transport in semiconductors based on the maximum entropy principle. Zbl 1211.82061
Blokhin, A. M.; Bushmanov, R. S.; Romano, V.
2004
Discretization of semiconductor device problems. II. Zbl 1207.78001
Anile, A. M.; Nikiforakis, N.; Romano, V.; Russo, G.
2005
Cross-validation of numerical schemes for extended hydrodynamical models of semiconductors. Zbl 1214.76012
Anile, Angelo Marcello; Junk, Michael; Romano, Vittorio; Russo, Giovanni
2000
Numerical simulation of a hydrodynamic subband model for semiconductors based on the maximum entropy principle. Zbl 1252.82113
Mascali, G.; Romano, V.
2012
Cross validation of discontinuous Galerkin method and Monte Carlo simulations of charge transport in graphene on substrate. Zbl 1374.82028
Coco, Marco; Majorana, Armando; Romano, Vittorio
2017
Maximum entropy moment system of the semiconductor Boltzmann equation using Kane’s dispersion relation. Zbl 1097.78005
Junk, Michael; Romano, Vittorio
2005
A hydrodynamical model for covalent semiconductors with a generalized energy dispersion relation. Zbl 1307.78006
Alì, Giuseppe; Mascali, Giovanni; Romano, Vittorio; Torcasio, Rosa Claudia
2014
Asymptotic waves for the hydrodynamical model of semiconductors. Zbl 0925.76048
Romano, Vittorio
1996
Central schemes for systems of balance laws. Zbl 0926.35081
Liotta, Salvatore Fabio; Romano, Vittorio; Russo, Giovanni
1999
Quantum corrections to the semiclassical hydrodynamical model of semiconductors based on the maximum entropy principle. Zbl 1153.81424
Romano, V.
2007
The maximum entropy principle hydrodynamical model for holes in silicon semiconductors: The case of the warped bands. Zbl 1143.82032
La Rosa, Salvatore; Romano, Vittorio
2008
Charge transport in low dimensional semiconductor structures. The maximum entropy approach. Zbl 1447.82002
Camiola, Vito Dario; Mascali, Giovanni; Romano, Vittorio
2020
Quantum corrected hydrodynamic models for charge transport in graphene. Zbl 1423.82024
Luca, Liliana; Romano, Vittorio
2019
Semiconductor device design using the BiMADS algorithm. Zbl 1302.78018
Stracquadanio, Giovanni; Romano, Vittorio; Nicosia, Giuseppe
2013
2DEG-3DEG charge transport model for MOSFET based on the maximum entropy principle. Zbl 1291.82132
Camiola, V. D.; Romano, V.
2013
Global existence for the system of the macroscopic balance equations of charge transport in semiconductors. Zbl 1063.35110
Blokhin, A. M.; Bushmanov, R. S.; Romano, V.
2005
Symmetry analysis and exact invariant solutions for a class of energy-transport models of semiconductors. Zbl 0994.82101
Romano, V.; Valenti, A.
2002
Improved mobility models for charge transport in graphene. Zbl 1426.82058
Nastasi, G.; Romano, V.
2019
Existence and uniqueness for a two-temperature energy-transport model for semiconductors. Zbl 1457.80004
Alì, G.; Romano, V.
2017
Stability of the equilibrium state for a hydrodynamical model of charge transport in semiconductors. Zbl 1072.82573
Blokhin, A. M.; Bushmanova, A. S.; Romano, V.
2001
Asymptotic stability of the equilibrium state for the macroscopic balance equations of charge transport in semiconductiors. Zbl 1032.35034
Blokhin, A. M.; Bushmanov, R. S.; Romano, Vittorio
2003
Exact invariant solutions for a class of energy-transport models of semiconductors in the two dimensional stationary case. Zbl 1064.35197
Romano, V.; Valenti, A.
2005
A full coupled drift-diffusion-Poisson simulation of a GFET. Zbl 1452.82036
Nastasi, Giovanni; Romano, Vittorio
2020
On group analysis of a class of energy-transport models of semiconductors in the two dimensional stationary case. Zbl 1065.35019
Romano, V.; Valenti, A.
2004
Symmetry analysis for the quantum drift-diffusion model of semiconductors. Zbl 1345.82021
Romano, V.; Torrisi, M.; Tracinà, R.
2006
A hydrodynamical model for holes in silicon semiconductors. Zbl 1358.82039
Mascali, Giovanni; Romano, Vittorio
2012
Jump conditions for a radiating relativistic gas. Zbl 0809.76097
Ali, G.; Romano, V.
1994
Some mathematical properties of radiating gas model obtained with a variable Eddington factor. Zbl 0866.76074
Blokhin, A. M.; Romano, V.; Trakhinin, Yu. L.
1996
Existence and uniqueness of asymptotic wave solutions for the hydrodynamical model of semiconductors. Zbl 0880.76003
Palagachev, D. K.; Romano, V.
1997
Maximum entropy principle in relativistic radiation hydrodynamics. Zbl 0884.76101
Mascali, Giovanni; Romano, Vittorio
1997
Gunn oscillations described by the MEP hydrodynamical model of semiconductors. Zbl 1135.82036
Mascali, G.; Romano, V.; Sellier, J. M.
2006
Approximate solutions to the quantum drift-diffusion model of semiconductors. Zbl 1121.82045
Romano, V.; Torrisi, M.; Tracinà, R.
2007
Mixed finite element numerical simulation of a 2D silicon MOSFET with the non-parabolic MEP energy-transport model. Zbl 1157.78307
Anile, A. M.; Marrocco, A.; Romano, V.; Sellier, J. M.
2006
Charge transport in low dimensional semiconductor structures. The maximum entropy approach. Zbl 1447.82002
Camiola, Vito Dario; Mascali, Giovanni; Romano, Vittorio
2020
A full coupled drift-diffusion-Poisson simulation of a GFET. Zbl 1452.82036
Nastasi, Giovanni; Romano, Vittorio
2020
Quantum corrected hydrodynamic models for charge transport in graphene. Zbl 1423.82024
Luca, Liliana; Romano, Vittorio
2019
Improved mobility models for charge transport in graphene. Zbl 1426.82058
Nastasi, G.; Romano, V.
2019
Charge transport in graphene including thermal effects. Zbl 1371.82144
Mascali, Giovanni; Romano, Vittorio
2017
Cross validation of discontinuous Galerkin method and Monte Carlo simulations of charge transport in graphene on substrate. Zbl 1374.82028
Coco, Marco; Majorana, Armando; Romano, Vittorio
2017
Existence and uniqueness for a two-temperature energy-transport model for semiconductors. Zbl 1457.80004
Alì, G.; Romano, V.
2017
DSMC method consistent with the Pauli exclusion principle and comparison with deterministic solutions for charge transport in graphene. Zbl 1349.82114
Romano, Vittorio; Majorana, Armando; Coco, Marco
2015
Hydrodynamical model for charge transport in graphene. Zbl 1310.82052
Camiola, V. D.; Romano, V.
2014
A hydrodynamical model for covalent semiconductors with a generalized energy dispersion relation. Zbl 1307.78006
Alì, Giuseppe; Mascali, Giovanni; Romano, Vittorio; Torcasio, Rosa Claudia
2014
Simulation of a double-gate MOSFET by a non-parabolic energy-transport subband model for semiconductors based on the maximum entropy principle. Zbl 1297.81176
Camiola, Vito Dario; Mascali, Giovanni; Romano, Vittorio
2013
Semiconductor device design using the BiMADS algorithm. Zbl 1302.78018
Stracquadanio, Giovanni; Romano, Vittorio; Nicosia, Giuseppe
2013
2DEG-3DEG charge transport model for MOSFET based on the maximum entropy principle. Zbl 1291.82132
Camiola, V. D.; Romano, V.
2013
Numerical simulation of a double-gate MOSFET with a subband model for semiconductors based on the maximum entropy principle. Zbl 1263.82061
Camiola, Vito Dario; Mascali, Giovanni; Romano, Vittorio
2012
A non parabolic hydrodynamical subband model for semiconductors based on the maximum entropy principle. Zbl 1255.82064
Mascali, Giovanni; Romano, Vittorio
2012
A hydrodynamic model for covalent semiconductors with applications to GaN and SiC. Zbl 1254.82041
Alì, Giuseppe; Mascali, Giovanni; Romano, Vittorio; Torcasio, Rosa Claudia
2012
Numerical simulation of a hydrodynamic subband model for semiconductors based on the maximum entropy principle. Zbl 1252.82113
Mascali, G.; Romano, V.
2012
A hydrodynamical model for holes in silicon semiconductors. Zbl 1358.82039
Mascali, Giovanni; Romano, Vittorio
2012
A hydrodynamical model for holes in silicon semiconductors: the case of non-parabolic warped bands. Zbl 1211.82062
Mascali, Giovanni; Romano, Vittorio
2011
Electron-phonon hydrodynamical model for semiconductors. Zbl 1339.82018
Romano, V.; Zwierz, M.
2010
2d numerical simulations of an electron-phonon hydrodynamical model based on the maximum entropy principle. Zbl 1231.78043
Romano, Vittorio; Rusakov, Alexander
2010
Exact maximum entropy closure of the hydrodynamical model for si semiconductors: the 8-moment case. Zbl 1197.82118
La Rosa, Salvatore; Mascali, Giovanni; Romano, Vittorio
2009
The maximum entropy principle hydrodynamical model for holes in silicon semiconductors: The case of the warped bands. Zbl 1143.82032
La Rosa, Salvatore; Romano, Vittorio
2008
2D numerical simulation of the MEP energy-transport model with a finite difference scheme. Zbl 1216.82035
Romano, V.
2007
Quantum corrections to the semiclassical hydrodynamical model of semiconductors based on the maximum entropy principle. Zbl 1153.81424
Romano, V.
2007
Approximate solutions to the quantum drift-diffusion model of semiconductors. Zbl 1121.82045
Romano, V.; Torrisi, M.; Tracinà, R.
2007
Linear asymptotic stability of the equilibrium state for the 2-D MEP hydrodynamical model of charge transport in semiconductors. Zbl 1105.35015
Blokhin, A. M.; Bushmanov, R. S.; Rudometova, A. S.; Romano, V.
2006
Nonlinear asymptotic stability of the equilibrium state for the MEP model of charge transport in semiconductors. Zbl 1109.35108
Blokhin, A. M.; Bushmanov, R. S.; Romano, V.
2006
Symmetry analysis for the quantum drift-diffusion model of semiconductors. Zbl 1345.82021
Romano, V.; Torrisi, M.; Tracinà, R.
2006
Gunn oscillations described by the MEP hydrodynamical model of semiconductors. Zbl 1135.82036
Mascali, G.; Romano, V.; Sellier, J. M.
2006
Mixed finite element numerical simulation of a 2D silicon MOSFET with the non-parabolic MEP energy-transport model. Zbl 1157.78307
Anile, A. M.; Marrocco, A.; Romano, V.; Sellier, J. M.
2006
Simulation of Gunn oscillations with a non-parabolic hydrodynamical model based on the maximum entropy principle. Zbl 1071.78031
Mascali, Giovanni; Romano, Vittorio
2005
Discretization of semiconductor device problems. II. Zbl 1207.78001
Anile, A. M.; Nikiforakis, N.; Romano, V.; Russo, G.
2005
Maximum entropy moment system of the semiconductor Boltzmann equation using Kane’s dispersion relation. Zbl 1097.78005
Junk, Michael; Romano, Vittorio
2005
Global existence for the system of the macroscopic balance equations of charge transport in semiconductors. Zbl 1063.35110
Blokhin, A. M.; Bushmanov, R. S.; Romano, V.
2005
Exact invariant solutions for a class of energy-transport models of semiconductors in the two dimensional stationary case. Zbl 1064.35197
Romano, V.; Valenti, A.
2005
Asymptotic stability of the equilibrium state for the hydrodynamical model of charge transport in semiconductors based on the maximum entropy principle. Zbl 1211.82061
Blokhin, A. M.; Bushmanov, R. S.; Romano, V.
2004
On group analysis of a class of energy-transport models of semiconductors in the two dimensional stationary case. Zbl 1065.35019
Romano, V.; Valenti, A.
2004
Recent developments in hydrodynamical modeling of semiconductors. Zbl 1036.82027
Anile, A. M.; Mascali, G.; Romano, V.
2003
Asymptotic stability of the equilibrium state for the macroscopic balance equations of charge transport in semiconductiors. Zbl 1032.35034
Blokhin, A. M.; Bushmanov, R. S.; Romano, Vittorio
2003
2D simulation of a silicon MESFET with a nonparabolic hydrodynamical model based on the maximum entropy principle. Zbl 0995.82525
Romano, Vittorio
2002
Hydrodynamical model of charge transport in GaAs based on the maximum entropy principle. Zbl 1029.82045
Mascali, Giovanni; Romano, Vittorio
2002
Symmetry analysis and exact invariant solutions for a class of energy-transport models of semiconductors. Zbl 0994.82101
Romano, V.; Valenti, A.
2002
Non-parabolic band hydrodynamical model of silicon semiconductors and simulation of electron devices. Zbl 0981.35040
Romano, Vittorio
2001
Stability of the equilibrium state for a hydrodynamical model of charge transport in semiconductors. Zbl 1072.82573
Blokhin, A. M.; Bushmanova, A. S.; Romano, V.
2001
Central schemes for balance laws of relaxation type. Zbl 0982.65093
Liotta, Salvatore Fabio; Romano, Vittorio; Russo, Giovanni
2000
Non-parabolic band transport in semiconductors: Closure of the production terms in the moment equations. Zbl 0962.82085
Romano, Vittorio
2000
Extended hydrodynamical model of carrier transport in semiconductors. Zbl 0966.35076
Anile, Angelo Marcello; Romano, Vittorio; Russo, Giovanni
2000
Hydrodynamical modeling of charge carrier transport in semiconductors. Zbl 1082.82010
Anile, Angelo Marcello; Romano, Vittorio
2000
Numerical solution for hydrodynamical models of semiconductors. Zbl 1012.82027
Romano, Vittorio; Russo, Giovanni
2000
Cross-validation of numerical schemes for extended hydrodynamical models of semiconductors. Zbl 1214.76012
Anile, Angelo Marcello; Junk, Michael; Romano, Vittorio; Russo, Giovanni
2000
Non parabolic band transport in semiconductors: closure of the moment equations. Zbl 1080.82584
Anile, Angelo Marcello; Romano, Vittorio
1999
Application of weak equivalence transformations to a group analysis of a drift-diffusion model. Zbl 0947.35009
Romano, Vittorio; Torrisi, Mariano
1999
Central schemes for systems of balance laws. Zbl 0926.35081
Liotta, Salvatore Fabio; Romano, Vittorio; Russo, Giovanni
1999
Existence and uniqueness of asymptotic wave solutions for the hydrodynamical model of semiconductors. Zbl 0880.76003
Palagachev, D. K.; Romano, V.
1997
Maximum entropy principle in relativistic radiation hydrodynamics. Zbl 0884.76101
Mascali, Giovanni; Romano, Vittorio
1997
Asymptotic waves for the hydrodynamical model of semiconductors. Zbl 0925.76048
Romano, Vittorio
1996
Some mathematical properties of radiating gas model obtained with a variable Eddington factor. Zbl 0866.76074
Blokhin, A. M.; Romano, V.; Trakhinin, Yu. L.
1996
Jump conditions for a radiating relativistic gas. Zbl 0809.76097
Ali, G.; Romano, V.
1994
all top 5
#### Cited by 195 Authors
31 Romano, Vittorio 15 Mascali, Giovanni 13 Blokhin, Aleksandr Mikhaĭlovich 8 Muscato, Orazio 7 Shu, Chi-Wang 6 Martínez Gamba, Irene 6 Majorana, Armando 5 Bushmanov, R. S. 5 Camiola, Vito Dario 5 di Stefano, Vincenza 5 Torrisi, Mariano 4 Alì, Giuseppe 4 Carrillo de la Plata, José Antonio 4 Nastasi, Giovanni 4 Rossani, Alberto 4 Ruggeri, Tommaso 4 Tkachev, Dmitry L. 4 Tracinà, Rita 3 Ballestra, Luca Vincenzo 3 Boscarino, Sebastiano 3 Cimmelli, Vito Antonio 3 Nishikawa, Hiroaki 3 Pareschi, Lorenzo 3 Qamar, Shamsul 3 Struchtrup, Henning 3 Xing, Yulong 2 Anile, Angelo Marcello 2 Banda, Mapundi Kondwani 2 Barletti, Luigi 2 Bessemoulin-Chatard, Marianne 2 Bîlă, Nicoleta Virginia 2 Chainais-Hillairet, Claire 2 Coco, Marco 2 Frank, Martin 2 Frosali, Giovanni 2 Jou, David 2 Jüngel, Ansgar 2 Junk, Michael 2 Klar, Axel 2 Kurganov, Alexander 2 Mathis, Hélène 2 Morandi, Omar 2 Mulet, Pep 2 Ren, Kui 2 Rogolino, Patrizia 2 Sacco, Riccardo 2 Seaïd, Mohammed 2 Sellitto, Antonio 2 Semisalov, Boris Vladimirovich 2 Taniguchi, Shigeru 2 Torcasio, Rosa Claudia 2 Vecil, Francesco 1 Ahmed, Munshoor 1 Alldredge, Graham W. 1 Ams, Alfons 1 Artale, Valeria 1 Ashraf, Waqas 1 Auzhani, Yerkanat 1 Bellomo, Nicola 1 Bertolazzi, Enrico 1 Bittner, Kai 1 Böhlke, Thomas 1 Bozhkov, Yuri Dimitrov 1 Brachtendorf, Hans Georg 1 Brull, Stephane 1 Bruzón, Maria Santos 1 Budday, Johannes 1 Bürger, Raimund 1 Cáceres, María-José 1 Calderón-Muñoz, Williams R. 1 Carlomagno, Isabella 1 Casas-Vázquez, José 1 Castiglione, Tina 1 Chen, Duan 1 Cheng, Yingda 1 Conforto, Fiammetta 1 Črnjarić-Žic, Nelida 1 Crouseilles, Nicolas 1 Degond, Pierre 1 Dehghan Takht Fooladi, Mehdi 1 di Domenico, Maria Carla 1 Dimas, Stylianos 1 Donat, Rosa 1 Dreyer, Wolfgang 1 Dubroca, Bruno 1 Dudyński, Marek 1 Eberl, Hermann J. 1 Falsaperla, Paolo 1 Freire, Igor Leite 1 Fryer, Michael J. 1 Gaebler, Harry J. 1 Gámiz, Francisco 1 Gandarias Núñez, Maria Luz 1 Godoy, Andrés 1 Goudon, Thierry 1 Guerrero, Francisco 1 Harmon, Michael 1 Hauck, Cory D. 1 He, Yuan 1 Hu, Jingwei ...and 95 more Authors
all top 5
#### Cited in 56 Serials
26 Journal of Computational Physics 8 Continuum Mechanics and Thermodynamics 6 ZAMP. Zeitschrift für angewandte Mathematik und Physik 6 COMPEL 6 Mathematical and Computer Modelling 6 Journal of Scientific Computing 5 Journal of Statistical Physics 5 Physica A 5 Applied Numerical Mathematics 4 Ricerche di Matematica 4 Communications in Applied and Industrial Mathematics 3 Journal of Mathematical Analysis and Applications 3 Journal of Mathematical Physics 3 Applied Mathematics and Computation 3 Acta Applicandae Mathematicae 3 European Journal of Applied Mathematics 3 SIAM Journal on Applied Mathematics 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 Communications in Nonlinear Science and Numerical Simulation 3 Nonlinear Analysis. Real World Applications 2 Computers and Fluids 2 Computer Methods in Applied Mechanics and Engineering 2 Wave Motion 2 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 2 Mathematics of Computation 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Quarterly of Applied Mathematics 2 Physica D 2 Journal of Nonlinear Mathematical Physics 2 Entropy 1 Acta Mechanica 1 Computers & Mathematics with Applications 1 Computer Physics Communications 1 International Journal of Engineering Science 1 International Journal of Heat and Mass Transfer 1 International Journal for Numerical Methods in Fluids 1 Mathematical Methods in the Applied Sciences 1 Mathematics and Computers in Simulation 1 Monatshefte für Mathematik 1 Numerische Mathematik 1 Chinese Annals of Mathematics. Series B 1 Acta Mathematicae Applicatae Sinica. English Series 1 Journal of Symbolic Computation 1 Numerical Methods for Partial Differential Equations 1 Applied Mathematics Letters 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Journal of Non-Equilibrium Thermodynamics 1 Boletim da Sociedade Brasileira de Matemática. Nova Série 1 SIAM Journal on Scientific Computing 1 Computational and Applied Mathematics 1 Mathematics and Mechanics of Solids 1 Abstract and Applied Analysis 1 Mathematical and Computer Modelling of Dynamical Systems 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Matematicheskoe Modelirovanie 1 Journal of Applied Mathematics
all top 5
#### Cited in 17 Fields
100 Statistical mechanics, structure of matter (82-XX) 72 Partial differential equations (35-XX) 49 Numerical analysis (65-XX) 49 Fluid mechanics (76-XX) 19 Optics, electromagnetic theory (78-XX) 18 Classical thermodynamics, heat transfer (80-XX) 7 Mechanics of deformable solids (74-XX) 7 Quantum theory (81-XX) 3 Ordinary differential equations (34-XX) 3 Biology and other natural sciences (92-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Measure and integration (28-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Computer science (68-XX) 1 Geophysics (86-XX) | 2021-09-17 02:02:11 | {"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": 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": 0.5958238244056702, "perplexity": 11319.101147123192}, "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/1631780053918.46/warc/CC-MAIN-20210916234514-20210917024514-00152.warc.gz"} |
https://www.rousette.org.uk/archives/using-texts-to-make-pandoc-painless/ | ### Using Texts to make Pandoc painless
software
#### Using Pandoc
Regular readers will know that my love for Pandoc is great and all-encompassing. I love the simplicity of writing in Markdown syntax and then being able to export to any final format I might wish to use, such as HTML, LaTeX, PDF or even Word. Pandoc gets more powerful all the time, and while there are still occasional glitches to a smooth workflow (depending upon what you want to do) it’s a pretty magical system. I use it a lot, but tend not to use it for short documents because the overhead of setting things up how you want and remembering what commands you need to use seems like a barrier when you just want to get on and write something.
Over the years I’ve tried various ways of simplifying Pandoc’s extensive and flexible — but consequently rather difficult to remember — commands. The problem is that I either forget to use my simplified system or I forget how to use it, and I’m back at the barrier to entry problem again. I may possibly have just found a much easier way to get the power of Pandoc with the ease of use of TextEdit: Texts.
#### Enter Texts
I only came across Texts by accident, but now I’m wondering why it isn’t better known. It’s a cross-platform1 application that allows you to enter text in a similar way to a simple word processor, but behind the scenes it saves the text in Markdown format. It’s rather like TaskPaper, if you’re familiar with that. The editor window presents you with your text styled according to the structure that you impose, so that bold and emphasised text is shown styled, but that is translated to standard Markdown format in the file. It goes much further than that, though, because you can view images and tables styled up inline too. No matter how many times I check the required syntax, I always find it difficult to remember how to produce a table, and it’s a tweaky, fussy task in plain text. Texts makes it completely trivial to produce a nice looking table, and shows you it styled.
##### Editing features
It’s a very sleek, keyboard-driven application, and all of the formatting tasks can be easily accomplished without your hands leaving the keyboard, including entering links and footnotes, and entering and navigating around lists and tables.
Here’s an image of the previous image in-line in the editor window2:
Some nice features:
• Lists auto-continue. For a bulleted list (unordered list in HTML), you create the first item by typing a - then space, and it automatically formats on screen as a bullet point.
• When you hit return, the next item is automatically entered.
• Sub-items are easy too:
• You hit tab to indent a bullet point
• And stay on that level until you hit shift-tab
• Like so!
Numbered lists (ordered lists in HTML) are equally easy:
1. You just enter 1. then space to start a list.
2. The styling on the page automatically increments the numbers for you.
1. And indented lists…
2. Are also possible using tab the same way as with unordered lists.
LaTeX equations are also easy to add, though they don’t get styled in the editor window. When you export the document to XeLaTeX/PDF, Word or HTML, the equations are formatted (via MathJax I think for HTML).
There are simple themes you can switch between to change the styling of the editor window. This styling is done via CSS files, so you can copy an alter a style if you like to tweak it to your liking.
You can display the word or character count, and it displays the count of the selected text if there is any. You can also use a keyboard shortcut to move paragraphs up and down which is handy, but otherwise the text editing commands are much the same as any other Mac OS X editor.
##### Exporting
Texts also makes exporting to different formats very easy. Under the bonnet3 it uses Pandoc to do the conversions, or you can can switch to other flavours of markup and conversion if you really want to. By choosing from a menu, you can export to HTML5, Word Document, RTF, EPUB, PDF or XeLaTeX. If you are repeatedly exporting one kind of format, you can repeat the last export with a keyboard shortcut.
Even better, you can provide templates for the export process. The documentation on this is very thin at the moment, so I’m not sure how Word Document templates would work, for example, but XeLaTeX (and hence PDF) templates work extremely well. I’ve set up a couple of templates for a simple article and a more complex report that style the text the way I want. You can download a PDF of this article styled from the source as a simple article and a complex report if you’re curious. I used the memoir document class and XeLaTeX font directives to get a nice, modern-looking document.
#### Conclusion
The ease of writing in Texts and the convenience of one-click export to a nice PDF format means that I can easily use Texts for writing short documents or reports — a situation in which I might have turned to Pages before. The benefit of using Texts is that I have the source document in a tiny, human-readable, future-proof text-only format, that can be kept under version control very easily.
Texts is still in fairly early development, so there are a few things missing that would be very convenient to have. For example in my ‘complex report’ template, I construct a title page with a title, author, affiliation and so on. Currently, I have that hard-coded in the template, but Pandoc allows you to add metadata (in recent versions, as a YAML block) that could be hooked into the template very conveniently. It’s also currently not possible to use Pandoc’s citation facility. However, some of these features appear to be planned, and I’m sure the capabilities will improve with time. As it is, Texts’ sheer convenience trumps any missing features. If you need more complex formatting, you can always export to XeLaTeX and tweak the final output there, so you are not locked in at all.
If you use Pandoc, I highly recommend taking a look at Texts.
Updated 07/12/2013: I’ve uploaded the templates used in the downloadable PDF files as Gists so that people can download them to try out and adapt. If you have a Github account and improve them, do fork and share your improvements!
1. Windows and Mac OS, anyway. There’s no Linux version at the moment.
2. We’re in danger of going a bit ‘Inception’, here.
3. ‘hood’ if you prefer. | 2019-01-20 09:10:25 | {"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": 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": 0.5237776041030884, "perplexity": 1524.8721267140997}, "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-2019-04/segments/1547583705091.62/warc/CC-MAIN-20190120082608-20190120104608-00006.warc.gz"} |
https://programmatic.solutions/yadrg9/effect-of-serial-repetition-on-soundness-of-a-pcp-and-what-is-special-with-1-2 | Theoretical Computer Science
cc.complexity-theory pcp
Updated Thu, 23 Jun 2022 19:02:39 GMT
# Effect of serial repetition on soundness of a PCP, and what is special with 1/2?
As far as I know, following operations convert a $PCP_{1,s}[O(\log n),O(1)]$ , to a $PCP_{1,s}[O(\log n),O(1)]$, with following $s$ :
• By constant number of applications of serial repetition: can get every constant s>=1/2;
• By constant number of applications of parallel repetition: can get every constant s>0;
• By $\theta(\log n)$ number of applications of Dinurs gap amplification transformation: can get some constant $s\geq1/2$; (see Gap Amplification Fails Below 1/2)
My questions:
1. Could you please correct me if I have made any mistakes?
2. What is special with in serial repetition or Dinurs transformation? why not another constant, like 1/3 or else?
3. Are such a results true for PCPs with imperfect completeness?
remark: with $PCP_{c,s}$, I mean PCP with completeness c and soundness error s.
## Solution
Sequential repetition can give you any constant soundness error larger than 0, not just soundness error $\geq 1/2$. Dinur's approach gives you a constant soundness error which is not only at least half, but, in fact, extremely close to 1, maybe 0.99999. The note of Andrej Bogdanov that you linked to shows that getting a soundness error smaller than half inherently won't work using Dinur's approach. The reason is specific to this approach, and is explained well in the note.
The soundness amplification results work for imperfect completeness as well. It's pretty straightforward to convince yourself of that in the case of sequential/parallel repetition. Dinur's approach can also be adapted to imperfect completeness.
