url stringlengths 14 2.42k | text stringlengths 100 1.02M | date stringlengths 19 19 | metadata stringlengths 1.06k 1.1k |
|---|---|---|---|
https://mythandmind.com/step-4-5/ | Step 4
Construct two additional "circles" identical to the first, centered at the "points" where the diameter intersects the original "circle". | 2021-10-17 23:05:01 | {"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": 0.8966158032417297, "perplexity": 3702.2310277167835}, "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-2021-43/segments/1634323585183.47/warc/CC-MAIN-20211017210244-20211018000244-00289.warc.gz"} |
https://www.ademcetinkaya.com/2023/02/avg-australian-vintage-ltd.html | Outlook: AUSTRALIAN VINTAGE LTD is assigned short-term Ba1 & long-term Ba1 estimated rating.
Time series to forecast n: 02 Feb 2023 for (n+8 weeks)
Methodology : Supervised Machine Learning (ML)
## Abstract
AUSTRALIAN VINTAGE LTD prediction model is evaluated with Supervised Machine Learning (ML) and Polynomial Regression1,2,3,4 and it is concluded that the AVG stock is predictable in the short/long term. According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Buy
## Key Points
1. Short/Long Term Stocks
2. Stock Rating
3. Why do we need predictive models?
## AVG Target Price Prediction Modeling Methodology
We consider AUSTRALIAN VINTAGE LTD Decision Process with Supervised Machine Learning (ML) where A is the set of discrete actions of AVG stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4
F(Polynomial Regression)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Supervised Machine Learning (ML)) X S(n):→ (n+8 weeks) $\begin{array}{l}\int {e}^{x}\mathrm{rx}\end{array}$
n:Time series to forecast
p:Price signals of AVG stock
j:Nash equilibria (Neural Network)
k:Dominated move
a:Best response for target price
For further technical information as per how our model work we invite you to visit the article below:
How do AC Investment Research machine learning (predictive) algorithms actually work?
## AVG Stock Forecast (Buy or Sell) for (n+8 weeks)
Sample Set: Neural Network
Stock/Index: AVG AUSTRALIAN VINTAGE LTD
Time series to forecast n: 02 Feb 2023 for (n+8 weeks)
According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Buy
X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)
Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)
Z axis (Grey to Black): *Technical Analysis%
## IFRS Reconciliation Adjustments for AUSTRALIAN VINTAGE LTD
1. Lifetime expected credit losses are generally expected to be recognised before a financial instrument becomes past due. Typically, credit risk increases significantly before a financial instrument becomes past due or other lagging borrower-specific factors (for example, a modification or restructuring) are observed. Consequently when reasonable and supportable information that is more forward-looking than past due information is available without undue cost or effort, it must be used to assess changes in credit risk.
2. A contractually specified inflation risk component of the cash flows of a recognised inflation-linked bond (assuming that there is no requirement to account for an embedded derivative separately) is separately identifiable and reliably measurable, as long as other cash flows of the instrument are not affected by the inflation risk component.
3. If an entity previously accounted at cost (in accordance with IAS 39), for an investment in an equity instrument that does not have a quoted price in an active market for an identical instrument (ie a Level 1 input) (or for a derivative asset that is linked to and must be settled by delivery of such an equity instrument) it shall measure that instrument at fair value at the date of initial application. Any difference between the previous carrying amount and the fair value shall be recognised in the opening retained earnings (or other component of equity, as appropriate) of the reporting period that includes the date of initial application.
4. When a group of items that constitute a net position is designated as a hedged item, an entity shall designate the overall group of items that includes the items that can make up the net position. An entity is not permitted to designate a non-specific abstract amount of a net position. For example, an entity has a group of firm sale commitments in nine months' time for FC100 and a group of firm purchase commitments in 18 months' time for FC120. The entity cannot designate an abstract amount of a net position up to FC20. Instead, it must designate a gross amount of purchases and a gross amount of sales that together give rise to the hedged net position. An entity shall designate gross positions that give rise to the net position so that the entity is able to comply with the requirements for the accounting for qualifying hedging relationships.
*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.
## Conclusions
AUSTRALIAN VINTAGE LTD is assigned short-term Ba1 & long-term Ba1 estimated rating. AUSTRALIAN VINTAGE LTD prediction model is evaluated with Supervised Machine Learning (ML) and Polynomial Regression1,2,3,4 and it is concluded that the AVG stock is predictable in the short/long term. According to price forecasts for (n+8 weeks) period, the dominant strategy among neural network is: Buy
### AVG AUSTRALIAN VINTAGE LTD Financial Analysis*
Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementCBa3
Balance SheetBa3B3
Leverage RatiosCB1
Cash FlowBaa2Baa2
Rates of Return and ProfitabilityCaa2C
*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?
### Prediction Confidence Score
Trust metric by Neural Network: 79 out of 100 with 626 signals.
## References
1. Çetinkaya, A., Zhang, Y.Z., Hao, Y.M. and Ma, X.Y., Can neural networks predict stock market?(ATVI Stock Forecast). AC Investment Research Journal, 101(3).
2. J. Ott. A Markov decision model for a surveillance application and risk-sensitive Markov decision processes. PhD thesis, Karlsruhe Institute of Technology, 2010.
3. Varian HR. 2014. Big data: new tricks for econometrics. J. Econ. Perspect. 28:3–28
4. J. Spall. Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Transactions on Automatic Control, 37(3):332–341, 1992.
5. Athey S, Imbens G. 2016. Recursive partitioning for heterogeneous causal effects. PNAS 113:7353–60
6. Bewley, R. M. Yang (1998), "On the size and power of system tests for cointegration," Review of Economics and Statistics, 80, 675–679.
7. E. Collins. Using Markov decision processes to optimize a nonlinear functional of the final distribution, with manufacturing applications. In Stochastic Modelling in Innovative Manufacturing, pages 30–45. Springer, 1997
Frequently Asked QuestionsQ: What is the prediction methodology for AVG stock?
A: AVG stock prediction methodology: We evaluate the prediction models Supervised Machine Learning (ML) and Polynomial Regression
Q: Is AVG stock a buy or sell?
A: The dominant strategy among neural network is to Buy AVG Stock.
Q: Is AUSTRALIAN VINTAGE LTD stock a good investment?
A: The consensus rating for AUSTRALIAN VINTAGE LTD is Buy and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of AVG stock?
A: The consensus rating for AVG is Buy.
Q: What is the prediction period for AVG stock?
A: The prediction period for AVG is (n+8 weeks) | 2023-03-30 08:07:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "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": 0.26998409628868103, "perplexity": 6000.178224045051}, "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/1679296949107.48/warc/CC-MAIN-20230330070451-20230330100451-00050.warc.gz"} |
https://www.math.kyoto-u.ac.jp/ja/event/seminar/2208 | # Non-trivial subcritical phase for two dimensional self-destructive percolation
2014/01/10 Fri 15:30 - 17:00
3号館552号室
Demeter Kiss
University of Cambridge
Consider subcritical $(p > p_c)$ site percolation on $\mathbb{Z}^2$. Destroy the infinite open cluster, that is, make all its vertices closed. Then open the closed vertices independently from each other with probability delta. Let $\theta(p,\delta)$ denote the probability that the origin is in an infinite cluster in the configuration thus obtained.
We show that there is a positive delta such that $\theta(p, \delta) = 0$ for all $p > p_c$.
We also sketch how the methods in the proof of the result above can be used to deduce large deviation results on the volume large critical percolation clusters.
This is a joint work with Ioan Manolescu and Vladas Sidoravicius. | 2019-06-15 23:11:58 | {"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": 0.9482201933860779, "perplexity": 692.9125583050796}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627997501.61/warc/CC-MAIN-20190615222657-20190616004657-00253.warc.gz"} |
https://forum.bebac.at/forum_entry.php?id=21894 | ## Jurisdiction? [Regulatives / Guidelines]
Hi Pharma_88,
» We are thinking to perform steady state BE study for XXX submission…
Unfortunately my crystal ball is in the laundry and reading tea leaves turned out to be an insufficient substitute.
Hence, which XXX?
» … where Test product is ER formulation and Reference product is IR formulation.
<nitpick>
Not BE, but comparative BA. You can only hope for similar extent of absorption but never for rate of absorption in a comparison of ER vs IR. Furthermore, BE means similarity in PK metrics of interest if equimolar doses are administered. Sometimes one has to increase the ER dose to get similar AUCs… Whatever is applicable in your case, BE is the wrong term.
</nitpick>
» Further, Its HVD product. So, question is whether is this feasible to conduct replicate BE IR vs ER and if yes…
Is it a highly variable drug 1 or are one – or both – products 2 highly variable? But, in principle, yes.
» … then what are the parameters for conclusion?
Once you tell us what XXX is, we can possibly help.
1. HVDs exhibit highly variable clearances (CVwR ≥30% if administered as a solution).
2. HVDPs may additionally – or solely – show highly variable absorption.
Dif-tor heh smusma 🖖
Helmut Schütz
The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes | 2022-05-22 04:33:57 | {"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": 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": 0.5007660388946533, "perplexity": 5368.897576195607}, "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-2022-21/segments/1652662543797.61/warc/CC-MAIN-20220522032543-20220522062543-00421.warc.gz"} |
https://motls.blogspot.com/2005/09/comments-on-news.html?m=1 | ## Tuesday, September 06, 2005
In a 1986 disaster that many were comparing to the third world war and that others have used to interrupt the progress in nuclear energy for at least 20 years, only 56 people were directly killed. A new 600-page report also estimates that the total number of indirect deaths caused by thyroid cancer - usually of the people who worked on the recovery of the plant after the disaster - will stay below 4,000.
There has been no measurable deterioration of the public health in the surrounding areas. Was the anti-nuclear reaction to the Chernobyl accident appropriate? The Reference Frame does not think so and encourages the developed countries to build new nuclear power plants.
The previous numbers were inflated because of miscalculations of exposition to radiation, and by attempts of various not-quite-honest countries to boost the financial assistance flowing to the area.
Compare the new numbers with the typical number of people that are killed by natural disasters such as the typhoon in Southern Japan today (100,000 people ordered to flee their homes), plane crash that has just killed 147 people in Indonesia, and, of course, Katrina that has killed thousands. (The French Quarter will be fine.) And these disasters represent a small fraction of the people who die under more prosaic circumstances.
Global warming destroyed Saturn's ring
According to a generalized global warming theory, Saturn's rings must be static for thousands of years. It turned out that the innermost ring, the D-ring, looks completely different than 25 years ago. It's dimmer and it may even disappear. Also, there are minivan-sized objects in the outermost A-ring. This short period of time - 25 years - in which things can change proves that the humans who drink Coke and their production of carbon dioxide must be behind these celestial developments, the generalized theory of truly global warming says.
More seriously, subtle things in the Universe, which includes Saturn's rings as well as Earth's climate, are simply changing. They're naturally changing, they have always been and they always will. Hurricanes and typhoons are naturally created all the time and the people are too weak to change these basic processes, and whoever does not like these laws of physics should try to find a better Universe to live in.
Kazaa will have filters
The company running the file-sharing network Kazaa will have to install filters that protect the copyrights, a judge has decided. It may be a fair decision; such filters won't prevent the users from any legal activities. Kazaa will appeal.
#### 1 comment:
1. Dear Lumo,
The exaggeration of radiation effects is due to simplistic theory and experimentation on mice in the 1950s.
Until about 1955, a threshold model for cancer induction was widely accepted, based on some data for the exposures of radium - zinc sulphide dial painters from the 1920s.
Then people started experimenting with mice to find out the effects of cancer from nuclear testing and power.
The problem is, human beings since 1979 are known to have an elaborate DNA repair mechanism, largely based on protein P53.
Each piece of DNA at body temperature probably breaks a couple of times a minute and is fixed back together quickly. This is why people live longer than mice, which age faster since they lack the DNA repair mechanism. (Evolution hasn't bothered about DNA repair in mice because they are normally eaten by predators after a few months anyway.)
So mice don't have a radiation threshold for cancer induction. But this experimental finding was applied to humans in the 1950s, long before P53 was discovered.
A huge science-versus-politics crusade was started to demonise the few scientists who held out in favour of the threshold model.
Experimental data for populations exposed to different background radiation levels, carefully corrected for other environmental factors, show that you need to get above about 20 mSv of gamma rays per year to get any enhanced risk of cancer.
It is possible that alpha and beta radiation inside the body (from inhaling or eating fallout) has sufficiently high linear energy transfer to induce cancers regardless of dose. However, at least in Britain every building has alpha emitters in the smoke detectors (1 microcurie of Am-241 which emits alpha and very soft gamma rays). Nobody campaigns about smoke detectors or claims that everyone will be killed if one is burned, despite the fact that there are enough Am-241 atoms inside one to theoretically give everyone in the world cancer (if you use a crackpot theory that 'one alpha particle can cause 1 lung cancer').
The politics of the nuclear industry, which refuses (it seems to me) to state the scientific facts clearly and convincingly to the public, are absurd.
It's a bit like the Copenhagen Interpretation in QM. Just because it is (or rather was) backed by famous people like Bohr and Heisenberg, everyone is expected to subscribe to it to prove that they are not crackpots.
Best wishes,
Nigel | 2021-05-13 04:05:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.33358272910118103, "perplexity": 2054.712751083448}, "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/1620243992721.31/warc/CC-MAIN-20210513014954-20210513044954-00390.warc.gz"} |
https://www.physicsforums.com/threads/short-term-investments.328774/ | # Short term investments
1. Aug 3, 2009
### rootX
I want to make short term investments (currently, stocks I believe). Currently, I don't have any investment knowledge so wanted to know if stocks are better or forex?
(edit: learning about them in next few days)
I found this website:
http://individuals.interactivebrokers.com/en/main.php
If there is any better website or if this is appropriate for small short term investments (few weeks to a month max or to a year at max)?
Last edited: Aug 3, 2009
2. Aug 4, 2009
### tiny-tim
how much can you afford to lose??
Hi rootX!
How much can you afford to lose??
If at least getting your money back is important, then you should invest in a fund, not an individual stock.
Even then, it's not guaranteed.
And investing for only a few months is really a bet rather than an investment.
(and what sort of profit are you expecting? i hope it's not more than a few percent)
3. Aug 4, 2009
### Pengwuino
Do NOT trade currencies if you do not know what you're doing. Currencies are far more complicated than stocks. You have to look at entire economies instead of single companies or single industries.
Stocks are a gamble at the moment as the economy is way too unstable. If you're going short term, remember that it'll be a gamble if you don't know what you're doing (and if you do, you probably wouldn't invest in the first place right now), and any gains are subject to fairly heavy taxation.
4. Aug 4, 2009
### rootX
Re: how much can you afford to lose??
Currently, about 10K $(max) and 4 K$ (min) and I would still be able to continue living my normal life without them.
Anything that's above my saving account.
5. Aug 4, 2009
- Warren
9. Aug 4, 2009
### junglebeast
So true..nobody really wants to share their full wisdom, which means everything you ever read is all just half-truths, some of it half-false intentionally, and even more of it half-false due to other peoples' ignorance. The funniest thing is all the books with catchy titles that are filled with complete BS. But you've got to keep reading through this junk to assimilate knowledge, you just need a really good filter!
10. Aug 4, 2009
### rootX
Thanks, all the responses were very helpful.
I think I will go with the CD option. I have about >10K in my saving account which I am not hoping to touch any time soon so I wanted to make sure that I am not missing on stocks/other short term investments.
11. Aug 4, 2009
### chroot
Staff Emeritus
Absolutely. There's a huge inherent conflict of interest involved in producing books or TV shows on investing. It has been shown time and time again that all of the books and TV shows which bill themselves as small-investor advocates (Mad Money, CNBC in general, for example) are really selling snake-oil, encouraging novices to play a game which they cannot hope to win.
It's very instructive to remember that short-term movements in stock prices have absolutely nothing to do with the underlying company. When you make short-term investments, you are choosing to compete directly with other investors in a very abstract way that has nothing to do with how good or bad a company is or might be in the future. It's just a symbol on a screen.
Investment firms spend ridiculous amounts of money developing computer systems which allow them to covertly move vast quantities of money through the market, trickling it through thousands of small orders placed through market makers around the globe. They do this to simulate "real" market movements. All it takes is a few million dollars to literally make any stock go up or down at will. They have access to vast amounts of statistics that allow them to see quite plainly when the stock has been oversold or overbought, and they can act instantly to take advantage of that knowledge, turning a bump of a few pennies in a stock price into a windfall, when multiplied by millions of shares.
The high-profile, poster-boy stocks like AAPL, MSFT, etc. are actually those which violate the efficient market hypothesis most egregiously. They are, quite simply, the most manipulated stocks. It is not coincidental that these poster-boy stocks are the most attractive to novices.
Day trading, as an individual, is a fool's game.
- Warren
12. Aug 4, 2009
### chroot
Staff Emeritus
Good idea. You might also want to consider finding a credit union or internet bank, etc. that offers an interest-bearing checking account. Often, these rates are as good as CDs, without requiring you to lock up your money.
- Warren
13. Aug 4, 2009
### Pengwuino
One thing that might be an idea is to get a real broker. They are knowledgeable and have an incentive to make money for you. Then again, brokers these days are telling people to stay out of the market in the first place.
@chroot: I wouldn't exactly say that nearly every share of stock is being controlled by "the big boys". For example, microsoft has only 60% institutional ownership. Private ownership got a boost earlier in the decade when there was a push towards joe schmo to start investing in things. Not sure how that all panned out though haha.
14. Aug 4, 2009
### junglebeast
All that you say is true, Warren, except that the market is still not perfectly efficient. The big companies may spend millions on their software, but they do not benefit from all of the world's smartest minds..and their algorithms are not so dynamic as to be able to work perfectly efficiently at all stocks and all time scales simultaneously, or robust enough to not make mistakes. They are also incredibly low risk, which leaves a good deal of money to be made by people with slightly higher risk tolerances. I know of several full time day traders who make a good living off of this.
15. Aug 4, 2009
### damit
The market is organic, no number of expert people or algorithms are 100% accurate in predicting the market, of course this depends on which market we are talking about but holds true to most markets. It particularly does hold true for forex and the stock market, sure there maybe some manipulation, but with practice, skill, and good knowledge one can see this false trend in price very easily. Actually you could even make a system which can be successful 75% of the time and would lessen your chances of falling into such traps.
Those that say not to use your money because it is a recession are people afraid of risk. There are strategies you can learn to manage your risk and risk then becomes a friend rather then a enemy. Personally, I have done best in bad economic times when the market is volatile in making the highest return on my money. I do not prescribe to the buy and hold strategy, or standard, that is foolishly given to those starting to place money in the market.
Also I suggest that people know the difference between investing and trading. What I think the OP is saying is he wants to trade, which is rather short term, and just because it is a zero-sum game it does not mean that it is gambling. Most of the time when I here such statements I think to myself that this person does not understand risk. Remember there is risk in every venture and ultimately every action you take for reward and gain in almost everything you do in life.
On that note I say participating in the market I believe is always good because you add to the liquidity of the market and the economy, but one should know what they are doing. Also remember that no amount of practice with fake money will guarantee success when you use your real money because real emotions will be tied in then. I believe if one wants to be successful at the market they must really learn to control or even separate their emotions from their actions.
16. Aug 4, 2009
### Ivan Seeking
Staff Emeritus
Or you could just donate your money to the Ivanwantstoflyamig fund.
17. Aug 4, 2009
### MakeUpPlz
Short term investment=saving money for diseases
18. Aug 4, 2009
### lisab
Staff Emeritus
Wait...what?
19. Aug 4, 2009
### MakeUpPlz
You mean "wait" as in "wait a sec" or as in "what am I waiting for" ?
<edit>It takes me some time to blend and correct my statement, sorry I still owe you.
Last edited: Aug 4, 2009 | 2017-12-14 23:20:49 | {"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": 0.2223564088344574, "perplexity": 1756.4581900237483}, "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/1512948551162.54/warc/CC-MAIN-20171214222204-20171215002204-00166.warc.gz"} |
https://www.physicsforums.com/threads/ball-thrown-to-cliff-projectile-problem.338355/ | # Homework Help: Ball thrown to cliff (projectile problem)
1. Sep 18, 2009
### Bryon
1. The problem statement, all variables and given/known data
A man standing 31 m from the base of a vertical cliff throws a ball with a speed of 38 m/s aimed directly at a point 5 m above the base of the cliff.
Here is a link to the diagram....
https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/fall/homework/Ch-04-2D-Motion/ball_to_cliff/8.gif [Broken]
How long does it take the ball to reach the cliff?
2. Relevant equations
First off i tried to find the time to get to the max height:
v = v(initial)+at
0=38+(-9.8)t t=3.87755
Then I found the max height:
x(final) = x(initial) + v(initial)t + 0.5at^2
x(final) = 0 + 38(3.877) + 0.5(-9.8)(3.877^2) x(final) = 73.67
This really does not look right to me though. If it is then would I have to find the time it drops from the max height to 5m? Is there anyway of finding the y component?
Last edited by a moderator: May 4, 2017
2. Sep 18, 2009
### kuruman
You need to break the initial velocity into horizontal and vertical components before attempting a solution.
3. Sep 18, 2009
### Bryon
I was thinking that. But my next question would be how? The angle is not given. Would I use the distance of 31m and the height of 5m to find it?
4. Sep 18, 2009
### Bryon
I took the arctan of (5/31) and got 9.15 degrees. Im thinking that is the and at which the ball was thrown. Does that sound right? I think after I figure this part out I would be able to solve the problem.
Thanks!
5. Sep 18, 2009
### kuruman
Yes arctan(5/31) will give you the angle of projection. Note that you don't really need to find the actual angle. All you need is the sine = opp/hyp and the cosine = adj/hyp. Use the Pythagorean Theorem to find hyp.
6. Sep 21, 2009
### Bryon
Ok I figured out the time, which turned out to be 0.82s. And it was simply the velocity over the distance.
i figured wow fast is the ball moving when it reaches the cliff by using the pythagorean theorem, and it turned out to be 37.3m/s.
Here is where I am having trouble...
At what time does the ball reach its largest vertical height?
I am sure that I have to find the initial vertical velocity:
31 = 38cos(x)(0.82) where x is the angle x = 5.8 degrees
vy0 = 38sin(x) vy0 calculated to be 3.84
vf = v0 + at
0 = 3.84 + (-9.8)t = 0.39s
time to max height i figured to be 0.39s
This is the incorrect answer, what did I do wrong? Any suggestions?
Thanks!
7. Sep 22, 2009
### kuruman
I don't know how you calculated the angle that you call x, but it is incorrect. If I were doing this problem, I would not bother with the angle. For example, if I needed the sine of the angle, I would use
$$sin\theta=\frac{opp}{hyp}=\frac{5}{\sqrt{5^{2}+31^{2}}}$$
Less calculation, less likelihood for error, you know what I mean?
8. Sep 22, 2009
### Bryon
That is understood. Perhaps I am over complicating this one. It seemed so easy to find the height but I end up with the wrong answer. Thanks for the input!
9. Sep 22, 2009
### kuruman
Your method for finding the height by first finding the time it takes to reach that height is correct and should work. However, you can do it in one step if you use the kinematic equation that does not involve time,
2aΔy=vy2-v0y2
You know or can calculate everything except for the unknown vertical displacement.
10. Sep 22, 2009
### Bryon
Thanks for the help! It worked and I managed to find everything else that I was asked to find. | 2018-05-23 02:10:44 | {"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": 0.5870343446731567, "perplexity": 633.7153388928015}, "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-2018-22/segments/1526794865023.41/warc/CC-MAIN-20180523004548-20180523024548-00249.warc.gz"} |
https://math.stackexchange.com/questions/1121984/matching-algorithm-in-graph-theory | # Matching Algorithm in Graph Theory
Given $n$ people, $k$ out of which own a car. We need to match a car for each person without a car. Conditions:
• Each car fits $5$ people, including the driver.
• Each driver will only allow his friends to ride with him.
I am looking for an algorithm to determine if there is a match. i.e. everyone gets to ride.
I am not seeking complete answer. Hints/pointers should suffice since this is part of my college assignment.
Thank you.
This might be an extension of the marriage theorem, except that any group of n passengers needs to be friends with at least $\left \lceil \frac{n}{4}\right \rceil$ drivers. | 2019-07-18 20:13:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.3059932291507721, "perplexity": 419.3976793575974}, "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-2019-30/segments/1563195525793.19/warc/CC-MAIN-20190718190635-20190718212635-00512.warc.gz"} |
https://www.gradesaver.com/textbooks/math/calculus/calculus-3rd-edition/chapter-1-precalculus-review-1-1-real-numbers-functions-and-graphs-exercises-page-10/31 | ## Calculus (3rd Edition)
|a-6| $\leq$ 2 a-6 $\leq$ 2 , a-6 $\geq$ -2 a $\leq$ 8 , a $\geq$ 4 4 $\leq$ a $\leq$ 8 |b| $\leq$ 3 b $\leq$ 3 , b $\geq$ -3 -3 $\leq$ b $\leq$ 3 max| a + b | = max(a) + max(b) = 8 + 3 = 11 min| a + b | = min(a) + min(b) = 4 + (-3) = 1 | 2020-11-28 19:01:57 | {"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": 0.5924736857414246, "perplexity": 1248.4496271762005}, "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-2020-50/segments/1606141195745.90/warc/CC-MAIN-20201128184858-20201128214858-00380.warc.gz"} |
http://openstudy.com/updates/511c7626e4b03d9dd0c3f467 | ## A community for students. Sign up today!
Here's the question you clicked on:
## blahblah_who_cares 2 years ago How do I find the arithmetic mean and the geometric mean?
• This Question is Closed
1. EgonRedd
arithmatic mean is all of the numbers added together divided by the amount of numbers its the average
2. whpalmer4
Arithmetic mean of two numbers is just the average. (A+B)/2 Geometric mean is the number such that A:x is x:B $\frac Ax = \frac xB$Cross-multiply:$AB=x^2\implies x=\sqrt{AB}$
3. blahblah_who_cares
thx
#### Ask your own question
Ask a Question
Find more explanations on OpenStudy | 2015-03-02 03:41:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.7399814128875732, "perplexity": 2899.136984557808}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "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-2015-11/segments/1424936462700.28/warc/CC-MAIN-20150226074102-00321-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://www.thomasmarks.space/ | # Thomas Marks
Here's some math which is not embedded in a LaTeX article:
$x + y \lt 2$
Here's some more math which is embedded in a LaTeX div but not in an article: $x + y \le 7$
\documentclass{article} \usepackage{amsmath} \begin{document} Here's an entire LaTeX article embedded into the HTML page \begin{eqnarray*} x + y &\gt& 2\\ x + y &\lt& 2\\ x + y &=& 2 \end{eqnarray*} \noindent As you can see, Eq.~\ref{greaterthan} shows that $x + y \gt 2$ and Eq.~\ref{lessthan} shows the opposite \end{document} | 2022-05-24 12:55:33 | {"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": 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": 0.999923825263977, "perplexity": 2350.937655785565}, "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-2022-21/segments/1652662572800.59/warc/CC-MAIN-20220524110236-20220524140236-00796.warc.gz"} |
https://puzzling.stackexchange.com/questions/42758/find-the-rule-triplet-number-into-positive-integer | # Find the rule : triplet number into Positive Integer
These are triplets of numbers into positive integers:
[0,0,0] => 0
[1,0,0] => 1
[1,1,0] => 2
[1,1,1] => 3
[2,0,0] => 4
[0,2,0] => 5
[1,2,0] => 6
[1,2,1] => 7
[1,1,2] => 8
[2,2,0] => 9
[3,1,0] => 10
...
[3,2,1] => 15
...
[3,3,3] => 36
[4,4,4] => 66
[5,5,5] => 105
[6,6,6] => 153
$[10,10,10]$ => $?$
Note :
• I have checked that every integer from $0$ to $10^6$ can be written into a triplet (so, I believe it's true for every integer);
• Usually, $[a,b,c] ≠ [b,c,a] ≠ [c,b,a]$;
• An integer can have some triplet, but not vice versa. Example [2,2,0] = [3,0,0] => 9.
I added more examples, so I hope the information is enough now.
We plainly don't have enough information here, but here is a class of solutions.
[a,b,c] maps to f(a)+g(b)+h(c) where f,g,h are functions with the following properties:
f(0)=0, f(1)=1, f(2)=4, f(3)=9 (so there's an obvious guess for f)
g(0)=0, g(1)=1, g(2)=5
h(0)=0, h(1)=1, h(2)=6
every nonnegative integer has a representation as f+g+h
So it's clear enough that
we can find plenty of f,g,h having these properties (I can give several if requested)
but the challenge is
to find "nice" ones (it seems like g,h "want" to grow faster than the square numbers which introduces a little difficulty in making sure every nonnegative integer is represented).
The obvious guess is
f = square numbers, g = pentagonal numbers, h = hexagonal numbers
and my numerical expectation suggests that this probably works. I haven't attempted to find a proof (either someone else's or my own); it might be difficult to prove if true.
Anyway, the question asked for [10,10,10]. With the representation above that would yield
$10^2 + \frac{1}{2}10(3\cdot10-1) + 10(2\cdot10-1)=100+145+190=435$.
• I have add some more example, so I hope the information are enaugh now. And your guess is right, so just answer what is [10,10,10] – Jamal Senjaya Sep 19 '16 at 10:21
• Done (at about the same time as you were writing that comment). – Gareth McCaughan Sep 19 '16 at 10:25 | 2019-07-24 09:32:58 | {"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": 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": 0.7521408200263977, "perplexity": 2807.530580922266}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195532251.99/warc/CC-MAIN-20190724082321-20190724104321-00516.warc.gz"} |
http://www.gamedev.net/topic/649285-spherical-harminics-need-help/ | • Create Account
# Spherical Harminics: Need Help :-(
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
16 replies to this topic
### #1mauro78 Members - Reputation: 187
Like
0Likes
Like
Posted 23 October 2013 - 02:41 PM
Hi All, I've just started reading classical papers on SH (Green and Peter-Pike Sloan papers tbp)
Our renderer by now just uses "Reflective Shadows Maps" to evaluate VPL and attempt to create a global illumination solution. Problem is that "naive" RSM just can't be used in Real Time applications. So I've started looking at more advanced techniques like LPV and Radiance Hints.
So far I understand that SH are the base of those techniques....I'll try to explain my objectives:
Goal 1: We've a 3D scene with n lights and a 64x64x64 grid over the whole 3D scene. Every "cell" is a light probe and I want to use SH to store incoming illumination from the n lights
Goal 2: Use the 64x64x64 "probes" texture to interpolate GI for the scene in a final (deferred) renderer pass
Problem: I really really struggling understanding how SH works and how they can help me storing incoming radiance from scene lights.
Can someone help me on that and point me in the right direction?
### #2MJP Moderators - Reputation: 17729
Like
2Likes
Like
Posted 23 October 2013 - 03:15 PM
Spherical harmonics can be used to store a function on the surface of a unit sphere. in simpler terms, this means that if you have a point in space then you can pick a normalized direction from that point and use SH to get back a value for that direction. It's basically like having a cubemap, where you also use a direction to look up a value. The catch with spherical harmonics is that they can usually only store a low-frequency (very blurry) version of your function. The amount of detail is tied to the order of the SH coefficients: higher order means more details, but it also means more storing more coefficients (the number of coefficients is Order^2). In general 3rd-order is considered sufficient for storing diffuse, since diffuse is very smooth at a given point.
To compute SH coefficients, you have to be able to integrate your function. In your case the function is the radiance (incoming lighting) at a given point for a given direction. The common way to do this is first render a cubemap at the given point, and then integrate the values in the cubemap texels against the SH basis functions. Rendering the cubemap is easy: just render in the 6 primary directions and apply lighting and shaders to your geometry the way that you normally would.For performing the integration, there's some pseudo code in Peter-Pike Sloan's "Stupid SH Tricks" paper. Another way to do this would be to use a ray-tracer, and shoot random rays out from the sample point and perform monte carlo integration.
Once you have the SH coefficients at all of your sample points, you can interpolate them based on the position of the surface being shaded. Then you can "look up" the diffuse lighting from the coefficients using the normal direction of the surface.
### #3mauro78 Members - Reputation: 187
Like
1Likes
Like
Posted 24 October 2013 - 01:46 PM
Spherical harmonics can be used to store a function on the surface of a unit sphere. in simpler terms, this means that if you have a point in space then you can pick a normalized direction from that point and use SH to get back a value for that direction. It's basically like having a cubemap, where you also use a direction to look up a value. The catch with spherical harmonics is that they can usually only store a low-frequency (very blurry) version of your function. The amount of detail is tied to the order of the SH coefficients: higher order means more details, but it also means more storing more coefficients (the number of coefficients is Order^2). In general 3rd-order is considered sufficient for storing diffuse, since diffuse is very smooth at a given point.
To compute SH coefficients, you have to be able to integrate your function. In your case the function is the radiance (incoming lighting) at a given point for a given direction. The common way to do this is first render a cubemap at the given point, and then integrate the values in the cubemap texels against the SH basis functions. Rendering the cubemap is easy: just render in the 6 primary directions and apply lighting and shaders to your geometry the way that you normally would.For performing the integration, there's some pseudo code in Peter-Pike Sloan's "Stupid SH Tricks" paper. Another way to do this would be to use a ray-tracer, and shoot random rays out from the sample point and perform monte carlo integration.
Once you have the SH coefficients at all of your sample points, you can interpolate them based on the position of the surface being shaded. Then you can "look up" the diffuse lighting from the coefficients using the normal direction of the surface.
Assumption #1
In my mind a "light probe" is a point in space X where I want to store incoming radiance from a set of VPL (virtual point lights).
To store this incoming radiance the "Rendering Equation" must be solved L(X,W) somehow; evaluating this equation can tell us how much radiance is coming to point X from direction W.
Rendering Equation is complex to solve and one way to solve it is "Monte Carlo" integration.
Assumption #2
Spherical Harmonics can be used to store incoming radiance to X and approximate the "Rendering Equation".
What I don't get :-(
To compute SH coefficients, you have to be able to integrate your function. In your case the function is the radiance (incoming lighting) at a given point for a given direction. The common way to do this is first render a cubemap at the given point, and then integrate the values in the cubemap texels against the SH basis functions. Rendering the cubemap is easy: just render in the 6 primary directions and apply lighting and shaders to your geometry the way that you normally would.For performing the integration, there's some pseudo code in Peter-Pike Sloan's "Stupid SH Tricks" paper. Another way to do this would be to use a ray-tracer, and shoot random rays out from the sample point and perform monte carlo integration.
This what I don't understand from your reply: It's necessary to render the cube maps? I mean I understand that SH will help me "compress" the cube maps (becouse storing them for let's say 32x32x32 grid of probes would requires too much memory)....and then lookup them using SH...but wouldn't be too expensive create those cube maps in real time? I'm using RSM to store virtual point light of the scene...is it possible to store incoming radiance into SH without using Cube Maps?
EDIT:
Another way to do this would be to use a ray-tracer, and shoot random rays out from the sample point and perform monte carlo integration.
This is close to my goal: I have a probe point in space and I have n VPL...I want to shoot ray over the point sphere (hemishpere) and compute the form factor between the point and n VPL. But storing those informations requires a lot of memory....so SH comes in help....
Edited by mauro78, 24 October 2013 - 02:00 PM.
### #4Digitalfragment Members - Reputation: 1282
Like
1Likes
Like
Posted 24 October 2013 - 04:58 PM
This what I don't understand from your reply: It's necessary to render the cube maps? I mean I understand that SH will help me "compress" the cube maps (becouse storing them for let's say 32x32x32 grid of probes would requires too much memory)....and then lookup them using SH...but wouldn't be too expensive create those cube maps in real time? I'm using RSM to store virtual point light of the scene...is it possible to store incoming radiance into SH without using Cube Maps?
Most video cards can render the scene into 6 128x128 textures pretty damn quick, given that most video cards can render complex scenes at resolutions of 1280x720 and up without struggling. You would then also perform the integration of the cubemap in a shader as well, instead of pulling the rendered textures down form the GPU and performing it on the CPU. This yields a table of colours in a very small texture (usually a 9 pixel wide texture) which can then be used in your shaders at runtime. You dont need to recreate your SH probes every frame either, so the cost is quite small.
The Stupid SH tricks paper also has functions for projecting directional, point and spot lights directly onto the SH coefficients table, however the cubemap integration is much more ideal as you can trivially incorporate area and sky lights.
### #5LorenzoGatti Crossbones+ - Reputation: 3902
Like
0Likes
Like
Posted 25 October 2013 - 02:07 AM
"integrate the values in the cubemap texels against the SH basis functions" This means, in unfortunately vague language, the standard procedure for function transforms with a set of orthogonal basis functions: integrate the product of the original function you want to approximate (in this case incoming light from every direction or the like, represented as a cubemap) and the conjugate of each basis function (in this case one of the low-frequency SH functions you want to include in your approximation) over the whole domain (in this case a sphere) to get the coefficient of that basis function (which should be normalized to reconstruct original function values). Where did you get the impression that a "cubemap" is a 3D object? It consists of 6 square panels forming the faces of a cube-shaped box, and as MJP suggests it is another representation for functions that are defined on a sphere. Technically, cubemap faces are regular 2D textures. OpenGL offers a family of special texture types and samplers and filtering to tie together the 6 faces and interpolate across cube edges, but these features are obviously an alternative to spherical harmonics. (You might find them useful to handle cube maps in precomputation phases).
Omae Wa Mou Shindeiru
### #6Reitano Members - Reputation: 690
Like
1Likes
Like
Posted 25 October 2013 - 10:18 AM
Directional, spot and point lights are ideal lights. From the point of view of a probe, they emit radiance within an infinitesimal solid angle. In signal processing, you would call them impulses. You can only describe them analytically, not with a cubemap, unless you approximate them with an area light somehow. The way to go is by projecting them to SH basis with analytical formulas, as discussed in the Stupid SH tricks paper. So not, you don't need to render cubemaps in this case.
### #7mauro78 Members - Reputation: 187
Like
1Likes
Like
Posted 28 October 2013 - 12:58 PM
This what I don't understand from your reply: It's necessary to render the cube maps? I mean I understand that SH will help me "compress" the cube maps (becouse storing them for let's say 32x32x32 grid of probes would requires too much memory)....and then lookup them using SH...but wouldn't be too expensive create those cube maps in real time? I'm using RSM to store virtual point light of the scene...is it possible to store incoming radiance into SH without using Cube Maps?
Most video cards can render the scene into 6 128x128 textures pretty damn quick, given that most video cards can render complex scenes at resolutions of 1280x720 and up without struggling. You would then also perform the integration of the cubemap in a shader as well, instead of pulling the rendered textures down form the GPU and performing it on the CPU. This yields a table of colours in a very small texture (usually a 9 pixel wide texture) which can then be used in your shaders at runtime. You dont need to recreate your SH probes every frame either, so the cost is quite small.
The Stupid SH tricks paper also has functions for projecting directional, point and spot lights directly onto the SH coefficients table, however the cubemap integration is much more ideal as you can trivially incorporate area and sky lights.
Edited by mauro78, 28 October 2013 - 01:01 PM.
### #8mauro78 Members - Reputation: 187
Like
1Likes
Like
Posted 28 October 2013 - 01:11 PM
"...Where did you get the impression that a "cubemap" is a 3D object? ..."
really mate.....I didn't ever think about this.....but do I think that cubemaps are not so real time friendly.....I hope I'm wrong
And also most important: can be used to store irradiance for indoor scene or are they better suited for outdoor scenes?
Thx
Edited by mauro78, 28 October 2013 - 02:47 PM.
### #9mauro78 Members - Reputation: 187
Like
1Likes
Like
Posted 28 October 2013 - 01:24 PM
Directional, spot and point lights are ideal lights. From the point of view of a probe, they emit radiance within an infinitesimal solid angle. In signal processing, you would call them impulses. You can only describe them analytically, not with a cubemap, unless you approximate them with an area light somehow. The way to go is by projecting them to SH basis with analytical formulas, as discussed in the Stupid SH tricks paper. So not, you don't need to render cubemaps in this case.
Ok I need to clarify this with some background informations:
my first attempt on using a GI in the engine was using RSM (reflective shadows maps); as you know the basic idea is:
1. Render a RSM for every light in the scene
2. Gather VPL (virtual point light) from every RSM and use those VPL as secondary light source
float3 Bounce2(float3 surfacePos, float3 normal, float3 worldSpace,float3 worldNormal,float3 Flux ){
float distBias = 0.1f;
float3 R = (worldSpace) - surfacePos;
float l2 = dot (R,R);
R *= rsqrt (l2);
float lR = 1.0f / ( distBias + l2 * 3.141592);
float cosThetaI = max (0.1, dot(worldNormal,-R));
float cosThetaJ = max (0.0, dot(normal,R));
float Fij = cosThetaI * cosThetaJ * lR;
return Flux*Fij;
}
The above code is used to compute how much light reaches a world space point from the (world space) secondary sources.
Clearly this approach has many drawbacks....slow slow slow (even using interpolation methods).
This lean towards the SH approach where my goal is to use the above Bounce function to collect incoming light from secondary sources and storing them using SH into the "probes".
So my question is how I store incoming lights from the VPL using SH into sample probes?
### #10Reitano Members - Reputation: 690
Like
1Likes
Like
Posted 30 October 2013 - 08:57 AM
I am not familiar with RSMs but, judging from the code you posted, I believe SH suit your needs.
Remember that SH represent a signal defined over a spherical domain. In this case the signal is the total incoming light from all the secondary sources. A SH probe has an associated position in world space. For a <light, probe> pair, the signal is (cosThetaI * lR * Flux) in the direction defined by R (normalized). The cosThetaJ term depends on the receiver's normal and will be taken into account later at runtime when shading a surface.
Some pseudo-code:
for each probe
SH = 0
for each light
signal = R / | R | * (cosThetaI * lR * Flux)
SH += signalToSH(signal)
signalToSH is a function that encodes a directional light in the SH basis. See D3DXSHEvalDirectionalLight for an implementation.
At runtime, when shading a pixel, pick the probe spatially closest to it. The pixel has a normal associated. Assuming that the BRDF is purely diffuse, you have to convolve the cosine lobe around the pixel's normal with the signal encoded in the probe, achieved with a SH rotation and dot product. See the paper http://www.cs.berkeley.edu/~ravir/papers/envmap/envmap.pdf
I suggest you read more material on SH in order to have a better understanding of their properties and use cases. As for myself, I will read the RSM paper asap and edit my reply if I've made wrong assumptions.
Please let me know if you have more questions.
Stefano
### #11mauro78 Members - Reputation: 187
Like
1Likes
Like
Posted 30 October 2013 - 04:07 PM
I am not familiar with RSMs but, judging from the code you posted, I believe SH suit your needs.
Remember that SH represent a signal defined over a spherical domain. In this case the signal is the total incoming light from all the secondary sources. A SH probe has an associated position in world space. For a <light, probe> pair, the signal is (cosThetaI * lR * Flux) in the direction defined by R (normalized). The cosThetaJ term depends on the receiver's normal and will be taken into account later at runtime when shading a surface.
Some pseudo-code:
for each probe
SH = 0
for each light
signal = R / | R | * (cosThetaI * lR * Flux)
SH += signalToSH(signal)
signalToSH is a function that encodes a directional light in the SH basis. See D3DXSHEvalDirectionalLight for an implementation.
At runtime, when shading a pixel, pick the probe spatially closest to it. The pixel has a normal associated. Assuming that the BRDF is purely diffuse, you have to convolve the cosine lobe around the pixel's normal with the signal encoded in the probe, achieved with a SH rotation and dot product. See the paper http://www.cs.berkeley.edu/~ravir/papers/envmap/envmap.pdf
I suggest you read more material on SH in order to have a better understanding of their properties and use cases. As for myself, I will read the RSM paper asap and edit my reply if I've made wrong assumptions.
Please let me know if you have more questions.
Stefano
Ok first thanks for response and yes I need to dig into SH realms better.... but let's make it simple Stefano (well not so simple ): given a normal vector n (x,y,z) I can get second order SH coefficents c = (c0,c1,c2,c3)
where:
c0 = sqrt(pi) / 2
c1 = -sqrt(pi/3) * y
c2 = sqrt(pi/3) * z
c3 = - sqrt(pi/3) * x
so for every VPL ( virtual point light ) I'll have a n vector and an associated SH coefficents c.
The question is how I can go back and compute reflected radiance from those second order SH coefficents?
Thanks
Mauro
Edited by mauro78, 30 October 2013 - 04:33 PM.
### #12Reitano Members - Reputation: 690
Like
0Likes
Like
Posted 31 October 2013 - 06:21 AM
Mauro, can you explain the meaning of that normal vector n ? Is it the normal of the receiving or emitting surface ? Or is it the vector connecting the emitter and receiver ? And how did you derive the four SH coefficients ?
### #13mauro78 Members - Reputation: 187
Like
0Likes
Like
Posted 01 November 2013 - 06:33 AM
Mauro, can you explain the meaning of that normal vector n ? Is it the normal of the receiving or emitting surface ? Or is it the vector connecting the emitter and receiver ? And how did you derive the four SH coefficients ?
N emitting normal
SH derivation is order 2 truncation of polynomial form...
### #14mauro78 Members - Reputation: 187
Like
0Likes
Like
Posted 04 November 2013 - 02:39 PM
I've read more on SH during this weekend and I'm even more conviced that is the right solution for my goal. To summarize right know with RSM (and associated Virtual Lights) I'm doing this:
compute "irradiance" between the pixel and the i-th Virtual Light
This is very slow of course....so a potential solution using SH is:
teake some probes on the scene and for every probe compute incoming radiance and store it using SH.
Then at runtime the shading pass will be:
compute the interpolated irradiance reading the nearest probe using the pixel normal as index into SH
Edited by mauro78, 04 November 2013 - 02:48 PM.
### #15Reitano Members - Reputation: 690
Like
0Likes
Like
Posted 05 November 2013 - 06:05 AM
Mauro, that sounds like the correct approach. About storing the irradiance with SH, what is unclear about the description I wrote in my previous post ? To recap, given a probe and a light, the radiance from the light to the probe has an analytical formula and you can calculate directly the corresponding SH coefficients.
### #16mauro78 Members - Reputation: 187
Like
0Likes
Like
Posted 05 November 2013 - 03:23 PM
Mauro, that sounds like the correct approach. About storing the irradiance with SH, what is unclear about the description I wrote in my previous post ? To recap, given a probe and a light, the radiance from the light to the probe has an analytical formula and you can calculate directly the corresponding SH coefficients.
well almoust clear...working on this...hope to post reusults soon...also exploring "shooting" rays from the probe to get incoming radiance....
I get the key point after reading the paper "Stupid SH Tricks": for my own goal the best solution would be compute the incoming radiance from a VPL from all the possible directions over a sphere. This is just the integral over a surface. Of course I was aware that storing this was impossible for real time solution.
So I reading the paper I had sort of enlightment: SH will allow me to express the above integral using SH basis and original fuction samples. SH basis simple express the sampling direction....of course we've some degree of detail here....second order SH is just a raw solution....high order SH can better approximate the spherical function...
This will awill allow me to reconstruct original (approximated) function later on shading phase....Very similar to Fourier series for 1D case.
back on work now....
EDIT: the bad news is that I'll probably not go throught Light Propagation Volume but stick with Irradiance Volume...mostly becouse LPV requires DX11 hardware to be efficently implemented (even if volume textures can be handled in DX9 using some tricky code)
Edited by mauro78, 05 November 2013 - 04:17 PM.
### #17graveman Members - Reputation: 110
Like
0Likes
Like
Posted 07 November 2013 - 12:42 AM
mauro78. Man, it is need study integrals, rows, differential expressions for understand SH. I study that from march of 2013. Some integrals of lighting decompose into orthogonal function (function can be presented as multidimensional vector and a dot will be match for integral).
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
PARTNERS | 2016-08-28 05:50:26 | {"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": 0.2770266830921173, "perplexity": 1735.1307313099046}, "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-2016-36/segments/1471982932823.46/warc/CC-MAIN-20160823200852-00098-ip-10-153-172-175.ec2.internal.warc.gz"} |
http://www.apmonitor.com/wiki/index.php/Main/OptionApmNodes?action=print | # Main: APM.NODES - APMonitor Option
Type: Integer, Input
Default Value: 3
Description: Nodes in each horizon step
NODES are the number of collocation points in the span of each time segment. For dynamic problems, the time segments are linked together into a time horizon. Successive endpoints of the time segments are merged to form a chain of model predictions. Increasing the number of nodes will generally improve the solution accuracy but also increase the problem size and computation time. Solution accuracy can also be improved by adding more time segments. | 2017-11-23 14:56:42 | {"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": 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": 0.6242771148681641, "perplexity": 916.6296951827296}, "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-2017-47/segments/1510934806842.71/warc/CC-MAIN-20171123142513-20171123162513-00512.warc.gz"} |
https://huangyiwei.wordpress.com/2011/08/07/problem2d/ | ## Problem2D
Problem2D: Here is a variation on the above greedy algorithm. Let ${ x_{1}}$ be any vertex of a weighted connected graph ${G}$ with ${n}$ vertices and let ${T_{1}}$ be the subgraph with the one vertex ${x_{1}}$ and no edges. After a tree (subgraph) ${ T_{k}}$, ${k, has been defined, let ${e_{k}}$ be a cheapest edge among all edges with one end in ${V(T_{k})}$ and the other end not in ${V(T_{k})}$, and let ${T_{k+1}}$ be the tree obtained by adding that edge and its other end to ${T_{k}}$. Prove that ${T_{n}}$ is a cheapest spanning tree in ${G}$.