Remark: Dinur's approach, just like the other two approaches, requires a number of iterations/repetitions that depends on the soundness you start with and the soundness you want to get. In her case it's $\Theta(\log(\frac{1}{1-s}))$ iterations to get to constant soundness. Irit starts with $s\approx 1-\frac{1}{n}$, and that's why she needs $\Theta(\log n)$ iterations. | 2023-03-23 20:32:25 | {"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": 0.7175946235656738, "perplexity": 1476.9936279745114}, "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/1679296945183.40/warc/CC-MAIN-20230323194025-20230323224025-00439.warc.gz"} |
https://brokenco.de/2020/10/22/smalltalk-inspiring-otto.html | ## Taking inspiration from Smalltalk for Otto steps
I have recently been spending more time thinking about how Otto should handle “steps” in a CI/CD pipeline. As I mentioned in my previous post on the step libraries concept, one of the big unanswered questions with the prototype has been managing flow-control of the pipeline from a step. To recap, a “step” is currently being defined as an artifact (.tar.gz) which self-describes its parameters, an entrypoint, and contains all the code/assets necessary to execute the step. The execution flow is fairly linear in this concept: an agent iterates through a sequence of steps, executing each along the way, end. In order for a step to change the state of the pipeline, this direction of flow control must be reversed. Allowing steps to communicate changes to the agent which spawned them requires a control socket.
The agent control socket will allow steps to send a fixed number of message types back to the agent during their execution. My current thinking is that the control socket should speak Nanomsg, which puts a little bit more system level requirements on the steps to be able to communicate with that protocol. My first thought was just lines of JSON encoded over the wire, but there are a number of practical problems with trying to send JSON over a unix socket, for example.
Update 2020-10-30: I have since decided to shy away from Nanomsg for the control socket and instead have opted for a small HTTP server listening on a unix socket. I chose this approach to make the debugging and client interactions much easier, even a totally bash-based shell step would be able to interact with it!
For the first implementation, I am planning to have a single long-lived socket for the duration of a pipeline’s execution by the agent. By adding the ipc field to the invocation file (below), I should have the flexibility to allow an agent to create a single IPC socket for each step to avoid any accidental overlap.
---
configuration:
ipc: 'ipc:///tmp/agent-5171.ipc'
parameters:
script: 'ls -lah'
The types of messages that come to mind are:
• Terminate the pipeline
• Change the pipeline’s running status (e.g. unstable)
• Capture a variable
The last item really struck me as necessary but I have been struggling with it quite a bit. In a declarative Jenkinsfile there is no provision for setting variables. It wouldn’t otherwise be very declarative! This restriction leads to some confusing hacks in real-world pipelines. The most common hack is to use the script {} block as an escape hatch, such as:
stage('Build') {
steps {
sh 'make'
script {
def output = readYaml file: 'output.yml'
sh "./deploy.sh \${output.stage}"
}
}
}
There are numerous legitimate reasons to capture and utilize variables inside of a CI/CD pipeline. I want to support variables in some fashion without building a full-on interpreter or sacrificing clarity in the pipeline modeling language.
As I wrestled with the concept, I noticed that my pseudo-code I was writing for how variables might be used looked familiar:
prompt msg: 'What is the best color for a bike shed?', into: 'color'
To me, this looks a lot like Smalltalk. Mmmm Smalltalk. If you have some spare time, and haven’t yet experienced Smalltalk, you should go download Pharo and explore! It’s a wonderful language and development environment, and well-worth experimenting with in your career.
Anyways, back to Otto.
The syntax above would be the prompt step saving some user-provided string (hand-waves right now on how that would manifest in a GUI) and storing it in the color variable.
With variables, storing is one part of the problem, but using is the other much more interesting part. I knew I didn’t want if color == 'red' { } type blocks littering the code, lest a user think that this pipeline language is a programming language for them to build application in! (This is a very real problem with Scripted Jenkins Pipelines).
A related problem I had set aside the day prior was how to handle “block-scoped steps”, such as the following in Jenkins:
stage('Build') {
steps {
sh 'make'
dir('deploy') {
echo 'Deploying from the deploy/ directory'
sh './shipit.sh'
}
}
}
All steps executed within the dir block are executed with a current working directory of deploy/.
Variable use and block-scoped steps both led me to a very Smalltalk syntax, which honestly has me quite excited to explore further! In Smalltalk there is no control structures in the traditional sense. No if, no for, etc. Instead one can send the ifTrue/ifFalse message to a Boolean:
color = 'red'
ifTrue: [
"Great choice!"
]
ifFalse: [
"Why did you chose wrong?!"
]
Fully embracing this Smalltalk-inspired concept would also be convenient to implement. Anything that isn’t a defined step can be looked at like a variable, using an approach similar to #method_missing in Ruby (which is actually just Smalltalk striking again! It’s called the doesNotUnderstand message in Smalltalk).
Exploring what this would look like in a more concrete pipeline snippet:
sh 'ls -lah'
prompt msg: 'Which file should I dump?', into: 'filename'
then: [
echo 'Stop trying to pwn me!'
],
else: [
# Not sure on this yet, I _think_ I want to avoid raw string interpolation syntax
format pattern: 'cat {}', with: [filename], into: 'dumpcmd'
sh script: dumpcmd
]
dir 'deploy' [
echo 'Deploying from the deploy/ directory'
sh './shipit.sh'
]
# Intentionally drop the filename variable, which would go out of scope
# at the end of the stage anyways
drop 'filename'
A couple notes on the above pseudo-code:
• I’m not yet sold on the syntax. The benefit of this approach rather than copying Smalltalk directly is that this syntax will make it easier support more robust string operations in the future. The other benefit of this syntax is that it makes everything behave step-like, insofar as a stringvariable internal/hidden step could use the parameters, including the two blocks, and just execute the block scoped steps like any other step.
• The block syntax is intentionally different from the directive syntax (to use Jenkins terminology) of curly braces I think will help make the code more readable.
• I don’t want to actually implement a full Smalltalk interpreter here, but I am liking that the syntax does keep things (subjectively) simple.
In order to implement block-scope steps, I am planning to refactor some of the step execution code into an agent crate which will allow steps to re-use the logic for executing steps. From a data structure standpoint the invocation file for the dir in the example might look like:
---
configuration:
ipc: 'ipc:///tmp/foo.ipc'
parameters:
directory: 'deploy'
block:
- symbol: echo
parameters:
msg: 'Deploying from the deploy/ directory'
- symbol: sh
parameters:
script: './shipit.sh'
At runtime the process tree on the agent machine would look something like:
.
└── agent
└── dir
└── echo
Despite the state of these ideas right now I haven’t actually implemented them! I typically like to sketch out syntax and run through use-cases before I go running into Rust code.
Part of why I am sharing these early thoughts is because I want to make sure my love of Smalltalk is not blinding me to usability issues with this approach. I think this pattern will allow some non-declarative functionality in the pipeline without requiring an actual interpreted language to be used, but these thoughts are still fresh. If you’ve got some thoughts on what could be improved, or pitfalls to be aware of, feel free to join #otto on Freenode, or email me (about)! | 2021-03-08 23:01:12 | {"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": 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": 0.33684858679771423, "perplexity": 2942.1174752456272}, "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-2021-10/segments/1614178385529.97/warc/CC-MAIN-20210308205020-20210308235020-00232.warc.gz"} |
https://socratic.org/questions/if-you-mixed-80-tons-of-sand-12-tons-of-rock-and-4-0-tons-to-make-concrete-what- | # If you mixed 80 tons of sand, 12 tons of rock, and 4.0 tons of cement to make concrete, what would the percent by weight of sand be?
Aug 29, 2016
The percent by mass would be 83 %.
#### Explanation:
The mass percent of a component in a mixture is given by the formula
color(blue)(|bar(ul(color(white)(a/a) "Mass Percent" = "Mass of component"/"Mass of mixture" × 100 % color(white)(a/a)|)))" "
$\text{Mass of sand = 80 T}$
$\text{Mass of mixture" = "mass of sand + mass of rock + mass of cement" = "80 T + 12 T + 4 T" = "96 T}$
"Mass percent of sand" = ( 80 color(red)(cancel(color(black)("T"))))/(96 color(red)(cancel(color(black)("T")))) × 100 % = 83 % | 2020-01-26 17:46:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 4, "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": 0.538571834564209, "perplexity": 4737.275157574265}, "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/1579251690095.81/warc/CC-MAIN-20200126165718-20200126195718-00004.warc.gz"} |
https://www.coursehero.com/sg/college-algebra/functions-and-graphs/ | # Functions and Graphs
## Overview
### Description
A function is a relationship between two sets of numbers: the domain and range. Each number in the domain maps to a unique value in the range. Functions may be represented in different forms, including tables, graphs, and equations. The graph of a function can be used to find information about the function, such as the domain, range, maximum values, and minimum values. Graphs of functions may be transformed by translations, stretches, compressions, and reflections.
### At A Glance
• A function is a relation between two sets called the domain and range, in which each element of the domain corresponds to exactly one element of the range. The relationship can be represented by a mapping diagram, an algebraic rule, or a graph.
• The domain and range of a function are the sets of values that define a function. The domain is all possible inputs to the function. The range is all possible outputs from the function.
• A function can be evaluated for a specific element in the domain by finding the corresponding element of the range.
• Functions can be added, subtracted, multiplied, and divided.
• A graph of a function is a visual representation of the function. An algebraic rule can be used to produce the graph of a function.
• The vertical line test uses vertical lines to determine whether a relation is a function.
• A piecewise function consists of separate pieces of the same function. Each piece behaves differently based on the rules of their defined intervals.
• Functions can be identified as even, odd, or neither. An even function is a line of symmetry about the $y$-axis. An odd function has rotational symmetry about the origin.
• Determining whether a graph is increasing, decreasing, or constant depends on how the $x$- and $y$-values increase, decrease, or remain the same.
• A function's maxima and minima are determined by the lowest and highest points at specific intervals, called local minimum and local maximum, as well as the function's highest point, called the global maximum, and its lowest point, called the global minimum.
• The most basic function from a family of functions is called a parent function. Related functions can be graphed by modifying the graph of the parent function.
• The graph of a function can be translated vertically or horizontally by performing addition or subtraction within the function rule.
• The graph of a function can be stretched or compressed vertically or horizontally by performing multiplication within the function rule by a positive constant.
• The graph of a function can be reflected across the $x$- or $y$-axis by performing multiplication within the function rule by –1.
• The graph of a function can be transformed by using a combination of translations, stretches, compressions, and reflections. | 2018-11-21 18:20:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "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": 0.6169383525848389, "perplexity": 224.87188685871155}, "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/1542039749562.99/warc/CC-MAIN-20181121173523-20181121195523-00554.warc.gz"} |
https://scigraph.springernature.com/person.014277615521.05 | # A S Biselli
Ontology type: schema:Person
NAME
A S
SURNAME
Biselli
### Publications in SciGraph latest 50 shown
• 2013-01 Deep exclusive π+ electroproduction off the proton at CLAS in THE EUROPEAN PHYSICAL JOURNAL A
• 2012-11 Ratios of dijet production cross sections as a function of the absolute difference in rapidity between jets in proton–proton collisions at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt{s} = 7\ \mathrm{TeV}$\end{document} in THE EUROPEAN PHYSICAL JOURNAL C
• 2012-09 Measurement of the underlying event in the Drell–Yan process in proton–proton collisions at in THE EUROPEAN PHYSICAL JOURNAL C
• 2012-06 Measurement of the cross section for production of decaying to muons in pp collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2012-06 Measurement of the inclusive production cross sections for forward jets and for dijet events with one forward and one central jet in pp collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2012-06 Measurement of the Z/γ* + b-jet cross section in pp collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2012-05 Search for quark compositeness in dijet angular distributions from pp collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2012-05 Centrality dependence of dihadron correlations and azimuthal anisotropy harmonics in PbPb collisions at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt{s_{NN}}= 2.76\ \mbox{TeV}$\end{document} in THE EUROPEAN PHYSICAL JOURNAL C
• 2012-05 Suppression of non-prompt J/ψ, prompt J/ψ, and (1S) in PbPb collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2012-04 Search for microscopic black holes in pp collisions at in JOURNAL OF HIGH ENERGY PHYSICS
• 2012-04 Search for a Higgs boson in the decay channel H → ZZ(*) → qℓ−ℓ+ in pp collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2012-04 Inclusive b-jet production in pp collisions at in JOURNAL OF HIGH ENERGY PHYSICS
• 2012-03 Search for the standard model Higgs boson in the H → ZZ → 2ℓ2ν channel in pp collisions at in JOURNAL OF HIGH ENERGY PHYSICS
• 2012-03 Study of high-pT charged particle suppression in PbPb compared to pp collisions at in THE EUROPEAN PHYSICAL JOURNAL C
• 2012-03 Search for the standard model Higgs boson in the H → ZZ → ℓ+ℓ−τ+τ− decay channel in pp collisions at in JOURNAL OF HIGH ENERGY PHYSICS
• 2012-02 J/ψ and ψ(2S) production in pp collisions at in JOURNAL OF HIGH ENERGY PHYSICS
• 2012-01 Measurement of the production cross section for pairs of isolated photons in pp collisions at in JOURNAL OF HIGH ENERGY PHYSICS
• 2012-01 Exclusive γγ → μ+μ− production in proton-proton collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2012-01 Jet production rates in association with W and Z bosons in pp collisions at in JOURNAL OF HIGH ENERGY PHYSICS
• 2012-01 Forward energy flow, central charged-particle multiplicities, and pseudorapidity gaps in W and Z boson events from pp collisions at TeV in THE EUROPEAN PHYSICAL JOURNAL C
• 2011-11 Measurement of energy flow at large pseudorapidities in pp collisions at and 7 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-10 Measurement of the inclusive W and Z production cross sections in pp collisions at TeV with the CMS experiment in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-10 Measurement of the Drell-Yan cross section in pp collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-09 Measurement of the underlying event activity at the LHC with TeV and comparison with TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-09 Measurement of the production cross section in pp collisions at TeV using the kinematic properties of events with leptons and jets in THE EUROPEAN PHYSICAL JOURNAL C
• 2011-08 Charged particle transverse momentum spectra in pp collisions at and 7 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-08 Measurement of the inclusive Z cross section via decays to tau pairs in pp collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-08 Search for same-sign top-quark pair production at TeV and limits on flavour changing neutral currents in the top sector in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-08 Search for new physics with jets and missing transverse momentum in pp collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-08 Dependence on pseudorapidity and on centrality of charged hadron production in PbPb collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-08 Search for supersymmetry in pp collisions at TeV in events with a single lepton, jets, and missing transverse momentum in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-07 Search for supersymmetry in events with b jets and missing transverse momentum at the LHC in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-07 Long-range and short-range dihadron angular correlations in central PbPb collisions at = 2.76 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-07 Measurement of the production cross section and the top quark mass in the dilepton channel in pp collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-07 Search for light resonances decaying into pairs of muons as a signal of new physics in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-06 Search for supersymmetry in events with a lepton, a photon, and large missing transverse energy in pp collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-06 Search for physics beyond the standard model in opposite-sign dilepton events in pp collisions at in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-06 Search for new physics with same-sign isolated dilepton events with jets and missing transverse energy at the LHC in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-05 Search for large extra dimensions in the diphoton final state at the Large Hadron Collider in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-05 Measurement of Bose-Einstein correlations in pp collisions at and 7 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-05 Search for resonances in the dilepton mass distribution in pp collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-05 Strange particle production in pp collisions at and 7 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-04 Measurement of the lepton charge asymmetry in inclusive W production in pp collisions at in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-03 Inclusive b-hadron production cross section with muons in pp collisions at in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-03 Search for heavy stable charged particles in pp collisions at in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-03 Prompt and non-prompt J/ψ production in pp collisions at TeV in THE EUROPEAN PHYSICAL JOURNAL C
• 2011-03 Measurement of angular correlations based on secondary vertex reconstruction at in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-01 Measurements of inclusive W and Z cross sections in pp collisions at TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2011-01 Charged particle multiplicities in pp interactions at , 2.36, and 7 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2010-12 CMS tracking performance results from early LHC operation in THE EUROPEAN PHYSICAL JOURNAL C
### Identifiers
JSON-LD is the canonical representation for SciGraph data.
TIP: You can open this SciGraph record using an external JSON-LD service:
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HOW TO GET THIS DATA PROGRAMMATICALLY:
JSON-LD is a popular format for linked data which is fully compatible with JSON.
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https://www.nature.com/articles/s41598-019-48818-6?error=cookies_not_supported&code=d3cd7670-09de-4fe5-9a46-ac3d45e3fc56 | # Endangered Atlantic Sturgeon in the New York Wind Energy Area: implications of future development in an offshore wind energy site
## Abstract
Imminent development of offshore wind farms on the outer continental shelf of the United States has led to significant concerns for marine wildlife. The scarcity of empirical data regarding fish species that may utilize development sites, further compounded by the novelty of the technology and inherent difficulty of conducting offshore research, make identification and assessment of potential stressors to species of concern problematic. However, there is broad potential to mitigate putatively negative impacts to seasonal migrants during the exploration and construction phases. The goal of this study was to establish baseline information on endangered Atlantic Sturgeon in the New York Wind Energy Area (NY WEA), a future offshore development site. Passive acoustic transceivers equipped with acoustic release mechanisms were used to monitor the movements of tagged fish in the NY WEA from November 2016 through February 2018 and resulted in detections of 181 unique individuals throughout the site. Detections were highly seasonal and peaked from November through January. Conversely, fish were relatively uncommon or entirely absent during the summer months (July–September). Generalized additive models indicated that predictable transitions between coastal and offshore habitat were associated with long-term environmental cues and localized estuarine conditions, specifically the interaction between photoperiod and river temperature. These insights into the ecology of marine-resident Atlantic Sturgeon are crucial for both defining monitoring parameters and guiding threat assessments in offshore waters and represent an important initial step towards quantitatively evaluating Atlantic Sturgeon at a scale relevant to future development.
## Introduction
Offshore wind endeavors are increasingly being regarded as readily-available sources of renewable energy1,2,3,4,5. Favorable domestic policy, coupled with the rapid development and maturation of overseas wind energy markets during the last two decades, has created impetus for the exploitation of offshore wind energy resources in the US6,7,8,9. The majority of near-term activities are concentrated in the Northeast and Mid-Atlantic regions of the US where a number of projects in federal waters of the Outer Continental Shelf (OCS) have been proposed or are in the planning stages, dependent on clean energy goals and initiatives of individual states.
Imminent development of the OCS has led to concerns about the potential for offshore wind farms to negatively impact marine ecosystems and fauna10,11,12,13. The novelty of the technology and the inherent difficulty of conducting offshore research make identification and assessment of potential stressors to marine wildlife problematic12,14. Impacts of operational offshore wind farms—both positive and negative—are often locally influenced and contingent on specific site, species’ spatial and temporal distribution, and management objectives; however, there is broad potential to mitigate negative impacts during the exploration and construction phases through spatial and temporal considerations, particularly for migratory species that may only utilize a development site on a seasonal basis15,16,17.
Studies regarding the impacts of offshore wind development have largely focused on marine mammals and seabirds18,19,20,21 and there is a relative scarcity of information regarding marine fish species22,23,24,25. The lack of empirical data, particularly for commercially important and federally protected marine fish species, underscores the need for targeted research to better quantify the likely effects of offshore wind energy development14,16,26. Baseline data collection and modeling are critical for future decision making and regulation in wind energy areas and are especially important when designing impact assessments for species of concern with limited or no existing information on offshore distribution or abundance16.
The federally protected Atlantic Sturgeon (Acipenser oxyrinchus oxyrinchus) is a species of concern that may occupy marine habitat allocated for future offshore wind development. Atlantic Sturgeon are an anadromous, long-lived species with a broad distribution along the Atlantic Coast of the US. Atlantic Sturgeon are highly migratory and exhibit a complex life-history that is dependent on access to both freshwater and marine environments, contingent on life-stage. Although adults undertake obligatory migrations into natal river systems for spawning purposes, the majority of the late-juvenile and adult life-stages are spent in coastal marine waters27. Delayed sexual maturity and the subsequent increase in reproductive output that occurs at later ages indicate that a focus on the reduction of mortality in the marine resident life-stages of Atlantic Sturgeon is necessary to restore depleted populations28,29,30. Despite this, basic knowledge of Atlantic Sturgeon in marine waters is limited and, consequently, the identity and magnitude of current and emerging threats are often difficult to assess.
In the New York Bight (NYB), limited scientific and commercial fisheries data suggest that Atlantic Sturgeon spend significant time in near-coastal marine waters31,32,33,34,35,36. Documented movements and aggregation areas of Atlantic Sturgeon in the NYB are concentrated along the coasts of New York and New Jersey and have been observed within 13-km of the shoreline33. Commercial fisheries bycatch of Atlantic Sturgeon has been observed in offshore areas that are beyond recognized aggregation sites34,37. The Hudson River stock makes up a large part of the coastal bycatch of Atlantic Sturgeon in the NYB (42.2–46.3%38); however, the mixing of coast-wide genetic stocks that occurs in marine waters emphasizes the potential for emerging, localized threats (i.e., offshore wind farm development) to affect multiple stocks39,40.
The New York Wind Energy Area (NY WEA; Equinor, Lease OCS-A 0512), located between Long Island and the coast of New Jersey, is an offshore wind-lease area in the exploration and site assessment phase of development that will ostensibly host active construction in the near-future; as such, the area provides a unique opportunity to study the spatial and temporal trends of Atlantic Sturgeon in a future offshore wind energy site. Because effective management of Atlantic Sturgeon requires an understanding of marine movements and habitat use, the identification of the temporal and spatial trends of Atlantic Sturgeon in the NY WEA will provide important baseline information regarding habitat use and environmental preferences in offshore marine waters. These data are critical to informing management decisions in the NY WEA and are necessary to inform required statutory consultations and impact assessments under the Endangered Species Act and the Outer Continental Shelf Lands Act41,42. Consequently, the goal of this study was to establish threshold information on endangered Atlantic Sturgeon in a future offshore wind energy site, with the specific objectives of identifying: (1) spatiotemporal trends in offshore occurrence; (2) residency in the NY WEA; and (3) environmental predictors of offshore movement.
## Methods
### Study site
The NY WEA encompasses approximately 79,350 acres of offshore euhaline habitat in the NYB region of the western Atlantic Ocean, east of the Hudson Shelf Valley (Fig. 1). Located in federal waters off the coast of New York and New Jersey, the site extends 22–48 km (11.5–24.0 nm) southeast of Long Island, New York, and forms an expanding wedge positioned between the Ambrose to Nantucket (eastbound) and Hudson Canyon to Ambrose (northwest-bound) traffic lanes. The Cholera Bank feature, located adjacent to the westernmost end of the NY WEA, was removed from the original lease area43. Water depths in the NY WEA range from 23 to 41 m and generally increase away from shore in a southeasterly direction44. The bottom habitat is characterized as relatively flat and primarily composed of sandy sediments, although isolated patches of gravelly, muddy sand exist44,45. Seasonal fluctuations are strong in the study area and bottom temperatures range from 2 to 22 °C. Thermal stratification between bottom and surface waters generally occurs from April to August, with turnover during the fall months44.
### Fish sampling
All methods for the capture and handling of Atlantic Sturgeon in this study were performed in accordance with relevant guidelines and regulations and were authorized by the National Marine Fisheries Service (NMFS; Endangered Species Permits 16422 and 20351), New York State Department of Environmental Conservation (Endangered/Threatened Species Scientific License 336), and Stony Brook University’s (SBU) Institutional Animal Care and Use Committee (IRB-1022451–4).
Marine resident Atlantic Sturgeon [i.e., juvenile (500–1,000 mm fork length [FL]), sub-adult (1,000–1,300 mm FL), and adult (>1,300 mm FL) life-stages, based on NMFS permitting definitions] were opportunistically sampled in May 2016–2018 and October 2017 during targeted research tows aboard the RV Seawolf. Tows occurred peripheral to the study site and targeted known marine aggregations located off the Rockaway Peninsula, New York; sampling relied on previously described trawl gear33,34. Tows occurred in relatively shallow waters (8–20 m) at speeds of 3.0–3.5 knots for short durations (5–15 min) in order to maximize capture efficiency while minimizing the stress placed on captured fish.
Atlantic Sturgeon were immediately sorted from the catch and transferred to an onboard live-well where they were allowed to recover. All fish were then examined for internal and external tags. If none was found, a passive integrated transponder tag was inserted into the body musculature beneath the fourth dorsal scute and an external dart tag was inserted near the dorsal fin base. Measurements of total length, FL, and weight were recorded. Age-at-capture was estimated using the von Bertalanffy growth function46 and parameter estimates for Atlantic Sturgeon from the NYB distinct population segment (L = 278.87, K = 0.057, t0 = −1.2747). A uniquely-coded VEMCO (Halifax, Nova Scotia) acoustic transmitter (V-16 6 H; 69 kHz; tag delay 70–150 s; estimated battery life = 3,650 d) was then surgically implanted into each individual fish48,49. Following surgeries, fish were returned to the live-well and monitored for 5–10 min until they had fully recovered before being released near their original capture site.
### Passive acoustic telemetry
In November 2016, a stationary array consisting of 24 acoustic-release transceivers (VEMCO VR2AR) with omnidirectional hydrophones was deployed throughout the NY WEA to monitor movements of acoustically tagged fish (Fig. 1). Submerged transceivers were attached to anchored buoys and deployed so that they were suspended approximately 2 m from the seabed. Transceivers were placed in a grid pattern with nearest-adjacent transceiver stations located less than 4 km apart [mean (range) = 3.43 (2.87–3.94) km]. Preliminary range testing at transceivers was accomplished using a transponding hydrophone (VEMCO VR100) and revealed an average maximum detection radius of approximately 600 m (range = 200–1,000 m), depending on sea state. Previous studies utilizing acoustic receiver arrays in coastal waters have assumed a 600 m detection radius based on high detection rates of tags at similar ranges (e.g., ~65% at 600 m and a maximum range of 1,400 m50). Although the western-most transceiver was not directly positioned in the NY WEA, the assumed detection radius of 600 m overlapped with the study site and was therefore included in analyses.
An onboard tracking receiver and transponding hydrophone permitted surface communication with individual transceivers; acoustic-release and recovery of transceivers was facilitated through remote detachment of the transceiver from a sacrificial anchor during download and maintenance. Transceivers with acoustic release mechanisms allowed for deeper and longer deployments in offshore marine waters without the need for diver retrieval. Transceiver array download and maintenance cruises occurred in August 2017 and February 2018. The transceiver array operated throughout the entire course of the study (November 10, 2016–February 5, 2018) with the exception of a single station which was not recovered during the final download cruise; data for this station were unavailable for the period of August 4, 2017–February 5, 2018 (Fig. 1).
Telemetry data were carefully reviewed to identify and remove any spurious detections that were obvious based on the spatial and temporal chronology of individual fish51. Data management and analysis were primarily performed in R52. Additional detections of Atlantic Sturgeon that were tagged by SBU researchers during previous sampling efforts were included in analyses to increase the robustness of the study (~380 previously tagged Atlantic Sturgeon assumed at-large in fall 201653).
### Environmental data
Potential environmental predictors were compiled from a variety of sources and matched to daily unique counts of Atlantic Sturgeon detections in the NY WEA. Environmental variables were selected based on putative biological significance to Atlantic Sturgeon as reported in previous studies as well as availability and completeness of datasets during the time-period of interest. Daily photoperiod and moon-fraction illumination were calculated using the R package “suncalc”52. Sea surface temperatures were compiled from environmental monitoring stations maintained by the National Data Buoy Center (NDBC) in nearshore-coastal and offshore waters, including: the entrance to New York Harbor (NOAA NDBC Station 44065), coastal Barnegat Bay, New Jersey (NOAA NDBC Station 44091), coastal Montauk Point, New York (NOAA National NDBC Station 44017), and offshore New York (NOAA NDBC Station 44025; Fig. 1). Hudson River environmental data, including temperature and discharge, were obtained from the United States Geological Survey (USGS) gauging station located at river kilometer (rkm) 115 in the lower Hudson River below Poughkeepsie, New York (USGS 01372058; Fig. 1). Average hourly bottom temperatures in the NY WEA were compiled from transceiver records; from these, monthly point values at transceiver locations were interpolated onto a raster surface using an inverse distance weighted technique in ArcGIS to simplify visual comparison of monthly temperatures in the NY WEA. Because anadromous Atlantic Sturgeon migrate between heterogeneous environments, pair-wise differences between water temperatures were also examined to explore potential triggers of movement between habitats.
### Residency and movement
Periods of residency and movement were calculated using the behavioral event qualifier in the R package “V-Track”53,54,55. A residence event was defined as a minimum of two successive detections of an individual at a single transceiver station over a minimum period of two hrs. Residence events were terminated by either a detection of the individual on another transceiver station or a period of 12 hrs without detection (i.e., time-out period). Movement events were defined as non-residence events (i.e., movements of an individual between two transceivers) and were limited to non-residence events of less than five days. Rate of movement (ROM) was calculated using a transceiver-distance matrix that assumed direct distance movements and a 600 m detection radius for each transceiver. When available, calculations were aided by detections of Atlantic Sturgeon from cooperative arrays located outside of the study area.
Unique daily counts of Atlantic Sturgeon in the NY WEA were modeled using generalized additive models (GAMs)56. All GAMs were built in the R package “mgcv”57 using thin plate splines58,59. A log-link function with a quasi-Poisson error distribution was used to account for overdispersion in the count data. Independence of daily counts was assumed to be valid based on previously reported movement rates of Atlantic Sturgeon that suggest that daily mixing can occur. The initial model included photoperiod, moon-fraction illuminated, water temperatures, and discharge, and considered complexity up to first-order interactions. Stepwise backwards elimination of explanatory variables was performed to determine a minimally adequate model using minimization of the generalized cross validation (GCV) criterion to guide the process. AIC is not available for quasi-Poisson models, and GCV is an acceptable alternative in subset regression60,61. During model selection, GCV scores were compared with and without an explanatory variable to determine which terms to remove. Smoothing functions were replaced by linear terms if the estimated degrees of freedom approached a value of one, suggesting that a smooth was essentially a straight line62. Because the water temperatures for the New York Harbor and Hudson River estuary were highly correlated predictors (r2 = 0.91), only the latter was used to capture potential cues in river temperature associated with Atlantic Sturgeon movement. As a test of the quality of the selection process, the final and full models were compared using an F-ratio test to determine if the final (i.e., selected) model explained significantly less of the residual error compared to the full model62. A significant result would indicate that the final model explained less of the residual error than the full model and that the final model was under-parameterized.
## Results
### Fish sampling and acoustic telemetry
Atlantic Sturgeon (n = 133) were captured via targeted bottom trawling and tagged with acoustic transmitters during sampling cruises in May 2016 (n = 40), May 2017 (n = 81), and October 2017 (n = 12). The size range of the tagged fish was 619 to 2,050 mm FL, with a mean FL of 855 mm. Tagged fish were representative of juvenile (n = 114), sub-adult (n = 17), and adult (n = 2) life-stages, with age-at-capture estimates ranging from 4 to 28 years. Detections of Atlantic Sturgeon tagged during this study as well as at-large fish tagged by SBU researchers during previous sampling efforts were included in analyses to increase the robustness and scope of the study53.
Telemetry data indicated that Atlantic Sturgeon were present in the NY WEA during array operation. Total confirmed detections for Atlantic Sturgeon ranged from 1 to 310 detections per individual, with a total of 5,490 valid detections of 181 unique individuals. Detections in the NY WEA were representative of Atlantic Sturgeon tagged during the study (n = 39; 1,028 detections; Table 1) as well as at-large Atlantic Sturgeon tagged by SBU researchers during previous sampling efforts (n = 142; 4,462 detections; Supplementary Table S1). Atlantic Sturgeon occurred throughout the study site and were detected on all transceivers in the array (Fig. 2); importantly, Atlantic Sturgeon were observed on the most distal transceiver station, located 44.3 km offshore (21 total detections of 5 unique fish). Total counts and detections of unique fish were highest nearer to shore and appeared to decrease with distance from shore. Counts at each station ranged between 21–909 total detections and 4–59 unique detections of Atlantic Sturgeon.
Atlantic Sturgeon were regularly detected in the NY WEA throughout the study period and 55 individuals were observed in the site during multiple years. During 2016 and 2018, transceivers were only operational in the study site for a short period (November 10–December 31, 2016 and January 1–February 5, 2018) but 87 unique fish (2,098 detections) and 30 unique fish (761 detections) were detected, respectively. In 2017, the array was operational for the entire year and 126 Atlantic Sturgeon (2,631 detections) were observed in the study site. Monthly counts of individuals in the NY WEA were highest during the months of November, December, and January, and peaked in December 2016 (n = 58) (Figs 3 and 4). Importantly, two years of data are available for these months and similar abundances were observed for both datasets (e.g., relatively high abundances of Atlantic Sturgeon occurred during November and December 2016–2017 and January 2017–2018). Atlantic Sturgeon were relatively uncommon (i.e., <2 individuals detected) or entirely absent from the NY WEA during July, August, and September (Figs 3 and 4).
Within the NY WEA, both temporal and spatial variation in unique counts of Atlantic Sturgeon were observed (Fig. 4). The majority of individual fish were detected on transceivers located nearer to shore except during months of relatively high abundance when fish were more widely distributed throughout the array. The highest observed abundance of Atlantic Sturgeon at a single station (n = 22; 23.4 km from shore) occurred in November 2017; however, during this month individuals were observed in the study site >40 km from shore, demonstrating the wide distribution of fish in the NY WEA. During the months of December and January, fish were present and evenly distributed across the majority of transceivers in the NY WEA and in December 2016 Atlantic Sturgeon were detected on all transceivers in the array. Average monthly bottom temperatures observed in the study site ranged from 2.1 to 19.0 °C, with local minimum temperatures in February–March and local maximum temperatures in August–October (Fig 4). Evident temperature stratification between bottom and surface waters in the study site was observed April–November (Supplementary Fig. S2).
### Residency and movement
Residence events at individual transceiver stations in the NY WEA were uncommon (n = 22) and were only observed on five transceivers during the study period, with the majority of residence behaviors associated with near-shore stations in the NY WEA (Fig. 5). The station with the highest number of observed residence events (n = 8) was located 24.9 km from shore, and no residence events were observed beyond 30.1 km from shore. Residence events were of short duration [mean (SD) = 10.1 (14.0) hrs; range = 2.1–70.1 hrs] and the maximum ROM observed between stations was 0.86 m/s, although slower rates were common [mean (SD) = 0.31 (0.20) m/s]. By assuming the maximum observed ROM of 0.86 m/s and maximum straight-line distance of 40.6 km between stations from the transceiver-distance matrix, the minimum transit time for an Atlantic Sturgeon through the NY WEA at its longest point was estimated to be 13.1 hrs. This suggests that daily mixing could occur and, consequently, that the assumption of independence for daily counts used to model the data was valid.
The final, simplified GAM model contained a smooth term for the interaction between Hudson River estuary water temperature and photoperiod and a linear term for river discharge as predictors of unique daily counts of Atlantic Sturgeon in the NY WEA:
$${\rm{U}}{\rm{D}}{\rm{C}}\sim s({{\rm{H}}{\rm{R}}}_{{\rm{t}}{\rm{e}}{\rm{m}}{\rm{p}}},\,{\rm{P}})+{{\rm{H}}{\rm{R}}}_{{\rm{d}}{\rm{i}}{\rm{s}}{\rm{c}}{\rm{h}}{\rm{a}}{\rm{r}}{\rm{g}}{\rm{e}}}$$
where UDC is unique daily count of Atlantic Sturgeon in the NY WEA, HRtemp is daily mean water temperature (°C) in the lower Hudson River, HRdischarge is daily mean discharge (ft3/s) in the lower Hudson River, P is daily photoperiod (hrs), and s() indicates a smoother was used. The final model explained 61.0% of the deviance and had a GCV score of 0.9407. No significant difference was found between the final and full model (F7.04,409.23 = 1.58, p = 0.1389), providing evidence that the selection process identified an appropriately complex model.
Exploration of the relationship between daily abundance of Atlantic Sturgeon in the NY WEA and the two-way interaction term above allows for clarification of the model structure (Fig. 6). Both temperature and photoperiod terms are cyclical (i.e., the same value can occur during a positive or negative trend) and out of phase. As water temperatures in the Hudson River decreased below 20 °C during the fall months along with decreasing daily photoperiod, daily counts of Atlantic Sturgeon in the NY WEA were observed to increase and reached a maximum as water temperature in the Hudson River approached its annual minimum (~0.0 °C). Conversely, as water temperatures in the Hudson River increased during the spring and into the summer months along with increasing daily photoperiod, detections of Atlantic Sturgeon in the NY WEA decreased and fish were entirely absent when temperature was at its summer maximum. While water temperature in the Hudson River was strongly correlated to photoperiod (r2 = 0.49), there was a notable temporal lag of ~ 35 days, presumably because of the high heat capacity of water. During this lag in the late summer, Atlantic Sturgeon were not detected in the NY WEA when temperatures in the river were near their maximum, despite the decreasing trend in photoperiod. The response curve for the linear discharge term had a clear, decreasing trend, and suggests that high daily abundance of Atlantic Sturgeon in the NY WEA was more likely in the fall and winter during periods of low river discharge (less than 20,000 ft3/s; Supplementary Fig. S3).
## Discussion
This study provides benchmark information regarding the incidence and seasonality of marine-resident Atlantic Sturgeon use of offshore waters in the NY WEA and, importantly, identifies potential estuarine drivers of offshore occurrence. With the development of offshore wind energy in the United States comes the recognized need to prioritize offshore research and monitoring in the context of ecological risk assessment and mitigation; here, we establish effective baseline criteria regarding spatial and temporal trends of Atlantic Sturgeon within the putative area of effect—an obligatory prerequisite for evaluating the impact of activities during all stages of offshore wind energy development. Furthermore, this study demonstrates the effectiveness of acoustic-release transceivers for discerning cryptic behaviors of species of concern in an offshore wind energy site through the targeted monitoring of acoustically tagged individuals.
Overall, the results of this study suggest that offshore distribution of Atlantic Sturgeon in the NY WEA is highly seasonal. Observations of fish on the acoustic array broadly corroborate and expand the current knowledge of marine movements in the mid-Atlantic Bight31,32,33,34,37,38. However, the fine-scale documentation of Atlantic Sturgeon trends in the NY WEA and the identification of putative migratory pathways beyond the extent of traditional survey data may have important implications on species conservation. Consistent spatial and temporal trends of Atlantic Sturgeon occurrence were evident from telemetry data and indicated expansion into deeper, offshore waters of the NY WEA during the fall and winter months. High incidences of Atlantic Sturgeon during the winter were observed in both years, with a marked increase in unique counts and total detections in November and December. The absence of Atlantic Sturgeon in the NY WEA during the summer months, particularly from June through September, suggests a putative shift to nearshore habitat and corresponds with periods of known-residence in shallow, coastal waters that are associated with juvenile and sub-adult aggregations as well as adult spawning migrations29,55,63,64,65.
Despite the recent focus on coastal research, as well as the consequent designation of in-river critical habitat (n = 31 Critical Habitat Units)66, the offshore trends and distribution of Atlantic Sturgeon remain relatively unknown and the biological and physical features essential for their conservation in marine habitats have not been identified. The results of this study should help define monitoring parameters in offshore waters and guide future assessments in marine wind energy areas. An important finding from the telemetry data was that Atlantic Sturgeon used the majority of habitat available to them within the NY WEA. Individual counts and total detections of Atlantic Sturgeon were highest on transceivers located in shallow waters and exhibited a generally decreasing trend with increased depth and distance from shore. Although limited observations of adult Atlantic Sturgeon have been described on shelf waters at depths of up to 40 m32, the ubiquity of Atlantic Sturgeon documented throughout the study site was unexpected and suggests that the distribution and habitation of these fish in marine waters is greater than previously assumed. Throughout the range, research is needed to further characterize the extent of the offshore distribution of Atlantic Sturgeon; however, these results demonstrate the importance of targeted studies in marine waters where more traditional survey- or fisheries-dependent methodologies may underestimate habitat use, particularly at intermediate scales or at the boundaries of the known distribution of highly migratory fish.
The influence of environmental factors on Atlantic Sturgeon counts in the NY WEA suggests that transitions between coastal and offshore habitat are predictable and associated with long-term cues and localized estuarine conditions. Anadromous fish populations are known to undertake extensive annual migrations to optimize temporally predictable foraging and spawning conditions67,68; these migrations are assumed to be governed, at least in part, by seasonal and ontogenetic responses to complex abiotic factors67. In sturgeon species, photoperiod and water temperature (and, to a lesser extent, discharge) are recognized as factors that act to modulate migratory strategies69,70. Although the specific mechanisms driving movements and ontogenetic migrations of Atlantic Sturgeon are not well known, clinal variations in abiotic conditions have been broadly associated with temporal distribution and habitat selection35,51,71. The final GAM model indicates that a small subset of abiotic factors provide context-dependent cues regarding the timing of offshore migration. Day-length (i.e., photoperiod) is a reliable long-term trigger of migration that is largely autonomous of annual variation in environmental conditions, while both river temperature and discharge provide short-term signals that result from dynamic, localized conditions. Further evaluation of these cues as predictors of offshore migration is necessary on both a regional and coast wide scale; regardless, the identification of specific abiotic factors that trigger migration and, consequently, offshore distribution has important management implications for monitoring and conservation efforts in future wind energy sites.
Movements and distributions of Atlantic Sturgeon in marine habitats are widely acknowledged to be indicative of preferential selection for covarying environmental properties that are encountered in-situ35,72. Interestingly, although we considered various marine predictors from both within and outside of the study area, terms used as proxies of marine environmental conditions were not represented in the final model. The elimination of these terms during model selection was informative and suggests that in-river conditions have a significantly greater influence on annual offshore transitions than those encountered while at sea, at least on the scale considered in this study. Likewise, coastal or latitudinal movements, which might otherwise have been inferred from the influence of pair-wise differences in nearby marine conditions (e.g., Barnegat Bay, New Jersey, or Montauk Point, New York), were not indicated by the final model. Although telemetry detections from this study were limited and do not provide evidence of relocations outside of the NY WEA, the seasonal occurrence of marine-migrant Atlantic Sturgeon in near-shore and coastal waters is well documented and corresponds to periods when few or no fish were detected in the study site. In the Hudson River estuary, specifically, marine-migrant life-stages are present from April until the end of November63,64,65 and aggregate in adjacent coastal waters during May, June, September, and October before dispersing34,35, which is suggestive of temporal and spatial resource partitioning.
Preferential distribution of Atlantic Sturgeon on bottom types associated with high prey density, most notably sand and gravelly-sand substrates, has been inferred based on commercial bycatch and stomach content analysis31,73 but a clear linkage between foraging behavior and resource utilization in marine waters has yet to be determined. The presence of Atlantic Sturgeon over sand-dominated substrates throughout the NY WEA is informative and adds to the literature regarding marine habitat use; however, it does not provide direct evidence of foraging activities in the area. Additional information regarding vertical distributions of Atlantic Sturgeon and, particularly, the relationship between swimming depth and bottom depth could provide further indication as to habitat use74; however, the current criteria for defining foraging habitat in marine environments remain largely circumstantial or unknown, and further characterization of ecological correlates of foraging area use with environmental parameters is necessary.
The delineation of behavior modes from telemetry data allows for more informative conclusions regarding perceived habitat selection within the NY WEA as well as explicit guidance for identifying areas of concern at a scale relevant to future development. Over the course of this study, residence events were uncommon and of short duration, despite the use of a relatively non-restrictive time constraint (i.e., minimum residency period of two hrs) to discern any apparent spatial trends in behavior. Importantly, residence behaviors were generally limited to shallow water sites (i.e., depth < 30 m), which suggests the increased potential for negative interactions to occur in these areas during development activities. Site-fidelity of Atlantic Sturgeon in offshore waters is likely highly-variable based on resource availability and, moreover, may occur at a broad spatial scale beyond the scope of this study, as suggested by the migratory life-history of Atlantic Sturgeon and limited observations of mesoscale distribution32,35. Individual direct-distance movement rates observed in the NY WEA are comparable to estimates associated with adult foraging behavior in estuarine habitats75,76; however, because of the necessary assumption of direct movement, further classification of these behaviors as directional (i.e., transitory) or non-directional (i.e., foraging) is problematic. Regardless, the delineation of sub-seasonal behavior modes is an important step in linking habitat and resource utilization in marine waters.
While biotelemetry itself is not a new technique77, the use of acoustic release mechanisms to complement telemetry data collection is a recent development that allows research in deeper offshore areas where conventional array maintenance and data retrieval are problematic78. To our knowledge, the current study is the first to use transceivers equipped with acoustic release mechanisms to monitor fish behavior at an offshore wind energy site and may represent a new paradigm for future assessments. Passive acoustic monitoring techniques, coupled with acoustic release technology, provide long-term functionality and situational flexibility as necessary to inform baseline ecological characterization and subsequent ecological impact assessments in offshore wind energy leases. The recent proliferation of long-term acoustic tagging programs along the Atlantic coast of the US not only allows for the possibility of supplemental detections and increased sample size (e.g., the incorporation of previously tagged individuals into the current study) but also illustrates the need for an integrated approach to allow for among-site or comparative analyses. Although the primary focus of our study was to provide baseline pre-construction data, the methodology used could be modified or extended to provide data throughout all phases of development, including informing behavioral changes or fine-scale spatial shifts in distribution of Atlantic Sturgeon over time.
The findings of this study indicate that mitigation of potentially negative impacts of wind energy development, such as multiple-pulse sound sources, is possible through spatial and temporal avoidance during periods of increased Atlantic Sturgeon incidence. Detections of individuals on all transceivers in the study array provide strong evidence that Atlantic Sturgeon use a large amount of the habitat available to them in NY WEA, albeit on a highly seasonal basis. While previous studies have primarily associated the extreme noise from pile-driving during the construction phase with negative impacts to fish assemblages79,80, there is still large uncertainty in the literature regarding the physiological effects or behavioral responses of fish to these disturbances. Likewise, data are limited in regards to response distances and areas of potential effect16. The low relative abundance of Atlantic Sturgeon in offshore waters of the NY WEA that was observed during the summer months, when sub-adult and adult life-stages were putatively aggregated in riverine or more near-coastal habitats, suggests that the negative impacts of pile-driving activities on Atlantic Sturgeon could be reduced or largely avoided by incorporating data-directed management measures during the planning stages. Conversely, an increased emphasis on impact monitoring is suggested during periods of increased Atlantic Sturgeon abundance during the winter months—particularly November, December, and January—if construction activities cannot be avoided.
From a more general management standpoint, the observed occurrence of Atlantic Sturgeon in offshore waters of the NY WEA underscores the importance of long-term monitoring to recovery efforts, particularly with regard to life-stages and habitats that may be underrepresented in the literature. While considerable research and management attention has recently focused on riverine and coastal waters81, empirical evaluations of Atlantic Sturgeon populations in marine waters are inadequate and limited by a lack of basic knowledge. Recent annual survival rate estimates for Atlantic Sturgeon are already below the suggested threshold for recovery35,82,83,84 and, despite a lack of information regarding the magnitude of emerging threats such as offshore wind energy development, it is apparent that even a moderate increase in mortality resulting from anthropogenic sources could negatively impact Atlantic Sturgeon stocks. Further characterization of the broad spatiotemporal trends of Atlantic Sturgeon in offshore waters are necessary to better define monitoring parameters and guide threat assessments in marine wind energy areas; regardless, this study represents an important initial step towards quantitatively evaluating Atlantic Sturgeon in marine waters at a scale relevant to future development.
## Data Availability
Atlantic Sturgeon telemetry detections used in the current study are archived and publicly viewable on the Harvard Dataverse website: https://dataverse.harvard.edu/. The complete environmental datasets analyzed during the current study are available from the corresponding author on reasonable request.
## References
1. 1.
Esteban, M. D., Diez, J. J., Lopez, J. S. & Negro, V. Why offshore wind energy? Renew. Energy 36, 444–450 (2011).
2. 2.
Panwar, N. L., Kaushik, S. C. & Kothari, S. Role of renewable energy sources in environmental protection: a review. Renew. Sust. Energ. Rev. 15, 1513–1524 (2011).
3. 3.
United States Department of Energy. Wind Vision: A New Era for Wind Power in the United States. DOE/GO-102015-4557. (U.S. Department of Energy Office of Energy Efficiency and Renewable Energy, 2015).
4. 4.
Gilman, P. et al. National Offshore Wind Strategy: Facilitating the Development of the Offshore Wind Industry in the United States. DOE/GO-102016-4866. (U.S. Department of Energy; U.S. Department of the Interior 2016).
5. 5.
Li, J. & Yu, X. Onshore and offshore wind energy potential assessment near Lake Erie shoreline: a spatial and temporal analysis. Energy 147, 1092–1107 (2018).
6. 6.
Kaldellis, J. K. & Kapsali, M. Shifting towards offshore wind energy—recent activity and future development. Energy Policy 53, 136–148 (2013).
7. 7.
Higgins, P. & Foley, A. The evolution of offshore wind power in the United Kingdom. Renew. Sust. Energ. Rev. 37, 599–612 (2014).
8. 8.
Kota, S., Bayne, S. B. & Nimmagadda, S. Offshore wind energy: a comparative analysis of UK, USA and India. Renew. Sust. Energ. Rev. 41, 685–694 (2015).
9. 9.
Davis, C., Bollinger, L. A. & Dijkema, G. P. J. The state of the states: data-driven analysis of the US Clean Power Plan. Renew. Sust. Energ. Rev. 60, 631–652 (2016).
10. 10.
Gill, A. B. Offshore renewable energy: ecological implications of generating electricity in the coastal zone. J. Appl. Ecol. 42, 605–615 (2005).
11. 11.
Inger, R. et al. Marine renewable energy: potential benefits to biodiversity? An urgent call for research. J. Appl. Ecol. 46, 1145–1153 (2009).
12. 12.
Boehlert, G. W. & Gill, A. B. Environmental and ecological effects of ocean renewable energy development. Oceanography 23, 68–81 (2010).
13. 13.
Verfuss, U. K., Sparling, C. E., Arnot, C., Judd, A. & Coyle, M. Review of offshore wind farm impact monitoring and mitigation with regard to marine mammals. Adv. Exp. Med. Biol. 875, 1172–1182 (2016).
14. 14.
Vallejo, G. C. et al. Responses of two marine top predators to an offshore wind farm. Ecol. Evol. 7, 8698–8708 (2017).
15. 15.
Leonhard, S. B., Stenberg, C. & Støttrup, J. G. Effect of the Horns Rev 1 Offshore Wind Farm on Fish Communities: Follow-up Seven Years after Construction. (DTU Aqua National Institute of Aquatic Resources, 2011).
16. 16.
Bailey, H., Brookes, K. L. & Thompson, P. M. Assessing environmental impacts of offshore wind farms: lessons learned and recommendations for the future. Aquat. Biosyst. 10, 8 (2014).
17. 17.
Bergstrom, L. et al. Effects of offshore wind farms on marine wildlife—a generalized impact assessment. Environ. Res. Lett. 9, https://doi.org/10.1088/1748-9326/9/3/034012 (2014).
18. 18.
Drewitt, A. L. & Langston, R. H. W. Assessing the impacts of wind farms on birds. Ibis 148, 29–42 (2006).
19. 19.
Gilles, A., Scheidat, M. & Siebert, U. Seasonal distribution of harbor porpoises and possible interference of offshore wind farms in the German North Sea. Mar. Ecol. Prog. Ser. 383, 295–307 (2009).
20. 20.
Thompson, P. M. et al. Framework for assessing impacts of pile-driving noise from offshore wind farm construction on a harbour seal population. Environ. Impact Asses. 43, 73–85 (2013).
21. 21.
Russell, D. J. F. et al. Avoidance of wind farms by harbor seals is limited to pile driving activities. J. Appl. Ecol. 53, 1642–1652 (2016).
22. 22.
Wahlberg, M. & Westerberg, H. Hearing in fish and their reactions to sounds from offshore wind farms. Mar. Ecol. Prog. Ser. 288, 295–309 (2005).
23. 23.
Kituchi, R. Risk formulation for the sonic effects of offshore wind farms on fish in the EU region. Mar. Pollut. Bull. 60, 172–177 (2010).
24. 24.
Bergstrom, L., Sundqvist, F. & Bergstrom, U. Effects of an offshore wind farm on temporal and spatial patterns in the demersal fish community. Mar. Ecol. Prog. Ser. 485, 199–210 (2013).
25. 25.
Reubens, J. T., Pasotti, F., Degraer, S. & Vincx, M. Residency, site fidelity and habitat use of Atlantic cod (Gadus morhua) at an offshore wind farm using acoustic telemetry. Mar. Environ. Res. 90, 128–135 (2013).
26. 26.
Furness, R. W., Wade, H. M. & Masden, E. A. Assessing vulnerability of marine bird populations to offshore wind farms. J. Environ. Manage. 119, 56–66 (2013).
27. 27.
Smith, T. I. J. The fishery, biology, and management of Atlantic Sturgeon, Acipenser oxyrhynchus, in North America. Environ. Biol. Fishes 4, 61–72 (1985).
28. 28.
Boreman, J. Sensitivity of North American sturgeons and paddlefish to fishing mortality. Environ. Biol. Fishes 48, 399–405 (1997).
29. 29.
Van Eenennaam, J. P. & Doroshov, S. I. Effects of age and body size on gonadal development of Atlantic Sturgeon. J. Fish Biol. 53, 624–637 (1998).
30. 30.
Atlantic Sturgeon Status Review Team. Status review of Atlantic Sturgeon (Acipenser oxyrinchus oxyrinchus). Report to National Marine Fisheries Service, Northeast Regional Office (2007).
31. 31.
Stein, A. B., Friedland, K. D. & Sutherland, M. Atlantic Sturgeon marine distribution and habitat use along the Northeastern Coast of the United States. Trans Am Fish Soc. 133, 527–537 (2004).
32. 32.
Erickson, D. L. et al. Use of pop-up satellite tags to identify oceanic-migratory patterns for adult Atlantic Sturgeon, Acipenser oxyrinchus oxyrinchus Mitchell, 1815. J. Appl. Ichthyol. 27, 356–365 (2011).
33. 33.
Dunton, K. J., Jordaan, A., McKown, K. A., Conover, D. O. & Frisk, M. G. Abundance and distribution of Atlantic Sturgeon (Acipenser oxyrinchus) within the Northwest Atlantic Ocean, determined from five fishery-independent surveys. Fish. Bull. 108, 450–465 (2010).
34. 34.
Dunton, K. J. et al. Marine distribution and habitat use of Atlantic Sturgeon in New York lead to fisheries interactions and bycatch. Mar. Coast. Fish. 7, 18–32 (2015).
35. 35.
Melnychuk, M. C., Dunton, K. J., Jordaan, A., McKown, K. A. & Frisk, M. G. Informing conservation strategies for the endangered Atlantic Sturgeon using acoustic telemetry and multi-state mark–recapture models. J. Appl. Ecol. 54, 914–925 (2017).
36. 36.
Breece, M. W., Fox, D. A., Haulsee, D. E., Wirgin, I. I. & Oliver, M. J. Satellite driven distribution models of endangered Atlantic Sturgeon occurrence in the mid-Atlantic Bight. ICES J. Mar. Sci. 75, https://doi.org/10.1093/icesjms/fsx187 (2017).
37. 37.
Stein, A. B., Friedland, K. D. & Sutherland, M. Atlantic Sturgeon marine bycatch and mortality on the continental shelf of the Northeast United States. N. Am. J. Fish. Manag. 24, 171–183 (2004).
38. 38.
Wirgin, I., Maceda, L., Grunwald, C. & King, T. L. Population origin of Atlantic Sturgeon Acipenser oxyrinchus oxyrinchus by-catch in U.S. Atlantic coast fisheries. J. Fish Biol. 86, 1251–1270 (2015).
39. 39.
Dunton, K. J. et al. Genetic mixed-stock analysis of Atlantic Sturgeon Acipenser oxyrinchus oxyrinchus in a heavily exploited marine habitat indicates the need for routine genetic monitoring. J. Fish Biol. 80, 207–217 (2012).
40. 40.
O’Leary, S. J., Dunton, K. J., King, T. L., Frisk, M. G. & Chapman, D. D. Genetic diversity and effective number of breeders of Atlantic Sturgeon, Acipenser oxyrhinchus oxyrhinchus. Conserv. Genet. 15, 1173–1181 (2014).
41. 41.
McDonald, J. Critical habitat designation under the Endangered Species Act: a road to recovery? Environ. Law 28, 671–700 (1998).
42. 42.
Robbins, K. Recovery of an endangered provision: untangling and reviving critical habitat under the Endangered Species Act. Buffalo Law Rev. 58, 1–31 (2010).
43. 43.
Bureau of Ocean Energy Management. Commercial Wind Lease Issuance and Site Assessment Activities on the Atlantic Outer Continental Shelf Offshore New York: Revised Environmental Assessment. (U.S. Department of the Interior Bureau of Ocean Energy Management Office of Renewable Energy Programs, 2016).
44. 44.
Guida, V. et al. Habitat Mapping and Assessment of Northeast Wind Energy Areas. OCS Study BOEM 2017-088 (U.S. Department of the Interior, Bureau of Ocean Energy Management, 2017).
45. 45.
Poti, M., Kinlan, B. P. & Menza, C. Chapter 2: Bathymetry. In A Biogeographic Assessment of Seabirds, Deep Sea Corals and Ocean Habitats of the New York Bight: Science to Support Offshore Spatial Planning (eds Menza, C. et al.) 9–32 (NOAA Technical Memorandum NOS NCCOS 141, 2012).
46. 46.
von Bertalanffy, L. A quantitative theory of organic (inquiries on growth laws, II). Hum. Biol. 10, 181–213 (1938).
47. 47.
Dunton, K. J. et al. Age and growth of Atlantic Sturgeon in the New York Bight. N. Am. J. Fish. Manag. 36, 62–73 (2016).
48. 48.
Moser, M. L. et al. A Protocol for Use of Shortnose and Atlantic Sturgeons. NOAA Technical Memorandum NMFS-OPR-18 (2000).
49. 49.
Boone, S. S. et al. Evaluation of four suture materials for surgical incision closure in Siberian Sturgeon. Trans. Am. Fish Soc. 142, 649–659 (2013).
50. 50.