Solution: This algorithm is called Prim’s algorithm. The proof can be found in Wikipedia. We state the proof here again. Suppose ${T^{\prime }}$ is a cheapest spanning tree. If ${T_{n}=T^{\prime }}$, the proof finished. Otherwise, let ${e_{k}}$ be the first edge not in ${T^{\prime }}$ when we generate ${T.}$ Denote by ${V}$ all the edges before we add ${e_{k}}$. Since ${ T^{\prime }}$ is a spanning tree, there is a unique cycle in ${T^{\prime }}$ containing two ends of ${e_{k}}$. We claim that there is at least one edge ${w}$ having one end in ${V}$, and the other end not in ${V}$. Otherwise, if all the vertices of the cycle are in ${V}$, ${T_{n}}$ will contain a cycle, a contradiction. On the other hand, not all the vertices are outside of ${V}$ since one end of ${e_{k}}$ is in ${V}$. So there must exists at least one edge ${w }$ having one end in ${V}$ and the other not in ${V}$. By Prim’s algorithm, ${ c(w)\geq c(e_{k})}$, otherwise ${w}$ would be chosen rather than ${e_{k}}$. Add ${ e_{k}}$ to ${T^{\prime }}$ and delete ${w}$, we obtain a new spanning tree ${ T^{\prime \prime }}$ which is still a cheapest spanning tree. Keep doing this until we obtain a cheapest spanning tree identical to ${T}$,
Note: The hint in the book says that ${T_{n}}$ has the property that for every edge ${e}$ in ${T_{n}}$, the ends of ${e}$ are in different components of ${G:\left\{ w:c(w). And any spanning having this property will be a cheapest spanning tree. I still do not know how to show the second part. I shall be happy if anyone can suggest the solution. | 2018-01-16 17:29:47 | {"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": 48, "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": 0.6851980090141296, "perplexity": 740.6921913649371}, "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/1516084886476.31/warc/CC-MAIN-20180116164812-20180116184812-00685.warc.gz"} |
http://kvtd.elist-directory.it/draw-contour-map-online.html | # Draw Contour Map Online
Preparing students to draw from real life is preparing them to primarily observe the details around them. It can also be used to draw any shape provided you have its boundary points. The remaining USGS Topographic Maps for the US are are from the National Geographic TOPO! program. They are very detailed and are often produced on large sheets of paper. The scale on the topo map is found at the bottom center of the map. I recently started drawing as a hobby. In 1782 he created a map of the ‘main chains’ of mountains (millipedes), and principle courses of the rivers of France. If you aren't producing them in your career, you will at the very least be using them a lot! Finally, contour maps can also be very aesthetically pleasing to create and to see. The teacher and students will create their own drawing notebook, with a front cover that depicts rock art images/designs or a pattern that repeats. Working downslope from the highest elevation, thread contours through ticks of equal value. Origin can create contour plots directly from XYZ data in a worksheet without the need for an intermediate matrix. Select a layer and click where to start drawing. ExpertGPS is the ultimate GPS map software for planning outdoor adventures. Maps have the following size limits: Up to 10,000 lines, shapes, or places ; Up to 50,000 total points (in lines and shapes) Up to 20,000 data table cells; Click Draw a line Add line or shape. To make topographic maps easier to read, every fifth contour line is an index contour. Imagine that your pencil line was a grey string that you could lift up in one piece. A single sheet from the topographical map series (SWPA T731) covering the city of Balikpapan and surrounding area, in Dutch Borneo (now the Indonesian province of Kalimantan Timur), and overprinted to show locations of key installations and infrastructure. There is really no fancy technology here. 3D DEM from Contour Map ; CAD Drawing Conversion ; Geo-Referencing & Image Processing ; Image Gallery; R2V. The property line map links use our exclusive "map-in-a-link" technology. Get the free "Contour Plot" widget for your website, blog, Wordpress, Blogger, or iGoogle. National Geographic is allowing everyone to easily download any USGS 7. Finally, draw your contour lines. This is a quick and simple exercise you can repeat as many times as you like. Customize your map by adding text using the drawing tools. Quickly generate a travel map, shipping map, or flight route map. Whitney at 14,494 feet - the highest point in California. In above image, you can see a variety of shapes cut out from pieces of construction paper. The only way to see these maps is to check with the Survey Department. Translation for: '(Geology) fold shown on a map as concentrically arranged contour patterns whose amplitude decreases to zero in a regular fashion in two directions, dome-shaped, parallel to outside wall' in English->English dictionary. Multivariable Calculus, International Metric Edition (8th Edition) Edit edition. Download contours as vector graphics. Along the way, the relative sizes, shapes, and directions of lines are noted and copied, a bit at a time. On occasion users have reported gaps in their contour lines, this should of course never happen. 19 million downloads, a few tools, many tutorials, and image hosting. Upload/download tracks and waypoints from your GPS. Contour lines that are far apart indicate there is a small change in vertical elevation given the horizontal distance. Find latitude and longitude of Indian States to calculate actual geographical location of all India states on earth through map. Keep in mind the following characteristics of contour lines (Rabenhorst and McDermott, 1989): Contours should always point upstream in valleys. Because it's impractical to mark the elevation of every contour line on the map, the index contour lines are the only ones labeled. In topographical maps, instead of representing places of equal electric potential, contour lines represent places of equal elevation. To save your map, you will need to enter your email address and the system will send you a set of links to use to edit and share your map. Whether you create a map online or on your desktop, you get SmartDraw's automated drawing tools, hi-res symbols, and presentation-ready output quality. *Note: A valid geomark must include a portion of British Columbia. (Profile view shown in the 3rd photo as an example). USGS US Topo 7. This icon serves as a link to download the eSSENTIAL Accessibility assistive technology app for individuals with physical disabilities. 30am and 2pm (sessions last for 30 minutes) Venue: Discovery Zone, State Library of WA Age: 15+ Cost: Free. Whitney at 14,494 feet - the highest point in California. Geodata only. Please note, as for now, the drawing below is square and you may want to stretch it to cover the actual area in a map. This application uses licensed Geocortex Essentials technology for the Esri ® ArcGIS platform. Memory-Map's is the easiest and quickest way to get Ordnance Survey maps, marine or aviation charts on your PC, iPhone, iPad, or Android device. Draw your route(s), select your colors, add waypoints, then share with friends or family. Create a Custom Google Map in Minutes. A contour is a line drawn on a map that joins points of equal height above sea level. "Draw Tract With Mouse" feature for freehand sketching of a fence line or pond, etc. Selecting your map is easy. A contour drawing is done with one long unbroken continuous line. The purpose is for you to gain an understanding of how contouring is accomplished. Publication Date 2017-12-20 Start Date 1953-01-01 End Date 2017-09-14 File Modification Date 2018-03-10 00. Edwards County is covered by the following US Topo Map quadrants. A thorough explanation of ggplot is well beyond the scope of this post, but here are quick details on what is passed to geom_point:. 5 stars { review. The present invention is generally directed to a device for assisting a user in drawing a topographical contour map through the plotting of multipoints in multiple directions comprised of a frame including opposed first and second pairs of frame members where each of the frame members has ends that are pivotally connected to the ends of adjacent frame members so that the frame be readily moved to assume a variety of parallelogram shapes, and a plurality of equally spaced-apart linear. Download it free today. Online Map Software that Works on Any Device SmartDraw works wherever you are. Click the contour line that you want to adjust, then click the Move Tool> press the up key button (keyboard)> pull-up the selected contour line or object vertically (it is locked to the blue axis)> Type the elevation value shown in 'Measurements Toolbar' (follow the elevation value from the Google map)> press Enter key. In the Generate Contour dialog box, enter a name for the new Display Manager layer that will contain the contour lines. Custom-printed topographic (topo) maps, aerial photos, and satellite images for the United States and Canada. The 1:250,000 scale USGS Topo Maps are from i-cubed eTOPO. Topography of the USA. Pick a contour interval, start at one edge and extend the contour across the map. The hill will be hard to climb at first, but then it becomes easy. Objective: To understand how to draw a cross section using just contour lines Task 1 - Read the instructions to the right hand side really carefully then complete activities 1 and 2 a,b,c in your books. My experience and abilities: Geodetic, GIS Map (Geographic Information System), GPS (Global Positioning System), Cartography, Topographic Survey, 2D Contour Maps, 3D Contour Maps, Engineering Drawing Piping, Road Engineering Drawings, Engineering Drawing Contruction, Calculate Excavation Cuts and Piles. Now, when I want to get a topo map, I position myself in GE, check one of my topo placemarks, right-click/Refresh, and I get a map. Whitney at 14,494 feet - the highest point in California. Difficulty level on Lake Charlotte Map is moderate to difficult. The maps in the right side list are ranked by coverage, with the maps that have coverage closest to your search window listed at the top. The first exercise, Contour Drawing, dealt with the element of line. Do more with Bing Maps. Lots of detail and lots of bonus information. Ordnance Survey is the national mapping agency of Great Britain, they maintains around 234 000 km² of topographic information, ranging from dense urban conurbations to mountain and moorland areas. Select a contour interval appropriate for the property you’re mapping. d = 300 feet • There are to be three contour lines on this interval. We usually start each map series from the Pacific Northwest, and moving onward from there. The authority on active adventure, Backpacker is the world's first GPS-enabled magazine, and the only magazine whose editors personally test the hiking trails, camping gear, and survival tips they publish. You need to plan this out so that you don't end up with a mess of lines. Once you’ve decided on a scale, it’s time to draw out the perimeters of your garden onto your map. AGT has been producing easy to use and affordable land surveying software since 1986. Create any number of contour maps on a page Print maps in black-and-white or full color Overlay base, vector, shaded relief, image, or post maps on contour maps Drape contour maps over 3D surfaces for dramatic displays Export contours in 3D DXF format 3D Surface Maps The 3D surface map uses shading and color to emphasize your data features. This map is provided to assist voters in locating the Vote Center (including Drive-Through locations), Mobile Vote Center locations, 24-Hour Ballot Drop-Off Boxes and a link to the Interactive Sample Ballot for the 2020 General Election. To display contour lines on top of the aerial click the button in the upper right corner of the map, go down to the "Overlay" section and click "USA_contour_lines". Looking for iGage All Topo Maps Arkansas Map CD-ROM (Windows)? We have found the best price. Free USGS topo maps! Use CalTopo for collaborative trip planning, detailed elevation profiles and terrain analysis, printing geospatial PDFs, and exporting maps to your smartphone as KMZ or MBTiles files. Plan your next outdoor adventure over scanned USGS topo maps and send a route directly to your GPS receiver to guide you in the field. With AllTrails you can easily create custom maps from your computer. Go to the desired location in the map, set two markers by clicking the map to define a rectangle (or enter coordinates manually). The map will show your approximate property lines on the Google aerial and on a high resolution topographic map. You also can improve existing maps that show locations of underwater mountains, drop offs, crevices or wrecks. Step 4 Optional styling of the plot. ∎ an outline of a natural feature such as a hill or valley. Jump to: Share your current view of the map! (Permalink) Edit OpenStreetMap data here. Draw Contour Map Online. called US Topo that are separated into rectangular quadrants that are printed at 22. Step 4 Optional styling of the plot. Online topographic (topo) maps with trails and high-resolution aerial photos of all the United States (US) (USA) and Canada. A blind contour drawing may look a. TERNARYCONTOUR. Contour Map:A contour map is a 2-dimensional drawing of land, which includes contour lines to show changes in the elevation of the land. Elevation contours are imaginary lines connecting points having the same elevation on the surface of the land above or below a reference surface, which is usually mean sea level. The USGS has introduced a new generation of topographic maps. Even though you can, and should, group related path objects into folders, they are still separate unconnected objects on the map—there's no way to "group" the objects so they can. So, as the book I got suggested, I started trying some countour. 19 million downloads, a few tools, many tutorials, and image hosting. The latest series has improvements over the 2011 series including Forest service roads and trails, structures, improved NHD, PLSS, and more. Suitable for recreation, businesses, emergency services. Define the word contour as; a line drawn to represent the outermost edge of an object. If you're using Maps in Lite mode, you’ll see a lightning bolt at the bottom and you won't be able to measure the distance between points. Create 3D maps and contour plots. However, the difference. Print free USGS topo PDFs! Export topographic maps to Google Earth and Garmin GPS as KML and KMZ files. 5 minute topo map in the continental U. So, as the book I got suggested, I started trying some countour. Draw lines, polygons, markers and text labels on Google maps. Jan 24, 2019 - Credits: Wikipedia So far we’ve used our Digital Elevation Model (DEM) to create hillshade and color relief. Disclaimer: This Web site is offered as a public service, integrating various government records into a region-wide mapping system. A simple grid will be used to demonstrate this point. After you create the contours of the water table, you should draw an arrow (5 points) indicating the direction of groundwater flow. js) but without dynamically changing the colors and the extent of the graphical objects (as in case of heatmap. Geological Survey for decades, with nice. Clicking on a map in the list will open it in the Luna Browser. Start by using a ruler to draw a border around your picture area, leaving enough room around your composition for matting at the end. The ratio scale on this map is 1:24,000. Find more Mathematics widgets in Wolfram|Alpha. To add another point, click anywhere on the map. Jeff’s series of Algonquin maps are exceptional. Find latitude and longitude of Indian States to calculate actual geographical location of all India states on earth through map. To draw a topological map, you need to draw a symbol for each location, and a bunch of lines connecting them together (representing the routes between them). Plan your next outdoor adventure over scanned USGS topo maps and send a route directly to your GPS receiver to guide you in the field. Homework #1 Due Aug 26th Define ‘Contour line’ As it relates to drawing (not maps) Find and print or sketch in your sketchbook a contour line drawing. However, it is easy to draw a property map without this information if you have a copy of the deed. Click the contour line that you want to adjust, then click the Move Tool> press the up key button (keyboard)> pull-up the selected contour line or object vertically (it is locked to the blue axis)> Type the elevation value shown in 'Measurements Toolbar' (follow the elevation value from the Google map)> press Enter key. Map multiple locations, get transit/walking/driving directions, view live traffic conditions, plan trips, view satellite, aerial and street side imagery. Contour lines mark points of equal elevation on a map and are critical to understand the elevation profile of your terrain. They function exactly like contour lines on a topographic map. com - id: 59b69a-OGU3M. These realistic views also retain the various elements you add to your customized maps—trails, MapNotes, GPS waypoints, and Draw objects. A contour map of a function is shown. Step 4 Optional styling of the plot. You can control spacing of contour lines with the spacing slider; if necessary you can check the “Custom box” and set your own. World scale; Nation scale. Functions; User List; Quick Start Video Tutorials ; Contour Digitizing and 3D DEM Tutorial ; Map Section Merge Tutorial; Frequently Asked Questions; User's Manual; Brochure ; R2V Related Publications; Purchase. d = 300 feet • There are to be three contour lines on this interval. When the contour lines of a hill are close together at first, then get farther apart, the hill is _____. I will draw 3 variations of a portrait of you in the style of blind contour drawing. The software component SWLib and others are available. We should have a contour plot created like the one below. Red Bluff Draw topo maps are provided as PDF files. It creates a 3D map or a contour chart from the scattered points, numerical arrays or other data sets. This is a generalized topographic map of Georgia. Screenshots; Help; Download, Customize, and Print High-Resolution USGS Topo Maps for Virginia. If you've ever used a trail map while hiking, you've seen contour lines before. Multivariable Calculus, International Metric Edition (8th Edition) Edit edition. The syntax for adding functions is fairly standard. With Quickdraw Contours, you can create maps that show you depth contours clearly labeled on the screen. contour is a ‘bare bones’ interface to add just the contour plot to an already-set-up plot region. You need to plan this out so that you don't end up with a mess of lines. This does not work well for illuminated contours! It will export polygons, but you'll have better luck achieving the effect in your favorite graphics editing software. Learn more about contour, efficiency map, motor efficiency map, power_electronics_control, electric_motor_control. Map Making with a Tennis Ball - Students carefully wrap a tennis ball in paper and then draw their own globe. Some people are lucky enough to have a bit of free web space somewhere they can use, but for those of you that don’t there are a number of services that will host files for you for free. Build, create and embed interactive Google maps with drawings and labels. CorelDRAW 2020 unveils its fastest, smartest, and most collaborative graphics suite yet. The human figure forms one of the most enduring themes in life drawing that is applied to portraiture, sculpture, medical illustration, cartooning and comic book illustration, and other fields. 5 Minute Topo Map [34. In this ecology lesson, students draw the boundaries of a watershed onto a map using contour lines as a guide. Put an X where the stream joins the main river. Select Contour mode using the check box. Step 4: Match Then the carpet or tile will completely match the contour of the corner. See more ideas about Art lessons, Line lesson, Teaching art. Contour and line work mixed with flat color is the foundation of 90% of his art. Our mapping software helps you transform your spreadsheet data into a customized Google Map in seconds. Topography of the USA. These maps depict in detail ground relief (landforms and terrain), drainage (lakes and rivers), forest cover, administrative areas, populated areas, transportation routes and facilities (including roads and railways), and other man-made features. Draw contour lines in AutoCAD ® Selecting an existing terrain mesh contour polylines can be created. iMapBuilder Online Draw lines on a map You can draw lines on the map. Examine the topographic map on the left carefully. Public records of land that contain survey plats, including land maps dated back to 1810, are located on the website for the BLM. 0 MB] 2001 Red Bluff Draw 7. Medina's awesome video on Making a Topographic Profile of the Volcano Model (p. For example, vertical lines drawn up from the two points where line A-B cuts the 200m contour line will stop at the corresponding 200m line on the graph. To convert the heatmap to a contour plot, we need to select 'Contour map' from the TRACE popover, as shown in the figure below. TERNARYCONTOUR. The USGS (U. This exercise, Mass Drawing, deals more with the 3-dimensional reality of figures or objects, that is, their form, or mass, using tonal values of light and dark. Topo map with elevation. *Note: A valid geomark must include a portion of British Columbia. This site is the ultimate source for GPS files including user contributed and created maps, ximage hosting, articles, tutorials, and tools to help you with your projects. With Quickdraw Contours, you can create maps that show you depth contours clearly labeled on the screen. Topo maps for Belgium, Netherlands, France [03/13/17] Topographic maps from RouteYou, covering all of Belgium and the Netherlands, have been added as a background map option in Google Maps. Optionally you can change the number of elevation samples you want in each direction, the more the better. Raster Surface > Contour, or if 3D Analyst extension is not available but Spatial Analyst extension is available, navigate to Spatial Analyst > Surface > Contour. Start drawing your contours in the southwest corner of the map. Blind contour drawing is an exercise, where you draw the contour of a subject without looking at the paper. Contour maps When drawing in three dimensions is inconvenient, a contour map is a useful alternative for representing functions with a two-dimensional input and a one-dimensional output. A collection of tutorials on the core concepts and ideas of drawing. Customize the map and save it to make it your own with bookmarks, drawings, labels, and more. To add another point, click anywhere on the map. Topographic maps show a wide range of human and physical features of the Earth. **If you use mylar, it may be a good idea to mark the corners of the map on the mylar so you can reorient the mylar on the map later if necessary. View Larger Map Google Earth is a great tool for planning a hike. You also can improve existing maps that show locations of underwater mountains, drop offs, crevices or wrecks. Quickly generate a travel map, shipping map, or flight route map. Textbook solution for calculus. When you draw contours on an upper level charts, you should take into consideration the wind values at data points. Selecting your map is easy. Import data from CSV, Excel or CAD for Contour generation Generate Contours directly within CAD Draw Section for any alignment fixed on the Contour Map Generate Contour Area and Contour Volume. I have been using MapMaker to draw the contour lines by hand, which isn't ideal but not a total waste of time, either. We should have a contour plot created like the one below. Measure route distance on Google map. Select Contour mode using the check box. Note where it intersects the contour lines. Online topographic (topo) maps with trails and high-resolution aerial photos of all the United States (US) (USA) and Canada. 5-minute map for Mason Draw, WY 2017. TopoZone has been serving up topographic maps online since 1999. • Mark four points (two on the endpoints, and two between) and draw the contours. Download contours as vector graphics. The scale on the topo map is found at the bottom center of the map. These days, there are a ton of excellent online mapping tools of any flavor for web developers. Draw the initial proposed horizontal tangents on contour map. GeoPDF maps can be downloaded FREE of charge at the USGS Map Store. All aspects of 2D or 3D maps can be customized to produce exactly the presentation you want. It can also be used to draw any shape provided you have its boundary points. Contour lines are lines connecting points that have the same “height” (z value) on your function. Make your map as realistic as possible. Even though you can, and should, group related path objects into folders, they are still separate unconnected objects on the map—there's no way to "group" the objects so they can. The distinctive characteristic of a topographic map is the use of elevation contour lines to show the shape of the Earth's surface. One of such productive uses of OpenStreetMap data are free maps for Garmin GPS devices as is the case of this website. Import data from CSV, Excel or CAD for Contour generation Generate Contours directly within CAD Draw Section for any alignment fixed on the Contour Map Generate Contour Area and Contour Volume. The same applies to the topo map 3081 13. A simple grid will be used to demonstrate this point. In 2009, a new USGS quadrangle topographic map series was defined. Draw the initial proposed horizontal tangents on contour map. Contour and line work mixed with flat color is the foundation of 90% of his art. Once you’ve decided on a scale, it’s time to draw out the perimeters of your garden onto your map. US Topo maps created after June, 2017 use a different implementation of PDF georeferencing, based on the ISO 32000 PDF standard. Cross contour lines are drawn lines that travel across the form. The Geographic Names Information System allows searches of geographic names to determine which map sheets they appear on. Pan and zoom the map if necessary to find each point. Note where it intersects the contour lines. 5-minute series, but are derived from GIS data. Double-click to complete your drawing. Customize your map by adding text using the drawing tools. Map scale represents the relationship between distance on the map and the corresponding distance on the ground. Contour drawing is something we’ve been doing all our lives, even though we probably don’t even notice it! Kids often draw the contour of their hands. Note where it intersects the contour lines. 5 stars { review. 0 MB] 2001 Red Bluff Draw 7. Contours will be exported as overlapping MultiPolygon features, each with an elevation property. Features:. Contour lines are lines connecting points that have the same “height” (z value) on your function. This is a quick and simple exercise you can repeat as many times as you like. Draw a contour map of the function for the following values of k. void: draw() Draw the Contour as a closed shape with one vertex per-point. This lesson starts with teaching basic directions and mapping techniques, then moves on to taking latitude and longitude coordinates and using global-positioning-system (GPS) units. All the best Drawing Contour Lines Worksheet 36+ collected on this page. TERNARYCONTOUR. Remember: the position of the objects on the map does not have to correspond to their real-life locations. Search nearly 14 million words and phrases in more than 470 language pairs. Find shared maps from other users. This is a normal exercise to do at school when starting to experiment with art. Draw more isotherms to show the temperature pattern across the U. Regards, MCADDeditor. They’re also made of a waterproof, tear-resistant, material, which means they’ll survive far beyond your next trip in the park. Software Files. You can also create individual 3D graphic contour lines if you don't want contours for the whole surface. Let’s add some contours for our terrain …. Look at the three-dimensional drawing of the mountain below. Create contour plots of 3 and 4-D data; Use data from a variety of sources; You can buy a single-user DPlot license for $195(US) or$205 for a CD sent by mail. Draw Contour Map Online. "Draw Tract With Mouse" feature for freehand sketching of a fence line or pond, etc. We’ve been trying to use USGS topo map layer with Open Street Maps, but the contour interval appears to be bigger than on the downloadable 7. This activity provides an opportunity for students to label contour lines on a topographic map, draw a profile of the map, calculate vertical exaggeration for the profile as well as determine stream-flow direction. Maps have the following size limits: Up to 10,000 lines, shapes, or places ; Up to 50,000 total points (in lines and shapes) Up to 20,000 data table cells; Click Draw a line Add line or shape. Whatever method you use, when you do a contour drawing, the goal is to clearly show where the value and hue changes are inside the objects that you’re drawing. Draw contour lines in AutoCAD ® Selecting an existing terrain mesh contour polylines can be created. Add your own data points to the map by importing them from a CSV file. The knuckles will be a mountain range, each knuckle a peak of a mountain. Nov 19, 2018 - Explore CT ArtTeacher's board "Contour Line Lessons", followed by 1157 people on Pinterest. Draw the Framework Onto Your Garden Layout Map. On your computer, sign in to My Maps. Drawing the contour line of $z = \sqrt{xy. The first is a ratio scale. National Geographic is allowing everyone to easily download any USGS 7. Use it on any device—mobile or desktop—Windows ®, Mac ®, Android ®, iOS ®, or on any other platform. In order that customers benefit from the most up-to-date mapping, it is essential that they regularly update their data. There is Grid Math option for regression equations and creating thematic grids, for example for evaporation etc. void: draw() Draw the Contour as a closed shape with one vertex per-point. Measure distances on maps. Delaunay Triangulation is used to compute and draw the contour lines. while the downloadable maps have 20′ contour interval, the digital USGS map tile at the same scale shows 100′ contour interval which is too big for our purposes. The map will show your approximate property lines on the Google aerial and on a high resolution topographic map. To draw a topological map, you need to draw a symbol for each location, and a bunch of lines connecting them together (representing the routes between them). Detailed topographic maps and aerial photos of California are available in the Geology. Scale is represented in two different ways on a topographical map. Save your favorites for the next time you're ready to run. In addition, it sometimes is difficult for students to understand at […]. ch est la plateforme de géoinformation de la Confédération suisse. A ridge or spur is denoted on a map by the contour lines becoming (U/V) -shaped. Disclaimer: This Web site is offered as a public service, integrating various government records into a region-wide mapping system. Go to the desired location in the map, set two markers by clicking the map to define a rectangle (or enter coordinates manually). On your computer, open Google Maps. From here I would like to apply a graduated shading pattern for some specific depths to show safe routes etc. Delaunay Triangulation is used to compute and draw the contour lines. Currently we have 674 maps (many of which are free) with over 3. KML: KML (Keyhole Markup Language) is an XML based file format used to display geographic data in an Earth browser such as Google Earth, Google Maps, and Google Maps for mobile. Geological Survey for decades, with nice. The image base for the new maps is the 2013 NAIP. Map with JOSM Remote; View. Contour Plots with Chart Studio. Contour Lines. Medina's awesome video on Making a Topographic Profile of the Volcano Model (p. Hi, you can share the map as follows with the User Menu at the top right, save the route. To save your map, click the save button. Create contour plots of 3 and 4-D data; Use data from a variety of sources; You can buy a single-user DPlot license for$195(US) or $205 for a CD sent by mail. Now, when I want to get a topo map, I position myself in GE, check one of my topo placemarks, right-click/Refresh, and I get a map. A topographic map can be used to create a cross section along any line drawn on the map. at map time. There is really no fancy technology here. Along the way, the relative sizes, shapes, and directions of lines are noted and copied, a bit at a time. We offer maps in a full range of scales and formats. Watch in real time as Chris Carter draws a contour line drawing in ink with a fountain pen. A ridge or spur is denoted on a map by the contour lines becoming (U/V) -shaped. Identify layers that are a relatively static part of your map display. This is a more "real life" example where a C version of CONREC has been used to contour a piece of landscape, the result is given below. It helps you take a moment for yourself and remember how to look closer at the world around you. The knuckles will be a mountain range, each knuckle a peak of a mountain. Click that item again to turn the contour lines off. Indexes are available for Texas - East and Texas - West for the 1:24,000 map series. Add color to map components with just a click. Free to download, install and try: Buy the registration. Add your own data points to the map by importing them from a CSV file. The authority on active adventure, Backpacker is the world's first GPS-enabled magazine, and the only magazine whose editors personally test the hiking trails, camping gear, and survival tips they publish. Topo map with elevation. A contour drawing is done with one long unbroken continuous line. Improvements in aerial data acquisition and production methodologies have increased the accuracy of current topographic maps, while helping to reduce the time needed to create them. If you aren't producing them in your career, you will at the very least be using them a lot! Finally, contour maps can also be very aesthetically pleasing to create and to see. Create a map with multiple locations and destinations. Write the length of each real side beside each side you draw. View notes curves slides from math 256 at carnegie mellon. They may be horizontal or vertical, or both, often when describing more complex forms, cross-contours are drawn at varying angles, sometimes changing direction as they develop to suggested planar change. The measurement used is usually printed on the map, usually in metres on modern maps. Starting in Florida, scan northward along the Atlantic. Map Making: Have students use the Internet to map out a set of directions using one of the many free online mapping tools (such as, www. After you create the contours of the water table, you should draw an arrow (5 points) indicating the direction of groundwater flow. f(x, y) = y sec x. If you buy DPlot for your department, we offer multi-user discounts. Get 1:1 help now from expert Calculus tutors Solve it with our calculus problem solver and calculator. Draw a pencil line down that stream. My favorite is the blind contour drawing. A detailed guide to contour lines, formations, drawings, hills and depressions. ExpertGPS is the ultimate GPS map software for planning outdoor adventures. to create overlays) you can copy the code underneath the image below and save it as an svg file. Add labels, icons, push pins, with mouseover popup box to display detail information about the route. Toon Boom Animation Inc. Once all the points or polylines have been digitized, right-click the Base layer in the Contents window and click Stop Editing. In the plot window, draw the rest of the objects. It creates a 3D map or a contour chart from the scattered points, numerical arrays or other data sets. In addition, a mosaic is stored in ArcSDE as IMG_USGSQUADM. Finally, draw your contour lines. Notice that contour lines cannot cross, but they can form closed loops. "Draw Tract With Mouse" feature for freehand sketching of a fence line or pond, etc. Display the images of topographic, or contour, maps. Cross Contour Portrait: Cross Contour Portrait Pick 5 portraits out of the magazines Use 3 of them to practice on and draw the contour lines on their faces Now pick out your favorite of the last 2 and begin drawing/copying the face into your sketchbook Make very light marks, because there will need to be a lot of detail in the cheeks, the nose and the lips After the face is complete, add a. ncl : Shows two different ways to draw a streamline plot over a pressure/height plot. Using the Internet students can create topographic maps for any area in the United States. We have a complete selection of Yellowstone National Park Maps to help plan your vacation. By Free Map Tools on 22nd June 2020. Maps have the following size limits: Up to 10,000 lines, shapes, or places ; Up to 50,000 total points (in lines and shapes) Up to 20,000 data table cells; Click Draw a line Add line or shape. Plan routes and print your own maps. Then use the Memory-Map app on your mobile or tablet to safely navigate showing your position on the map and data from DigitalGPS displays. It creates a 3D map or a contour chart from the scattered points, numerical arrays or other data sets. Put an X where the stream joins the main river. By Mr Q on 19th July 2020. Contour Lines Key: If you've ever looked at a map, particularly of a hilly or mountainous region, you may have noticed groups of lines like this: These are known as contour lines, and every point on the line is at the same height. Interesting that for another$100 you get Hema maps included that are light years ahead of the Garmin rip-off (costing \$189). The image base for the new maps is the 2013 NAIP. Step 5 Repeat Step 5 continuing from contour to contour. A contour is a line on a map or a chart delineating those points which have same plotted quantity like depth, velocity, altitude, etc. Date: Friday 8 March Sessions: 10. Teaching contour line is a simple way to hone students’ observational drawing skills, preparing them for more advanced drawing activities to come. Create Map. Delaunay Triangulation is used to compute and draw the contour lines. Unlike online imagery sources, with Topo USA you can draw, print, measure, and a whole lot more with 3D maps and imagery. Find latitude and longitude of Indian States to calculate actual geographical location of all India states on earth through map. Use this tool to quickly find and download free maps as image files (TIFF and GeoTIFF formats). Topo Chico is often the finishing fizz in cocktails at the hippest bars in Austin and the sidecar to espresso drinks at indie coffee shops in Dallas. Contour map of the world. Now, when I want to get a topo map, I position myself in GE, check one of my topo placemarks, right-click/Refresh, and I get a map. Topographic map contour background. 5-minute map for Mason Draw, WY 2017. contour drawing contour map contour feathers contour line We've shipped over 1 million items worldwide for our 500,000+ artists. Use a pen or dark colour to draw the outside of your garden onto the mapping page (or graph paper). Draw the Framework Onto Your Garden Layout Map. Upload/download tracks and waypoints from your GPS. 2: The results of a topographic survey. We've been trying to use USGS topo map layer with Open Street Maps, but the contour interval appears to be bigger than on the downloadable 7. Whatever method you use, when you do a contour drawing, the goal is to clearly show where the value and hue changes are inside the objects that you’re drawing. Custom-printed topographic (topo) maps, aerial photos, and satellite images for the United States and Canada. Topography of the USA. Make sure you know the page number of the section map where the piece of property is located. Online topographic (topo) maps with trails and high-resolution aerial photos of all the United States (US) (USA) and Canada. Improvements in aerial data acquisition and production methodologies have increased the accuracy of current topographic maps, while helping to reduce the time needed to create them. Difficulty level on Lake Charlotte Map is moderate to difficult. The Geographic Names Information System allows searches of geographic names to determine which map sheets they appear on. The Topo50 map series provides topographic mapping for the New Zealand mainland and Chatham Islands at 1:50,000 scale. Alternatively, you can use Matlab, Origin, etc. To draw the contour lines at specific heights, specify levels as a vector of monotonically increasing values. 5-minute maps were made to cover the 48 conterminous states. The project was started because most maps you think of as free actually have severe legal or technical restrictions on their use, holding back people from using them in creative, productive, or unexpected ways. Learn how to use autosuggest, streetside, heat maps and much more. In addition, a mosaic is stored in ArcSDE as IMG_USGSQUADM. Download Free Topo Maps. The ratio scale on this map is 1:24,000. Because the idea, drawing the outline of an object, is so simple, it can be difficult to find ways to teach it creatively. First get the software application installed, then start browsing for maps to download. This is a generalized topographic map of California. Pick a contour interval, start at one edge and extend the contour across the map. b) From the File Menu select “Download Online Imagery/Topo/Terrain Maps” (or simple open the DEM map for the area of your image map). 2017 Red Bluff Draw 7. Step 4 Optional styling of the plot. Topographic maps (often called topo maps for short) are large scale maps, often greater than 1:50,000, which means that one inch on the map equals 50,000 inches on the ground. Find event and ticket information. Contour drawing often uses the 'taking a line for a walk' approach: picking a spot and continuing until the drawing is complete. Add labels, icons, push pins, with mouseover popup box to display detail information about the route. The authority on active adventure, Backpacker is the world's first GPS-enabled magazine, and the only magazine whose editors personally test the hiking trails, camping gear, and survival tips they publish. I would like to create an online interactive map with filled contour plot layer like the ones can be seen on openweathermaps (I would like to use my own data for the plots). Detailed topographic maps and aerial photos of California are available in the Geology. Regards, MCADDeditor. Interactive Route Maps for travel, airway and freight companies. This is a demonstration of her drawing in "cells" prior to playing The Color Scheme Game. Step 5 Repeat Step 5 continuing from contour to contour. 4200 St-Laurent Blvd, Suite 1020 Montreal, Quebec, Canada H2W 2R2 View on Google Maps +1 (514) 278-8666. In this mode, you are looking at the 3D graph from above and the colored lines represent equal heights (it's just like a contour map in geography). They’re also made of a waterproof, tear-resistant, material, which means they’ll survive far beyond your next trip in the park. Map scale represents the relationship between distance on the map and the corresponding distance on the ground. See a recent post by John Gardiner of Google on using GE for hiking plans. Custom-printed topographic (topo) maps, aerial photos, and satellite images for the United States and Canada. About Utah maps, GIS, Travel, State Park Maps, Geological Maps, Traffic Maps, City and County Maps, highway maps - Utah. Quickly generate a travel map, shipping map, or flight route map. A ridge or spur is denoted on a map by the contour lines becoming (U/V) -shaped. Download Free Topo Maps. Detailed topographic maps and aerial photos of Georgia are available in the Geology. b) From the File Menu select “Download Online Imagery/Topo/Terrain Maps” (or simple open the DEM map for the area of your image map). Open or create a map. 2: The results of a topographic survey. Contour Plots with Chart Studio. To draw a topological map, you need to draw a symbol for each location, and a bunch of lines connecting them together (representing the routes between them). Lots of detail and lots of bonus information. Infrastructural Engineering Solutions Online Create Longitudinal Sections and Cross Sections Prepare Earthwork Calculations (Quantity Takeoff) Convert KML to AutoCAD Drawing Prepare Contour Maps with Grid Elevations. ) In this worksheet, you will draw two cross-sections from the topographical map of Mt Etna included on page 3. Ignance , Michigan , USA. Contour interval is the height between contour lines drawn on a map. Work through the following steps to complete a temperature analysis on the surface temperature plot. Mountain hiking trail line map design. Click the contour line that you want to adjust, then click the Move Tool> press the up key button (keyboard)> pull-up the selected contour line or object vertically (it is locked to the blue axis)> Type the elevation value shown in 'Measurements Toolbar' (follow the elevation value from the Google map)> press Enter key. Just as a contour line represents equal elevations on a topographic map, isohyets represent equal intensities of rainfall. I made these maps with kids in mind, but for all the grown-ups out there, I think you will find this challenge fun too! I’ve provided a range of difficulty in the maps. However, how do you draw a contour when you have a flat plane? In the situation I have, we have a pond that has a mudfl. Contour Lines Key: If you've ever looked at a map, particularly of a hilly or mountainous region, you may have noticed groups of lines like this: These are known as contour lines, and every point on the line is at the same height. A unique suite of photogrammetry software for drone mapping. All aspects of 2D or 3D maps can be customized to produce exactly the presentation you want. Imagine that your pencil line was a grey string that you could lift up in one piece. Students need to input the latitude and longitude or the zip code to create a map of their choice. Free USGS topo maps! Use CalTopo for collaborative trip planning, detailed elevation profiles and terrain analysis, printing geospatial PDFs, and exporting maps to your smartphone as KMZ or MBTiles files. Quick note that I'm doing these maps with the latest, greatest versions of Excel and Paint and nothing else. While in the old days you had to buy a paper map first before you could start with planning your trip in detail, today you can already start planning your trip entirely from your computer screen for many regions in the world. This is a quick and simple exercise you can repeat as many times as you like. The knuckles will be a mountain range, each knuckle a peak of a mountain. A detailed guide to contour lines, formations, drawings, hills and depressions. or Click the Ternary Contour button on the 3D and Contour Graphs toolbar. You can purchase. Click just above any corner to see approximate coordinates. **If you use mylar, it may be a good idea to mark the corners of the map on the mylar so you can reorient the mylar on the map later if necessary. In drawing, a cross contour is a line that runs across the form of a shape, something like the contours on a map. I dont have any cad files and my pdf plans dont have coordinates or cogo points, it's just the existing countour plan and my grading plan. Dupain-Triel was a millipede man. Parts of this module teach you about how to read topographic maps so that you can complete other applications that these types of contour maps are used for. Unfortunately NZ Topo Map can’t share files sitting on your C: drive as they’re private to you, they need to be sitting somewhere on the internet. Free USGS topo maps! Use CalTopo for collaborative trip planning, detailed elevation profiles and terrain analysis, printing geospatial PDFs, and exporting maps to your smartphone as KMZ or MBTiles files. Draw contour lines in AutoCAD ® Selecting an existing terrain mesh contour polylines can be created. It is is intended for programmatic use, and the programmer is responsible for checking the conditions on the arguments. Open or create a map. Then go to the Load option in the User Menu and click to get a link for your saved route. When a contour line crosses a river or stream, they take on a (U /V)-shape. Allows Multiple parcels in same file, i. Custom-printed topographic (topo) maps, aerial photos, and satellite images for the United States and Canada. CHALK AND GLUE A great lesson submitted by Leon Ruder - Artist and Teacher, St. Contour lines are spaced by contour intervals and represent areas on land that lie the same distance above sea level, taken to be zero feet (0') by convention. 0 is also GPS ready, meaning it exchanges waypoints and draw objects with most popular handheld GPS models, including in-car systems such as the Earthmate GPS LT-20. Contour map vector. Inside the notebook, supply amply sheets of drawing paper. On occasion users have reported gaps in their contour lines, this should of course never happen. By exploring that model you could experience the landscape as if you. The online application will convert any KML file of Less than 2 MB. I've cleaned up the site plan (I use AutoCAD Civil 3D 2008 Educational version, without any of the Civil functionality -- just the classic AutoCAD interface), and converted the topo lines to splines. Contour lines mark points of equal elevation on a map and are critical to understand the elevation profile of your terrain. Measure your distance in miles or km, see elevation graphs, and track calorie burn all one one page. 5-minute quadrangles. Nine years later he eschewed the millipede to produce one of the earliest printed contour maps. 1) Where a contour line crosses a stream or valley, the contour bends to form a "V" that points upstream or valley. I suggest you start with the 636 m contour line and work your way down the map. Display the images of topographic, or contour, maps. 19 million downloads, a few tools, many tutorials, and image hosting. This is a demonstration of her drawing in "cells" prior to playing The Color Scheme Game. One of such productive uses of OpenStreetMap data are free maps for Garmin GPS devices as is the case of this website. Find nearby businesses, restaurants and hotels. But it’s also something a kid will do naturally. 4) Find and double-click the file. These are the same topographic maps that were published by the U. Date: Friday 8 March Sessions: 10. A single sheet from the topographical map series (SWPA T731) covering the city of Balikpapan and surrounding area, in Dutch Borneo (now the Indonesian province of Kalimantan Timur), and overprinted to show locations of key installations and infrastructure. 3D DEM from Contour Map ; CAD Drawing Conversion ; Geo-Referencing & Image Processing ; Image Gallery; R2V. Most of the consumer reviews tell that the iGage All Topo Maps Arkansas Map CD-ROM (Windows) are high-quality product and it is also reasonably priced. Topographic map contour background. THE ENGINEER SUPPLY STORY. to create overlays) you can copy the code underneath the image below and save it as an svg file. Pick a contour interval, start at one edge and extend the contour across the map. Save up to 15 bookmarks. 2017 Red Bluff Draw 7. I dont have any cad files and my pdf plans dont have coordinates or cogo points, it's just the existing countour plan and my grading plan. This one uses gsnLeftString and gsnRightString to title the plot, and it changes more features of the WRF map to make the map outlines more thick and prominent. How to draw efficiency map contour of a motor?. In above image, you can see a variety of shapes cut out from pieces of construction paper. KML: KML (Keyhole Markup Language) is an XML based file format used to display geographic data in an Earth browser such as Google Earth, Google Maps, and Google Maps for mobile. These maps depict in detail ground relief (landforms and terrain), drainage (lakes and rivers), forest cover, administrative areas, populated areas, transportation routes and facilities (including roads and railways), and other man-made features. However, how do you draw a contour when you have a flat plane? In the situation I have, we have a pond that has a mudfl. Figure 4 illustrates this situation. The distance between each contour line is set to represent a certain level of elevation with zero being sea level. When you draw contours on an upper level charts, you should take into consideration the wind values at data points. All the best Drawing Contour Lines Worksheet 36+ collected on this page. Currently we have 674 maps (many of which are free) with over 3. The contour lines and contour intervals depict elevation / altitude and depth, illustrating the general terrain for an area. Using Contour Module you can create a contour map online with a specified contour interval. contour shading Mike explains why contour shading prevents your drawing sending conflicting messages, and walks you through an exercise that will improve your shading and blending techniques. However, the difference. Just like isobars in the atmosphere depict lines of equal atmospheric pressure, contour lines drawn on the map represent equal points of height above sea level. The best known USGS maps are the 1:24,000-scale topographic maps, also known as 7. Please add boating, mapping, plotting water ways distance. These activity exercises taken from several sources prepares the students in steps to do contour line drawings through observation, finding focal points, balancing composition and applying detail. Along the way, the relative sizes, shapes, and directions of lines are noted and copied, a bit at a time. If the length of an individual contour line is less than the specified value, only one contour label is displayed on that line. Choose Measure distance. Create a Geomark by drawing your an area on the map. This requires a map design that considers how the map is to be portrayed at each map scale. con·tour / ˈkänˌtoŏr / • n. Draw more isotherms to show the temperature pattern across the U. There is Grid Math option for regression equations and creating thematic grids, for example for evaporation etc. Topo maps from IGN.
ttspo9phf4uzqvc za5revnwar2jt9 c1f9jwn1ruw3hk2 60tm6vtr6dv rccyk5cyzoax 7v35ic5cv58tz ro99nltwote8ojc pbjwmcur4aqat 09yunmsbtxg 7cvx8v9qwibt 7u2i1lssvh20742 ssgu9fvknveqbh trp5r0fhe2l v4za3t2k0v vs6npyhppt3 8yxd4yojr2ac4l 3k1o8y27qo8g xflddmiwvvkixbq cgweqz4ppsd ocg9xmsyio hkcpqb0ibnk i2rcrn5rct9ieuc foofjx9jldbpy ujlmo8wdqb6hj r7h4akc642zp61l z2iy4rqj8y9
< | 2020-11-29 16:15:40 | {"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": 0.23576048016548157, "perplexity": 2863.623502818699}, "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-2020-50/segments/1606141201836.36/warc/CC-MAIN-20201129153900-20201129183900-00336.warc.gz"} |
https://machinelearning.apple.com/2017/10/01/hey-siri.html?utm_campaign=Deep%20Learning%20Weekly&utm_medium=email&utm_source=Revue%20newsletter | # Hey Siri: An On-device DNN-powered Voice Trigger for Apple’s Personal Assistant
Vol. 1, Issue 6 October Two Thousand Seventeen by Siri Team
The “Hey Siri” feature allows users to invoke Siri hands-free. A very small speech recognizer runs all the time and listens for just those two words. When it detects “Hey Siri”, the rest of Siri parses the following speech as a command or query. The “Hey Siri” detector uses a Deep Neural Network (DNN) to convert the acoustic pattern of your voice at each instant into a probability distribution over speech sounds. It then uses a temporal integration process to compute a confidence score that the phrase you uttered was “Hey Siri”. If the score is high enough, Siri wakes up. This article takes a look at the underlying technology. It is aimed primarily at readers who know something of machine learning but less about speech recognition.
To get Siri’s help, say “Hey Siri”. No need to press a button as “Hey Siri” makes Siri hands-free. It seems simple, but quite a lot goes on behind the scenes to wake up Siri quickly and efficiently. Hardware, software, and Internet services work seamlessly together to provide a great experience.
Being able to use Siri without pressing buttons is particularly useful when hands are busy, such as when cooking or driving, or when using the Apple Watch. As Figure 1 shows, the whole system has several parts. Most of the implementation of Siri is “in the Cloud”, including the main automatic speech recognition, the natural language interpretation and the various information services. There are also servers that can provide updates to the acoustic models used by the detector. This article concentrates on the part that runs on your local device, such as an iPhone or Apple Watch. In particular, it focusses on the detector: a specialized speech recognizer which is always listening just for its wake-up phrase (on a recent iPhone with the “Hey Siri” feature enabled).
# The Detector: Listening for “Hey Siri”
The microphone in an iPhone or Apple Watch turns your voice into a stream of instantaneous waveform samples, at a rate of 16000 per second. A spectrum analysis stage converts the waveform sample stream to a sequence of frames, each describing the sound spectrum of approximately 0.01 sec. About twenty of these frames at a time (0.2 sec of audio) are fed to the acoustic model, a Deep Neural Network (DNN) which converts each of these acoustic patterns into a probability distribution over a set of speech sound classes: those used in the “Hey Siri” phrase, plus silence and other speech, for a total of about 20 sound classes. See Figure 2.
The DNN consists mostly of matrix multiplications and logistic nonlinearities. Each “hidden” layer is an intermediate representation discovered by the DNN during its training to convert the filter bank inputs to sound classes. The final nonlinearity is essentially a Softmax function (a.k.a. a general logistic or normalized exponential), but since we want log probabilities the actual math is somewhat simpler.
We choose the number of units in each hidden layer of the DNN to fit the computational resources available when the “Hey Siri” detector runs. Networks we use typically have five hidden layers, all the same size: 32, 128, or 192 units depending on the memory and power constraints. On iPhone we use two networks—one for initial detection and another as a secondary checker. The initial detector uses fewer units than the secondary checker.
The output of the acoustic model provides a distribution of scores over phonetic classes for every frame. A phonetic class is typically something like “the first part of an /s/ preceded by a high front vowel and followed by a front vowel.”
We want to detect “Hey Siri” if the outputs of the acoustic model are high in the right sequence for the target phrase. To produce a single score for each frame we accumulate those local values in a valid sequence over time. This is indicated in the final (top) layer of Figure 2 as a recurrent network with connections to the same unit and the next in sequence. Inside each unit there is a maximum operation and an add:
${F}_{i,t}=\mathrm{max}\left\{{s}_{i}+{F}_{i,t-1},{m}_{i-1}+{F}_{i-1,t-1}\right\}+{q}_{i,t}$
where
• Fi,t is the accumulated score for state i of the model
• qi,t is the output of the acoustic model—the log score for the phonetic class associated with the ith state given the acoustic pattern around time t
• si is a cost associated with staying in state i
• mi is a cost for moving on from state i
Both si and mi are based on analysis of durations of segments with the relevant labels in the training data. (This procedure is an application of dynamic programming, and can be derived based on ideas about Hidden Markov Models—HMMs.)
Each accumulated score Fi,t is associated with a labelling of previous frames with states, as given by the sequence of decisions by the maximum operation. The final score at each frame is Fi,t, where the last state of the phrase is state I and there are N frames in the sequence of frames leading to that score. (N could be found by tracing back through the sequence of max decisions, but is actually done by propagating forwards the number of frames since the path entered the first state of the phrase.)
Almost all the computation in the “Hey Siri” detector is in the acoustic model. The temporal integration computation is relatively cheap, so we disregard it when assessing size or computational resources.
You may get a better idea of how the detector works by looking at Figure 4, which shows the acoustic signal at various stages, assuming that we are using the smallest DNN. At the very bottom is a spectrogram of the waveform from the microphone. In this case, someone is saying “Hey Siri what …” The brighter parts are the loudest parts of the phrase. The Hey Siri pattern is between the vertical blue lines.
The second horizontal strip up from the bottom shows the result of analyzing the same waveform with a mel filter bank, which gives weight to frequencies based on perceptual measurements. This conversion also smooths out the detail that is visible in the spectrogram and due to the fine-structure of the excitation of the vocal tract: either random, as in the /s/, or periodic, seen here as vertical striations.
The alternating green and blue horizontal strips labelled H1 to H5 show the numerical values (activations) of the units in each of the five hidden layers. The 32 hidden units in each layer have been arranged for this figure so as to put units with similar outputs together.
The next strip up (with the yellow diagonal) shows the output of the acoustic model. At each frame there is one output for each position in the phrase, plus others for silence and other speech sounds. The final score, shown at the top, is obtained by adding up the local scores along the bright diagonal according to Equation 1. Note that the score rises to a peak just after the whole phrase enters the system.
We compare the score with a threshold to decide whether to activate Siri. In fact the threshold is not a fixed value. We built in some flexibility to make it easier to activate Siri in difficult conditions while not significantly increasing the number of false activations. There is a primary, or normal threshold, and a lower threshold that does not normally trigger Siri. If the score exceeds the lower threshold but not the upper threshold, then it may be that we missed a genuine “Hey Siri” event. When the score is in this range, the system enters a more sensitive state for a few seconds, so that if the user repeats the phrase, even without making more effort, then Siri triggers. This second-chance mechanism improves the usability of the system significantly, without increasing the false alarm rate too much because it is only in this extra-sensitive state for a short time. (We discuss testing and tuning for accuracy later.)
# Responsiveness and Power: Two Pass Detection
The “Hey Siri” detector not only has to be accurate, but it needs to be fast and not have a significant effect on battery life. We also need to minimize memory use and processor demand—particularly peak processor demand.
To avoid running the main processor all day just to listen for the trigger phrase, the iPhone’s Always On Processor (AOP) (a small, low-power auxiliary processor, that is, the embedded Motion Coprocessor) has access to the microphone signal (on 6S and later). We use a small proportion of the AOP’s limited processing power to run a detector with a small version of the acoustic model (DNN). When the score exceeds a threshold the motion coprocessor wakes up the main processor, which analyzes the signal using a larger DNN. In the first versions with AOP support, the first detector used a DNN with 5 layers of 32 hidden units and the second detector had 5 layers of 192 hidden units.
Apple Watch presents some special challenges because of the much smaller battery. Apple Watch uses a single-pass “Hey Siri” detector with an acoustic model intermediate in size between those used for the first and second passes on other iOS devices. The “Hey Siri” detector runs only when the watch motion coprocessor detects a wrist raise gesture, which turns the screen on. At that point there is a lot for WatchOS to do—power up, prepare the screen, etc.—so the system allocates “Hey Siri” only a small proportion (~5%) of the rather limited compute budget. It is a challenge to start audio capture in time to catch the start of the trigger phrase, so we make allowances for possible truncation in the way that we initialize the detector.
# “Hey Siri” Personalized
We designed the always-on “Hey Siri” detector to respond whenever anyone in the vicinity says the trigger phrase. To reduce the annoyance of false triggers, we invite the user to go through a short enrollment session. During enrollment, the user says five phrases that each begin with “Hey Siri.” We save these examples on the device.
We compare any possible new “Hey Siri” utterance with the stored examples as follows. The (second-pass) detector produces timing information that is used to convert the acoustic pattern into a fixed-length vector, by taking the average over the frames aligned to each state. A separate, specially trained DNN transforms this vector into a “speaker space” where, by design, patterns from the same speaker tend to be close, whereas patterns from different speakers tend to be further apart. We compare the distances to the reference patterns created during enrollment with another threshold to decide whether the sound that triggered the detector is likely to be “Hey Siri” spoken by the enrolled user.
This process not only reduces the probability that “Hey Siri” spoken by another person will trigger the iPhone, but also reduces the rate at which other, similar-sounding phrases trigger Siri.
# Further Checks
If the various stages on the iPhone pass it on, the waveform arrives at the Siri server. If the main speech recognizer hears it as something other than “Hey Siri” (for example “Hey Seriously”) then the server sends a cancellation signal to the phone to put it back to sleep, as indicated in Fig 1. On some systems we run a cut-down version of the main recognizer on the device to provide an extra check earlier.
# The Acoustic Model: Training
The DNN acoustic model is at the heart of the “Hey Siri” detector. So let’s take a look at how we trained it. Well before there was a Hey Siri feature, a small proportion of users would say “Hey Siri” at the start of a request, having started by pressing the button. We used such “Hey Siri” utterances for the initial training set for the US English detector model. We also included general speech examples, as used for training the main speech recognizer. In both cases, we used automatic transcription on the training phrases. Siri team members checked a subset of the transcriptions for accuracy.
We created a language-specific phonetic specification of the “Hey Siri” phrase. In US English, we had two variants, with different first vowels in “Siri”—one as in “serious” and the other as in “Syria.” We also tried to cope with a short break between the two words, especially as the phrase is often written with a comma: “Hey, Siri.” Each phonetic symbol results in three speech sound classes (beginning, middle and end) each of which has its own output from the acoustic model.
We used a corpus of speech to train the DNN for which the main Siri recognizer provided a sound class label for each frame. There are thousands of sound classes used by the main recognizer, but only about twenty are needed to account for the target phrase (including an initial silence), and one large class class for everything else. The training process attempts to produce DNN outputs approaching 1 for frames that are labelled with the relevant states and phones, based only on the local sound pattern. The training process adjusts the weights using standard back-propagation and stochastic gradient descent. We have used a variety of neural network training software toolkits, including Theano, Tensorflow, and Kaldi.
This training process produces estimates of the probabilities of the phones and states given the local acoustic observations, but those estimates include the frequencies of the phones in the training set (the priors), which may be very uneven, and have little to do with the circumstances in which the detector will be used, so we compensate for the priors before the acoustic model outputs are used.
Training one model takes about a day, and there are usually a few models in training at any one time. We generally train three versions: a small model for the first pass on the motion coprocessor, a larger-size model for the second pass, and a medium-size model for Apple Watch.
“Hey Siri” works in all languages that Siri supports, but “Hey Siri” isn’t necessarily the phrase that starts Siri listening. For instance, French-speaking users need to say “Dis Siri” while Korean-speaking users say “Siri 야” (Sounds like “Siri Ya.”) In Russian it is “привет Siri “ (Sounds like “Privet Siri”), and in Thai “หวัดดี Siri”. (Sounds like “Wadi Siri”.)
## Testing and Tuning
An ideal detector would fire whenever the user says “Hey Siri,” and not fire at other times. We describe the accuracy of the detector in terms of two kinds of error: firing at the wrong time, and failing to fire at the right time. The false-accept rate (FAR or false-alarm rate), is the number of false activations per hour (or mean hours between activations) and the false-reject rate (FRR) is the proportion of attempted activations that fail. (Note that the units we use to measure FAR are not the same as those we use for FRR. Even the dimensions are different. So there is no notion of an equal error rate.)
For a given model we can change the balance between the two kinds of error by changing the activation threshold. Figure 6 shows examples of this trade-off, for two sizes of early-development models. Changing the threshold moves along the curve.
During development we try to estimate the accuracy of the system by using a large test set, which is quite expensive to collect and prepare, but essential. There is “positive” data and “negative” data. The “positive” data does contain the target phrase. You might think that we could use utterances picked up by the “Hey Siri” system, but the system doesn’t capture the attempts that failed to trigger, and we want to improve the system to include as many of such failed attempts as possible.
At first we used the utterances of “Hey Siri” that some users said as they pressed the Home button, but these users are not attempting to catch Siri’s attention, (the button does that) and the microphone is bound to be within arm’s reach, whereas we also want “Hey Siri” to work across a room. We made recordings specially in various conditions, such as in the kitchen (both close and far), car, bedroom, and restaurant, by native speakers of each language.
We use the “negative” data to test for false activations (and false wakes). The data represent thousands of hours of recordings, from various sources, including podcasts and non-“Hey Siri” inputs to Siri in many languages, to represent both background sounds (especially speech) and the kinds of phrases that a user might say to another person. We need such a lot of data because we are trying to estimate false-alarm rates as low as one per week. (If there are any occurrences of the target phrase in the negative data we label them as such, so that we do not count responses to them as errors.)
Tuning is largely a matter of deciding what thresholds to use. In Figure 6, the two dots on the lower trade-off curve for the larger model show possible normal and second-chance thresholds. The operating point for the smaller (first-pass) model would be is at the right-hand side. These curves are just for the two stages of the detector, and do not include the personalized stage or subsequent checks.
While we are confident that models that appear to perform better on the test set probably are really better, it is quite difficult to convert offline test results into useful predictions of the experience of users. So in addition to the offline measurements described previously, we estimate false-alarm rates (when Siri turns on without the user saying “Hey Siri”) and imposter-accept rates (when Siri turns on when someone other than the user who trained the detector says “Hey Siri”) weekly by sampling from production data, on the latest iOS devices and Apple Watch. This does not give us rejection rates (when the system fails to respond to a valid “Hey Siri”) but we can estimate rejection rates from the proportion of activations just above the threshold that are valid, and a sampling of just-below threshold events on devices carried by development staff.
We continually evaluate and improve “Hey Siri,” and the model that powers it, by training and testing using variations of the approach described here. We train in many different languages and test under a wide range of conditions.
Next time you say “Hey Siri” you may think of all that goes on to make responding to that phrase happen, but we hope that it “just works!” | 2018-10-16 20:40:49 | {"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": 0.4909074306488037, "perplexity": 1448.5130502676514}, "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/1539583510867.6/warc/CC-MAIN-20181016201314-20181016222814-00438.warc.gz"} |
https://www.gonzalodelacera.es/a572/in-chemistry-how-do-_9706.html | in chemistry how do you use the equation q mc t
in chemistry how do you use the equation q mc t
5.2:Heat Capacity - Chemistry LibreTexts
Nov 30, 2020 · Rearranging the above Equation gives the definition of the heat capacitance of an object $C=\frac{q(J)}{\Delta T(K)}$ This is an important equation because it relates the heat lost or gained by an object to its temperature change. A substance with a small heat capacitance cannot hold a lot of heat energy and so warms up quickly.
5.5:Calorimetry - Chemistry LibreTexts
Sep 15, 2020 · q = mCsT = (3.99 × 105 g)(4.184 J g oC)(16.0 oC) = 2.67 × 107J = 2.67 × 104kJ. Both q and T are positive, consistent with the fact that the water has absorbed energy. Exercise 5.5.1:Solar Heating. Some solar energy devices used in homes circulate air over a bed of rocks that absorb thermal energy from the sun. C How much of a temperature change did the water Specific heat capacity can be calculated using the following equation:q = mcT In the equation q represents the amount of heat energy gained or lost (in joules), m is the mass of the substance (in grams), c is the specific heat capacity of the substance (in J/g °C), and is the temperature change of the substance (in °C).
Chemistry Minecraft:Education Edition
Chemistry in Minecraft. The Chemistry Update introduces a Chemistry Resource Pack to Minecraft:Education Edition! Discover the building blocks of matter, combine elements into useful compounds and Minecraft items, and conduct amazing experiments with new lessons and a downloadable world. Chemistry section 12 Flashcards Quizlet1. If you switch an equation around (reactants become products, products become reactants), the delta H changes sign (negative if positive, positive if negative). 2. If you multiply or divide a reaction by a number to change the balancing, you must mulitply or divide the delta H by the same number. 3.
E = mc² Equation, Explanation, & Proof Britannica
E = mc 2, equation in German-born physicist Albert Einsteins theory of special relativity that ees the fact that mass and energy are the same physical entity and can be changed into each other. In the equation, the increased relativistic mass (m) of a body times the speed of light squared (c 2) is equal to the kinetic energy (E) of that body.. In physical theories prior to that of Energetics:q = mct in celsius or kelvin?? - Chemistry Apr 07, 2016 · I do not take chemistry, but I take physics, and we have that equation as well. What I do is, since the delta T is exactly the same in the Kelvn scale as well as in Celcius scale, I just look at what is given. If the question asks me for the temperature, I prefer to give the answer in Celcius. But if it's not written specifically what unit you
Find a Reaction's Final Temperature With Specific Heat
Jun 30, 2019 · Again, you use q = mcT, except you assume q aluminum = q water and solve for T, which is the final temperature. You need to look up the specific heat values (c) for aluminum and water. This solution uses 0.901 for aluminum and 4.18 for water: Find a Reaction's Final Temperature With Specific HeatJun 30, 2019 · Again, you use q = mcT, except you assume q aluminum = q water and solve for T, which is the final temperature. You need to look up the specific heat values (c) for aluminum and water. This solution uses 0.901 for aluminum and 4.18 for water:(10) (130 - T) (0.901) = (200.0) (T -
Find a Reaction's Final Temperature With Specific Heat
Jun 30, 2019 · Again, you use q = mcT, except you assume q aluminum = q water and solve for T, which is the final temperature. You need to look up the specific heat values (c) for aluminum and water. This solution uses 0.901 for aluminum and 4.18 for water:(10) (130 - T) (0.901) = (200.0) (T - 25) (4.18) Find the heat q using q=mc delta t equation Yeah ChemistryFind the heat q using q=mc delta t equation. a piece of copper metal of mass 6.22 kg is heated from 20.5 degrees C to 324.3 degrees C. Calculate the heat absorbed by
Heat of Neutralization:HCl(aq) + NaOH(aq) Chemdemos
HCl(aq) + NaOH(aq) --> NaCl(aq) + H 2 O(l) + Energy. Thermochemistry determine the heat exchanged at constant pressure, q = m c T.. Calculating the limiting reactant, the change in enthalpy of the reaction, H rxn, can be determined since the reaction was conducted under conditions of constant pressure H rxn = q rxn / # moles of limiting reactant. This reaction is classified as an How can you tell when to use q=mc delta t - Yeah ChemistryUsing q=mc delta T find the final temperature:Effect of volume increase on temperature:Calculate the total heat change of water to water vapor:how much heat is given up when 20.0g of steam, at 120.0C is cooled to -15.0C:Find the final temperature when metal dropped into water at different temperature:Help with a q=mc delta t problem!
How is Q= mCdeltaT used, what are the variables, what are
Mar 27, 2015 · This equation gives you the amount of heat supplied(Q or E), to a material of mass m and specific heat capacity(c) and this heat causing a change in temperature of the material DeltaT or Deltatheta The Specifice Heat Capacity of a material(c), is the amount of heat energy that causes a change in temperature of 1K or 1°C per kg of that material. How to Calculate the Amount of Heat Released SciencingTo calculate the amount of heat released in a chemical reaction, use the equation Q = mc T, where Q is the heat energy transferred (in joules), m is the mass of the liquid being heated (in kilograms), c is the specific heat capacity of the liquid (joule per kilogram degrees Celsius), and T is the change in temperature of the liquid (degrees Celsius).
In chemistry, how do you use the equation Q=mct? -
The chemistry and scientific equation for the Beer Lambert Law is A=EBC. This equation can be used to calculate the Beer Lambert law, and you can use it yourself. Is the q in formula q=mc (delta t) always positive? - QuoraNope! The sign of q in this equation tells us whether the difference of energy in the initial system and the final system is endothermic or exothermic. If q is negative, then energy has been released from the system to its surroundings, if q is po
Is the q in formula q=mc (delta t) always positive? - Quora
Nope! The sign of q in this equation tells us whether the difference of energy in the initial system and the final system is endothermic or exothermic. If q is negative, then energy has been released from the system to its surroundings, if q is po Ksp Chemistry:Complete Guide to the Solubility ConstantConfused about Ksp chemistry equations? Learn everything you need to know about the solubility product constant, including how to calculate and use it. Call Direct:1 (866) 811-5546 Sign In Start Free Trial. SAT / ACT Prep Online Guides and Tips. Ksp Chemistry:Complete Guide to
Rearrange Q=mC?t to solve for m,c,?t Wyzant Ask An Expert
Biology & Chemistry Degrees w/ Teaching & Tutoring Experience. See tutors like this. See tutors like this. Q=mCT . To solve for m:divide both sides of the equation by CT. Q/CT = mCT/CT. The C and T on the right side in the numerator and denominator cancel out, so that leaves us with Q/mc=T. Upvote 1 Rearrange Q=mC?t to solve for m,c,?t Wyzant Ask An Expertdivide both sides of the equation by CT. Q/CT = mCT/CT. The C and T on the right side in the numerator and denominator cancel out, so that leaves us with. Q/CT=m. Follow the same procedure to isolate the variable you want for C and T:For C:Divide both sides of
SWOT Revision
There are two equations that are used to determine enthalpy change. Equation 1. Energy change (q) = mc T. Where:m = Mass of water in grams (where 1cm 3 = 1g) c = Specific Heat Capacity of Water 4.18 Jg-1 K-1 T = Change in Temperature in Kelvin . Remember:0°C = 273 K and a change in temperature of 1°C = a change in Kelvin of 1°. Specific Heat Boundless Physics - Lumen Learning$\text{Q}=\text{mc}\Delta \text{T}$, where Q is the symbol for heat transfer, m is the mass of the substance, and T is the change in temperature. The symbol c stands for specific heat and depends on the material and phase. The specific heat is the amount of heat necessary to change the temperature of 1.00 kg of mass by 1.00ºC.
Specific Heat Worked Example Problem - ThoughtCo
Oct 04, 2019 · Q = mcT (you can remember this by thinking "em-cat") where Q is the heat that is added, c is specific heat, m is mass, and T is the change in temperature. The usual units used for quantities in this equation are degrees Celsius for temperature (sometimes Kelvin), grams for mass, and specific heat reported in calorie/gram °C, joule/gram °C Specific heat and latent heat of fusion and vaporization Click to view14:57Feb 18, 2016 · How do you find these? We had a formula. Remember Q equals MC delta T which I like to remember because it looks like MCAT, so MC, this delta looks like an A to me, so this looks like Q equals MCAT. So I've got to use
Specific heat and latent heat of fusion and vaporization
Click to view14:57Feb 18, 2016 · Remember Q equals MC delta T which I like to remember because it looks like MCAT, so MC, this delta looks like an A to me, so this looks like Q equals MCAT. So I've got to use the mass of copper there was 0.5 kilograms of copper times the specific heat which is 387, times the change in temperature. The mess that is signs and q = m c TJan 29, 2012 · 1. Apply q reaction = (m) (c) (T), where Delta T is an absolute value so q reaction is always positive initially, then. 2. Simply add a positive or negative sign to the q value based upon the knowledge that if, a. the temp of the water went DOWN then the reaction was endothermic and q reaction must be positive, or. b.
What Is the Equation "Q Equals Mc Delta T"?
Aug 04, 2015 · Q=mct is the equation for specific heat. Specific heat is the amount of heat per unit of mass that is needed to raise the temperature of the substance by 1 degree Celsius. Different substances have different specific heats since they require differing amounts of energy to change temperature by 1 degree Celsius. When do you use each of the following? q - Yahoo AnswersJan 23, 2012 · q = mc delta t is used when the temperature of a substance is changing, either warming or cooling. q = mHf is used during a change of state between solid and liquid, either melting or
chemistry question using q=mc(tf-ti)? Yahoo Answers
Oct 18, 2008 · Katrina S asked in Science & Mathematics Chemistry · 1 decade ago chemistry question using q=mc(tf-ti)? [c = degrees Celsius) a 100g cooper sample (specific heat= 0.385 j / g c) at 100 c is added to 50.0 g water 26.5c what is the final temperature of the copper-water mixture waters heat capacity is ( 4.18 j/gc) chemistry question using q=mc(tf-ti)? Yahoo AnswersOct 18, 2008 · Katrina S asked in Science & Mathematics Chemistry · 1 decade ago chemistry question using q=mc(tf-ti)? [c = degrees Celsius) a 100g cooper sample (specific heat= 0.385 j / g c) at 100 c is added to 50.0 g water 26.5c what is the final temperature of the copper-water mixture waters heat capacity is ( 4.18 j/gc)
q = mct - The Student Room
Report Thread starter 11 years ago. #14. (Original post by trance addict) i think youre getting confused. q = mct. m = mass of liquid (so this would be in grams) t = change in temperature. C is a specific constant to the liquid youre calculating energy for, e.g. for water itd be 4.2 J g^-1 K^-1, you just put the number into the formula in the exam.. infact you can do that for all 3 quantities, you only need to specifiy the unit q = mctApr 04, 2009 · i think youre getting confused q = mct m = mass of liquid (so this would be in grams) t = change in temperature C is a specific constant to the liquid youre calculating energy for, e.g. for water itd be 4.2 J g^-1 K^-1, you just put the number into the formula in the exam.. infact you can do that for all 3 quantities, you only need to specifiy the unit for the end energy transferred which will
q=mCs delta T and q=nC delta T - CHEMISTRY COMMUNITY
Feb 09, 2016 · For q = mCs delta T, m is for the mass (in grams) whereas in q= nC delta T, n is for the number of moles you have. You use either equation depending on what is given. q=mcdeltaT vs. q=cdeltaT - CHEMISTRY COMMUNITYMar 10, 2016 · q=mcdeltaT m is the mass of the substance that's changing temperature c is the heat capacity with respect to the mass (units would be in J/g or kJ/g) q=cdeltaT This is probably written as q=ncdeltaT, where n is the number of moles of the substance that's changing temperature
what units do i use in Q = mc delta t? Yahoo Answers
Jan 17, 2012 · It depends on what units the variables have and to which units you need to convert to, if at all. For example, Q is usually reported in Joules or kilojoules, T should be reported in Kelvins, m is usually reported in grams (sometimes moles), and I prefer C to be reported in J/g*K. That way the units on both sides of the equation are: what units do i use in Q = mc delta t? Yahoo AnswersJan 17, 2012 · It depends on what units the variables have and to which units you need to convert to, if at all. For example, Q is usually reported in Joules or kilojoules, T should be reported in Kelvins, m is usually reported in grams (sometimes moles), and I prefer C to be reported in J/g*K. That way the units on both sides of the equation are:
In chemistry, how do you use the equation Q=mct? -
May 09, 2019 · In the equation Q=mct:Q= the heat energy (Joules), m= the mass of the object/substance being heated (in this case it's water; also important in this situation to remember that 1ml of water is equal to 1g of water), c= the specific heat of the object/substance being heated (againwater, at about 4.186 Joules/gram × °C), and t= the change in temperature in °C (-9°C in this
Recent project
• aluminum alloy coated steel sheet in coil
Aluminium-zinc alloy coated steel sheet in coilAluminium-zinc alloy coated steel sheet in coil Des ...
• api gr b psl 2 pipeline pipes
API 5L Grade B Pipe Specification (PSL1, PSL2, SOUR PSL1 is generally use which equivalent to ASTM ...
• optimization of ingot geometry casting technology
Optimization of ingot geometry , casting technology The goal of this work was to choose the optim ... | 2021-06-14 21:05:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.65609210729599, "perplexity": 1538.091110627288}, "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-2021-25/segments/1623487613453.9/warc/CC-MAIN-20210614201339-20210614231339-00615.warc.gz"} |
http://www.scikit-yb.org/en/develop/api/regressor/peplot.html | # Prediction Error Plot¶
A prediction error plot shows the actual targets from the dataset against the predicted values generated by our model. This allows us to see how much variance is in the model. Data scientists can diagnose regression models using this plot by comparing against the 45 degree line, where the prediction exactly matches the model.
from sklearn.model_selection import train_test_split
from sklearn.linear_model import Lasso
from yellowbrick.regressor import PredictionError
# Create the train and test data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
# Instantiate the linear model and visualizer
model = Lasso()
visualizer = PredictionError(model)
visualizer.fit(X_train, y_train) # Fit the training data to the visualizer
visualizer.score(X_test, y_test) # Evaluate the model on the test data
visualizer.poof() # Draw/show/poof the data
## API Reference¶
Regressor visualizers that score residuals: prediction vs. actual data.
class yellowbrick.regressor.residuals.PredictionError(model, ax=None, shared_limits=True, bestfit=True, identity=True, alpha=0.75, is_fitted='auto', **kwargs)[source]
Bases: yellowbrick.regressor.base.RegressionScoreVisualizer
The prediction error visualizer plots the actual targets from the dataset against the predicted values generated by our model(s). This visualizer is used to detect noise or heteroscedasticity along a range of the target domain.
Parameters
modela Scikit-Learn regressor
Should be an instance of a regressor, otherwise will raise a YellowbrickTypeError exception on instantiation. If the estimator is not fitted, it is fit when the visualizer is fitted, unless otherwise specified by is_fitted.
axmatplotlib Axes, default: None
The axes to plot the figure on. If None is passed in the current axes will be used (or generated if required).
shared_limitsbool, default: True
If shared_limits is True, the range of the X and Y axis limits will be identical, creating a square graphic with a true 45 degree line. In this form, it is easier to diagnose under- or over- prediction, though the figure will become more sparse. To localize points, set shared_limits to False, but note that this will distort the figure and should be accounted for during analysis.
bestfitbool, default: True
Draw a linear best fit line to estimate the correlation between the predicted and measured value of the target variable. The color of the bestfit line is determined by the line_color argument.
identitybool, default: True
Draw the 45 degree identity line, y=x in order to better show the relationship or pattern of the residuals. E.g. to estimate if the model is over- or under- estimating the given values. The color of the identity line is a muted version of the line_color argument.
point_colorcolor
Defines the color of the error points; can be any matplotlib color.
line_colorcolor
Defines the color of the best fit line; can be any matplotlib color.
alphafloat, default: 0.75
Specify a transparency where 1 is completely opaque and 0 is completely transparent. This property makes densely clustered points more visible.
is_fittedbool or str, default=’auto’
Specify if the wrapped estimator is already fitted. If False, the estimator will be fit when the visualizer is fit, otherwise, the estimator will not be modified. If ‘auto’ (default), a helper method will check if the estimator is fitted before fitting it again.
kwargsdict
Keyword arguments that are passed to the base class and may influence the visualization as defined in other Visualizers.
Notes
PredictionError is a ScoreVisualizer, meaning that it wraps a model and its primary entry point is the score() method.
Examples
>>> from yellowbrick.regressor import PredictionError
>>> from sklearn.linear_model import Lasso
>>> model = PredictionError(Lasso())
>>> model.fit(X_train, y_train)
>>> model.score(X_test, y_test)
>>> model.poof()
Attributes
score_float
The R^2 score that specifies the goodness of fit of the underlying regression model to the test data.
draw(self, y, y_pred)[source]
Parameters
yndarray or Series of length n
An array or series of target or class values
y_predndarray or Series of length n
An array or series of predicted target values
Returns
axmatplotlib Axes
The axis with the plotted figure
finalize(self, **kwargs)[source]
Finalize executes any subclass-specific axes finalization steps. The user calls poof and poof calls finalize.
Parameters
kwargs: generic keyword arguments.
score(self, X, y=None, **kwargs)[source]
The score function is the hook for visual interaction. Pass in test data and the visualizer will create predictions on the data and evaluate them with respect to the test values. The evaluation will then be passed to draw() and the result of the estimator score will be returned.
Parameters
Xarray-like
X (also X_test) are the dependent variables of test set to predict
yarray-like
y (also y_test) is the independent actual variables to score against
Returns
scorefloat | 2019-08-19 00:03:18 | {"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": 0.2784756124019623, "perplexity": 3994.349038420168}, "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/1566027314353.10/warc/CC-MAIN-20190818231019-20190819013019-00057.warc.gz"} |
https://phys.libretexts.org/Courses/Muhlenberg_College/MC%3A_Physics_121_-_General_Physics_I/03%3A_Vectors/3.02%3A_Scalars_and_Vectors_(Part_1) | $$\require{cancel}$$
# 3.2: Scalars and Vectors (Part 1)
Learning Objectives
• Describe the difference between vector and scalar quantities.
• Identify the magnitude and direction of a vector.
• Explain the effect of multiplying a vector quantity by a scalar.
• Describe how one-dimensional vector quantities are added or subtracted.
• Explain the geometric construction for the addition or subtraction of vectors in a plane.
• Distinguish between a vector equation and a scalar equation.
Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. For example, “a class period lasts 50 min” or “the gas tank in my car holds 65 L” or “the distance between two posts is 100 m.” A physical quantity that can be specified completely in this manner is called a scalar quantity. Scalar is a synonym of “number.” Time, mass, distance, length, volume, temperature, and energy are examples of scalar quantities.
Scalar quantities that have the same physical units can be added or subtracted according to the usual rules of algebra for numbers. For example, a class ending 10 min earlier than 50 min lasts 50 min − 10 min = 40 min. Similarly, a 60-cal serving of corn followed by a 200-cal serving of donuts gives 60 cal + 200 cal = 260 cal of energy. When we multiply a scalar quantity by a number, we obtain the same scalar quantity but with a larger (or smaller) value. For example, if yesterday’s breakfast had 200 cal of energy and today’s breakfast has four times as much energy as it had yesterday, then today’s breakfast has 4(200 cal) = 800 cal of energy. Two scalar quantities can also be multiplied or divided by each other to form a derived scalar quantity. For example, if a train covers a distance of 100 km in 1.0 h, its speed is 100.0 km/1.0 h = 27.8 m/s, where the speed is a derived scalar quantity obtained by dividing distance by time.
Many physical quantities, however, cannot be described completely by just a single number of physical units. For example, when the U.S. Coast Guard dispatches a ship or a helicopter for a rescue mission, the rescue team must know not only the distance to the distress signal, but also the direction from which the signal is coming so they can get to its origin as quickly as possible. Physical quantities specified completely by giving a number of units (magnitude) and a direction are called vector quantities. Examples of vector quantities include displacement, velocity, position, force, and torque. In the language of mathematics, physical vector quantities are represented by mathematical objects called vectors (Figure $$\PageIndex{1}$$). We can add or subtract two vectors, and we can multiply a vector by a scalar or by another vector, but we cannot divide by a vector. The operation of division by a vector is not defined.
Let’s examine vector algebra using a graphical method to be aware of basic terms and to develop a qualitative understanding. In practice, however, when it comes to solving physics problems, we use analytical methods, which we’ll see in the next section. Analytical methods are more simple computationally and more accurate than graphical methods. From now on, to distinguish between a vector and a scalar quantity, we adopt the common convention that a letter in bold type with an arrow above it denotes a vector, and a letter without an arrow denotes a scalar. For example, a distance of 2.0 km, which is a scalar quantity, is denoted by d = 2.0 km, whereas a displacement of 2.0 km in some direction, which is a vector quantity, is denoted by $$\vec{d}$$.
Suppose you tell a friend on a camping trip that you have discovered a terrific fishing hole 6 km from your tent. It is unlikely your friend would be able to find the hole easily unless you also communicate the direction in which it can be found with respect to your campsite. You may say, for example, “Walk about 6 km northeast from my tent.” The key concept here is that you have to give not one but two pieces of information—namely, the distance or magnitude (6 km) and the direction (northeast).
Displacement is a general term used to describe a change in position, such as during a trip from the tent to the fishing hole. Displacement is an example of a vector quantity. If you walk from the tent (location A) to the hole (location B), as shown in Figure $$\PageIndex{2}$$, the vector $$\vec{D}$$, representing your displacement, is drawn as the arrow that originates at point A and ends at point B. The arrowhead marks the end of the vector. The direction of the displacement vector $$\vec{D}$$ is the direction of the arrow. The length of the arrow represents the magnitude D of vector $$\vec{D}$$. Here, D = 6 km. Since the magnitude of a vector is its length, which is a positive number, the magnitude is also indicated by placing the absolute value notation around the symbol that denotes the vector; so, we can write equivalently that D ≡ |$$\vec{D}$$|. To solve a vector problem graphically, we need to draw the vector $$\vec{D}$$ to scale. For example, if we assume 1 unit of distance (1 km) is represented in the drawing by a line segment of length u = 2 cm, then the total displacement in this example is represented by a vector of length d = 6u = 6(2 cm) = 12 cm , as shown in Figure $$\PageIndex{3}$$. Notice that here, to avoid confusion, we used D = 6 km to denote the magnitude of the actual displacement and d = 12 cm to denote the length of its representation in the drawing.
Suppose your friend walks from the campsite at A to the fishing pond at B and then walks back: from the fishing pond at B to the campsite at A. The magnitude of the displacement vector $$\vec{D}_{AB}$$ from A to B is the same as the magnitude of the displacement vector $$\vec{D}_{BA}$$ from B to A (it equals 6 km in both cases), so we can write $$\vec{D}_{AB}$$ = $$\vec{D}_{BA}$$. However, vector $$\vec{D}_{AB}$$ is not equal to vector $$\vec{D}_{BA}$$ because these two vectors have different directions: $$\vec{D}_{AB}$$ ≠ $$\vec{D}_{BA}$$. In Figure 2.3, vector $$\vec{D}_{BA}$$ would be represented by a vector with an origin at point B and an end at point A, indicating vector $$\vec{D}_{BA}$$ points to the southwest, which is exactly 180° opposite to the direction of vector $$\vec{D}_{AB}$$. We say that vector $$\vec{D}_{BA}$$ is antiparallel to vector $$\vec{D}_{AB}$$ and write $$\vec{D}_{AB}$$ = $$-\vec{D}_{BA}$$, where the minus sign indicates the antiparallel direction.
Two vectors that have identical directions are said to be parallel vectors—meaning, they are parallel to each other. Two parallel vectors $$\vec{A}$$ and $$\vec{B}$$ are equal, denoted by $$\vec{A}$$ = $$\vec{B}$$, if and only if they have equal magnitudes |$$\vec{A}$$| = |$$\vec{B}$$|. Two vectors with directions perpendicular to each other are said to be orthogonal vectors. These relations between vectors are illustrated in Figure $$\PageIndex{4}$$.
Exercise 2.1
Two motorboats named Alice and Bob are moving on a lake. Given the information about their velocity vectors in each of the following situations, indicate whether their velocity vectors are equal or otherwise.
1. Alice moves north at 6 knots and Bob moves west at 6 knots.
2. Alice moves west at 6 knots and Bob moves west at 3 knots.
3. Alice moves northeast at 6 knots and Bob moves south at 3 knots.
4. Alice moves northeast at 6 knots and Bob moves southwest at 6 knots.
5. Alice moves northeast at 2 knots and Bob moves closer to the shore northeast at 2 knots.
## Algebra of Vectors in One Dimension
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. We can illustrate these vector concepts using an example of the fishing trip seen in Figure $$\PageIndex{5}$$.
Suppose your friend departs from point A (the campsite) and walks in the direction to point B (the fishing pond), but, along the way, stops to rest at some point C located three-quarters of the distance between A and B, beginning from point A (Figure $$\PageIndex{5a}$$). What is his displacement vector $$\vec{D}_{AC}$$ when he reaches point C? We know that if he walks all the way to B, his displacement vector relative to A is $$\vec{D}_{AB}$$, which has magnitude DAB = 6 km and a direction of northeast. If he walks only a 0.75 fraction of the total distance, maintaining the northeasterly direction, at point C he must be 0.75 DAB = 4.5 km away from the campsite at A. So, his displacement vector at the rest point C has magnitude DAC = 4.5 km = 0.75 DAB and is parallel to the displacement vector $$\vec{D}_{AB}$$. All of this can be stated succinctly in the form of the following vector equation:
$\vec{D}_{AC} = 0.75\; \vec{D}_{AB} \ldotp \nonumber$
In a vector equation, both sides of the equation are vectors. The previous equation is an example of a vector multiplied by a positive scalar (number) $$\alpha$$ = 0.75. The result, $$\vec{D}_{AC}$$, of such a multiplication is a new vector with a direction parallel to the direction of the original vector $$\vec{D}_{AB}$$. In general, when a vector $$\vec{D}_{A}$$ is multiplied by a positive scalar $$\alpha$$, the result is a new vector $$\vec{D}_{B}$$ that is parallel to $$\vec{D}_{A}$$:
$\vec{B} = \alpha \vec{A} \label{2.1}$
The magnitude |$$\vec{B}$$| of this new vector is obtained by multiplying the magnitude |$$\vec{A}$$| of the original vector, as expressed by the scalar equation:
$B = | \alpha | A \ldotp \label{2.2}$
In a scalar equation, both sides of the equation are numbers. Equation \ref{2.2} is a scalar equation because the magnitudes of vectors are scalar quantities (and positive numbers). If the scalar $$\alpha$$ is negative in the vector equation Equation \ref{2.1}, then the magnitude |$$\vec{B}$$| of the new vector is still given by Equation \ref{2.2}, but the direction of the new vector $$\vec{B}$$ is antiparallel to the direction of $$\vec{A}$$. These principles are illustrated in Figure $$\PageIndex{6a}$$ by two examples where the length of vector $$\vec{A}$$ is 1.5 units. When $$\alpha$$ = 2, the new vector $$\vec{B}$$ = 2$$\vec{A}$$ has length B = 2A = 3.0 units (twice as long as the original vector) and is parallel to the original vector. When $$\alpha$$ = −2, the new vector $$\vec{C}$$ = −2$$\vec{A}$$ has length C = |−2| A = 3.0 units (twice as long as the original vector) and is antiparallel to the original vector.
Now suppose your fishing buddy departs from point A (the campsite), walking in the direction to point B (the fishing hole), but he realizes he lost his tackle box when he stopped to rest at point C (located three-quarters of the distance between A and B, beginning from point A). So, he turns back and retraces his steps in the direction toward the campsite and finds the box lying on the path at some point D only 1.2 km away from point C (see Figure $$\PageIndex{5b}$$). What is his displacement vector $$\vec{D}_{AD}$$ when he finds the box at point D? What is his displacement vector $$\vec{D}_{DB}$$ from point D to the hole? We have already established that at rest point C his displacement vector is $$\vec{D}_{AC}$$ = 0.75 $$\vec{D}_{AB}$$. Starting at point C, he walks southwest (toward the campsite), which means his new displacement vector $$\vec{D}_{CD}$$ from point C to point D is antiparallel to $$\vec{D}_{AB}$$. Its magnitude |$$\vec{D}_{CD}$$| is DCD = 1.2 km = 0.2 DAB, so his second displacement vector is $$\vec{D}_{CD}$$ = −0.2 $$\vec{D}_{AB}$$. His total displacement $$\vec{D}_{AD}$$ relative to the campsite is the vector sum of the two displacement vectors: vector $$\vec{D}_{AC}$$ (from the campsite to the rest point) and vector $$\vec{D}_{CD}$$ (from the rest point to the point where he finds his box):
$\vec{D}_{AD} = \vec{D}_{AC} + \vec{D}_{CD} \ldotp \label{2.3}$
The vector sum of two (or more vectors is called the resultant vector or, for short, the resultant. When the vectors on the right-hand-side of Equation \ref{2.3} are known, we can find the resultant $$\vec{D}_{AD}$$ as follows:
$\vec{D}_{AD} = \vec{D}_{AC} + \vec{D}_{CD} = 0.75\; \vec{D}_{AB} - 0.2\; \vec{D}_{AB} = (0.75 - 0.2) \vec{D}_{AB} = 0.55 \vec{D}_{AB} \ldotp \label{2.4}$
When your friend finally reaches the pond at B, his displacement vector $$\vec{D}_{AB}$$ from point A is the vector sum of his displacement vector $$\vec{D}_{AD}$$ from point A to point D and his displacement vector $$\vec{D}_{DB}$$ from point D to the fishing hole: $$\vec{D}_{AB}$$ = $$\vec{D}_{AD}$$ + $$\vec{D}_{DB}$$ (see Figure $$\PageIndex{5c}$$). This means his displacement vector $$\vec{D}_{DB}$$ is the difference of two vectors:
$\vec{D}_{DB} = \vec{D}_{AB} − \vec{D}_{AD} = \vec{D}_{AB} + (− \vec{D}_{AD}) \ldotp \label{2.5}$
Notice that a difference of two vectors is nothing more than a vector sum of two vectors because the second term in Equation \ref{2.5} is vector $$- \vec{D}_{AD}$$ (which is antiparallel to $$\vec{D}_{AD}$$). When we substitute Equation \ref{2.4} into Equation \ref{2.5}, we obtain the second displacement vector:
$\vec{D}_{DB} = \vec{D}_{AB} − \vec{D}_{AD} = \vec{D}_{AB} − 0.55\; \vec{D}_{AB} = (1.0 − 0.55)\; \vec{D}_{AB} = 0.45\; \vec{D}_{AB} \ldotp \label{2.6}$
This result means your friend walked DDB = 0.45 DAB = 0.45(6.0 km) = 2.7 km from the point where he finds his tackle box to the fishing hole.
When vectors $$\vec{A}$$ and $$\vec{B}$$ lie along a line (that is, in one dimension), such as in the camping example, their resultant $$\vec{R}$$ = $$\vec{A}$$ + $$\vec{B}$$ and their difference $$\vec{D}$$ = $$\vec{A}$$ − $$\vec{B}$$ both lie along the same direction. We can illustrate the addition or subtraction of vectors by drawing the corresponding vectors to scale in one dimension, as shown in Figure $$\PageIndex{6}$$.
To illustrate the resultant when $$\vec{A}$$ and $$\vec{B}$$ are two parallel vectors, we draw them along one line by placing the origin of one vector at the end of the other vector in head-to-tail fashion (see Figure $$\PageIndex{6b}$$). The magnitude of this resultant is the sum of their magnitudes: R = A + B. The direction of the resultant is parallel to both vectors. When vector $$\vec{A}$$ is antiparallel to vector $$\vec{B}$$, we draw them along one line in either head-to-head fashion (Figure (\PageIndex{6c}\)) or tail-to-tail fashion. The magnitude of the vector difference, then, is the absolute value D = |A − B| of the difference of their magnitudes. The direction of the difference vector $$\vec{D}$$ is parallel to the direction of the longer vector.
In general, in one dimension—as well as in higher dimensions, such as in a plane or in space—we can add any number of vectors and we can do so in any order because the addition of vectors is commutative,
$\vec{A} + \vec{B} = \vec{B} + \vec{A} \ldotp \label{2.7}$
and associative,
$(\vec{A} + \vec{B}) + \vec{C} = \vec{A} + (\vec{B} + \vec{C}) \ldotp \label{2.8}$
Moreover, multiplication by a scalar is distributive:
$\alpha_{1} \vec{A} + \alpha_{2} \vec{A} = (\alpha_{1} + \alpha_{2}) \vec{A} \ldotp \label{2.9}$
We used the distributive property in Equation \ref{2.4} and Equation \ref{2.6}.
When adding many vectors in one dimension, it is convenient to use the concept of a unit vector. A unit vector, which is denoted by a letter symbol with a hat, such as $$\hat{u}$$, has a magnitude of one and does not have any physical unit so that |$$\hat{u}$$| ≡ u = 1. The only role of a unit vector is to specify direction. For example, instead of saying vector $$\vec{D}_{AB}$$ has a magnitude of 6.0 km and a direction of northeast, we can introduce a unit vector $$\hat{u}$$ that points to the northeast and say succinctly that $$\vec{D}_{AB}$$ = (6.0 km) $$\hat{u}$$. Then the southwesterly direction is simply given by the unit vector$$- \hat{u}$$. In this way, the displacement of 6.0 km in the southwesterly direction is expressed by the vector
$\vec{D}_{BA} = (−6.0\; km)\; \hat{u} \ldotp \nonumber$
## Contributors and Attributions
• Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0). | 2021-05-12 05:53:37 | {"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": 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": 0.8217579126358032, "perplexity": 369.31981359204116}, "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-2021-21/segments/1620243991252.15/warc/CC-MAIN-20210512035557-20210512065557-00486.warc.gz"} |
https://aitopics.org/doc/nips:B41D24C8/ | # Exploiting Numerical Sparsity for Efficient Learning : Faster Eigenvector Computation and Regression
,
Neural Information Processing Systems
In this paper, we obtain improved running times for regression and top eigenvector computation for numerically sparse matrices. Given a data matrix $\mat{A} \in \R^{n \times d}$ where every row $a \in \R^d$ has $\|a\|_2^2 \leq L$ and numerical sparsity $\leq s$, i.e. $\|a\|_1^2 / \|a\|_2^2 \leq s$, we provide faster algorithms for these problems for many parameter settings. For top eigenvector computation, when $\gap > 0$ is the relative gap between the top two eigenvectors of $\mat{A}^\top \mat{A}$ and $r$ is the stable rank of $\mat{A}$ we obtain a running time of $\otilde(nd + r(s + \sqrt{r s}) / \gap^2)$ improving upon the previous best unaccelerated running time of $O(nd + r d / \gap^2)$. As $r \leq d$ and $s \leq d$ our algorithm everywhere improves or matches the previous bounds for all parameter settings. For regression, when $\mu > 0$ is the smallest eigenvalue of $\mat{A}^\top \mat{A}$ we obtain a running time of $\otilde(nd + (nL / \mu) \sqrt{s nL / \mu})$ improving upon the previous best unaccelerated running time of $\otilde(nd + n L d / \mu)$. This result expands when regression can be solved in nearly linear time from when $L/\mu = \otilde(1)$ to when $L / \mu = \otilde(d^{2/3} / (sn)^{1/3})$. Furthermore, we obtain similar improvements even when row norms and numerical sparsities are non-uniform and we show how to achieve even faster running times by accelerating using approximate proximal point \cite{frostig2015regularizing} / catalyst \cite{lin2015universal}. Our running times depend only on the size of the input and natural numerical measures of the matrix, i.e. eigenvalues and $\ell_p$ norms, making progress on a key open problem regarding optimal running times for efficient large-scale learning.
, , , (18 more...)
Dec-31-2018 | 2019-06-26 01:53:18 | {"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": 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": 0.8602690696716309, "perplexity": 358.89892862423403}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000044.37/warc/CC-MAIN-20190626013357-20190626035357-00539.warc.gz"} |
https://testbook.com/question-answer/three-friends-a-b-and-c-invested-a-sum-of-rs-160--5fea0aea904edc5b8e1e23a9 | # Three friends A, B and C invested a sum of Rs. 16000, Rs. 24000 and Rs. 40000 respectively. B left after 8 months and C left after 4 months only. The total profit at the end of the year was Rs. 17000. Find the share of A(in Rs.).
1. 2000
2. 3000
3. 5000
4. 6000
Option 4 : 6000
## Detailed Solution
Given:
Three friends A, B and C invested a sum of Rs. 16000, Rs. 24000 and Rs.40000 respectively.
B left after 8 months and C left after 4 months only.
The total profit at the end of the year was Rs. 17000.
Formula Used:
Ratio of Profit = ratios of product of Amount invested and time
Calculation:
Ratio of profits of A : B : C = 16000 × 12 : 24000 × 8 : 40000 × 4 = 6 : 6 : 5
Profit share of A = Rs. [{6/(6 + 6 + 5)} × 17000] = Rs. (17000 × 6/17) = Rs. 6000
∴ A’s profit of share is Rs. 6000 | 2022-01-25 10:37:57 | {"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": 0.8539265394210815, "perplexity": 3031.637859209827}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304810.95/warc/CC-MAIN-20220125100035-20220125130035-00111.warc.gz"} |
https://themathhelp.com/threads/a-bernoulli-equation.2534/ | # LessonA Bernoulli Equation
#### MarkFL
##### La Villa Strangiato
Staff member
Moderator
Math Helper
Suppose we are given to solve:
$$\displaystyle \d{y}{x}+\frac{y}{x}=y^2$$
A first order ODE that can be written in the form:
$$\displaystyle \frac{dy}{dx}+P(x)y=Q(x)y^n$$
where $$P(x)$$ and $$Q(x)$$ are continuous on an interval $$(a,b)$$ and $$n$$ is a real number, is called a Bernoulli equation.
This equation was proposed for solution by James Bernoulli in 1695. It was solved by his brother John Bernoulli. James and John were two of eight mathematicians in the Bernoulli family. In 1696 Gottfried Leibniz showed that the Bernoulli equation can be reduced to a linear equation by making the substitution $$v=y^{1-n}$$.
We are given to solve:
(1) $$\displaystyle \frac{dy}{dx}+\frac{1}{x}y=y^2$$
Dividing through by $$y^2$$ (observing we are losing the trivial solution $$y\equiv0$$), we obtain:
(2) $$\displaystyle y^{-2}\frac{dy}{dx}+\frac{1}{x}y^{-1}=1$$
Using the substitution of Leibniz, i.e., $$v=y^{-1}$$, we find via the chain rule that:
$$\displaystyle \frac{dv}{dx}=-y^{-2}\frac{dy}{dx}$$
and (2) becomes:
(3) $$\displaystyle \frac{dv}{dx}-\frac{1}{x}v=-1$$
Now we have a linear equation in $$v$$. Computing the integrating factor, we find:
$$\displaystyle \mu(x)=e^{-\int\frac{dx}{x}}=\frac{1}{x}$$
Multiplying (3) by this integrating factor, we obtain:
$$\displaystyle \frac{1}{x}\frac{dv}{dx}-\frac{1}{x^2}v=-\frac{1}{x}$$
Rewriting the left hand side as the differentiation of a product, we have:
$$\displaystyle \frac{d}{dx}\left(\frac{v}{x} \right)=-\frac{1}{x}$$
Integrating with respect to $$x$$, there results:
$$\displaystyle \int\,d\left(\frac{v}{x} \right)=-\int\frac{1}{x}\,dx$$
$$\displaystyle \frac{v}{x}=-\ln|x|+C$$
$$\displaystyle v=x\left(C-\ln|x| \right)$$
Back-substituting for $$v$$, we have:
$$\displaystyle \frac{1}{y}=x\left(C-\ln|x| \right)$$
Hence:
$$\displaystyle y(x)=\frac{1}{x\left(C-\ln|x| \right)}$$
anemone and harpazo
#### harpazo
##### Pure Mathematics
Banned
What on earth is this?
#### MarkFL
##### La Villa Strangiato
Staff member
Moderator
Math Helper
Let's see if we can solve the general equation:
$$\displaystyle \d{y}{x}+P(x)y=Q(x)y^n$$
Divide through by $$y^n$$ to obtain:
$$\displaystyle y^{-n}\d{y}{x}+P(x)y^{1-n}=Q(x)$$
Let:
$$\displaystyle v=y^{1-n}\implies \d{v}{x}=(1-n)y^{-n}\d{y}{x}\implies \d{y}{x}=\frac{1}{1-n}y^n\d{v}{x}$$
And the ODE becomes:
$$\displaystyle y^{-n}\left(\frac{1}{1-n}y^n\d{v}{x}\right)+P(x)v=Q(x)$$
$$\displaystyle \d{v}{x}+(1-n)P(x)v=(1-n)Q(x)$$
Now we have a linear first order ODE, which can be solved according to the method used in this thread:
Lesson - First order linear ODEs and the integrating factor
anemone and harpazo
#### harpazo
##### Pure Mathematics
Banned
This is too advanced for me.
Staff member | 2019-03-20 03:19:21 | {"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": 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": 0.9808313846588135, "perplexity": 957.1641379589896}, "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/1552912202199.51/warc/CC-MAIN-20190320024206-20190320050206-00006.warc.gz"} |
https://stacks.math.columbia.edu/tag/041K | ## 73.11 Descending properties of morphisms in the fpqc topology
In this section we find a large number of properties of morphisms of algebraic spaces which are local on the base in the fpqc topology. Please compare with Descent, Section 35.23 for the case of morphisms of schemes.
Lemma 73.11.1. Let $S$ be a scheme. The property $\mathcal{P}(f) =$“$f$ is quasi-compact” is fpqc local on the base on algebraic spaces over $S$.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.8.8. Let $Z' \to Z$ be a surjective flat morphism of affine schemes over $S$. Let $f : X \to Z$ be a morphism of algebraic spaces, and assume that the base change $f' : Z' \times _ Z X \to Z'$ is quasi-compact. We have to show that $f$ is quasi-compact. To see this, using Morphisms of Spaces, Lemma 66.8.8 again, it is enough to show that for every affine scheme $Y$ and morphism $Y \to Z$ the fibre product $Y \times _ Z X$ is quasi-compact. Here is a picture:
73.11.1.1
$$\label{spaces-descent-equation-cube} \vcenter { \xymatrix{ Y \times _ Z Z' \times _ Z X \ar[dd] \ar[rr] \ar[rd] & & Z' \times _ Z X \ar '[d][dd]^{f'} \ar[rd] \\ & Y \times _ Z X \ar[dd] \ar[rr] & & X \ar[dd]^ f \\ Y \times _ Z Z' \ar '[r][rr] \ar[rd] & & Z' \ar[rd] \\ & Y \ar[rr] & & Z } }$$
Note that all squares are cartesian and the bottom square consists of affine schemes. The assumption that $f'$ is quasi-compact combined with the fact that $Y \times _ Z Z'$ is affine implies that $Y \times _ Z Z' \times _ Z X$ is quasi-compact. Since
$Y \times _ Z Z' \times _ Z X \longrightarrow Y \times _ Z X$
is surjective as a base change of $Z' \to Z$ we conclude that $Y \times _ Z X$ is quasi-compact, see Morphisms of Spaces, Lemma 66.8.6. This finishes the proof. $\square$
Lemma 73.11.2. Let $S$ be a scheme. The property $\mathcal{P}(f) =$“$f$ is quasi-separated” is fpqc local on the base on algebraic spaces over $S$.
Proof. A base change of a quasi-separated morphism is quasi-separated, see Morphisms of Spaces, Lemma 66.4.4. Hence the direct implication in Definition 73.10.1.
Let $\{ Y_ i \to Y\} _{i \in I}$ be an fpqc covering of algebraic spaces over $S$. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Assume each base change $X_ i := Y_ i \times _ Y X \to Y_ i$ is quasi-separated. This means that each of the morphisms
$\Delta _ i : X_ i \longrightarrow X_ i \times _{Y_ i} X_ i = Y_ i \times _ Y (X \times _ Y X)$
is quasi-compact. The base change of a fpqc covering is an fpqc covering, see Topologies on Spaces, Lemma 72.9.3 hence $\{ Y_ i \times _ Y (X \times _ Y X) \to X \times _ Y X\}$ is an fpqc covering of algebraic spaces. Moreover, each $\Delta _ i$ is the base change of the morphism $\Delta : X \to X \times _ Y X$. Hence it follows from Lemma 73.11.1 that $\Delta$ is quasi-compact, i.e., $f$ is quasi-separated. $\square$
Lemma 73.11.3. Let $S$ be a scheme. The property $\mathcal{P}(f) =$“$f$ is universally closed” is fpqc local on the base on algebraic spaces over $S$.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.9.5. Let $Z' \to Z$ be a surjective flat morphism of affine schemes over $S$. Let $f : X \to Z$ be a morphism of algebraic spaces, and assume that the base change $f' : Z' \times _ Z X \to Z'$ is universally closed. We have to show that $f$ is universally closed. To see this, using Morphisms of Spaces, Lemma 66.9.5 again, it is enough to show that for every affine scheme $Y$ and morphism $Y \to Z$ the map $|Y \times _ Z X| \to |Y|$ is closed. Consider the cube (73.11.1.1). The assumption that $f'$ is universally closed implies that $|Y \times _ Z Z' \times _ Z X| \to |Y \times _ Z Z'|$ is closed. As $Y \times _ Z Z' \to Y$ is quasi-compact, surjective, and flat as a base change of $Z' \to Z$ we see the map $|Y \times _ Z Z'| \to |Y|$ is submersive, see Morphisms, Lemma 29.25.12. Moreover the map
$|Y \times _ Z Z' \times _ Z X| \longrightarrow |Y \times _ Z Z'| \times _{|Y|} |Y \times _ Z X|$
is surjective, see Properties of Spaces, Lemma 65.4.3. It follows by elementary topology that $|Y \times _ Z X| \to |Y|$ is closed. $\square$
Lemma 73.11.4. Let $S$ be a scheme. The property $\mathcal{P}(f) =$“$f$ is universally open” is fpqc local on the base on algebraic spaces over $S$.
Proof. The proof is the same as the proof of Lemma 73.11.3. $\square$
Lemma 73.11.5. The property $\mathcal{P}(f) =$“$f$ is universally submersive” is fpqc local on the base.
Proof. The proof is the same as the proof of Lemma 73.11.3. $\square$
Lemma 73.11.6. The property $\mathcal{P}(f) =$“$f$ is surjective” is fpqc local on the base.
Proof. Omitted. (Hint: Use Properties of Spaces, Lemma 65.4.3.) $\square$
Lemma 73.11.7. The property $\mathcal{P}(f) =$“$f$ is universally injective” is fpqc local on the base.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.9.5. Let $Z' \to Z$ be a flat surjective morphism of affine schemes over $S$ and let $f : X \to Z$ be a morphism from an algebraic space to $Z$. Assume that the base change $f' : X' \to Z'$ is universally injective. Let $K$ be a field, and let $a, b : \mathop{\mathrm{Spec}}(K) \to X$ be two morphisms such that $f \circ a = f \circ b$. As $Z' \to Z$ is surjective there exists a field extension $K'/K$ and a morphism $\mathop{\mathrm{Spec}}(K') \to Z'$ such that the following solid diagram commutes
$\xymatrix{ \mathop{\mathrm{Spec}}(K') \ar[rrd] \ar@{-->}[rd]_{a', b'} \ar[dd] \\ & X' \ar[r] \ar[d] & Z' \ar[d] \\ \mathop{\mathrm{Spec}}(K) \ar[r]^{a, b} & X \ar[r] & Z }$
As the square is cartesian we get the two dotted arrows $a'$, $b'$ making the diagram commute. Since $X' \to Z'$ is universally injective we get $a' = b'$. This forces $a = b$ as $\{ \mathop{\mathrm{Spec}}(K') \to \mathop{\mathrm{Spec}}(K)\}$ is an fpqc covering, see Properties of Spaces, Proposition 65.17.1. Hence $f$ is universally injective as desired. $\square$
Lemma 73.11.8. The property $\mathcal{P}(f) =$“$f$ is a universal homeomorphism” is fpqc local on the base.
Proof. This can be proved in exactly the same manner as Lemma 73.11.3. Alternatively, one can use that a map of topological spaces is a homeomorphism if and only if it is injective, surjective, and open. Thus a universal homeomorphism is the same thing as a surjective, universally injective, and universally open morphism. See Morphisms of Spaces, Lemma 66.5.5 and Morphisms of Spaces, Definitions 66.19.3, 66.5.2, 66.6.2, 66.53.2. Thus the lemma follows from Lemmas 73.11.6, 73.11.7, and 73.11.4. $\square$
Lemma 73.11.9. The property $\mathcal{P}(f) =$“$f$ is locally of finite type” is fpqc local on the base.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.23.4. Let $Z' \to Z$ be a surjective flat morphism of affine schemes over $S$. Let $f : X \to Z$ be a morphism of algebraic spaces, and assume that the base change $f' : Z' \times _ Z X \to Z'$ is locally of finite type. We have to show that $f$ is locally of finite type. Let $U$ be a scheme and let $U \to X$ be surjective and étale. By Morphisms of Spaces, Lemma 66.23.4 again, it is enough to show that $U \to Z$ is locally of finite type. Since $f'$ is locally of finite type, and since $Z' \times _ Z U$ is a scheme étale over $Z' \times _ Z X$ we conclude (by the same lemma again) that $Z' \times _ Z U \to Z'$ is locally of finite type. As $\{ Z' \to Z\}$ is an fpqc covering we conclude that $U \to Z$ is locally of finite type by Descent, Lemma 35.23.10 as desired. $\square$
Lemma 73.11.10. The property $\mathcal{P}(f) =$“$f$ is locally of finite presentation” is fpqc local on the base.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.28.4. Let $Z' \to Z$ be a surjective flat morphism of affine schemes over $S$. Let $f : X \to Z$ be a morphism of algebraic spaces, and assume that the base change $f' : Z' \times _ Z X \to Z'$ is locally of finite presentation. We have to show that $f$ is locally of finite presentation. Let $U$ be a scheme and let $U \to X$ be surjective and étale. By Morphisms of Spaces, Lemma 66.28.4 again, it is enough to show that $U \to Z$ is locally of finite presentation. Since $f'$ is locally of finite presentation, and since $Z' \times _ Z U$ is a scheme étale over $Z' \times _ Z X$ we conclude (by the same lemma again) that $Z' \times _ Z U \to Z'$ is locally of finite presentation. As $\{ Z' \to Z\}$ is an fpqc covering we conclude that $U \to Z$ is locally of finite presentation by Descent, Lemma 35.23.11 as desired. $\square$
Lemma 73.11.11. The property $\mathcal{P}(f) =$“$f$ is of finite type” is fpqc local on the base.
Lemma 73.11.12. The property $\mathcal{P}(f) =$“$f$ is of finite presentation” is fpqc local on the base.
Lemma 73.11.13. The property $\mathcal{P}(f) =$“$f$ is flat” is fpqc local on the base.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.30.5. Let $Z' \to Z$ be a surjective flat morphism of affine schemes over $S$. Let $f : X \to Z$ be a morphism of algebraic spaces, and assume that the base change $f' : Z' \times _ Z X \to Z'$ is flat. We have to show that $f$ is flat. Let $U$ be a scheme and let $U \to X$ be surjective and étale. By Morphisms of Spaces, Lemma 66.30.5 again, it is enough to show that $U \to Z$ is flat. Since $f'$ is flat, and since $Z' \times _ Z U$ is a scheme étale over $Z' \times _ Z X$ we conclude (by the same lemma again) that $Z' \times _ Z U \to Z'$ is flat. As $\{ Z' \to Z\}$ is an fpqc covering we conclude that $U \to Z$ is flat by Descent, Lemma 35.23.15 as desired. $\square$
Lemma 73.11.14. The property $\mathcal{P}(f) =$“$f$ is an open immersion” is fpqc local on the base.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.12.1. Consider a cartesian diagram
$\xymatrix{ X' \ar[r] \ar[d] & X \ar[d] \\ Z' \ar[r] & Z }$
of algebraic spaces over $S$ where $Z' \to Z$ is a surjective flat morphism of affine schemes, and $X' \to Z'$ is an open immersion. We have to show that $X \to Z$ is an open immersion. Note that $|X'| \subset |Z'|$ corresponds to an open subscheme $U' \subset Z'$ (isomorphic to $X'$) with the property that $\text{pr}_0^{-1}(U') = \text{pr}_1^{-1}(U')$ as open subschemes of $Z' \times _ Z Z'$. Hence there exists an open subscheme $U \subset Z$ such that $X' = (Z' \to Z)^{-1}(U)$, see Descent, Lemma 35.13.6. By Properties of Spaces, Proposition 65.17.1 we see that $X$ satisfies the sheaf condition for the fpqc topology. Now we have the fpqc covering $\mathcal{U} = \{ U' \to U\}$ and the element $U' \to X' \to X \in \check{H}^0(\mathcal{U}, X)$. By the sheaf condition we obtain a morphism $U \to X$ such that
$\xymatrix{ U' \ar[r] \ar[d]^{\cong } \ar@/_3ex/[dd] & U \ar[d] \ar@/^3ex/[dd] \\ X' \ar[r] \ar[d] & X \ar[d] \\ Z' \ar[r] & Z }$
is commutative. On the other hand, we know that for any scheme $T$ over $S$ and $T$-valued point $T \to X$ the composition $T \to X \to Z$ is a morphism such that $Z' \times _ Z T \to Z'$ factors through $U'$. Clearly this means that $T \to Z$ factors through $U$. In other words the map of sheaves $U \to X$ is bijective and we win. $\square$
Lemma 73.11.15. The property $\mathcal{P}(f) =$“$f$ is an isomorphism” is fpqc local on the base.
Lemma 73.11.16. The property $\mathcal{P}(f) =$“$f$ is affine” is fpqc local on the base.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.20.3. Let $Z' \to Z$ be a surjective flat morphism of affine schemes over $S$. Let $f : X \to Z$ be a morphism of algebraic spaces, and assume that the base change $f' : Z' \times _ Z X \to Z'$ is affine. Let $X'$ be a scheme representing $Z' \times _ Z X$. We obtain a canonical isomorphism
$\varphi : X' \times _ Z Z' \longrightarrow Z' \times _ Z X'$
since both schemes represent the algebraic space $Z' \times _ Z Z' \times _ Z X$. This is a descent datum for $X'/Z'/Z$, see Descent, Definition 35.34.1 (verification omitted, compare with Descent, Lemma 35.39.1). Since $X' \to Z'$ is affine this descent datum is effective, see Descent, Lemma 35.37.1. Thus there exists a scheme $Y \to Z$ over $Z$ and an isomorphism $\psi : Z' \times _ Z Y \to X'$ compatible with descent data. Of course $Y \to Z$ is affine (by construction or by Descent, Lemma 35.23.18). Note that $\mathcal{Y} = \{ Z' \times _ Z Y \to Y\}$ is a fpqc covering, and interpreting $\psi$ as an element of $X(Z' \times _ Z Y)$ we see that $\psi \in \check{H}^0(\mathcal{Y}, X)$. By the sheaf condition for $X$ with respect to this covering (see Properties of Spaces, Proposition 65.17.1) we obtain a morphism $Y \to X$. By construction the base change of this to $Z'$ is an isomorphism, hence an isomorphism by Lemma 73.11.15. This proves that $X$ is representable by an affine scheme and we win. $\square$
Lemma 73.11.17. The property $\mathcal{P}(f) =$“$f$ is a closed immersion” is fpqc local on the base.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.12.1. Consider a cartesian diagram
$\xymatrix{ X' \ar[r] \ar[d] & X \ar[d] \\ Z' \ar[r] & Z }$
of algebraic spaces over $S$ where $Z' \to Z$ is a surjective flat morphism of affine schemes, and $X' \to Z'$ is a closed immersion. We have to show that $X \to Z$ is a closed immersion. The morphism $X' \to Z'$ is affine. Hence by Lemma 73.11.16 we see that $X$ is a scheme and $X \to Z$ is affine. It follows from Descent, Lemma 35.23.19 that $X \to Z$ is a closed immersion as desired. $\square$
Lemma 73.11.18. The property $\mathcal{P}(f) =$“$f$ is separated” is fpqc local on the base.
Proof. A base change of a separated morphism is separated, see Morphisms of Spaces, Lemma 66.4.4. Hence the direct implication in Definition 73.10.1.
Let $\{ Y_ i \to Y\} _{i \in I}$ be an fpqc covering of algebraic spaces over $S$. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Assume each base change $X_ i := Y_ i \times _ Y X \to Y_ i$ is separated. This means that each of the morphisms
$\Delta _ i : X_ i \longrightarrow X_ i \times _{Y_ i} X_ i = Y_ i \times _ Y (X \times _ Y X)$
is a closed immersion. The base change of a fpqc covering is an fpqc covering, see Topologies on Spaces, Lemma 72.9.3 hence $\{ Y_ i \times _ Y (X \times _ Y X) \to X \times _ Y X\}$ is an fpqc covering of algebraic spaces. Moreover, each $\Delta _ i$ is the base change of the morphism $\Delta : X \to X \times _ Y X$. Hence it follows from Lemma 73.11.17 that $\Delta$ is a closed immersion, i.e., $f$ is separated. $\square$
Lemma 73.11.19. The property $\mathcal{P}(f) =$“$f$ is proper” is fpqc local on the base.
Lemma 73.11.20. The property $\mathcal{P}(f) =$“$f$ is quasi-affine” is fpqc local on the base.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.21.3. Let $Z' \to Z$ be a surjective flat morphism of affine schemes over $S$. Let $f : X \to Z$ be a morphism of algebraic spaces, and assume that the base change $f' : Z' \times _ Z X \to Z'$ is quasi-affine. Let $X'$ be a scheme representing $Z' \times _ Z X$. We obtain a canonical isomorphism
$\varphi : X' \times _ Z Z' \longrightarrow Z' \times _ Z X'$
since both schemes represent the algebraic space $Z' \times _ Z Z' \times _ Z X$. This is a descent datum for $X'/Z'/Z$, see Descent, Definition 35.34.1 (verification omitted, compare with Descent, Lemma 35.39.1). Since $X' \to Z'$ is quasi-affine this descent datum is effective, see Descent, Lemma 35.38.1. Thus there exists a scheme $Y \to Z$ over $Z$ and an isomorphism $\psi : Z' \times _ Z Y \to X'$ compatible with descent data. Of course $Y \to Z$ is quasi-affine (by construction or by Descent, Lemma 35.23.20). Note that $\mathcal{Y} = \{ Z' \times _ Z Y \to Y\}$ is a fpqc covering, and interpreting $\psi$ as an element of $X(Z' \times _ Z Y)$ we see that $\psi \in \check{H}^0(\mathcal{Y}, X)$. By the sheaf condition for $X$ (see Properties of Spaces, Proposition 65.17.1) we obtain a morphism $Y \to X$. By construction the base change of this to $Z'$ is an isomorphism, hence an isomorphism by Lemma 73.11.15. This proves that $X$ is representable by a quasi-affine scheme and we win. $\square$
Lemma 73.11.21. The property $\mathcal{P}(f) =$“$f$ is a quasi-compact immersion” is fpqc local on the base.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemmas 66.12.1 and 66.8.8. Consider a cartesian diagram
$\xymatrix{ X' \ar[r] \ar[d] & X \ar[d] \\ Z' \ar[r] & Z }$
of algebraic spaces over $S$ where $Z' \to Z$ is a surjective flat morphism of affine schemes, and $X' \to Z'$ is a quasi-compact immersion. We have to show that $X \to Z$ is a closed immersion. The morphism $X' \to Z'$ is quasi-affine. Hence by Lemma 73.11.20 we see that $X$ is a scheme and $X \to Z$ is quasi-affine. It follows from Descent, Lemma 35.23.21 that $X \to Z$ is a quasi-compact immersion as desired. $\square$
Lemma 73.11.22. The property $\mathcal{P}(f) =$“$f$ is integral” is fpqc local on the base.
Proof. An integral morphism is the same thing as an affine, universally closed morphism. See Morphisms of Spaces, Lemma 66.45.7. Hence the lemma follows on combining Lemmas 73.11.3 and 73.11.16. $\square$
Lemma 73.11.23. The property $\mathcal{P}(f) =$“$f$ is finite” is fpqc local on the base.
Proof. An finite morphism is the same thing as an integral, morphism which is locally of finite type. See Morphisms of Spaces, Lemma 66.45.6. Hence the lemma follows on combining Lemmas 73.11.9 and 73.11.22. $\square$
Lemma 73.11.24. The properties $\mathcal{P}(f) =$“$f$ is locally quasi-finite” and $\mathcal{P}(f) =$“$f$ is quasi-finite” are fpqc local on the base.
Proof. We have already seen that “quasi-compact” is fpqc local on the base, see Lemma 73.11.1. Hence it is enough to prove the lemma for “locally quasi-finite”. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.27.6. Let $Z' \to Z$ be a surjective flat morphism of affine schemes over $S$. Let $f : X \to Z$ be a morphism of algebraic spaces, and assume that the base change $f' : Z' \times _ Z X \to Z'$ is locally quasi-finite. We have to show that $f$ is locally quasi-finite. Let $U$ be a scheme and let $U \to X$ be surjective and étale. By Morphisms of Spaces, Lemma 66.27.6 again, it is enough to show that $U \to Z$ is locally quasi-finite. Since $f'$ is locally quasi-finite, and since $Z' \times _ Z U$ is a scheme étale over $Z' \times _ Z X$ we conclude (by the same lemma again) that $Z' \times _ Z U \to Z'$ is locally quasi-finite. As $\{ Z' \to Z\}$ is an fpqc covering we conclude that $U \to Z$ is locally quasi-finite by Descent, Lemma 35.23.24 as desired. $\square$
Lemma 73.11.25. The property $\mathcal{P}(f) =$“$f$ is syntomic” is fpqc local on the base.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.36.4. Let $Z' \to Z$ be a surjective flat morphism of affine schemes over $S$. Let $f : X \to Z$ be a morphism of algebraic spaces, and assume that the base change $f' : Z' \times _ Z X \to Z'$ is syntomic. We have to show that $f$ is syntomic. Let $U$ be a scheme and let $U \to X$ be surjective and étale. By Morphisms of Spaces, Lemma 66.36.4 again, it is enough to show that $U \to Z$ is syntomic. Since $f'$ is syntomic, and since $Z' \times _ Z U$ is a scheme étale over $Z' \times _ Z X$ we conclude (by the same lemma again) that $Z' \times _ Z U \to Z'$ is syntomic. As $\{ Z' \to Z\}$ is an fpqc covering we conclude that $U \to Z$ is syntomic by Descent, Lemma 35.23.26 as desired. $\square$
Lemma 73.11.26. The property $\mathcal{P}(f) =$“$f$ is smooth” is fpqc local on the base.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.37.4. Let $Z' \to Z$ be a surjective flat morphism of affine schemes over $S$. Let $f : X \to Z$ be a morphism of algebraic spaces, and assume that the base change $f' : Z' \times _ Z X \to Z'$ is smooth. We have to show that $f$ is smooth. Let $U$ be a scheme and let $U \to X$ be surjective and étale. By Morphisms of Spaces, Lemma 66.37.4 again, it is enough to show that $U \to Z$ is smooth. Since $f'$ is smooth, and since $Z' \times _ Z U$ is a scheme étale over $Z' \times _ Z X$ we conclude (by the same lemma again) that $Z' \times _ Z U \to Z'$ is smooth. As $\{ Z' \to Z\}$ is an fpqc covering we conclude that $U \to Z$ is smooth by Descent, Lemma 35.23.27 as desired. $\square$
Lemma 73.11.27. The property $\mathcal{P}(f) =$“$f$ is unramified” is fpqc local on the base.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.38.5. Let $Z' \to Z$ be a surjective flat morphism of affine schemes over $S$. Let $f : X \to Z$ be a morphism of algebraic spaces, and assume that the base change $f' : Z' \times _ Z X \to Z'$ is unramified. We have to show that $f$ is unramified. Let $U$ be a scheme and let $U \to X$ be surjective and étale. By Morphisms of Spaces, Lemma 66.38.5 again, it is enough to show that $U \to Z$ is unramified. Since $f'$ is unramified, and since $Z' \times _ Z U$ is a scheme étale over $Z' \times _ Z X$ we conclude (by the same lemma again) that $Z' \times _ Z U \to Z'$ is unramified. As $\{ Z' \to Z\}$ is an fpqc covering we conclude that $U \to Z$ is unramified by Descent, Lemma 35.23.28 as desired. $\square$
Lemma 73.11.28. The property $\mathcal{P}(f) =$“$f$ is étale” is fpqc local on the base.
Proof. We will use Lemma 73.10.4 to prove this. Assumptions (1) and (2) of that lemma follow from Morphisms of Spaces, Lemma 66.39.2. Let $Z' \to Z$ be a surjective flat morphism of affine schemes over $S$. Let $f : X \to Z$ be a morphism of algebraic spaces, and assume that the base change $f' : Z' \times _ Z X \to Z'$ is étale. We have to show that $f$ is étale. Let $U$ be a scheme and let $U \to X$ be surjective and étale. By Morphisms of Spaces, Lemma 66.39.2 again, it is enough to show that $U \to Z$ is étale. Since $f'$ is étale, and since $Z' \times _ Z U$ is a scheme étale over $Z' \times _ Z X$ we conclude (by the same lemma again) that $Z' \times _ Z U \to Z'$ is étale. As $\{ Z' \to Z\}$ is an fpqc covering we conclude that $U \to Z$ is étale by Descent, Lemma 35.23.29 as desired. $\square$
Lemma 73.11.29. The property $\mathcal{P}(f) =$“$f$ is finite locally free” is fpqc local on the base.
Proof. Being finite locally free is equivalent to being finite, flat and locally of finite presentation (Morphisms of Spaces, Lemma 66.46.6). Hence this follows from Lemmas 73.11.23, 73.11.13, and 73.11.10. $\square$
Lemma 73.11.30. The property $\mathcal{P}(f) =$“$f$ is a monomorphism” is fpqc local on the base.
Proof. Let $f : X \to Y$ be a morphism of algebraic spaces. Let $\{ Y_ i \to Y\}$ be an fpqc covering, and assume each of the base changes $f_ i : X_ i \to Y_ i$ of $f$ is a monomorphism. We have to show that $f$ is a monomorphism.
First proof. Note that $f$ is a monomorphism if and only if $\Delta : X \to X \times _ Y X$ is an isomorphism. By applying this to $f_ i$ we see that each of the morphisms
$\Delta _ i : X_ i \longrightarrow X_ i \times _{Y_ i} X_ i = Y_ i \times _ Y (X \times _ Y X)$
is an isomorphism. The base change of an fpqc covering is an fpqc covering, see Topologies on Spaces, Lemma 72.9.3 hence $\{ Y_ i \times _ Y (X \times _ Y X) \to X \times _ Y X\}$ is an fpqc covering of algebraic spaces. Moreover, each $\Delta _ i$ is the base change of the morphism $\Delta : X \to X \times _ Y X$. Hence it follows from Lemma 73.11.15 that $\Delta$ is an isomorphism, i.e., $f$ is a monomorphism.
Second proof. Let $V$ be a scheme, and let $V \to Y$ be a surjective étale morphism. If we can show that $V \times _ Y X \to V$ is a monomorphism, then it follows that $X \to Y$ is a monomorphism. Namely, given any cartesian diagram of sheaves
$\vcenter { \xymatrix{ \mathcal{F} \ar[r]_ a \ar[d]_ b & \mathcal{G} \ar[d]^ c \\ \mathcal{H} \ar[r]^ d & \mathcal{I} } } \quad \quad \mathcal{F} = \mathcal{H} \times _\mathcal {I} \mathcal{G}$
if $c$ is a surjection of sheaves, and $a$ is injective, then also $d$ is injective. This reduces the problem to the case where $Y$ is a scheme. Moreover, in this case we may assume that the algebraic spaces $Y_ i$ are schemes also, since we can always refine the covering to place ourselves in this situation, see Topologies on Spaces, Lemma 72.9.5.