Kilfoil, J. P., Wetherbee, B. M., Carlson, J. K. & Fox, D. A. Targeted catch-and-release of prohibited sharks: sand tigers in coastal Delaware waters. Fisheries 42, 281–287 (2017).
51. 51.
Ingram, E. C. & Peterson, D. L. Annual spawning migrations of adult Atlantic Sturgeon in the Altamaha River, Georgia. Mar. Coast. Fish. 8, 595–606 (2016).
52. 52.
R Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria (2018).
53. 53.
Dunton, K. J. Population dynamics of juvenile Atlantic Sturgeon, Acipenser oxyrinchus oxyrinchus, within the northwest Atlantic Ocean. Doctoral Dissertation. Stony Brook University (2014).
54. 54.
Campbell, H. A., Watts, M. E., Dwyer, R. G. & Franklin, C. E. V-Track: software for analysing and visualising animal movement from acoustic telemetry detections. Mar. Freshwater Res. 63, 815–820 (2012).
55. 55.
Breece, M. W., Fox, D. A. & Oliver, M. J. Environmental drivers of adult Atlantic Sturgeon movement and residency in Delaware Bay. Mar. Coast. Fish. 10, 269–280 (2018).
56. 56.
Hastie, T. J. & Tibshirani, R. J. Generalized Additive Models. (Chapman & Hall, 1990).
57. 57.
Wood, S. N. Mixed GAM Computation Vehicle with Automatic Smoothness. R package version 1.8-27 (2011).
58. 58.
Duchon, J. Splines minimizing rotation-invariant semi-norms in Solobev spaces. In Construction Theory of Functions of Several Variables (eds Schempp, W. & Zeller, K.) 85–100 (Springer, 1977).
59. 59.
Wood, S. N. Thin plate regression splines. J. R. Stat. Soc. Series B Stat. Methodol. 65, 95–114 (2003).
60. 60.
Golub, G. H., Health, M. & Wahba, G. Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21, 215–223 (1979).
61. 61.
Burnham, K. P. & Anderson, D. R. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. (Springer-Verlag, 1998).
62. 62.
Wood, S. N. Generalized Additive Models: An Introduction with R. (Chapman & Hall/CRC, 2006).
63. 63.
Dovel, W. L. & Berggren, T. J. Atlantic Sturgeon of the Hudson Estuary, New York. New York Fish Game J. 30, 140–172 (1983).
64. 64.
Bain, M. B. Atlantic and shortnose sturgeons of the Hudson River: common and divergent life history attributes. Environ. Biol. Fishes 48, 347–358 (1997).
65. 65.
Bain, M., Haley, N., Peterson, D., Waldman, J. R. & Arend, K. Harvest and habitats of Atlantic Sturgeon Acipenser oxyrinchus Mitchell, 1815 in the Hudson River estuary: lessons for sturgeon conservation. Bol. Inst. Esp. Oceanogr. 16, 43–54 (2000).
66. 66.
United States Office of the Federal Register. Endangered and threatened species; designation of Critical Habitat for the endangered New York Bight, Chesapeake Bay, Carolina and South Atlantic Distinct Population Segments of Atlantic Sturgeon and the threatened Gulf of Maine Distinct Population Segment of Atlantic Sturgeon. U.S. Office of the Federal Register 82, 39160–39274 (2017).
67. 67.
Gross, M. R., Coleman, R. M. & McDowall, R. M. Aquatic productivity and the evolution of diadromous fish migration. Science 239, 1291–1293 (1988).
68. 68.
Dingle, H. & Drake, V. A. What is migration? BioScience 57, 113–121 (2007).
69. 69.
Cech, J. J. Jr. & Doroshov, S. I. Environmental requirements, preferences, and tolerance limits of North American sturgeons. In Sturgeons and Paddlefish of North America (eds LeBreton, G. T. O., Beamish, F. W. H. & McKinley, S. R.) 73–86 (Springer, 2004).
70. 70.
Papoulious, D. M., DeLonay, A. J., Annis, M. L., Wildhaber, M. L. & Tillitt, D. E. Characterization of environmental cues for intitiation of reproductive cycling and spawning in shovelnose sturgeon Scaphirhynchus platorynchus in the Lower Missouri River, USA. J. Appl. Ichthyol. 27, 335–342 (2011).
71. 71.
Kieffer, M. C. & Kynard, B. Annual movements of shortnose and Atlantic Sturgeon in the Merrimack River, Massachusetts. Trans. Am. Fish. Soc. 122, 1088–1103 (1993).
72. 72.
Breece, M. W. et al. Dynamic seascapes predict the marine occurrence of an endangered species: Atlantic Sturgeon Acipenser oxyrinchus oxyrinchus. Methods Ecol. Evol. 7, 725–733 (2016).
73. 73.
Johnson, J. H., Dropkin, D. S., Warkentine, B. E., Rachlin, J. W. & Andrews, W. D. Food habits of Atlantic Sturgeon off the central New Jersey coast. Trans. Am. Fish Soc. 126, 166–170 (1997).
74. 74.
Stokesbury, M. J. W. et al. Atlantic Sturgeon spatial and temporal distribution in Minas Passage, Nova Scotia, Canada, a region of future tidal energy extraction. PLoS ONE 11, https://doi.org/10.1371/journal.pone.0158387 (2016).
75. 75.
Hatin, D., Fortin, R. & Caron, F. Movements and aggregation areas of adult Atlantic Sturgeon (Acipenser oxyrinchus) in the St Lawrence River estuary, Quebec, Canada. J. Appl. Ichthyol. 18, 586–594 (2002).
76. 76.
McClean, M. F., Simpfendorfer, C. A., Heupel, M. R., Dadswell, M. J. & Stokesbury, M. J. W. Diversity of behavioural patterns displayed by a summer feeding aggregation of Atlantic Sturgeon in the intertidal region of Minas Basin, Bay of Fundy, Canada. Mar Ecol Prog Ser. 496, 59–69 (2014).
77. 77.
Johnson, J. H. Sonic tracking of adult salmon at Bonneville Dam, 1957. Fishery Bulletin 176 (United States Fish and Wildlife Service 1960).
78. 78.
Afonso, P. et al. Vertical migrations of a deep-sea fish and its prey. PLoS ONE 9, https://doi.org/10.1371/journal.pone.0097884 (2014).
79. 79.
Popper, A. N. & Hastings, M. C. The effects of anthropogenic sources of sound on fish. J. Fish Biol. 75, 455–489 (2009).
80. 80.
Halvorsen, M. B., Casper, B. M., Matthews, F., Carlson, T. J. & Popper, A. N. Effects of exposure to pile-driving sounds on the lake sturgeon, Nile tilapia, and hogchoker. Proc. Royal Soc. B. 279, 4705–4714 (2012).
81. 81.
Hilton, E. J., Kynard, B., Balazik, M. T., Horodysky, A. Z. & Dillman, C. B. Review of the biology, fisheries, and conservation status of the Atlantic Sturgeon (Acipenser oxyrinchus oxyrinchus, Mitchill, 1815). J. Appl. Ichthyol. 32, 30–66 (2016).
82. 82.
Atlantic States Marine Fisheries Commission. Estimation of Atlantic Sturgeon Bycatch in Coastal Atlantic Commercial Fisheries of New England and the Mid-Atlantic. Atlantic States Marine Fisheries Commission, Washington, DC (2007).
83. 83.
Hightower, J. E., Loeffler, M., Post, W. C. & Peterson, D. L. Estimated survival of subadult and adult Atlantic Sturgeon in four river basins in the southeastern United States. Mar. Coast. Fish. 7, 514–522 (2015).
84. 84.
Dadswell, M. J. et al. The annual marine feeding aggregation of Atlantic Sturgeon Acipenser oxyrinchus in the inner Bay of Fundy: population characteristics and movement. J. Fish Biol. 89, 2107–2132 (2016).
## Acknowledgements
Funding for this project was provided in part by New York State Department of Environmental Conservation (NYSDEC) and the U.S. Department of the Interior Bureau of Ocean Energy Management (BOEM) through Cooperative Agreement M16AC00003 between the U.S. Department of the Interior Bureau of Ocean Energy Management and The Research Foundation for the State University of New York. In particular, we would like to extend our gratitude and thanks to Brian Hooker (BOEM) and Kim McKown (NYSDEC) for their role in administering project funding. Additional financial support for graduate studies was provided by the Hudson River Foundation for Science and Environmental Research through the Mark B. Bain Graduate Fellowship. We appreciate the invaluable field assistance provided by Justin Lashley, Kellie McCartin, Jill Olin, Joshua Zacharias, Catherine Ziegler, and Captain Christian Harter and the crew of the RV Seawolf.
## Author information
K.J.D., E.C.I. and M.G.F. conceived the study and secured project funding. E.C.I. and K.J.D. contributed to field work and data collection. E.C.I. and R.M.C. analyzed the results. E.C.I. drafted the manuscript. All authors reviewed and provided editorial comments on the draft manuscript.
Correspondence to Evan Corey Ingram.
## Ethics declarations
### Competing Interests
The authors declare no competing interests.
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Reprints and Permissions | 2019-12-12 15:50:57 | {"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": 0.42220208048820496, "perplexity": 9903.513672436116}, "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-2019-51/segments/1575540544696.93/warc/CC-MAIN-20191212153724-20191212181724-00424.warc.gz"} |
http://cs.stackexchange.com/questions/6751/improving-time-bound-of-this-algorithm-past-on2 | # Improving Time Bound of this Algorithm past $O(n^2)$
I recently came across the following interesting problem - one is given a sequence of Xs and Ys such as XXYXYXYYXYXXXYX, and consider a sequence to be good if, as you start at the left and move right, the number of Xs is greater than or equal to the number of Ys at any point except at the very end, at which the two quantities must be equal.
One must determine the number of points at which changing either a single X to Y or a single Y to X in a given sequence will yield a good sequence.
I initially considered traveling through the sequence linearly and checking if toggling the letter at that point would yield a good sequence, however that approach is on the order of $O(n\cdot n)=O(n^2)$ in the worst case where n is the length of the sequence. However, I was wondering if there was some faster method to do it.
EDIT: I made the observation that for any sequence, if the number of possible changes is greater than 0, than only one type of change will work (either changing an X to Y or Y to X) given the condition at the end that the number of X and Y must be equal.
-
## migrated from cstheory.stackexchange.comNov 19 '12 at 0:55
This question came from our site for theoretical computer scientists and researchers in related fields.
More appropriate for cs.stackexchange. – Yuval Filmus Nov 18 '12 at 19:44
Here is a hint. Suppose the sequence contains $n-1$ Xs and $n+1$ Ys, so that you need to change some Y to X. You can compute for each position $k \in [1,\ldots,2n]$ the number of Xs minus the number of Ys; let's call that a "report". Changing a Y to an X affects the report in a certain, easy to describe, way. On the other hand, whether a sequence is good corresponds to a very simple property of the report.
Putting everything together, you should get an $O(n)$ algorithm. | 2015-01-25 16:16:47 | {"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": 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": 0.8758264183998108, "perplexity": 254.0070797156103}, "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-2015-06/segments/1422115900160.86/warc/CC-MAIN-20150124161140-00210-ip-10-180-212-252.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/59065/intersections-of-conjugates-of-the-icosahedral-group-in-so3/59068 | # Intersections of conjugates of the icosahedral group in SO(3)
(Related question)
Let $I$ be the group of orientation preserving symmetries of a regular icosahedron. This is a $60$ element subgroup of $SO(3)$, isomorphic with the alternating group $A_5$. It is also perfect and self-normalizing in $SO(3)$.
For each $g\in SO(3)$ the conjugate ${}^gI=gIg^{-1}$ is the group of rotations which leave invariant a rotated icosahedron. My question concerns which groups can appear as intersections of conjugates. In particular, can anyone supply a proof or disproof of the following statement?
For any $g\in SO(3)$ the group ${}^gI\cap I$ is either trivial, or equal to $I$.
This elementary group theory question arose when studying numerical homotopy invariants of the Poincaré sphere $X=SO(3)/I$. In particular, I would like the fixed point sets of the two-point stabilisers of the standard action of $SO(3)$ on $X$ to be path-connected.
It's obvious when you put it like that (and that the quarter turn can be replaced with anything between $0$ and $\pi$, and the same can be done for the $3$- and $5$-fold symmetry). Now I wonder if the groups appearing as intersections of conjugates are necessarily cyclic? Thanks for your speedy and accurate reply! – Mark Grant Mar 22 '11 at 6:59 | 2016-05-28 02:35:37 | {"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": 0.9202500581741333, "perplexity": 115.79103256354264}, "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-2016-22/segments/1464049277286.69/warc/CC-MAIN-20160524002117-00156-ip-10-185-217-139.ec2.internal.warc.gz"} |
http://wulixb.iphy.ac.cn/en/article/doi/10.7498/aps.68.20190113 | x
## 留言板
Ab initio calculation of hyperfine-structure constant A of Fr and evaluation of magnetic dipole moments of Fr isotopes
## Ab initio calculation of hyperfine-structure constant A of Fr and evaluation of magnetic dipole moments of Fr isotopes
Lou Bing-Qiong, Li Fang, Wang Pei-Yan, Wang Li-Ming, Tang Yong-Bo
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• #### Abstract
As the heaviest atom in alkali-metal elements, Fr atom has been regarded as a candidate for the search of the permanent electric dipole moment of the electron and of parity-nonconservation effects. Accurate knowledge of Fr atomic properties is of great interest. In this work, we use a relativistic coupled-cluster method to calculate the magnetic dipole hyperfine structure constants for nS (n = 7－12), nP (n = 7－12) and nD (n = 6－11) states of 212Fr. A finite B-spline basis set is used to expand the Dirac radial function, including completely the single and double excitation in correlation calculation. Our results are compared with available theoretical and experimental values. The comparison shows that our method can offer accurate calculation of magnetic dipole hyperfine structure constant. For 7P state the differences between our results and experimental values are within 1%. The magnetic dipole hyperfine structure constants for 12S, nP (n = 9－12) and nD (n = 10－11) states are reported for the first time, which are very useful as benchmarks for experimental measurements and calculations by other theoretical methods of these quantities. In the relativistic coupled-cluster theoretical framework, we study the electron correlation effect on hyperfine-structure constant A for the S, P, and D states of Fr. We observe that the electron correlation effect is very important for hyperfine-structure constant properties. The D state has a considerable correlation effect. At the same time, we also investigate contribution trends of individual electron correlation effects involving direct, core-polarization and pair-correlation ones in S, P, and D Rydberg series. It is found that the dominant contributions for the S1/2, P1/2,3/2 and nD3/2 (n = 7－11) states are to from the direct effect; however, the dominant contributions for the 6D3/2, and nD5/2 (n = 6－11) states are due to the pair-correlation and the core-polarization, respectively. For D5/2 states, there is very strong cancellation among these individual correlation effects. The knowledge of these correlation trends is useful for studying the permanent electric dipole moment and parity-nonconservation effect of Fr in future. Moreover, the magnetic dipole moment ${\mu}$ for each of isotopes 207−213,220−228Fr is determined by combining with experimental values for magnetic dipole hyperfine structure constant of 7P state. For each of isotope 207−213Fr, our magnetic dipole moment ${\mu}$ is perfectly consistent with the experimental value, and our uncertainties are twice smaller than those in the experiments . For each of isotope 220−228Fr, our magnetic dipole moment ${\mu}$ has a larger uncertainty, but is still in agreement with the experimental magnetic dipole moment ${\mu}$.
#### References
[1] Grant I P 2007 Relativistic Quantum Theory of Atoms and Molecules (New York: Springer) pp533−577 [2] Fischer C F, Brage T, Jönsson P 1997 Computational Atomic Structure: An MCHF Approach (UK: Institute of Physics) pp1−67 [3] Jönsson P, Gaigalas G, Bieroń J, Fishcher C F, Grant I 2013 Computer Physics Communications. 184 2197 [4] Jönsson P, He X, Fishcher C F, Grant I 2007 Computer Physics Communications. 177 597 [5] Dzuba V A, Flambaum V V, Kozlov M G 1996 Phys. Rev. A 54 3948 [6] Dzuba V A, Johnson W R 1998 Phys. Rev. A 57 2459 [7] Angstmann E J, Dzuba V A, Flambaum V V 2004 Phys. Rev. A 70 014102 [8] Dinh T H, Dzuba V A, Flambaum V V, Ginges J S M 2008 Phys. Rev. A 78 054501 [9] Kozlov M G, Porsev S G, Johnson W R 2001 Phys. Rev. A 64 052107 [10] Pal R, Safronova M S, Johnson W R, Derevianko A, Porsev S G 2007 Phys. Rev. A 75 042515 [11] Blundell S A, Johnson W R, Liu Z W, Sapirstein 1989 Phys. Rev. A 40 2233 [12] Eliav E, Vikas M J, Ishikawa Y, Kaldor U 2005 Chem. Phys. 311 163 [13] Mani B K, Angom D 2011 Phys. Rev. A 83 012501 [14] Kallay M, Nataraj H S, Sahoo B K, Das B P, Visscher L 2011 Phys. Rev. A 83 030503 [15] Nandy D K, Singh Y, Sahoo B K 2014 Phys. Rev. A 89 062509 [16] Borschevsky A, Eliav E, Vilkas M J, Ishikawa Y, Kaldor U 2007 Phys. Rev. A 75 042514 [17] Eliav E, Kaldor U, Ishikawa Y 1996 Phys. Rev. A 53 3050 [18] Chaudhuri R K, Chattopadhyay S, Mahapatra U S 2013 J. Phys. Chem. A 117 12616 [19] Tang Y B, Lou B Q, Shi T Y 2017 Phys. Rev. A 96 022513 [20] Tang Y B, Gao N N, Lou B Q, Shi T Y 2018 Phys. Rev. A 98 062511 [21] Byrnes T M R, Dzuba V A, Flambaum F F, Murray D W 1999 Phys. Rev. A 59 3082 [22] Mukherjee D, Sahoo B K, Nataraj H S, Das B P 2009 J. Phys. Chem. A 113 12549 [23] Sakemi Y, Harada K, Hayamizu T, Itoh M, Kawamura H, Liu S, Nataraj H S, Oikawa A, Saito M, Sato T 2011 J. Phys. Conf. Ser. 302 012051 [24] Sahoo B K, Aoki T, Das B P, Sakemi Y 2016 Phys. Rev. A 93 032520 [25] Atutov S N, Calabrese R, Corradi L, Dainelli A, Mauro C D, Khanbekyan A, Mariotti E, Minguzzi P, Moi L, Sanguinetti S, Stancari G, Tomassetti L 2008 Proc. SPIE 7027 70270C [26] Ekström C, Ingelman S, Wannberg G, Skarestad M 1978 Physica Scripta 18 51 [27] Coc A, Thibault C, Touchard F, Duong H T, Juncar P, Liberman S, Pinard J, Lermé J, Vialle J L, Büttgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1985 Phys. Lett. B 163 66 [28] Coc A, Thibault C, Touchard F, Duong H T, Juncar P, Liberman S, Pinard J, Carre M, Lermé J, Vialle J L, Büttgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1987 Nucl. Phys. A 468 1 [29] Arnold E, Borchers W, Duong H T, Juncar P, Lermé J, Lievens P, Neu W, Neugart R, Pellerin M, Pinard J, Vialle J L, Wendt K, the ISOLDE Collaboration 1990 J. Phys. B 23 3511 [30] Arnold E, Borchers W, Carré M, Duong H T, Juncar P, Lermé J, Liberman S, Neu W, Neugart R, Otten W, Pellerin M, Pinard J, Pesnelle A, Vialle J L, Wendt K, the ISOLDE Collaboration 1989 J. Phys. B 22 L391 [31] Bauche J, Duong H T, Juncar P, Liberman S, Pinard J, Coc A, Thibault C, Touchard F, Lermé J, Vialle J L, Büttgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1986 J. Phys. B 19 L593 [32] Grossman J S, Orozco L A, Simsarian J E, Sprouse G D, Zhao W Z 1999 Phys. Rev. Lett. 83 935 [33] Sansonetti J E 2007 J. Phys. Chem. Ref. Data 36 497 [34] Gomez E, Aubin S, Orozco L A, Sprouse G D, Iskrenova-Tchoukova E, Safronova M S 2008 Phys. Rev. Lett. 100 172502 [35] Dzuba V A, Flambaum V V, Sushkov O P 1984 J. Phys. B: At. Mol. Phys. 17 1953 [36] Owusu A, Dougherty R W, Gowri G, Das T P 1997 Phys. Rev. A 56 305 [37] Safronova M S, Johnson W R, Derevianko A 1999 Phys. Rev. A 60 4476 [38] Sahoo B K, Nandy D K, Das B P, Sakemi Y 2015 Phys. Rev. A 91 042507 [39] Duong H T, Juncar P, Liberman S, Mueller A C, Neugart R, Otten E W, Peuse B, Pinard J, Stoke H H, Thibault C, Touchard F, Vialle J L, Wendt K, the ISOLDE Collaboration 1987 Europhys. Lett. 3 175 [40] Barber Z W, Stalnaker J E, Lemke N D, Poli N, Oates C W, Fortier T M, Diddams S A, Hollberg L, Hoyt C W, Taichenachev A V, Yudin V I 2008 Phys. Rev. Lett. 100 103002 [41] Kien F L, Balykin V I, Hakuta K 2005 J. Phys. Soc. Jpn. 74 910 [42] Ingvar L 1978 Int. J. Quantum Chem. 12 33 [43] Sinha D, Mukhopadhyay S, Mukherjee D 1986 Chem. Phys. Lett. 129 369 [44] Blundell S A, Johnson W R, Sapiratein J 1991 Phys. Rev. A 43 3407 [45] Porsev S G, Beloy K, Derevianko A 2010 Phys. Rev. D 82 036008 [46] Sahoo B K, Sur C, Beier T, Das B P, Chaudhuri R K, Mukherjee D 2007 Phys. Rev. A 75 042504 [47] Safronova M S, Safronova U I 2011 Phys. Rev. A 83 052508
#### Cited By
• 图 1 212Fr原子S1/2, P1/2, P3/2, D3/2和D5/2态磁偶极超精细结构常数中的电子关联效应
Figure 1. Electron correlation effects in hyperfine-structure constant A for S1/2, P1/2, P3/2, D3/2 and D5/2 states of 212Fr.
图 2 直接效应ADF、核极化效应ACP、对关联效应APC, 以及相对于CCSD的3种效应的总和AT = ADF + ACP + APC, 针对主量子数n的S, P和D态的结果A的比率 (a) ADF/A; (b) ACP/A; (c) APC/A; (d) AT/A
Figure 2. Ratios of direct effect ADF, core polarization effect ACP, pair correlation effect APC, and the total of the three effects AT = ADF + APC + ACP to the CCSD, results A for S, P and D states against the principal quantum number n: (a) ADF/A; (b) ACP/A; (c) APC/A; (d) AT/A.
• [1] Grant I P 2007 Relativistic Quantum Theory of Atoms and Molecules (New York: Springer) pp533−577 [2] Fischer C F, Brage T, Jönsson P 1997 Computational Atomic Structure: An MCHF Approach (UK: Institute of Physics) pp1−67 [3] Jönsson P, Gaigalas G, Bieroń J, Fishcher C F, Grant I 2013 Computer Physics Communications. 184 2197 [4] Jönsson P, He X, Fishcher C F, Grant I 2007 Computer Physics Communications. 177 597 [5] Dzuba V A, Flambaum V V, Kozlov M G 1996 Phys. Rev. A 54 3948 [6] Dzuba V A, Johnson W R 1998 Phys. Rev. A 57 2459 [7] Angstmann E J, Dzuba V A, Flambaum V V 2004 Phys. Rev. A 70 014102 [8] Dinh T H, Dzuba V A, Flambaum V V, Ginges J S M 2008 Phys. Rev. A 78 054501 [9] Kozlov M G, Porsev S G, Johnson W R 2001 Phys. Rev. A 64 052107 [10] Pal R, Safronova M S, Johnson W R, Derevianko A, Porsev S G 2007 Phys. Rev. A 75 042515 [11] Blundell S A, Johnson W R, Liu Z W, Sapirstein 1989 Phys. Rev. A 40 2233 [12] Eliav E, Vikas M J, Ishikawa Y, Kaldor U 2005 Chem. Phys. 311 163 [13] Mani B K, Angom D 2011 Phys. Rev. A 83 012501 [14] Kallay M, Nataraj H S, Sahoo B K, Das B P, Visscher L 2011 Phys. Rev. A 83 030503 [15] Nandy D K, Singh Y, Sahoo B K 2014 Phys. Rev. A 89 062509 [16] Borschevsky A, Eliav E, Vilkas M J, Ishikawa Y, Kaldor U 2007 Phys. Rev. A 75 042514 [17] Eliav E, Kaldor U, Ishikawa Y 1996 Phys. Rev. A 53 3050 [18] Chaudhuri R K, Chattopadhyay S, Mahapatra U S 2013 J. Phys. Chem. A 117 12616 [19] Tang Y B, Lou B Q, Shi T Y 2017 Phys. Rev. A 96 022513 [20] Tang Y B, Gao N N, Lou B Q, Shi T Y 2018 Phys. Rev. A 98 062511 [21] Byrnes T M R, Dzuba V A, Flambaum F F, Murray D W 1999 Phys. Rev. A 59 3082 [22] Mukherjee D, Sahoo B K, Nataraj H S, Das B P 2009 J. Phys. Chem. A 113 12549 [23] Sakemi Y, Harada K, Hayamizu T, Itoh M, Kawamura H, Liu S, Nataraj H S, Oikawa A, Saito M, Sato T 2011 J. Phys. Conf. Ser. 302 012051 [24] Sahoo B K, Aoki T, Das B P, Sakemi Y 2016 Phys. Rev. A 93 032520 [25] Atutov S N, Calabrese R, Corradi L, Dainelli A, Mauro C D, Khanbekyan A, Mariotti E, Minguzzi P, Moi L, Sanguinetti S, Stancari G, Tomassetti L 2008 Proc. SPIE 7027 70270C [26] Ekström C, Ingelman S, Wannberg G, Skarestad M 1978 Physica Scripta 18 51 [27] Coc A, Thibault C, Touchard F, Duong H T, Juncar P, Liberman S, Pinard J, Lermé J, Vialle J L, Büttgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1985 Phys. Lett. B 163 66 [28] Coc A, Thibault C, Touchard F, Duong H T, Juncar P, Liberman S, Pinard J, Carre M, Lermé J, Vialle J L, Büttgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1987 Nucl. Phys. A 468 1 [29] Arnold E, Borchers W, Duong H T, Juncar P, Lermé J, Lievens P, Neu W, Neugart R, Pellerin M, Pinard J, Vialle J L, Wendt K, the ISOLDE Collaboration 1990 J. Phys. B 23 3511 [30] Arnold E, Borchers W, Carré M, Duong H T, Juncar P, Lermé J, Liberman S, Neu W, Neugart R, Otten W, Pellerin M, Pinard J, Pesnelle A, Vialle J L, Wendt K, the ISOLDE Collaboration 1989 J. Phys. B 22 L391 [31] Bauche J, Duong H T, Juncar P, Liberman S, Pinard J, Coc A, Thibault C, Touchard F, Lermé J, Vialle J L, Büttgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1986 J. Phys. B 19 L593 [32] Grossman J S, Orozco L A, Simsarian J E, Sprouse G D, Zhao W Z 1999 Phys. Rev. Lett. 83 935 [33] Sansonetti J E 2007 J. Phys. Chem. Ref. Data 36 497 [34] Gomez E, Aubin S, Orozco L A, Sprouse G D, Iskrenova-Tchoukova E, Safronova M S 2008 Phys. Rev. Lett. 100 172502 [35] Dzuba V A, Flambaum V V, Sushkov O P 1984 J. Phys. B: At. Mol. Phys. 17 1953 [36] Owusu A, Dougherty R W, Gowri G, Das T P 1997 Phys. Rev. A 56 305 [37] Safronova M S, Johnson W R, Derevianko A 1999 Phys. Rev. A 60 4476 [38] Sahoo B K, Nandy D K, Das B P, Sakemi Y 2015 Phys. Rev. A 91 042507 [39] Duong H T, Juncar P, Liberman S, Mueller A C, Neugart R, Otten E W, Peuse B, Pinard J, Stoke H H, Thibault C, Touchard F, Vialle J L, Wendt K, the ISOLDE Collaboration 1987 Europhys. Lett. 3 175 [40] Barber Z W, Stalnaker J E, Lemke N D, Poli N, Oates C W, Fortier T M, Diddams S A, Hollberg L, Hoyt C W, Taichenachev A V, Yudin V I 2008 Phys. Rev. Lett. 100 103002 [41] Kien F L, Balykin V I, Hakuta K 2005 J. Phys. Soc. Jpn. 74 910 [42] Ingvar L 1978 Int. J. Quantum Chem. 12 33 [43] Sinha D, Mukhopadhyay S, Mukherjee D 1986 Chem. Phys. Lett. 129 369 [44] Blundell S A, Johnson W R, Sapiratein J 1991 Phys. Rev. A 43 3407 [45] Porsev S G, Beloy K, Derevianko A 2010 Phys. Rev. D 82 036008 [46] Sahoo B K, Sur C, Beier T, Das B P, Chaudhuri R K, Mukherjee D 2007 Phys. Rev. A 75 042504 [47] Safronova M S, Safronova U I 2011 Phys. Rev. A 83 052508
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##### Publishing process
• Received Date: 21 January 2019
• Accepted Date: 09 March 2019
• Available Online: 06 June 2019
• Published Online: 01 May 2019
## Ab initio calculation of hyperfine-structure constant A of Fr and evaluation of magnetic dipole moments of Fr isotopes
###### Corresponding author: Tang Yong-Bo, ybtang@whu.edu.cn
• 1. College of Physics and Materials Science, Henan Normal University, Xinxiang 453000, China
• 2. Faculty of Arts and Sciences, Shenzhen Technology University, Shenzhen 518118, China
Abstract: As the heaviest atom in alkali-metal elements, Fr atom has been regarded as a candidate for the search of the permanent electric dipole moment of the electron and of parity-nonconservation effects. Accurate knowledge of Fr atomic properties is of great interest. In this work, we use a relativistic coupled-cluster method to calculate the magnetic dipole hyperfine structure constants for nS (n = 7－12), nP (n = 7－12) and nD (n = 6－11) states of 212Fr. A finite B-spline basis set is used to expand the Dirac radial function, including completely the single and double excitation in correlation calculation. Our results are compared with available theoretical and experimental values. The comparison shows that our method can offer accurate calculation of magnetic dipole hyperfine structure constant. For 7P state the differences between our results and experimental values are within 1%. The magnetic dipole hyperfine structure constants for 12S, nP (n = 9－12) and nD (n = 10－11) states are reported for the first time, which are very useful as benchmarks for experimental measurements and calculations by other theoretical methods of these quantities. In the relativistic coupled-cluster theoretical framework, we study the electron correlation effect on hyperfine-structure constant A for the S, P, and D states of Fr. We observe that the electron correlation effect is very important for hyperfine-structure constant properties. The D state has a considerable correlation effect. At the same time, we also investigate contribution trends of individual electron correlation effects involving direct, core-polarization and pair-correlation ones in S, P, and D Rydberg series. It is found that the dominant contributions for the S1/2, P1/2,3/2 and nD3/2 (n = 7－11) states are to from the direct effect; however, the dominant contributions for the 6D3/2, and nD5/2 (n = 6－11) states are due to the pair-correlation and the core-polarization, respectively. For D5/2 states, there is very strong cancellation among these individual correlation effects. The knowledge of these correlation trends is useful for studying the permanent electric dipole moment and parity-nonconservation effect of Fr in future. Moreover, the magnetic dipole moment ${\mu}$ for each of isotopes 207−213,220−228Fr is determined by combining with experimental values for magnetic dipole hyperfine structure constant of 7P state. For each of isotope 207−213Fr, our magnetic dipole moment ${\mu}$ is perfectly consistent with the experimental value, and our uncertainties are twice smaller than those in the experiments . For each of isotope 220−228Fr, our magnetic dipole moment ${\mu}$ has a larger uncertainty, but is still in agreement with the experimental magnetic dipole moment ${\mu}$.