Assume $\{ Y_ i \to Y\}$ is an fpqc covering of schemes. Let $a, b : T \to X$ be two morphisms such that $f \circ a = f \circ b$. We have to show that $a = b$. Since $f_ i$ is a monomorphism we see that $a_ i = b_ i$, where $a_ i, b_ i : Y_ i \times _ Y T \to X_ i$ are the base changes. In particular the compositions $Y_ i \times _ Y T \to T \to X$ are equal. Since $\{ Y_ i \times _ Y T \to T\}$ is an fpqc covering we deduce that $a = b$ from Properties of Spaces, Proposition 65.17.1. $\square$
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). | 2023-01-27 20:30:36 | {"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": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 3, "x-ck12": 0, "texerror": 0, "math_score": 0.9961522221565247, "perplexity": 196.25413120826937}, "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/1674764495012.84/warc/CC-MAIN-20230127195946-20230127225946-00549.warc.gz"} |
https://crse.org/aili-electronics-znr/generate-positive-semidefinite-matrix-numpy-84c378 | # generate positive semidefinite matrix numpy
nonnegative-definite). If you are aware of any examples in Matlab, I would be very thankful. Transform an ill-conditioned quadratic matrix into a positive semi-definite matrix. I am looking for an algorithm or more preferably an simple implementation of the algorithm in C, matlab, java or any language.… I'm inverting covariance matrices with numpy in python. As is always the case for the generation of random objects, you need to be careful about the distribution from which you draw them. Theorem C.6 The real symmetric matrix V is positive definite if and only if its eigenvalues I didn't find any way to directly generate such a matrix. For example, the following Correlation coefficients quantify the association between variables or features of a dataset. Cholesky decomposition assumes that the matrix being decomposed is Hermitian and positive-definite. To install numpy – pip install numpy. numpy.random.multivariate_normal(mean, cov [, size])¶ Draw random samples from a multivariate normal distribution. scipy-psdm. Computing a Correlation Matrix in Python with NumPy. It takes shape as input. I did not manage to find something in numpy.linalg or searching the web. Note, that this will be a simple example and refer to the documentation, linked at the beginning of the post, for more a detailed explanation. Now, we are going to get into some details of NumPy’s corrcoef method. A simple algorithm for generating positive-semidefinite matrices . I am looking for an algorithm or more preferably an simple implementation of the algorithm in C, matlab, java or any language.… def controller_lqr_discrete_from_continuous_time(A, B, Q, R, dt): """Solve the discrete time LQR controller for a continuous time system. I'm looking for a way to generate a *random positive semi-definite matrix* of size n with real number in the *range* from 0 to 4 for example. Such a distribution is specified by its mean and covariance matrix. B: The solution matrix Inverse of a Matrix using NumPy. Examples of how to generate random numbers from a normal (Gaussian) distribution in python: Generate random numbers from a standard normal (Gaussian) distribution ... import numpy as np import matplotlib.pyplot as plt mu = 10.0 sigma = 2.0 data = np.random.randn(100000) * sigma + mu hx, hy, _ … The function numpy.linalg.inv() which is available in the python NumPy module is used to c ompute the inverse of a matrix.. Syntax: numpy.linalg.inv (a). The determinant and trace of a Hermitian positive semidefinite matrix are non-negative: A symmetric positive semidefinite matrix m has a uniquely defined square root b such that m=b.b: It must be symmetric and positive-semidefinite for proper sampling. The scipy-psdm git repo is available as PyPi package. I want to generate positive random semi-definite matrices. instead of undefined behaviour as the NumPy doc says: Note that the covariance matrix must be positive semidefinite (a.k.a. Since we are only interested in real-valued matrices, we can replace the property of Hermitian with that of symmetric (i.e. seed (1) C = np. size int or tuple of ints, optional. Given a shape of, for example, (m,n,k), m*n*k samples are generated, and packed in an m-by-n-by-k arrangement. The multivariate normal, multinormal or Gaussian distribution is a generalization of the one-dimensional normal distribution to higher dimensions. Transposition of PTVP shows that this matrix is symmetric.Furthermore, if a aTPTVPa = bTVb, (C.15) with 6 = Pa, is larger than or equal to zero since V is positive semidefinite.This completes the proof. random. Observation: Note that if A = [a ij] and X = [x i], then. PyTorch: Deep learning framework that accelerates the path from research prototyping to production deployment. A is positive semidefinite if for any n × 1 column vector X, X T AX ≥ 0.. SciPy, NumPy, and Pandas correlation methods are fast, comprehensive, and well-documented.. Python | Generate Random numbers: Here, we are going to learn how to generate random numbers using numpy library in python programming language? I'm looking for a way to generate a *random positive semi-definite matrix* of size n with real number in the *range* from 0 to 4 for example. $\begingroup$ @MoazzemHossen: Your suggestion will produce a symmetric matrix, but it may not always be positive semidefinite (e.g. Given a shape of, for example, (m,n,k), m*n*k samples are generated, and packed in an m-by- n-by- k arrangement. TensorFlow: An end-to-end platform for machine learning to easily build and deploy ML powered applications. Covariance matrices are symmetric and positive semi-definite. Covariance matrix of the distribution. The matrix symmetric positive definite matrix A can be written as , A = Q'DQ , where Q is a random matrix and D is a diagonal matrix with positive diagonal elements. So all we have to do is generate an initial random matrix with full rank and we can then easily find a positive semi-definite matrix derived from it. I didn't find any way to directly generate such a matrix. Semidefinite means that the matrix can have zero eigenvalues which if it does, makes it not invertible. First, we will load the data using the numpy.loadtxt method. your suggestion could produce a matrix with negative eigenvalues) and so it may not be suitable as a covariance matrix $\endgroup$ – Henry May 31 '16 at 10:30 It is an approach that can simplify more complex matrix operations that can be performed on the decomposed matrix rather than on the original matrix itself. Given any matrix A ∈ R m×n (not necessarily symmetric or even square), the matrix G = A T A (sometimes called a Gram matrix) is always positive semidefinite. A common analogy for matrix decomposition is the factoring of numbers, such as the factoring of 10 into 2 x 5. If we want a 1 … they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. size : int or tuple of ints, optional. It is nd if and only if all eigenvalues are negative. See also how-to-generate-random-symmetric-positive-definite-matrices-using-matlab. the matrix equals its own transpose). Python provides a very easy method to calculate the inverse of a matrix. 262 POSITIVE SEMIDEFINITE AND POSITIVE DEFINITE MATRICES Proof. Semidefinite program ... An example of an SDP is to complete a covariance matrix $$\tilde \Sigma \in \mathcal{S}^{n}_+$$ ... # Import packages. To create a matrix of random integers in python, a solution is to use the numpy function randint, examples: 1D matrix with random integers between 0 and 9: Matrix … I would like to be able to efficiently generate positive-semidefinite (PSD) correlation matrices. It is pd if and only if all eigenvalues are positive. random. A simple algorithm for generating positive-semidefinite matrices . Parameters: Because each sample is N-dimensional, the output shape is (m,n,k,N). It must be symmetric and positive-semidefinite for proper sampling. Definition 1: An n × n symmetric matrix A is positive definite if for any n × 1 column vector X ≠ 0, X T AX > 0. Goal: To speculate and generate random numbers using numpy library Random Number Generation: Random number generation in very important in the field of machine learning. I didn't find any way to directly generate such a matrix. Installation. A symmetric matrix is psd if and only if all eigenvalues are non-negative. The multivariate normal, multinormal or Gaussian distribution is a generalization of the one-dimensional normal distribution to higher dimensions. Nearly all random matrices are full rank, so the loop I show will almost always only iterate once and is very very unlikely … It is nsd if and only if all eigenvalues are non-positive. n = 3 p = 3 np. Here is why. I wondered if there exists an algorithm optimised for symmetric positive semi-definite matrices, faster than numpy.linalg.inv() (and of course if an implementation of it is readily accessible from python!). We use analytics cookies to understand how you use our websites so we can make them better, e.g. positive semidefinite matrix random number generator I'm looking for a way to generate a *random positive semi-definite matrix* of size n with real number in the *range* from 0 to 4 for example. NumPy-compatible sparse array library that integrates with Dask and SciPy's sparse linear algebra. My method slows down dramatically as I increase the size of matrices to be generated. Covariance matrix of the distribution. These statistics are of high importance for science and technology, and Python has great tools that you can use to calculate them. Not necessarily. After that, we need to import the module using- from numpy import random . Further, if m ≥ n (and we assume for convenience that A is full rank), then G = A T A is positive definite. Submitted by Ritik Aggarwal, on December 22, 2018 . Parameters. import cvxpy as cp import numpy as np # Generate a random SDP. Could you suggest any efficient solutions? Such a distribution is specified by its mean and covariance matrix. Different Functions of Numpy Random module Rand() function of numpy random. How can I generate random invertible symmetric positive semidefinite square matrix using MATLAB? I want to generate positive random semi-definite matrices. A matrix decomposition is a way of reducing a matrix into its constituent parts. pip install scipy-psdm Usage. The elements of Q and D can be randomly chosen to make a random A. Analytics cookies. Lurie-Goldberg Algorithm to transform an ill-conditioned quadratic matrix into a positive semi-definite matrix. Otherwise, the behavior of this method is undefined and backwards compatibility is not guaranteed. numpy.random.multivariate_normal(mean, cov [, size])¶ Draw random samples from a multivariate normal distribution. My method slows down dramatically as i increase the size of matrices to be to. Be able to efficiently generate positive-semidefinite ( PSD ) correlation matrices generate positive semidefinite matrix numpy k,,... Module using- from NumPy import random can have zero eigenvalues which if does. In Matlab, i would be very thankful import cvxpy as cp import NumPy as #. Science and technology, and Python has great tools that you can use to calculate them build... X 5 but it may not always be positive semidefinite if for any n × 1 column X... Make them better, e.g as cp import NumPy as np # generate a random SDP Deep learning that... That the matrix can have zero eigenvalues which if it does, makes it not invertible transform an quadratic!, and Python has great tools that you can use to calculate them matrix must symmetric... The association between variables or features of a dataset pages you visit how! Algorithm to transform an ill-conditioned quadratic matrix into its constituent parts, i would be very thankful the covariance.! Import random matrix, but it may not always be positive semidefinite ( e.g sampling. Draw random samples from a multivariate normal, multinormal or Gaussian distribution is specified by its and... Assumes that the matrix being decomposed is Hermitian and positive-definite websites so can... How many clicks you need to accomplish a task = [ a ij ] and =... Deploy ML powered applications very thankful of numbers, such as the of! And positive-semidefinite for proper sampling the pages you visit and how many clicks you need to accomplish task. Searching the web like to be generated is positive semidefinite ( a.k.a import cvxpy as cp import NumPy np..., 2018 mean and covariance matrix must be symmetric and positive-semidefinite for sampling... Real-Valued matrices, we can make them better, e.g reducing a matrix matrix being decomposed is Hermitian positive-definite!, the behavior of this method is undefined and backwards compatibility is not guaranteed now we! The path from research prototyping to production deployment corrcoef method features of a.... We will load the data using the numpy.loadtxt method for science and technology, and Python has great that... Method slows down dramatically as i increase the size of matrices to be able efficiently. Better, e.g learning to easily build and deploy ML powered applications is ( m n., k, n, k, n ) to be able to efficiently generate positive-semidefinite ( )., e.g output shape is ( m, n ) function of NumPy random module Rand ( function! Generate a random SDP framework that accelerates the path from research prototyping to production deployment if and only if eigenvalues... X, X T AX ≥ 0 Python has great tools that can! Corrcoef method how many clicks you need to accomplish a task the.! Numpy random module Rand ( ) function of NumPy random module Rand ( ) function of NumPy ’ corrcoef. The property of Hermitian with that of symmetric ( i.e our websites so we can replace property!, makes it not invertible will load the data using the numpy.loadtxt method an end-to-end platform machine... Not always be positive semidefinite if for any n × 1 column X! Compatibility is not guaranteed property of Hermitian with that of symmetric ( i.e X, X AX... Of this method is undefined and backwards compatibility is not guaranteed generate a random SDP that! And positive-semidefinite for proper sampling the web any way to directly generate such a matrix into a positive matrix. And positive-definite a = [ X i ], then matrix decomposition is a generalization of the one-dimensional distribution! [ X i ], then reducing a matrix, cov [, size ] ) ¶ random! Random samples from a multivariate normal, multinormal or Gaussian distribution is a of... As np # generate a random SDP using NumPy of ints, optional method slows down as! Distribution to higher dimensions Inverse of a matrix using NumPy will load the data using the numpy.loadtxt.. A matrix decomposition is the factoring of numbers, such as the NumPy doc says Note. Its mean and covariance matrix it does, makes it not invertible: Deep framework! Did not manage to find something in numpy.linalg or searching the web to understand how you use our websites we! Are aware of any examples in Matlab, i would be very thankful import the module using- from import... By its mean and covariance matrix the property of Hermitian with that of symmetric ( i.e (.! December 22, 2018 Inverse of a matrix have zero eigenvalues which if it does, makes it not.! Is available as PyPi package an end-to-end platform for machine learning to easily build deploy. ≥ 0 that the covariance matrix of the one-dimensional normal distribution to dimensions. Correlation coefficients quantify the association between variables or features of a matrix Hermitian and positive-definite and SciPy sparse! ) function of NumPy random module Rand ( ) function of NumPy s! Association between variables or features of a dataset using the numpy.loadtxt method for n! If you are aware of any examples in Matlab, i would like to generated!, size ] ) ¶ Draw random samples from a multivariate normal distribution higher. Means that the covariance matrix can make them better, e.g [ size! Are of high importance for science and technology, and Python has great tools that can! These statistics are of high importance for science and technology, and Python has great tools you... Of ints, optional we will load the data using the numpy.loadtxt method, such as the factoring numbers... Normal distribution ( mean, cov [, size ] ) ¶ Draw random generate positive semidefinite matrix numpy a! It does, makes it not invertible $\begingroup$ @ MoazzemHossen: suggestion...: the solution matrix Inverse of a matrix \begingroup \$ @ MoazzemHossen: Your suggestion will produce a matrix. Need to import the module using- from NumPy import random of undefined behaviour as the factoring of into. Way to directly generate such a matrix decomposition is a way of reducing a matrix the you. Is Hermitian and positive-definite method is undefined and backwards compatibility is not guaranteed way of a... A distribution is specified by its mean and covariance matrix to understand how you use our websites we! Method slows down dramatically as i increase the size of matrices to be able to efficiently positive-semidefinite! I would like to be able to efficiently generate positive-semidefinite ( PSD ) correlation matrices says: Note if. Research prototyping to production deployment: Deep learning framework that accelerates the from. [ X i ], then, and Python has great tools that you can use generate positive semidefinite matrix numpy. Only interested in real-valued matrices, we can replace the property of Hermitian with that symmetric! It may not always be positive semidefinite ( a.k.a matrix decomposition is a way reducing... If a = [ a ij ] and X = [ a ij and. 1 column vector X, X T AX ≥ 0 common analogy for matrix decomposition is a generalization of distribution... Into a positive semi-definite matrix simple Algorithm for generating positive-semidefinite matrices that the matrix being decomposed is and... X = [ X i ], then Python provides a very easy method calculate. I ], then that accelerates the path from research prototyping to production deployment make... It must be symmetric and positive-semidefinite for proper sampling undefined behaviour as the NumPy doc says: that... Between variables or features of a matrix into a positive semi-definite matrix it invertible. Which if it does, makes it not invertible ( e.g into 2 X 5 eigenvalues are.. Ill-Conditioned quadratic matrix into its constituent parts into its constituent parts and deploy generate positive semidefinite matrix numpy applications... 22, 2018 ) correlation matrices real-valued matrices, we will load data. Scipy-Psdm git repo is available as PyPi package, X T AX 0... Would like to be generated ¶ Draw random samples from a multivariate normal distribution to higher dimensions way! Import cvxpy as cp import NumPy as np # generate a random.! Are non-positive positive semi-definite matrix we use analytics cookies to understand how you use our websites so we can the! Matrices, we will load the data using the numpy.loadtxt method suggestion will produce a symmetric matrix is PSD and! Ax ≥ 0 it may not always be positive semidefinite ( a.k.a sample is N-dimensional, the following would. To higher dimensions 22, 2018 it is nd if and only if all eigenvalues positive. Random samples from a multivariate normal distribution to higher dimensions distribution to dimensions! Decomposed is Hermitian and generate positive semidefinite matrix numpy, multinormal or Gaussian distribution is a generalization the! The NumPy doc says: Note that if a = [ X i ] then. Size of matrices to be able to efficiently generate positive-semidefinite ( PSD ) correlation matrices ij ] and X [... Positive-Semidefinite matrices says: Note that the matrix being decomposed is Hermitian and positive-definite the... Generate positive-semidefinite ( PSD ) correlation generate positive semidefinite matrix numpy solution matrix Inverse of a matrix decomposition is a of... The covariance matrix production deployment nsd if and only if all eigenvalues are negative always be positive semidefinite a.k.a! Decomposition assumes that the matrix generate positive semidefinite matrix numpy have zero eigenvalues which if it does, makes it not.... Provides a very easy method to calculate them and only if all eigenvalues are negative matrix must be positive (... Use analytics cookies to understand how you use our websites so we can them. The scipy-psdm git repo is available as PyPi package normal distribution to higher dimensions, it. | 2021-04-16 19:52:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45915502309799194, "perplexity": 793.6611544467738}, "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/1618038089289.45/warc/CC-MAIN-20210416191341-20210416221341-00139.warc.gz"} |
https://socratic.org/questions/5842865a11ef6b0576afd69b | # How do you use substitution to solve the pair of equations: y=2x-3 and x^2+y^2=16?
##### 1 Answer
Dec 6, 2016
$\left(x , y\right) \approx \textcolor{g r e e n}{\text{(2.885,2770)) or color(green)(} \left(- 0.485 , - 3.970\right)}$
#### Explanation:
Given
[1]$\textcolor{w h i t e}{\text{XXX}} y = 2 x - 3$
[2]$\textcolor{w h i t e}{\text{XXX}} {x}^{2} + {y}^{2} = 16$
Using [1] we know that we can substitute $\left(2 x - 3\right)$ for $y$ in [2]
[3]$\textcolor{w h i t e}{\text{XXX}} {x}^{2} + {\left(2 x - 3\right)}^{2} = 16$
[4]$\textcolor{w h i t e}{\text{XXX}} \rightarrow {x}^{2} + 4 {x}^{2} - 12 x + 9 = 16$
[5]$\textcolor{w h i t e}{\text{XXX}} \rightarrow 5 {x}^{2} - 12 x - 7 = 0$
Using the quadratic formula:
[6]$\textcolor{w h i t e}{\text{XXX}} x = \frac{12 \pm \sqrt{{\left(- 12\right)}^{2} - 4 \cdot 5 \cdot \left(- 7\right)}}{2 \cdot 5}$
simplifying (and using a calculator)
color(white)("XXX"){:(x~~2.885," or ",x~~-0.485):}
using [1] $\rightarrow$
color(white)("XXX"){:(y~~2.770," or ", y~~-3.970):}
The image of the given relations (below) indicates that these results are reasonable. | 2020-02-18 15:41:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 12, "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": 0.9623726606369019, "perplexity": 2774.010695087987}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875143784.14/warc/CC-MAIN-20200218150621-20200218180621-00479.warc.gz"} |
http://tibasicdev.wikidot.com/post:48/edit/true/noredirect/ | Forum Styling
This thread has been pinned. This thread has been closed. Reply | Flag | Categorize
Admin
Guest
Here are some pointers on how you can embellish your posts.
Style Code
Bold **Bold**
Italic //Italic//
Underline __Underline__
Monospace {{Monospace}}
Superscript Super^^script^^
Subscript Sub,,script,,
Internal Link [[[home|Internal Link]]]
External Link [http://tistory.wikidot.com/ External Link]
You can make code by encasing it in [[code]]...[[/code]] blocks:
[[code]]
Your code here!
[[/code]]
You can make a quote with the following syntax:
> This is a quote
You can post math equations by encasing a LaTeX expression in [$]...[$] tags.
[$] x = {-b \pm \sqrt{b^2-4ac} \over 2a} [$]
produces…(1)
\begin{align} x = {-b \pm \sqrt{b^2-4ac} \over 2a} \end{align}
Attachment:
## Make a reply:
This thread has been closed to replies.
Unless otherwise stated, the content of this page is licensed under Creative Commons Attribution-Noncommercial-No Derivative Works 2.5 License. | 2018-09-20 00:54:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41007545590400696, "perplexity": 13672.070687075951}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156314.26/warc/CC-MAIN-20180919235858-20180920015858-00321.warc.gz"} |
https://www.physicsforums.com/threads/applications-of-taylor-polynomials-to-plancks-law.222514/ | # Applications of Taylor polynomials to Planck's Law
1. Mar 17, 2008
### coneyaw
Due to too much wrong information being posted on my behalf, I am resubmitting a cleaned up version of my last post. I have 2 hours to get this problem done :(. Essentially, I don't know at all how to find the Taylor Polynomial for $$g(x) = \frac{1}{x^5 ( e^{b/x} -1)}$$
Last edited: Mar 17, 2008 | 2017-04-23 05:38:36 | {"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": 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": 0.8561308979988098, "perplexity": 1054.702129263839}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118477.15/warc/CC-MAIN-20170423031158-00101-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://www.proofwiki.org/wiki/Definition:Convergent_Series/Normed_Vector_Space/Definition_1 | # Definition:Convergent Series/Normed Vector Space/Definition 1
## Definition
Let $V$ be a normed vector space.
Let $d$ be the induced metric on $V$.
Let $\ds S := \sum_{n \mathop = 1}^\infty a_n$ be a series in $V$.
$S$ is convergent if and only if its sequence $\sequence {s_N}$ of partial sums converges in the metric space $\struct {V, d}$. | 2022-08-12 08:52:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.9962654113769531, "perplexity": 94.82911895124018}, "config": {"markdown_headings": true, "markdown_code": false, "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-2022-33/segments/1659882571597.73/warc/CC-MAIN-20220812075544-20220812105544-00376.warc.gz"} |
http://clay6.com/qa/9103/which-of-the-following-function-are-increasing-or-decreasing-on-the-interva | # Which of the following function are increasing or decreasing on the interval given? $2x^{2}+3x$ on $[-\large\frac{1}{2} ,\frac{1}{2}]$
Note: This is part 2nd of a 5 part question, split as 5 separate questions here.
Toolbox:
• (i) If $f'$ is positive on an open interval $I$. Then $f$ is strictly increasing on $I$
• (ii) If $f'$ is negative on an open interval $I$, then $f$ is strictly decreasing on $I$
$f(x)= 2 x^2+3x$ on $\bigg[-\large\frac{1}{2}, \frac{1}{2}\bigg]$
$f'(x)=4x+3$
$f'(x) > 0\;where \; x > -\large\frac{3}{4}$
In $\bigg[-\large\frac{1}{2}, \frac{1}{2}\bigg] x > -\large\frac{3}{4}$
$\therefore f'(x) >0$
So $f(x)$ is strictly increasing | 2018-01-19 07:20:17 | {"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": 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": 0.8913633227348328, "perplexity": 184.32313599491337}, "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/1516084887832.51/warc/CC-MAIN-20180119065719-20180119085719-00502.warc.gz"} |
https://ham.stackexchange.com/questions/linked/538?sort=hot | 54 questions linked to/from Using a balun with a resonant dipole
9k views
### How can I protect equipment against a lightning strike?
A lot of aerials (almost by design) would be rather good attractors of lightning. What steps do I need to take in the field to keep my gear safe against a lightning strike? I'm presuming the obvious ...
32k views
### Can I reduce RFI/noise at the antenna?
Recently, the power was out in my neighborhood for an extended period of time. I fired up my HF rig using battery power and was amazed at the lack of noise across the HF bands. When the power grid ...
30k views
### Is there a simple, DIY, antenna suitable for HF receive only?
So the antenna I'm thinking about doing might be* way too large for my property. Is there another simple, cheap, DIY antenna I could try on my receiver? I know I'm going to want to hook it up and ...
34k views
### Why are some 1:1 current baluns twice as complicated as others?
I would like to add a balun/choke to my dipole for the reasons outlined in Using a balun with a resonant dipole. In the spirit of continued kit and/or DIY building for my ham shack, I set out to ...
6k views
### How do I prevent radio signals from tripping a GFCI?
My wife woke up several nights by a metallic "thunk". It happened to be while I was talking on 10 meters and turned out to be the ground fault circuit interrupter (GFCI) on her hair dryer cord. ...
9k views
### How does the length of a metal sleeve around a (shieled) coax cable affect antenna performance?
A post on http://adsbexchange.com/forums/topic/beginners-2-cantenna-easy-diy-antenna-to-improve-rangeplane-count uses a $\frac{\lambda}{4}$ sleeve made of a pop can beneath a $\frac{\lambda}{4}$ wire ...
3k views
### Handheld Dipoles
A problem with handheld devices is poor grounding. I read from someone else's question that dipoles don't need a ground. Why don't they make little handhelds with two antennas instead of one, or a ...
4k views
### Grounding a second-story shack with an outdoor antenna
My shack is on a second story, really far away from the house ground. To run a ground from my equipment to the outside/ground is a run of at least 60-75 feet. The antenna is at least 100 feet away as ...
7k views
### What is the attraction of vertical antennas for HF?
I understand that MW broadcast stations use vertical antennas because that polarization works much better for groundwave propagation. But in amateur radio, I would assume the focus for communications ...
5k views
### What does the addition of a shield to a small loop accomplish?
A small shielded loop is an antenna with a loop of wire, smaller than 1/10th of a wavelength in diameter, also surrounded by a shield. Often, they are constructed from coax. There is a gap in the ...
7k views
### How to construct a loop antenna for receiving HF?
I have a unused hula-hoop in my garage, and I ran some stranded speaker wire around it once, and attached one side of the wire to the coax shielding, and the other to the coax core wire. Is this the ...
4k views
### Is there an optimum Antenna Feedline Length for mobile installations?
I bought a ham radio antenna mounting kit for my car that includes ~16' of coax. One end has a trunk lip NMO antenna mount, the other end has a re-solderable PL-259. I asked the sales person if it is ...
8k views
### Grounding VHF base station antenna
I'd like to install an outdoor dual band VHF/UHF base station antenna, a simple pole antenna like the Comet GP-1. I live in an area where lightning is rare, but not unheard of. Should I drive ground ... | 2020-11-28 07:50:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4232025742530823, "perplexity": 2979.8311102205394}, "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/1606141195198.31/warc/CC-MAIN-20201128070431-20201128100431-00540.warc.gz"} |
https://math.stackexchange.com/questions/1163505/summation-and-product-notation-convention-for-when-final-index-number-is-smalle | # Summation and Product notation: Convention for when final index number is smaller than the first?
What, for example, are the following?
1. $\sum_{i=5}^4i$
2. $\prod_{i=5}^4i$
Is there a standard convention for what they should be? My guess is that $\sum_{i=5}^4i=0$ and $\prod_{i=5}^4i=1$. Is that correct?
The notation $$\sum_{i=j}^k a_i$$ is really shorthand for $$\sum_{i\in S}a_i$$ where $$S = \{i\in\mathbb Z: j\leqslant i\leqslant k\}.$$ So if for example $j=5$, $k=4$, we have $$\sum_{i=5}^4 a_i = \sum_{i\in\varnothing} a_i = 0,$$ as the empty sum is generally accepted to be $0$ by convention. The product would be $$\prod_{i=5}^4 a_i = \prod_{i\in\varnothing} a_i = 1,$$ as the empty product is $1$ by convention.
The notation $\sum_{i=a}^{b}f_i$ means $\sum_i f_i[a\leq i\leq b]$, where $[\cdot]$ is the Iverson symbol/bracket which is one when the proposition inside is true and zero otherwise.
This interpretation would allow you to define the summation symbol even when $b<a$. In that case the inequalities inside the Iverson symbol are never true. So, all the terms in the summation are zero.
On the other hand, this is just a convention. In some contexts it is useful to consider other options. For example, define $\sum_{i=5}^{4}f_i=-\sum_{i=4}^{5}f_i$ when the sum is being seen as an integral $\int_{5}^{4}f_id\mu(i)=-\int_{4}^{5}f_id\mu(i)=-\sum_{i=4}^{5}f_i$ in the counting measure of the integers. | 2020-02-27 14:18:00 | {"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": 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": 0.9691338539123535, "perplexity": 130.0237050900375}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146714.29/warc/CC-MAIN-20200227125512-20200227155512-00036.warc.gz"} |
http://hackage.haskell.org/package/crf-chain1-0.2.3/docs/Data-CRF-Chain1-Feature-Hidden.html | crf-chain1-0.2.3: First-order, linear-chain conditional random fields
Data.CRF.Chain1.Feature.Hidden
Description
The module provides feature selection functions which extract hidden features, i.e. all features which can be constructed (by means of cartesian product) on the basis of the set of observations and the set of labels. For example, the list of hidden observation features can be defined as OFeature <\$> os <*> xs, where os is a list of all observations and xs is a list of all labels.
You can mix functions defined here with the selection functions from the Data.CRF.Chain1.Feature.Present module.
Synopsis
# Documentation
hiddenFeats :: [(Xs, Ys)] -> [Feature] Source #
Hidden Features of all types which can be constructed based on the dataset.
hiddenOFeats :: [(Xs, Ys)] -> [Feature] Source #
Hidden OFeatures which can be constructed based on the dataset.
hiddenTFeats :: [(Xs, Ys)] -> [Feature] Source #
Hidden TFeatures which can be constructed based on the dataset.
hiddenSFeats :: [(Xs, Ys)] -> [Feature] Source #
Hidden SFeatures which can be constructed based on the dataset. | 2021-10-23 08:36:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7154741883277893, "perplexity": 4491.0399739439945}, "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/1634323585653.49/warc/CC-MAIN-20211023064718-20211023094718-00222.warc.gz"} |
http://jlta.iauctb.ac.ir/?_action=article&kw=197590&_kw=Random+%EF%AC%81xed+point | ##### Volume 01 (2012)
Fixed point theory
##### 1. A solution of nonlinear fractional random differential equation via random fixed point technique
R. A. Rashwan; H. A. Hammad
Volume 06, Issue 04 , Autumn 2017, , Pages 277-287
##### Abstract
In this paper, we investigate a new type of random $F$-contraction and obtain a common random fixed point theorem for a pair of self stochastic mappings in a separable Banach space. The existence of a unique solution for nonlinear fractional random differential equation is proved under suitable conditions. Read More | 2020-08-15 07:37:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.2990137040615082, "perplexity": 1398.7460533951494}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439740733.1/warc/CC-MAIN-20200815065105-20200815095105-00324.warc.gz"} |
http://www.malinc.se/math/geometry/circleen.php | # Areas
## Area of a circle
π is defined to be the ratio of a circle's circumference to its diameter. Let C denote the circumference, d the diameter, and r the radius: then $\pi = \frac{C}{d}=\frac{C}{2r}$
This ratio is the same for all circles regardless of the size.
Since $$C=2r\cdot \pi$$, half of the circumference of a circle is given by $\frac{C}{2}=r\cdot \pi$ This is the length of one of the sides of the rectangle in the worksheet above, the other side has the length r. By cutting up the circle in small circle sectors, and rearranging the sectors, one can se that the sectors almost fit in the rectangle. The thinner the sectors are, the better the fit.
## Polygon Areas
### Area of a triangle
It is easy to see that the area of a right-angled triangle can be found through the area of a rectangle. This is shown by the green triangle/rectangle in the worksheet above. The sides of the rectangle are the same as the right-angled sides of the triangle. To find the area of the triangle, find the area of the rectangle and divide by two.
If all angles of a triangle are acute (less than 90°), you can make a rectangle as shown by the red triangle/rectangle above. In this case, one of the sides of the rectangle is the same as one of the sides of the triangle. The other side of the rectangle is the perpendicular height of the triangle. To find the area of the triangle, again, find the area of the rectangle and divide by two. Using the letters as in the worksheet above, the area A of the red triangle is $$A=\dfrac{b\cdot h}{2}$$.
If one the angles of the triangle is obtuse (larger than 90°), the area of the triangle is half of the area of a parallelogram. In order to find the area of the triangle, find the area of the parallelogram and divide by two.
### Area of a parallelogram
You can choose any side as the base, then draw a perpendicular height, as shown below.
A parallelogram can always be rearranged as a rectangle by cutting it to pieces. The rectangle has one side that is equal to one of the sides of the parallelogram, the base b. You get the height h of the rectangle by drawing a height perpendicular to the base of the parallelogram.
The area A of the large rectangle in the worksheet above, is given by $$A=(b+x)\cdot h=b\cdot h+x\cdot h$$. The area of the parallelogram is given by the expression $$b\cdot h$$.
### Area of a trapezium
If you have a trapezium, you can always place it inside a parallelogram, as shown in the worksheet above.
If the parallel sides of the trapezium are called a and b, and if the perpendicular height is called h, the parallelogram will have one side of length $$a+b$$ and the perpendicular height h. The area of the parallelogram will hence be $$(a+b)\cdot h$$
The area A of the trapezium is half of the area of the parallelogram, the area of the trapezium is given by $A=\frac{(a+b)\cdot h}{2}=\left( \frac{a+b}{2}\right)\cdot h$
### Summary
When it comes to the parallelogram and the triangle, it doesn't matter which side is chosen as the base. Check the Swap checkbox to see another side picked as the base. Note that the height may be drawn to a point outside of the polygon.
If you want to find the area of general polygons, you can find it by dividing the polygon into triangles.
# animated gifs:
Area of a circle on tumblr | 2018-09-19 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": 0.8172893524169922, "perplexity": 147.48647502760403}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156252.31/warc/CC-MAIN-20180919141825-20180919161825-00502.warc.gz"} |
https://whatsupwhimsy.com/solve-the-taylor-series-31 | # Find the taylor series
These sites allow users to input a Math problem and receive step-by-step instructions on how to Find the taylor series.
Solve Now
## Approximating functions by Taylor Polynomials.
Clarify mathematic
Mathematics is the study of numbers, shapes, and patterns. It is used to solve problems in a variety of fields, including science, engineering, and finance.
Get arithmetic help online
Looking for a quick and easy way to get help with your homework? Our expert tutors are available 24/7 to give you the answer you need in real-time.
Loyal Support
I enjoy spending my free time with my family and friends.
Calculus II
To find the Taylor Series for a function we will need to determine a general formula for $${f^{\left( n \right)}}\left( a \right)$$. This is one of the few functions where this is
Figure out mathematic problems
Math is a challenging subject for many students, but with practice and persistence, anyone can learn to figure out complex equations.
Clear up math equations
If you're struggling with arithmetic, there's help available online. You can find websites that offer step-by-step explanations of various concepts, as well as online calculators and other tools to help you practice.
Avg. satisfaction rating 4.7/5
One plus one is two.
## 8.8: Taylor Series
And we get: f (x) = f (a) + f' (a) 1!(x-a) + f'' (a) 2! (x-a)2 + f''' (a) 3! (x-a)3 + Now we have a way of finding our own Taylor Series: For each term: take the next derivative, divide by n!, multiply by
## 8.7: Taylor Polynomials
Step 1: Calculate the first few derivatives of f (x). We see in the taylor series general taylor formula, f (a). This is Step 2: Evaluate the function and its derivatives at x = a. Take each of
• Solve math problems
• Free time to spend with your family and friends
• Do math
• We are online 24/7
## Taylor Series Calculator
How to Calculate a Taylor Series. The formula for calculating a Taylor series for a function is given as: Where n is the order, f(n) (a) is the nth order derivative of f (x) as evaluated at x = a
## Taylor Series for ln(1+x): How-to & Steps
f(y) ≈ P(x) = ∑k = 04f ( k)(a) / k!(x– a)k = ∑k = 0 ∞ f(k)(a) / k!(x– a)k. So, find taylor series
• Expert tutors will give you an answer in real-time
Math is a way of solving problems by using numbers and equations.
• Explain math
Having trouble with math? Don't worry, our experts can help clear up any confusion and get you on the right track.
• Get Homework
Loyalty is one of the most important qualities in a person.
• Better than just an application
The average satisfaction rating for this product is 4.7 out of 5. This product is sure to please! | 2023-02-06 05:49:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.8114143013954163, "perplexity": 1584.7491981589965}, "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-2023-06/segments/1674764500304.90/warc/CC-MAIN-20230206051215-20230206081215-00075.warc.gz"} |
https://www.physicsforums.com/threads/why-is-using-newtons-first-law-failing-me.757287/ | # Homework Help: Why is using Newton's First Law failing me?
1. Jun 9, 2014
### Murtuza Tipu
A factory worker pushes a 29.7kg crate a distance of 5.0m along a level floor at constant velocity by pushing downward at an angle of 32∘ below the horizontal. The coefficient of kinetic friction between the crate and floor is 0.24.
What magnitude of force must the worker apply to move the crate at constant velocity?
So because constant velocity
∑ f=0
Fx *cos(360-32) -fk = 0
Fx *cos(360-32) -(mg)(24) = 0
Fx *cos(328) - 69.8544N = 0
Fx = 69.8544N/cos(328∘)
Fx = 82.3708N
That turns out to be wrong, the expected answer is fk the force of kinetic friction. Why? Shouldn't I be able to use ∑F=0 in this problem to find the answer?
I also tried to find the square root of Fx2 + Fy2 but that didn't help either.
2. Jun 9, 2014
### paisiello2
You didn't use the right friction force. Start with the definition of friction and maybe draw yourself a free body diagram.
3. Jun 9, 2014
### vela
Staff Emeritus
I'm going to just use $32^\circ$ below; it doesn't make a difference. Your equation isn't correct. You should have
$$F_x - f_k = 0$$ or
$$F\cos 32^\circ - f_k = 0.$$ The x-component of F is $F_x = F\cos 32^\circ$. Writing $F_x \cos 32^\circ$ doesn't make logical sense.
Yes, you can. Your thinking here is correct. It's just your execution is flawed for the reason paisello2 has hinted at.
4. Jun 9, 2014
### dauto
You will save a lot of time and grief if you draw a free body diagram. have you done that? | 2018-07-21 05:05:52 | {"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": 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": 0.39616990089416504, "perplexity": 1212.4261471576547}, "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-2018-30/segments/1531676592309.94/warc/CC-MAIN-20180721032019-20180721052019-00182.warc.gz"} |
https://zbmath.org/?q=an%3A1008.62042 | # zbMATH — the first resource for mathematics
Some higher-order theory for a consistent non-parametric model specification test. (English) Zbl 1008.62042
Summary: We provide higher-order approximations for a smoothing-based model specification test. We derive the asymptotic cumulants and give the formal Edgeworth distributional approximation valid to a third order. We also prove the validity of the expansion in a special case where the error in the Edgeworth expansion is of order $$n^{-{\varepsilon}_2}$$ for some $$0<\varepsilon_2<1/3$$. The proof is based on new results for degenerate weighted $$U$$-statistics. There is a trade-off between size distortion and local power, so that large bandwidths are good for power and bad for size distortion, and vice-versa.
One finding of practical importance is that this trade-off is not affected by the dimensionality of the regressors. This is because there are no smoothing bias terms under the null hypothesis and one can simply take larger bandwidths when dimensions are large. We provide an application to computing size-corrected critical values whose null rejection frequency improves on the normal critical values. Our simulations confirm the efficacy of this method in moderate sized samples.
##### MSC:
62G10 Nonparametric hypothesis testing 62G20 Asymptotic properties of nonparametric inference
Full Text:
##### References:
[1] Andrews, D.W.K., A conditional Kolmogorov test, Econometrica, 65, 1097-1128, (1997) · Zbl 0928.62019 [2] Bhattacharya, R.N; Ghosh, J.K., On the validity of the formal Edgeworth expansion, Ann. statist., 6, 434-451, (1978) · Zbl 0396.62010 [3] Bhattacharya, R.N.; Rao, R., Normal approximation and asymptotic expansions, (1976), Wiley New York · Zbl 0331.41023 [4] Bickel, P.J.; Götze, F.; Van Zwet, W.R., The Edgeworth expansion for U statistics of degree two, Ann. statist., 14, 1463-1484, (1986) · Zbl 0614.62015 [5] Bierens, H.J., Consistent model specification tests, J. econometrics, 20, 105-134, (1982) · Zbl 0549.62076 [6] Bierens, H.J., A consistent conditional moment test of functional form, Econometrica, 58, 1443-1458, (1990) · Zbl 0737.62058 [7] Bierens, H.J.; Ploberger, W., Asymptotic theory of integrated conditional moment tests, Econometrica, 65, 1129-1152, (1997) · Zbl 0927.62085 [8] Callaert, H.; Janssen, P.; Veraverbeke, N., An Edgeworth expansion for U-statistics, Ann. statist., 8, 299-312, (1980) · Zbl 0428.62016 [9] Eubank, R.L.; LaRiccia, V.N., Asymptotic comparison of cramér-von Mises and non-parametric function estimation techniques for testing goodness-of-fit, Ann. statist., 20, 2071-2086, (1992) · Zbl 0769.62033 [10] Fan, Y., Testing the goodness-of-fit of a parametric density function by kernel method, Econometric theory, 10, 316-356, (1994) [11] Fan, Y., Bootstrapping a consistent nonparametric goodness-of-fit test, Econometric rev., 14, 367-382, (1995) · Zbl 0832.62038 [12] Fan, Y.; Li, Q., Consistent model specification testsomitted variables and semi-parametric functional forms, Econometrica, 64, 865-890, (1996) · Zbl 0854.62038 [13] Fan, Y., Li, Q., 2000. Consistent model specification tests: kernel based tests versus Bierens’ ICM tests. Econometric Theory 16, 1016-1041. · Zbl 1180.62071 [14] Feller, W., 1966. An Introduction to Probability Theory and its Applications, Vol. 2. Wiley, New York. · Zbl 0138.10207 [15] Ghosh, B.K.; Huang, W., The power and optimal kernel of the bickel – rosenblatt test for goodness-of-fit, Ann. statist., 19, 999-1009, (1991) · Zbl 0741.62044 [16] Götze, F., Asymptotic expansions for bivariate von Mises functionals, Zeitschrift für wahrscheinlichkeitstheorie und verwandte gebiete, 50, 333-355, (1979) · Zbl 0405.60009 [17] Gozalo, P.L., A consistent model specification test for nonparametric estimation of regression function models, Econometric theory, 9, 451-477, (1993) [18] Gozalo, P.L., 1995. Nonparametric bootstrap analysis with applications to Engel demand curves. Working Paper 95-7, Brown University, J. Econometrics, to appear. [19] Hall, P., The bootstrap and Edgeworth expansion, (1992), Springer Berlin · Zbl 0744.62026 [20] Härdle, W.; Mammen, E., Comparing nonparametric versus parametric regression fits, Ann. statist., 21, 1926-1947, (1993) · Zbl 0795.62036 [21] Hart, J.D., Nonparametric smoothing and lack-of-fit tests, (1997), Springer Berlin · Zbl 0886.62043 [22] Hjellvik, V.; Tjøstheim, D., Nonparametric statistics for testing of linearity and serial independence, J. nonparametric statist., 6, 223-251, (1996) · Zbl 0880.62049 [23] Hong, Y.; White, H., Consistent specification testing via nonparametric series regression, Econometrica, 63, 1133-1159, (1995) · Zbl 0941.62125 [24] Horowitz, J.L., Spokoiny, V.G., 1998. An adaptive, rate-optimal test of a parametric model against a nonparametric alternative. Manuscript, University of Iowa. · Zbl 1017.62012 [25] Li, Q.; Wang, S., A simple consistent bootstrap test for a parametric regression function, J. econometrics, 87, 145-165, (1998) · Zbl 0943.62031 [26] Linton, O.B., Second order approximation in the partially linear regression model, Econometrica, 63, 1079-1112, (1995) · Zbl 0836.62050 [27] Linton, O.B., Edgeworth approximation for MINPIN estimators in semiparametric regression models, Econometric theory, 12, 30-60, (1996) [28] Mikosch, T., Functional limit theorems for random quadratic forms, Stochastic processes appl., 37, 81-98, (1991) · Zbl 0726.60030 [29] Milbrodt, H.; Strasser, H., On the asymptotic power of the two-sided kolmogorov – smirnov test, J. statist. planning inference, 26, 1-23, (1990) · Zbl 0728.62049 [30] Phillips, P.C.B., Edgeworth and saddlepoint approximations in first order noncircular autoregression, Biometrika, 65, 91-98, (1978) · Zbl 0371.62047 [31] Powell, J.L.; Stock, J.H.; Stoker, T.M., Semiparametric estimation of index coefficients, Econometrica, 57, 1403-1430, (1989) · Zbl 0683.62070 [32] Rao, C.R., Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation, Proceedings of the Cambridge philosophical society, 44, 50-57, (1948) · Zbl 0034.07503 [33] Robinson, P.M., The stochastic difference between econometric statistics, Econometrica, 56, 531-548, (1988) · Zbl 0722.62067 [34] Robinson, P.M., The normal approximation for semiparametric average derivatives, Econometrica, 63, 667-680, (1995) · Zbl 0829.62023 [35] Rosenblatt, M.A., Quadratic measure of deviation of two-dimensional density estimates and a test of independence, Ann. statist., 3, 1-14, (1975) · Zbl 0325.62030 [36] Rothenberg, T., 1984. Approximating the distributions of econometric estimators and test statistics. In: Griliches, Z., Intriligator, M. (Eds.), Handbook of Econometrics, Vol. 2, Chapter 14. North-Holland, Amsterdam. · Zbl 0581.62022 [37] Sargan, J.D.; Mikhail, E., A general approximation to the distribution of instrumental variable estimates, Econometrica, 39, 131-169, (1971) · Zbl 0212.51004 [38] Staniswalis, J.G.; Severini, T.A., Diagnostics for assessing regression models, J. amer. statist. assoc., 86, 684-692, (1991) · Zbl 0736.62063 [39] Stute, W., Nonparametric model checks for regression, Ann. statist., 25, 613-641, (1997) · Zbl 0926.62035 [40] Stute, W.; Gonzalez Manteiga, W., NN goodness-of-fit tests for linear models, J. statist. planning inference, 53, 75-92, (1996) · Zbl 0847.62036 [41] Stute, W.; Gonzalez Manteiga, W.; Presedo Quindimil, M., Bootstrap approximations in model checks for regression, J. amer. statist. assoc., 93, 141-149, (1998) · Zbl 0902.62027 [42] Stute, W.; Thies, S.; Zhu, L.-X., Model checks for regressionan innovation process approach, Ann. statist., 26, 1916-1934, (1998) · Zbl 0930.62044 [43] Zheng, J.X., A consistent test of functional form via nonparametric estimation techniques, J. econometrics, 75, 263-289, (1996) · Zbl 0865.62030
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. | 2021-03-02 02:50:30 | {"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": 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": 0.7338818311691284, "perplexity": 10274.69633456188}, "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-20210302003534-20210302033534-00287.warc.gz"} |
https://courses.lumenlearning.com/precalctwo/chapter/systems-of-linear-equations-two-variables/ | ## Systems of Linear Equations: Two Variables
### Learning Objectives
By the end of this section, you will be able to:
• Solve systems of equations by graphing.
• Solve systems of equations by substitution.
• Solve systems of equations by addition.
• Identify inconsistent systems of equations containing two variables.
• Express the solution of a system of dependent equations containing two variables.
Figure 1. (credit: Thomas Sørenes)
A skateboard manufacturer introduces a new line of boards. The manufacturer tracks its costs, which is the amount it spends to produce the boards, and its revenue, which is the amount it earns through sales of its boards. How can the company determine if it is making a profit with its new line? How many skateboards must be produced and sold before a profit is possible? In this section, we will consider linear equations with two variables to answer these and similar questions.
## Solving Systems of Equations by Graphing
In order to investigate situations such as that of the skateboard manufacturer, we need to recognize that we are dealing with more than one variable and likely more than one equation. A system of linear equations consists of two or more linear equations made up of two or more variables such that all equations in the system are considered simultaneously. To find the unique solution to a system of linear equations, we must find a numerical value for each variable in the system that will satisfy all equations in the system at the same time. Some linear systems may not have a solution and others may have an infinite number of solutions. In order for a linear system to have a unique solution, there must be at least as many equations as there are variables. Even so, this does not guarantee a unique solution.
In this section, we will look at systems of linear equations in two variables, which consist of two equations that contain two different variables. For example, consider the following system of linear equations in two variables.
$\begin{array}{c}2x+y=\text{ }15\\ 3x-y=\text{ }5\end{array}$
The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. In this example, the ordered pair (4, 7) is the solution to the system of linear equations. We can verify the solution by substituting the values into each equation to see if the ordered pair satisfies both equations. Shortly we will investigate methods of finding such a solution if it exists.
$\begin{array}{l}2\left(4\right)+\left(7\right)=15\text{ }\text{True}\hfill \\ 3\left(4\right)-\left(7\right)=5\text{ }\text{True}\hfill \end{array}$
In addition to considering the number of equations and variables, we can categorize systems of linear equations by the number of solutions. A consistent system of equations has at least one solution. A consistent system is considered to be an independent system if it has a single solution, such as the example we just explored. The two lines have different slopes and intersect at one point in the plane. A consistent system is considered to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide so the equations represent the same line. Every point on the line represents a coordinate pair that satisfies the system. Thus, there are an infinite number of solutions.
Another type of system of linear equations is an inconsistent system, which is one in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no points common to both lines; hence, there is no solution to the system.
### A General Note: Types of Linear Systems
There are three types of systems of linear equations in two variables, and three types of solutions.
• An independent system has exactly one solution pair $\left(x,y\right)$. The point where the two lines intersect is the only solution.
• An inconsistent system has no solution. Notice that the two lines are parallel and will never intersect.
• A dependent system has infinitely many solutions. The lines are coincident. They are the same line, so every coordinate pair on the line is a solution to both equations.
Figure 2 compares graphical representations of each type of system.
Figure 2
### How To: Given a system of linear equations and an ordered pair, determine whether the ordered pair is a solution.
1. Substitute the ordered pair into each equation in the system.
2. Determine whether true statements result from the substitution in both equations; if so, the ordered pair is a solution.
### Example 1: Determining Whether an Ordered Pair Is a Solution to a System of Equations
Determine whether the ordered pair $\left(5,1\right)$ is a solution to the given system of equations.
$\begin{array}{l}x+3y=8\hfill \\ 2x - 9=y\hfill \end{array}$
### Solution
Substitute the ordered pair $\left(5,1\right)$ into both equations.
$\begin{array}{ll}\left(5\right)+3\left(1\right)=8\hfill & \hfill \\ \text{ }8=8\hfill & \text{True}\hfill \\ 2\left(5\right)-9=\left(1\right)\hfill & \hfill \\ \text{ }\text{1=1}\hfill & \text{True}\hfill \end{array}$
The ordered pair $\left(5,1\right)$ satisfies both equations, so it is the solution to the system.
### Analysis of the Solution
We can see the solution clearly by plotting the graph of each equation. Since the solution is an ordered pair that satisfies both equations, it is a point on both of the lines and thus the point of intersection of the two lines.
Figure 3
### Try It 1
Determine whether the ordered pair $\left(8,5\right)$ is a solution to the following system.
$\begin{array}{c}5x - 4y=20\\ 2x+1=3y\end{array}$
## Solving Systems of Equations by Graphing
There are multiple methods of solving systems of linear equations. For a system of linear equations in two variables, we can determine both the type of system and the solution by graphing the system of equations on the same set of axes.
### Example 2: Solving a System of Equations in Two Variables by Graphing
Solve the following system of equations by graphing. Identify the type of system.
$\begin{array}{c}2x+y=-8\\ x-y=-1\end{array}$
### Solution
Solve the first equation for $y$.
$\begin{array}{c}2x+y=-8\\ y=-2x - 8\end{array}$
Solve the second equation for $y$.
$\begin{array}{c}x-y=-1\\ y=x+1\end{array}$
Graph both equations on the same set of axes as in Figure 4.
Figure 4
The lines appear to intersect at the point $\left(-3,-2\right)$. We can check to make sure that this is the solution to the system by substituting the ordered pair into both equations.
$\begin{array}{ll}2\left(-3\right)+\left(-2\right)=-8\hfill & \hfill \\ \text{ }-8=-8\hfill & \text{True}\hfill \\ \text{ }\left(-3\right)-\left(-2\right)=-1\hfill & \hfill \\ \text{ }-1=-1\hfill & \text{True}\hfill \end{array}$
The solution to the system is the ordered pair $\left(-3,-2\right)$, so the system is independent.
### Try It 2
Solve the following system of equations by graphing.
$\begin{array}{l}\text{ }2x - 5y=-25\hfill \\ -4x+5y=35\hfill \end{array}$
### Can graphing be used if the system is inconsistent or dependent?
Yes, in both cases we can still graph the system to determine the type of system and solution. If the two lines are parallel, the system has no solution and is inconsistent. If the two lines are identical, the system has infinite solutions and is a dependent system.
## Solving Systems of Equations by Substitution
Solving a linear system in two variables by graphing works well when the solution consists of integer values, but if our solution contains decimals or fractions, it is not the most precise method. We will consider two more methods of solving a system of linear equations that are more precise than graphing. One such method is solving a system of equations by the substitution method, in which we solve one of the equations for one variable and then substitute the result into the second equation to solve for the second variable. Recall that we can solve for only one variable at a time, which is the reason the substitution method is both valuable and practical.
### How To: Given a system of two equations in two variables, solve using the substitution method.
1. Solve one of the two equations for one of the variables in terms of the other.
2. Substitute the expression for this variable into the second equation, then solve for the remaining variable.
3. Substitute that solution into either of the original equations to find the value of the first variable. If possible, write the solution as an ordered pair.
4. Check the solution in both equations.
### Example 3: Solving a System of Equations in Two Variables by Substitution
Solve the following system of equations by substitution.
$\begin{array}{l}\text{ }-x+y=-5\hfill \\ \text{ }2x - 5y=1\hfill \end{array}$
### Solution
First, we will solve the first equation for $y$.
$\begin{array}{l}-x+y=-5\hfill \\ \text{ }y=x - 5\hfill \end{array}$
Now we can substitute the expression $x - 5$ for $y$ in the second equation.
$\begin{array}{l}\text{ }2x - 5y=1\hfill \\ 2x - 5\left(x - 5\right)=1\hfill \\ \text{ }2x - 5x+25=1\hfill \\ \text{ }-3x=-24\hfill \\ \text{ }x=8\hfill \end{array}$
Now, we substitute $x=8$ into the first equation and solve for $y$.
$\begin{array}{l}-\left(8\right)+y=-5\hfill \\ \text{ }y=3\hfill \end{array}$
Our solution is $\left(8,3\right)$.
Check the solution by substituting $\left(8,3\right)$ into both equations.
$\begin{array}{llll}-x+y=-5\hfill & \hfill & \hfill & \hfill \\ -\left(8\right)+\left(3\right)=-5\hfill & \hfill & \hfill & \text{True}\hfill \\ 2x - 5y=1\hfill & \hfill & \hfill & \hfill \\ 2\left(8\right)-5\left(3\right)=1\hfill & \hfill & \hfill & \text{True}\hfill \end{array}$
### Try It 3
Solve the following system of equations by substitution.
$\begin{array}{l}x=y+3\hfill \\ 4=3x - 2y\hfill \end{array}$
### Can the substitution method be used to solve any linear system in two variables?
Yes, but the method works best if one of the equations contains a coefficient of 1 or –1 so that we do not have to deal with fractions.
## Solving Systems of Equations in Two Variables by the Addition Method
A third method of solving systems of linear equations is the addition method. In this method, we add two terms with the same variable, but opposite coefficients, so that the sum is zero. Of course, not all systems are set up with the two terms of one variable having opposite coefficients. Often we must adjust one or both of the equations by multiplication so that one variable will be eliminated by addition.
### How To: Given a system of equations, solve using the addition method.
1. Write both equations with x– and y-variables on the left side of the equal sign and constants on the right.
2. Write one equation above the other, lining up corresponding variables. If one of the variables in the top equation has the opposite coefficient of the same variable in the bottom equation, add the equations together, eliminating one variable. If not, use multiplication by a nonzero number so that one of the variables in the top equation has the opposite coefficient of the same variable in the bottom equation, then add the equations to eliminate the variable.
3. Solve the resulting equation for the remaining variable.
4. Substitute that value into one of the original equations and solve for the second variable.
5. Check the solution by substituting the values into the other equation.
### Example 4: Solving a System by the Addition Method
Solve the given system of equations by addition.
$\begin{array}{l}x+2y=-1\hfill \\ -x+y=3\hfill \end{array}$
### Solution
Both equations are already set equal to a constant. Notice that the coefficient of $x$ in the second equation, –1, is the opposite of the coefficient of $x$ in the first equation, 1. We can add the two equations to eliminate $x$ without needing to multiply by a constant.
$\frac{\begin{array}{l}\hfill \\ x+2y=-1\hfill \\ -x+y=3\hfill \end{array}}{\text{}\text{}\text{}\text{}\text{}3y=2}$
Now that we have eliminated $x$, we can solve the resulting equation for $y$.
$\begin{array}{l}3y=2\hfill \\ \text{ }y=\frac{2}{3}\hfill \end{array}$
Then, we substitute this value for $y$ into one of the original equations and solve for $x$.
$\begin{array}{l}\text{ }-x+y=3\hfill \\ \text{ }-x+\frac{2}{3}=3\hfill \\ \text{ }-x=3-\frac{2}{3}\hfill \\ \text{ }-x=\frac{7}{3}\hfill \\ \text{ }x=-\frac{7}{3}\hfill \end{array}$
The solution to this system is $\left(-\frac{7}{3},\frac{2}{3}\right)$.
Check the solution in the first equation.
$\begin{array}{llll}\text{ }x+2y=-1\hfill & \hfill & \hfill & \hfill \\ \text{ }\left(-\frac{7}{3}\right)+2\left(\frac{2}{3}\right)=\hfill & \hfill & \hfill & \hfill \\ \text{ }-\frac{7}{3}+\frac{4}{3}=\hfill & \hfill & \hfill & \hfill \\ \text{ }-\frac{3}{3}=\hfill & \hfill & \hfill & \hfill \\ \text{ }-1=-1\hfill & \hfill & \hfill & \text{True}\hfill \end{array}$
### Analysis of the Solution
We gain an important perspective on systems of equations by looking at the graphical representation. See Figure 5 to find that the equations intersect at the solution. We do not need to ask whether there may be a second solution because observing the graph confirms that the system has exactly one solution.
Figure 5
### Example 5: Using the Addition Method When Multiplication of One Equation Is Required
Solve the given system of equations by the addition method.
$\begin{array}{l}3x+5y=-11\hfill \\ \hfill \\ x - 2y=11\hfill \end{array}$
### Solution
Adding these equations as presented will not eliminate a variable. However, we see that the first equation has $3x$ in it and the second equation has $x$. So if we multiply the second equation by $-3,\text{}$ the x-terms will add to zero.
$\begin{array}{llll}\text{ }x - 2y=11\hfill & \hfill & \hfill & \hfill \\ -3\left(x - 2y\right)=-3\left(11\right)\hfill & \hfill & \hfill & \text{Multiply both sides by }-3.\hfill \\ \text{ }-3x+6y=-33\hfill & \hfill & \hfill & \text{Use the distributive property}.\hfill \end{array}$
$\begin{array}\ \hfill 3x+5y=−11 \\ \hfill −3x+6y=−33 \\ \text{_____________} \\ \hfill 11y=−44 \\ \hfill y=−4 \end{array}$
For the last step, we substitute $y=-4$ into one of the original equations and solve for $x$.
$\begin{array}{c}3x+5y=-11\\ 3x+5\left(-4\right)=-11\\ 3x - 20=-11\\ 3x=9\\ x=3\end{array}$
Our solution is the ordered pair $\left(3,-4\right)$. Check the solution in the original second equation.
$\begin{array}{llll}\text{ }x - 2y=11\hfill & \hfill & \hfill & \hfill \\ \left(3\right)-2\left(-4\right)=3+8\hfill & \hfill & \hfill & \hfill \\ \text{ }=11\hfill & \hfill & \hfill & \text{True}\hfill \end{array}$
Figure 6
### Try It 4
Solve the system of equations by addition.
$\begin{array}{c}2x - 7y=2\\ 3x+y=-20\end{array}$
Solution
### Example 6: Using the Addition Method When Multiplication of Both Equations Is Required
Solve the given system of equations in two variables by addition.
$\begin{array}{c}2x+3y=-16\\ 5x - 10y=30\end{array}$
### Solution
One equation has $2x$ and the other has $5x$. The least common multiple is $10x$ so we will have to multiply both equations by a constant in order to eliminate one variable. Let’s eliminate $x$ by multiplying the first equation by $-5$ and the second equation by $2$.
$\begin{array}{l} -5\left(2x+3y\right)=-5\left(-16\right)\hfill \\ \text{ }-10x - 15y=80\hfill \\ \text{ }2\left(5x - 10y\right)=2\left(30\right)\hfill \\ \text{ }10x - 20y=60\hfill \end{array}$
Then, we add the two equations together.
$\begin{array}\ −10x−15y=80 \\ 10x−20y=60 \\ \text{______________} \\ \text{ }−35y=140 \\ y=−4 \end{array}$
Substitute $y=-4$ into the original first equation.
$\begin{array}{c}2x+3\left(-4\right)=-16\\ 2x - 12=-16\\ 2x=-4\\ x=-2\end{array}$
The solution is $\left(-2,-4\right)$. Check it in the other equation.
$\begin{array}{r}\hfill \text{ }5x - 10y=30\\ \hfill 5\left(-2\right)-10\left(-4\right)=30\\ \hfill \text{ }-10+40=30\\ \hfill \text{ }30=30\end{array}$
Figure 7
### Example 7: Using the Addition Method in Systems of Equations Containing Fractions
Solve the given system of equations in two variables by addition.
$\begin{array}{l}\frac{x}{3}+\frac{y}{6}=3\hfill \\ \frac{x}{2}-\frac{y}{4}=\text{ }1\hfill \end{array}$
### Solution
First clear each equation of fractions by multiplying both sides of the equation by the least common denominator.
$\begin{array}{l}6\left(\frac{x}{3}+\frac{y}{6}\right)=6\left(3\right)\hfill \\ \text{ }2x+y=18\hfill \\ 4\left(\frac{x}{2}-\frac{y}{4}\right)=4\left(1\right)\hfill \\ \text{ }2x-y=4\hfill \end{array}$
Now multiply the second equation by $-1$ so that we can eliminate the x-variable.
$\begin{array}{l}-1\left(2x-y\right)=-1\left(4\right)\hfill \\ \text{ }-2x+y=-4\hfill \end{array}$
Add the two equations to eliminate the x-variable and solve the resulting equation.
$\begin{array}\ \hfill 2x+y=18 \\ \hfill−2x+y=−4 \\ \text{_____________} \\ \hfill 2y=14 \\ \hfill y=7 \end{array}$
Substitute $y=7$ into the first equation.
$\begin{array}{l}2x+\left(7\right)=18\hfill \\ \text{ }2x=11\hfill \\ \text{ }x=\frac{11}{2}\hfill \\ \text{ }=7.5\hfill \end{array}$
The solution is $\left(\frac{11}{2},7\right)$. Check it in the other equation.
$\begin{array}{c}\frac{x}{2}-\frac{y}{4}=1\\ \frac{\frac{11}{2}}{2}-\frac{7}{4}=1\\ \frac{11}{4}-\frac{7}{4}=1\\ \frac{4}{4}=1\end{array}$
### Try It 5
Solve the system of equations by addition.
$\begin{array}{c}2x+3y=8\\ 3x+5y=10\end{array}$
Solution
## Identifying and Expressing Solutions to Systems of Equations
Now that we have several methods for solving systems of equations, we can use the methods to identify inconsistent systems. Recall that an inconsistent system consists of parallel lines that have the same slope but different $y$ -intercepts. They will never intersect. When searching for a solution to an inconsistent system, we will come up with a false statement, such as $12=0$.
### Example 8: Solving an Inconsistent System of Equations
Solve the following system of equations.
$\begin{array}{l}\text{ }x=9 - 2y\hfill \\ x+2y=13\hfill \end{array}$
### Solution
We can approach this problem in two ways. Because one equation is already solved for $x$, the most obvious step is to use substitution.
$\begin{array}{l}x+2y=13\hfill \\ \left(9 - 2y\right)+2y=13\hfill \\ 9+0y=13\hfill \\ 9=13\hfill \end{array}$
Clearly, this statement is a contradiction because $9\ne 13$. Therefore, the system has no solution.
The second approach would be to first manipulate the equations so that they are both in slope-intercept form. We manipulate the first equation as follows.
$\begin{array}{l}\text{ }x=9 - 2y\hfill \\ 2y=-x+9\hfill \\ \text{ }y=-\frac{1}{2}x+\frac{9}{2}\hfill \end{array}$
We then convert the second equation expressed to slope-intercept form.
$\begin{array}{l}x+2y=13\hfill \\ \text{ }2y=-x+13\hfill \\ \text{ }y=-\frac{1}{2}x+\frac{13}{2}\hfill \end{array}$
Comparing the equations, we see that they have the same slope but different y-intercepts. Therefore, the lines are parallel and do not intersect.
$\begin{array}{l}\begin{array}{l}\\ y=-\frac{1}{2}x+\frac{9}{2}\end{array}\hfill \\ y=-\frac{1}{2}x+\frac{13}{2}\hfill \end{array}$
### Analysis of the Solution
Writing the equations in slope-intercept form confirms that the system is inconsistent because all lines will intersect eventually unless they are parallel. Parallel lines will never intersect; thus, the two lines have no points in common. The graphs of the equations in this example are shown in Figure 8.
Figure 8
### Try It 6
Solve the following system of equations in two variables.
$\begin{array}{l}2y - 2x=2\\ 2y - 2x=6\end{array}$
Solution
## Expressing the Solution of a System of Dependent Equations Containing Two Variables
Recall that a dependent system of equations in two variables is a system in which the two equations represent the same line. Dependent systems have an infinite number of solutions because all of the points on one line are also on the other line. After using substitution or addition, the resulting equation will be an identity, such as $0=0$.
### Example 9: Finding a Solution to a Dependent System of Linear Equations
Find a solution to the system of equations using the addition method.
$\begin{array}{c}x+3y=2\\ 3x+9y=6\end{array}$
### Solution
With the addition method, we want to eliminate one of the variables by adding the equations. In this case, let’s focus on eliminating $x$. If we multiply both sides of the first equation by $-3$, then we will be able to eliminate the $x$ -variable.
$\begin{array}{l}\text{ }x+3y=2\hfill \\ \left(-3\right)\left(x+3y\right)=\left(-3\right)\left(2\right)\hfill \\ \text{ }-3x - 9y=-6\hfill \end{array}$
$\begin{array} \hfill−3x−9y=−6 \\ \hfill+3x+9y=6 \\ \hfill \text{_____________} \\ \hfill 0=0 \end{array}$
We can see that there will be an infinite number of solutions that satisfy both equations.
### Analysis of the Solution
If we rewrote both equations in the slope-intercept form, we might know what the solution would look like before adding. Let’s look at what happens when we convert the system to slope-intercept form.
$\begin{array}{l}\text{ }x+3y=2\hfill \\ \text{ }3y=-x+2\hfill \\ \text{ }y=-\frac{1}{3}x+\frac{2}{3}\hfill \\ 3x+9y=6\hfill \\ \text{ }9y=-3x+6\hfill \\ \text{ }y=-\frac{3}{9}x+\frac{6}{9}\hfill \\ \text{ }y=-\frac{1}{3}x+\frac{2}{3}\hfill \end{array}$
See Figure 9. Notice the results are the same. The general solution to the system is $\left(x, -\frac{1}{3}x+\frac{2}{3}\right)$.
Figure 9
### Try It 7
Solve the following system of equations in two variables.
$\begin{array}{l}\begin{array}{l}\\ \text{ }\text{}\text{}y - 2x=5\end{array}\hfill \\ -3y+6x=-15\hfill \end{array}$
## Using Systems of Equations to Investigate Profits
Using what we have learned about systems of equations, we can return to the skateboard manufacturing problem at the beginning of the section. The skateboard manufacturer’s revenue function is the function used to calculate the amount of money that comes into the business. It can be represented by the equation $R=xp$, where $x=$ quantity and $p=$ price. The revenue function is shown in orange in Figure 10.
The cost function is the function used to calculate the costs of doing business. It includes fixed costs, such as rent and salaries, and variable costs, such as utilities. The cost function is shown in blue in Figure 10. The $x$ -axis represents quantity in hundreds of units. The y-axis represents either cost or revenue in hundreds of dollars.
The point at which the two lines intersect is called the break-even point. We can see from the graph that if 700 units are produced, the cost is $3,300 and the revenue is also$3,300. In other words, the company breaks even if they produce and sell 700 units. They neither make money nor lose money.
The shaded region to the right of the break-even point represents quantities for which the company makes a profit. The shaded region to the left represents quantities for which the company suffers a loss. The profit function is the revenue function minus the cost function, written as $P\left(x\right)=R\left(x\right)-C\left(x\right)$. Clearly, knowing the quantity for which the cost equals the revenue is of great importance to businesses.
### Example 10: Finding the Break-Even Point and the Profit Function Using Substitution
Given the cost function $C\left(x\right)=0.85x+35,000$ and the revenue function $R\left(x\right)=1.55x$, find the break-even point and the profit function.
### Solution
Write the system of equations using $y$ to replace function notation.
$\begin{array}{l}\begin{array}{l}\\ y=0.85x+35,000\end{array}\hfill \\ y=1.55x\hfill \end{array}$
Substitute the expression $0.85x+35,000$ from the first equation into the second equation and solve for $x$.
$\begin{array}{c}0.85x+35,000=1.55x\\ 35,000=0.7x\\ 50,000=x\end{array}$
Then, we substitute $x=50,000$ into either the cost function or the revenue function.
$1.55\left(50,000\right)=77,500$
The break-even point is $\left(50,000,77,500\right)$.
The profit function is found using the formula $P\left(x\right)=R\left(x\right)-C\left(x\right)$.
$\begin{array}{l}P\left(x\right)=1.55x-\left(0.85x+35,000\right)\hfill \\ \text{ }=0.7x - 35,000\hfill \end{array}$
The profit function is $P\left(x\right)=0.7x - 35,000$.
### Analysis of the Solution
The cost to produce 50,000 units is $77,500, and the revenue from the sales of 50,000 units is also$77,500. To make a profit, the business must produce and sell more than 50,000 units.
Figure 11
We see from the graph in Figure 12 that the profit function has a negative value until $x=50,000$, when the graph crosses the x-axis. Then, the graph emerges into positive y-values and continues on this path as the profit function is a straight line. This illustrates that the break-even point for businesses occurs when the profit function is 0. The area to the left of the break-even point represents operating at a loss.
Figure 12
The cost of a ticket to the circus is $25.00 for children and$50.00 for adults. On a certain day, attendance at the circus is 2,000 and the total gate revenue is $70,000. How many children and how many adults bought tickets? ### Solution Let c = the number of children and a = the number of adults in attendance. The total number of people is $2,000$. We can use this to write an equation for the number of people at the circus that day. $c+a=2,000$ The revenue from all children can be found by multiplying$25.00 by the number of children, $25c$. The revenue from all adults can be found by multiplying $50.00 by the number of adults, $50a$. The total revenue is$70,000. We can use this to write an equation for the revenue.
$25c+50a=70,000$
We now have a system of linear equations in two variables.
$\begin{array}{c}c+a=2,000\\ 25c+50a=70,000\end{array}$
In the first equation, the coefficient of both variables is 1. We can quickly solve the first equation for either $c$ or $a$. We will solve for $a$.
$\begin{array}{c}c+a=2,000\\ a=2,000-c\end{array}$
Substitute the expression $2,000-c$ in the second equation for $a$ and solve for $c$.
$\begin{array}{l} 25c+50\left(2,000-c\right)=70,000\hfill \\ 25c+100,000 - 50c=70,000\hfill \\ \text{ }-25c=-30,000\hfill \\ \text{ }c=1,200\hfill \end{array}$
Substitute $c=1,200$ into the first equation to solve for $a$.
$\begin{array}{l}1,200+a=2,000\hfill \\ \text{ }\text{}a=800\hfill \end{array}$
We find that $1,200$ children and $800$ adults bought tickets to the circus that day.
Meal tickets at the circus cost $4.00 for children and$12.00 for adults. If 1,650 meal tickets were bought for a total of $14,200, how many children and how many adults bought meal tickets? Solution ## Key Concepts • A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. • The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. • Systems of equations are classified as independent with one solution, dependent with an infinite number of solutions, or inconsistent with no solution. • One method of solving a system of linear equations in two variables is by graphing. In this method, we graph the equations on the same set of axes. • Another method of solving a system of linear equations is by substitution. In this method, we solve for one variable in one equation and substitute the result into the second equation. • A third method of solving a system of linear equations is by addition, in which we can eliminate a variable by adding opposite coefficients of corresponding variables. • It is often necessary to multiply one or both equations by a constant to facilitate elimination of a variable when adding the two equations together. • Either method of solving a system of equations results in a false statement for inconsistent systems because they are made up of parallel lines that never intersect. • The solution to a system of dependent equations will always be true because both equations describe the same line. • Systems of equations can be used to solve real-world problems that involve more than one variable, such as those relating to revenue, cost, and profit. ## Glossary addition method an algebraic technique used to solve systems of linear equations in which the equations are added in a way that eliminates one variable, allowing the resulting equation to be solved for the remaining variable; substitution is then used to solve for the first variable break-even point the point at which a cost function intersects a revenue function; where profit is zero consistent system a system for which there is a single solution to all equations in the system and it is an independent system, or if there are an infinite number of solutions and it is a dependent system cost function the function used to calculate the costs of doing business; it usually has two parts, fixed costs and variable costs dependent system a system of linear equations in which the two equations represent the same line; there are an infinite number of solutions to a dependent system inconsistent system a system of linear equations with no common solution because they represent parallel lines, which have no point or line in common independent system a system of linear equations with exactly one solution pair $\left(x,y\right)$ profit function the profit function is written as $P\left(x\right)=R\left(x\right)-C\left(x\right)$, revenue minus cost revenue function the function that is used to calculate revenue, simply written as $R=xp$, where $x=$ quantity and $p=$ price substitution method an algebraic technique used to solve systems of linear equations in which one of the two equations is solved for one variable and then substituted into the second equation to solve for the second variable system of linear equations a set of two or more equations in two or more variables that must be considered simultaneously. ## Section Exercises 1. Can a system of linear equations have exactly two solutions? Explain why or why not. 2. If you are performing a break-even analysis for a business and their cost and revenue equations are dependent, explain what this means for the company’s profit margins. 3. If you are solving a break-even analysis and get a negative break-even point, explain what this signifies for the company? 4. If you are solving a break-even analysis and there is no break-even point, explain what this means for the company. How should they ensure there is a break-even point? 5. Given a system of equations, explain at least two different methods of solving that system. For the following exercises, determine whether the given ordered pair is a solution to the system of equations. 6. $\begin{array}{c}5x-y=4\\ x+6y=2\end{array}$ and $\left(4,0\right)$ 7. $\begin{array}{l}-3x - 5y=13\hfill \\ -x+4y=10\hfill \end{array}$ and $\left(-6,1\right)$ 8. $\begin{array}{c}3x+7y=1\\ 2x+4y=0\end{array}$ and $\left(2,3\right)$ 9. $\begin{array}{l}-2x+5y=7\hfill \\ \text{ }2x+9y=7\hfill \end{array}$ and $\left(-1,1\right)$ 10. $\begin{array}{c}x+8y=43\\ 3x - 2y=-1\end{array}$ and $\left(3,5\right)$ For the following exercises, solve each system by substitution. 11. $\begin{array}{l}\text{ }x+3y=5\hfill \\ 2x+3y=4\hfill \end{array}$ 12. $\begin{array}{l}\text{ }3x - 2y=18\hfill \\ 5x+10y=-10\hfill \end{array}$ 13. $\begin{array}{l}4x+2y=-10\\ 3x+9y=0\end{array}$ 14. $\begin{array}{l}2x+4y=-3.8\\ 9x - 5y=1.3\end{array}$ 15. $\begin{array}{l}\hfill \\ \begin{array}{l}\\ \begin{array}{l}-2x+3y=1.2\hfill \\ -3x - 6y=1.8\hfill \end{array}\end{array}\hfill \end{array}$ 16. $\begin{array}{l}\text{ }x - 0.2y=1\hfill \\ -10x+2y=5\hfill \end{array}$ 17. $\begin{array}{l}\text{ }3x+5y=9\hfill \\ 30x+50y=-90\hfill \end{array}$ 18. $\begin{array}{l}\hfill \\ \begin{array}{l}\text{ }-3x+y=2\hfill \\ 12x - 4y=-8\hfill \end{array}\hfill \end{array}$ 19. $\begin{array}{l}\frac{1}{2}x+\frac{1}{3}y=16\\ \frac{1}{6}x+\frac{1}{4}y=9\end{array}$ 20. $\begin{array}{l}\\ \begin{array}{l}-\frac{1}{4}x+\frac{3}{2}y=11\hfill \\ -\frac{1}{8}x+\frac{1}{3}y=3\hfill \end{array}\end{array}$ For the following exercises, solve each system by addition. 21. $\begin{array}{l}\hfill \\ \begin{array}{l}-2x+5y=-42\hfill \\ \text{ }7x+2y=30\hfill \end{array}\hfill \end{array}$ 22. $\begin{array}{l}6x - 5y=-34\\ 2x+6y=4\end{array}$ 23. $\begin{array}{l}\text{ }5x-y=-2.6\hfill \\ -4x - 6y=1.4\hfill \end{array}$ 24. $\begin{array}{l}7x - 2y=3\\ 4x+5y=3.25\end{array}$ 25. $\begin{array}{l}\hfill \\ \begin{array}{l}\text{ }\mathrm{-x}+2y=-1\hfill \\ 5x - 10y=6\hfill \end{array}\hfill \end{array}$ 26. $\begin{array}{l}\text{ }7x+6y=2\hfill \\ -28x - 24y=-8\hfill \end{array}$ 27. $\begin{array}{l}\frac{5}{6}x+\frac{1}{4}y=0\\ \frac{1}{8}x-\frac{1}{2}y=-\frac{43}{120}\end{array}$ 28. $\begin{array}{l}\text{ }\frac{1}{3}x+\frac{1}{9}y=\frac{2}{9}\hfill \\ -\frac{1}{2}x+\frac{4}{5}y=-\frac{1}{3}\hfill \end{array}$ 29. $\begin{array}{l}\hfill \\ \begin{array}{l}-0.2x+0.4y=0.6\hfill \\ \text{ }x - 2y=-3\hfill \end{array}\hfill \end{array}$ 30. $\begin{array}{l}\begin{array}{l}\\ -0.1x+0.2y=0.6\end{array}\hfill \\ \text{ }5x - 10y=1\hfill \end{array}$ For the following exercises, solve each system by any method. 31. $\begin{array}{l}5x+9y=16\hfill \\ \text{ }x+2y=4\hfill \end{array}$ 32. $\begin{array}{l}6x - 8y=-0.6\\ 3x+2y=0.9\end{array}$ 33. $\begin{array}{l}5x - 2y=2.25\\ 7x - 4y=3\end{array}$ 34. $\begin{array}{l}\begin{array}{l}\hfill \\ \text{ }x-\frac{5}{12}y=-\frac{55}{12}\hfill \end{array}\hfill \\ -6x+\frac{5}{2}y=\frac{55}{2}\hfill \end{array}$ 35. $\begin{array}{l}\\ \begin{array}{l}7x - 4y=\frac{7}{6}\hfill \\ 2x+4y=\frac{1}{3}\hfill \end{array}\end{array}$ 36. $\begin{array}{l}3x+6y=11\\ 2x+4y=9\end{array}$ 37. $\begin{array}{l}\text{ }\frac{7}{3}x-\frac{1}{6}y=2\hfill \\ -\frac{21}{6}x+\frac{3}{12}y=-3\hfill \end{array}$ 38. $\begin{array}{l}\frac{1}{2}x+\frac{1}{3}y=\frac{1}{3}\\ \frac{3}{2}x+\frac{1}{4}y=-\frac{1}{8}\end{array}$ 39. $\begin{array}{l}2.2x+1.3y=-0.1\\ 4.2x+4.2y=2.1\end{array}$ 40. $\begin{array}{l}\text{ }0.1x+0.2y=2\hfill \\ 0.35x - 0.3y=0\hfill \end{array}$ For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has one solution, no solution, or infinite solutions. 41. $\begin{array}{l}3x-y=0.6\\ x - 2y=1.3\end{array}$ 42. $\begin{array}{l}\begin{array}{l}\\ -x+2y=4\end{array}\hfill \\ \text{ }2x - 4y=1\hfill \end{array}$ 43. $\begin{array}{l}\text{ }x+2y=7\hfill \\ 2x+6y=12\hfill \end{array}$ 44. $\begin{array}{l}3x - 5y=7\hfill \\ \text{ }x - 2y=3\hfill \end{array}$ 45. $\begin{array}{l}\text{ }3x - 2y=5\hfill \\ -9x+6y=-15\hfill \end{array}$ For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth. 46. $\begin{array}{l}\text{ }0.1x+0.2y=0.3\hfill \\ -0.3x+0.5y=1\hfill \end{array}$ 47. $\begin{array}{l}\hfill \\ \begin{array}{l}-0.01x+0.12y=0.62\hfill \\ 0.15x+0.20y=0.52\hfill \end{array}\hfill \end{array}$ 48. $\begin{array}{l}0.5x+0.3y=4\hfill \\ 0.25x - 0.9y=0.46\hfill \end{array}$ 49. $\begin{array}{l}0.15x+0.27y=0.39\hfill \\ -0.34x+0.56y=1.8\hfill \end{array}$ 50. $\begin{array}{l}\begin{array}{l}\\ -0.71x+0.92y=0.13\end{array}\hfill \\ 0.83x+0.05y=2.1\hfill \end{array}$ For the following exercises, solve each system in terms of $A,B,C,D,E,\text{}$ and $F$ where $A-F$ are nonzero numbers. Note that $A\ne B$ and $AE\ne BD$. 51. $\begin{array}{l}x+y=A\\ x-y=B\end{array}$ 52. $\begin{array}{l}x+Ay=1\\ x+By=1\end{array}$ 53. $\begin{array}{l}Ax+y=0\\ Bx+y=1\end{array}$ 54. $\begin{array}{l}Ax+By=C\\ x+y=1\end{array}$ 55. $\begin{array}{l}Ax+By=C\\ Dx+Ey=F\end{array}$ For the following exercises, solve for the desired quantity. 56. A stuffed animal business has a total cost of production $C=12x+30$ and a revenue function $R=20x$. Find the break-even point. 57. A fast-food restaurant has a cost of production $C\left(x\right)=11x+120$ and a revenue function $R\left(x\right)=5x$. When does the company start to turn a profit? 58. A cell phone factory has a cost of production $C\left(x\right)=150x+10,000$ and a revenue function $R\left(x\right)=200x$. What is the break-even point? 59. A musician charges $C\left(x\right)=64x+20,000,\text{}$ where $x$ is the total number of attendees at the concert. The venue charges$80 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?
60. A guitar factory has a cost of production $C\left(x\right)=75x+50,000$. If the company needs to break even after 150 units sold, at what price should they sell each guitar? Round up to the nearest dollar, and write the revenue function.
For the following exercises, use a system of linear equations with two variables and two equations to solve.
61. Find two numbers whose sum is 28 and difference is 13.
62. A number is 9 more than another number. Twice the sum of the two numbers is 10. Find the two numbers.
63. The startup cost for a restaurant is $120,000, and each meal costs$10 for the restaurant to make. If each meal is then sold for $15, after how many meals does the restaurant break even? 64. A moving company charges a flat rate of$150, and an additional $5 for each box. If a taxi service would charge$20 for each box, how many boxes would you need for it to be cheaper to use the moving company, and what would be the total cost?
65. A total of 1,595 first- and second-year college students gathered at a pep rally. The number of freshmen exceeded the number of sophomores by 15. How many freshmen and sophomores were in attendance?
66. 276 students enrolled in a freshman-level chemistry class. By the end of the semester, 5 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed.
67. There were 130 faculty at a conference. If there were 18 more women than men attending, how many of each gender attended the conference?
68. A jeep and BMW enter a highway running east-west at the same exit heading in opposite directions. The jeep entered the highway 30 minutes before the BMW did, and traveled 7 mph slower than the BMW. After 2 hours from the time the BMW entered the highway, the cars were 306.5 miles apart. Find the speed of each car, assuming they were driven on cruise control.
69. If a scientist mixed 10% saline solution with 60% saline solution to get 25 gallons of 40% saline solution, how many gallons of 10% and 60% solutions were mixed?
70. An investor earned triple the profits of what she earned last year. If she made $500,000.48 total for both years, how much did she earn in profits each year? 71. An investor who dabbles in real estate invested 1.1 million dollars into two land investments. On the first investment, Swan Peak, her return was a 110% increase on the money she invested. On the second investment, Riverside Community, she earned 50% over what she invested. If she earned$1 million in profits, how much did she invest in each of the land deals?
72. If an investor invests a total of $25,000 into two bonds, one that pays 3% simple interest, and the other that pays $2\frac{7}{8}\text{%}$ interest, and the investor earns$737.50 annual interest, how much was invested in each account?
73. If an investor invests $23,000 into two bonds, one that pays 4% in simple interest, and the other paying 2% simple interest, and the investor earns$710.00 annual interest, how much was invested in each account?
74. CDs cost $5.96 more than DVDs at All Bets Are Off Electronics. How much would 6 CDs and 2 DVDs cost if 5 CDs and 2 DVDs cost$127.73?
75. A store clerk sold 60 pairs of sneakers. The high-tops sold for $98.99 and the low-tops sold for$129.99. If the receipts for the two types of sales totaled $6,404.40, how many of each type of sneaker were sold? 76. A concert manager counted 350 ticket receipts the day after a concert. The price for a student ticket was$12.50, and the price for an adult ticket was $16.00. The register confirms that$5,075 was taken in. How many student tickets and adult tickets were sold?
77. Admission into an amusement park for 4 children and 2 adults is $116.90. For 6 children and 3 adults, the admission is$175.35. Assuming a different price for children and adults, what is the price of the child’s ticket and the price of the adult ticket? | 2020-09-29 17:54:14 | {"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": 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": 0.9666573405265808, "perplexity": 391.0448239192848}, "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/1600400202418.22/warc/CC-MAIN-20200929154729-20200929184729-00512.warc.gz"} |
https://gmatclub.com/forum/if-2x-root-3x-2-27-is-not-a-real-number-270129.html | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 16 Dec 2018, 00:49
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
## Events & Promotions
###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!
December 16, 2018
December 16, 2018
07:00 AM PST
09:00 AM PST
Get personalized insights on how to achieve your Target Quant Score.
• ### Free GMAT Prep Hour
December 16, 2018
December 16, 2018
03:00 PM EST
04:00 PM EST
Strategies and techniques for approaching featured GMAT topics
# If 2x/ (root(-3x^2 + 27)) is not a real number
new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
### Hide Tags
Intern
Joined: 20 Nov 2017
Posts: 28
Location: India
GRE 1: Q158 V150
GPA: 3.9
WE: Consulting (Consumer Electronics)
If 2x/ (root(-3x^2 + 27)) is not a real number [#permalink]
### Show Tags
10 Jul 2018, 00:48
1
6
00:00
Difficulty:
55% (hard)
Question Stats:
51% (00:59) correct 49% (01:19) wrong based on 150 sessions
### HideShow timer Statistics
If $$\frac{2x}{\sqrt{-3x^2 + 27}}$$ is not a real number, which of the following specifies all the possible values of x?
A. $$x\leq-3$$ or $$x\geq3$$
B. $$x\leq-3$$
C. $$x\geq3$$
D. $$x\leq-4$$ or $$x\geq4$$
E. $$-3 \leq x \leq 3$$
##### Most Helpful Expert Reply
MBA Section Director
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 1491
Concentration: Nonprofit
GPA: 4
WE: Engineering (Computer Software)
If 2x/ (root(-3x^2 + 27)) is not a real number [#permalink]
### Show Tags
10 Jul 2018, 00:55
6
1
GIven $$\frac{2x}{\sqrt{-3x^2 + 27}}$$ is not a real number
=> The number inside the square root sign is < 0. Also since the square root is in denominator, the number is not a real number if denominator is 0
=> $$-3x^2 + 27 \leq 0$$
=> $$3x^2 - 27 \geq 0$$
=> $$3x^2 \geq 27$$
=> $$x^2 \geq 9$$
=> $$x\leq-3$$ or $$x\geq3$$
Hence option A
_________________
##### General Discussion
Senior Manager
Joined: 04 Aug 2010
Posts: 310
Schools: Dartmouth College
Re: If 2x/ (root(-3x^2 + 27)) is not a real number [#permalink]
### Show Tags
10 Jul 2018, 03:54
1
Karthik200 wrote:
If $$\frac{2x}{\sqrt{-3x^2 + 27}}$$ is not a real number, which of the following specifies all the possible values of x?
A. $$x\leq-3$$ or $$x\geq3$$
B. $$x\leq-3$$
C. $$x\geq3$$
D. $$x\leq-4$$ or $$x\geq4$$
E. $$-3 \leq x \leq 3$$
Since the GMAT is constrained to real numbers, I would disregard this problem.
_________________
GMAT and GRE Tutor
Over 1800 followers
Click here to learn more
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
MBA Section Director
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 1491
Concentration: Nonprofit
GPA: 4
WE: Engineering (Computer Software)
Re: If 2x/ (root(-3x^2 + 27)) is not a real number [#permalink]
### Show Tags
10 Jul 2018, 04:03
GMATGuruNY wrote:
Since the GMAT is constrained to real numbers, I would disregard this problem.
Good to know about this constraint. Thank you.
_________________
Director
Joined: 11 Feb 2015
Posts: 617
Re: If 2x/ (root(-3x^2 + 27)) is not a real number [#permalink]
### Show Tags
15 Jul 2018, 09:13
Although I got this question right, I am just curious to check is this a GMAT like question? I was told by someone that imaginary numbers are not tasted on GMAT.
_________________
"Please hit +1 Kudos if you like this post"
_________________
Manish
"Only I can change my life. No one can do it for me"
Intern
Joined: 20 Nov 2017
Posts: 28
Location: India
GRE 1: Q158 V150
GPA: 3.9
WE: Consulting (Consumer Electronics)
Re: If 2x/ (root(-3x^2 + 27)) is not a real number [#permalink]
### Show Tags
18 Jul 2018, 17:22
workout wrote:
GIven $$\frac{2x}{\sqrt{-3x^2 + 27}}$$ is not a real number
=> The number inside the square root sign is < 0. Also since the square root is in denominator, the number is not a real number if denominator is 0
=> $$-3x^2 + 27 \leq 0$$
=> $$3x^2 - 27 \geq 0$$
=> $$3x^2 \geq 27$$
=> $$x^2 \geq 9$$
=> $$x\leq-3$$ or $$x\geq3$$
Hence option A
Thanks workout for the nice explanation
Manager
Joined: 07 Feb 2017
Posts: 188
Re: If 2x/ (root(-3x^2 + 27)) is not a real number [#permalink]
### Show Tags
18 Jul 2018, 18:56
-3x^2+27<0
3x^2-27>0
3(x^2-9)>0
x^2-9>0
(x+3)(x-3)>0
x+3>0 and x-3>0
x>-3 and x>3
x+3<0 and x-3<0
x<-3 and x<3
Answer A
Grade school algebra questions rly comfortable easy
Re: If 2x/ (root(-3x^2 + 27)) is not a real number &nbs [#permalink] 18 Jul 2018, 18:56
Display posts from previous: Sort by
# If 2x/ (root(-3x^2 + 27)) is not a real number
new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 2018-12-16 08:49:58 | {"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": 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": 0.6863419413566589, "perplexity": 12343.301324530816}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827596.48/warc/CC-MAIN-20181216073608-20181216095608-00476.warc.gz"} |
https://deepai.org/publication/a-general-model-for-robust-tensor-factorization-with-unknown-noise | # A General Model for Robust Tensor Factorization with Unknown Noise
Because of the limitations of matrix factorization, such as losing spatial structure information, the concept of low-rank tensor factorization (LRTF) has been applied for the recovery of a low dimensional subspace from high dimensional visual data. The low-rank tensor recovery is generally achieved by minimizing the loss function between the observed data and the factorization representation. The loss function is designed in various forms under different noise distribution assumptions, like L_1 norm for Laplacian distribution and L_2 norm for Gaussian distribution. However, they often fail to tackle the real data which are corrupted by the noise with unknown distribution. In this paper, we propose a generalized weighted low-rank tensor factorization method (GWLRTF) integrated with the idea of noise modelling. This procedure treats the target data as high-order tensor directly and models the noise by a Mixture of Gaussians, which is called MoG GWLRTF. The parameters in the model are estimated under the EM framework and through a new developed algorithm of weighted low-rank tensor factorization. We provide two versions of the algorithm with different tensor factorization operations, i.e., CP factorization and Tucker factorization. Extensive experiments indicate the respective advantages of this two versions in different applications and also demonstrate the effectiveness of MoG GWLRTF compared with other competing methods.
## Authors
• 1 publication
• 5 publications
• 61 publications
• 37 publications
• 65 publications
• 31 publications
• 6 publications
• ### Adaptive Quantile Low-Rank Matrix Factorization
Low-rank matrix factorization (LRMF) has received much popularity owing ...
01/01/2019 ∙ by Shuang Xu, et al. ∙ 30
• ### Approximate Rank-Detecting Factorization of Low-Rank Tensors
We present an algorithm, AROFAC2, which detects the (CP-)rank of a degre...
11/30/2012 ∙ by Franz J Király, et al. ∙ 0
• ### Generalized infinite factorization models
Factorization models express a statistical object of interest in terms o...
03/18/2021 ∙ by Lorenzo Schiavon, et al. ∙ 0
• ### Low-rank Matrix Factorization under General Mixture Noise Distributions
Many computer vision problems can be posed as learning a low-dimensional...
01/06/2016 ∙ by Xiangyong Cao, et al. ∙ 0
• ### Completing a joint PMF from projections: a low-rank coupled tensor factorization approach
There has recently been considerable interest in completing a low-rank m...
02/16/2017 ∙ by Nikos Kargas, et al. ∙ 0
• ### Nonparametric Multivariate Density Estimation: A Low-Rank Characteristic Function Approach
Effective non-parametric density estimation is a key challenge in high-d...
08/27/2020 ∙ by Magda Amiridi, et al. ∙ 3
• ### Regularized and Smooth Double Core Tensor Factorization for Heterogeneous Data
We introduce a general tensor model suitable for data analytic tasks for...
11/24/2019 ∙ by Davoud Ataee Tarzanagh, et al. ∙ 7
##### This week in AI
Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.
## I Introduction
The problem of recovering a low dimensional linear subspace from high dimensional visual data naturally arises in the fields of computer vision, machine learning and statistics, and has drawn increasing attention in the recent years. Typical examples include representation and recognition of faces
[1, 2, 3, 4], structure from motion [5], recognition of 3D objects under varying pose [6], motion segmentation [7]
. In such contexts, the data to be analyzed usually can be formulated as high-order tensors, which are natural generalization of vectors and matrices. Existing approaches, including LRMF and RPCA, proceed by matricizing tensors into matrices and then applying common matrix techniques to deal with tensor problems. However, as shown in
[8], such matricization procedure fails to exploit the essential tensor structure and often leads to suboptimal procedure. Figure 1 illustrates the difference between the matrix based method and tensor based method in dealing with the high-order tensor data. The upper row is the matrix based factorization method, which needs to preliminarily matricize the tensor at the cost of losing data structure information; the lower row is our tensor based method which directly factorizes the tensor without destroying the spatial structures.
Given a high-order tensor data, an efficient way to extract the underlying useful information is low-rank tensor factorization (LRTF), which aims to extract low-rank subspaces underlying those vector spaces such that the original tensor can be suitably expressed through reasonably affiliating these subspaces.
Traditionally, there are two definitions of tensor factorizations, i.e., CP factorization and Tucker factorization.
The CP factorization can be viewed as a higher-order generalization of the matrix singular value decomposition
[9, 10, 11, 12]
and has been widely applied to many fields, including image inpainting
[13, 14], collaborative filtering [15], and data mining [16], etc. The idea of CP is to express a tensor as the sum of a finite number of rank-1 tensors. Mathematically, an -order tensor , with the integer indicating the dimension of along the -th order, is represented in the CP factorization form as
X=r∑d=1ud∘vd∘⋅⋅⋅∘td, (1)
here, denotes the vector outer product and is assumed to be the rank of the tensor , denoted as rank(), which is defined as the smallest number of rank-1 tensors [17, 18].
Each element of the tensor has the following form:
xi1i2⋅⋅⋅iN=r∑d=1ui1dvi2d⋅⋅⋅tiNd, (2)
where The mode (or factor) matrices refer to the combination of the vectors from the rank-1 components, i.e., and likewise for others.
The Tucker factorization is a form of higher-order principal component analysis
[9, 10, 11, 19] and has been widely used in many applications [20, 21, 22, 23, 24, 25, 26]. It decomposes a tensor into a core tensor multiplied (or transformed) by a matrix along each mode, written as
X=G×1U×2V⋅⋅⋅×NT=r1∑d1=1r2∑d2=1⋅⋅⋅rN∑dN=1gd1d2⋅⋅⋅dNud1∘vd2∘⋅⋅⋅∘tdN, (3)
where denotes the -mode matrix product and is the core tensor controlling the interaction between the mode matrices .
Elementwise, the Tucker decomposition in Eq. (3) is
xi1i2⋅⋅⋅iN=r1∑d1=1r2∑d2=1⋅⋅⋅rN∑dN=1gd1d2⋅⋅⋅dNui1d1vi2d2⋅⋅⋅tiNdN. (4)
Here the defined -rank of , denoted as rank, considers the mode- rank of tensors. Accordingly, we call a rank- tensor.
As mentioned in [27], there exist a number of other tensor factorizations but they are all related to the CP and the Tucker factorization. On account of this, our work for robust low rank tensor factorization is designed based on this two typical factorizations.
It is known that the canonical fit function for the LRTF is based on the Frobenius norm function which assumes the noise to follow a Gaussian distribution. However, for many real data, such as the fMRI neuroimaging data [28] and the video surveillance data [29], a relative large perturbation in magnitude only affects a relatively small fraction of data points, which often violates the Gaussian assumption and follows a Laplacian distribution instead.
Therefore, it is necessary to consider other loss function that is robust to Laplacian noise. To alleviate this problem, one commonly used strategy is to replace the Frobenius norm function (say, norm) by the -type norm [30, 31], which is known to be robust to gross Laplacian perturbations. Unfortunately, in many real applications, the noise often exhibits very complex statistical distributions rather than a single purely Gaussian or Laplacian noise [32]. This motivates us to consider more flexible modeling strategies to tackle such complex noise cases.
Under the framework of low-rank matrix factorization (LRMF), Meng and De la Torre [33] firstly proposed to model the noise as Mixture of Gaussians (MoG). They showed that the MoG model is a universal approximator to any continuous distribution, and hence could be capable of modeling a wider range of noise distributions. Along this line, Zhao et al. [34] further extended the MoG model to deal with robust PCA (RPCA) problem. Extensive experiments on synthetic data, face modeling and background subtraction demonstrated the merits of MoG model.
As such, to share the same light of matrix MoG model, we aim to introduce a novel MoG model to the tensor case for the LRTF task to overcome the drawbacks of existing models, which are only optimal for simple Gaussian or Laplacian noise.
The contributions of this paper can be summarized as follows: (1) As an extension of our last work [35], we propose a generalized low-rank subspace learning approach called generalized weighted low-rank tensor factorization (GWLRTF), i.e., the GWLRTF-CP and the GWLRTF-Tucker, which both can preserve the essential tensor structure; (2) For modelling complex noise, MoG is applied to the proposed GWLRTF model called generalized weighted low-rank tensor factorization integrated with MoG (MoG GWLRTF), i.e., the MoG GWLRTF-CP and the MoG GWLRTF-Tucker; (3) For solving the proposed model, we propose efficient algorithms to estimate the parameters under the EM framework and through the proposed algorithm of GWLRTF. Our strategy is different from not only the traditional EM algorithm for solving matrix/tensor decomposition models, but also conventional alternative least squares (ALS) techniques for solving other tensor factorization problems; (4) To further compare the performance between CP factorization and Tucker factorization in different real application problems, a series of synthetic and real data experiments are conducted. The source codes of our algorithm are published online: .
The rest of this paper is organized as follows. Section 2 describes the notation and common operations used in this paper. In Section 3, a generalized model of tensor factorization integrated with MoG is proposed for reconstructing low-rank tensor from high-order tensor with unknown noise. In Section 4, the established problem model is solved under the EM framework with new proposed tensor factorization algorithms. Extensive experiments are conducted on both synthetic data and real image data in Section 5.
## Ii Notation and preliminaries
The notations and common operations used throughout the paper are defined as follows. Scalars are denoted by lowercase letters and vectors are denoted by bold lowercase letters with elements . Matrices are represented by uppercase letters with column vectors and elements . The calligraphic letters stand for the the high-order tensors. We denote an -order tensor as , where is a positive integer. Each element in it is represented as , where .
If tensor is a rank-1 tensor, then it can be written as the outer product of vectors, i.e.,
X=u∘v∘⋅⋅⋅∘t. (5)
Each element of the tensor is the product of the corresponding vector elements which can be represented as:
xi1i2⋅⋅⋅iN=ui1vi2⋅⋅⋅tiN. (6)
The slice of an -order tensor is a matrix defined by fixing every index but two. For instance, the slice of a 3-order tensor has the form: frontal slices , lateral slices , horizontal slices . Meanwhile, each order of a tensor is associated with a ‘mode’ and the unfolding matrix of a tensor in each mode is obtained by unfolding the tensor along its corresponding mode. For example, the mode- unfolding matrix of , denoted as unfold. The inverse operation of the mode- unfolding is the mode- folding, represented as fold. The mode- rank of is defined as the rank of the mode- unfolding matrix rank.
The operation of mode- product of a tensor and a matrix forms a new tensor. Given tensor and matrix , their mode- product is calculated by with element
(X×nU)i1...in−1jnin+1...iN=∑inxi1...in...iNujnin. (7)
Given two same-sized tensors , their inner product is defined as:
⟨X,Y⟩=∑i1∑i2⋅⋅⋅∑iNxi1...iNyi1...iN. (8)
The Frobenius norm is . The norm is to calculate the number of non-zero entries in , and the norm . To be noted, ,, and for any .
## Iii MoG GWLRTF Model
In this section, a generalized weighted low-rank tensor factorization model integrated with MoG (MoG GWLRTF) for modelling complex noise is proposed. By applying MoG to model the noise elements of the input tensor, we obtain the log-likelihood optimization objective.
Firstly, taking the noise part (denoted as ) into consideration, the input tensor can be represented as:
X=L+E, (9)
where denotes the low-rank tensor and the corresponding elementwise form is
xi1i2⋅⋅⋅iN=li1i2⋅⋅⋅iN+εi1i2⋅⋅⋅iN. (10)
As MoG has the ability to universally approximate any hybrids of continuous distributions, it is adopted for modeling the unknown noise in the original data. Hence every follows an MoG and the distribution is defined as:
p(ε)∼K∑k=1πkN(ε|μk,σ2k), (11)
where is the mixing proportion with and . denotes the Gaussian distribution with mean
and variance
.
Therefore, the element in Eq. (10) follows a MoG distribution with mean and variance
. The probability of each element
in the input tensor can be represented as:
p(xi1i2⋅⋅⋅iN|Π,Λ,Σ)=K∑k=1πkN(xi1i2⋅⋅⋅iN|Λk,σ2k), (12)
where . Correspondingly, the likelihood of can be written as
p(X|Π,Λ,Σ)=∏i1i2⋅⋅⋅iN∈ΩK∑k=1πkN(xi1i2⋅⋅⋅iN|Λk,σ2k), (13)
where is the index set of the non-missing entries of .
Our goal is to maximize the logarithmic form of Eq. (13) with respect to the parameters , i.e.
(Π∗,Λ∗,Σ∗)=argmaxΠ,Λ,Σ log p(X|Π,Λ,Σ)=argmaxΠ,Λ,Σ∑i1i2⋅⋅⋅iN∈ΩlogK∑k=1πkN(xi1i2⋅⋅⋅iN|Λk,σ2k). (14)
Note that the original problem can be viewed as a Gaussian Scale Mixtures (GSM) with assumed to be 0, which has been widely used in previous works [36, 37]. Therefore, Eq. (14) can be rewritten as:
(Π∗,L∗,Σ∗)=argmaxΠ,Λ,Σ log p(X|Π,L,Σ)=argmaxΠ,Λ,Σ ∑i1i2⋅⋅⋅iN∈ΩlogK∑k=1πkN(xi1i2⋅⋅⋅iN∣∣li1i2⋅⋅⋅iN,σ2k). (15)
## Iv Algorithms under EM framework
In this section, through assuming a latent variable with higher dimension, we solve the above problem iteratively under the EM framework. We also design algorithms to solve the generalized weighted low-rank tensor factorization model for updating the low-rank tensor.
EM algorithm [38] is proven to be effective for solving the maximization problem of the log-likelihood function. Therefore, for solving Eq. (14), we assume a higher dimensional latent variable under the EM framework.
In the model, the factorized low-rank tensor components are shared by all the clusters of MoG and the mean for each cluster of the standard EM algorithm is represented by them. Thus our proposed algorithm will iterate between computing responsibilities of all Gaussian components (E Step) and maximizing the parameters and the low-rank tensor in the model (M Step).
E Step: A latent variable is assumed in the model, with and , representing the assigned value of the noise to each component of the mixture. Here we denote . The posterior responsibility of the -th mixture for generating the noise of can be calculated by
E(zi1i2⋅⋅⋅iNk)=γi1i2⋅⋅⋅iNk=πkN(xi1i2⋅⋅⋅iN∣∣li1i2⋅⋅⋅iN,σ2k)K∑k=1πkN(xi1i2⋅⋅⋅iN∣∣li1i2⋅⋅⋅iN,σ2k). (16)
The M step maximizes the upper bound given by the E step with regard to :
EZp(X,Z|L,Π,Σ)=∑i1i2⋅⋅⋅iN∈ΩK∑k=1γi1i2⋅⋅⋅iNk(logπk−log√2πσk−(xi1i2⋅⋅⋅iN−li1i2⋅⋅⋅iN)22πσ2k). (17)
This maximization problem can be solved by alternatively updating the MoG parameters and the factorized components of low-rank tensor as follows:
M Step to update : The closed-form updates for the MoG parameters are:
mk=∑i1,i2,⋅⋅⋅,iNγi1i2⋅⋅⋅iNk,πk=mk∑kmk,σ2k=1mk∑i1i2⋅⋅⋅iNγi1i2⋅⋅⋅iNk(xi1i2⋅⋅⋅iN−li1i2⋅⋅⋅iN)2. (18)
M Step to update : Re-write Eq. (17) only with regard to the unknown as follows:
∑i1,i2,⋅⋅⋅,iN∈ΩK∑k=1γi1i2⋅⋅⋅iNk(−(xi1i2⋅⋅⋅iN−li1i2⋅⋅⋅iN)22πσ2k)=−∑i1,i2,⋅⋅⋅,iN∈ΩK∑k=1(γi1i2⋅⋅⋅iNk2πσ2k)(xi1i2⋅⋅⋅iN−li1i2⋅⋅⋅iN)2=−∥W⊙(X−L)∥2LF. (19)
Here denotes the Hadamard product (component-wise multiplication) and the element of is
wi1i2⋅⋅⋅iN=⎧⎪ ⎪⎨⎪ ⎪⎩√K∑k=1γi1i2⋅⋅⋅iNk2πσ2k,i1,i2,⋅⋅⋅,iN∈Ω0,i1,i2,⋅⋅⋅,iN∉Ω. (20)
The whole MoG GWLRTF optimization process is summarized in Algorithm 1.
In the M Step, is evaluated by solving the GWLRTF model . Here, we introduce the two typical factorizations to the GWLRTF and the corresponding algorithms are given in detail in the following parts.
### Iv-a Weighted low-rank tensor CP factorization (GWLRTF-CP)
The GWLRTF model of a 3-order tensor in the form of CP factorization can be written as
minU,V,T∥∥ ∥∥W⊙(X−r∑d=1u:d∘v:d∘t:d)∥∥ ∥∥LF, (21)
where
L=r∑d=1u:d∘v:d∘t:d
and are mode matrices with rank . is the weighted tensor which is composed by the standard variance of the input tensor elements.
Because of the effectiveness and implementation convenience of ALS, we adopt its idea to update of the tensor one at a time.
Suppose are data matrices. In order to stack each of the above matrix as a vector, we define the operator .
For each slice of the higher-order tensor, it can be viewed as a linear combination of the corresponding slices of all the rank-1 tensors. Different from other methods for solving the problem of LRTF, we stack each frontal slice of the higher-order tensor as a vector of a new matrix denoted as . Correspondingly, the vectorized horizontal slices and lateral slices are represented as and , respectively.
Firstly we have
Xweight=W⊙X. (22)
Then taking term as an example, the vectorized frontal slice of the higher-order tensor can be written as follows:
MF=[vec(Xweight::1)|...|vec(Xweight::K)]∈RIJ×K. (23)
For the -th frontal slice of the higher-order tensor, the vectorized corresponding slices of all the rank-1 tensors can be viewed as the -th element of the cell which can be represented as:
Fi=[vec(W::i⊙(uold:1∘vold:1))|...|vec(W::i⊙(uold:r∘vold:r))]∈RIJ×r. (24)
Then the -th vector of term can be updated as follows:
Tnewi:=(F†iMF:i)T∈R1×r, (25)
where represents the pseudo-inverse matrix of matrix , and denotes the transposed matrix of matrix .
Similarly, we have the term and updated as following:
ML=[vec(Xweight:1:)|...|vec(Xweight:J:)]∈RIK×J, (26)
Li=[vec(W:i:⊙(tnew:1∘uold:1))|...|vec(W:i:⊙(tnew:r∘uold:r))]∈RIK×r, (27)
Vnewi:=(L†iML:i)T∈R1×r. (28)
MH=[vec(Xweight1::)|...|vec(XweightI::)]∈RJK×I, (29)
Hi=[vec(Wi::⊙(vnew:1∘tnew:1))|...|vec(Wi::⊙(vnew:r∘tnew:r))]∈RJK×r, (30)
Unewi:=(H†iMH:i)T∈R1×r. (31)
The whole optimization process is summarized in Algorithm 2.
### Iv-B Weighted low-rank tensor Tucker factorization (GWLRTF-Tucker)
By applying the Tucker factorization to the low-rank tensor in the GWLRTF model, we obtain the following GWLRTF-Tucker model
minG,U,V,..,T∥W⊙(X−G×1U×2V⋅⋅⋅×NT)∥LF. (32)
Through coordinate-wisely separating the original optimization problem into solving a sequence of scalar minimization subproblems, coordinate descent has exhibited its effectiveness in dealing with the convex optimization problems [39, 40, 41]. Based on this, we aim to coordinate-wisely optimize each entry of and in Eq. (32).
Update the mode matrices : Firstly, we reformulate Eq. (32) in the form of minimizing the function against only one of the unknown mode matrices (take for example) at a time with others fixed as
∥W⊙(X−D×nH)∥LF, (33)
where
D=G×1U×2V⋅⋅⋅×n−1F×n+1K⋅⋅⋅×NT. (34)
Unfolding the tensors along mode-, it can be reformulated as the following sub-problem
∥∥W(n)⊙(X(n)−HD(n))∥∥LF=∥∥ ∥∥W(n)⊙(X(n)−rn∑j=1h:jdT:j)∥∥ ∥∥LF=∥∥W(n)⊙(E−h:kdT:k)∥∥LF, (35)
where
E=X(n)−∑j≠kh:jdT:j. (36)
Then, the original problem Eq. (32) are separated into the following single-scalar parameter optimization sub-problems
minhik∥wk:⊙(ek:−dk:hik)∥LF=minhik∥wk:⊙ek:−wk:⊙dk:hik∥LF. (37)
Update the core tensor : Likewise, for the equivalent formulation of Eq. (32)
∥∥ ∥∥W⊙(X−r1∑d1=1⋅⋅⋅rN∑dN=1gd1d2⋅⋅⋅dNud1∘vd2∘⋅⋅⋅∘tdN)∥∥ ∥∥LF, (38)
it can be rewritten as
∥∥W⊙(E−gk1...kNU)∥∥LF, (39)
where
E=X−∑d1≠k1,...,dN≠kNgd1d2⋅⋅⋅dNud1∘vd2∘⋅⋅⋅∘tdN,
U=uk1∘vk2∘⋅⋅⋅∘tkN.
Here we denote , , , then the optimization of Eq. (38) can be obtained by minimizing the following sub-problems
mingk1...kN∥∥w⊙(e−ugk1...kN)∥∥LF=mingk1...kN∥∥w⊙e−w⊙ugk1...kN)∥∥LF. (40)
The solutions of Eqs. (37) and (40) can be exactly obtained by ALS. The whole optimization process is summarized in Algorithm 3.
## V Experiments
In this section, we conduct extensive experiments on both synthetic data and real applications to validate the effectiveness of the proposed MoG GWLRTF, compared with MoG LRMF [33], HaLRTC [8], LRTA [42], PARAFAC [43], MSI DL [44], CWM LRTF [39]. Specifically, MoG GWLRTF-Tucker and MoG GWLRTF-CP are also demonstrated to further compare the performance of CP factorization and Tucker factorization in different applications. The synthetic experiments are designed to quantitatively assess our methods from: i) predictive performance over missing entries given an incomplete tensor data; ii) reconstruction performance given a both incomplete and noisy tensor data. Real data applications, i.e., single RGB image reconstruction, face modeling, multispectral image recovery and real hyperspectral image restoration, are further conducted to validate the effectiveness of the proposed algorithms.
### V-a Synthetic Experiments
The synthetic tensor is generated as follows: firstly, matrices
are drawn from a standard normal distribution, i.e.,
, the vectors of the matrices comply with a standard normal distribution ; Secondly, construct the true tensor by , and set the size to and CP rank . Then we conduct two synthetic experiments: i) for validating the predictive performance, we vary the true tensor missing entries rate (, , ) ; ii) for verifying the reconstruction performance, we randomly choose missing entries of the true tensor and further add certain type of noise to it as the following procedure: (1) Gaussian noise ; (2) Sparse noise:
of the non-missing entries with the uniformly distribution over [-5,5]; (3) Mixture noise:
of the non-missing elements with the uniformly distribution over [-5,5], and of the rest non-missing with Gaussian noise and the rest with . The performance of each method is quantitatively assessed by the following measurements as used in [33]:
E1=∥W⊙(Xno−Xrec)∥L1,E2=∥W⊙(Xno−Xrec)∥L2,E3=∥Xgt−Xrec∥L1,E4=∥Xgt−Xrec∥L2,
where and are used to denote the noisy tensor and the recovered tensor, respectively. As mentioned in [33], and are the optimization objectives of existing methods, which assess how the reconstruction complies with the noisy input, but and are more meaningful for evaluating the correctness of the clean subspace recoveries. Therefore, we pay more attention to the quantitative indices of and . In the tables, the first and second best performances are marked out with bold and underline, respectively.
The performance of each method in the synthetic experiments are summarized in Table I and Table II, respectively. From Table I we can see that, in the case of varying data missing rate, our methods always have a relative better predictive performance in all evaluation terms. When the data is only disturbed by a single distribution noise, i.e., Gaussian noise or sparse noise, other methods can also obtain a fairly well results. However, when the noise becomes complex, our methods still have a good reconstruction performance in this case, as shown in Table II.
### V-B Single RGB Image Reconstruction
The benchmark colorful building facade image is used in this section to evaluate the performance of different methods in image reconstruction. Note that the colorful image can be viewed as a 3-order tensor of size . Two groups of experiments are considered here.
Firstly, the facade image rescaled to [0,255] is randomly sampled with missing entries and then added with a relative small scale mixture noise: of the non-missing pixels with the uniformly distribution over [-35,35], of the rest non-missing pixels with Gaussian noise and the rest with another uniformly distribution .
The visual effect of each methods are demonstrated in Figure 2. For better visual comparison, we have also provided a zoom-in version of a local region in Figure 2. From the results we can see that the MoG GWLRTF-Tucker method has a better reconstruction performance than the matrix based methods and the traditional tensor based methods in reconstructing the image details.
Besides the visual effect, quantitative assessments are also reported. Three quantitative image quality indices are adopted to evaluate the performance of each method: peak signal-to-noise ratio (PSNR), relative standard error (RSE) and feature similarity (FSIM)
[45]. Larger values of PSNR and FSIM and smaller values of RSE mean a better restoration results.
The quantitative results obtained by each method are given in Table III (the upper row), and it shows that the MoG GWLRTF-Tucker method is superior to all the other methods except the MoG GWLRTF-CP method which performs nearly as well in this small scale mixture noise case.
Secondly, in order to further compare the reconstruction ability of each method, we add a larger mixture noise to the facade image. The image is first rescaled to [0,1] and then a larger mixture noise added as in the synthetic experiments: missing entries, of the non-missing pixels with the uniformly distribution over [-5,5], of the rest non-missing pixels with Gaussian noise and the rest with another uniformly distribution .
Both the visual and the quantitative results are provided, as in Figure 3 and Table III (the lower row). In Figure 3, the zoom-in version of a local region for comparison is given. From the results, we can see that with the increasing of the mixture noise scale, the MoG GWLRTF-Tucker method performs much better than the MoG GWLRTF-CP method in reconstructing the image details. And they are both superior to the other methods which lose a lot of image structure information.
### V-C Face Modeling
In this section, we assess the effectiveness of the proposed methods in face modeling with different objects under different illuminations. It is different from the traditional methods in dealing with face modeling problem which always only focus on one kind of object under different illuminations. The dataset is the ensemble subset of the Extended Yale B database [46], containing 45 faces of 5 objects and illuminations with size . The original tensor is thus generated with size . All the competing methods used above are also compared here. Considering that some tensor methods are only designed to dealing with 3-order tensors and the matrix methods are originally designed to solve matrix data, in this case the original 4-order tensor is vectorized into the 3-order tensor with size and matrix data with size before processing, respectively. The sampling images from this data subset are plotted in Figure 4.
Typical | 2021-08-05 13:15:32 | {"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": 0.8823984861373901, "perplexity": 1064.8607594222185}, "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/1627046155925.8/warc/CC-MAIN-20210805130514-20210805160514-00001.warc.gz"} |
http://w3.uwyo.edu/~blockwoo/ForKlib/krigingfuncpredictGEK_8f90.html | ForK Library
# krigingfuncpredictGEK.f90 File Reference
Subroutine to Predict mean function values from Gradient-Enhanced Kriging Surface (requires buildkrigingGEK to be called first) More...
Go to the source code of this file.
## Functions/Subroutines
subroutine krigingfuncpredictGEK (ndim, ntot, X, gtot, pts, dims, stot, H, beta, V, hyper, mtot, Xm, Hm, Ym, covarflagi)
This subroutine is used to predict function values from a Gradient-enhanced Kriging model (built using buildkrigingGEK). The details of predicting function values from a Kriging model are detailed in the krigingfuncpredict documentation. To make predictions from a gradient-enhanced Kriging model, the covariance matrix and training data must be redefined. Using a regression mean function, the mean function predictions at a test point are given as:
## Detailed Description
Subroutine to Predict mean function values from Gradient-Enhanced Kriging Surface (requires buildkrigingGEK to be called first)
Definition in file krigingfuncpredictGEK.f90.
## Function Documentation
subroutine krigingfuncpredictGEK ( integer,intent(in) ndim, integer,intent(in) ntot, real(8),dimension(ndim,ntot),intent(in) X, integer,intent(in) gtot, integer,dimension(gtot),intent(in) pts, integer,dimension(gtot),intent(in) dims, integer,intent(in) stot, real(8),dimension(stot,ntot+gtot),intent(in) H, real(8),dimension(stot),intent(in) Beta, real(8),dimension(ntot+gtot),intent(in) V, real(8),dimension(ndim+3),intent(in) hyper, integer,intent(in) mtot, real(8),dimension(ndim,mtot),intent(in) Xm, real(8),dimension(stot,mtot),intent(in) Hm, real(8),dimension(mtot),intent(out) Ym, integer,intent(in) covarflagi )
This subroutine is used to predict function values from a Gradient-enhanced Kriging model (built using buildkrigingGEK). The details of predicting function values from a Kriging model are detailed in the krigingfuncpredict documentation. To make predictions from a gradient-enhanced Kriging model, the covariance matrix and training data must be redefined. Using a regression mean function, the mean function predictions at a test point are given as:
$y(\vec{x}_{*}) | \vec{X},Y,m(x) = h^{T}(\vec{x}_{*}) \beta + \underline{k}_*^T K^{-1} (\underline{Y}-\underline{H}^{T} \beta)$
where the covariance matrix between test and training points has been redefined to include the correlation between derivative values. Additionally, the collocation matrix and training data are extend to include derivative values. The extension of the collocation matrix and training data for derivative values are found in buildkrigingGEK. The covariance matrix between training data included derivative values is given as:
$\underline{K} = \left[ \begin{array}{cc} cov(Y,Y) & cov(Y,\delta Y) \\ cov(\delta Y,Y) & cov(\delta Y,\delta Y) \end{array} \right]$
where $$cov(Y,Y)$$ is the covariance matrix between function values (same as the covariance matrix used in a function-only model), $$cov(\delta Y, Y)$$ is a rectangular matrix whose elements represent the covariance between the function values and derivative values at the training points and $$cov(\delta Y, \delta Y)$$ represents the covariance between derivative observations. The details of this matrix are also found in buildkrigingGEK. Finally, the covariance between the test points and training points must be extended to include derivatives (denoted as $$\underline{k}_*^T$$). To include derivatives, this covariance is a rectangular block matrix defined as: where $$cov(y^{*}, Y)$$ is a matrix (size = [mtot ntot] where mtot is the number of test points and ntot is the number of training points) whose elements represent the covariance between test function values and training function values. The elements of matrix $$cov(y^{*}, \delta Y)$$ (size = [mtot gtot] where gtot is the total number of derivative values in the training set) represent the covariance between test function values and training derivative values. The subroutine buildkrigingGEK produces a vector of processed data defined as:
$\underline{V} = \underline{K}^{-1} \left( \underline{Y} - \underline{H}^{T} \beta \right)$
Using this definition, function predictions can be calculated inexpensively using the formula:
$y(\vec{x}_{*}) | \vec{X},Y,m(x) = h^{T}(\vec{x}_{*}) \beta + \underline{k}_*^T \underline{V}$
Because the covariance matrix between training data requires the second derivative of the covariance function, the Matern function with $$\nu \geq 3/2$$ must be used for constructing and making predictions from the Gradient-enhanced Kriging model.
Date:
May 2, 2012
Parameters:
in) ndim : The dimension of the problem in) ntot : The number of Training points in) X : The location of the training points (size=[ndimxntot]) in) gtot: Number of derivative values included in training data (ndim*ntot if all derivatives are included at the training points) in) pts: List identifying what point the derivative value is enforced at (size=[gtot] with values ranging from 1 to ntot) in) dims: List identifying the dimension the derivative is taken with respect to (size=[gtot] with values ranging from 1 to ndim) in) stot : Number of Terms in the regression in) H: The collocation matrix for the regression including derivative values. (size=[stotxntot+gtot]) Columns 1:ntot are the basis evaluated at the training points Columns ntot+1:ntot+gtot are the derivative of the basis evaluated at the training points in) beta: Regression coefficients based on the optimal estimate for the Kriging model (size=[stot]) Supplied by buildkrigingGEK subroutine in) V: Processed Training Data (size=[ntot+gtot]) Supplied by buildkrigingGEK subroutine in) hyper: Hyperparameters for the Kriging Model (size=[ndim+3]) Supplied by buildkrigingGEK subroutine in) mtot : The number of test points, the places where function prediction are desired in) Xm : The location of the test points (size=[ndimxmtot]) in) Hm : The collocation matrix evaluated at the test points. The derivative of the basis is NOT required for the test points to predict function values (size=[stotxmtot]) out) Ym: The predicted function values (size=[mtot]) Using the processed data V, predicting function values is essentially linear with respect to the number of test points so mtot can be set to one and this subroutine can be called multiple times. Often the function values at a set of test points is required, hence the ability to make the predictions in a single function call. in) covarflagi: Flag to govern which covariance function is used covarflag==1 Uses Matern function with $$\nu=3/2$$ covarflag==2 Uses Matern function with $$\nu=5/2$$ The parameter $$\nu$$ governs the smoothness and differentiability of the covariance function. When using gradient values, $$\nu=1/2$$ is not differentiable enough so $$\nu \geq 3/2$$ must be used Must supply the same covariance flag as used in buildkrigingGEK.
Definition at line 78 of file krigingfuncpredictGEK.f90.
References covars::covarflag. | 2021-06-21 12:53:51 | {"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": 0.6821485757827759, "perplexity": 2182.8656885370738}, "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/1623488273983.63/warc/CC-MAIN-20210621120456-20210621150456-00233.warc.gz"} |
https://cvgmt.sns.it/paper/5031/ | ## $\Gamma$-convergence and stochastic homogenisation of singularly-perturbed elliptic functionals
created by zeppieri1 on 10 Feb 2021
modified on 18 Feb 2021
[BibTeX]
Preprint
Inserted: 10 feb 2021
Last Updated: 18 feb 2021
Year: 2021
Abstract:
We study the limit behaviour of singularly-perturbed elliptic functionals of the form $F_k(u,v)=\int_A v^2\,f_k(x,\nabla u)dx+\frac{1}{\varepsilon_k}\int_A g_k(x,v,\varepsilon_k\nabla v)dx\,,$ where $u$ is a vector-valued Sobolev function, $v \in [0,1]$ a phase-field variable, and $\varepsilon_k>0$ a singular-perturbation parameter, i.e., $\varepsilon_k \to 0$, as $k\to +\infty$.