Reference (47)
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https://www.jobilize.com/physics1/course/14-6-bernoulli-s-equation-fluid-mechanics-by-openstax?qcr=www.quizover.com&page=5 | # 14.6 Bernoulli’s equation (Page 6/8)
Page 6 / 8
David rolled down the window on his car while driving on the freeway. An empty plastic bag on the floor promptly flew out the window. Explain why.
Based on Bernoulli’s equation, what are three forms of energy in a fluid? (Note that these forms are conservative, unlike heat transfer and other dissipative forms not included in Bernoulli’s equation.)
Potential energy due to position, kinetic energy due to velocity, and the work done by a pressure difference.
The old rubber boot shown below has two leaks. To what maximum height can the water squirt from Leak 1? How does the velocity of water emerging from Leak 2 differ from that of Leak 1? Explain your responses in terms of energy.
Water pressure inside a hose nozzle can be less than atmospheric pressure due to the Bernoulli effect. Explain in terms of energy how the water can emerge from the nozzle against the opposing atmospheric pressure.
The water has kinetic energy due to its motion. This energy can be converted into work against the difference in pressure.
## Problems
Verify that pressure has units of energy per unit volume.
$\begin{array}{}\\ \\ \hfill F& =\hfill & pA⇒p=\frac{F}{A},\hfill \\ \hfill \left[p\right]& =\hfill & {\text{N/m}}^{2}=\text{N}·{\text{m/m}}^{3}={\text{J/m}}^{3}=\text{energy/volume}\hfill \end{array}$
Suppose you have a wind speed gauge like the pitot tube shown in [link] . By what factor must wind speed increase to double the value of h in the manometer? Is this independent of the moving fluid and the fluid in the manometer?
If the pressure reading of your pitot tube is 15.0 mm Hg at a speed of 200 km/h, what will it be at 700 km/h at the same altitude?
−135 mm Hg
Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 mph) when the jet stream descends during early spring. Approximately what is the force due to the Bernoulli equation on a roof having an area of $220{\text{m}}^{2}$ ? Typical air density in Boulder is $1.14{\text{kg/m}}^{3}$ , and the corresponding atmospheric pressure is $8.89\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}{\text{N/m}}^{2}$ . (Bernoulli’s principle as stated in the text assumes laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.)
What is the pressure drop due to the Bernoulli Effect as water goes into a 3.00-cm-diameter nozzle from a 9.00-cm-diameter fire hose while carrying a flow of 40.0 L/s? (b) To what maximum height above the nozzle can this water rise? (The actual height will be significantly smaller due to air resistance.)
a. $1.58\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{6}\phantom{\rule{0.2em}{0ex}}{\text{N/m}}^{2}$ ; b. 163 m
(a) Using Bernoulli’s equation, show that the measured fluid speed v for a pitot tube, like the one in [link] (b), is given by $v={\left(\frac{2{\rho }^{\prime }gh}{\rho }\right)}^{1\text{/}2}$ , where h is the height of the manometer fluid, ${\rho }^{\prime }$ is the density of the manometer fluid, $\rho$ is the density of the moving fluid, and g is the acceleration due to gravity. (Note that v is indeed proportional to the square root of h , as stated in the text.) (b) Calculate v for moving air if a mercury manometer’s h is 0.200 m.
A container of water has a cross-sectional area of $A=0.1\phantom{\rule{0.2em}{0ex}}{\text{m}}^{2}$ . A piston sits on top of the water (see the following figure). There is a spout located 0.15 m from the bottom of the tank, open to the atmosphere, and a stream of water exits the spout. The cross sectional area of the spout is ${A}_{\text{s}}=7.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}{\text{m}}^{2}$ . (a) What is the velocity of the water as it leaves the spout? (b) If the opening of the spout is located 1.5 m above the ground, how far from the spout does the water hit the floor? Ignore all friction and dissipative forces.
a. ${v}_{2}=3.28\frac{\text{m}}{\text{s}}$ ;
b. $t=0.55\phantom{\rule{0.2em}{0ex}}\text{s}$
$x=vt=1.81\phantom{\rule{0.2em}{0ex}}\text{m}$
A fluid of a constant density flows through a reduction in a pipe. Find an equation for the change in pressure, in terms of ${v}_{1},{A}_{1},{A}_{2}$ , and the density.
#### Questions & Answers
What is a volt equal to?
list and explain the 3 ways of charging a conductor
conduction convention rubbing
Asdesaw
formula of magnetic field
Integral of a vector
define surface integral of a vector?
Rahat
the number of degree freedom of a rigid body in2-dimantion is:
1
Nathan
A block (A) of weight 5 kN is to be raised by means of a 20° wedge (B) by the application of a horizontal force (P) as shown in Fig.1. The block A is constrained to move vertically by the application of a horizontal force (S). Find the magnitude of the forces F and S, when the coefficient of fricti
Danilo
A body receives impulses of 24Ns and 35Ns inclined 55 degree to each other. calculate the total impulse
A body receives impulses of 24Ns and 35Ns inclined 55 degree to each other. calculate the total impulse
Previous
twenty four square plus thirty-five square minus to multiple thirty five twenty four and equal answer number square Via this equation defined Total Total impulse
Cemal
why simple pendulum do not vibrate indefinitely?
Zirmal
define integral vector
Rahat
what is matar
define surface integral vector?
Rahat
The uniform boom shown below weighs 500 N, and the object hanging from its right end weighs 400 N. The boom is supported by a light cable and by a hinge at the wall. Calculate the tension in the cable and the force on the hinge on the boom. Does the force on the hinge act along the boom?
A 11.0-m boom, AB , of a crane lifting a 3000-kg load is shown below. The center of mass of the boom is at its geometric center, and the mass of the boom is 800 kg. For the position shown, calculate tension T in the cable and the force at the axle A .
Jave
what is the S.I unit of coefficient of viscosity
Derived the formula of Newton's law of universal gravitation Fg=G(M1M2)/R2
hi
Asdesaw
yes
Cemal
a non-uniform boom of a crane 15m long, weighs 2800nts, with its center of gravity at 40% of its lenght from the hingr support. the boom is attached to a hinge at the lower end. rhe boom, which mAKES A 60% ANGLE WITH THE HORIZONTAL IS SUPPORTED BY A HORIZONTAL GUY WIRE AT ITS UPPER END. IF A LOAD OF 5000Nts is hung at the upper end of the boom, find the tension in the guywire and the components of the reaction at the hinge.
what is the centripetal force
Of?
John
centripetal force of attraction that pulls a body that is traversing round the orbit of a circle toward the center of the circle. Fc = MV²/r
Sampson
centripetal force is the force of attraction that pulls a body that is traversing round the orbit of a circle toward the center of the circle. Fc = MV²/r
Sampson
I do believe the formula for centripetal force is F=MA or F=m(v^2/r)
John
I mean the formula is Fc= Mass multiplied by square of velocity all over the Radius of the circle
Sampson
Yes
John
The force is equal to the mass times the velocity squared divided by the radius
John
That's the current chapter I'm on in my engineering physics class
John
Centripetal force is a force of attraction which keeps an object round the orbit towards the center of a circle. Mathematically Fc=mv²/r
In Example, we calculated the final speed of a roller coaster that descended 20 m in height and had an initial speed of 5 m/s downhill. Suppose the roller coaster had had an initial speed of 5 m/s uphill instead, and it coasted uphill, stopped, and then rolled back down to a final point 20 m bel
A steel lift column in a service station is 4 meter long and .2 meter in diameter. Young's modulus for steel is 20 X 1010N/m2. By how much does the column shrink when a 5000- kg truck is on it?
hi
Abdulrahman
mola mass
Abdulrahman
hi
Asdesaw
what exactly is a transverse wave | 2021-01-21 10:38:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 14, "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": 0.6968414783477783, "perplexity": 769.7690403639368}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2021-04/segments/1610703524743.61/warc/CC-MAIN-20210121101406-20210121131406-00232.warc.gz"} |
https://www.physicsforums.com/threads/forces-question-acceleration-of-a-rocket.115300/ | # Forces question - acceleration of a rocket
1. Mar 23, 2006
### QueenFisher
A simple rocket flying towards the moon has a constant thrust from its engine. Will the acceleration remain constant? If not, how will it vary with time?
this is a question i've been given to think about. obviously i don't want any outright answers, can anyone tell me if i'm going in the right direction here?
i think that as it gets further away from the earth, the gravitational attraction between the rocket and the earth becomes less. as the acceleration depends on the resultant force, as it gets further away, the acceleration will increase. at the equilibrium point, will it have zero acceleration?
after the equilibrium point, the gravitational attraction between the rocket and the moon will be increasing as the rocket approaches the moon, so the reultant force will be increasing, so the acceleration will be increasing.
any comments would be great
2. Mar 23, 2006
### Hootenanny
Staff Emeritus
Sounds like a very lucid explanation to me
3. Mar 23, 2006
### Chi Meson
Also consider what happens to the mass of the rocket as it uses its fuel.
4. Mar 23, 2006
### QueenFisher
as in, as it uses more fuel, it's mass will be less, so the gravitational attraction will be less? does that mean it can accelerate at a faster rate?
also, is the physics ok in my first post?
5. Mar 23, 2006
### Hootenanny
Staff Emeritus
You've got it!
Your post sounds good to me
6. Mar 23, 2006
### Chi Meson
the thrust force of the rocket remains constant. The mass decreases. even without consideration of the gravitational force, the acceleration will increase due to Newton's second law, a=F/m.
In your OP, what did you mean by "equilibrium point"? The net zero gravitational point between Earth and Moon? The acceleration won't be zero there (Rocket is still thrusting, or is it?).
7. Mar 23, 2006
### Hootenanny
Staff Emeritus
I think she may have meant on take off. That was my take on it anyway.
8. Mar 28, 2006
### QueenFisher
nah i meant where the earth's and the moon's gravitational forces can be considered to cancel each other out. i think it's at that point that there will be a constant acceleration...as opposed to constantly changing acceleration?
9. Mar 28, 2006
### Chi Meson
(Thread comes back from the dead)
At the earth-moon equilibrium pont, the gravitational force will not contribute to the rocket's acceleration, but...
All the way to, through, and beyond this point the Earth will pull less and less and the Moon will pull more and more. So the acceleration of the rocket will continue to increase as it gets closer to its destination.
The fact that the mass is decreasing the entire time will be a more significant factor to cause an increase in acceleration (as long as the thrust force is constant).
10. Mar 29, 2006
### QueenFisher
does that mean that the rocket's acceleration is increasing at a greater rate when it is losing mass due to fuel consumption that if it were not?
11. Mar 29, 2006
### Hootenanny
Staff Emeritus
Yes, remember Newton's law $F = ma$, so the same force will acclerate an object of a lower mass faster.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook | 2017-05-27 17:57:00 | {"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": 0.5536326766014099, "perplexity": 1001.8049797145425}, "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-2017-22/segments/1495463608984.81/warc/CC-MAIN-20170527171852-20170527191852-00414.warc.gz"} |
https://codeoverflow.wordpress.com/category/programming/ | # Category Archives: Programming
## To sit or 2-SAT
Yeah yeah yeah – lame title. But I just can’t help it 😉
Here we are going to discuss Satisfiability (or SAT) and especially 2-SAT based problems. SAT problems refer to checking if the following kinds of boolean formulae are satisfiable.
$\neg(x \vee \neg z \vee (\neg w \vee x)) \vee (x \wedge \neg y)$
However, since the above is too general to represent with a data-structure, we typically reduce such formulae into the Causal Normal Form (CNF) as shown –
$(\ldots \vee \ldots \vee \ldots \vee \ldots)\wedge \ldots \wedge(\ldots \vee \ldots \vee \ldots \vee \ldots)$
Read here if you want to know how to convert any formula to a CNF. Each sub-formula which is joined by $\wedge$ is called a clause and each variable a literal. We know that the satisfiability of CNF composed of clauses with more than 2 literals is NP Hard. These are represented as 3-SAT, 4-SAT etc. We will only explore the satisfiability of 2-CNF. An example 2-CNF is $(\neg x \vee y) \wedge ( y \vee z) \wedge (x \vee \neg z) \wedge (z \vee \neg y)$
## Solving 2-SAT
2-SAT problems are polynomial time decidable. The problem can be modelled as a graph problem. We will have two vertices for each literal. One vertex represents $x$ and the other $\neg x$.
Now we add an edge from $x$ and $y$ iff we have a clause of the form $(\neg x \vee y)$
Hence for every 2-SAT clause, we will have two edges one for $(x \vee y)$ and another for $(y \vee x)$. Since we require a clause of the form $(\neg x \vee y)$ to create an edge, we will change $(x \vee y)$ to $(\neg (\neg x) \vee y)$ and draw an edge from $\neg x$ to $y$ and another edge $\neg y$ to $x$.
### Why
The edges represent a ‘If Then’ relationship. A condition like $(x \vee y)$ can be re-written as –
if not x then y
else if NOT Y then X
This is precisely what we represent when we add an edge. We add an edge for each of the IF conditions.
Taking $(\neg x \vee y) \wedge ( y \vee z) \wedge (x \vee \neg z) \wedge (z \vee \neg y)$ as an example, here is how the edges can be drawn out.
To figure out if the given 2-CNF is satisfiable, we just need to check if there is a path from $\neg x$ to $x$ (similarly for y and z). You can do this via a DFS or a BFS. A faster way is to check for component Components. If $\neg x$ to $x$ (similarly for y and z) lie in the same component, it isn’t satisfiable.
One other way (and quicker to code) is to use Floyd-Warshall. It is quick to write and easy to remember.
Here is a problem for practice: SRM 464 – Div 1 – 550.
The trick is to create a 2-CNF where we add a clause everytime we cannot add a pair of vertices (A, B). The clause will take the form – NOT (A AND B) or in a CNF form – (NOT A OR NOT B).
I hope you found this useful!
## Greatest Hits – Side A
I didn’t realize that almost a year has gone by and I haven’t updated my blog. With a lot of free time on my hand now, its time to conjure up another post! I wanted to write this one for some time now but I just haven’t found the strength to punch the keys (and trust me, it takes quite a lot of effort).
Like I mentioned, I have a lot of free time now and I decided to go back to doing something I always loved – solving problems on Topcoder. So I started the Arena, logged in (I was surprised I could still remember my password) and went straight to SRM 411 Div 2. It was a problem set I had already solved and I wanted my first practice contest in almost 10 months to be easy. Well – it wasn’t! I thought I coded the 250 right but the tests revealed that I missed the easiest edge cases. It took me a lot of thinking and a little searching to finally figure out how to do the 600 and the 900 was a bit easy on the mind but impossible to code! I compared this against my performance the last time around and the contest was like that between me and Petr on a live SRM!
I am not going to share anything related to this experience though. Just to encourage myself, I am going to look into eternal abyss (actually my memory – things fall in rather quick but never quite make it back when I need it!) and share some problems (in a never ending Saga) that I was able to solve but which many of my more established peers could not (or so I would like to think), during a live contest!
## TCO 2012 Round 2A – 300:
Don’t be fooled just because its a 300 point problem. This problem saw over 800 submission but only 38% passed! Also, this is Round 2, so there are hardly any rookies left and I remember a large number of red coders failing the system test. Maybe it was a 300 point problem and people took it lightly. But I knew, I could only solve this one, since the 450 and 1000 were bit on the harder side for me!
The only reason I was able to solve this problem was that I had just learnt how to solve problems involving bi-partite matching (just the easy ones though). And when you have learnt a new technique, suddenly every problem fits the bill and you can see a bipartite graph in every problem. Fortunately, it was true for this problem.
First thing to notice was that if it was not a bipartite graph, there was no solution possible as the system would be inconsistent. Also, if there was no matching possible on this graph for any vertex, then again the system would be inconsistent (Notice that if one switch does not have an associated lamp, then either one switch is connected to two lamps or there is a lamp without a switch). However, this turned out to be the easy part!
I tried a lot of different simple techniques to figure out the number of experiments I would need but everything had one flaw or another. It was in the dying minutes of the contest that I jumped up with ‘Eureka’! What I realized was that lets say there is a set of switches A which can be mapped to another set of lamps B (note: n(A) always equals n(B)). Then the number of experiments needed is log(n(A)).
Why? Lets say the system had 4 switches and lamps. Then if I switch on 2 and switch off 2, in one experiment I would have identified 2 switches and their respective lamps. Now I have two groups of 2 sets each. Notice that they are independent of each other (experimenting on one does not affect the result of another – which means that in one experiment I can set the states of switches and figure everything out!). If I repeat this again then in 2 experiments I would have the answer for these 4 sets of switches and lamps. The property that experiments are independent meant that if you identified all such groups and figured out what is the largest number of experiments needed to solve any of the groups, that would be your final answer.
## Google Code Jam 2011 Round 2 C. Expensive Dinner
This problem is a source of both happiness and sorrow. Happiness – because I figured out how to solve it; sorrow- because I got lazy in implementing it and the hard cases broke this code. If I hadn’t been lazy, I would have qualified for Round 3 which would have been a moment of great pride. I did end up in the top 1000 for which they sent me a nice GCJ t-shirt but alas – the wrong size!
When is the waiter called: everytime the LCM of first K numbers is not equal to the LCM of first K-1 numbers. This is the most important observation.
The problem statement asks us to find two permutations of first N numbers A and B such that A results in the smallest number of waiter calls and B in the largest. Just by looking at the test cases you can figure out that the largest way is to keep the numbers in sorted order. But what is this value? It turns out this is the sum of the largest power of prime number such that it is less than equal N.
How? Consider first 10 numbers. When 1 comes in, he will call. So will 2 and so will 3. At this point the LCM is 6. But when 4 comes in, he will need to multiply the LCM by 2 so even he will have to call. So will 5, but when 6 comes in, he does not have to since 2 and 3 have already taken care of his needs! 7 will again call and so will 8 (since we need another factor of 2 to satisfy the condition) and 9 (factor of 3 this time). But when 10 comes in, he will not need it. So the total calls here is 8 – which is 1 (1^1) + 3 (for 2^3)) + 2 ( for 3^2) + 1 ( for 5^1) + 1 ( for 7^1) = 8.
What is the smallest such possibility? Simple, if the largest power of a prime, comes first he will ensure that none of the other factors need to be called. In essence, the number of prime numbers less than equals to N. But instead of doing these seperately, you can do this in one loop by reducing by 1, the value you find in the above explanation.
Just to point out where I blundered: When calculating the largest power I used log function. While mathematically there is nothing wrong with it, in practice log has an error associated with it which is greatly magnified with larger numbers. Not that I did not know this when I was implementing it, just that I got bloody lazy!
Any hoot, we all learn from mistakes and so did I!
Do try solving these problems on your own and let me know how that went!
I almost forgot – to my ardent fans – A Very Happy New Year! That’s it for now!
## Mystic Regex
You are a Dev and have been so for more than a year now ( or maybe more or less). Your editor of choice has always been emacs/vim. Your mode of operation starts with a sip of ‘darker than coal’ coffee and ends with making your keyboard – your pillow. You are an expert at typing and programming but the one weapon you have been missing from your arsenal is writing/understanding something like this –
$out =~ s/(^[a-zA-Z0-9]+)\.([a-z]+)/<a href="\"\1\.\2"">\1<\/A>/g;</a> What does it do? I hope you will be able to tell me after reading through this. This post is to add to your arsenal – an Intercontinental ballistic missile of programming or what others call – Regex! ## The Basics ### Literals This is just plain text. If I need to match cat in Bell the cat, I would just use cat as a regex! ### Regex Special Characters The following characters – []{}().+*\|^$ are native to regex. If you need to use them as literals you need to escape them by preceding it with \, for eg – \{. Now what do these do –
##### Examples
[] Character class [abcd] – Anything that is either one of a,b,c or d.
[^abcd] Match anything which is neither of a,b,c or d
. Dot character class Matches any single character except \n
* Star Matches any character class preceding it; of any length including 0 length. So, if you use .*cat, it will match pussycat and also cat
+ Plus Matches anything of length >=1. So, if you use .+cat, it will match pussycat and but not cat
| Alternation This works similar to a ‘or’ in a regex. If you want to match dog in the string My dogs name is Tiger, but also match cat in My cats name is puff. These are almost similar string and so your regex would be My cats|dogs name is .*
{} Limited Repitition Let say you want to ensure the number of times a pattern is to be matched. Or even better, you know the minimum and the maximum. In such a case you would use {}. For eg – [0-9]{2,5} means match it to any 2 digit, 3digit, 4 digit or 5 digit number ( with leading zeros). If you want only 2 digit numbers – [0-9]{2}, or if you want atleast 2 digit numbers [0-9]{2,} (note the comma ,)
$End line Anchor This is a regex end line anchor. If your regex ends with this character, you are trying to say that ‘The pattern must occur at end of line’. For eg, If you want to ensure that the match ends with your pattern like I am What I am, if you search using am, it will match both but if you search am$, it matches the last one only.
^ Start line anchor This is a regex start line anchor. If your regex starts with this character, you are trying to say that ‘The pattern must occur at the start of line’. For eg, If you want to ensure that the match starts with your pattern like I am What I am, if you search using I, it will match both but if you search ^I, it matches the first one only.
### Optional Items and Regex Greediness
Suppose you want to use a regex to match an HTML tag, assuming your input is a well formed HTML file.
You would think that <.+> will solve easily. But be surprised when they test it on a string like This is my <TAG>first</TAG> test. You might expect the regex to match <TAG> and when continuing after that match, </TAG>.
But it does not. The regex will match <TAG>first</TAG>; not what we wanted. The reason is that the plus is greedy. That is, the plus causes the regex engine to repeat the preceding token as often as possible. Only if that causes the entire regex to fail, will the regex engine backtrack. That is, it will go back to the plus, make it give up the last iteration, and proceed with the remainder of the regex. To avoid such pitfalls, use ?. You can see this in the above regex.
It can also be used like optionals. If you want to match February but also Feb, you can use Feb(ruary)?
## Performance of Regex
In one word – Better. The regex engine will perform better than anything you or I can write to match a pattern, unless you write your own regex engine. And even in that case, the standard Regex will beat you to it! Also, the more simpler your regex, the faster it run (Obviously). Using back-referencing will slow down your regex. A very simple example is grep. This utility only allows simple regex characters and tends to be faster than egrep which allows much more advanced stuff but at a price!
Now, after going through all this, I hope you can answer what the first regex I introduced you to, did! Its in perl and s/<PATTERN>/<REPLACE>/g replaces <PATTERN> with <REPLACE>, globally.
I hope you are able to now add regex to your programming arsenal and hope this has helped you understand it. For more info, you can always google 😉
## Linear Recurrences
How often has it happened to you in a programming contest (or elsewhere) that you thought it was impossible to solve it faster than O(N) and yet the limits imposed suggest that it has to be done faster. Well, if not all, atleast a majority of them have a solution based on the idea of linear recurrences. In this blog post, I intend to help you out on this !!
In this post, we are going to do a – Solve and Learn strategy ; You will be given a question and I will show you how to apply the concepts on them.
### TYPE 1 :: The Simplest :
If a post mentions recurrences, then it has to mention Fibonacci (Gosh, if only I had a penny for every mention of Fibo in tutorials. )
The recurrence is of type : F(n) = F(n-1) + F(n-2).
I am pretty sure you know to code the linear version of it which runs in O(N) but can you do it in O(log N) ? If you throw google to good use, you will come up with a solution which says there is a Matrix M which when raised to power N, will give you the N-th fibonacci number. And since you can always exponentiate in logN time, you have your answer. But to those, who wondered if this Matrix is magical- read on!
Firstly the answer- No; Its not magical. How. Lets do a little Algebra (yumm… My favourite! )
$F(n)=F(n-1)+F(n-2)\\ \\ F(n+1) =F(n)+F(n-1)\\ \\ F(n+2)=F(n+1)+F(n)$
Obviously enough, the value of N-th term, depends on two previous terms (or states). This implies that all values depend on just the first two states in the sequence. As you can see here –
$\begin{pmatrix}F(n+2)\\ F(n+1)\end{pmatrix}=\begin{pmatrix}1&1\\ 1&0\\ \end{pmatrix}\times\begin{pmatrix}F(n+1)\\ F(n)\end{pmatrix}\\ \\ and\\ \\ \begin{pmatrix}F(n+1)\\ F(n)\end{pmatrix}=\begin{pmatrix}1&1\\ 1&0\\ \end{pmatrix} \times \begin{pmatrix}F(n)\\ F(n-1)\end{pmatrix} \\ \\ Hence \\ \\ \begin{pmatrix}F(n+2)\\ F(n+1)\end{pmatrix}=\begin{pmatrix}1&1\\ 1&0\\ \end{pmatrix} ^2 \times \begin{pmatrix}F(n)\\ F(n-1)\end{pmatrix} \\ \\ \begin{pmatrix}F(n+2)\\ F(n+1)\end{pmatrix}=\begin{pmatrix}1&1\\ 1&0\\ \end{pmatrix}^3 \times \begin{pmatrix}F(n-1)\\ F(n-2)\end{pmatrix}$
Hence in General, we may write ::
$\begin{pmatrix}F(n)\\ F(n-1)\end{pmatrix}=\begin{pmatrix}1&1\\ 1&0\\ \end{pmatrix}^{n-1} \times \begin{pmatrix}1\\ 0\end{pmatrix}$
I hope that has helped you in understanding how to frame such equations and solving it with a matrix.
### TYPE 2 : Simplest ++
Now that we have a basic understanding. Try the following recurrence :
F(n) = F(n-1) + F(n-2) + F(n-3).
It is the same as the previous recurrence but with an additional state. I won’t go on explaining the hows (again!). I am going to share the solution.
$\begin{pmatrix}F(n)\\ F(n-1)\\ F(n-2) \end{pmatrix}=\begin{pmatrix}1&1&1\\ 1&0&0\\ 0&1&0 \end{pmatrix}^{n-2} \times \begin{pmatrix}2\\ 1\\ 1\end{pmatrix}$
### TYPE 3: Simplest << 1
Consider the following scenario ::
$G(n) = a . G(n-1) + b . G(n-2) + c . H(n)\\ \\ and \\ \\ H(n)= d . H(n-1) + e . H(n-2)$
This one is a lot trickier. First thing to notice is that we will need 4 states in a matrix to fully define the next state. The reason for using 4 and not 3 is that H(n) depends on 2 states and thus we need 2 states (and not just 1) to represent it.