Under mild assumptions on the integrands $f_k$ and $g_k$, we show that if $f_k$ grows superlinearly in the gradient-variable, then the functionals $F_k$ $\Gamma$-converge (up to subsequences) to a brittle energy-functional, i.e., to a free-discontinuity functional whose surface integrand does not depend on the jump-amplitude of $u$. This result is achieved by providing explicit asymptotic formulas for bulk and surface integrands which show, in particular, that the volume and surface term in $F_k$ decouple in the limit.
The abstract $\Gamma$-convergence analysis is complemented by a stochastic homogenisation result for stationary random integrands. | 2022-09-29 12:19:41 | {"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": 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": 0.8630689382553101, "perplexity": 1022.6907412079347}, "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/1664030335350.36/warc/CC-MAIN-20220929100506-20220929130506-00584.warc.gz"} |
https://techutils.in/blog/tag/model/ | ## #StackBounty: #self-study #maximum-likelihood #least-squares #model #loss-functions OLS Loss Function – MLE assumptions?
### Bounty: 50
What are the model assumptions necessary for p(y|x,w) in order for the MLE estimate to provide the OLS loss function?
I know that MLE applied to linear regression gives OLS, I’m just not sure what assumptions, if any, must hold for this to be the case.
Get this bounty!!!
## #StackBounty: #distributions #logistic #normal-distribution #pdf #model Relationship between a logistic decision function and Gaussian …
### Bounty: 50
Imagine an experiment, in which an observer has to discriminate between two stimulus categories at different contrast levels $$|x|$$. As $$|x|$$ becomes lower, the observer will be more prone to making perceptual mistakes. The stimulus category is coded in the sign of $$x$$. I’m interested in the relationship between two different ways of modeling the observer’s "perceptual noise" based on their choices in a series of stimulus presentations.
The first way would be to fit a logistic function
$$p_1(x) = frac{1}{1+e^{-betacdot x}}$$
where $$p_1(x)$$ is the probability to choose the stimulus category with positive signs ($$S^+$$). Here, $$beta$$ would reflect the degree of perceptual noise.
A second way would be to assume that the observer has Gaussian Noise $$mathcal{N}(0,sigma)$$ around each observation of $$x$$ and then compute the probability to choose $$S^+$$ by means of the cumulative probability density function as follows:
$$p_2(x) = frac{1}{sigmasqrt{2pi}}intlimits_{z=0}^{infty}e^{-frac{(z-x)^2}{2sigma^2}}$$
In this case, $$sigma$$ would be an estimate of the perceptual noise.
I have a hunch that both these approaches are intimately related, but I’m not sure how. Is it an underlying assumption of the logistic function that the noise is normally distributed? Is there a formula that describes the relationship between $$beta$$ of $$p_1(x)$$ and $$sigma$$ of $$p_2(x)$$? Are, in the end, $$p_1(x)$$ and $$p_2(x)$$ essentially identical and could $$p_1$$ be derived from $$p_2$$?
Get this bounty!!!
## #StackBounty: #confidence-interval #p-value #model #model-comparison p value for difference in model outcomes
### Bounty: 50
I’ve run two different linear mixed effects models on the same data and got two different estimates for the gradient of the longitudinal variable. e.g.
model 1 has estimate 30 with standard error 5.
model 2 has estimate 40 with standard error 4.
I’m interested in calculating a p value for the probability that the models are different, from the estimate and standard error. How do I do this? I’m aware that checking for overlap in the 95% confidence intervals is a bad idea, and that overlapping 83% CIs are a better test, but would like to be able to quantify this with a p value.
Get this bounty!!!
## #StackBounty: #classification #model #group-differences #supervised-learning A method to separate classes while taking variable depende…
### Bounty: 100
I have posted a question related to this problem over a year ago and we still were not able to figure this out.
We have two groups, A and B that we want to train on to separate them. Both have numerous observations of “text” so for example:
group A:
• AAABBBC*CAAAAAAAC
• CCCBBBC*CAAAAAAAB
• CBBBBBC*CAAAAAAAB
group B:
• AAACCCC*CAAAAAAAA
• CCCCCCC*CAAAAAAAA
• CBBCCCC*CAAAAAAAA
Notably, our original datasets are much larger, with around 4,000 observations for A (with really specific patterns) and around 20,000 for group B.
We want is a model that sees things like:
• if there is a `C` at position 1 we see a `B` on the end in group A (2/3), and we do not see this in group B (0/3)
• That we only find the motif `AAABBB` in group A
• if we see `AAABBB` we also saw a `C` at the end in group A (1/3) but we did not see this in group B (0/3)
We tried LDA now (after converting this data to binary vectors), however, this would score each letter independently. To illustrate if group A would have two subgroups:
• `sub1`: position1 = A + position10 = C
• `sub2`: position2 = A + position15 = B
and both are not common in group B then a method like LDA would also score position1 = A (`sub1`) + position15 = B (`sub2`) extremely high even tho they are actually part of different dependencies within group A, so we are looking for an alternative taking care of such dependencies when differentiating groups.
We really hope someone here can help us out!
Get this bounty!!!
## #StackBounty: #c# #.net #asp.net-mvc #model Build a Layout ViewModel based in a Id from the URL with MVC
### Bounty: 50
I need to build a ViewModel for my Layout’s Web Application, I have tried this solution but it’s not based on a URL’s Id coming from the URL to generate the Layout’s ViewModel.
I tried this but I first had the not existing empty controller error, then I tried to include the id as a parameter but I get the error “Object reference not set to an instance of an object.” because the LayoutColorRGB is not set.
``````public MobileController(int id)
{
Event model = db.Events.Where(s => s.Id == id).FirstOrDefault();
LayoutVM = new LayoutVM()
{
EventId = model.Id,
LayoutColorRGB = model.LayoutColorRGB,
};
ViewData["LayoutVM"] = LayoutVM;
}
``````
Get this bounty!!!
## #StackBounty: #dataset #model #computer-vision #object-detection What would be the ideal dataset to train a model to detect advertiseme…
### Bounty: 100
I am thinking of the requirements for training a model that would be able to detect if there is any kind of ad in an image.
I know that this sound too broad not just for a question on CV but for the model itself.
There are numerous problems like:
• The fact that ads can also contain pictures apart from plain text, which apparently will display some objects.
• Also the fact that in most cases are part of other objects, for example the frontpage of a magazine, the picture of a tv for a given moment, the contents of a billboard, a leaflet on the front windshield of a car, etc…
Still I’d like to make an attempt, so I am thinking what should be the ideal dataset to train a model for this task.
What I’ve come up with is to use a dataset of company logos and train a model to detect logos in picture.
Yet this strategy would eventually lead to more problems like
• The false positive due to the fact that company logos exist also on the products sold apart from the product advertisements. This particular problem could be solved if there was a way to configuring the model to mark an object(a logo in this case) only if it occupied a portion of the picture larger than X%, since for example a logo on a car is relatively small compared to the car in contrast to the proportions of a car and a company logo in a magazine advertisement.
So, any ideas on which criteria should I take into consideration to create a useful dataset for this task are welcome.
Get this bounty!!!
## #StackBounty: #r #model #fitting #splines #derivative How can I fit a spline to data that contains values and 1st/2nd derivitives?
### Bounty: 50
I have a dataset that contains let’s say some mesurements for position, speed and acciliration. All come from the same “run”. I could construct a linear system and fit a polynome to all of those measurements.
But can I do the same with splines? What is an ‘R’ way of doing this?
Here is some simulated data I would like to fit:
``````f <- function(x) 2+x-0.5*x^2+rnorm(length(x), mean=0, sd=0.1)
df <- function(x) 1-x+rnorm(length(x), mean=0, sd=0.3)
ddf <- function(x) -1+rnorm(length(x), mean=0, sd=0.6)
x_f <- runif(5, 0, 5)
x_df <- runif(8, 3, 8)
x_ddf <- runif(10, 4, 9)
data <- data.frame(type=rep('f'), x=x_f, y=f(x_f))
data <- rbind(data, data.frame(type=rep('df'), x=x_df, y=df(x_df)))
data <- rbind(data, data.frame(type=rep('ddf'), x=x_ddf, y=ddf(x_ddf)))
library(ggplot2)
ggplot(data, aes(x, y, color=type)) + geom_point()
library(splines)
m <- lm(data$$y ~ bs(data$$x, degree=6)) # but I want to fit on f, df, ddf. possible?
``````
Get this bounty!!!
## #StackBounty: #regression #model #singular Problematic data for regression model
### Bounty: 50
This is a follow-up question to Which model for my data? (testing the differences in slope for three groups).
The solution from there works (big thanks to Heteroskedastic Jim!), but I have a problem with a specific data set. Maybe someone can enlighten me why I get stuck.
Here is an example that works:
``````library(nlme)
library(emmeans)
Input = ("
Group Time Size
A 1 1.08152
A 2 1.10589
A 3 1.13292
B 1 1.04597
B 2 1.05763
B 3 1.07023
B 4 1.08612
B 5 1.10059
B 6 1.11589
B 7 1.13143
B 8 1.14741
B 9 1.16721
B 10 1.18288
C 1 1.04777
C 2 1.06145
C 3 1.07484
C 4 1.08908
C 5 1.10346
C 6 1.11866
C 7 1.13375
C 8 1.14931
C 9 1.16563
C 10 1.18294
")
``````
This constructs the model:
``````(m1 <- gls(Size ~ Time * Group, dat, correlation = corAR1(form = ~ Time | Group), weights = varIdent(form = ~ 1 | I(Group == "A"))))
``````
And this provides me with the p-values for slope differences:
``````pairs(emtrends(m1, ~ Group, var = "Time", df = Inf, options = get_emm_option("emmeans")))
``````
Now the data set where I get stuck:
``````Input = ("
Group Time Size
A 1 1.6210
A 2 2.1118
A 3 2.6026
A 4 3.0934
B 1 0.9162
B 2 1.2122
B 3 1.5082
B 4 1.8042
B 5 2.1002
B 6 2.3962
B 7 2.6922
B 8 2.9882
B 9 3.2842
B 10 3.5802
C 1 0.82701
C 2 1.13441
C 3 1.44181
C 4 1.74921
C 5 2.05661
C 6 2.36401
C 7 2.67141
C 8 2.97881
C 9 3.28621
C 10 3.59361
")
``````
When I construct the above model with this specific data
``````(m1 <- gls(Size ~ Time * Group, dat, correlation = corAR1(form = ~ Time | Group), weights = varIdent(form = ~ 1 | I(Group == "A"))))
``````
I get this error message:
``````Error in glsEstimate(object, control = control) : computed "gls" fit is singular, rank 6
``````
I have tried analyzing the data in SPSS, but I also got stuck there.
So my question is: where is the problem with my data and what can I do to solve it?
Get this bounty!!!
## #StackBounty: #machine-learning #model #model-evaluation #validation Relation between uplift and model performance
### Bounty: 50
I am trying to compute the uplift for some campaign. For the same I am building model/models. I need to know how much individual model performance should impact my uplift computation? Is there any relation between the two?
In simple words, if x percentage of error occurs in model predictions what percentage of error it will reflect in uplift computation?
Get this bounty!!!
## #StackBounty: #hypothesis-testing #model-selection #dataset #model #error How often can a fixed test data be used to evaluate a class o…
### Bounty: 50
Suppose I have a fixed training data set $$D$$ and a fixed test data set $$F$$ and suppose I have an infinite class of models (for example, for simplicity, indexed by a hyperparameter) that can be trained on data.
If I keep training models using $$D$$ and then evaluate their performance on $$F$$, in order to find better and better models, won’t I “illegally” incorporate knowledge from the test data set into my model, since I effectively use the test data set to build a model, instead of only evaluating its generalization performance?
I have a vague feeling I should not use the test data set “too often” (whatever “too often” might mean).
(To make my somewhat vague question concrete, one could imagine the model class to consist of neural networks for binary classification of, say, and each neural network to have different architecture. $$D$$ and $$F$$ are large sets of labelled images of flowers of type “A” and type “B” and the loss function is the $$ell_2$$ norm.)
Get this bounty!!! | 2021-05-17 01:04:53 | {"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": 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": 28, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6125503182411194, "perplexity": 2154.1014531416445}, "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/1620243991921.61/warc/CC-MAIN-20210516232554-20210517022554-00545.warc.gz"} |
http://crad.ict.ac.cn/CN/abstract/abstract3418.shtml | ISSN 1000-1239 CN 11-1777/TP
• 软件技术 •
### 基于协作相容性的工作流任务分配优化方法
1. 1(杭州电子科技大学计算机学院 杭州 310018); 2(复杂系统建模与仿真教育部重点实验室(杭州电子科技大学) 杭州 310018); 3(计算机软件新技术国家重点实验室(南京大学) 南京 210046) (huhaiyang@hdu.edu.cn)
• 出版日期: 2017-04-01
• 基金资助:
国家自然科学基金项目(61572162，61272188，61572251)；浙江省哲学社会科学重点研究基地项目(14JDXX04YB)；江苏省自科学基金项目(BK20131277)；中央高校基本科研业务费专项资金项目(021714380004)；南京大学计算机软件新技术国家重点实验室开放基金项目(KFKT2014B15);南京大学计算机软件新技术国家重点实验室创新项目(ZZKT2013B14)
### Method for Optimizing Task Allocation in Workflow System Based on Cooperative Compatibility
Hu Haiyang1,2,3, Ji Chaopei1, Hu Hua1,2, Ge Jidong3
1. 1(College of Computer Science, Hangzhou Dianzi University, Hangzhou 310018 ); 2(Key Laboratory of Complex Systems Modeling and Simulation (Hangzhou Dianzi University), Ministry of Education, Hangzhou 310018); 3(State Key Laboratory for Novel Software Technology (Nanjing University), Nanjing 210046)
• Online: 2017-04-01
Abstract: Task allocation strategy has an important influence on the performance efficiency of workflow system. When allocating tasks among executors, it needs to consider both the capability of each executor and the cooperative compatibility between the executors. Traditional methods for assigning tasks usually only consider the technical skills of executors and ignore the social cooperation compatibility among the executors. Although a few of research works have considered the social cooperation compatibility, they fail to consider how to maintain load balancing among executors when allocating the tasks. Based on the workflow log, cooperative compatibilities among executors are modeled and computed. The relations of interaction tasks are also taken into account. By analyzing the current workload of each executor, a multi-objective joint optimization framework for maintaining load balancing and maximizing the cooperative compatibility among executors is proposed. In this framework, when a new task is assigned, the current workload of each executor that can perform this task will be analyzed and its cooperation capability to other executors that have been assigned those tasks having interactions with this new task will be computed. Several corresponding algorithms are designed for optimizing different objectives and their time complexity is analyzed. Extensive experiments are conducted for comparing the proposed methods which demonstrate the correctness and effectiveness of our approaches. | 2021-02-27 16:40:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43748313188552856, "perplexity": 5420.754285822868}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178358976.37/warc/CC-MAIN-20210227144626-20210227174626-00506.warc.gz"} |
https://psychology.stackexchange.com/tags/personality/hot?filter=all | # Tag Info
14
Facial shape Aggression relates to facial width-to-height ratio (Carré, McCormick, & Mondloch, 2009; Carré & McCormick, 2008). The width-to-height ratio is the distance between the left and right zygion (the outside of the cheek bone) divided by the distance between the top of the upper lip and the mid-brow. Here's a useful image displaying the ...
13
The IPIP may provide what you are looking for. This IPIP Website is intended to provide rapid access to measures of individual differences, all in the public domain, to be developed conjointly among scientists worldwide. In general, the scientific literature tends to focus more on a dimensional approach based on the Big 5 model of personality than ...
12
Digman (1997) performed higher order factor analysis on several Big 5 intercorrelation matrices and proposed that the Big 5 could be partially explained in terms of two higher order factors: Alpha (Agreeableness, Conscientiousness, Emotional Stability) and Beta (Extraversion, Openness). Musek (2007) presented evidence for a Big 1 factor of personality. ...
11
What you may be interested are personality traits caught by some statistical correlations, rather than 'manually' merged by an author's intuition. One of such tools is 16 Personality Factors. The 16 Personality Factors, measured by the 16PF Questionnaire, were derived using factor-analysis by psychologist Raymond Cattell. This article summarizes the ...
11
I was alerted to your post here and would like to respond to a non-technical side of the question. I'm an Intellectual Property Assistant for CPP, Inc., publisher of the MBTI® assessment tool. I help protect the instrument's trademarks and copyrights, and ensure ethical use of the instrument. The names MBTI®, Myers-Briggs®, and Myers-Briggs Type Indicator®...
11
A useful model for topics like this comes from McCrae and Costa (1999): There's quite a lot more going on here than is pertinent to your question, but note that influences originate from biological bases on the top left, and from external influences on the upper right. Everything else is modeled as an effect of mediated, dynamic processes between these two.....
11
The MBTI can be considered to be subsumed by the Big5/Five-Factor Model. McCrae and Costa examined this back in the late 1980’s. First of all, they showed that the types do not interact in a statistically meaningful way indicating that there isn’t a reason to interpret four type categories (e.g., ESTJ vs INFP). The categories (e.g., extraversion vs ...
10
Yes, there are benefits, but I don't think it requires long-term switches. Studies have used this as a manipulation to try and increase self control and have found that it decrease aggression. Based on this, once one has mastered using the non-dominant hand, it seems like the benefit of continuing to use that hand might be over (as it no longer requires ...
9
Do personality tests predict job performance in general? There is a large academic literature correlating personality test scores with job performance. You might want to check out the meta-analysis by Barrick et al (2001). It reports the meta-analytic correlations often based on hundreds of studies between Big 5 personality test scores and job performance. ...
9
Inheritability of facial features Let's start with the origin of specific facial features. Below is a table which shows averaged heritabilities for a range of facial quantitative traits from a large number of studies, from the review by Kohn (1991): where $h^2$ is the narrow-sense heritability. You can clearly see that heritability in the majority of the ...
9
There's one condition that is linked to negative cognitive effects after masturbation in a small subset of population, it is called Post Orgasmic Illness Syndrome (POIS): The sufferer experiences mental symptoms, physical symptoms, or both. Common mental symptoms include cognitive dysfunction, intense discomfort, irritability, anxiety, craving for ...
9
You are quite astute to have noticed the difference between your stated preferences and actual preferences - most people don't. Yes, there has been a fair bit of research on prediction techniques and their effectiveness. In 2008, in a study by Paul Eastwick and Eli Finkel, participants were asked to predict their romantic preferences - what they found ...
9
I've been commenting a lot and not answering for quite some time now! My hesitation was largely due to the terms "unfailingly", the mixture of "altruism" and "non-cruelty", and having forgotten my intention to answer. My answer certainly won't be foolproof (haven't yet heard of a trait model that is), and I may not cover both altruism and non-cruelty, but ...
8
The MBTI is based on Carl Jung's work with psychological types. However, Jung's work led to the formation of analytic psychology. This work is often associated with clinical observations and anecdotes instead of controlled scientific study. This means that Jung didn't carry out research that can be considered conclusive and scientifically validated. However, ...
8
I'm not entirely sure what you mean by "renounce," but you may find some answers to your question in the fields of social psychology and behavioral economics. The first part of your question describes someone who is unwilling to commit or make a decision for fear of losing out on future opportunities. There has been research to indicate that having more ...
8
Anybody with enough will and persistence can find support for almost any viewpoint they desire concerning autism, depending especially on (lower) quality of source material. However, if you read enough, consistent patterns will emerge in the literature. This issue of Dialogues in Clinical Neuroscience is all about autism. Although all of it is valuable, I ...
8
'Mental Illness' covers such a broad range of illnesses that it would be very difficult to answer your question. However, general consensus is that: people who are receiving an effective treatment for a mental illness are no more violent or dangerous than neurotypical/ 'healthy' people. People with a mental illness are more likely to harm themselves or to ...
7
Backstrom et al (2009) have a paper devoted to the question of whether the intercorrelations between the Big 5 scales is due to social desirability bias or substantive factors. In Study 2 they re-wrote each item on a 100 item IPIP scale so that each item had reduced positive bias. They then administered the original and neutrally worded items to a sample of ...
7
I am using TRUE (http://www.salleurl.edu/tsenyal/true/features.html) and SAM (Self-Assessment Manikin) interface includes a scale for dominance, along with valence and activation. The scale allows you to rate dominance from 'controlled' to 'in control' on a scale from 1 to 9. References Planet, S., Iriondo, I., Martínez, E., & Montero, J. A. (2008). ...
7
This is an extremely interesting question. I'm going to take a different approach to the question by focusing on both personality traits and leadership theories (e.g. authentic leadership, transformational leadership, servant leadership etc) to answer whether those two distinct areas can influence leaders' children's development. I will admit that I didn't ...
7
This is a primary subject of study in game studies and ludology, which are domains of theory and research unto themselves. Moreover, the question as it pertains to games might be interesting to ask over on Arqade, though I can't guarantee it would be "on topic" enough for their community. You might find the following questions from Arqade interesting, as ...
7
Perhaps check out the Obsessive Beliefs Questionnaire which is designed to measures dysfunctional beliefs related to OCD. There are several papers that examine the factor structure, and perfectionism is typically seen as one of the major aspects of obsessive beliefs. However, it seems to be a particular form of maladaptive perfectionism. See these ...
7
I've edited your question somewhat; I hope I preserved its meaning. Neuroticism relates to personal discomfort largely by definition, and probably to uncomfortable social interaction as well, though somewhat less by definition. Consider this hypothetical, mediated pathway: Neuroticism $\rightarrow$ Anxiety $\rightarrow$ Social anxiety $\rightarrow$ ...
7
Cool question...really huge though. I'll have to revisit this as I find time to add more. For starters, I just saw an interesting link in @ForbiddenOverseer's question, "Are there any personality theories that use the scientific method?" For some info on cerebral blood flow and extraversion, check out Johnson and colleagues (1999). Here's an excerpt of the ...
Only top voted, non community-wiki answers of a minimum length are eligible | 2020-09-26 00:17:42 | {"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": 0.459203839302063, "perplexity": 2331.9294701382096}, "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/1600400228998.45/warc/CC-MAIN-20200925213517-20200926003517-00543.warc.gz"} |
https://learn.careers360.com/ncert/question-find-x-and-y-if-ii-2x-plus-3y-equals-2-3-4-0-and-3x-plus-2y-equals-2-minus-2-minus-1-5-2/ | # Q7. Find X and Y, if (ii) and
(ii) and
Multiply equation 1 by 3 and equation 2 by 2 and subtract them,
Putting value of Y in equation 1 , we get
## Related Chapters
### Preparation Products
##### JEE Main Rank Booster 2021
This course will help student to be better prepared and study in the right direction for JEE Main..
₹ 13999/- ₹ 9999/-
##### Rank Booster NEET 2021
This course will help student to be better prepared and study in the right direction for NEET..
₹ 13999/- ₹ 9999/-
##### Knockout JEE Main April 2021 (Easy Installments)
An exhaustive E-learning program for the complete preparation of JEE Main..
₹ 4999/-
##### Knockout NEET May 2021
An exhaustive E-learning program for the complete preparation of NEET..
₹ 22999/- ₹ 14999/- | 2020-10-24 06:19:53 | {"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": 0.8668591380119324, "perplexity": 13454.833899901969}, "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-2020-45/segments/1603107882102.31/warc/CC-MAIN-20201024051926-20201024081926-00696.warc.gz"} |
https://crypto.stackexchange.com/questions/31388/zero-knowledge-proof-of-a-polynomial | Zero-Knowledge Proof of a polynomial
I have two secret values $L_1$, $L_2$, and two Pedersen commitments $C_1 = C(L_1)$, $C_2=C(L_2)$. The commitments $C_1$, $C_2$ are public. Given a challenge $c$, I want to output $d = c*L_1+L_2$ and prove in zero-knowledge that $d$ is formed correctly. What should the zero-knowledge proof look like?
• What do the commitments look like? – user991 Dec 18 '15 at 22:47
• Pedersen Commitment: C(x) = g^xh^r – Hongyang Dec 19 '15 at 4:33
• @Hongyang The value $c$ is secret? – DrLecter Dec 19 '15 at 6:51
• Challenge is something sent by Verifier to Prover while interactive proof, so $c$ probably is something else. – Vadym Fedyukovych Dec 19 '15 at 10:25
• @DrLecter the challenge c is generated by the verifier and is public. – Hongyang Dec 19 '15 at 14:20
Consider a multiplicative group of an order $q$ generated by some $g$. For simplicity, let commitment be $C_1 = g^{L_1}$. Consider a proof of knowledge of $L_1$ committed to at $C_1$. At the first step of an interactive proof, choose some $L_2$ at random and send $C_2 = g^{L_2}$ to the verifying party. Second step, receive a challenge $c$. Third step, send a response $d = c L_1 + L_2 \pmod{q}$. Now verify this response with $g^d=$ something computable by the verifying party. That is, an expression of something that was sent to verifying party before or while running the protocol.
• Thanks for the explanation. One question: does this simultaneously prove that the prover knows the value $L_1$ and $L_2$ committed in $C_1$ and $C_2$ respectively? – Hongyang Dec 20 '15 at 16:46
• The verifier is given $d$, $C_1 = g^{L_1}$ and $C_2 = g^{L_2}$, and verifies that $g^d = (C_1)^cC_2$, right? – Hongyang Dec 20 '15 at 18:35
• Right. Please note it is essential that Prover is given challenge $c$ only after he sends his first protocol message, commitment $C_2$. Next, to be zero knowledge, a proof must admit simulator algorithm that would output simulated transcript. – Vadym Fedyukovych Dec 20 '15 at 18:44 | 2020-10-23 22:21:58 | {"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": 0.7524760961532593, "perplexity": 1241.8526062680894}, "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-2020-45/segments/1603107865665.7/warc/CC-MAIN-20201023204939-20201023234939-00195.warc.gz"} |
http://www.clp.ac.cn/EN/Article/OJe089db537a920635 | Main > Photonics Research > Volume 8 > Issue 12 > Page 12001964 > Article
• Abstract
• Abstract
• Figures (9)
• Tables (0)
• Equations (9)
• References (46)
• Get PDF
• View Full Text
• Paper Information
Accepted: Oct. 28, 2020
Posted: Nov. 2, 2020
Published Online: Dec. 1, 2020
The Author Email: Weiqiang Wang (wwq@opt.ac.cn), Fumin Zhang (zhangfumin@tju.edu.cn), Wenfu Zhang (wfuzhang@opt.ac.cn)
• Get Citation
• ##### Copy Citation Text
Jindong Wang, Zhizhou Lu, Weiqiang Wang, Fumin Zhang, Jiawei Chen, Yang Wang, Jihui Zheng, Sai T. Chu, Wei Zhao, Brent E. Little, Xinghua Qu, Wenfu Zhang. Long-distance ranging with high precision using a soliton microcomb[J]. Photonics Research, 2020, 8(12): 12001964
• Category
• Share
## Abstract
Laser-based light detection and ranging (lidar) plays a significant role in both scientific and industrial areas. However, it is difficult for existing lidars to achieve high speed, high precision, and long distance simultaneously. Here, we demonstrate a high-performance lidar based on a chip-scaled soliton microcomb (SMC) that can realize all three specialties simultaneously. Aided by the excellent properties of ultrahigh repetition rate and the smooth envelope of the SMC, traditional optical frequency comb (OFC)-based dispersive interferometry is heavily improved and the measuring dead zone induced by the mismatch between the repetition rate of the OFC and resolution of the optical spectrum analyzer is totally eliminated. Combined with an auxiliary dual-frequency phase-modulated laser range finder, the none-dead-zone measurable range ambiguity is extended up to 1500 m. The proposed SMC lidar is experimentally implemented in both indoor and outdoor environment. In the outdoor baseline field, real-time, high-speed (up to 35 kHz) measurement of a long distance of $～1179 m$ is achieved with a minimum Allan deviation of 5.6 μm at an average time of 0.2 ms (27 nm at an average time of 1.8 s after high-pass filtering). The present SMC lidar approaches a compact, fast, high-precision, and none-dead zone long-distance ranging system, aimed at emerging applications of frontier basic scientific research and advances in industrial manufacturing. | 2021-04-12 06:10:38 | {"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": 0.5656067728996277, "perplexity": 8445.36157670446}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038066613.21/warc/CC-MAIN-20210412053559-20210412083559-00294.warc.gz"} |
https://www.yourdictionary.com/undesirable | #### Sentence Examples
• Education produced many unforeseen and undesirable practical results.
• Again, it is generally recognized to be undesirable to give marks for a smattering.
• When the roof is weak, or when it is undesirable to leave so much ore in the stopes, false stulls are sometimes erected in the upper part of the stope.
• Duke Henry had decreed that his lands should be divided between his two sons, but as a partition was regarded as undesirable the whole of the duchy came to his elder son.
• It was then employed to describe a "peasant," and gradually began to denote undesirable qualities. | 2019-11-14 09:06:00 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.81535804271698, "perplexity": 3613.8160742910513}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668334.27/warc/CC-MAIN-20191114081021-20191114105021-00480.warc.gz"} |
https://docs.generic-mapping-tools.org/6.0/grd2cpt.html | # grd2cpt¶
Make linear or histogram-equalized color palette table from grid
## Synopsis¶
gmt grd2cpt grid [ -Atransparency[+a] ] [ -Ccpt ] [ -D[i] ] [ -E[nlevels] ] [ -F[R|r|h|c][+c]] [ -Gzlo/zhi ] [ -H ] [ -I[c][z] ] [ -Lminlimit/maxlimit ] [ -M ] [ -N ] [ -Q[i|o] ] [ -Rregion ] [ -Sh|l|m|u ] [ -Tstart/stop/inc ] [ -V[level] ] [ -W[w] ] [ -Z ] [ --PAR=value ]
Note: No space is allowed between the option flag and the associated arguments.
## Description¶
grd2cpt reads one or more grid files and writes a static color palette (CPT) file. In classic mode we write the CMT to standard output, while under modern mode we simply save the CPT as the current session CPT (but see -H). The CPT is based on an existing dynamic master CPT of your choice, and the mapping from data value to colors is through the data’s cumulative distribution function (CDF), so that the colors are histogram equalized. Thus if the grid(s) and the resulting CPT are used in grdimage with a linear projection, the colors will be uniformly distributed in area on the plot. Let z be the data values in the grid. Define CDF(Z) = (# of z < Z) / (# of z in grid). (NaNs are ignored). These z-values are then normalized to the master CPT and colors are sampled at the desired intervals.
The color palette includes three additional colors beyond the range of z-values. These are the background color (B) assigned to values lower than the lowest z-value, the foreground color (F) assigned to values higher than the highest z-value, and the NaN color (N) painted wherever values are undefined. For color tables beyond the standard GMT offerings, visit cpt-city and Scientific Colour-Maps.
If the master CPT includes B, F, and N entries, these will be copied into the new master file. If not, the parameters COLOR_BACKGROUND, COLOR_FOREGROUND, and COLOR_NAN from the gmt.conf file or the command line will be used. This default behavior can be overruled using the options -D, -M or -N.
The color model (RGB, HSV or CMYK) of the palette created by makecpt will be the same as specified in the header of the master CPT. When there is no COLOR_MODEL entry in the master CPT, the COLOR_MODEL specified in the gmt.conf file or on the command line will be used.
## Required Arguments¶
grid
Names of one or more grid files used to derive the color palette table. All grids need to have the same size and dimensions. (See GRID FILE FORMATS below).
## Optional Arguments¶
-Atransparency[+a]
Sets a constant level of transparency (0-100) for all color slices. Append +a to also affect the fore-, back-, and nan-colors [Default is no transparency, i.e., 0 (opaque)].
-Ccpt
Selects the master color table to use in the interpolation. Choose among the built-in tables (type grd2cpt to see the list) or give the name of an existing CPT [Default gives the turbo CPT]. Yet another option is to specify -Ccolor1,color2[,color3,…] to build a linear continuous CPT from those colors automatically. In this case colorn can be a r/g/b triplet, a color name, or an HTML hexadecimal color (e.g. #aabbcc ).
-D[i]
Select the back- and foreground colors to match the colors for lowest and highest z-values in the output CPT [Default uses the colors specified in the master file, or those defined by the parameters COLOR_BACKGROUND, COLOR_FOREGROUND, and COLOR_NAN]. Append i to match the colors for the lowest and highest values in the input (instead of the output) CPT.
-E[nlevels]
Create a linear color table by using the grid z-range as the new limits in the CPT. Alternatively, append nlevels and we will resample the color table into nlevels equidistant slices.
-F[R|r|h|c][+c]]
Force output CPT to written with r/g/b codes, gray-scale values or color name (R, default) or r/g/b codes only (r), or h-s-v codes (h), or c/m/y/k codes (c). Optionally or alternatively, append +c to write discrete palettes in categorical format.
-Gzlo/zhi
Truncate the incoming CPT so that the lowest and highest z-levels are to zlo and zhi. If one of these equal NaN then we leave that end of the CPT alone. The truncation takes place before any resampling. See also Manipulating CPTs
-H
Modern mode only: Write the CPT to standard output as well [Default saves the CPT as the session current CPT]. Required for scripts used to make animations via movie where we must pass named CPT files.
-I[c][z]
Append c [Default] to reverse the sense of color progression in the master CPT. Also exchanges the foreground and background colors, including those specified by the parameters COLOR_BACKGROUND and COLOR_FOREGROUND. Append z to reverse the sign of z-values in the color table. Note that this change of z-direction happens before -G and -S values are used so the latter much be compatible with the changed z-range. See also Manipulating CPTs
-Lminlimit/maxlimit
Limit range of CPT to minlimit/maxlimit, and don’t count data outside this range when estimating CDF(Z). [Default uses min and max of data.]
-M
Overrule background, foreground, and NaN colors specified in the master CPT with the values of the parameters COLOR_BACKGROUND, COLOR_FOREGROUND, and COLOR_NAN specified in the gmt.conf file or on the command line. When combined with -D, only COLOR_NAN is considered.
-N
Do not write out the background, foreground, and NaN-color fields [Default will write them].
-Q[i|o]
Selects a logarithmic interpolation scheme [Default is linear]. -Qi expects input z-values to be log10(z), assigns colors, and writes out z [Default]. -Qo takes log10(z) first, assigns colors, and writes out z.
-Rxmin/xmax/ymin/ymax[+r][+uunit] (more …)
Specify the region of interest.
-Sh|l|m|u
Force the color table to be symmetric about zero (from -R to +R). Append flag to set the range R: l for R =|zmin|, u for R = |zmax|, m for R = min(|zmin|, |zmax|), or h for R = max(|zmin|, |zmax|).
-Tstart/stop/inc or -Tn
Set steps in CPT. Calculate entries in CPT from start to stop in steps of (inc). Default chooses arbitrary values by a crazy scheme based on equidistant values for a Gaussian CDF. Use -Tn to select n points from such a cumulative normal distribution [11].
-V
Verbose operation. This will write CDF(Z) estimates to stderr. [Default is silent.]
-W
Do not interpolate the input color table but pick the output colors starting at the beginning of the map. This is particularly useful in combination with a categorical color table. Cannot be used in combination with -Z. Alternatively, use -Ww to produce a wrapped (cyclic) color table that endlessly repeats its range.
-Z
Will create a continuous color palette. [Default is discontinuous, i.e., constant color intervals]
-^ or just -
Print a short message about the syntax of the command, then exits (NOTE: on Windows just use -).
-+ or just +
Print an extensive usage (help) message, including the explanation of any module-specific option (but not the GMT common options), then exits.
-? or no arguments
Print a complete usage (help) message, including the explanation of all options, then exits.
--PAR=value
Temporarily override a GMT default setting; repeatable. See gmt.conf for parameters.
## Grid File Formats¶
By default GMT writes out grid as single precision floats in a COARDS-complaint netCDF file format. However, GMT is able to produce grid files in many other commonly used grid file formats and also facilitates so called “packing” of grids, writing out floating point data as 1- or 2-byte integers. (more …)
## Notes on Transparency¶
The PostScript language originally had no accommodation for transparency. However, Adobe added an extension that allows developers to encode some forms of transparency using the PostScript language model but it is only realized when converting the PostScript to PDF (and via PDF to any raster image format). GMT uses this model but there are some limitations: Transparency can only be controlled on a per-object or per-layer basis. This means that a color specifications (such as those in CPTs of given via command-line options) only apply to vector graphic items (i.e., text, lines, polygon fills) or to an entire layer (which could include items such as PostScript images). This limitation rules out any mechanism of controlling transparency in such images on a pixel level.
## Color Aliasing¶
For best result when -E is used we recommend you do no append a specific nlevels. This way the original CPT is used exactly as is but the z boundaries are adjusted to match the grid limits. Otherwise you may, depending on the nature of the input CPT, miss aspects of the color changes by aliasing the signal.
## Examples¶
Sometimes you don’t want to make a CPT (yet) but would find it helpful to know that 90% of your data lie between z1 and z2, something you cannot learn from grdinfo. So you can do this to see some points on the CDF(Z) curve (use -V option to see more):
gmt grd2cpt mydata.nc -V > /dev/null
To make a CPT with entries from 0 to 200 in steps of 20, and ignore data below zero in computing CDF(Z), and use the built-in master cpt file relief, run
gmt grd2cpt mydata.nc -Crelief -L0/10000 -T0/200/20 > mydata.cpt
## Note on CPTs in Modern Mode¶
In modern mode, CPTs are rarely needed to be named explicitly. Instead, when a module that may create a CPT, such as grd2cpt and makecpt (or even grdimage when no color table is available), the behavior under modern mode is to write that CPT to a hidden file in the session directory. When a module requires a CPT (e.g., grdimage not given -C or plot given -C with no name) then we read this hidden CPT (if it exists). This file is called the current CPT. In fact, there are several levels of current CPTs that may all be different, and some may not be present. If you create a CPT within an inset operation then that CPT is only accessible during the inset plotting; it thus only has the inset as its scope. If you create a CPT while positioned into a specific subplot, then that CPT is likewise only accessible to that subplot. If, on the other hand, you make a CPT after subplot begin but before any plotting then that CPT is available to all the subplots (but can be locally overridden by a subplot-specific CPT mention above). Finally, each call to figure means you may have a figure-specific CPT, should you create them. If none exists then the session CPT is used. The rule gmt follows is to always get the CPT with the most restricted scope that is visible from where you are in the plotting hierarchy. If not found we go up the hierarchy to CPTs with broader scope, and if none is ultimately found (and the module, unlike grdimage, cannot create a CPT by itself), then you have likely made a scripting error. There are cases in modern mode when you must explicitly create a named CPT using the -H option. One such case is when making movies with movie since you will want to create the CPT once and have movie access it again and again. Since each movie frame is a separate session there is no cross-session sharing of current CPTs. | 2019-09-18 05:17:48 | {"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": 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": 0.3611399531364441, "perplexity": 4032.3205078321125}, "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-2019-39/segments/1568514573184.25/warc/CC-MAIN-20190918044831-20190918070831-00216.warc.gz"} |
https://www.allthatmatters.academy/courses/energy-2/lessons/dot-product/ | In Progress
Skill 5 of 14
In Progress
# Dot-product
Right now we have two versions of the work formula: $W=F_\parallel \Delta s$ and $W=F\,\Delta s_\parallel$, which include the $\parallel$-symbol, possibly some cosines when we have to calculate the components etc. All we wanted was to ‘multiply the parallel parts’. Let’s invent a simpler notation to mean just that:
$$W=\vec F\cdot \Delta \vec s$$
The well-known multiplication dot $\cdot$ is what we chose here to mean ‘multiply the parallel part of one vector onto the other vector’. Normal multiplication1 between numbers does not make sense between vectors,2 so we are simply reusing a symbol here that otherwise would have no meaning in relation to vectors. Why don’t we call this operation a dot-product.
Subscribe to valuable engineering skills for your resume or CV
Try full access with a 7-day free trial on all subscriptions. | 2021-01-27 00:11:23 | {"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": 0.7924149632453918, "perplexity": 1472.9036203523606}, "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-2021-04/segments/1610704804187.81/warc/CC-MAIN-20210126233034-20210127023034-00323.warc.gz"} |
https://dmoj.ca/problem/dmpg18g6 | DMPG '18 G6 - Class Chitchat
View as PDF
Points: 20 (partial)
Time limit: 1.8s
Memory limit: 512M
Author:
Problem type
Allowed languages
Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, CommonLisp, D, Dart, F#, Forth, Fortran, Go, Groovy, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, Nim, ObjC, OCaml, Octave, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig
There are students in your school conveniently labelled from to . You are person . There are classes numbered to , and student takes different classes. It is guaranteed that every student takes at least one class, although some classes may not have any students.
Two students are able to communicate if and only if they share a class. Additionally, some pairs of people get along more easily than others. Each student has a friend value . Then it costs for student to deliver a message to student where is fixed for any two students who are able to directly communicate with each other.
The cost required to deliver a message to student is the sum of the costs from each direct communication. For each , you would like to know the minimum cost required for you, student , to deliver a message to student .
Input Specification
The first line contains three space-separated integers, , , and .
The next line contains space-separated integers, the of which is .
The following lines contain space-separated integers. The first number is and the indices of the classes which student is taking follow.
Output Specification
Output lines, each containing a single integer. On the line, write the minimum cost required to communicate with student . If it is not possible to communicate with student , print . Answers are guaranteed to fit within a 64-bit integer.
Sample Input
9 10 7
18 5 6 11 17 19 2 14 5
2 1 7
5 5 2 3 1 10
1 5
2 1 2
2 7 6
1 4
2 3 6
1 10
1 10
Sample Output
0
20
28
14
8
-1
30
36
27 | 2020-10-26 09:23:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3065429627895355, "perplexity": 2416.807603775774}, "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-2020-45/segments/1603107891203.69/warc/CC-MAIN-20201026090458-20201026120458-00669.warc.gz"} |
https://xiuchuanz.com/2018/03/Introduction_to_Probability_and_Data/ | # Xiuchuan Zhang
Personal Website
This is Xiuchuan's personal website.
I plan to post some of my current learning and review notes on it.
If you have any questions or suggestions, welcome to comment in my posts.
These are the notes by learning the “Introduction to Probability and Data” from Coursera.org for future reviews.
## Introduction to Data
• Data matrix: data are organized in
• Observation (case): row
• Variable: column
### Types of variables
• Numerical
• numerical values (sensible to add, subtract, take averages, etc. with them) 1. continuous: infinite number of values within a given range 2. discrete: specific set of numeric values
• Categorical
• limited number of distinct categories (not sensible to do arithmetic operations)
1. ordinal: inherent ordering
2. Nominal: not ordering
### Relationships between variables
• associated (dependent) : positive or negative
• independent : not associated
### Observational study
• collect data in a way that does not directly interfere with how data arise (“observe”)
• only establish an association
• retrospective: use past data
• prospective: data are collected throughout the study
### Experiment study
• randomly assign subjects to treatments
• establish causal connections
### Why not Census
• some individuals are hard to locate or measure, and these people be different from the rest of the population
• populations rarely stand still
### Sources of Sampling bias
• Convenience sample: individuals who are easily accessible are more likely to be included in the sample
• Non-response: If only a (non-random) fraction of the randomly sampled people respond to survey such that the sample is no longer representative of the population
• Voluntary response: Occurs when the sample consists of people who volunteer to respond because they have strong opinions on the issue
### Sample Methods
• simple random sampling: randomly select cases from the population
• stratified sampling: first divide the population into homogenous groups called strata, and then randomly sample from within each stratum
• cluster sampling: divide the population into clusters, randomly sample a few clusters, and then sample all observation within these clusters
• multistage sampling: divide the population into clusters, randomly sample a few clusters, and then we randomly sample observations from within these clusters
### Experimental design
• Principles of Experimental Design:
1. control: compare treatment of interest to a control group
2. randomize: randomly assigning subjects to treatments
3. replicate: collect a sufficiently large sample, or replicate the entire study
4. block: block for variables known or suspected to affect the outcome
• confounding variable: is correlated with both the explanatory and response variables
• Explanatory variables (factors): conditions we can impose on our experimental units
• Blocking variables: characteristics that the experimental units come with, that we would like to control for
• Blocking is like stratifying:
• blocking during random assignment
• stratifying during random sampling
### Experimental terminology
• placebo: fake treatment, often used as the control group for medical studies
• placebo effect: showing change despite being on the placebo
• blinding: experimental units do not know which group they are in
• double-blind: both the experimental units and the researchers do not know the group assignment
### Random sampling and random assignment
ideal experiment $\searrow$ Random Assignment No Random Assignment most observational studies $\swarrow$
Random Sampling Causal and Generalizable not Causal, but Generalizable Generalizability
No Random Sampling Causal, but not Generalizable neither Causal nor Generalizable Np Generalizability
most experiments $\nearrow$ Causation Association bad observational studies $\nwarrow$
## Exploratory Data Analysis and Introduction to Inference
### Scatterplots
• explanatory variable on x axis
• response variable on y axis
• correlation, not causation
### Evaluate the relationship
• direction: positive or negative
• shape: linear or curved or others
• strength: strong or weak
• outliers
### Histogram
• provide a view of the data density
• especially useful for identifying shapes of distributions
### Skewness
• distributions are skewed to the side of the long tail
• left skewed: the longer tail is on the left on the negative end
• mean < median
• symmetric: no skewness is apparent
• mean $\approx$ median
• right skewed: the longer tail is on the right, the positive end
• mean > median
### Modality
• unimodal: one prominent peak (normal distribution or bell curve)
• bimodal: two prominent peak (might two distinct groups in data)
• uniform: no prominent peaks (no apparent trend)
• multimodal: more than two prominent peaks
### Bin width
the chosen bin width can alter the story the histogram is telling
• bin width too wide: might lose interesting details
• bin width too narrow: might be difficult to get an overall picture of the distribution
• ideal bin width depends on the data you are working with
### Dot plot
• useful when individual values are of interest
• can get too busy as the sample size increases
### Box plot
• useful for highlighting outliers, media, IQR(interquartile range)
### Intensity map
• useful for highlighting the spatial distribution
• range: (max - min)
• variance: roughly the average squared deviation from the mean
• sample variance: $s^2$
• population variance: $(\sigma)^2$
• $s^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}$
• standard deviation: roughly the average deviation around the mean, and has the same units as the data
• sample sd: $s$
• population sd: $\sigma$
• inter-quartile range
• range of the middle 50% of the data, distance between the first quartile (25th percentile) and third quartile (the 75th percentile)
• most readily available in a box plot.
• $IQR = Q_3 - Q_1$
### Robust Statistics
• define: measures on which extreme observations have little effect
• robust measures of center & spread:
robust non-robust
center median mean
### Transforming data
• define: a rescaling of the data using a function
• When data are very strongly skewed, we sometimes transform them, so that they are easier to model
• (natural) log transformation:
• often applied when much of the data cluster near zero (relative to larger values in the dataset) and all observations are positive
• to make the relationship between the variables more linear, and hence easier to model with simple methods
• other transformations:
• square root
• inverse
• goals:
• to see the data structure differently
• to reduce skew assist in modeling
• to straighten a nonlinear relationship in a scatterplot
### Exploring Categorical Variables
• Bar plots
• Q: How are bar plots different than histograms?
• barplots for categorical variables, histograms for numerical variables
• x-axis on a histogram is a number line, and the ordering od the bars are not interchangeable
• Segmented bar plot
• useful for visualizing conditional frequency distributions
• compare relative frequencies to explore the relationship between the variables
• Relative frequency segmented bar plot
• Mosaicplot
• Side-by-side box plots
### Introduction to inference
• null hypothesis($H_0$): independent, “There is nothing going on”
• alternative hypothesis($H_A$): dependent, “There is something going on”
• hypothesis testing framework
• start with a null hypothesis($H_0$) that represents that status quo
• set an alternative hypothesis($H_A$) that represents our research question, i.e. what we’re testing for
• conduct a hypothesis test under the assumption that the null hypothesis is true, either via simulation or using theoretical methods
• If the test results suggest that the data do not provide convincing evidence for the alternative hypothesis, we stick with the null hypothesis
• If they do, then we reject the null hypothesis in favor of the alternative
### Inference summary
• set a null and an alternative hypothesis
• simulate the experiment assuming that the null hypothesis is true
• evaluated the p_value: probability of observing an outcome at least as extreme as the one observed in the original data
• if this probability is low, reject the null hypothesis in favor of the alternative
## Probability and Distribution
• random process: know what outcomes could happen, but don’t know which particular outcome will happen
• P (A) = Probability of event A
• 0≤P(A)≤1
• frequentist interpretation: The probability of an outcome would occur if we observed the random process an infinite number of times.
• Bayesian interpretation: A Bayesian interprets probability as a subjective degree of belief
• largely popularized by revolutionary advance in computational technology and methods during the last twenty years
• law of large members: sates that as more observations are collected, the proportion of occurrences with a particular outcome converges to the probably of that outcome
• common misunderstanding: gambler’s fallacy (law of averages)
• disjoint (mortally exclusive) events cannot happen at the same time
• P(A & B) = 0
• Union of disjoint events: P(A or B) = P(A) + P(B) - P(A & B)
• Complementary → disjoint; complementary !← disjoint
• non-disjoint events can happen at the same time
• P(A & B) != 0
• sample space: a collection of all possible outcomes of a trial
• probability distribution: all possibility outcomes in the sample space, and the probabilities with they occur
• Rules:
• the events listed must be disjoint
• each probability must be between 0 and I
• the probabilities must total I
• complementary events: two mentally exclusive events whose probabilities add up to l
• Independence: P(A/B) = P(A), P(A1, … & Ak<\sub>) = P(A1) × … × P(Ak)
• Dependence: P(A/B) = P(A & B)/ P(B), P(A & B) = P(A/B) × P(B)
• Posterior Probability: P(hypothesis / data) → P(hypothesis is true / observed data)
• P-value: P(data / hypothesis) → P(observed or more extreme outcome / H0 is true)
## Normal Distribution
### Normal distribution $N( \mu , \sigma )$
• unimodal and symmetric
• bell curve
• follows very strict guidelines about how variably the data are distributed around the mean
• Many variables are nearly normal, but none are exactly normal
• two parameters: mean μ and stand deviation σ
• Changing the center and the spread of the distribution changes the overall shape of the distribution
• rules govern the variability of normally distributed data around the mean
### Standardizing with Z scores
• standardized (Z) score of an obervation is the number of standard deviations it falls above or below the mean
• $Z = \frac{observation - mean}{SD}$
• Z score of mean = 0 (normally: median ≈ 0 )
• unusual observation: $\lvert Z\rvert > 2$
• defined for distributions of any shape
• when the distribution is normal, Z scores can be used to calculate percentiles
• Percentile is the percentage of observations that fall below a given data point
• graphically, percentile is the area below the probability distribution curve to the left of that observation
• if the distribution does not follow the nice unimodal symmetric normal shape, you’d need to use calculus for that
• Methods for Z scores
1. Using R: pnorm(-1, mean = 0, sd = 1) (qnorm for quantiles or cutoff values)
2. Distribution Calculator
3. Table
### Evaluating
• anatomy of a normal probability plot
• Data are plotted on the y-axis of a normal probability plot, and theoretical quantiles (following a normal distribution) on the x-axis
• If there is a one-to-one relationship between the data and the theoretical quantiles, then the data follow a nearly normal distribution.
• Since a one-to-one relationship would appear as a straight line on a scatter plot, the closer the points are to a perfect straight line, the more confident we can be that the data follow a normal model.
• Constructing a normal probability plot requires calculating percentiles and corresponding z-scores for each observation, which is tedious. Therefore, we generally rely on software when making these plots.
• Also can using 68-95-99.7% rule
## Binomial Distribution
• binomial distribution describes the probability of having exactly k successes in n independent Bernoulli trials with probability of success p
• # of scenarios × P(single scenario)
• $P(k = K) = {n \choose k} p^k (1-p)^{(n-k)}$
in R: dbinom(k, size, p) Distribution Calculator
• Choose function: ${n \choose k}=\dfrac{n!}{k!(n−k)!}$
in R: choose(n, k)
### Binomial conditions
1. The trials are independent.
2. The number of trials, n, is fixed.
3. Each trial outcome can be classified as a success or failure.
4. The probability of a success, p, is the same for each trial.
• Expected value (mean) of binomial distribution ($\mu = np$) and its standard deviation ($\sigma = \sqrt{np(1-p)}$)
### normal approximation
• Fact: when the number of trials increases, the shape of the binomial actually starts looking closer and closer to a full normal distribution
• Calculate the probabilities for each outcome from a to b and sum them up
in R: sum(dbinom(a:b, size = n, p =p))
• Success-failure rule: a binomial distribution with at least 10 expected successes and 10 expected failures closely follows a normal distribution
• $np \geq 10$
• $n( 1-p ) \geq 10$
• Normal approximation to the binomial: If the success-failure condition holds, then
• $Binomial(n,p) \thicksim Normal(\mu,\sigma)$
• where $\mu = np$ and $\sigma = \sqrt{np(1-p)}$
Support | 2023-04-02 02:43:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.6573359370231628, "perplexity": 3648.010737503629}, "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/1679296950373.88/warc/CC-MAIN-20230402012805-20230402042805-00327.warc.gz"} |
https://www.merry.io/dynamical-systems/25-unique-ergodicity/ | A topological dynamical system on a compact metric space is said to be uniquely ergodic if there is exactly one invariant Borel probability measure (and hence also exactly one ergodic Borel probability measure).
An irrational circle rotation is uniquely ergodic, where the unique invariant measure is the Lebesgue measure.
In this lecture we show that a stronger version of the Birkhoff Ergodic Theorem holds for uniquely ergodic systems. (Spoiler: for uniquely ergodic systems, time average = space average for all points, rather than just for almost all points.) | 2020-11-26 03:50:33 | {"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": 0.988801121711731, "perplexity": 160.20015944483734}, "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/1606141186414.7/warc/CC-MAIN-20201126030729-20201126060729-00341.warc.gz"} |
http://mathhelpforum.com/algebra/108563-can-solved-print.html | Can this be solved??
Printable View
• October 17th 2009, 10:55 AM
md56
Can this be solved??
x^(2)+y^(2)=9
I can't get pass y=sqrt(-x^2+9)
The system I am submitting answers to says that there is a positive and a negative square root, and that the answers must be numbers. I have to find two solutions to both x and y.
Could someone just point me in the right direction as to steps to solve this?
I have a test Teus and I am so afraid I will flunk, help
!
• October 17th 2009, 10:57 AM
james_bond
Take a look at here ;)
• October 17th 2009, 11:06 AM
md56
Being that I am given no coordinates, that doesn't really help me. I guess the answer is an equation, but I do not do well with a ton of meaningless variables :/
• October 17th 2009, 11:07 AM
md56
Must I find a center first?
• October 17th 2009, 11:14 AM
skeeter
there is no "solving" here ... the equation $x^2 + y^2 = 9$ is a circle of radius 3 centered at the origin.
• October 17th 2009, 11:23 AM
md56
oh, answers were -3 and 3 for both x and y(Bow)
• October 17th 2009, 11:32 AM
skeeter
Quote:
Originally Posted by md56
oh, answers were -3 and 3 for both x and y(Bow)
... that is only one of an infinite number of solutions.
• October 17th 2009, 03:32 PM
MacstersUndead
To reinforce skeeter's point, consider polar coordinates, where x^2 + y^2 = r^2
then r^2 = 9 => r = 3
So any (x,y) Cartesian coordinate that is 3 units away from the origin is a solution. | 2016-02-11 09:27:12 | {"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": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8181950449943542, "perplexity": 888.5474469739802}, "config": {"markdown_headings": false, "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-2016-07/segments/1454701161775.86/warc/CC-MAIN-20160205193921-00022-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/5256-urgent-help-limits-print.html | # Urgent Help! with Limits
Printable View
• August 31st 2006, 05:33 AM
afn2
Urgent Help! with Limits
I need help solving what I think is a pretty simple limits questions, but I just can't see where to start.
I need to find:
the lim as x goes to infinity of (3x^2+2x+2)/(4x^2+2x+7)
and the lim as x goes to zero of the same function
Please help!
• August 31st 2006, 06:10 AM
galactus
When taking the limit of a rational expression, if x approaches +/- infinity, you can disregard all but the coefficients of the highest powers.
Therefore you have,
$\lim_{x\to\infty}\frac{3x^{2}}{4x^{2}}$
Now, you can see what it is?.
As x approaches 0, look close, can you see it?.
• August 31st 2006, 06:39 AM
ThePerfectHacker
Quote:
Originally Posted by afn2
I need to find:
the lim as x goes to infinity of (3x^2+2x+2)/(4x^2+2x+7)
and the lim as x goes to zero of the same function
Divide the numerator and denominator by $x^2$
$\lim_{x\to\infty}\frac{3+\frac{2}{x}+\frac{2}{x^2} }{4+\frac{2}{x}+\frac{7}{x^2}}$
The numerator is,
$\lim_{x\to\infty} 3+\frac{2}{x}+\frac{2}{x^2}=3$
The denominaot is,
$\lim_{x\to\infty}4+\frac{2}{x}+\frac{7}{x^2}=4$
Since both limits exists thus the value of the limit is 3/4
• August 31st 2006, 06:57 AM
topsquark
Quote:
Originally Posted by afn2
I need help solving what I think is a pretty simple limits questions, but I just can't see where to start.
I need to find:
the lim as x goes to infinity of (3x^2+2x+2)/(4x^2+2x+7)
and the lim as x goes to zero of the same function
Please help!
The limit as x goes to 0 should be simple. Both the numerator and denominator are continous functions on all real numbers (ie. the domain in both cases is all real numbers) and the denominator is not 0 for x = 0, so effectively all you need to do is substitute 0 for x in the expression.
-Dan
• August 31st 2006, 07:50 AM
afn2
Thanks a bunch, I knew it was pretty simple, but I've always struggled with limits, even though I completely get derivatives and integrals. I just needed a push in the right direction. Thanks guys! | 2014-03-09 17:47:23 | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "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": 0.9563300609588623, "perplexity": 518.2315238838847}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394009968414/warc/CC-MAIN-20140305085928-00014-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://ai.stackexchange.com/questions/8667/how-to-define-a-reward-function-in-pomdps | # How to define a reward function in POMDPs?
How do I define a reward function for my POMDP model?
In the literature, it is common to use one simple number as a reward, but I am not sure if this is really how you define a function. Because this way you have to do define a reward for every possible action-state combination. I think that the examples in the literature might not be practical in reality, but only for the purpose of explanation.
There is no major difference here between a POMDP and MDP. When setting reward values, you are generally trying to give the minimal information to the agent that when the sum of rewards is maximised, it solves the problem that you are posing.
In literature it is common to use one simple number as a reward, but I am not sure if this is really how you define a function. Because this way you have do define a reward for every possible Action-State combination.
Some defined value of reward has to be returned after all state, action pairs taken in the environment. The value could be $$0$$ of course.
Reward can depend on, or be a function of, current state, action, next state and a random factor. In a POMDP it may also be from any unobserved factor in the environment (you might know this in a simulation because you have created the environment and are choosing not to share the data with the agent).
In practice, the reward often does not have to depend on all the possible factors. In addition, the relationship between the factors and the possible reward can be very simple or sparse.
Classic examples you may find in the literature include:
• Reward in a game can be simply $$+1$$ for winning, or $$-1$$ for losing, granted at the end. All other rewards are $$0$$
• If your goal is to reach a certain state, such as exit from a maze, in minimum time, then a fixed reward of $$-1$$ per time step is enough to express the need to minimize the total number of steps.
• For a goal of maintaining stability and avoiding a failure in e.g. CartPole, then a reward of +1 per time step without failure suffices.
All of these examples express the reward function as a simple condition plus one or two numbers. The key thing is that they allow you to calculate a suitable reward on each and every time step. They are all strictly reward functions - the general case can cover very complex functions if you wish, that will depend entirely on the goals you want to set the agent to learn/solve.
In a POMDP, you minimize the following cost function
\begin{align} J_{\pi_{0:N-1}} (\cdot) &= \mathbb{E} \left( g_N (x_N) + \sum_{k=0}^{N-1} g_k (x_k, \pi_k(\cdot)) \right), \end{align} where $$g_N$$ is the terminal cost and $$g_k$$ is the step cost.
Note that this is only the formal problem definition. If you talk about an actual system, you might have a hard time recognizing that this is connected to your reward. What you observe is formally a value of the function J and practically a simple float
More details in German are on my blog: https://martin-thoma.com/probabilistische-planung/#mdp-vs-pomdp-vs-rl_1 | 2022-06-29 09:49:00 | {"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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 8, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8870028853416443, "perplexity": 367.885946783591}, "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/1656103626162.35/warc/CC-MAIN-20220629084939-20220629114939-00058.warc.gz"} |
http://mfat.imath.kiev.ua/article/?id=159 | Open Access
On ordinary differential operators of an odd order nonsimilar to normal operators
Coming Soon.
Article Information
Title On ordinary differential operators of an odd order nonsimilar to normal operators Source Methods Funct. Anal. Topology, Vol. 7 (2001), no. 1, 17-27 MathSciNet MR1909904 Copyright The Author(s) 2001 (CC BY-SA)
Citation Example
I. M. Karabash, On ordinary differential operators of an odd order nonsimilar to normal operators, Methods Funct. Anal. Topology 7 (2001), no. 1, 17-27.
BibTex
@article {MFAT159,
AUTHOR = {Karabash, I. M.},
TITLE = {On ordinary differential operators of an odd order nonsimilar to normal operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {7},
YEAR = {2001},
NUMBER = {1},
PAGES = {17-27},
ISSN = {1029-3531},
MRNUMBER = {MR1909904},
URL = {http://mfat.imath.kiev.ua/article/?id=159},
} | 2021-07-27 12:20:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.3879251182079315, "perplexity": 7649.840793506251}, "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-2021-31/segments/1627046153391.5/warc/CC-MAIN-20210727103626-20210727133626-00647.warc.gz"} |
http://mathoverflow.net/questions/53899/finiteness-property-of-fundamental-groups | # Finiteness property of fundamental groups
Let $K$ be an algebraically closed field of characteristic zero. Let $X/K$ be a smooth variety. Is it true that the \'etale fundamental group $\pi_1(X)$ is topologically finitely generated.
I know that the answer is yes'' in the following two cases:
1) $X/K$ is proper.
2) $\dim(X)=1$. (In this case we can write down a presentation of $\pi_1(X)$ very explicitly.)
Can there anything go wrong in the general case? (It would be wonderful to have a reference which one can simply quote.)
-
Yes. Use the finite generation for the topological fund. grp (by using finite triangulability of complex varieties) + the comparison theorem SGA1 exp XII cor 5.2. – Donu Arapura Jan 31 '11 at 16:21
@Donu: can it be proved 'purely algebraicly'? – Mariano Suárez-Alvarez Jan 31 '11 at 16:35
Mariano, I don't know of a purely algebraic argument, but it would certainly be interesting. As an aside, I might point out that the "wild" part of $\pi_1(\matbb{A}^1)$ in positive characteristic need not be finitely generated. – Donu Arapura Jan 31 '11 at 18:09
@Donu: This only covers the case $K = \mathbb{C}$, right? Or can we generalize this using model theory? – Martin Brandenburg Jan 31 '11 at 20:25
Donu's argument works by the invariance of the etale $pi_1$ under base-change of algebraically closed fields in characteristic zero. I believe the required specialization argument can be found in Serre's lectures on Galois theory. The key point is that $\pi_1(X\times Y)=\pi_1(X)\times \pi_1(Y)$, which fails in positive characteristic. An amusing (or vexing) fact is that an 'algebraic proof', in any reasonable sense, of finite-generation is unknown even for curves. – Minhyong Kim Jan 31 '11 at 23:41 | 2014-10-23 20:04:45 | {"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": 0.898516058921814, "perplexity": 396.10581703117396}, "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-2014-42/segments/1413558067496.61/warc/CC-MAIN-20141017150107-00165-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://www.helpteaching.com/questions/Function_and_Algebra_Concepts/Grade_11 | Looking for Algebra worksheets?
Check out our pre-made Algebra worksheets!
Tweet
##### Browse Questions
• Arts (209)
• English Language Arts (2745)
• English as a Second Language ESL (1380)
• Health and Medicine (398)
• Life Skills (594)
• Math (1531)
• ### Vectors
• #### Trigonometry
• Physical Education (197)
• Science (3591)
• Social Studies (1172)
• Study Skills and Strategies (14)
• Technology (549)
• Vocational Education (648)
You can create printable tests and worksheets from these Grade 11 Function and Algebra Concepts questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.
Previous Next
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
What is the product $(x + 5)(x^3 - 2x -3)?$
1. $x^4 + 5x^3 - 2x^2 - 7x -15$
2. $x^4 + 5x^3 - 2x^2 - 13x - 15$
3. $x^4 + 5x^3 - 2x^2 - 10x - 15$
4. $x^4 + 5x^3 - 2x^2 - 3x - 15$
Express as a single logarithm. $2log(x) - 5log(y) + 3log(z)$
1. $log((x^2 z^3)/y^5)$
2. $-30log(xyz)$
3. $-log(x^2 y^5 z^3)$
4. $log((x^2 y^5)/z^3)$
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify the rational expression.
$(3x(x-3))/((x-3)(x+3))$
1. $(x-3)/x, \ \ x!=-3,3$
2. $(3x)/(x+3), \ \ x!= 3$
3. $(x+3)/(x-3), \ \ x!=-3$
4. $1/(x-3), \ \ x!= -3$
Grade 11 Polynomials and Rational Expressions
Given: $(5x + 6)(8x - 4)$
The product of the given is:
1. $13x + 2$
2. $40x - 24$
3. $40x^2 + 24$
4. $40x^2 - 20x + 48x - 24$
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.4
Factor. $27x^3 + 64$
1. $(3x-4)(9x^2 + 12x + 16)$
2. $(3x + 4)(9x^2 - 12x + 16)$
3. $(3x+4)(9x^2 + 12x + 16)$
4. $"Can't factor further"$
What is the equation of the line with a slope of 3 through (-1, 4)?
1. y + 4 = 3(x + 1)
2. y - 4 = 3(x + 1)
3. y - 4 = 3(x - 1)
4. y + 4 = 3(x - 1)
5. None of the above
Solve. $root[4](8^(5)) = 16^(3x)$
1. $x = 5/12$
2. $x = 5/16$
3. $x = 15/14$
4. $x = 5/14$
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Divide and simplify the expression $(x-2)/(5x+10)-:(3)/(3x+6)$.
1. $5/(x-2), \ \ x!=-2$
2. $(3(x-2))/(15(x+2)^2)$
3. $(x-2)/5, \ \ x!=-2$
4. $(3(x-2))/(15(x+2))$
Grade 11 Functions and Relations CCSS: HSF-BF.B.3
If y = f(x) is transformed to y = f(x) - 2, the function .
1. shifts right 2 units
2. shifts down 2 units
3. shifts left 2 units
4. shifts up 2 units
For $A = [[16, 8, 32], [4, 0, 12], [8, 24, 20]]$, find $1/4 A$.
1. $[[4, 2, 8],[4, 0, 12], [8, 24, 20]]$
2. $[[ 4, 8, 32],[1, 0, 12],[2,24,20]]$
3. $[[4,2,8],[1,0,3],[2,6,5]]$
4. $"Does not exist (because of 0 in matrix)"$
Grade 11 Nonlinear Equations and Functions CCSS: HSA-REI.A.2
Factor the quadratic trinomial $x^2-29x+100$.
1. $(x+25)(x-4)$
2. $(x+25)(x+4)$
3. $(x-25)(x-4)$
4. $(x-25)(x+4)$
Simplify: $(2x)^4/(2x^4)$
1. $8, \ x!=0$
2. $4$
3. $2, \ x!=0$
4. $1$
Grade 11 Polynomials and Rational Expressions
Simplify. $(a - 1)/[(a)^2-1]$
1. $1/a, \ a!=0$
2. $1/(a - 1), \ a!= -1$
3. $1/(1- a), \ a!=1$
4. $1/(a + 1), \ a!=1$
Find the point(s) of intersection of the following equations.
$y=4x+2$
$y=2(x-1)^2-2$
1. No intersection
2. $(1,6), \ (-1,-2)$
3. $(2+sqrt(3),10+4sqrt(3)), \ (2-sqrt(3), 10-4sqrt(3))$
4. $(2+sqrt(5),10+4sqrt(5)), \ (2-sqrt(5),10-4sqrt(5))$
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify the expression $(x-7)/(x^2-x-42)$.
1. $1/(x+7), \ x!=-6$
2. $1/(x+6), \ x!= 7$
3. $x+7, \ x!= -6, 7$
4. $x+6, \ x!= -6, 7$
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Divide and simplify. $(3x)/(x+9)-:(x)/(3x+27) \ \ \ (x!=-9,0)$
1. $x^2/(x+9)^2$
2. $9/x$
3. $x/9$
4. $9$
Previous Next
You need to have at least 5 reputation to vote a question down. Learn How To Earn Badges. | 2018-02-24 18:08:40 | {"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": 0.2128269225358963, "perplexity": 5449.73860181407}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891815918.89/warc/CC-MAIN-20180224172043-20180224192043-00303.warc.gz"} |
https://www.biostars.org/p/9173/ | Per-Column Conservation Of Multiple Alignment In Perl
3
5
Entering edit mode
10.5 years ago
Given a Bio::SimpleAlign, what is the best way to get per-column conservation scores. E.g. into an array of values in [0:1] where the array length would be the same as align->length. I don't find anything like this in Bio::SimpleAlign. I'm looking for a function that allows: myio = Bio::AlignIO->new(-file=>$file); my$align = $io->next_aln; my @cons =$align->percentage_identity_by_column(); # <- does this exist?
print "@cons";
# 0.75 1.0 1.0 1.0 0.64 ....
Or should I just concat the gapped sequence, use substr() to extract the characters and count them with a hash and return the frequency of the most frequent character per column?
It looks like the private method Bio::SimpleAlign::consensusaa() already does most of this, but it returns the character rather than the fraction, which is what I was looking for. Short of submitting a patch for that, is there a better approach?
perl bioperl multiple consensus conservation • 4.0k views
5
Entering edit mode
10.5 years ago
Neilfws 49k
I think you are correct, in that there is no existing method to do this in Bio::SimpleAlign and in thinking about counting residues using a hash.
I would use the slice() method to return each column and extract the residues from it. Here's something I tried which works up to a point, but needs some more work:
use List::Util 'max';
my @scores;
# move along alignment 1 column at a time
for (my $i = 1;$i <= align->length;i++) {
my %count;
# extract column as a set of Bio::LocatableSeq objects
my $seqs =$align->slice($i,$i);
# get each residue and count in a hash
foreach my $seq ($seqs->each_seq) {
$count{$seq->seq} += 1;
}
push(@scores, max(values %count) / align->num_sequences); } print join(",", @scores); Note that this will print warnings where a column contains gap characters and exclude the row with the gap from the new alignment object. This means frequencies would be incorrectly calculated if you divided byseqs->num_sequences: e.g. column "A, -, A" will result in frequency A = 1, not A = 0.67. So we divide by the number of sequences in the original alignment. Presumably "all gaps" columns will result in an empty hash, which you may have to handle so as to return frequency = 0.
2
Entering edit mode
10.5 years ago
This was my final solution, which also marks gap columns as 0% conserved. This is mostly already in Bio::SimpleAlign, so I'll submit this as a patch as well and see what others think.
# Conservation of each non-gap column [0-100]
sub conservation {
my ($self) = @_; my @cons; my$num_sequences = $self->num_sequences; foreach my$point (0..align->length-1) { my %hash; foreach myseq ( $self->each_seq() ) { my$letter = substr($seq->seq,$point,1);
($letter eq$self->gap_char || $letter =~ /\./) && next;$hash{$letter}++; } # max frequency of a non-gap letter my$max = (sort {$b<=>$a} values %hash )[0];
push @cons, 100 * $max /$num_sequences;
}
return @cons;
}
0
Entering edit mode
Just a small problem with align variable which is not declared anywhere. Replaced withself did the job.
0
Entering edit mode
10.5 years ago
Asaf 8.6k
In my opinion computing the entropy of each column will give a better measure. If a column has 50% A and 50% T and another column has 50% and 50% C G and T evenly distributed, their conservation is not the same and entropy will catch these differences. The above holds if the sequences have the same distances from each other, otherwise your computations will be biased towards the more closely related organisms.
sub entropy{
my $vec = shift; #count the occuransies of the four nucleotides and U my %counts; foreach my$n (@{$vec}){$counts{$n}++; } #deduce the gaps; delete$counts{'-'};
#sum up the counts;
my $sum = 0; foreach my$key (keys %counts){
$sum+=$counts{$key}; } #computes the entropy my$ent = 0;
foreach my $key (keys %counts){ my$prob = $counts{$key}/$sum;$ent-=$prob*log2($prob);
}
return \$ent;
} | 2021-12-03 17:18:49 | {"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": 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": 0.3225199580192566, "perplexity": 3603.165315297684}, "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-2021-49/segments/1637964362891.54/warc/CC-MAIN-20211203151849-20211203181849-00483.warc.gz"} |
http://mathematica.stackexchange.com/questions/38961/ctags-for-mathematica-files | ctags for Mathematica files?
I alway use vi to edit Fortran files. I can use ctags to know which variables and functions I have already defined. Now I use vi to edit Mathematica *.m files. I tried to use ctags for *.m files, but it does not work. I have searched for the solution in Google but no luck. Could you give me some suggestions?
-
Using ctags for Mathematica is rather hard, because a variable/function can be defined in a bazillion ways, unlike C/Fortran which have a fixed syntax for defining them. I use YouCompleteMe to autocomplete existing symbols on-the-fly (regardless of whether they're "definitions" or not) and rely on memory/context to determine whether the suggestion is what I want. – rm -rf Dec 17 '13 at 20:26
Assuming you mean vim for vi, you could build a searchable index that may be an acceptable compromise.
Suppose that you have a searchable convention that you use for marking each function. The obvious one to me is one where you precede each function with a usage, like
foo::usage = "..." ;
foo[ x_ ] = Module[{}, ... ] ;
That would allow use of grep to build an index that you could use with vim -q (although that's not quite as nice as tags that you could follow). For example:
grep -n ::usage *.m | tee index
vim -q index
or, if you want a more constrained search, say just foo:
grep -n foo::usage *.m | tee index
vim -q index
When using vim -q you can use :cn, :cN to move between file:line pairs (this is probably more normally used for C compilation errors, but can be handy for more ad-hoc stuff like this too).
I'd imagine that it's possible that you could use Mathematica itself to read all your Modules and build a call graph of all the functions and variables defined along with their filename and line numbers. If that was done, it's probably not too much harder to make Mathematica produce a ctags format file that you could use within vi.
[EDIT] The ctags format isn't that complicated. Here's a quick hack of a perl script that can generate it (again provided that you have a ::usage for each symbol of interest)
#!/usr/bin/perl
use warnings ;
use strict ;
my @tags = () ;
open my $fh, "grep ::usage *.m | sed 's/::usage.*//'|" or die ; while (<$fh>)
{
chomp ;
/(.*):(.*)/ or die ;
my ($filename,$symbolname) = ($1,$2) ;
push( @tags, "$symbolname\t$filename\t/${symbolname}::usage/\n" ) ; } close$fh or die ;
print \$_ foreach (sort @tags) ;
This probably works for non-vim vi's too.
- | 2014-10-20 10:01:45 | {"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": 0.32044050097465515, "perplexity": 4095.820702271046}, "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-2014-42/segments/1413507442420.22/warc/CC-MAIN-20141017005722-00194-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://khoahoc.com.vn/giai-cau-1-bai-luyen-tap-sgk-toan-4-trang-133-43200 | # Giải câu 1 bài Luyện tập sgk Toán 4 trang 133
• 1 Đánh giá
Câu 1: Trang 133 sgk toán lớp 4
Tính (theo mẫu):
Mẫu: x 5 = x $\frac{5}{1}$ =$\frac{2 \times 5}{9 \times 1}$ = $\frac{10}{9}$
Ta có thể viết gọn như sau: : x 5 = $\frac{2 \times 5}{9}$ = $\frac{10}{9}$
a) x 8 b) $\frac{5}{6}$ x 7
c) x 1 d) $\frac{5}{8}$ x 0
Bài làm:
a) x 8 = x $\frac{8}{1}$ = $\frac{9 \times 8}{11 \times 1}$ = $\frac{72}{11}$
Viết gọn: x 8 = $\frac{9 \times 8}{11 }$ = $\frac{72}{11}$
b) x 7 = x $\frac{7}{1}$ = $\frac{5 \times 7}{6 \times 1}$ = $\frac{35}{6}$
Viết gọn: x 7 = $\frac{5 \times 7}{6 }$ = $\frac{35}{6}$
c) x 1 = x $\frac{1}{1}$ = $\frac{4 \times 1}{5 \times 1}$ =
Viết gọn: x 1 = $\frac{4 \times 1}{5}$ =
d) x 0 = x $\frac{0}{1}$ = $\frac{5 \times 0}{8 \times 1}$ = $\frac{0}{8}$ = 0
Viết gọn: x 0 = $\frac{5 \times 0}{8}$ = $\frac{0}{8}$ = 0
• 6 lượt xem
Cập nhật: 07/09/2021 | 2022-05-22 01:57:04 | {"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": 0.29237574338912964, "perplexity": 8157.778085529961}, "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/1652662543264.49/warc/CC-MAIN-20220522001016-20220522031016-00795.warc.gz"} |
https://web2.0calc.com/questions/absolute-value_50 | +0
# absolute value????
0
51
1
-3l6n - 3pl (If n = 4 and p = 12)
Oct 19, 2021
#1
+415
+1
If you didn't know, the absolute value is how far away a number is from 0 (btw, simplified definition).
Here's how you would solve it:
First, plug in the values of n and p into the equation.
-3 * | 6*4 - 3*12 |
Second, subtract the numbers inside the | |
-3 * | 24 - 36 | = -3 * | -12 |
Third, take the absolute value of the number inside the | |, which will end up being 12.
Finally, multiply the final two numbers.
-3 * 12 = -36
Hope this helps!
$$\infty$$
Oct 19, 2021 | 2021-11-28 06:08:25 | {"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": 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": 0.8356330990791321, "perplexity": 2131.4588734938984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358469.34/warc/CC-MAIN-20211128043743-20211128073743-00070.warc.gz"} |
http://math.stackexchange.com/questions/191306/sum-of-angles-in-mathbbrn?answertab=votes | # Sum of angles in $\mathbb{R}^n$
Given three vectors $v_1,v_2$ and $v_3$ in $\mathbb{R}^n$ with the standard scalar product the follwing is true $$\angle(v_1,v_2)+\angle(v_2,v_3)\geq \angle(v_1,v_3).$$
It tried to substitute $\angle(v_1,v_2) = cos^{-1}\frac{v_1 \cdot v_2}{\Vert v_1 \Vert \Vert v_2 \Vert}$ but I could not show the resulting inequality. What is the name of the inequality and do you know reference that one can cite in an article?
-
## 2 Answers
I'd like to suggest "triangle inequality in spherical geometry".
-
Any reference for this? – warsaga Sep 5 '12 at 10:33
I don't find a reference for this either! – warsaga Sep 5 '12 at 11:58
You can reduce the problem to $\mathbb{R}^3$, and there wlog v2=(0,0,1) then one gets an easy to prove inequality if one writes everything in polar coordinates.
- | 2015-08-30 03:56:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8958613872528076, "perplexity": 724.1872229548151}, "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-2015-35/segments/1440644064869.18/warc/CC-MAIN-20150827025424-00037-ip-10-171-96-226.ec2.internal.warc.gz"} |
http://icesp.org.br/equitable-bank-wlz/how-to-find-the-degree-of-algebraic-expression-5f7db9 | 10x^2+4x^2-6x^2=(10+4-6)x^2=8x^2. Polynomials with one degree are called linear, with two are called quadratic and three are cubic polynomials. Evaluate To find the value of an algebraic expression by substituting a number for a variable. Thus,8xy â 3xy = (8 â 3 )xy, i.e., 5xy. To Practice factoring binomials recall the reverse method Of Distributive Law means In Short-Distributing the factor. The formula just found is an example of a polynomial, which is a sum of or difference of terms, each consisting of a variable raised to a nonnegative integer power.A number multiplied by a variable raised to an exponent, such as $384\pi$, is known as a coefficient.Coefficients can be positive, negative, or zero, and can be whole numbers, decimals, or fractions. Therefore, the answer is 3x - 7y, 4. An algebraic expression of only three non-zero terms is called a "Trinomial". of an expression, such as when we wish to check whether a particular value of a variable satisfies a given equation or not. Now we will determine the exponent of the term. So, the degree of negative seven ð¦ Here the first term is 2x2, the second term is -3x5 and the third term is 5x6. interesting about this expression. An algebraic expression is a combination of constants, variables and algebraic operations (+, -, ×, ÷). Learn more about our Privacy Policy. The term 4xy in the expression 4xy + 7 is a product of factors x, y and 4. 3. (i) a + b, In an algebraic equation or plynomial the highest degree among the degress of different terms is called degree of algebraic equation/ polynomial. All that which can be done is to connect them by the sign of addition and leave the result in the form 2ab + 4bc. Introduction to Algebra. 1. While, on the basis of terms, it can be classified as monomial expression, binomial expression, and trinomial expression. find the degree of an algebraic expression. = (-9)z5 + (4)z3 + (7)z + 2 → simplify. Therefore, 7mn + (-9mn) + (-8mn) = -10mn, 2. =(3x-37)/((x+1)(x-4)), The terms which have the same literal coefficients raised to the same powers but may only differ in numerical coefficient are called similar or like terms, solution: We at Embibe will help you make the learning process easy and smooth. Here, the like terms are 5x2y, - 9yx2 since each of them having the same literal coefficients x2y. Rules for number patterns We shall see more such examples in the next section. We know that the value of an algebraic expression depends on the values of the variables forming the expression. - 9451018 The unlike terms 2ab and 4bc cannot be added together to form a single term. (100 pts. Degree of a Polynomial. exponent of that variable which appears in our polynomial. We have seen earlier also that formulas and rules in mathematics can be written in a concise = 4a + 6b - 2ab, 2. The first one is xy and the second is yz. For each algebraic expression : . Polynomials in two variables are algebraic expressions consisting of terms in the form $$a{x^n}{y^m}$$. = -9z5 + 4z3 + 7z + 2, While adding and subtracting like terms we collect different groups of like terms, then we find the sum and the difference of like terms in each group. term. 1.8x 1 32 20 °C 2x2 10x2 8x3y2z 8x2 9x3 8x2 5x 1 3y 1 8 5x 1 3y 1 8 c GOAL Identify the parts of an algebraic expression. | EduRev Class 10 Question is disucussed on EduRev Study Group by 137 Class 10 Students. So, itâs a polynomial. For example, 5ab is a monomial in algebraic expression. So, weâre asked to find the degree The degree of the polynomial is the greatest of the exponents (powers) of its various terms. =x[(-1)(x-5)] EXAMPLE:Find the value of the following expressions for a = 3, b = 2. 2xz: 1 + 1 = 2. Examples of polynomials and its degree. When we add two algebraic expressions, the like terms are added as given this Product is expressed by writing the number of factors in it to the right of the quantity and slightly raised. 8/(x+1)-5/(x-4)=(8(x-4))/((x+1)(x-4))-(5(x+1))/((x+1)(x-4)) Find the subtraction of 2 ( 3a - b ) - 7 ( - 2a + 3b ) In (3x^2â 5) we first obtain x^2, and multiply it by 3 to get 3x^2.From 3x^2, we subtract 5 to finally arrive at 3x^2â 5. Polynomials in one variable. For example, a - b will remain same as it is. Combine the like terms and simplify -5z5 + 2 - 3z3 + 8z + 7z3 - 4z5 - z. the biggest of these numbers. Find the Degree of this Polynomial: 5x 5 +7x 3 +2x 5 +9x 2 +3+7x+4. term, negative seven ð¦ squared. Nikita Nagabandhi. Power of literal quantities means when a quantity is multiplied by itself, any number of times, the product is called a power of that quantity. rules Meritpath is on-line e-learning education portal with dynamic interactive hands on sessions and worksheets. For this, we use the SHARE. Sum of all three digit numbers divisible by 6. Look at how the following expressions are obtained: The terms of an expression and their factors are (5x-3) If the total number of 25 paise coins is four times that of 50 paise coins, find the number of each type of coins. And we can see something Problem And the unlike terms are 5xy and - 2ab. 9a4b2c3 = 3 × 3 × a × a × a × a × b × b × c × c × c. Here we will learn the basic concept of polynomial and the "Degree Of A Polynomial". So highest degree is 4, thus polynomial has degree 4. The given algebraic expression xy+yz has two terms. problem And the unlike terms are 4xy2, - xy since each of them having the different literal coefficients. 1. constant has a fixed value. Now we will determine the exponent of each term. Add 7mn, -9mn, -8mn Suppose the difference between two like terms is a single like term; but the two unlike terms cannot be subtracted to get a single term. 2. =(x^2+5x+1-4x+5+7x+9)/(x+3) Here we see that all the terms of the given expression are unlike. Its degree will just be the highest Therefore, the difference of a positive and a negative unlike terms m and -n = m + n. To find the difference of a negative and a positive unlike terms suppose, take n from -m, we need to connect both the terms by using a subtraction sign [(-m) - n] and express the result in the form of -m - n. = -5z5 - 4z5 - 3z3 + 7z3 + 8z - z + 2 → arrange the like terms. Express -5 × 3 × p × q × q × r in exponent form. The sum will be another like term with coefficient 7 + (-9) + (-8) = -10 Here the first term is 7x and the second term is -4 And the degree of our polynomial is A variable can take various values. The degree of the polynomial is the greatest of the exponents (powers) of its various terms. And in fact, we can use the exact Here the first term is 16, the second term is 8x, the third term is - 12x2, the fourth term is 15x3 and the fifth term is - x4. 18:47. 1. If a natural number is denoted by n, 2n is an even number and (2n + 1) an odd number. Power Or Degree Of Algebraic Expressions: Using algedraic expressions â formulas and rules. =((x+1)(x-2))/((x+3)(x-2))+((2x+5)(x+3))/((x+3)(x-2)) Terms which have different algebraic factors are unlike terms. Finding square root using long division. We observe that the three terms of the trinomial (3x, We observe that the four terms of the polynomials (11m, m × m has two factors so to express it we can write m × m = m, b × b × b has three factors so to express it we can write b × b × b = b, z × z × z × z × z × z × z has seven factors so to express it we can write z × z × z × z × z × z × z = z, Product of 3 × 3 × 3 × 3 × 3 is written as 3, The perimeter of an equilateral triangle = 3 à (the length of its side). Specifically a one term expression is called a monomial; a two-term expression is called a binomial; Mountains are rocky. Answer. for factoring the binomials we need to find the common factor in each term so that we can find out the common factor. … also obtain expressions by combining variables with themselves or with other variables. Directions: Identify the kind of algebraic expression and determine the degree, variables and constant. A bag contains 25 paise and 50 paise coins whose total values is ₹ 30. Sum of 5xyz, -7xyz, -9xyz and 10xyz The unlike terms 2ab and 4bc cannot be subtracted to form a single term. Identify the degrees of the expressions being combined and the degree of the result And the total age of Sima and Tina is 40. In 4xy + 7, we first obtain xy, multiply it by 4 to get 4xy and add 7 to 4xy to get the expression. For example, the addition of the terms 4xy and 7 gives the expression 4xy + 7. 4. We observe that the above polynomial has five terms. 2. Thus, we observed that for solving the problems on subtracting like terms we can follow the same rules, as those used for solving subtraction of integers. So, the above trinomial is made up of three unlike or dissimilar terms. Practice the worksheet on factoring binomials to know how to find the common factor from the binomials. Algebraic Expression An expression that contains at least one variable. known. An algebraic sum with two terms is called a binomial, and an algebraic sum with three terms is called a trinomial. Therefore, the degree of the polynomial 16 + 8x - 12x2 + 15x3 - x4 = 4. Translating the word problems in to algebraic expressions. We now know very well what a variable is. We observe that the above polynomial has four terms. Suppose, to find the sum of two unlike terms -x and -y, we need to connect both the terms by using an addition symbol [(-x) + (-y)] and express the result in the form of -x - y. We use letters x, y, l, m, ... etc. We observe that the above polynomial has three terms. = (4)a + (6)b + (-2)ab → simplify positive integer values. Since, the greatest exponent is 6, the degree of 2x2 - 3x5 + 5x6 is also 6. Feb 17,2021 - Find the degree of the given algebraic expression ax2 + bx + ca)0b)1c)2d)3Correct answer is option 'B'. EStudy Tree 2,868 views. Degree of Polynomial is highest degree of its terms when Polynomial is expressed in its Standard Form. Write a × a × b × b × b in index form. =1/(5(x+1)). An algebraic expression which consists of one, two or more terms is called a "Polynomial". so finally the expression 52x2 - 9x + 36 = 7m + 82, solution: Here are some examples of polynomials in two variables and their degrees. But First: make sure the rational expression is in lowest terms! In xy, we multiply the variable x with another variable y. Thus,x xx y = xy. terms 4x^2 and 3 are left as they are. If we denote the length of a rectangle by l and its breadth by b, then the area of the rectangle = l xx b = lb. 1. fourth power minus seven ð¦ squared. x xx x = x^2, The expression 2y^2 is obtained from y: 2y^2. (iii) a^2+ 2ab + b^2, variable, and we can see its exponent. For example, Sima age is thrice more than Tina. Large parts of land have different types of trees growing close to one another. The degree of each term in a polynomial in two variables is the sum of the exponents in each term and the degree of the polynomial is the largest such sum. 2. above; the unlike terms are left as they are. The expression 4x + 5 is obtained from the variable x, first Express 9a4b2c3 in product form. List out the like terms from each set: Problem Terms are added to make an expression. 5ab, 5a, 5ac are unlike terms because they do not have identical variables. 1 . We observe that the above polynomial has one term. All that which can be done is to connect them by the sign of subtraction and leave the result in the form 2ab - 4bc. a × a × b × b × b = a2b3, 2. Here degree is the sum of exponents of variables and the exponent values are non-negative integers. Similarly, if b stands for the base and h for the height of a triangle, then the area of the They are much bigger than hills. 2a + 5b is a polynomial of two terms in two variables a and b. m + n is a binomial in two variables m and n. x + y + z is a trinomial in three variables x, y and z. P + Q Is A Multinomial Of Two Terms In Two Variables P And Q. = 5x - 3. An Algebraic Expression Of Two Terms Or More Than Three Terms Is Called A "Multinomial". = 11x - 2x - 3x - 7y. = 6x - 7y (here 7y is an unlike term), 3. The difference will be another like term with coefficient 27 - 12 = 15 =(-x)(x-5). The terms which do not have the same literal coefficients raised to the same powers are called dissimilar or unlike terms. It is sum of exponents of the variables in term. All that which can be done is to connect them by the sign of subtraction and leave the result in the form 2ab - 4bc. L.C.M method to solve time and work problems. Nagwa uses cookies to ensure you get the best experience on our website. =(x+5), Subtraction Of Algebraic Expressions Therefore, the sum of two unlike terms x and y = x + y. 5. So, the sum and the difference of several like terms is another like term whose coefficient is the sum and the difference of the coefficient of several like terms. 12x 2 y 3: 2 + 3 = 5. In algebraic expression 5x2 - 3y2 - 7x2 + 5xy + 4y2 + x2 - 2ab Examples of constants are: 4, 100, â17, etc. Coefficient of a Term. In other words, this expression is = 5x + 2x + 3x + 3y. 6xy 4 z: 1 + 4 + 1 = 6. 3xyz5 + 22 5. = (-5 - 4)z5 + (-3 + 7)z3 + (8 - 1)z + 2 → combine like terms. 1 . =(x^2-2x+x-2)/((x+3)(x-2))+(2x^2+6x+5x+15)/((x+3)(x-2)) Can you explain this answer? Addition or Subtraction of two or more polynomials: Collect the like terms together. There are a number of situations in which we need to find the value any natural number. For example: We find values of expressions, also, when we use formulas from geometry and from everyday mathematics. Sum of all three digit numbers divisible by 7 A desert is the part of earth which is very very dry.It is Answer to: Find two algebraic expressions for the area of the figure below : For one expression, view the figure as one large rectangle. Degree of Algebraic Expression: Highest power of the variable of an algebraic expression is called its degree. 10y â 20 is obtained by first multiplying y by 10 and then subtracting 20 from the product. Answer: 1 question Find the degree of each algebraic expression - the answers to estudyassistant.com ... What are the degree measures of the angles of triangle? and a three-term expression is called a trinomial. Based on the degree of polynomial, algebraic expressions can be classified as linear expressions, quadratic expressions, and cubic expressions. The sum (or difference) of two like termsis a like term with coefficient equal to the sum (or difference) of the coefficients of the two like terms. Subtract 12xy from 27xy We can work out the degree of a rational expression (one that is in the form of a fraction) by taking the degree of the top (numerator) and subtracting the degree of the bottom (denominator). An algebraic expression which consists of two non-zero terms is called a "Binomial". terms are added to form an expression.Just as the terms 5x and -3 are added to form an expression. So, letâs start with the first term The subtraction of unlike terms cannot be subtracted. Find the subtraction of 8/(x+1)-5/(x-4), Solution: variables. Grade 7 Maths Algebraic Expressions Short Answer Type Questions. On the other hand, a = 6x - 7y (here 7y is an unlike term). Problem =(3x^2+10x+13)/((x+3)(x-2)). (ii) 7a â 4b, recalling what we mean by the degree of a polynomial. Identify the kind of algebraIC expression and determine the degree, variables and constant. The difference will be another like term with coefficient 7 - 15 = -8 We observe that the above polynomial has two terms. Land is raised, flat, plain at some places. It is branch of mathematics in which … There is another type of asymptote, which is caused by the bottom polynomial only. Here 3x and 7y both are unlike terms so it will remain as it is. 1. Therefore, the degree of the polynomial 2x2 - 3x5 + 5x6 = 6. Sometimes anyone factor in a term is called the coefficient of the remaining part of the term. 2 . Remainder when 17 power 23 is divided by 16. Therefore, the difference of two positive unlike terms m and n = m - n. To find the difference of a positive and a negative unlike terms suppose, take -n from m, we need to connect both the terms by using a subtraction sign [m - (-n)] and express the result in the form of m + n. Obtain expressions by combining variables with themselves or with other variables terms which do not have the algebraic... Fact, we can find out the common factor → how to find the degree of algebraic expression the like ;... 3. x + 2x4 - 6x5 + 9x6 +10 4 5m2 - 3mn + 7m2n 5x +7x... Themselves or with other variables of ð¦ to the fourth power minus seven squared paise! Easy and smooth + 12 3. x + ( 7 ) z + 2 - 3x 5 + 5x.... A number for a variable is the highest exponent of each term and the! Land have different types of polynomials - Duration: 18:47 of triangle unlike term,. Having the different literal coefficients raised to the fourth power minus seven squared as monomial expression, and expression. Polynomial 2x 2 - 3z3 + 7z3 + 8z + 7z3 + 8z + 7z3 + 8z -.! And - 2ab subtraction, multiplication and division have different algebraic factors are unlike terms can not be to... Different algebraic factors binomial '' ) of its various terms identical variables (. Values is ₹ 30 also, when we use the operations of addition subtraction... Binomials we need to find the common factor from the binomials we to! - b will remain as it is branch of mathematics in which the 52x2. Each of them having the different literal coefficients raised to different powers -... Vertical Asymptotes first term in our polynomial + 2x4 - 6x5 + 9x6 +10..... what are the degree of negative seven ð¦ squared is a mathematical statement having an 'equal to ' between. 7M + 82 it consists of one, two or more terms called... And subtracting of numbers, whole numbers and integers Vertical Asymptotes in terms... Equation and using a formula, we have already come across expressions like 4x 5... Is called a binomial '' our expression, and we can see exponent... 1 for y ) x2 has degree 2. y has degree 4 having the different literal.... Close to one another we were able to show ð¦ to the fourth power minus seven squared!, i.e., natural numbers, whole numbers and integers is 2x2, the degree of a side the.: highest power of the exponents of each term earth which is very very dry.It is covered with sand factor. The third term is -3x5 and the second term is 5x6 its power degree! + ( 4 ) z3 + ( -y ) = x + y is the length a... Expressions may further be distinguished in the expression is called a Multinomial sometimes factor. A combination of constants, variables and their degrees we will determine the exponent of the part... A product of factors in it to the same algebraic factors are unlike terms x and -y = -... By 10 and then arrange it in ascending order of its terms when polynomial is numerical! 4Z5 - 3z3 + 7z3 - 4z5 - z across expressions like 4x + 5, 10y 20... Has a fixed value change in the expression difference of the expression depends on the other hand, constant! Other hand, a - b will remain as it is branch of mathematics in …! R in exponent form, 5ac are unlike terms can not be subtracted to form a single term basis... N × n × n × n × n × n × =! Sum or difference of the polynomial 16 + 8x - 12x2 + 15x3 - x4 4. Question, weâre asked to find the degree of ð¦ to the fourth power minus seven ð¦ squared same! Distributive Law means in Short-Distributing the factor trinomial, Multinomial = 4 polynomial: 5x 5 +7x +2x. Our second term is called a polynomial '', the like terms are and. As adding and subtracting like terms 82 it consists of 5 terms Finding Vertical Asymptotes it will remain it..., multiplication and division calledpolynomial algebraic expressions, the third term is -4 now will! Process easy and smooth p × q × q × r = -15pq2r, 4 while on. Some places has five terms or with other variables = 4x - 12y = 4x - 12y here... N, its successor is ( n + 1=11, which is caused by the bottom polynomial only 9x6 4! Having the different literal coefficients binomials we need to find the sum difference. Close to one another various concepts highest power of the trinomial have variables. Know very well what a variable is next section also obtain expressions by combining variables with or... 3Mn + 7m2n factors containing variables are raised to the fourth power seven... Left as they are: 4, 100, â17, etc xyz ) raised to integer... Of expressions, also, when we add two algebraic expressions may be. - Duration: 18:47 exponent is 6, the sum of monomials 4x + 3y, here. Whenever the bottom polynomial is the biggest of these terms r = -15pq2r, 4 x^n } { y^m \. -X + y = x - y +2x 5 +9x 2 +3+7x+4 the! Form \ ( a { x^n } { y^m } \ ), 5a, 5ac are unlike terms and! Again, thereâs only one non-zero term is -3x5 and the total age of and! Are 4xy2, - xy since each of them having the different literal coefficients same as and! In it to the same powers are called quadratic and three are cubic polynomials power ( 3 ) is... N, its successor is ( n + 1 ) or subtraction of two non-zero terms called... 15X - 12y - 11x = 15x - 11x = 15x - 11x = 15x - 11x = -. - 3 trinomial, Multinomial 2x2 + 5xy - 5x3 Finding Vertical.... Expression are unlike terms x and -y = ( 8 â 3 ) ''. Of factors in it to the same literal coefficients raised to the power... Power 23 is divided by 16 in two variables are algebraic expressions = xy + 5x6 how to find the degree of algebraic expression. Called the coefficient of the polynomial, binomial expression, binomial, trinomial, Multinomial 3y is an unlike ]! 7X and the degree, variables and constant ], 3 3, b =,! Be subtracted which consists of one, two or more terms Directions Identify... Variable, and trinomial expression 2 → simplify terms, it can be as. This question, we ’ re asked to find the degree of square! Negative seven ð¦ squared how to find the degree of algebraic expression 17 equation or plynomial the highest degree among the degress of different is... Up of four like terms are 4xy2, - xy since each of having! 7 Identify the kind of algebraic expressions: using algedraic expressions â formulas and rules which the expression -... We shall see more such examples in the next section, 5ac are unlike can. Sima and Tina is 40 not be subtracted of constants are: monomial, polynomial, combine like. 5Ab, 5a, 5ac are unlike can be classified as monomial,... Interactive hands on sessions and worksheets it in ascending order of its terms when polynomial is length... And then subtracting 20 from the binomials expression: highest power of the variable of an algebraic expression xy+yz polynomials... 5Ab, 5a, 5ac are unlike terms because they do not identical. Which appears in our polynomial left as they are by recalling what we mean by the polynomial. Is another Type of asymptote, which is caused by the bottom polynomial is a. The third term is -4 now we will determine the degree, and! At least one variable, and an algebraic expression which consists of 5 terms polynomials two... Expression is a product of factors in it to the same algebraic factors with dynamic hands. From everyday mathematics Standard form 3 = 5 above polynomial has degree 4 ( 3 ) = -! Binomial '' ( powers ) of its various terms to be algebraic factors are terms!, 5 than three terms a constant has a fixed value that not. 12X 2 y 3: 2 + 3 = 5 how to find the degree of algebraic expression of its roots we! The learning process easy and smooth trinomial '' remainder when 17 power 23 divided... A desert is the sum of two unlike terms 2ab and 4bc can not subtracted! One term × m × m × m how to find the degree of algebraic expression n × n × n power... Is -4 now we will determine the exponent of each term sum of monomials of our variables are to. = x + y dissimilar terms the learning process easy and smooth separate like & unlike terms x and =. Mean by the bottom polynomial only term is 7x and the exponent each... Binomials to know how to find the degree of a square is l^2 ` where. Short-Distributing the factor, it becomes difficult for students to understand the various concepts of trees growing close one! Variables degree constant 1 + 5, 10y â 20 thevalue of an algebraic expression highest! Having an 'equal to ' symbol between two algebraic expressions consisting of terms in the term some examples of in... Sima and Tina is 40, it can be classified as monomial expression, binomial expression and. Add two algebraic expressions is 1, the sum or difference of the following five.! We use the exact same method to find the degree of our variables are algebraic expressions the how to find the degree of algebraic expression addition... | 2021-09-20 16:25:42 | {"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": 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": 0.6613832116127014, "perplexity": 679.4731899950101}, "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/1631780057083.64/warc/CC-MAIN-20210920161518-20210920191518-00657.warc.gz"} |
https://chemistry.stackexchange.com/questions/145146/deciding-which-group-twists-out-of-the-plane-when-ortho-effect-takes-place | # Deciding which group twists out of the plane when ortho effect takes place
I'm going to take a few stills from 3D conformers of the following compounds available on PubChem in which ortho effect is applicable to show what I'm referring to.
In the compounds above due to steric repulsions between the groups present, one group needs to be twisted out of the plane of the benzene ring. My question is, how do we theoretically explain which group shifts out of the plane, and which doesn't?
To my understanding, two things would effect this; one would be the extra stabilisation/destabilisation of a group due to not being in resonance any longer once it moves out of the plane of the benzene ring, and the second would be the "bulkiness" of the group itself, which would energetically be measured as the group's A-Value.
For the above three compounds in the same order, from the perspective of A-Values (the text in brackets mentions what actually happens):
1. ($$\ce{COOH}$$ twists out of the plane) The A-Values are $$\ce{COOH} = 1.2, \ce{NO2} = 1.0$$, so it makes sense for $$\ce{COOH}$$ to stay in the plane of the ring.
2. ($$\ce{NMe2}$$ twists out of the plane) A-Values $$\ce{NMe2} = 2.1, \ce{NO2} = 1.0$$ so it makes sense for $$\ce{NMe2}$$ to stay in the plane.
3. ($$\ce{COMe}$$ slightly twists out of the plane) A-Values $$\ce{NH2} = 1.6, \ce{COMe} = 1.17$$ so it makes sense for $$\ce{NH2}$$ to stay in the plane.
(data from here and here)
I understand that A-Values are not the only thing which we need to consider, since resonance plays a part (maybe even other stuff?), but I haven't been able to figure out convincing reasoning as to why in the above examples the group which shifts out of the plane does so. Does the volume occupied by the groups play a crucial part as well, since so far I am yet to come across a compound in which the smaller group (by volume) shifts out of the plane? Are A-Values even relevant to such a scenario?
(I'm looking for a list of factors which need to be considered, whether this can even be explained/predicted theoretically, and/or explanations for the any of the above compounds. I understand that this could be slightly lengthy, so I'd be more than happy for answers which address any one of these, but I feel talking about the three compounds was necessary to explain the question properly, and hence the somewhat broad question.)
I am not sure the 3D conformation stills as reported on PubChem are all that accurate. Although crystal structures are sometimes referenced for specific molecules, some of the displays are in fact models, some of which do not make sense to me.
Here are some observations regarding the three molecules you noted.
2-Nitrobenzoic acid
The PubChem model shows both oxygen atoms of the nitro- group to be precisely coplanar with the phenyl ring. In the crystal structure, these oxygen atoms have a dihedral angle of $$125.5^\circ$$ and $$129.1^\circ$$ with respect to the aryl, i.e. away from coplanarity.
The PubChem model shows both oxygen atoms of the carboxylic acid to be precisely normal to the phenyl ring. In the crystal structure, these oxygen atoms have a dihedral angle of $$152.9^\circ$$ and $$162.7^\circ$$ with respect to the aryl, i.e. closer to coplanarity.
Pubchem Crystal structure entry CCSJWHN
N,N-Dimethyl-2-nitroaniline
I could not find the crystal structure of this molecule. However, I’m not sure it makes sense that the N,N-dimethyl amine adopt an $$\ce{sp^2}$$ character at the nitrogen center, at least as far as the Pubchem model representation is concerned. In such a pose, there can’t be extended resonance from the phenyl to amine as obtained with unsubstituted aniline. Either the methyls are near coplanar with the aryl to allow the pi orbitals to enter resonance or the amine is in $$\ce{sp^3}$$.
2’-Aminoacetophenone
I could not find the crystal structure of this molecule. What I found was the 4,5-dimethyl variant as 1-(2-amino-4,5-dimethylphenyl)ethan-1-one.
The 2’-Aminoacetophenone PubChem model shows the acetone oxygen to be precisely $$30.0^\circ$$ out of the aniline plane. In contrast, the crystal structure of 1-(2-amino-4,5-dimethylphenyl)ethan-1-one indicates that oxygen to be precisely in plane with the aniline. This coplanarity may not be surprising in this case as there is an intramolecular hydrogen bond between the two substituents.
Pubchem Crystal structure entry 1825318 (BEXTUW)
2'-Aminoacetophenone 1-(2-amino-4,5-dimethylphenyl)ethan-1-one
Original Post:
To my understanding, two things would effect this; one would be the extra stabilisation/destabilisation of a group due to not being in resonance any longer once it moves out of the plane of the benzene ring, and the second would be the "bulkiness" of the group itself, which would energetically be measured as the group's A-Value.
I think steric hindrance, you noted as “bulkiness” and estimated with an A-Values is the primary factor. There is little room for compromise on this one as two atoms can’t occupy the same space. The second factor is resonance as you noted. Another influencing factor is the presence of intramolecular interactions, such as a hydrogen bond. Solvation and pH are other influential factors to the ortho effect. | 2021-07-30 23:46:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7165838479995728, "perplexity": 875.3165966488694}, "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-2021-31/segments/1627046154032.75/warc/CC-MAIN-20210730220317-20210731010317-00666.warc.gz"} |
https://www.physicsforums.com/threads/binary-decimals-dual-expansion.288306/ | # Binary Decimals - Dual Expansion
1. Jan 29, 2009
### clg211
Hi,
I'm trying to prove that there's a bijection between the open interval (0,1) and the set of all sequences whose elements are 0 or 1 in order to show cardinality continuum.
So let C={a1, a2, a3,...|ai is either 0 or 1} which is the set of all sequences of 0's and 1's
and let D={0.b1b2b3...|bi is either 0 or 1} which is the set of all binary decimals on the closed interval [0,1]
I think it's pretty clear that there's a bijection between these two sets.
Then the open interval (0,1)=D\{0.000...., binary decimals with tails of repeating 1's} which is the part that gives me problems.
I'm trying to get rid of the dual expansions by getting rid of the tails of 1's. For example, I have both 0.1 and 0.0111..... in D which are the same number, and I want to get rid of 0.0111.....
Can someone please explain to me the rational numbers that will have this dual expansion in binary? A denominator of what form will cause this? I think this will help me in explicitly defining (0,1) in terms of D. Any other thoughts on what I've already stated would be appreciated as well.
2. Jan 29, 2009
### CRGreathouse
Repeating tails of 1 in the binary expansions correspond to numbers with denominators that are powers of two. | 2016-12-05 02:48:07 | {"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": 0.8854233622550964, "perplexity": 310.19408329148206}, "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-2016-50/segments/1480698541518.17/warc/CC-MAIN-20161202170901-00439-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://solvedlib.com/the-stockholders-equity-section-of-joshua-company,252874 | # The stockholders' equity section of Joshua Company shows the following on December 31, 2019 Preferred stock,...
The stockholders' equity section of Joshua Company shows the following on December 31, 2019 Preferred stock, 6%, 50 par value, 5.000 shares outstanding Common stock, 55 par value, 80,000 shares outstanding Paid-in capital in excess of par, common stock Retained earnings $250.000 00000 200,000 Total stockholders' equity 210.000$1.060.000 Required: Assume that the corporation has determined to pay out $90,000 in dividends at December 31, 2019. The last time that dividends were paid was on December 31, 2017. Calculate the amount of dividends that would be paid to preferred shareholders and the amount that would be paid to common shareholders under the following independent situations: a. The preferred stock is noncumulative and nonparticipating. b. The preferred stock is cumulative and nonparticipating. c. The preferred stock is cumulative and fully participating. ## Answers #### Similar Solved Questions 4 answers ##### The W tolerance IS rocket 8 +/-200 sled Problem can 019 1 Unitsconstanti1 the W tolerance IS rocket 8 +/-200 sled Problem can 019 1 Units constanti 1... 1 answer ##### Which type of immunity involves antibodies targeting a viral envelope antigen? a. nonspecific immunity b. specific... Which type of immunity involves antibodies targeting a viral envelope antigen? a. nonspecific immunity b. specific immunity c. innate immunity d. adaptive immunity e. b and d... 5 answers ##### Find the present value of$7000 payable at the end of years, if money may be invested at 8% with interest compounded continuously:The present value of 57000 is $l(Round to the nearest cent as needed ) Find the present value of$7000 payable at the end of years, if money may be invested at 8% with interest compounded continuously: The present value of 57000 is $l (Round to the nearest cent as needed )... 5 answers ##### Answer true or false The average value of the function f(1,y) = 1*y over the rectangle [0,5] x [0,3] is 3 k K < vdyd: Answer true or false The average value of the function f(1,y) = 1*y over the rectangle [0,5] x [0,3] is 3 k K < vdyd:... 5 answers ##### Two of every 3 seniors at Lewis High apply for college_ Three of every 5 seniors at Lewis High who apply for college are female students: (If there is not enough information to answer question write NONE in the blank:) What fraction of the graduating seniors at Lewis High do not apply to college?What fraction of the seniors are males who apply for college?What is the ratio of males who apply for college to the number of graduating seniors?The number of females who apply for college is number of Two of every 3 seniors at Lewis High apply for college_ Three of every 5 seniors at Lewis High who apply for college are female students: (If there is not enough information to answer question write NONE in the blank:) What fraction of the graduating seniors at Lewis High do not apply to college? Wh... 5 answers ##### Consider the three vectors: Aa5m @ 30" B-9m @ 120" C-3m @ ~20" with angles measured relative the positive diagram of these vectors show below on the leftR-C+iR-A-c 'graphical vector addition Recall that graphical vector addition where we add We are going [0 practice So an expression where vectors are added; e & R=c+i resulting in & new vector vectors tai] t0 The resultant vector; R , Is determined by placing Vegor from R is done by placing them tail to tip. the tail Consider the three vectors: Aa5m @ 30" B-9m @ 120" C-3m @ ~20" with angles measured relative the positive diagram of these vectors show below on the left R-C+i R-A-c 'graphical vector addition Recall that graphical vector addition where we add We are going [0 practice So an expr... 1 answer ##### Match the argument with the response suggested by economi Match the argument with the response suggested... match the argument with the response suggested by economi Match the argument with the response suggested by economists. The jobs argument: Trade should be restricted A Trade restriction causes domestic prices to rise. The cost because it destroys jobs in industries that compete with imports to c... 5 answers ##### If a, b,and € are digits for which the following holds, thena+b+c=_2 If a, b,and € are digits for which the following holds, thena+b+c=_ 2... 5 answers ##### What is the oxidizing agent for the following RedoxReaction?The reaction of calcium hydroxide with lithium metal.choices: a) Li (s)b) LiOHc) Ca (s) d) Ca(OH)2 What is the oxidizing agent for the following Redox Reaction? The reaction of calcium hydroxide with lithium metal. choices: a) Li (s) b) LiOH c) Ca (s) d) Ca(OH)2... 5 answers ##### Answer the (ollawlng qucstians about the relationshlos betwccn palrs varlablcs and LRe vales the conect answcr (or morc than 0m ccstionKame & cemeldon coruaFennWeeeaaWh cntnntapcatti; positivo pnto untar Matinnr Dttett Ien Kanabischoose oneAhrnAtonJn Tult Telabonna pctattn mIno votableychoarconeFor uhlchidata Epateaat Gl[oGomc * corheaicchcose onewhkh dalo l CEHTDATIL {clrreetauLomp o cortclatlontao ni Answer the (ollawlng qucstians about the relationshlos betwccn palrs varlablcs and LRe vales the conect answcr (or morc than 0m ccstion Kame & cemeldon corua FennWeeeaa Wh cntnnt apcatti; positivo pnto untar Matinnr Dttett Ien Kanabis choose one Ahrn AtonJn Tult Telabonna pctattn mIno votabley c... 1 answer ##### Keesha Co, borrows$140,000 cash on December 1 of the current year by signing a 120-day,...
Keesha Co, borrows $140,000 cash on December 1 of the current year by signing a 120-day, 11%,$140,000 note 1. On what date does this note mature? 2. & 3. What is the amount of interest expense in the current year and the following year from this note? 4. Prepare journal entries to record (a) is...
##### We follow the success of 120 people who each buy onle lottery card a week for three weeks. The probability of each card winning a small prize is .25.1. First find the probability that a participant will win a prize on all three of his or her cards Now find the exact) probability that 3 or more participants will win a prize 0n all three of their cards_Use OUI Iule of thumb to decide whether Poisson approximation is reasonable here. Now redo the calculation in 1.) using Poisson approximation
We follow the success of 120 people who each buy onle lottery card a week for three weeks. The probability of each card winning a small prize is .25. 1. First find the probability that a participant will win a prize on all three of his or her cards Now find the exact) probability that 3 or more part...
##### 010,8 Uzlnael ,DetulsBERLEN 114042mhmacnelaliginponte Icrim trpicecnttben 0e777 0)r 4hnleLDous 0econactuence(6) Uee part (2) Mne torict totMu1 " 5mhaiuia @dllut 0" ConyeiQrnco . R7Ucc purt (b} to Eend bowcr utetor2Wisltnt EC _contenend;[416.65 PolntslDETAILS SCALCETE 11.9.025 MLLua Jat5Indetnte intean77 c4( What te ted Us 0t cony ergence[347 0-lkee] DetaILsScAlceto 11.9.042DorerloriialgEchula mtrare
010,8 Uzlnael , Detuls BERLEN 114042 mhmacnelaligin ponte Icrim trpicecnttben 0e 777 0)r 4 hnle LDous 0econactuence (6) Uee part (2) Mne torict tot Mu 1 " 5 mhaiuia @dllut 0" ConyeiQrnco . R7 Ucc purt (b} to Eend bowcr utetor 2 Wisltnt EC _ contenend; [416.65 Polntsl DETAILS SCALCETE 11....
##### In matlab, us the pseudo inverse function to create a linear fit from velocity-second matrix. Use...
In matlab, us the pseudo inverse function to create a linear fit from velocity-second matrix. Use the equation to project the speed when v=12 m/s. v [6 8 10] s [50 88 124]...
##### O sodium bromide precipitate forms. water forms. O no precipitate forms. QUESTION 5 When aqueous solutions...
O sodium bromide precipitate forms. water forms. O no precipitate forms. QUESTION 5 When aqueous solutions of sodium chloride and silver acetate are mixed a. sodium acetate precipitate forms. O b. silver acetate precipitate forms O c silver chloride precipitate forms O d. no precipitate forms. QUEST...
##### Score: 0 of 13 pts 2 of 3 (1 complete) HW Score: 24.73 % , 6.92...
Score: 0 of 13 pts 2 of 3 (1 complete) HW Score: 24.73 % , 6.92 of 28 pts 9.3.6-T Question Help A popular theory is that presidential candidates have an advantage if they are taler than their main opponents. Listed are heights (in centimeters) of randomly selected presidents along with the heights o...
##### Find the local maximum and minimum values and saddle point(s) of the function_ If you have three-dimensiona graphing soitware graph the function with domain and viewpoint that reveal all the important aspects of the function (Enter your answers as comma-separated list. Ifan answer does not exist, enter DNE_f(x, Y) = 9e* cos(y)Ioca maximum value s)Ioca minimum value(s)saddle point(s)(x,Y,f) =
Find the local maximum and minimum values and saddle point(s) of the function_ If you have three-dimensiona graphing soitware graph the function with domain and viewpoint that reveal all the important aspects of the function (Enter your answers as comma-separated list. Ifan answer does not exist, en...
##### You're in charge of running a scientific program (job) that simulates a physical system for as ma...
You're in charge of running a scientific program (job) that simulates a physical system for as many discrete steps as you can. The lab you're working in has two large supercomputers, which we'll call A and B, which are capable of processing this job. However, you're not one of the hi...
##### Question9 ptsFour nndomly selected 100-onm reslstors Jre €omiected In J series circuiL Suppose that it is known that te population such re sstor: OCnn distribulion with > mem ol J00 ohmns Drid stndard devlation = 18 ohmsWhat Jr (he mean JlId standard aton the sarrpllrik; distrlbution 0l the averare Olims _ randouly selected IOO-orm resistors?MieanWhal is the probability t Uhe Wn 98_ Onmis?iof Imne droult 6Questionapphonaibcezon sharird"
Question 9 pts Four nndomly selected 100-onm reslstors Jre €omiected In J series circuiL Suppose that it is known that te population such re sstor: OCnn distribulion with > mem ol J00 ohmns Drid # stndard devlation = 18 ohms What Jr (he mean JlId standard aton the sarrpllrik; distrlbution 0...
##### Question (4 points)What is the solubility product constant expression; Ksp: for calcium chloride?[Ca*2J[CI ]2 [Ca+?][C1-1 [CaC12] [Ca+2]ZICl ] 1.62181 X 10*12
Question (4 points) What is the solubility product constant expression; Ksp: for calcium chloride? [Ca*2J[CI ]2 [Ca+?][C1-1 [CaC12] [Ca+2]ZICl ] 1.62181 X 10*12...
##### After Prof. Toner has had a chance to review the theo Question 26 A local juice...
after Prof. Toner has had a chance to review the theo Question 26 A local juice manufacturer distributes juice in bottles labeled 12 ounces. A government agency thinks that the comme customers. The agency selects 20 of these bottles, measures their contents and obtain samen 117 hard deviation of 0.7...
##### The translation of all existing media into numerical data accessible for computers is the definition of:...
The translation of all existing media into numerical data accessible for computers is the definition of: Annotation Unsupervised learning Embeddedness New media...
##### I need to show B and C the same way as A if A is correct!...
I need to show B and C the same way as A if A is correct! Thanks! 3. Convert the following binary expansion to a hexadecimal expansion. A) (1111 0111) 1.27 +1.26 +1.25 +1.24 +0.23 +1.22 +1.21 + 1.20 = 128 +64 + 32 + 16 + 4 + 2 + 1 = 247 247 = 8.30 + 7 30 = 8.3 + 6 3 = 8.0+3 (367). B) (1010 1110 100...
##### Proportion Maybe? IDK
Marine biologists capture, tag, and release 100 Florida manatees. Several months later, of 90 captured manatees, 5 have tags. Estimate the population of Floridamanatees....
##### Experiment nLc Homework As1lanmentIn this lab, You will run a mixturc biphenyl, benzhydrol. andbenzophenone on silica gcl plales three diiierent solvents&1: Draw the three compounds ad rank them from most to least polar.02: Consider the strength of each solvent and howitwil interact wath the compounds in the mixture. Draw what you think each plate bok Ike for cach solvent testedHlar0nesDcyonebanaMeninn
Experiment nLc Homework As1lanment In this lab, You will run a mixturc biphenyl, benzhydrol. andbenzophenone on silica gcl plales three diiierent solvents &1: Draw the three compounds ad rank them from most to least polar. 02: Consider the strength of each solvent and howitwil interact wath the ...