If you carefully write down the LHS matrix and the RHS matrix, then we can frame the solution as . . .
$\begin{pmatrix}G(n)\\ G(n-1)\\ H(n+1)\\ H(n) \end{pmatrix}=\begin{pmatrix}a&b&c&0\\ 1&0&0&0\\ 0&0&d&e\\ 0&0&1&0 \end{pmatrix}^{n-1} \times \begin{pmatrix}G(1)\\ G(0)\\ H(2)\\ H(1)\end{pmatrix}$
### TYPE 4 : Ohhh !
The final hurdle can come in the name of a constant. If we add a constant C to the above recurrence we get –
$G(n) = a . G(n-1) + b . G(n-2) + c . H(n) + C\\ \\ and \\ \\ H(n)= d . H(n-1) + e . H(n-2)$
But to tell you the truth, its not that difficult if your concepts are clean. Now there is another additional state to hold the information about C. The solution will look like –
$\begin{pmatrix}G(n)\\ G(n-1)\\ H(n+1)\\ H(n)\\ C \end{pmatrix}=\begin{pmatrix}a&b&c&0&1\\ 1&0&0&0&0\\ 0&0&d&e&0\\ 0&0&1&0&0\\ 0&0&0&0&1 \end{pmatrix}^{n-1} \times \begin{pmatrix}G(1)\\ G(0)\\ H(2)\\ H(1)\\ C\end{pmatrix}$
I hope this post lived up to your expectations and I hope it was worth the wait :P. Please feel free to post comments/corrections/improvements to this post to make it really useful.
What is a Tree :
Tree is a heirarchial arrangement of nodes. From the literal meaning of Tree we know that it has root, branches, fruits and leaves. Well, in Algorithms also, we have a root – which is the origin of the tree. We have branches which connect to smaller trees and we have leaves, which do not have outgoing branches. And as far as the fruits are concern – depending on the complexity of operations that can be perform, we may label the fruits as sweet and sour !
The simplest tree would be a node which branches to exactly one other node, or in other words – a singly Link List. If every node branches to its child and also to its parent, we have a doubly link list. But in this post, we are not going to discuss these.
The next level of trees would be – where a single node may branch out to a maximum of two other nodes. Such a tree is call a binary tree. Binary trees are some of the most widely us datastructures in computers and we are going to discuss them in a series of posts. So lets begin.
One of the most important things to do is : Create a tree.
So what is it that we ne to create one. We will ne to represent the nodes and the links between nodes. And since we ne to connect to a maximum of two nodes, we will have two branches. We shall call these branches – left and right. Also, it will store some data in it. Our tree will be us to just store integers.
We will use the following structure to create it. FYI, everything here is in C++ and not C.
struct NODE {
int data;
NODE *left;
NODE *right;
};
Now whenever we ne to insert a node, we ne to make sure that there is a fix position at which the node will be insert given its value (Data in the node). Let us follow a simple strategy.
We will insert a node to the left of a ‘Parent node’, if its value is lesser than the value of the Parent, otherwise to the right. The binary trees which use such a strategy are call Binary Search Trees.
The obvious advantage of such a strategy is that we can search for elements in the tree in O(h) time, where h is the height of the tree. Do note that, in general, h does not equal logN. If we could actually have a tree where the height is inde logN, we would call such trees as Balanc Binary Search Trees.
Alright then, lets get our hands dirty with a code that will create the tree for us. The function insert takes as input the root of the tree and the value to be insert and returns the node which contains the data.
NODE * insert(NODE *root, int data) {
if(root==NULL) {
root=(NODE*)malloc(sizeof(NODE));
root->left=root->right=NULL;
root->data=data;
return root;
}
else {
while(root!=NULL) {
if(root->data>data) {
if(root->left!=NULL) root=root->left;
else break;
}
else {
if(root->right!=NULL) root=root->right;
else break;
}
}
NODE *new_node=new NODE;
new_node->data=data;
new_node->left=new_node->right=NULL;
if(root->data > data) {
root->left=new_node;
}
else root->right=new_node;
return new_node;
}
}
Another very useful and important property when using the above strategy is, that the INORDER traversal is sort!
Lets backup a bit. What are Traversals. It is like visiting many homes using the roads which connect them. Only that, the homes here are the NODEs and the roads are the links between each node.
There are many traversals but the three us very often are – PreOrder, InOrder and PostOrder.
In PreOrder, you print the current node and then visit its left and then its right children, recursively.
In InOrder, you first visit the left child, once you have return, you print the current value and then visit the right child.
In PostOrder, you visit both your children and then print the current value.
Here is the code snippet for the InOrder traversal (recursive version).
void inorder(NODE *root) {
if(root!=NULL) {
inorder(root->left);
printf("%d ",root->data);
inorder(root->right);
}
}
You could write an iterative version, where you would simulate the operations in a system stack, using your own stack. The obvious advantage is that you would be saving space (since you would now push as many values as the system would for a function call.)
However, there exists a really beautiful iterative version which does not use a stack. It assumes that two pointers can be check for equality. It is bas on thread trees and it was first written in 1979 by Morris and hence the name!
How does it work.
The only reason we ne a stack is so that we can do the “RETURN” from child nodes to parent nodes. This return is ne only from one node really. Consider a 5 node tree.
20
/ \
/ \
10 30
/ \
/ \
5 15
Now our stack would work like this.
1. Push 20. 2. Push 10. 3. Push 5. 4. Pop 5 and print 5. 5. Pop 10 and print 10. 6. Push 15. 7. Pop 15 and print 15. 8. Pop 20 and print 20. 9. Push 30. 10. Pop 30 and print 30.
If I write a non-resursive and non-stack version, my greatest headache would be to go to 20 from 15 (statements 7-8). So we need to link 15 and 20 so that we can go to 20 without problems. But that would mean that we are modifying the tree. Well, we could do it in two steps. First we link the two and in the next step once we have printed 20, we can destroy that link.
20
/ | \
/ | \
9 | 30
/ \ |
/ \|
5 15
And thus we have the following –
1. SET current as root.
2. if current is not null do –
2.a. if current has no left child, print current , set current as right child and REPEAT 2.
2.b. else goto the rightmost child of current’s left child.
2.b.a. If this is NULL, then link it to current and set current as left child of current and REPEAT 2.
2.b.b. else set the right child to NULL. Print Current. Set current as Current’s right child . REPEAT 2.
As a pseudocode we may write it as –
Morris-InOrder ( root )
current = root
while current != NULL do
if LEFT(current) == NULL then
print current
current=RIGHT(current)
else do
// set pre to left child of current
pre=LEFT(current)
// find rightmost child of the left child of current
while (RIGHT(pre) != NULL and RIGHT(pre) != current) do
pre=RIGHT(pre)
//if thus is null, link it to current and set current's left as current
if RIGHT(pre) == NULL then
RIGHT(pre)=current
current=LEFT(current)
// else unlink it, print current and set right child of current as current
else do
RIGHT(pre)=NULL
print current
current=RIGHT(current)
Looks nice aah. Let’s just write the code.
void MorrisInorder(NODE *root) {
NODE* current,*pre;
current=root;
while(current!=NULL) {
if(current->left==NULL) {
printf("%d ",current->data);
current=current->right;
}
else {
pre=current->left;
while(pre->right != NULL && pre->right !=current)
pre=pre->right;
if(pre->right==NULL) {
pre->right=current;
current=current->left;
}
else {
pre->right=NULL;
printf("%d ",current->data);
current=current->right;
}
}
}
}
Now, lets talk about the fruits!
Insert happens in O(h) time. Each of the traversals (recursive and iterative versions using stack) are in O(N) time and O(N) space (system stack or normal stack).
Morris Inorder runs in O(NlogN) time and O(1) space. One could say that it is slower which is true, but the fact that it does not use additional space can be a huge boost in situations where you are low on system memory!
The entire code is available on :PASTEBIN
I hope you gathered all that info well! I will post a Tree 102, in which I shall discuss the delete operation and talk more about balanced trees!
## Thou art Debugger
I have been a big fan of Visual Studio. It is an amazing IDE. It can be used to develop anything from a CLI to GUI and from Mobile Apps to Web Apps. But I have never really tried all that and that isn’t the reason why I liked it so much. As a starter, it can be very difficult to discover a bug in your program. You safely assume you have written what you wanted to write. But in reality that happens very rarely. Often, we miss a little small thing here and there and that creates havoc. The one thing that caught my eye as a young programmer was the Debugging features of VS. Gosh, its amazing.
Firstly, we will need to learn a bit about CPU registers. We will concentrate on the x86 architecture. If you have ever written code in x86 Assembly, then you would have heard about them. But let me just walk you through the functions of these registers.
CPU registers are just memory that the CPU can use to store data. But, it is the fastest accessible memory for the CPU. Ideally you would like to keep everything in it. Unfortunately, it is damn expensive and so a trade-off is done on the pricing and performance. Though there are 32 registers, the most commonly used ones(9 to be precise) for the purpose of executing instuctions are –
EAX : Accumulator : used to store. Used during add/sub/multiplication. Mult/Div cannot be done elsewehere except in EAX. Also used to store return values.
EDX : storage register Used in conjuction to EAX. It is like a side-kick.
ECX: count register: Used in looping. However, there is an interesting thing about it. It always counts downwards and not upwards.
for ex:
int a=100;
int b=0;
while(b<a)b++;
Then ECX will begin from 100 and not 0 and move to 99,98 … !
ESI : source index for data operations and holds location of input stream.(READING)
EDI : points to location where the result is stored of a data operation destination index. (WRITING)
ESP : Stack pointer
EBP: Base pointer
EBX: not designed for anything specific . can be used for extra storage.
EIP : Current instruction being executed.
Now that we understand this, lets see how a debugger works!
Depending on the type of breakpoint, one of the following happens :
Soft Breakpoint :
Let us assume we need to execute this instruction :
mov %eax,%ebx
And this is at location 0x44332211, and the 2 byte opcode for this is 0x8BC3. Hence what we will see is :
0x44332211 0x8BC3 mov %eax,%ebx
Now when we create a soft breakpoint at this instruction what the debugger does is – it takes the first byte (8B in this case) and replaces it with 0xCC.
So now, the opcode actually looks like – 0xCCC3. This is the opcode for INT 3 interrupt. INT 3 is used to halt the execution. Now when the CPU is happily executing everything till this one and suddenly sees the 0xCC it knows it has to stop(it may not really like it but – Rules are rules 😉 ). It then raises the INT 3 interrupt which the debugger will trap. It then checks the EIP register and sees if this intruction is actually in its list of breakpoints (just in case the program itself has a INT 3 inside it). If it is present, it will replace the first byte with the correct value (8B in this case) and then program execution can continue.
There are two kinds of soft breakpoint: One shot – Where the breakpoint occurs only once and after that the debugger removes the instruction from its list; and Persistent – where it keeps recurring. The debugger would replace the first byte with the correct byte but when execution is resumed, it will once again replace it with 0xCC and not remove it from its list.
Soft breakpoints have one caveat though.When we make a soft breakpoint it changes the software/program’s CRC (cyclic redundancy check) check sum. A CRC is a type of function which tells whether there has been any change or not. It is like a hash function and can be applied to memory/files etc.,. It compares against a known value and if the checksum fails, the CRC fails. This can be used to prevent Soft breakpoints like in malwares where if the CRC fails, the malware kills itself. To get around this we use Hardware breakpoints!
Hardware Breakpoints –
Though hardware breakpoints cannot be applied at everything, it is still very useful. Recall, the I said there are 32 registers. I introduced 9 in the previous section, let me add another 8 to that list. These eight – DR0 to DR7 are debug registers. DR0 – DR3 store the address of the breakpoints and thus we can have only 4 hardware breakpoints (Ouch!). DR4 and DR5 are reserved. DR6 is the status register which determines the type of debugging event once it is hit and DR7 is ON/OFF switch for hardware breakpoints and also stores different conditions like –
1. Break when an instruction is executed at a particular address.
2. Break when data is written to an address.
3. Break on reads or writes to an address but not execution.
As you can guess, you can only break 4 bytes of memory with hardware breakpoints but nonetheless they are very useful tools for reverse engineers. For creating hardware breakpoints, you can use hbreak command inside gdb.( More info ).
Memory breakpoints.
These arent really breakpoints. It is more like setting permissions on a section of memory or on an entire page, something similar to file permissions. When we set a particular permission, if any instruction tries to do something outside of these permissions on that memory, then a break occurs. The permissions available are – Page Execution (enables exec but throws access violation on read/write) , Page Read ( allows only read), Page Write (only write), and Guard Page (one time exception after which the page returns to its original status). Like in files, we can use combination of these to set permissions. In gdb, to break on write use watch, rwatch will break on read and awatch will break on read/write.
I hope you now have a better understanding of how debuggers work. You may feel this as being unnecessary info, but trust me it helps to know how things work for better usage.
I would like to thank all Source of knowledge – the World Wide Web. Please free to send me corrections/suggestions/criticism.
## Quick-Short
Hi,
The cheapest, fastest and most reliable components of a computer system are those that aren’t there.
-Gordon Bell
I am back with a new post. And this time its about one of my favourite algorithms (Yes, as a geek I am allowed to have fav algos 😛 ) – Quick Sort ! Whats so special about it – It is amazingly simple and very clearly complex. Quick sort can be implemented as horribly as follows –
void quicksort(int *x,int l,int u)
{
int i,j,t;
if(l>=u)return;
t=x[l];
i=l;
j=u+1;
for(;;)
{
do i++; while(i<=u && x[i]<t);
do j--;while(x[j]>t );
if(i>j)break;
swap(x[i],x[j]);
}
swap(x[l],x[j]);
quicksort(x,l,j-1);
quicksort(x,j+1,u);
}
or as simple as
void quicksort(int *x,int l,int u)
{
int i,j,t;
if(l>=u)return;
t=x[l];
i=l;
for(j=l+1;j<=u;j++)
{
if(x[j]<x[l])
swap(x[++i],x[j]);
}
swap(x[l],x[i]);
quicksort(x,l,i-1);
quicksort(x,i+1,u);
}
But in this post, we are not going to see its looks but rather we are going to explore its performance (real beauty).
Anyone who attended a class on ‘Algorithms and Data-structures’ or had the pleasure of learning it on your own (like me) knows that Quick Sort runs in O(nlogn) expected average time. Its a known fact that for any given quick-sort (standard implementation) there exists a case which will ensure that it runs in O(n^2) time (even for the purely randomized version. If you don’t know about it, feel free to comment at the bottom and I will let the secret out 😛 ) .
But what if I wanted to find the average expected time. I know there exists a mathematical derivation using Expectation and it shows that it is nlogn but what if I wanted to find out the exact number of comparisons made on the average. We are going to make an attempt on that.
Before we do that, we should take a minute to observe that there are two variables on which quicksort’s performance can be measured. One is the Number of SWAPS made and the second is the Number of Comparisons. We must select the variable which has the most impact in reducing its complexity. In this post I am using Comparisons over Swaps, Why? Simple because, the impact of a comparison is more than the impact of a Swap. How to prove it? Simple- Write a piece of CODE! (I will post the code a little later)
We will just add a new counter before the comparison inside the loop and when the sort exits, we will have the exact count of the comparisons made.
void quicksort(int *x,int l,int u)
{
int i,j,t;
if(l>=u)return;
t=x[l];
i=l;
for(j=l+1;j<=u;j++)
{
cmp++;
if(x[j]<x[l])
swap(x[++i],x[j]);
}
swap(x[l],x[i]);
quicksort(x,l,i-1);
quicksort(x,i+1,u);
}
A very basic optimization would be to add it outside the loop as shown.
void quicksort(int *x,int l,int u)
{
int i,j,t;
if(l>=u)return;
t=x[l];
i=l;
cmp+=u-l;
for(j=l+1;j<=u;j++)
{
if(x[j]<x[l])
swap(x[++i],x[j]);
}
swap(x[l],x[i]);
quicksort(x,l,i-1);
quicksort(x,i+1,u);
}
It is still slow and I want to speed it up. Is there any way I can get rid of that for loop. Actually, YES. I can remove it clearly. I know you are throwing away your thinking hat saying that -” WHAT WILL YOU SORT ? AND IF YOU AREN’T SORTING ANYTHING WHATS THE POINT ?” Well, you are right. I am not interested in sorting. I am only interested in estimating the time it will take to run on average. To do this, I don’t need to sort any array, I just need to simulate it and to simulate it quicker, I will remove the for loop and everything associated with it.
Now our simulator code looks like this. I have also removed the two variables and replaced it with the length I want to partition.
int quicksort_count(int L)
{
int m;
if(n<=1)return 0;
m=l+(rand()%L);
return n-1 + quicksort_count(m-1) + quicksort_count(L-m-1);
}
But, if we want to find the true average, we need to do this for every possible m that may be chosen. Hence we can modify our code to.
double quicksort_avg(int L)
{
if(n<=0)return 0;
double sum=0.0;
for(int m=1;m<=L;m++)
sum+=L-1 + quicksort_avg(m-1) + quicksort_avg(L-m);
return sum/L;
}
We can improve its runtime by using Dynamic Programming. We could use the Top-Down approach where we store the values that were previously computed in an array and look it up or we could do Bottom-Up and compute the values in increasing order.
double quicksort_avg(int L)
{
double dp[L+5];//5 is just taken for safety !
dp[0]=0;
for(int n=1;n<=L;n++)
{
double sum=0.0;
for(int m=1;m<=n;m++)
sum+=n-1 + dp[m-1] + dp[n-m];
dp[n]=sum/n;
}
return dp[L];
}
I am still not happy. It is using O(N^2) time which I obviously do not like. It may seem like its impossible to reduce it but in reality that is not the case. For example, if n=5, then the look ups would be :
0 and 5-1
1 and 5-2
2 and 5-3
3 and 5-4
4 and 5-5.
As you can see, I am looking up the same elements twice !
So, I could remove the two lookups and instead multiply it by 2. Also, I can remove the n-1 added every time in the loop (n times to be accurate) and then I divide it by n, leaving me n-1. With those changes, I can convert it to O(N) time.
double quicksort_avg(int L)
{
double dp[L+5],sum=0;
dp[0]=0;
for(int n=1;n<=L;n++)
{
sum+=2*dp[n-1];
dp[n]=n-1 + sum/n;
}
return dp[L];
}
Even now, I am not happy. ( Its impossible to make me happy, right ?). We can actually improve on the O(N) space, since we are only looking at the previous state. Now, our final piece looks like :
double quicksort_avg(int L)
{
double dp,sum=0;
dp=0;
for(int n=1;n<=L;n++)
{
sum+=2*dp;
dp=n-1 + sum/n;
}
return dp;
}
Beautiful isn’t it. In one for-loop using 2 variables, I can actually find out the average comparions made by quicksort for a given length of numbers.
What I (rather Jon Bentley) is trying to show is that – sometimes and almost always we can add functionality by actually removing code! Though this was a pretty small example (and a beautiful example), it seems to explain the idea pretty well.
Do watch the video.
The original video: Three Beautiful QuickSorts | 2017-06-28 03:39:28 | {"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": 32, "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": 0.42360880970954895, "perplexity": 994.4572452884186}, "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-2017-26/segments/1498128322320.8/warc/CC-MAIN-20170628032529-20170628052529-00229.warc.gz"} |
http://physics.stackexchange.com/questions/7922/in-quantum-mechanics-why-do-the-probabilities-of-the-possible-outcomes-of-a-mea/8004 | # In quantum mechanics, why do the probabilities of the possible outcomes of a measurement add up to 1?
The question assumes the standard formalism with projector-valued measures rather than POVMs. Suppose a measurement has two possible outcomes, and the corresponding probabilities are greater than 0 and less than 1. Neither outcome is therefore certain. Then why is it certain that either outcome is obtained (as it seems, if the probabilities add up to 1)?
Added after four answers: All the answers provided so far elaborate on the comment by @Vladimir: "It is not a 'quantum mechanical' feature but a consequence of probability definition." @Lubos and @Mark cast the question into a quantum-mechanical form, e.g., why do the absolute squares of the amplitudes associated with the possible outcomes of a measurement add up to 1? They also explain why the sum remains equal to 1. (However, for a decaying particle the probability of finding it decreases, while the probability of finding its decay products increases. So the "conservation of probability" has something to do with the proper conservation laws.) @David makes it clearest why these answers are insufficient.
Keep in mind that no actual measurement is perfect. While theorists may ignore this, experimenters know well enough that in many runs of a given experiment no outcome is obtained. (The efficiency of many real-world detectors is rather low.) This means that in order to make the probabilities add up to 1, one discards (does not consider) all those experiments in which no outcome is obtained.
So let me follow up with another question.
-
It is not a "quantum mechanical" feature but a consequence of probability definition. – Vladimir Kalitvianski Apr 2 '11 at 9:12
@Koantum Since you have a new question - or have clarified the old one to the extent it appears new - you might want to start a new thread so that the answers stay relevant to the question at hand. – Mark Eichenlaub Apr 3 '11 at 3:15
What could you possibly mean by "no outcome"? The experimenter is transported backwards in time and the experiment never happened? I think this is what Vladimir was alluding to above. At any rate try to define "no outcome" – sigoldberg1 Apr 3 '11 at 4:00
@sigoldberg1, a successful measurement has an outcome. An attempted measurement may or may not be successful. An unsuccessful measurement has no outcome. – Koantum Apr 3 '11 at 4:58
@Mark, as you suggested, I have posted the follow-up question separately. – Koantum Apr 3 '11 at 5:08
show 1 more comment
Suppose a measurement has two possible outcomes
That's why. One of the possible outcomes has to occur - it's the definition of "possible outcomes." Probability theory takes this as an axiom, the axiom of unit measure according to Wikipedia.
Note that we often have to normalize the probabilities so that they add up to 1.
-
Suppose we have a quantum state that is normalized at some time. Then it will remain normalized if the Hamiltonian is Hermitian.
$$\frac{\partial}{\partial t}\langle \Psi \mid \Psi \rangle = \left(\frac{\partial}{\partial t} \langle \Psi \right) \mid \Psi \rangle + \langle \Psi \mid \left(\frac{\partial}{\partial t} \Psi \rangle \right)$$
Schrodinger's equations says
$$\frac{\partial}{\partial t}\mid \Psi \rangle = \frac{-i}{h} H \mid \Psi \rangle$$
and
$$\frac{\partial}{\partial t} \langle \Psi \mid = \frac{i}{h} \langle H \Psi \mid = \frac{i}{h} \langle \Psi \mid H^*$$
Substituting in gives
$$\frac{\partial}{\partial t}\langle \Psi \mid \Psi \rangle = \frac{i}{h}\left( -\langle \Psi \mid H \Psi \rangle + \langle \Psi \mid H^* \Psi \rangle\right)$$
As long as $H = H^*$, this is zero. The initial normalization is a postulate, as David said.
This answer is pretty much an explicit way of saying what Lubos wrote - I was half way done when he posted, so check there for more detail.
-
Thanks, Mark, +1 for the relevant math supplement. ;-) – Luboš Motl Apr 2 '11 at 7:47
The probabilities of individual outcomes are given by the squared absolute values of the complex probability amplitudes $a_i$ associated with the individual outcomes. Their sum $${\rm Total\,\,probability} = \sum_{i} |a_i|^2$$ is therefore nothing else than a formula for the squared length of the state vector $|\psi\rangle$: note that it is a complexified version of the Pythagorean theorem.
In quantum mechanics, if the state vector (wave function) has the length equal to one at the beginning, it will have the length equal to one at all times - because of the so-called "unitarity". Unitarity means that the evolution according to Schrödinger's equation is essentially just a rotation around some "axes" in the Hilbert space - an element of $U(N)$ or $U(\infty)$, a complex and/or infinite-dimensional generalization of $O(N)$.
Unitarity means that the evolution of $|\psi\rangle$ - by Schrödinger's equation - preserves the length of the vector, and the squared length of the vector is nothing else than the sum of probabilities of all mutually exclusive outcomes of experiments, regardless of the orthogonal basis of the Hilbert space that we choose.
The unitarity condition is $U U^\dagger={\bf 1}$ for the evolution operators $U$ and may be reduced to $H=H^\dagger$, the hermiticity of the Hamiltonian, whenever the evolution is encoded in a Hamiltonian via $U=\exp(Ht/i\hbar)$, as Mark's answer shows explicitly.
It is important that in quantum mechanics, we don't have to normalize the probabilities in a way that would depend on the evolution: the preservation of the total probability is guaranteed by the equations of motion, namely by the hermiticity of the Hamiltonian that enters these equations of motion.
If an ad hoc normalization were required, quantum mechanics would be spoiled by a new source of non-locality and the "wave function collapse" would become observable. Both of these problems would lead to inconsistencies with the observations - and, from a theorist's viewpoint, internal logical inconsistencies in the theory.
-
An outcome is anything that can happen. You might not want to fail to detect a particle, but if you do, it's an outcome. It still causes quantum decoherence (and waveform collapse if you believe the Copenhagen interpretation), in that there will not be interference between waves that are there if the particle is detected and waves that are there if it isn't.
Also, it's entirely possible to predict the probability of not detecting the particle when it's there, and accidentally detecting the particle when it isn't. In case you're wondering, the decoherence is essentially from the detector. There will be interference between part of a waveform that missed the detector and part that just didn't manage to set it off.
-
@user2898, one needs to distinguish two cases. (i) If a 100% efficient detector doesn't detect a particle, there is no particle. (ii) If a real-world detector (which never is 100% efficient) fails to detect a particle, there may or may not be a particle. You could mock up a 100% efficient detector by ignoring all instances in which it failed to work, but this would beg the question. – Koantum Apr 3 '11 at 5:17
Lets look at simple probability theory.
Suppose you toss a coin $N$ times. And you get heads $H$ times and tails $T$ times. When you don't get heads you get tails.
This means $T = N - H$.
Now, probability of getting heads $P_h = \frac{H}{N}$ (by definition)
and probability of getting tails $P_t = \frac{T}{N} = \frac{N-H}{N}$
$P_h + P_t = \frac{H}{N} + \frac{N-H}{N} = \frac{H + N - H}{N} = \frac{N}{N} = 1$
-
What operationally is "no outcome"? As mentioned above this has nothing to to with quantum mechanics, since every quantum experiment must have a classical reading (Bohr's dictum). Perhaps this is the part of which you are unaware.
I have thought about it myself since yesterday. One definition of the absence of outcome is "no stability" or reproducibility. Something like, you think you see blue. You blink or wish or something and the outcome changes, you see green. Blink again and it changes again. Another possibility might be that the experimental apparatus is destroyed.
Also, merely apparent measurements of unphysical quantities may have no outcome, like trying to measure our absolute x,y,z coordinates in the universe, but even this is not operationally so well defined. Some purely statistical experiments like telepathy appear to have no outcome, as they change on reinterpretation.
Do you have other operational possibilities in mind for "no outcome"? Please focus on the meaning of "operational". This was the giant advance in 20th century physics.
-
Perhaps it is best to focus on a position measurement using an array of detectors. To simplify further, just two detectors and a state assigning to them a total probability of 1. Since no detector is perfect, no every one of these measurements will have an outcome. All Bohr would require in this case that the unsuccessful measurements be discarded or ignored, if we want to compare the predicted probabilities with the measured ones. – Koantum Apr 4 '11 at 1:42
Do this first with ants, in a Y shaped maze with cameras as detectors. There is the possibility that the ant a) "gets reflected", i.e. turns around, or b) "gets absorbed" in the apparatus, i.e. stops or gets eaten by a spider. To you both of these are "no outcome" results. Similarly, for atoms in a Stern-Gerlach apparatus, there can be poor beam focusing, or poor vacuum, etc. However, to me, in both these circumstances, there was indeed an outcome, namely that neither detector registers an ant or an atom (in the delta t assumed). Another outcome is that both detectors could register. – sigoldberg1 Apr 4 '11 at 2:30
Sorry, ran out of space. My basic criticism is that there is way too much theory in your definition of the "outcome" of an experiment. As an experimentalist, to me, the outcome is whatever comes out, which can more or less be anything. Your question has to do more with the rescalings of probabilities which occur all the time in real experiments, as you indicated. So to me you want to know whether there could be theories which always predict missing probability of detection, like missing energy or spin before neutrinos were discovered? But wouldn't we just call that particle decay? – sigoldberg1 Apr 4 '11 at 2:43
the outcomes isn't whatever "comes out." It's what is represented by a projector. My question is not: does QM "always predict missing probability of detection" but: can QM predict with certainty that a measurement will have one of its possible outcomes (which are represented by orthogonal projectors on an HS)? – Koantum Apr 5 '11 at 1:56 | 2014-03-07 15:55:27 | {"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": 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": 0.8050786852836609, "perplexity": 510.9389449193182}, "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-2014-10/segments/1393999645491/warc/CC-MAIN-20140305060725-00035-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://wulixb.iphy.ac.cn/en/article/Y2012/V61/I6/063202 | x
## 留言板
Photo-detachment of hydrogen negative ion in a magnetic field near a dielectric surface
## Photo-detachment of hydrogen negative ion in a magnetic field near a dielectric surface
Tang Tian-Tian, Wang De-Hua, Huang Kai-Yun, Wang Shan-Shan
• #### Abstract
Using the closed orbit theory, we study the photo-detachment of H- in a magnetic field near a dielectric surface. The photo-detachment cross section of this system is also derived and calculated. It is found that the photo-detachment cross section is not only related to the magnetic field strength, but also depends on the dielectric constant. For a given ion-surface distance and dielectric constant, with the increase of the magnetic field strength, the number of the closed orbits increases greatly and the oscillatory structure in the photo-detachment cross section becomes much more complicated. On the other hand, for a given magnetic field strength, the dielectric constant also has a great influence on the photo-detachment process of negative ion. Above the ionization threshold, the photo-detachment cross section becomes oscillatory. With the increase of the dielectric constant, the oscillatory structure in the cross-section becomes much more complicated. Therefore we can control the photo-detachment of negative ion by changing the magnetic field strength and the dielectric constant. This study provides a new understanding of the photo-detachment process of negative ion in the presence of external fields and surfaces.
#### Authors and contacts
###### Corresponding author: Wang De-Hua, jnwdh@sohu.com
• Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11074104, 10604045) and the High Educational Science and Technology Program of Shandong Province, China (Grant No. J09LA02).
#### References
[1] Blumberg W A M, Itano W M, Larson D J 1979 Phys. Rev. A 19 139 [2] Bryant H C, Mohagheghi A, Stewart J E, Donahue J B, Quick C R, Reeder R A, Yuan V, Hummer C R, Smith W W, Stanley C, William P R, Lillian O 1987 Phys. Rev. Lett. 58 2412 [3] Du M L, Delos J B 1988 Phys. Rev. A 38 1896 [4] Song X H, Lin S L 2003 Acta Phys. Sin. 52 1611 (in Chinese) [宋晓红, 林圣路 2003 物理学报 52 1611] [5] Peters A D, Jaffe C, Delos J B 1997 Phys. Rev. A 56 331 [6] Peters A D, Delos J B 1993 Phys. Rev. A 47 3020 [7] Liu Z Y, Wang D H 1997 Phys. Rev. A 55 4605 [8] Liu Z Y, Wang D H 1997 Phys. Rev. A 56 2670 [9] Petek H, Weida M J, Nagano H, Ogawa S 2000 Science 288 1402 [10] Sjakste J, Borisov A G, Gauyacq J P 2004 Phys. Rev. Lett. 92 156101 [11] Yang G C, Zheng Y Z, Chi X X 2006 J. Phys. B 39 1855 [12] Yang G C, Zheng Y Z, Chi X X 2006 Phys. Rev. A 73 043413 [13] Wang D H 2007 Eur. Phys. J. D 45 179 [14] Wang D H, Yu Y J 2008 Chin. Phys. B 17 1231 [15] Zhao H J, Du M L 2009 Phys. Rev. A 79 023408 [16] Rui K K, Yang G C 2009 Surf. Sci. 603 632 [17] Wang D H, Huang K Y 2010 Commun. Theor. Phys. 53 898 [18] Yang G C, Du M L 2010 J. Phys. B: At. Mol. Opt. Phys. 43 035002 [19] Huang K Y, Wang D H 2010 Acta Phys. Sin. 59 932 (in Chinese) [黄凯云, 王德华 2010 物理学报 59 932] [20] Wang D H, Tang T T,Wang S S 2010 J. Electron Spectrosc. Relat. Phenom. 177 30 [21] Du M L 1989 Phys. Rev. A 40 4984 063202-7
#### Cited By
• [1] Blumberg W A M, Itano W M, Larson D J 1979 Phys. Rev. A 19 139 [2] Bryant H C, Mohagheghi A, Stewart J E, Donahue J B, Quick C R, Reeder R A, Yuan V, Hummer C R, Smith W W, Stanley C, William P R, Lillian O 1987 Phys. Rev. Lett. 58 2412 [3] Du M L, Delos J B 1988 Phys. Rev. A 38 1896 [4] Song X H, Lin S L 2003 Acta Phys. Sin. 52 1611 (in Chinese) [宋晓红, 林圣路 2003 物理学报 52 1611] [5] Peters A D, Jaffe C, Delos J B 1997 Phys. Rev. A 56 331 [6] Peters A D, Delos J B 1993 Phys. Rev. A 47 3020 [7] Liu Z Y, Wang D H 1997 Phys. Rev. A 55 4605 [8] Liu Z Y, Wang D H 1997 Phys. Rev. A 56 2670 [9] Petek H, Weida M J, Nagano H, Ogawa S 2000 Science 288 1402 [10] Sjakste J, Borisov A G, Gauyacq J P 2004 Phys. Rev. Lett. 92 156101 [11] Yang G C, Zheng Y Z, Chi X X 2006 J. Phys. B 39 1855 [12] Yang G C, Zheng Y Z, Chi X X 2006 Phys. Rev. A 73 043413 [13] Wang D H 2007 Eur. Phys. J. D 45 179 [14] Wang D H, Yu Y J 2008 Chin. Phys. B 17 1231 [15] Zhao H J, Du M L 2009 Phys. Rev. A 79 023408 [16] Rui K K, Yang G C 2009 Surf. Sci. 603 632 [17] Wang D H, Huang K Y 2010 Commun. Theor. Phys. 53 898 [18] Yang G C, Du M L 2010 J. Phys. B: At. Mol. Opt. Phys. 43 035002 [19] Huang K Y, Wang D H 2010 Acta Phys. Sin. 59 932 (in Chinese) [黄凯云, 王德华 2010 物理学报 59 932] [20] Wang D H, Tang T T,Wang S S 2010 J. Electron Spectrosc. Relat. Phenom. 177 30 [21] Du M L 1989 Phys. Rev. A 40 4984 063202-7
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• Citation:
##### Metrics
• Abstract views: 1865
• Cited By: 0
##### Publishing process
• Received Date: 12 June 2011
• Accepted Date: 30 June 2011
• Published Online: 20 March 2012
## Photo-detachment of hydrogen negative ion in a magnetic field near a dielectric surface
###### Corresponding author: Wang De-Hua, jnwdh@sohu.com;
• 1. College of Physics, Ludong University, Yantai 264025, China
Fund Project: Project supported by the National Natural Science Foundation of China (Grant Nos. 11074104, 10604045) and the High Educational Science and Technology Program of Shandong Province, China (Grant No. J09LA02).
Abstract: Using the closed orbit theory, we study the photo-detachment of H- in a magnetic field near a dielectric surface. The photo-detachment cross section of this system is also derived and calculated. It is found that the photo-detachment cross section is not only related to the magnetic field strength, but also depends on the dielectric constant. For a given ion-surface distance and dielectric constant, with the increase of the magnetic field strength, the number of the closed orbits increases greatly and the oscillatory structure in the photo-detachment cross section becomes much more complicated. On the other hand, for a given magnetic field strength, the dielectric constant also has a great influence on the photo-detachment process of negative ion. Above the ionization threshold, the photo-detachment cross section becomes oscillatory. With the increase of the dielectric constant, the oscillatory structure in the cross-section becomes much more complicated. Therefore we can control the photo-detachment of negative ion by changing the magnetic field strength and the dielectric constant. This study provides a new understanding of the photo-detachment process of negative ion in the presence of external fields and surfaces.
Reference (21)
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https://it.mathworks.com/help/ident/ref/idnlarx.html | # idnlarx
Nonlinear ARX model
## Description
An idnlarx model represents a nonlinear ARX model, which is an extension of the linear ARX structure and contains linear and nonlinear functions.
A nonlinear ARX model consists of model regressors and an output function. The output function contains one or more mapping objects, one for each model output. Each mapping object can include a linear and a nonlinear function that act on the model regressors to give the model output and a fixed offset for that output. This block diagram represents the structure of a single-output nonlinear ARX model in a simulation scenario.
The software computes the nonlinear ARX model output y in two stages:
1. It computes regressor values from the current and past input values and the past output data.
In the simplest case, regressors are delayed inputs and outputs, such as u(t–1) and y(t–3). These kind of regressors are called linear regressors. You specify linear regressors using the linearRegressor object. You can also specify linear regressors by using linear ARX model orders as an input argument. For more information, see Nonlinear ARX Model Orders and Delay. However, this second approach constrains your regressor set to linear regressors with consecutive delays. To create polynomial regressors, use the polynomialRegressor object. To create periodic regressors that contain the sine and cosine functions of delayed input and output variables , use the periodicRegressor object. You can also specify custom regressors, which are nonlinear functions of delayed inputs and outputs. For example, u(t–1)y(t–3) is a custom regressor that multiplies instances of input and output together. Specify custom regressors using the customRegressor object.
You can assign any of the regressors as inputs to the linear function block of the output function, the nonlinear function block, or both.
2. It maps the regressors to the model output using an output function block. The output function block can include multiple mapping objectslinear, nonlinear, and offset blocks in parallel. For example, consider the following equation:
$F\left(x\right)={L}^{T}\left(x-r\right)+g\left(Q\left(x-r\right)\right)+d$
Here, x is a vector of the regressors, and r is the mean of x. $F\left(x\right)={L}^{T}\left(x-r\right)+{y}_{0}$ is the output of the linear function block. $g\left(Q\left(x-r\right)\right)+{y}_{0}$ represents the output of the nonlinear function block. Q is a projection matrix that makes the calculations well-conditioned. d is a scalar offset that is added to the combined outputs of the linear and nonlinear blocks. The exact form of F(x) depends on your choice of output function. You can select from the available mapping objects, such as tree-partition networks, wavelet networks, and multilayer neural networks. You can also exclude either the linear or the nonlinear function block from the output function.
When estimating a nonlinear ARX model, the software computes the model parameter values, such as L, r, d, Q, and other parameters specifying g.
The resulting nonlinear ARX models are idnlarx objects that store all model data, including model regressors and parameters of the output function. For more information about these objects, see Nonlinear Model Structures.
For more information on the idnlarx model structure, see What are Nonlinear ARX Models?.
For idnlarx object properties, see Properties.
## Creation
You can obtain an idnlarx object in one of two ways.
• Use the nlarx command to both construct an idnlarx object and estimate the model parameters.
sys = nlarx(data,reg)
• Use the idnlarx constructor to create the nonlinear ARX model and then estimate the model parameters using nlarx or pem.
sys = idnlarx(output_name,input_name,reg)
### Description
#### Specify Model Directly
example
sys = idnlarx(output_name,input_name,orders) specifies a set of linear regressors using ARX model orders. Use this syntax when you extend an ARX linear model, or when you plan to use only regressors that are linear with consecutive lags.
example
sys = idnlarx(output_name,input_name,Regressors) creates a nonlinear ARX model with the output and input names of output_name and input_name, respectively, and a regressor set in Regressors that contains any combination of linear, polynomial, periodic, and custom regressors. The software constructs sys using the default wavelet network ('idWaveletNetwork') mapping object for the output function.
example
sys = idnlarx(___,OutputFcn) specifies the output function OutputFcn that maps the regressors to the model output. You can use this syntax with any of the previous input argument combinations.
#### Initialize Model Values Using Linear Model
example
sys = idnlarx(linmodel) uses a linear model linmodel to extract certain properties such as names, units, and sample time, and to initialize the values of the linear coefficients of the model. Use this syntax when you want to create a nonlinear ARX model as an extension of, or an improvement upon, an existing linear model.
example
sys = idnlarx(linmodel,OutputFcn) specifies the output function OutputFcn that maps the regressors to the model output.
#### Specify Model Properties
sys = idnlarx(___,Name,Value) specifies additional properties of the idnlarx model structure using one or more name-value arguments.
### Input Arguments
expand all
ARX model orders, specified as the matrix [na nb nk]. na denotes the number of delayed outputs, nb denotes the number of delayed inputs, and nk denotes the minimum input delay. The minimum output delay is fixed to 1. For more information on how to construct the orders matrix, see arx.
When you specify orders, the software converts the order information into a linear regressor form in the idnlarx Regressors property. For an example, see Create Nonlinear ARX Model Using ARX Model Orders.
Discrete-time identified input/output linear model, specified as any linear model created using estimators, that is, an idpoly object, an idss object, an idtf object, or an idproc object with Ts > 0. Create this model using the constructor function for the object or estimate the model using the associated estimation command. For example, to create an ARX model, use arx, and specify the resulting idpoly object as linmodel.
## Properties
expand all
Regressor specification, specified as a column vector containing one or more regressor specification objects, which are the linearRegressor objects, polynomialRegressor objects, periodicRegressor objects, and customRegressor objects. Each object specifies a formula for generating regressors from lagged variables. For example:
• L = linearRegressor({'y1','u1'},{1,[2 5]}) generates the regressors y1(t–1), u1(t–2), and u2(t–5).
• P = polynomialRegressor('y2',4:7,2) generates the regressors y2(t–4)2, y2(t–5)2,y2(t–6)2, and y2(t–7)2.
• SC = periodicRegressor({'y1','u1'},{1,2}) generates the regressors y1(t-1)), cos(y1(t-1)), sin(u1(t-2)), and cos(u1(t-2)).
• C = customRegressor({'y1','u1','u2'},{1 2 2},@(x,y,z)sin(x.*y+z)) generates the single regressor sin(y1(t–1)u1(t–2)+u2(t–2)
.
For an example that implements these regressors, see Create and Combine Regressor Types.
To add regressors to an existing model, create a vector of specification objects and use dot notation to set Regressors to this vector. For example, the following code first creates the idnlarx model sys and then adds the regressor objects L, P, SC, and C to the regressors of sys.
sys = idnlarx({'y1','y2'},{'u1','u2'});
R = [L;P;SC;C];
sys.Regressors = R;
For an example of creating and using a linear regressor set, see Create Nonlinear ARX Model Using Linear Regressors.
Output function that maps the regressors of the idnlarx model into the model output, specified as a column array containing zero or more of the following strings or mapping objects:
'idWaveletNetwork' or idWaveletNetwork object Wavelet network 'idLinear' or '' or [] or idLinear object Linear function 'idSigmoidNetwork' or idSigmoidNetwork object Sigmoid network 'idTreePartition' or idTreePartition object Binary tree partition regression model 'idGaussianProcess' or idGaussianProcess object Gaussian process regression model (requires Statistics and Machine Learning Toolbox™) 'idTreeEnsemble' or idTreeEnsemble Regression tree ensemble model (requires Statistics and Machine Learning Toolbox) 'idSupportVectorMachine' or idSupportVectorMachine Kernel-based Support Vector Machine (SVM) regression model with constraints (requires Statistics and Machine Learning Toolbox) idFeedforwardNetwork object Neural network — Multilayer feedforward network of Deep Learning Toolbox™ idCustomNetwork object Custom network — Similar to idSigmoidNetwork, but with a user-defined replacement for the sigmoid function
The idWaveletNetwork, idSigmoidNetwork, idTreePartition, and idCustomNetwork objects contain both linear and nonlinear components. You can remove (not use) the linear components of idWaveletNetwork, idSigmoidNetwork, and idCustomNetwork by setting the LinearFcn.Use value to false.
The idFeedforwardNetwork object has only a nonlinear component that is the network (Deep Learning Toolbox) object of Deep Learning Toolbox. The idTreeEnsemble and idSupportVectorMachine objects also contain only a nonlinear component. The idLinear function, as the name implies, has only a linear component.
Specifying a character vector, for example 'idSigmoidNetwork', creates a mapping object with default settings. Alternatively, you can specify mapping object properties in two other ways:
• Create the mapping object using arguments to modify default properties.
MO = idSigmoidNetwork(15)
• Create a default mapping object first and then use dot notation to modify properties.
MO = idSigmoidNetwork;
MO.NumberOfUnits = 15
For ny output channels, you can specify mapping objects individually for each channel by setting OutputFcn to an array of ny mapping objects. For example, the following code specifies OutputFcn using dot notation for a system with two input channels and two output channels.
sys = idnlarx({'y1','y2'},{'u1','u2'});
sys.OutputFcn = [idWaveletNetwork; idSigmoidNetwork]
To specify the same mapping for all outputs, specify OutputFcn as a character vector or a single mapping object.
OutputFcn represents a static mapping function that transforms the regressors of the nonlinear ARX model into the model output. OutputFcn is static because it does not depend on the time. For example, if $y\left(t\right)={y}_{0}+{a}_{1}y\left(t-1\right)+{a}_{2}y\left(t-2\right)+\dots +{b}_{1}u\left(t-1\right)+{b}_{2}u\left(t-2\right)+\dots$, then OutputFcn is a linear function represented by the idLinear object.
For an example of specifying the output function, see Specify Output Function for Nonlinear ARX Model.
Regressor assignments to the linear and nonlinear components of the nonlinear ARX model, specified as an nr-by-nc table with logical entries that specify which regressors to use for which component. Here, nr is the number of regressors. nc is the total number of linear and nonlinear components in OutputFcn. The rows of the table correspond to individual regressors. The row names are set to regressor names. If the table value for row i and component index j is true, then the ith regressor is an input to the linear or nonlinear component j.
For multi-output systems, OutputFcn contains one mapping object for each output. Each mapping object can use both linear and nonlinear components or only one of the two components.
For an example of viewing and modifying the RegressorUsage property, see Modify Regressor Assignments to Output Function Components.
Regressor and output centering and scaling, specified as a structure. As the following table shows, each field in the structure contains a row vector with a length that is equal to the number of either regressors (nr) or model outputs (ny).
FieldDescriptionDefault Element Value
RegressorCenterRow vector of length nrNaN
RegressorScaleRow vector of length nrNaN
OutputCenterRow vector of length nyNaN
OutputScaleRow vector of length nyNaN
For a matrix X, with centering vector C and scaling vector S, the software computes the normalized form of X using Xnorm = (X-C)./S.
The following figure illustrates the normalization flow for a nonlinear ARX model.
In this figure:
1. The algorithm converts the inputs u(t) and y(t) into the regressor set R(t).
2. The algorithm uses the regressor centering and scaling parameters to normalize R(t) as RN(t).
3. RN(t) provides the input to the mapping function, which then produces the normalized output yN
4. The algorithm uses the output scaling and centering parameters to restore the original range, producing y(t).
Typically, the software normalizes the data automatically during model estimation, in accordance with the option settings in nlarxOptions for Normalize and NormalizationOptions. You can also directly assign centering and scaling values by specifying the values in vectors, as described in the previous table. The values that you assign must be real and finite. This approach can be useful, for example, when you are simulating your model using inputs that represent a different operating point from the operating point for the original estimation data. You can assign the values for any field independently. The software will estimate the values of any fields that remain unassigned (NaN).
Summary report that contains information about the estimation options and results for a nonlinear ARX model obtained using the nlarx command. Use Report to find estimation information for the identified model, including:
• Estimation method
• Estimation options
• Search termination conditions
• Estimation data fit
The contents of Report are irrelevant if the model was constructed using idnlarx.
sys = idnlarx('y1','u1',reg);
sys.Report.OptionsUsed
ans =
[]
If you use nlarx to estimate the model, the fields of Report contain information on the estimation data, options, and results.
sys = nlarx(z1,reg);
m.Report.OptionsUsed
Option set for the nlarx command:
IterativeWavenet: 'auto'
Focus: 'prediction'
Display: 'off'
Regularization: [1x1 struct]
SearchMethod: 'auto'
SearchOptions: [1x1 idoptions.search.identsolver]
OutputWeight: 'noise'
For more information on this property and how to use it, see Output Arguments in the nlarx reference page and Estimation Report.
Independent variable for the inputs, outputs, and—when available—internal states, specified as a character vector.
Noise variance (covariance matrix) of the model innovations e. The estimation algorithm typically sets this property. However, you can also assign the covariance values by specifying an ny-by-ny matrix.
Sample time, specified as a positive scalar representing the sampling period. This value is expressed in the unit specified by the TimeUnit property of the model.
Units for the time variable, the sample time Ts, and any time delays in the model, specified as one of the following values:
• 'nanoseconds'
• 'microseconds'
• 'milliseconds'
• 'seconds'
• 'minutes'
• 'hours'
• 'days'
• 'weeks'
• 'months'
• 'years'
Changing this property has no effect on other properties, and therefore changes the overall system behavior. Use chgTimeUnit (Control System Toolbox) to convert between time units without modifying system behavior.
Input channel names, specified as one of the following:
• Character vector — For single-input models, for example, 'controls'.
• Cell array of character vectors — For multi-input models.
Input names in Nonlinear ARX models must be valid MATLAB® variable names after you remove any spaces.
Alternatively, use automatic vector expansion to assign input names for multi-input models. For example, if sys is a two-input model, enter:
sys.InputName = 'controls';
The input names automatically expand to {'controls(1)';'controls(2)'}.
When you estimate a model using an iddata object, data, the software automatically sets InputName to data.InputName.
You can use the shorthand notation u to refer to the InputName property. For example, sys.u is equivalent to sys.InputName.
Input channel names have several uses, including:
• Identifying channels on model display and plots
• Extracting subsystems of MIMO systems
• Specifying connection points when interconnecting models
Input channel units, specified as one of the following:
• Character vector — For single-input models, for example, 'seconds'.
• Cell array of character vectors — For multi-input models.
Use InputUnit to keep track of input signal units. InputUnit has no effect on system behavior.
Input channel groups. The InputGroup property lets you assign the input channels of MIMO systems into groups and refer to each group by name. Specify input groups as a structure. In this structure, field names are the group names, and field values are the input channels belonging to each group. For example:
sys.InputGroup.controls = [1 2];
sys.InputGroup.noise = [3 5];
creates input groups named controls and noise that include input channels 1, 2 and 3, 5, respectively. You can then extract the subsystem from the controls inputs to all outputs using:
sys(:,'controls')
Output channel names, specified as one of the following:
• Character vector — For single-output models. For example, 'measurements'.
• Cell array of character vectors — For multi-output models.
Output names in Nonlinear ARX models must be valid MATLAB variable names after you remove any spaces.
Alternatively, use automatic vector expansion to assign output names for multi-output models. For example, if sys is a two-output model, enter:
sys.OutputName = 'measurements';
The output names automatically expand to {'measurements(1)';'measurements(2)'}.
When you estimate a model using an iddata object, data, the software automatically sets OutputName to data.OutputName.
You can use the shorthand notation y to refer to the OutputName property. For example, sys.y is equivalent to sys.OutputName.
Output channel names have several uses, including:
• Identifying channels on model display and plots
• Extracting subsystems of MIMO systems
• Specifying connection points when interconnecting models
Output channel units, specified as one of the following:
• Character vector — For single-output models. For example, 'seconds'.
• Cell array of character vectors — For multi-output models.
Use OutputUnit to keep track of output signal units. OutputUnit has no effect on system behavior.
Output channel groups. The OutputGroup property lets you assign the output channels of MIMO systems into groups and refer to each group by name. Specify output groups as a structure. In this structure, field names are the group names, and field values are the output channels belonging to each group. For example:
sys.OutputGroup.temperature = [1];
sys.InputGroup.measurement = [3 5];
creates output groups named temperature and measurement that include output channels 1, and 3, 5, respectively. You can then extract the subsystem from all inputs to the measurement outputs using:
sys('measurement',:)
System name, specified as a character vector. For example, 'system 1'.
Any text that you want to associate with the system, specified as a string or a cell array of character vectors. The property stores whichever data type you provide. For instance, if sys1 and sys2 are dynamic system models, you can set their Notes properties as follows.
sys1.Notes = "sys1 has a string.";
sys2.Notes = 'sys2 has a character vector.';
sys1.Notes
sys2.Notes
ans =
"sys1 has a string."
ans =
'sys2 has a character vector.'
Any data you want to associate with the system, specified as any MATLAB data type.
## Object Functions
For information about object functions for idnlarx, see Nonlinear ARX Models.
## Examples
collapse all
Create an idnlarx model by specifying an ARX model order vector.
Create an order vector of the form [na nb nk], where na and nb are the orders of the A and B ARX model polynomials and nk is the number of input/output delays.
na = 2;
nb = 3;
nk = 5;
orders = [na nb nk];
Construct a nonlinear ARX model sys.
output_name = 'y1';
input_name = 'u1';
sys = idnlarx(output_name,input_name,[2 3 5]);
View the output function.
disp(sys.OutputFcn)
Wavelet Network
Nonlinear Function: Wavelet network with number of units chosen automatically
Linear Function: uninitialized
Output Offset: uninitialized
Inputs: {'y1(t-1)' 'y1(t-2)' 'u1(t-5)' 'u1(t-6)' 'u1(t-7)'}
Outputs: {'y1(t)'}
NonlinearFcn: '<Wavelet and scaling function units and their parameters>'
LinearFcn: '<Linear function parameters>'
Offset: '<Offset parameters>'
EstimationOptions: '<Estimation options>'
By default, the model uses a wavelet network, represented by a idWaveletNetwork object, for the output function. The idWaveletNetwork object includes linear and nonlinear components.
View the Regressors property.
disp(sys.Regressors)
Linear regressors in variables y1, u1
Variables: {'y1' 'u1'}
Lags: {[1 2] [5 6 7]}
UseAbsolute: [0 0]
TimeVariable: 't'
The idnlarx constructor transforms the model orders into the Regressors form.
• The Lags array for y1, [1 2], is equivalent to the na value of 2. Both forms specify two consecutive output regressors, y1(t-1) and y1(t-2).
• The Lags array for u1, [5 6 7], incorporates the three delays specified by the nb value of 3, and shifts them by the nk value of 5. The input regressors are therefore u1(t-5), u1(t-6), and u1(t-7).
View the regressors.
getreg(sys)
ans = 5x1 cell
{'y1(t-1)'}
{'y1(t-2)'}
{'u1(t-5)'}
{'u1(t-6)'}
{'u1(t-7)'}
You can use the orders syntax to specify simple linear regressors. However, to create more complex regressors, use the regressor commands linearRegressor, polynomialRegressor, and customRegressor to create a combined regressor for the Regressors syntax.
Construct an idnlarx model by specifying linear regressors.
Create a linear regressor that contains two output lags and two input lags.
output_name = 'y1';
input_name = 'u1';
var_names = {output_name,input_name};
output_lag = [1 2];
input_lag = [1 2];
lags = {output_lag,input_lag};
reg = linearRegressor(var_names,lags)
reg =
Linear regressors in variables y1, u1
Variables: {'y1' 'u1'}
Lags: {[1 2] [1 2]}
UseAbsolute: [0 0]
TimeVariable: 't'
Regressors described by this set
The model contains the regressors y(t-1), y(t-2), u(t-1), and u(t-2).
Construct the idnlarx model and view the regressors.
sys = idnlarx(output_name,input_name,reg);
getreg(sys)
ans = 4x1 cell
{'y1(t-1)'}
{'y1(t-2)'}
{'u1(t-1)'}
{'u1(t-2)'}
View the output function.
disp(sys.OutputFcn)
Wavelet Network
Nonlinear Function: Wavelet network with number of units chosen automatically
Linear Function: uninitialized
Output Offset: uninitialized
Inputs: {'y1(t-1)' 'y1(t-2)' 'u1(t-1)' 'u1(t-2)'}
Outputs: {'y1(t)'}
NonlinearFcn: '<Wavelet and scaling function units and their parameters>'
LinearFcn: '<Linear function parameters>'
Offset: '<Offset parameters>'
EstimationOptions: '<Estimation options>'
View the regressor usage table.
disp(sys.RegressorUsage)
y1:LinearFcn y1:NonlinearFcn
____________ _______________
y1(t-1) true true
y1(t-2) true true
u1(t-1) true true
u1(t-2) true true
All the regressors are inputs to both the linear and nonlinear components of the wavenet object.
Create a nonlinear ARX model with a linear regressor set.
Create a linear regressor that contains three output lags and two input lags.
output_name = 'y1';
input_name = 'u1';
var_names = {output_name,input_name};
output_lag = [1 2 3];
input_lag = [1 2];
lags = {output_lag,input_lag};
reg = linearRegressor(var_names,lags)
reg =
Linear regressors in variables y1, u1
Variables: {'y1' 'u1'}
Lags: {[1 2 3] [1 2]}
UseAbsolute: [0 0]
TimeVariable: 't'
Regressors described by this set
Construct the nonlinear ARX model.
sys = idnlarx(output_name,input_name,reg);
View the Regressors property.
disp(sys.Regressors)
Linear regressors in variables y1, u1
Variables: {'y1' 'u1'}
Lags: {[1 2 3] [1 2]}
UseAbsolute: [0 0]
TimeVariable: 't'
sys uses idWavenetNetwork as the default output function. Reconfigure the output function to idSigmoidNetwork.
sys.OutputFcn = 'idSigmoidNetwork';
disp(sys.OutputFcn)
Sigmoid Network
Nonlinear Function: Sigmoid network with 10 units
Linear Function: uninitialized
Output Offset: uninitialized
Inputs: {'y1(t-1)' 'y1(t-2)' 'y1(t-3)' 'u1(t-1)' 'u1(t-2)'}
Outputs: {'y1(t)'}
NonlinearFcn: '<Sigmoid units and their parameters>'
LinearFcn: '<Linear function parameters>'
Offset: '<Offset parameters>'
Specify the sigmoid network output function when you construct a nonlinear ARX model.
Assign variable names and specify a regressor set.
output_name = 'y1';
input_name = 'u1';
r = linearRegressor({output_name,input_name},{1 1});
Construct a nonlinear ARX model that specifies the idSigmoidNetwork output function. Set the number of terms in the sigmoid expansion to 15.
sys = idnlarx(output_name,input_name,r,idSigmoidNetwork(15));
View the output function specification.
disp(sys.OutputFcn)
Sigmoid Network
Nonlinear Function: Sigmoid network with 15 units
Linear Function: uninitialized
Output Offset: uninitialized
Inputs: {'y1(t-1)' 'u1(t-1)'}
Outputs: {'y1(t)'}
NonlinearFcn: '<Sigmoid units and their parameters>'
LinearFcn: '<Linear function parameters>'
Offset: '<Offset parameters>'
Construct an idnlarx model that uses only linear mapping in the output function. An argument value of [] is equivalent to an argument value of idLinear.
sys = idnlarx([2 2 1],[])
sys =
Nonlinear ARX model with 1 output and 1 input
Inputs: u1
Outputs: y1
Regressors:
Linear regressors in variables y1, u1
List of all regressors
Output function: Linear with offset
Sample time: 1 seconds
Status:
Created by direct construction or transformation. Not estimated.
Create a regressor set that includes linear, polynomial, periodic, and custom regressors.
Specify L as the set of linear regressors ${\mathit{y}}_{1}\left(\mathit{t}-1\right)$, ${\mathit{u}}_{1}\left(\mathit{t}-2\right)$, and ${\mathit{u}}_{1}\left(\mathit{t}-5\right)$.
L = linearRegressor({'y1','u1'},{1, [2 5]});
Specify P as the set of polynomial regressors ${\mathit{y}}_{2}{\left(\mathit{t}-4\right)}^{2}$, ${\mathit{y}}_{2}{\left(\mathit{t}-5\right)}^{2}$,${\mathit{y}}_{2}{\left(\mathit{t}-6\right)}^{2}$, and ${\mathit{y}}_{2}{\left(\mathit{t}-7\right)}^{2}$.
P = polynomialRegressor('y2',4:7,2);
Specify SC as the set of periodic regressors $\mathrm{sin}\left({\mathit{y}}_{1}\left(\mathit{t}-1\right)\right)$, $\mathrm{cos}\left({\mathit{y}}_{1}\left(\mathit{t}-1\right)\right)$, $\mathrm{sin}\left({\mathit{u}}_{1}\left(\mathit{t}-2\right)\right)$, and $\mathrm{cos}\left({\mathit{u}}_{1}\left(\mathit{t}-2\right)\right)$.
SC = periodicRegressor({'y1','u1'},{1,2});
Specify C as the custom regressor $\mathrm{sin}\left({\mathit{y}}_{1}\left(\mathit{t}-1\right){\mathit{u}}_{1}\left(\mathit{t}-2\right)+{\mathit{u}}_{2}\left(\mathit{t}-2\right)\right)$, using the @ symbol to create an anonymous function handle.
C = customRegressor({'y1','u1','u2'},{1 2 2},@(x,y,z)sin(x.*y+z));
Combine the regressors into one regressor set R.
R = [L;P;SC;C]
R =
[4 1] array of linearRegressor, polynomialRegressor, periodicRegressor, customRegressor objects.
------------------------------------
1. Linear regressors in variables y1, u1
Variables: {'y1' 'u1'}
Lags: {[1] [2 5]}
UseAbsolute: [0 0]
TimeVariable: 't'
------------------------------------
2. Order 2 regressors in variables y2
Order: 2
Variables: {'y2'}
Lags: {[4 5 6 7]}
UseAbsolute: 0
AllowVariableMix: 0
AllowLagMix: 0
TimeVariable: 't'
------------------------------------
3. Periodic regressors in variables y1, u1 with 1 Fourier terms
Variables: {'y1' 'u1'}
Lags: {[1] [2]}
W: 1
NumTerms: 1
UseSin: 1
UseCos: 1
TimeVariable: 't'
UseAbsolute: [0 0]
------------------------------------
4. Custom regressor: sin(y1(t-1).*u1(t-2)+u2(t-2))
VariablesToRegressorFcn: @(x,y,z)sin(x.*y+z)
Variables: {'y1' 'u1' 'u2'}
Lags: {[1] [2] [2]}
Vectorized: 1
TimeVariable: 't'
Regressors described by this set
Create a nonlinear ARX model.
sys = idnlarx({'y1','y2'},{'u1','u2'},R)
sys =
Nonlinear ARX model with 2 outputs and 2 inputs
Inputs: u1, u2
Outputs: y1, y2
Regressors:
1. Linear regressors in variables y1, u1
2. Order 2 regressors in variables y2
3. Periodic regressors in variables y1, u1 with W = 1, and 1 Fourier terms
4. Custom regressor: sin(y1(t-1).*u1(t-2)+u2(t-2))
List of all regressors
Output functions:
Output 1: Wavelet network with number of units chosen automatically
Output 2: Wavelet network with number of units chosen automatically
Sample time: 1 seconds
Status:
Created by direct construction or transformation. Not estimated.
Use a linear ARX model instead of a regressor set to construct a nonlinear ARX model.
Construct a linear ARX model using idpoly.
A = [1 -1.2 0.5];
B = [0.8 1];
LinearModel = idpoly(A, B, 'Ts', 0.1);
Specify input and output names for the model using dot notation.
LinearModel.OutputName = 'y1';
LinearModel.InputName = 'u1';
Construct a nonlinear ARX model using the linear ARX model.
m1 = idnlarx(LinearModel)
m1 =
Nonlinear ARX model with 1 output and 1 input
Inputs: u1
Outputs: y1
Regressors:
Linear regressors in variables y1, u1
List of all regressors
Output function: Wavelet network with number of units chosen automatically
Sample time: 0.1 seconds
Status:
Created by direct construction or transformation. Not estimated.
You can create a linear ARX model from any identified discrete-time linear model.
Estimate a second-order state-space model from estimation data z1.
ssModel = ssest(z1,2,'Ts',0.1);
Construct a nonlinear ARX model from ssModel. The software uses the input and output names that ssModel extracts from z1.
m2 = idnlarx(ssModel)
m2 =
Nonlinear ARX model with 1 output and 1 input
Inputs: u1
Outputs: y1
Regressors:
Linear regressors in variables y1, u1
List of all regressors
Output function: Wavelet network with number of units chosen automatically
Sample time: 0.1 seconds
Status:
Created by direct construction or transformation. Not estimated.
Modify regressor assignments by modifying the RegressorUsage table.
Construct a nonlinear ARX model that has two inputs and two outputs.
Create the variable names and the regressors.
varnames = {'y1','y2','u1','u2'};
lags = {[1 2 3],[1 2],[1 2],[1 3]};
reg = linearRegressor(varnames,lags);
Create an output function specification fcn that uses idWaveletNetwork for mapping regressors to output y1 and idSigmoidNetwork for mapping regressors to output y2. Both mapping objects contain linear and nonlinear components.
fcn = [idWaveletNetwork;idSigmoidNetwork];
Construct the nonlinear ARX model.
output_name = {'y1' 'y2'};
input_name = {'u1' 'u2'};
sys = idnlarx(output_name,input_name,reg,fcn)
sys =
Nonlinear ARX model with 2 outputs and 2 inputs
Inputs: u1, u2
Outputs: y1, y2
Regressors:
Linear regressors in variables y1, y2, u1, u2
List of all regressors
Output functions:
Output 1: Wavelet network with number of units chosen automatically
Output 2: Sigmoid network with 10 units
Sample time: 1 seconds
Status:
Created by direct construction or transformation. Not estimated.
Display the RegressorUsage table.
disp(sys.RegressorUsage)
y1:LinearFcn y1:NonlinearFcn y2:LinearFcn y2:NonlinearFcn
____________ _______________ ____________ _______________
y1(t-1) true true true true
y1(t-2) true true true true
y1(t-3) true true true true
y2(t-1) true true true true
y2(t-2) true true true true
u1(t-1) true true true true
u1(t-2) true true true true
u2(t-1) true true true true
u2(t-3) true true true true
The rows of the table represent the regressors. The first two columns of the table represent the linear and nonlinear components of the mapping to output y1 (idWaveletNetwork). The last two columns represent the two components of the mapping to output y2 (idSigmoidNetwork).
In this table, all the input and output regressors are inputs to all components.
Remove the y2(t-2) regressor from the y2 nonlinear component.
sys.RegressorUsage{4,4} = false;
disp(sys.RegressorUsage)
y1:LinearFcn y1:NonlinearFcn y2:LinearFcn y2:NonlinearFcn
____________ _______________ ____________ _______________
y1(t-1) true true true true
y1(t-2) true true true true
y1(t-3) true true true true
y2(t-1) true true true false
y2(t-2) true true true true
u1(t-1) true true true true
u1(t-2) true true true true
u2(t-1) true true true true
u2(t-3) true true true true
The table displays false for this regressor-component pair.
Store the regressor names in Names.
Names = sys.RegressorUsage.Properties.RowNames;
Determine the indices of the rows that contain y1 or y2 and set the corresponding values of y1:NonlinearFcn to False.
idx = contains(Names,'y1')|contains(Names,'y2');
sys.RegressorUsage{idx,2} = false;
disp(sys.RegressorUsage)
y1:LinearFcn y1:NonlinearFcn y2:LinearFcn y2:NonlinearFcn
____________ _______________ ____________ _______________
y1(t-1) true false true true
y1(t-2) true false true true
y1(t-3) true false true true
y2(t-1) true false true false
y2(t-2) true false true true
u1(t-1) true true true true
u1(t-2) true true true true
u2(t-1) true true true true
u2(t-3) true true true true
The table values reflect the new assignments.
The RegressorUsage table provides complete flexibility for individually controlling regressor assignments. | 2022-08-16 14:15:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 16, "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": 0.5726132392883301, "perplexity": 6233.5469928904795}, "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/1659882572304.13/warc/CC-MAIN-20220816120802-20220816150802-00479.warc.gz"} |
http://www.mathnet.ru/php/archive.phtml?jrnid=im&wshow=issue&year=1974&volume=38&volume_alt=&issue=3&issue_alt=&option_lang=eng | RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PERSONAL OFFICE
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Izv. RAN. Ser. Mat.: Year: Volume: Issue: Page: Find
On Tate height and the representation of numbers by binary formsV. A. Dem'yanenko 459 A remark on endomorphisms of abelian varieties over function fields of finite characteristicYu. G. Zarhin 471 On a basis of the product of varieties of groups. IIYu. G. Kleiman 475 Orbits of the group $\mathbf{GL}(r,k[X_1,…,X_n])$V. A. Artamonov 484 On the algebraic dependence of the components of solutions of a system of linear differential equationsYu. V. Nesterenko 495 Characterization of $L_3(2^n)$ by Sylow 2-subgroupsV. D. Mazurov, S. A. Syskin 513 Existence of smooth ergodic flows on smooth manifoldsD. V. Anosov 518 Integrals and $n$-dimensional conjugate functionsT. P. Lukashenko 546 On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functionsV. P. Motornyi 583 Sufficient optimality conditions for differential imbeddingsV. I. Blagodatskikh 615 Asymptotics of the solution of the system $A(x,-ih\frac\partial{\partial x})$ as $h\to0$ in the case of characteristics of variable multiplicityV. V. Kucherenko 625 Estimates on the boundary for differential operators with constant coefficients in a half-spaceI. V. Gel'man, V. G. Maz'ya 663 | 2019-03-18 19:03:36 | {"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": 0.36146268248558044, "perplexity": 1713.0710304007669}, "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-2019-13/segments/1552912201521.60/warc/CC-MAIN-20190318172016-20190318194016-00122.warc.gz"} |
http://cryptography.wikia.com/wiki/Threefish | # Threefish
566pages on
this wiki
Template:Primary sources Template:Infobox block cipher Threefish is a tweakable block cipher designed as part of the Skein hash function, an entry in the NIST hash function competition. Threefish uses no S-boxes or other table lookups in order to avoid cache timing attacks;[1] its nonlinearity comes from alternating additions with exclusive ORs. In that respect, it's similar to Salsa20, TEA, and the SHA-3 candidates CubeHash and BLAKE.
Threefish and the Skein hash function were designed by Bruce Schneier, Niels Ferguson, Stefan Lucks, Doug Whiting, Mihir Bellare, Tadayoshi Kohno, Jon Callas, and Jesse Walker.
## SecurityEdit
In October 2010, an attack that combines rotational cryptanalysis with the rebound attack was published. The attack breaks collision resistance within 53 of 72 rounds in Threefish-256, and 57 of 72 rounds in Threefish-512. It also affects the Skein hash function.[2] This is a follow-up to the earlier attack published in February, which breaks 39 and 42 rounds respectively.[3]
In 2009, a related key boomerang attack against a reduced round Threefish version was published. For the 32-round version, the time complexity is $2^{226}$ and the memory complexity is $2^{12}$; for the 33-round version, the time complexity is $2^{352.17}$ with a negligible memory usage. The attacks also work against the tweaked version of Threefish: for the 32-round version, the time complexity is $2^{222}$ and the memory complexity is $2^{12}$; for the 33-round version, the time complexity is $2^{355.5}$ with a negligible memory usage.[4] | 2017-05-25 14:24:35 | {"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": 0.26458412408828735, "perplexity": 3911.7386065356472}, "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-2017-22/segments/1495463608084.63/warc/CC-MAIN-20170525140724-20170525160724-00477.warc.gz"} |
http://pub.acta.hu/acta/showCustomerArticle.action?id=10004&dataObjectType=article&returnAction=showCustomerVolume&sessionDataSetId=24ca2933f2c68547&style= | ACTA issues
## Lebesgue integrability of double Fourier transforms
Dang Vu Giang, Ferenc Móricz
Acta Sci. Math. (Szeged) 58:1-4(1993), 299-328
5550/2009
Abstract. First, we consider a complex-valued function \$f\$ defined and absolutely continuous on the positive quadrant \${\msbm R}_+^2\$ of the plane, and study the double cosine \$F_c,\$ double sine \$F_s\$, and cosine-sine Fourier transform \$F_{cs}\$ of \$f.\$ We give sufficient conditions, under which \$F_c, F_s,\$ and \$F_{cs}\$ are Lebesgue integrable on \${\msbm R}_+^2,\$ respectively; and the inversion formula holds. Our basic tools are Sidon type inequalities, which we elaborate also in this paper. Second, we deduce sufficient conditions for Lebesgue integrability of double cosine, double sine, and cosine-sine series on the two-dimensional torus \${\msbm T}^2.\$ Third, we extend these results to double complex Fourier transform of functions defined and absolutely continuous on the whole plane \${\msbm R}^2\$ as well as to double complex trigonometric series. Fourth, as a by-product, we obtain sufficient conditions for an absolutely continuous function to be the double complex Fourier transform of a Lebesgue integrable function on \${\msbm R}^2.\$ AMS Subject Classification (1991): 42B99, 42A38, 26A46 Keyword(s): double cosine, double sine, cosine-sine Fourier transforms, double complex Fourier transform, absolute continuity of function in two variables, Lebesgue integrability, inversion formula, double cosine, double sine, cosine-sine series, double complex trigonometric series, double null sequence of bounded variation, Fourier series, Hausdorff-Young inequality, Sidon type inequalities Received February 2, 1993. (Registered under 5550/2009.) | 2020-05-28 16:28:39 | {"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": 0.9249688386917114, "perplexity": 2596.3828826288923}, "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/1590347399820.9/warc/CC-MAIN-20200528135528-20200528165528-00208.warc.gz"} |
http://pdglive.lbl.gov/DataBlock.action?node=S060DML&home=BXXX045 | # ${\boldsymbol m}_{{{\boldsymbol \Xi}_{{b}}^{-}}}–{\boldsymbol m}_{{{\boldsymbol \Lambda}_{{b}}^{0}}}$ INSPIRE search
VALUE (MeV) DOCUMENT ID TECN COMMENT
$\bf{ 177.5 \pm0.5}$ OUR AVERAGE Error includes scale factor of 1.6.
$177.73$ $\pm0.33$ $\pm0.14$ 1
2017 BE
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$176.2$ $\pm0.9$ $\pm0.1$ 2
2013 AV
LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
$177.08$ $\pm0.47$ $\pm0.16$ 3
2017 BE
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$178.36$ $\pm0.46$ $\pm0.16$ 4, 5
2014 BJ
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
1 Combination of the original statistically independent measurements of AAIJ 2014BE and AAIJ 2017BJ taking into account correlation between systematic uncertainties.
2 Reconstructed in ${{\mathit \Xi}_{{b}}^{-}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \Xi}^{-}}$ decays.
3 Reconstructed in ${{\mathit \Xi}_{{b}}^{-}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \Lambda}}{{\mathit K}^{-}}$ decays. Reference decays ${{\mathit \Lambda}_{{b}}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \Lambda}}$ were used.
4 Reconstructed in ${{\mathit \Xi}_{{b}}^{-}}$ $\rightarrow$ ${{\mathit \Xi}_{{c}}^{0}}{{\mathit \pi}^{-}}$ , ${{\mathit \Xi}_{{c}}^{0}}$ $\rightarrow$ ${{\mathit p}}{{\mathit K}^{-}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$ decays. Reference ${{\mathit \Lambda}_{{b}}^{0}}$ $\rightarrow$ ${{\mathit \Lambda}_{{c}}^{+}}{{\mathit \pi}^{-}}$ .
5 Combined with AAIJ 2017BE.
References:
AAIJ 2017BE
PL B772 265 Observation of the ${{\mathit \Xi}_{{b}}^{-}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \Lambda}}{{\mathit K}^{-}}$ Decay
AAIJ 2014BJ
PRL 113 242002 Precision Measurement of the Mass and Lifetime of the ${{\mathit \Xi}_{{b}}^{-}}$ Baryon
AAIJ 2013AV
PRL 110 182001 Measurement of the ${{\mathit \Lambda}_{{b}}^{0}}$, ${{\mathit \Xi}_{{b}}^{-}}$ and ${{\mathit \Omega}_{{b}}^{-}}$ Baryon Masses | 2020-04-05 19:20:50 | {"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": 0.9426984190940857, "perplexity": 5097.440095850212}, "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-2020-16/segments/1585371609067.62/warc/CC-MAIN-20200405181743-20200405212243-00461.warc.gz"} |
http://mathhelpforum.com/algebra/50982-factorize-following-expression.html | # Math Help - Factorize the following expression.
1. ## Factorize the following expression.
At first glance this looked really easy to me. Boy was I proven wrong!
Anyway, I have to factorize:
$ax+3x+2a+6$
There's a relationship between the x's and a's since the sum of the coefficients of the first 3 parts is $1+3+2=6$. If this can be turned into a -6 then it would be easier to factorize.
Any help will be greatly appreciated.
2. $a{\color{red}x} + 3{\color{red}x} + 2a + 6 \ = \ {\color{red}x}{\color{blue}(a+3)} + 2{\color{blue}(a+3)}$
Factor the x out of the first 2 terms and factor out a 2 from the last 2. Now, notice that you can factor out the blue
3. ZOMG!
Wow, that is so obvious! I've been doing this waaaaay too much.
I have a test soon and i'm getting the jitters.
I was overcomplicating it like I usually do. :s | 2014-03-11 12:48:13 | {"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": 0, "img_math": 0, "codecogs_latex": 3, "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": 0.7904259562492371, "perplexity": 643.0507067502775}, "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-2014-10/segments/1394011192582/warc/CC-MAIN-20140305091952-00072-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/111699-linear-approximation.html | # Math Help - Linear approximation!
1. ## Linear approximation!
The linear approximation at x = 0 to f(x) = sqrt (7 + 7 x) is y =
any help will be appreciated!!
2. Originally Posted by frozenflames
The linear approximation at x = 0 to f(x) = sqrt (7 + 7 x) is y =
any help will be appreciated!!
http://www.mathhelpforum.com/math-he...gent-line.html
3. Originally Posted by skeeter
i use the same approach and get the following: .1889822x+2.64575
but it is incorrect. any thoughts?
4. Originally Posted by frozenflames
i use the same approach and get the following: .1889822x+2.64575
but it is incorrect. any thoughts?
first of all, put away the calculator.
what did you get for f'(x) ?
5. Originally Posted by skeeter
first of all, put away the calculator. | 2015-04-26 03:22:26 | {"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": 0.9189537167549133, "perplexity": 1833.2738540106386}, "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-2015-18/segments/1429246652296.40/warc/CC-MAIN-20150417045732-00130-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://brilliant.org/problems/circumscribes-many-notions/ | # Circumscribes many notions.
Let $$\left[ \begin{matrix} 2 & 1 \\ 1 & 0 \end{matrix} \right]^n=\left( a_{ij}(n) \right)$$
If $$\left( \displaystyle \lim_{n \to \infty} \dfrac{a_{12}(n)}{a_{22}(n)} \right)^2=\sqrt{A}+\sqrt{B} \quad \quad \left( A,B \in \mathbb{N}\right)$$
then find the value of $$A+B$$.
Notation: $$a_{ij}(n)$$ denotes the element in the $$i^{\text{th}}$$ row and $$j^{\text{th}}$$ column of matrix $$A$$.
× | 2018-01-24 09:50:17 | {"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": 0.9858913421630859, "perplexity": 373.7481404347822}, "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-2018-05/segments/1516084893629.85/warc/CC-MAIN-20180124090112-20180124110112-00643.warc.gz"} |
https://lists.snort.org/pipermail/snort-users/2005-February/042712.html | [Snort-users] Mapping of Rules to data structures
Sun Feb 27 19:59:46 EST 2005
```Hi
I wanted to ask 2 things
1. How are the various rules written in the
snort-2.3.0\rules\ *.rules files actually mapped to
the data structures (like RTN and OTNs) in SNORT
2. pls culd someone send me a detailed explanation of
the Activate/dynamic rule pairs
how are the two rules linked. is it thru the number in
the activates and Activated by (which is the same in
all the examples i have gone thru)
please could someone send me some examples of this
rule.
thanks and sorry for the botheration
Regards | 2019-07-23 00:25:45 | {"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": 0.9088735580444336, "perplexity": 6010.8298698373255}, "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-2019-30/segments/1563195528635.94/warc/CC-MAIN-20190723002417-20190723024417-00286.warc.gz"} |
https://brilliant.org/discussions/thread/ladders-on-the-walls/ | ×
# Ladders on the walls
Guys please help me with this problem... I've been eating my head off but cannot solve this problem. I used similarity and tried finding the values of AD and BC bt im left with a bi-quadratic equation y^4 - 20y^3 + 700y^2 - 14000y + 70000 = 0 where y = BC Please help. Thank you
Note by Sagnik Saha
4 years, 6 months ago
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Here's one approach. Note that:
$\frac{OE}{BC} = \frac{AE}{AB}, \ \frac{OE}{AD} = \frac{EB}{AB} \implies \frac{OE}{BC} + \frac{OE}{AD} = 1.$
If we denote $$x=AB$$, then this gives $$\frac{10}{\sqrt{30^2 - x^2}} + \frac{10}{\sqrt{40^2 - x^2}} = 1$$. You'll probably still get a quartic equation, but at least all terms are even powers of $$x$$ so you can substitute $$u = x^2$$ and solve there.
[ Edit: actually this doesn't seem to work since you still get a quartic equation in $$u$$ after expansion. ]
- 4 years, 6 months ago
According to what I have calculated, AB=28.5 m.
First we will use C Lim's approach.
OE/BC + OE/AD =1------------------(1)
OE/AD = OB/BD ---------------(2)
OE/BC = OA/AC ---------------(3)
Adding (2) and (3),
OE/AD + OE/BC = OB/BD + OA/AC
1 = OB/40 + OA/30 [From --------(1) and putting the values of BD and AC]
Solving further, we get an equation,
120=3(OB) +4(OA) --------------(4)
Now, ODA is similar to OBC, which gives us,
OD/OC = OB/OA
(BD-OB)/(AC-OA) = OB/OA
(40-OB)/(30-OA) = OB/OA
Solving further, we get, 4(OA) = 3(OB) --------------(5)
From (4) and (5), we get OA=15 m and OB=20 m.
Now, using pythagoras theorem in triangles OEA and OEB, we get
EA = 5 root5 m and EB = 10 root3 m.
AB = EA +EB = 5 x 2.236 + 10 x 1.732 = 28.5 m
- 4 years ago
There is no way to get a nice exact solution for this problem. Values were poorly chosen. Your equation is correct. The correct result is close to AB = 26.
They probably wanted AB = 24, AD = 32, BC = 18, but messed up by the choice of OE.
It is hard to choose 3 integer values for AC, BD and OE so that AB is integer. I can't find anything better than: BD = 119 AC = 105 OE = 30
- 4 years, 6 months ago
you should have assumed the sides as integers.i know it's a guess but worth trying.if you assume them as integers then you can easily conclude that the answer is 24
- 4 years, 6 months ago
how do u conclude? please elaborate a little. thank u
- 4 years, 6 months ago | 2018-02-24 10:08:27 | {"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": 0.9837788939476013, "perplexity": 3978.9219818771285}, "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/1518891815544.79/warc/CC-MAIN-20180224092906-20180224112906-00165.warc.gz"} |
https://electronics.stackexchange.com/questions/257156/is-vin-the-same-as-vcc/257164#257164 | # Is VIN the same as VCC?
I have a HMC5883L and its pins are labeled SDA, SCL, DRDY, VIN, and GND. SO I am following this tutorial and it has a VCC pin but mine doesn't have it so I was wondering if VIN is the same as VCC because VIN looks the closest to VCC.
• Have you tried looking up the datasheet on the internet (I found one in a few seconds Googling), and comparing that with the device you have? The ones I see have 16 pins, one of which is VDD, but no VIN. Sep 10 '16 at 21:08
• Find the VDD pin on the chip, and (with the power off) do a continuity test between there and the VIN pin on the module. Not every module designer will include a voltage regulator, but if they did, this sort of VDD vs VIN naming difference is exactly what would be used to differentiate the chip power pin from the module pin that supplies the regulator that powers the chip. Sep 11 '16 at 0:18
• @BenVoigt - Your probing plan is a good one. Too bad the LPCC chip is very difficult to probe. I would suggest just applying a DC voltage between +2.2 to +3.6 to "Vin". If the is a regulator on-board, no harm will result. If it is a direct run with no regulator, the magnetometer will come to life. Sep 11 '16 at 2:11
## 1 Answer
Nomenclature is always a problem, so sometimes one has to make a good guess. That HMC5883L requires a DC supply voltage. Does your module seem to have an on-board battery?...no?...then the DC supply likely comes from an external source. The pin labeled "GND" is required by the serial link (SDA,SCL) for data communication, but it can also be the ground return of this external source.
Another clue comes from the similarity of pin nomenclature to your tutorial photo. The only one that differs is "VIN" vs. "Vcc". You are thinking intelligently in relating these two.
Since power is likely supplied from an external source to this module, it is reasonable to say that this is an input pin. It inputs voltage to the module. Silk-screen labels must be short, so these cryptic labels are ubiquitous.
Some more info on "Vcc":What is the difference between $V_{CC}$, $V_{DD}$, $V_{EE}$, $V_{SS}$ | 2022-01-20 10:37:42 | {"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": 0.25937166810035706, "perplexity": 1505.316425947726}, "config": {"markdown_headings": true, "markdown_code": false, "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-2022-05/segments/1642320301737.47/warc/CC-MAIN-20220120100127-20220120130127-00556.warc.gz"} |
https://brilliant.org/discussions/thread/is-brilliant-the-right-place-for-the-beginners-str/ | # Is Brilliant the right place for the beginners striving to learn?
Hey there everyone, I am very new to this website and even intense independent learning as well. I was brought here to this site by a Quora post and so far it looks incredibly appealing to me. The problem for me, however, is that I am not sure of the potential of Brilliant for those who are are unaware of many of the basic principles of mathematics.
For example, I participated in the activity to qualify for skills here and was already stumped by Prime Factorization as I could not figure an efficient method to do it. I decided not to grind out the answer because I knew I wasn't familiar with the concepts.
To sum it up, is Brilliant just a really good outlet for practicing certain aspects of mathematics as you learn them, or is there a learning section hidden here that I am missing?
Note by Erik Carlson
5 years, 2 months ago
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Here You Can Learn More $$\rightarrow$$ Here
- 5 years, 2 months ago
There is a new (or at least somewhat new) techniques page with more lessons.
- 5 years, 2 months ago
Yeah , Already See and Started Use ! (I See All Change than Happens!)
- 5 years, 2 months ago
Thanks! :)
- 5 years, 2 months ago
:::) , Nothing !
- 5 years, 2 months ago
yes! it's the right place for beginners who are striving to learn independently. I also have joined this site yesterday!
- 5 years, 2 months ago
Welcome to Brilliant!
How did you hear about us? I'm intrigued because you strongly feel that we can help you learn independently, despite only joining yesterday. It must mean that we're doing something good :)
Staff - 5 years, 2 months ago
yes and thanks
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