##### How do Kepler’s Laws help calculate the radius of the synchronous orbit of an Earth-orbiting satellite?...
How do Kepler’s Laws help calculate the radius of the synchronous orbit of an Earth-orbiting satellite? Discuss why you think Kepler’s laws are relevant to other scientists who came after him...
##### How do the concepts of the customer’s willingness to pay, the firm’s costs and the market...
How do the concepts of the customer’s willingness to pay, the firm’s costs and the market price relate to competitive advantage?...
##### The financial statements for Royale and Cavalier companies are summarized here: Royale Company Cavalier Company Balance...
The financial statements for Royale and Cavalier companies are summarized here: Royale Company Cavalier Company Balance Sheet Cash $17,000$ 80,000 Accounts Receivable, Net 47,000 8,000 Inventory 94,000 9,000 Equipment, Net 534,000 144,000 Other Assets 132...
##### Chaoter DuGuontIatt EIindanTJoiMlh 1.00 molhydr09un 9747Ate180 mel ca mal 100Ne KOC DeaAlthydrogenTETEAanid 4,00MtDouc JJdcuzL0ilat 12u51LSjo mal AeantOC nn 400 mal nena ofthe Abo4oUantmetal poqueed Irom MLScoppur?CLla + AgNolaqCulho3ialngiTAAi00457 0.5+0 07472126 4tha rnluma ohyutouea Brlt MEE+AL andarumchlan A6in7STP rcheaed tom 270JJuminun
Chaoter DuGuont Iatt EIi ndan TJoiMlh 1.00 mol hydr09un 9747 Ate 180 mel ca mal 100Ne KOC Dea Alt hydrogen TETE Aanid 4,00 MtDouc JJdcuz L0ilat 12u51 LSjo mal Aeant OC nn 400 mal nena ofthe Abo4o Uant metal poqueed Irom MLS coppur? CLla + AgNolaq Culho3ialngi TAAi 00457 0.5+0 0747 2126 4 tha rnluma ...
##### FormulaNameFormulaNameCalcium phosphiteAmmonium chlorateHCISO4 2Fe(NO3)zSulfurous acidLithium bisulfateCa(OH)z 52-Co(OH)zNitric acidLithium permanganateHCIOzHzPO4
Formula Name Formula Name Calcium phosphite Ammonium chlorate HCI SO4 2 Fe(NO3)z Sulfurous acid Lithium bisulfate Ca(OH)z 52- Co(OH)z Nitric acid Lithium permanganate HCIOz HzPO4...
##### Translate each algebraic expression into words. (Answers may vary.)$x y z$
Translate each algebraic expression into words. (Answers may vary.) $x y z$...
##### A hollow shaft has an internal diameter of 58 mm and a wall thickness of 4.7...
A hollow shaft has an internal diameter of 58 mm and a wall thickness of 4.7 mm Calculate its polar second moment of area, J. Input your answer in units of 10A-9 mA4 to 2 decimal places. So, for example, if J is found to be 530.6x10A-12 mA4, you should input 0.53 as your answer....
##### Problem 1.5 and the transmission coefficient in second picture please 1.4 Compute the Poynting veclor Tor...
Problem 1.5 and the transmission coefficient in second picture please 1.4 Compute the Poynting veclor Tor the gehetai plat 1.5 A plane wave is normally incident on a dielectric slab of permittivity er and thickness d, where d λ0/ (4 v and λο is the free-space wavelength of the ... | 2023-02-01 15:19:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4173010289669037, "perplexity": 13563.704164988314}, "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/1674764499946.80/warc/CC-MAIN-20230201144459-20230201174459-00098.warc.gz"} |
https://testbook.com/question-answer/two-bodies-of-mass-4-kg-and-6-kg-are-tied-to-the-e--62b57279885077f74fd0a2b2 | # Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is :
1. g/5
2. g/10
3. g
4. g/2
Option 1 : g/5
Free
RPMT Optics Test 1
17.9 K Users
10 Questions 40 Marks 10 Mins
## Detailed Solution
CONCEPT:
The acceleration of the system in the string due to the two bodies is written as;
$$a = \frac{{({m_1} - {m_2})g}}{{({m_1} + {m_2})}}$$ ---(1)
Where m1 and m2 are the masses that are attached to the string.
g is the acceleration due to gravity.
CALCULATION:
Using equation (1) we have;
$$a = \frac{{({m_1} - {m_2})g}}{{({m_1} + {m_2})}};$$ where m1 > m2
Where, m1 = 6 kg and m2 = 4 kg (Given)
Therefore,
$$a = \frac{{(6 - 4)g}}{{6 + 4}}$$
⇒ $$a = \frac{{2g}}{{10}}$$
$$a = \frac{g}{5}$$
Hence, option 1) is the correct answer. | 2023-03-31 18:53:04 | {"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": 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": 0.6951982378959656, "perplexity": 1239.7388106288827}, "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/1679296949678.39/warc/CC-MAIN-20230331175950-20230331205950-00238.warc.gz"} |
https://biblio.ugent.be/publication/879105 | ### On a class of hyperplanes of the symplectic and Hermitian dual polar spaces.
Bart De Bruyn UGent (2009) 16(1). p.1-20
abstract
Let $\Delta$ be a symplectic dual polar space (2n-1,K)$or a Hermitian dual polar space (2n-1,K,\theta)$, \geq 2$. We define a class of hyperplanes of$\Delta$arising from its Grassmann-embedding and discuss several properties of these hyperplanes. The construction of these hyperplanes allows us to prove that there exists an ovoid of the Hermitian dual polar space (2n-1,K,\theta)$ arising from its Grassmann-embedding if and only if there exists an empty $\theta variety in$\PG(n-1,K)$. Using this result we are able to give the first examples of ovoids in thick dual polar spaces of rank at least 3 which arise from some projective embedding. These are also the first examples of ovoids in thick dual polar spaces of rank at least 3 for which the construction does not make use of transfinite recursion. Please use this url to cite or link to this publication: author organization year type journalArticle (original) publication status published subject keyword symplectic/Hermitian dual polar space, ovoid, Grassmann embedding journal title Electronic Journal of Combinatorics Electron. J. Combin. volume 16 issue 1 pages 1 - 20 Web of Science type Article Web of Science id 000262254700001 JCR category MATHEMATICS JCR impact factor 0.605 (2009) JCR rank 138/251 (2009) JCR quartile 3 (2009) ISSN 1077-8926 language English UGent publication? yes classification A1 copyright statement I don't know the status of the copyright for this publication id 879105 handle http://hdl.handle.net/1854/LU-879105 date created 2010-02-24 14:12:53 date last changed 2010-03-05 09:09:52 @article{879105, abstract = {Let \${\textbackslash}Delta\$be a symplectic dual polar space (2n-1,K)\$ or a Hermitian dual polar space (2n-1,K,{\textbackslash}theta)\$, {\textbackslash}geq 2\$. We define a class of hyperplanes of \${\textbackslash}Delta\$ arising from its Grassmann-embedding and discuss several properties of these hyperplanes. The construction of these hyperplanes allows us to prove that there exists an ovoid of the Hermitian dual polar space (2n-1,K,{\textbackslash}theta)\$arising from its Grassmann-embedding if and only if there exists an empty \${\textbackslash}theta variety in \${\textbackslash}PG(n-1,K)\$. Using this result we are able to give the first examples of ovoids in thick dual polar spaces of rank at least 3 which arise from some projective embedding. These are also the first examples of ovoids in thick dual polar spaces of rank at least 3 for which the construction does not make use of transfinite recursion.},
author = {De Bruyn, Bart},
issn = {1077-8926},
journal = {Electronic Journal of Combinatorics},
keyword = {symplectic/Hermitian dual polar space,ovoid,Grassmann embedding},
language = {eng},
number = {1},
pages = {1--20},
title = {On a class of hyperplanes of the symplectic and Hermitian dual polar spaces.},
volume = {16},
year = {2009},
}
Chicago
De Bruyn, Bart. 2009. “On a Class of Hyperplanes of the Symplectic and Hermitian Dual Polar Spaces.” Electronic Journal of Combinatorics 16 (1): 1–20.
APA
De Bruyn, B. (2009). On a class of hyperplanes of the symplectic and Hermitian dual polar spaces. Electronic Journal of Combinatorics, 16(1), 1–20.
Vancouver
1.
De Bruyn B. On a class of hyperplanes of the symplectic and Hermitian dual polar spaces. Electronic Journal of Combinatorics. 2009;16(1):1–20.
MLA
De Bruyn, Bart. “On a Class of Hyperplanes of the Symplectic and Hermitian Dual Polar Spaces.” Electronic Journal of Combinatorics 16.1 (2009): 1–20. Print. | 2016-07-24 10:45:12 | {"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": 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": 0.8316605687141418, "perplexity": 1392.0296256938789}, "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-2016-30/segments/1469257823996.40/warc/CC-MAIN-20160723071023-00093-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/235494/bounded-sequence-cluster-point-bolzano-weierstrass | # bounded sequence, cluster point, Bolzano-Weierstrass…
i am stuck in one of my homework problems, the question is like the following:
Let $(x_n)$ be a bounded sequence, and let $c$ be the greatest cluster point of $(x_n)$:
(a) Prove that for every $\epsilon > 0$ there is $N$ such that for $n > N$ we have $x_n < c + \epsilon.\;$ (Hint: use the Bolzano-Weierstrass theorem.)
(b) Let $b_m = \text{sup}\{x_n : n >=m\};\; b = \text{lim}\; b_m$. Prove that $b \le c.\;$ (Hint: use (a).)
For part a), I tried to show the contrapositive, i supposed suppose there is an ϵ>0 such that infinitely many xn's satisfy xn≥c+ϵ, then this determines a subsequence that has a cluster point ≥c+ϵ. But I cannot completely explain this
For part b, I see that For all ϵ>0 we have bm < c+ϵ for almost all m (i.e., for m>N for a fixed N∈N). So i have to show that the sequence (bm) is bounded and monotonic. Thus, it has a limit, and so its limit satisfies b≤c+ϵ. But again, i could not fully explain it.
Can somebody give me a hand? Thanks
-
You're on the right track for part (a). If you have a cluster point for a subsequence of $(x_n)$, do you have a cluster point for the main sequence? If so, and that cluster point is $\geq c+\epsilon$ and $\epsilon>0$, than what does this say about $c$? You're nearly there.
For part (b), you're also very close. If $x\leq y+\epsilon$ for all $\epsilon>0$, then what can you conclude about $x$ in relation to $y$?
- | 2014-12-22 17:49:25 | {"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": 0.8723803758621216, "perplexity": 204.48385951817448}, "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-2014-52/segments/1418802775656.66/warc/CC-MAIN-20141217075255-00114-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://www.mapleprimes.com/questions/229009-Order-Of-Coefficients-And-Brackets-In-Metric | # Question:Order of coefficients and brackets in metric
## Question:Order of coefficients and brackets in metric
Maple
I was starting to set up a curved axisymmetric metric using the Physics package and came across an error message that I could not resolve. I was actually writing the metric in the form given after output line (5) in the code attcahed below. This returned the error message:
Error, (in Physics:-Setup) invalid subscript selector
Then I started fiddling and discovered that somehow braces and order of coefficients are making a difference in the metric. I have written the flat space metric in three different ways after output line (2). The difference is only in the coefficient of the last $d\phi^2$ term. For some reason, $r^2 (sin(\theta))^2$ is shown as $r (sin(\theta))^4$ in output line (3). Removing the brackets around $sin(theta)$ or writing $r^2$ after it is resolving the problem. Is this in someway related to the whole square operation? Can you please help me understand why this is happening?
The original error message I was getting went away after I similarly changed the order of coefficients in the second term of the curved metric to get output (6). Here again, there was a whole square operation!
Thank you!
>
>
(1)
>
(2)
>
(3)
>
(4)
>
(5)
>
>
(6)
> | 2022-06-26 14:13:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8582629561424255, "perplexity": 699.8040654643439}, "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/1656103269583.13/warc/CC-MAIN-20220626131545-20220626161545-00501.warc.gz"} |
http://math.stackexchange.com/questions/234004/continuous-partials-at-a-point-but-not-differentiable-there?answertab=active | # Continuous partials at a point but not differentiable there?
In Question on differentiability at a point, it is mentioned (and in Equivalent condition for differentiability on partial derivatives it is cited from Apostol) that for $f:\mathbb{R}^2\to\mathbb{R}$ to be differentiable at a point, one sufficient condition is that both partials exist at the point, and one of the partials is continuous throughout a neighborhood of the point.
I have seen counterexamples (e.g. the one given on Wikipedia) of functions which have partials defined everywhere, but fail to be differentiable at some point. But the examples I've seen aren't satisfying because both partials aren't continuous at the point in question (in fact, the partials fail to have a limit at that point at all), let alone in a neighborhood of the point.
Can someone direct me to a function that shows why the "throughout a neighborhood" condition is required for the sufficient condition mentioned in Apostol? I'm having trouble imagining a function where a partial is continuous at the point, but not throughout a neighborhood of the point. One thought I had was to use something whose cross section looked like Volterra's function (centered at a point not in the fat Cantor set), but I'm not certain that this would work, and even if it does, I wonder if there's a nicer example.
-
"I'm having trouble imagining a function where a partial is continuous at the point, but not throughout a neighborhood of the point" Continuity in that neighborhood is not required, just that the partials exist there. That last condition is neccessary because if $a$ is an isolated point of $A$, a function defined on $A$ is always continuous at $a$. – Nameless Nov 10 '12 at 8:07
Nameless, I think your comment almost completely answers the question of "how far can we push this condition?". I'm editing my question to clarify what's left. – Mark S. Nov 10 '12 at 13:57
As @Nameless pointed out, that Apostol quote says something stronger: the nicer partial only needs to be defined in a neighborhood and continuous at the point. Therefore, there is no such function where both partials are defined at a point $P$ and one of them is defined in an open neighborhood of $P$ and continuous at $P$ and yet the function is somehow not differentiable at $P$. | 2014-12-21 16:33:34 | {"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": 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": 0.9405920505523682, "perplexity": 111.07313719469967}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802771716.117/warc/CC-MAIN-20141217075251-00084-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://chat.stackexchange.com/transcript/36/2019/11/17/21-24 | 00:00 - 21:0021:00 - 00:00
9:01 PM
I want to take a unit square with grid lines like this:
and CHANGE the coordinate system
and see if it's homeomorphic to the original coordinate system
Actually I think I really mean CURVILINEAR coordinates
Well, I have no idea what that means, so I can't help you. Sounds like you want to endow the set $\Bbb R\times \Bbb R$ with different metrics, and compare the induced metric topology? But I'm not quite sure.
I want to define two different metrics in the unit square and see if there is a map between them
the first metric being the usual euclidean metric as pictured above
9:19 PM
@Ultradark You really have to work on your mathematical precision my dude
5
@user193319 No. $\omega\wedge\eta = (-1)^{k\ell} \eta\wedge\omega$, when $\omega$ is a $k$-form or $k$-vector and $\eta$ is an $\ell$-form or $\ell$-vector.
s n i p e d
So, @Leaky, what's your progress report for the month?
being confused by everything in Tate's thesis
9:31 PM
I have never looked.
watching my home fall
Otherwise, classes are going well? Made friends?
Yeah, your homeland is very sad. But I find almost all the world pathetic these days.
a war is happening as we speak
inside a university
we just lost the main entrance
@TedShifrin you might be able to deconfuse me of the fact that there are two different norms on $K \otimes_\Bbb Q \Bbb R$
the euclidean norm $\|(x_1, x_2, \cdots, x_{r_1+r_2})\| = \sum \|x_i\|^2$, and the field norm $\|(x_1, x_2, \cdots, x_{r_1+r_2})\| = \prod_{i=1}^{r_1} x_i \prod_{i=r_1+1}^{r_1+r_2} \|x_i\|^2$
You're missing a square on the first one, also squares on the second?
Whoa. I have no idea what's going on now.
this is the lattice $\Bbb Z[\sqrt2]$
the purple curve is the units group
9:39 PM
So, for the Gaussian integers you get the same norm, but in general you get different ones. I still have no idea what you're asking.
it isn't really a question
I'm just very confused as to how I'm supposed to deal with the two different norms
The norm that shows up in Galois theory is not supposed to be a metric norm.
But you should talk to @Mathein. I'm sure he has a good answer.
When you work with real quadratic extensions, you get hyperbolas, and when you work with imaginary quadratic extensions, you get ellipses.
yeah
This is probably basic, but I'm not sure I understand what is meant by "cut out"
Suppose $A$ is a ring, and $I$ is a maximal ideal of $A$. If $f\in I$, show that the Zariski tangent space of $A/(f)$ is cut out in the Zariski tangent space of $A$ by $f\pmod {I^2}$.
"cut out" = "defined"
9:54 PM
So the Zariski tangent space of $A/(f)$ is given by taking the maximal ideal $I'$ of $A/(f)$ corresponding to $I\subset A$ over the canonical quotient map. Then we have the Zariski tangent spaces $(I'/I'^2)^\vee$ and $(I/I^2)^\vee$, which are respectively $(A/f)/I'$ and $A/I$ vector spaces.
So the claim is that $(I'/I'^2)^\vee$ is defined in $(I/I^2)^\vee$ by $f\pmod {I^2}$?
Does it mean that we can identify it with the $(A/I)f$?
To make sense of that, I'd probably have to first realise $f$ as a dual element
10:10 PM
@TedShifrin the more I learn the more I know what I don't know
this isn't very productive towards writing my paper though
That's a usual feeling for math people :)
11:02 PM
Is there a way to implement a cubic residue symbol in mathematica?
Cubic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x3 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of the main theorem, which states that if p and q are primary numbers in the ring of Eisenstein integers, both coprime to 3, the congruence x3 ≡ p (mod q) is solvable if and only if x3 ≡ q (mod p) is solvable. == History == Sometime before 1748 Euler made the first conjectures about the cubic residuacity of small integers, but they were not published until 1849, after his death.Gaus...
Here's a thought:
There's 46 hiragana characters
Here's 23 of them: はたみれるうにりろふかゆくぬよへけなしらちそや
What if you were asked to guess at the other half
(assuming you don't already know hiragana)
11:18 PM
@Mason why can't you use the formula they give
break it down
for example: How do I multiply two numbers and store in a variable and so on..
@AkivaWeinberger I'd apply a reflection over a vertical line
I guess you should make a class called ZZomega
00:00 - 21:0021:00 - 00:00 | 2020-03-29 04:00:56 | {"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": 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": 0.7482091188430786, "perplexity": 460.1670735166915}, "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-2020-16/segments/1585370493684.2/warc/CC-MAIN-20200329015008-20200329045008-00103.warc.gz"} |
http://everything.explained.today/color_temperature/ | # Color temperature explained
Not to be confused with warm and cool colors.
The color temperature of a light source is the temperature of an ideal black-body radiator that radiates light of a color comparable to that of the light source. Color temperature is a characteristic of visible light that has important applications in lighting, photography, videography, publishing, manufacturing, astrophysics, horticulture, and other fields. In practice, color temperature is meaningful only for light sources that do in fact correspond somewhat closely to the radiation of some black body, i.e., light in a range going from red to orange to yellow to white to blueish white; it does not make sense to speak of the color temperature of, e.g., a green or a purple light. Color temperature is conventionally expressed in kelvins, using the symbol K, a unit of measure for absolute temperature.
Color temperatures over 5000 K are called "cool colors" (bluish), while lower color temperatures (2700–3000 K) are called "warm colors" (yellowish). "Warm" in this context is an analogy to radiated heat flux of traditional incandescent lighting rather than temperature. The spectral peak of warm-coloured light is closer to infrared, and most natural warm-coloured light sources emit significant infrared radiation. The fact that "warm" lighting in this sense actually has a "cooler" color temperature often leads to confusion.[1]
## Categorizing different lighting
The color temperature of the electromagnetic radiation emitted from an ideal black body is defined as its surface temperature in kelvins, or alternatively in micro reciprocal degrees (mired).[2] This permits the definition of a standard by which light sources are compared.
To the extent that a hot surface emits thermal radiation but is not an ideal black-body radiator, the color temperature of the light is not the actual temperature of the surface. An incandescent lamp's light is thermal radiation, and the bulb approximates an ideal black-body radiator, so its color temperature is essentially the temperature of the filament. Thus a relatively low temperature emits a dull red and a high temperature emits the almost white of the traditional incandescent light bulb. Metal workers are able to judge the temperature of hot metals by their color, from dark red to orange-white and then white (see red heat).
Many other light sources, such as fluorescent lamps, or light emitting diodes (LEDs) emit light primarily by processes other than thermal radiation. This means that the emitted radiation does not follow the form of a black-body spectrum. These sources are assigned what is known as a correlated color temperature (CCT). CCT is the color temperature of a black-body radiator which to human color perception most closely matches the light from the lamp. Because such an approximation is not required for incandescent light, the CCT for an incandescent light is simply its unadjusted temperature, derived from comparison to a black-body radiator.
### The Sun
The Sun closely approximates a black-body radiator. The effective temperature, defined by the total radiative power per square unit, is about 5780 K.[3] The color temperature of sunlight above the atmosphere is about 5900 K.[4]
The Sun may appear red, orange, yellow, or white from Earth, depending on its position in the sky. The changing color of the Sun over the course of the day is mainly a result of the scattering of sunlight and is not due to changes in black-body radiation. Rayleigh scattering of sunlight by Earth's atmosphere causes the blue color of the sky, which tends to scatter blue light more than red light.
Some daylight in the early morning and late afternoon (the golden hours) has a lower ("warmer") color temperature due to increased scattering of shorter-wavelength sunlight by atmospheric particles – an optical phenomenon called the Tyndall effect.
Daylight has a spectrum similar to that of a black body with a correlated color temperature of 6500 K (D65 viewing standard) or 5500 K (daylight-balanced photographic film standard).
For colors based on black-body theory, blue occurs at higher temperatures, whereas red occurs at lower temperatures. This is the opposite of the cultural associations attributed to colors, in which "red" is "hot", and "blue" is "cold".[5]
## Applications
### Lighting
For lighting building interiors, it is often important to take into account the color temperature of illumination. A warmer (i.e., a lower color temperature) light is often used in public areas to promote relaxation, while a cooler (higher color temperature) light is used to enhance concentration, for example in schools and offices.[6]
CCT dimming for LED technology is regarded as a difficult task, since binning, age and temperature drift effects of LEDs change the actual color value output. Here feedback loop systems are used, for example with color sensors, to actively monitor and control the color output of multiple color mixing LEDs.[7]
### Aquaculture
In fishkeeping, color temperature has different functions and foci in the various branches.
• In freshwater aquaria, color temperature is generally of concern only for producing a more attractive display. Lights tend to be designed to produce an attractive spectrum, sometimes with secondary attention paid to keeping the plants in the aquaria alive.
• In a saltwater/reef aquarium, color temperature is an essential part of tank health. Within about 400 to 3000 nanometers, light of shorter wavelength can penetrate deeper into water than longer wavelengths,[8] [9] [10] providing essential energy sources to the algae hosted in (and sustaining) coral. This is equivalent to an increase of color temperature with water depth in this spectral range. Because coral typically live in shallow water and receive intense, direct tropical sunlight, the focus was once on simulating this situation with 6500 K lights. In the meantime higher temperature light sources have become more popular, first with 10000 K and more recently 16000 K and 20000 K. Actinic lighting at the violet end of the visible range (420–460 nm) is used to allow night viewing without increasing algae bloom or enhancing photosynthesis, and to make the somewhat fluorescent colors of many corals and fish "pop", creating brighter display tanks.
### Digital photography
In digital photography, the term color temperature sometimes refers to remapping of color values to simulate variations in ambient color temperature. Most digital cameras and raw image software provide presets simulating specific ambient values (e.g., sunny, cloudy, tungsten, etc.) while others allow explicit entry of white balance values in kelvins. These settings vary color values along the blue–yellow axis, while some software includes additional controls (sometimes labeled "tint") adding the magenta–green axis, and are to some extent arbitrary and a matter of artistic interpretation.[11]
### Photographic film
Photographic emulsion film does not respond to lighting color identically to the human retina or visual perception. An object that appears to the observer to be white may turn out to be very blue or orange in a photograph. The color balance may need to be corrected during printing to achieve a neutral color print. The extent of this correction is limited since color film normally has three layers sensitive to different colors and when used under the "wrong" light source, every layer may not respond proportionally, giving odd color casts in the shadows, although the mid-tones may have been correctly white-balanced under the enlarger. Light sources with discontinuous spectra, such as fluorescent tubes, cannot be fully corrected in printing either, since one of the layers may barely have recorded an image at all.
Photographic film is made for specific light sources (most commonly daylight film and tungsten film), and, used properly, will create a neutral color print. Matching the sensitivity of the film to the color temperature of the light source is one way to balance color. If tungsten film is used indoors with incandescent lamps, the yellowish-orange light of the tungsten incandescent lamps will appear as white (3200 K) in the photograph. Color negative film is almost always daylight-balanced, since it is assumed that color can be adjusted in printing (with limitations, see above). Color transparency film, being the final artefact in the process, has to be matched to the light source or filters must be used to correct color.
Filters on a camera lens, or color gels over the light source(s) may be used to correct color balance. When shooting with a bluish light (high color temperature) source such as on an overcast day, in the shade, in window light, or if using tungsten film with white or blue light, a yellowish-orange filter will correct this. For shooting with daylight film (calibrated to 5600 K) under warmer (low color temperature) light sources such as sunsets, candlelight or tungsten lighting, a bluish (e.g. #80A) filter may be used. More-subtle filters are needed to correct for the difference between, say 3200 K and 3400 K tungsten lamps or to correct for the slightly blue cast of some flash tubes, which may be 6000 K.
If there is more than one light source with varied color temperatures, one way to balance the color is to use daylight film and place color-correcting gel filters over each light source.
Photographers sometimes use color temperature meters. These are usually designed to read only two regions along the visible spectrum (red and blue); more expensive ones read three regions (red, green, and blue). However, they are ineffective with sources such as fluorescent or discharge lamps, whose light varies in color and may be harder to correct for. Because this light is often greenish, a magenta filter may correct it. More sophisticated colorimetry tools can be used if such meters are lacking.
### Desktop publishing
In the desktop publishing industry, it is important to know a monitor’s color temperature. Color matching software, such as Apple's ColorSync for Mac OS, measures a monitor's color temperature and then adjusts its settings accordingly. This enables on-screen color to more closely match printed color. Common monitor color temperatures, along with matching standard illuminants in parentheses, are as follows:
• 5000 K (D50)
• 5500 K (D55)
• 6500 K (D65)
• 7500 K (D75)
• 9300 K
D50 is scientific shorthand for a standard illuminant: the daylight spectrum at a correlated color temperature of 5000 K. Similar definitions exist for D55, D65 and D75. Designations such as D50 are used to help classify color temperatures of light tables and viewing booths. When viewing a color slide at a light table, it is important that the light be balanced properly so that the colors are not shifted towards the red or blue.
Digital cameras, web graphics, DVDs, etc., are normally designed for a 6500 K color temperature. The sRGB standard commonly used for images on the Internet stipulates (among other things) a 6500 K display white point.
### TV, video, and digital still cameras
The NTSC and PAL TV norms call for a compliant TV screen to display an electrically black and white signal (minimal color saturation) at a color temperature of 6500 K. On many consumer-grade televisions, there is a very noticeable deviation from this requirement. However, higher-end consumer-grade televisions can have their color temperatures adjusted to 6500 K by using a preprogrammed setting or a custom calibration. Current versions of ATSC explicitly call for the color temperature data to be included in the data stream, but old versions of ATSC allowed this data to be omitted. In this case, current versions of ATSC cite default colorimetry standards depending on the format. Both of the cited standards specify a 6500 K color temperature.
Most video and digital still cameras can adjust for color temperature by zooming into a white or neutral colored object and setting the manual "white balance" (telling the camera that "this object is white"); the camera then shows true white as white and adjusts all the other colors accordingly. White-balancing is necessary especially when indoors under fluorescent lighting and when moving the camera from one lighting situation to another. Most cameras also have an automatic white balance function that attempts to determine the color of the light and correct accordingly. While these settings were once unreliable, they are much improved in today's digital cameras and produce an accurate white balance in a wide variety of lighting situations.
### Artistic application via control of color temperature
Video camera operators can white-balance objects that are not white, downplaying the color of the object used for white-balancing. For instance, they can bring more warmth into a picture by white-balancing off something that is light blue, such as faded blue denim; in this way white-balancing can replace a filter or lighting gel when those are not available.
Cinematographers do not “white balance” in the same way as video camera operators; they use techniques such as filters, choice of film stock, pre-flashing, and, after shooting, color grading, both by exposure at the labs and also digitally. Cinematographers also work closely with set designers and lighting crews to achieve the desired color effects.
For artists, most pigments and papers have a cool or warm cast, as the human eye can detect even a minute amount of saturation. Gray mixed with yellow, orange, or red is a “warm gray”. Green, blue, or purple create “cool grays”. Note that this sense of temperature is the reverse of that of real temperature; bluer is described as “cooler” even though it corresponds to a higher-temperature black body.
"Warm" gray "Cool" gray Mixed with 6% yellow. Mixed with 6% blue.
Lighting designers sometimes select filters by color temperature, commonly to match light that is theoretically white. Since fixtures using discharge type lamps produce a light of a considerably higher color temperature than do tungsten lamps, using the two in conjunction could potentially produce a stark contrast, so sometimes fixtures with HID lamps, commonly producing light of 6000–7000 K, are fitted with 3200 K filters to emulate tungsten light. Fixtures with color mixing features or with multiple colors, (if including 3200 K) are also capable of producing tungsten-like light. Color temperature may also be a factor when selecting lamps, since each is likely to have a different color temperature.
## Correlated color temperature
### Motivation
Black-body radiators are the reference by which the whiteness of light sources is judged. A black body can be described by its temperature and produces light of a particular hue, as depicted above. This set of colors is called color temperature. By analogy, nearly Planckian light sources such as certain fluorescent or high-intensity discharge lamps can be judged by their correlated color temperature (CCT), the temperature of the Planckian radiator whose color best approximates them. For light source spectra that are not Planckian, matching them to that of a black body is not well defined; the concept of correlated color temperature was extended to map such sources as well as possible onto the one-dimensional scale of color temperature, where "as well as possible" is defined in the context of an objective color space.
### Background
The notion of using Planckian radiators as a yardstick against which to judge other light sources is not new.[12] In 1923, writing about "grading of illuminants with reference to quality of color ... the temperature of the source as an index of the quality of color", Priest essentially described CCT as we understand it today, going so far as to use the term "apparent color temperature", and astutely recognized three cases:[13]
• "Those for which the spectral distribution of energy is identical with that given by the Planckian formula."
• "Those for which the spectral distribution of energy is not identical with that given by the Planckian formula, but still is of such a form that the quality of the color evoked is the same as would be evoked by the energy from a Planckian radiator at the given color temperature."
• "Those for which the spectral distribution of energy is such that the color can be matched only approximately by a stimulus of the Planckian form of spectral distribution."
Several important developments occurred in 1931. In chronological order:
1. Raymond Davis published a paper on "correlated color temperature" (his term). Referring to the Planckian locus on the r-g diagram, he defined the CCT as the average of the "primary component temperatures" (RGB CCTs), using trilinear coordinates.[14]
2. The CIE announced the XYZ color space.
3. Deane B. Judd published a paper on the nature of "least perceptible differences" with respect to chromatic stimuli. By empirical means he determined that the difference in sensation, which he termed ΔE for a "discriminatory step between colors ... Empfindung" (German for sensation) was proportional to the distance of the colors on the chromaticity diagram. Referring to the (r,g) chromaticity diagram depicted aside, he hypothesized that[15]
KΔE = |c1c2| = max(|r1r2|, |g1g2|).
These developments paved the way for the development of new chromaticity spaces that are more suited to estimating correlated color temperatures and chromaticity differences. Bridging the concepts of color difference and color temperature, Priest made the observation that the eye is sensitive to constant differences in "reciprocal" temperature:[16]
Priest proposed to use "the scale of temperature as a scale for arranging the chromaticities of the several illuminants in a serial order". Over the next few years, Judd published three more significant papers:
The first verified the findings of Priest,[13] Davis,[14] and Judd,[15] with a paper on sensitivity to change in color temperature.[17]
The second proposed a new chromaticity space, guided by a principle that has become the holy grail of color spaces: perceptual uniformity (chromaticity distance should be commensurate with perceptual difference). By means of a projective transformation, Judd found a more "uniform chromaticity space" (UCS) in which to find the CCT. Judd determined the "nearest color temperature" by simply finding the point on the Planckian locus nearest to the chromaticity of the stimulus on Maxwell's color triangle, depicted aside. The transformation matrix he used to convert X,Y,Z tristimulus values to R,G,B coordinates was:[18]
\begin{bmatrix}R\G\B\end{bmatrix}=\begin{bmatrix}3.1956&2.4478&-0.1434\ -2.5455&7.0492&0.9963\ 0.0000&0.0000&1.0000\end{bmatrix}\begin{bmatrix}X\Y\Z\end{bmatrix}.
From this, one can find these chromaticities:[19]
u= 0.4661x+0.1593y y-0.15735x+0.2424
,v=
0.6581y y-0.15735x+0.2424
.
The third depicted the locus of the isothermal chromaticities on the CIE 1931 x,y chromaticity diagram.[20] Since the isothermal points formed normals on his UCS diagram, transformation back into the xy plane revealed them still to be lines, but no longer perpendicular to the locus.
### Calculation
Judd's idea of determining the nearest point to the Planckian locus on a uniform chromaticity space is current. In 1937, MacAdam suggested a "modified uniform chromaticity scale diagram", based on certain simplifying geometrical considerations:[21]
u=
4x -2x+12y+3
,v=
6y -2x+12y+3
.
This (u,v) chromaticity space became the CIE 1960 color space, which is still used to calculate the CCT (even though MacAdam did not devise it with this purpose in mind).[22] Using other chromaticity spaces, such as u'v, leads to non-standard results that may nevertheless be perceptually meaningful.[23]
The distance from the locus (i.e., degree of departure from a black body) is traditionally indicated in units of
\Deltauv
; positive for points above the locus. This concept of distance has evolved to become Delta E, which continues to be used today.
#### Robertson's method
Before the advent of powerful personal computers, it was common to estimate the correlated color temperature by way of interpolation from look-up tables and charts. The most famous such method is Robertson's,[24] who took advantage of the relatively even spacing of the mired scale (see above) to calculate the CCT Tc using linear interpolation of the isotherm's mired values:[25]
1 = Tc
1 + Ti
\theta1 \theta1+\theta2
\left(
1 Ti+1
-
1 Ti
\right),
where
Ti
and
Ti+1
are the color temperatures of the look-up isotherms and i is chosen such that
Ti<Tc<Ti+1
. (Furthermore, the test chromaticity lies between the only two adjacent lines for which
di/di+1<0
.)
If the isotherms are tight enough, one can assume
\theta1/\theta2\sin\theta1/\sin\theta2
1 = Tc
1 + Ti
di di-di+1
\left(
1 Ti+1
-
1 Ti
\right).
The distance of the test point to the i-th isotherm is given by
d
i=(vT-vi)-mi(uT-ui)
\sqrt
2 {1+m i
},
where
(ui,vi)
is the chromaticity coordinate of the i-th isotherm on the Planckian locus and mi is the isotherm's slope. Since it is perpendicular to the locus, it follows that
mi=-1/li
where li is the slope of the locus at
(ui,vi)
.
### Precautions
Although the CCT can be calculated for any chromaticity coordinate, the result is meaningful only if the light sources are nearly white.[26] The CIE recommends that "The concept of correlated color temperature should not be used if the chromaticity of the test source differs more than [$\scriptstyle\Delta_{uv} = 5 \times 10^{-2}$] from the Planckian radiator."[27] Beyond a certain value of
\scriptstyle\Deltauv
, a chromaticity co-ordinate may be equidistant to two points on the locus, causing ambiguity in the CCT.
### Approximation
If a narrow range of color temperatures is considered—those encapsulating daylight being the most practical case—one can approximate the Planckian locus in order to calculate the CCT in terms of chromaticity coordinates. Following Kelly's observation that the isotherms intersect in the purple region near (x = 0.325, y = 0.154),[28] McCamy proposed this cubic approximation:[29]
CCT(x,y)=-449n3+3525n2-6823.3n+5520.33,
where is the inverse slope line, and is the "epicenter"; quite close to the intersection point mentioned by Kelly. The maximum absolute error for color temperatures ranging from 2856 K (illuminant A) to 6504 K (D65) is under 2 K.
A more recent proposal, using exponential terms, considerably extends the applicable range by adding a second epicenter for high color temperatures:[30]
CCT(x,y)=A0+A1\exp(-n/t1)+A2\exp(-n/t2)+A3\exp(-n/t3)
where is as before and the other constants are defined below:
3–50 kK50–800 kK
xe0.33660.3356
ye0.17350.1691
A0−949.8631536284.48953
A16253.803380.00228
t10.921590.07861
A228.705995.4535×10−36
t20.200390.01543
A30.00004
t30.07125
The author suggests that one use the low-temperature equation to determine whether the higher-temperature parameters are needed.
The inverse calculation, from color temperature to corresponding chromaticity coordinates, is discussed in .
## Color rendering index
The CIE color rendering index (CRI) is a method to determine how well a light source's illumination of eight sample patches compares to the illumination provided by a reference source. Cited together, the CRI and CCT give a numerical estimate of what reference (ideal) light source best approximates a particular artificial light, and what the difference is.
## Spectral power distribution
Light sources and illuminants may be characterized by their spectral power distribution (SPD). The relative SPD curves provided by many manufacturers may have been produced using 10 nm increments or more on their spectroradiometer.[31] The result is what would seem to be a smoother ("fuller spectrum") power distribution than the lamp actually has. Owing to their spiky distribution, much finer increments are advisable for taking measurements of fluorescent lights, and this requires more expensive equipment.
## Color temperature in astronomy
In astronomy, the color temperature is defined by the local slope of the SPD at a given wavelength, or, in practice, a wavelength range. Given, for example, the color magnitudes B and V which are calibrated to be equal for an A0V star (e.g. Vega), the stellar color temperature
TC
is given by the temperature for which the color index
B-V
of a black-body radiator fits the stellar one. Besides the
B-V
, other color indices can be used as well. The color temperature (as well as the correlated color temperature defined above) may differ largely from the effective temperature given by the radiative flux of the stellar surface. For example, the color temperature of an A0V star is about 15000 K compared to an effective temperature of about 9500 K.[32]
• Book: Stroebel, Leslie . John Compton . Ira Current . Richard Zakia . Basic Photographic Materials and Processes . 2nd . Focal Press . Boston . 2000 . 0-240-80405-8.
• Book: Wyszecki, Günter. Stiles, Walter Stanley . 1982 . Color Science: Concept and Methods, Quantitative Data and Formulæ . 3.11: Distribution Temperature, Color Temperature, and Correlated Color Temperature. 224–229. Wiley . New York . 0-471-02106-7.
## Notes and References
1. See the comments section of this LightNowBlog.com article on the recommendations of the American Medical Association to prefer LED-lighting with cooler color temperatures (i.e. warmer color).
2. Book: Principles of Lighting. Wallace Roberts Stevens. Constable. 1951.
3. Web site: Williams . D. R. . 2004 . Sun Fact Sheet . . 2010-09-27 . live . https://web.archive.org/web/20131206053849/http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html . 2013-12-06 .
4. Web site: Principles of Remote Sensing . . 2012-06-18 . live . https://web.archive.org/web/20120702174159/http://www.crisp.nus.edu.sg/~research/tutorial/optical.htm . 2012-07-02 .
5. Book: Mastering Digital Flash Photography: The Complete Reference Guide . Chris George . . 2008 . 978-1-60059-209-6 . 11 .
6. Book: Encyclopedia of Laser Physics and Technology . Rüdiger Paschotta . Wiley-VCH . 2008 . 978-3-527-40828-3 . 219 .
7. Book: Sensors and Feedback Control of Multi-Color LED Systems . Thomas Nimz, Fredrik Hailer and Kevin Jensen . LED Professional . 2012 . 1993-890X . 2–5 . dead . https://web.archive.org/web/20140429162806/http://www.mazet.de/en/english-documents/english/featured-articles/sensors-and-feedback-control-of-multi-color-led-systems-1/download#.UX7VXYIcUZI . 2014-04-29 .
8. Web site: Water Absorption Spectrum. Chaplin. Martin. 2012-08-01. live. https://web.archive.org/web/20120717061228/http://www.lsbu.ac.uk/water/vibrat.html. 2012-07-17.
9. Pope R. M., Fry E. S. . 1997 . Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements . Applied Optics . 36 . 33 . 8710–8723 . Optical Society of America . 10.1364/AO.36.008710 . 1997ApOpt..36.8710P .
10. Book: Jerlov N. G. . Marine Optics. . Elsevie Oceanography Series. . 14 . 128–129 . 1976 . Elsevier Scientific Publishing Company . 0-444-41490-8 . Amsterdam . August 1, 2012 . live . https://web.archive.org/web/20171221064443/https://books.google.com/books?id=tzwgrtnW_lYC&lpg=PA128&pg=PA128#v=onepage&q&f=false . December 21, 2017 .
11. Web site: Reality Check: Ambiguity and Ambivalence in Digital Color Photography . Kern . Chris . 2011-03-11 . live . https://web.archive.org/web/20110722001411/http://www.chriskern.net/essay/realityCheck.html . 2011-07-22 .
12. Edward P.. Hyde. June 1911. This existence of a color match is a consequence of there being approximately the same energy distribution in the visible spectra.. The American Physical Society. Physical Review . Series I. 32. 632–633. 10.1103/PhysRevSeriesI.32.632. A New Determination of the Selective Radiation from Tantalum (abstract). 6.
13. Irwin G.. Priest. The colorimetry and photometry of daylight ·and incandescent illuminants by the method of rotatory dispersion. JOSA. 7. 12. 1175–1209. 1923. The color temperature of a source is the temperature at which a Planckian radiator would emit radiant energy competent to evoke a color of the same quality as that evoked by the radiant energy from the source in question. The color temperature is not necessarily the same as the 'true temperature' of the source; but this circumstance has no significance whatever in the use of the color temperature as a means to the end of establishing a scale for the quality of the color of illuminants. For this purpose no knowledge of the temperature of the source nor indeed of its emissive properties is required. All that is involved in giving the color temperature of any illuminant is the affirmation that the color of the luminant is of the same quality as the color of a Planckian radiator at the given temperature.. 10.1364/JOSA.7.001175. 1923JOSA....7.1175P.
14. Raymond. Davis. Raymond Davis, Jr.. A Correlated Color Temperature for Illuminants. Bureau of Standards Journal of Research. 7. 4. 659–681. 1931. The ideal correlated colour temperature of a light source is the absolute temperature at which the Planckian radiator emits radiant energy component to evoke a colour which, of all Planckian colours, most closely approximates the colour evoked by the source in question.. 10.6028/jres.007.039. from Research Paper 365
15. Chromaticity sensibility to stimulus differences. JOSA. Deane B.. Judd. 72–108. 22. 1931. 2. 10.1364/JOSA.22.000072.
16. A proposed scale for use in specifying the chromaticity of incandescent illuminants and various phases of daylight. Irwin G.. Priest. February 1933. JOSA. 23. 2. 42. 10.1364/JOSA.23.000041. 1933JOSA...23...41P.
17. Deane B.. Judd. January 1933. JOSA. 23. 1. Sensibility to Color-Temperature Change as a Function of Temperature. Regarding (Davis, 1931): This simpler statement of the spectral-centroid relation might have been deduced by combining two previous findings, one by Gibson (see footnote 10, p. 12) concerning a spectral-centroid relation between incident and transmitted light for daylight filters, the other by Langmuir and Orange (Trans. A.I.E.E., 32, 1944–1946 (1913)) concerning a similar relation involving reciprocal temperature. The mathematical analysis on which this latter finding is based was given later by Foote, Mohler and Fairchild, J. Wash. Acad. Sci. 7, 545–549 (1917), and Gage, Trans. I.E.S. 16, 428–429 (1921) also called attention to this relation.. 10.1364/JOSA.23.000007. 7. 1933JOSA...23....7J.
18. A Maxwell Triangle Yielding Uniform Chromaticity Scales. JOSA. Deane B.. Judd. 25. 1. January 1935. 24–35. An important application of this coordinate system is its use in finding from any series of colors the one most resembling a neighboring color of the same brilliance, for example, the finding of the nearest color temperature for a neighboring non-Planckian stimulus. The method is to draw the shortest line from the point representing the non-Planckian stimulus to the Planckian locus.. 10.1364/JOSA.25.000024. 1935JOSA...25...24J.
19. JOSA. Quantitative data and methods for colorimetry. 34. 11. November 1944. OSA Committee on Colorimetry. 633–688. 10.1364/JOSA.34.000633. 1944JOSA...34..633C. (recommended reading)
20. Estimation of Chromaticity Differences and Nearest Color Temperatures on the Standard 1931 I.C.I. Colorimetric Coordinate System. JOSA. Deane B.. Judd. 26. 11. 421–426. November 1936. 10.1364/JOSA.26.000421. 1936JOSA...26..421J.
21. Projective transformations of I.C.I. color specifications. David L.. MacAdam. JOSA. August 1937. 27. 8. 294–299. 10.1364/JOSA.27.000294. 1937JOSA...27..294M.
22. http://www.delta.dk/C1256ED600446B80/sysOakFil/i102/\$File/I102%20Correlated%20Colour%20Temperature.pdf The CIE definition of correlated color temperature (removed)
23. Correlated Color-Temperature Calculations in the CIE 1976 Chromaticity Diagram. Color Research & Application. Wiley Interscience. Schanda. Danyi. János. M.. 2. 4. 161–163. 1977. 10.1002/col.5080020403. Correlated color temperature can be calculated using the new diagram, leading to somewhat different results than those calculated according to the CIE 1960 uv diagram..
24. Computation of Correlated Color Temperature and Distribution Temperature. Alan R.. Robertson. JOSA. 58. 11. 1528–1535. November 1968. 10.1364/JOSA.58.001528. 1968JOSA...58.1528R.
25. http://www.brucelindbloom.com/index.html?Eqn_XYZ_to_T.html ANSI C implementation
26. Determination of correlated color temperature based on a color-appearance model. Wolfgang. Walter. Color Research & Application. 17. 1. 24–30. February 1992. 10.1002/col.5080170107. The concept of correlated color temperature is only useful for lamps with chromaticity points close to the black body….
27. Book: Schanda, János. Colorimetry: Understanding the CIE System. Wiley Interscience. 2007. 3: CIE Colorimetry. 37–46. 978-0-470-04904-4. 10.1002/9780470175637.ch3.
28. Kelly. Kenneth L.. August 1963. Lines of Constant Correlated Color Temperature Based on MacAdam's (u,v) Uniform Chromaticity Transformation of the CIE Diagram. JOSA. 53. 8. 999–1002. 10.1364/JOSA.53.000999. 1963JOSA...53..999K.
29. Correlated color temperature as an explicit function of chromaticity coordinates. 17. 2. 142–144. Color Research & Application. Calvin S.. April 1992. McCamy. 10.1002/col.5080170211. plus erratum
30. Calculating Correlated Color Temperatures Across the Entire Gamut of Daylight and Skylight Chromaticities. Javier. Hernández-Andrés. Applied Optics. 38. 27. 5703–5709. September 20, 1999. 10.1364/AO.38.005703. 18324081. Lee. RL. Romero. J. live. https://web.archive.org/web/20160401133754/http://www.usna.edu/Users/oceano/raylee/papers/RLee_AO_CCTpaper.pdf. April 1, 2016. 1999ApOpt..38.5703H.
31. Gretag's SpectroLino and X-Rite's ColorMunki have an optical resolution of 10 nm.
32. Book: Unsöld, Albrecht . Bodo Baschek . Der neue Kosmos . 6 . Springer . Berlin, Heidelberg, New York . 1999 . 3-540-64165-3. | 2020-06-02 19:51:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5405234694480896, "perplexity": 3201.7890367688638}, "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/1590347426801.75/warc/CC-MAIN-20200602193431-20200602223431-00519.warc.gz"} |
https://brilliant.org/problems/coin-tossed/ | # Coin Tossed
Discrete Mathematics Level 2
A fair coin is tossed $$six$$ times. The probability of obtaining $$4$$ or more heads is $$\text{__________}$$.
× | 2016-10-27 07:04:37 | {"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": 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": 0.7762657999992371, "perplexity": 1022.7768366796511}, "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-2016-44/segments/1476988721142.99/warc/CC-MAIN-20161020183841-00052-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://docs.itascacg.com/flac3d700/common/fish/doc/fish_manual/fish_fish/string_utilities/fish_string.csv.from.html | # string.csv.from
Syntax
l := string.csv.from(s<,sep>)
Separate the string into a token list using the comma-separated-values convention.
By default, the separator used will be a comma character ,, otherwise the separator will be the string provided.
Returns: l - A list of token strings generated using the comma-separated-values convention. s - The string to separate into tokens sep - the string to use as a delimiter. A single comma character , is used as the default. | 2022-09-30 06:40:30 | {"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": 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": 0.31932076811790466, "perplexity": 3990.2516774741716}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335444.58/warc/CC-MAIN-20220930051717-20220930081717-00070.warc.gz"} |
http://tex.stackexchange.com/questions/22386/difference-between-sexpr-and/22392 | # Difference between \Sexpr and <<>>=
I am new to sweave and learning a lot. For the most part \Sexpr works well for simple variables and also calling R functions.
But other times it will fail, I have found that I can get around this using the <<>>= command. I am interested to know what the difference is, and when I should use which one.
For instance:
I can use \Sexpr{parc.name(parc)} but \Sexpr{p_curve.data.points(p_curve.data);} will not work, however the following will work:
<<echo=false,results=tex>>=
p_curve.data.points(p_curve.data);
@
Where the functions are defined in a seperate file using source("filename.R")
parc.name <- function(code) {
conn <- connect();
res <- dbGetQuery(conn, paste("SELECT displayname FROM machinepark WHERE name='", code, "' LIMIT 1", sep=""));
disconnect(conn);
res$displayname[1]; } and p_curve.data.points <- function(pc_data) { rows <- length(pc_data$power);
for(i in 1:rows){
cat("(", pc_data$windspeed[i], ",", pc_data$power[i], ")");
}
}
-
cat is not appropriate in \Sexpr statements. I believe it tries to run cat on the value returned from evaluating what's inside the \Sexpr; since cat doesn't return a value, \Sexpr doesn't have anything to output.
See the following .Rnw file for examples.
\documentclass{article}
\begin{document}
<<>>=
sayhi <- function(k=2) {for(i in 1:k) cat("hi",i,"| ") }
sayhi()
@
But with Sexpr, {\tt sayhi()} prints <\Sexpr{sayhi()}>.
Note that {\tt sayhi()} returns nothing; that's why Sexpr doesn't work.
<<>>=
a <- sayhi()
cat(a)
@
<<>>=
savehi <- function(k=2) {
out <- c()
for(i in 1:k) {
out <- paste(out, "hi", i,"| ")
}
out
}
hi <- savehi()
cat(hi)
@
And with Sexpr, {\tt savehi()} prints <\Sexpr{savehi()}>.
\end{document}
Aside from original answer: Another "gotcha" with \Sexpr expressions is trying to use curly brackets. Curly brackets are not allowed in \Sexpr expressions. Instead do the computation in a hidden code chunk and use the result in an \Sexpr.
See the Sweave manual for details.
Also see this question at stackoverflow.
-
thanks for the pointer I have included more details to the question. – klonq Jul 8 '11 at 12:11 | 2016-05-30 12:42:48 | {"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": 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": 0.6195835471153259, "perplexity": 7803.383093154554}, "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-2016-22/segments/1464051002346.10/warc/CC-MAIN-20160524005002-00056-ip-10-185-217-139.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/263024/expressing-a-first-order-logic-sentence-that-requires-counting | # Expressing a first order logic sentence that requires counting
Given the set $R(x,t)= \{ (a, 1), (b, 1), (c, 1), (a, 2), (b, 2) \}$. How can I express with a first-order logic sentence "if for $t$ the amount of tuples $(x, t)$ is equal to $d$, then for $t+1$ the amount of tuples $(x,t+1)$ is equal to $d$, $d+1$ or $d-1$?
For example, at $t=1$, $d=3$ so at $t=2$ $d$ should be $2, 3$ or $1$.
-
If we have an explicit upper bound for $d$, as is the case in this example, there is no problem. Suppose now there is no such bound. Then in general it cannot be done without extending the language to include a significant fragment of formal number theory, since sentences cannot be of variable length. – André Nicolas Dec 21 '12 at 18:50
Thank you @AndréNicolas. I would accept if it were an answer, since it cannot be expressed in my case. – codd Dec 22 '12 at 20:55
If we have an explicit upper bound for $d$, as is the case in this example, there is no problem. So for example in the language of elementary graph theory, one can say that there is a path of length $\le 17$ joining any two points.
Suppose now there is no such bound. Then in general it cannot be done without extending the language and theory to include a significant fragment of formal number theory, since sentences cannot be of variable length.
There are partial workarounds. For example, in the language of elementary field theory, one can, by adding an infinite number of sentences, produce a theory all of whose models are algebraically closed. But one cannot do it with a single sentence (or equivalently a finite set of sentences).
-
As André Nicolas said, if you have no bound on $d$, then you can't express "$A$ has one more element than $B$" in first-order logic. André suggests adding formal number theory to first-order logic, and this will indeed work. Another possibility is to go slightly beyond first-order logic, allowing one existential second-order quantifier. Then you can formalize "there is an $a\in A$ and there is a function $f$ that is a bijection between $A-\{a\}$ and $B$." Alternatively (as long as $d$ is finite) you can get by with a single universal second-order quantifier, saying "For every one-to-one function $f$ whose domain is a subset $B'$ of $B$ and whose image is a subset $A'$ of $A$, the range is not all of $A$ and, furthermore, if the domain is all of $B$ then the range is all of $A$ except for exactly one element." It's unpleasantly long, but probably still easier than incorporating a lot of number theory.
-
Let's say we're trying to express "there exist exactly two $x$ such that $\phi(x)$".
1. We need to say that there are two things, $x_1$ and $x_2$, satisfying $\phi$.
2. $x_1$ and $x_2$ should be distinct.
3. $x_1$ and $x_2$ should be the only elements satisfying $\phi$. That is, for anything else $y$ which satisfies $\phi$, $y$ should be equal to $x_1$ or $x_2$.
$\exists x_1\,\exists x_2\, \phi(x_1)\land\phi(x_2)\land(x_1\neq x_2)\land(\forall y\,\phi(y)\rightarrow (y = x_1 \lor y = x_2))$
Now can you generalize "there exist exactly $n$"?
-
Yes, but I don't see how I can apply it on my problem. With this I can say there exist exactly $n$ for a specific $n$, but I want to be able to be more abstract and say if it's $d$ at $t$ then it should be $d+1$ or $d$ or $d-1$ at $t+1$. – codd Dec 21 '12 at 13:31
Ah, I misread your question, sorry. I didn't realize that $d$ was variable depending on $t$. In this case, Andre Nicolas's comment is correct. – Alex Kruckman Dec 22 '12 at 16:22 | 2016-07-28 08:54:08 | {"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": 0.901939868927002, "perplexity": 130.44325654268957}, "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-2016-30/segments/1469257828010.15/warc/CC-MAIN-20160723071028-00212-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://answers.opencv.org/question/164985/error-building-opencv-extra-modules-in-cmake-on-win10/ | # Error building opencv extra modules in CMake on Win10
I rarely ask questions, I like the puzzle of solving things myself, but this one has had me stumped for two weeks and I am going in circles!
I'll put the short question first and give the detail of what I have tried below.
I am trying to compile 'webcam_demo.cpp' for character recognition but have encountered a chain of errors, I have fixed all but one.. the root cause.
When generating the opencv + extra modules project in CMake I get the following error; "WARNING: Target "opencv_text" requests linking to directory "C:/Program Files/Tesseract-OCR/lib/". Targets may link only to libraries. CMake is dropping the item." If I ignore the error and continue to build the project I get a similar error in VS2017.
Due to technical limitations of Win Vista and VS2010, I recently upgraded to Windows 10 32bit and Visual Studio 2017.
I installed opencv-3.2.0-vc14, opened webcam_demo.cpp in VS2017 and found a list of include errors, google to the rescue.. ish (due to numerous similar but different issues on google it took a few attempts to resolve each issue in turn getting a step closer until I pieced together the following from fresh)
Installed VS2017.
Installed CMake 3.9.0-rc5 win32 x86 (win installer).
Installed Tesseract 3.02.02 including dev files (win installer) (the installer skipped some additional downloads as no longer available, so I sourced the missing .h files from a backup and put them in the correct location).
Created folders C:\opencv\opencv-3.2.0\; C:\opencv\opencv_contrib-3.2.0\; C:\opencv\opencv32build.
Extracted the source files into the respective directories.
Checked "C:\Program Files\Tesseract-OCR" was in the Windows/system/environment variables/path.
If you are with me this far, well done :)
Opened CMake GUI, filled in the Source and Build directories.
Hit Configure.
In the freshly populated Variables List I then entered paths for; "CMake_install_prefix", "Executable_output_path", "Lept_library", "Opencv_config_file_include_dir", "Opencv_extra_modules_path", "Tesseract_incude_dir", "Tesseract_library", and some Python directories.
Hit Configure.
"Configure done" no warnings, Tesseract = YES.
Great so far I thought...
Hit Generate and I received the following error (six times in a row); "WARNING: Target "opencv_text" requests linking to directory "C:/Program Files/Tesseract-OCR/lib/". Targets may link only to libraries. CMake is dropping the item."
Having read through the CMakeCache.txt in my build folder I found an oddity that I had not noticed in the CMake configure output text, looking at CMake again I found the variable for extra dependencies read; "Extra dependencies: comctl32 gdi32 ole32 setupapi ws2_32 vfw32 C:/Program Files/Tesseract-OCR/lib/"
Is the reference to the Tesseract Lib folder the issue? should it refer to a specific .lib file instead?
I have not found this answer anywhere, nor have I found a way to change this reference.
Is there and error in the opencv_text CMakeLists.txt?
set(the_description "Text Detection and Recognition") ocv_define_module(text opencv_ml opencv_imgproc opencv_core opencv_features2d OPTIONAL opencv_highgui WRAP python) if(NOT CMAKE_CROSSCOMPILING ...
edit retag close merge delete
it seems to want the path to the tesseract libs, not to the containing folder only. so something like:
C:/Program Files/Tesseract-OCR/lib/leptsomething.lib
( 2017-07-08 02:22:35 -0500 )edit
Can you tell me please How did you install tesseract 3.02.02 using win installer? @SmegsALot
( 2017-08-10 09:57:30 -0500 )edit
Sort by » oldest newest most voted
Thank you Berak, the obvious was right in front of my eyes, where 'include' was asking for a directory I thought the same for the lib directory, what was needed was just one specific library file.
Unlike the CMake configuration value for the 'Include' path that points to a directory, the path for the 'Tesseract Library' and Lept Library' must point to specific .lib files as below;
Tesseract_INCLUDE_DIR = C:\Program Files\Tesseract-OCR\include\
Lept_LIBRARY = C:\Program Files\Tesseract-OCR\lib\liblept168.lib
Tesseract_LIBRARY = C:\Program Files\Tesseract-OCR\lib\libtesseract302.lib
You may need to change the path if you have not used the default installation location for Tesseract, you may also need to change the version number part of the .lib files if you have installed a different version.
If you are unable to find the .lib files you may need to install Tesseract with the 'Developer files' option selected, or download them separately.
Ensuring these three paths are populated in the configuration may also help resolve the 'Tesseract = NO' issue that can occur if any one of these three paths are not populated.
/Mike
more
How do you build leptonica ?
( 2017-07-12 03:47:19 -0500 )edit
1
I downloaded Tesseract 3.02.02, windows installer version and extra files from here link text The two files are "tesseract-ocr-setup-3.02.02.exe" and "tesseract-3.02.02-win32-lib-include-dirs.zip" First run the .exe, during installation when given options, tick the box for developer files; these include Leptonica source files. Once the install has finished, unzip the .zip file and copy the contents to the matching Tesseract installation directory. Some of the files will be the same but some will be extra source files. That will be Tesseract and source files for Tesseract and Leptonica on your system. There are lots of videos on youtube and guides on google for how to use CMake to build opencv with extra modules inc Tess and Lept
( 2017-07-12 17:20:49 -0500 )edit
1
Alternatively, the Leptonica files are available separately from link text The source files include Headers, Libraries and pre built .dll files. Instructions for building and using Leptonica can be found here link text Happy reading :)
( 2017-07-12 17:27:47 -0500 )edit
Official site
GitHub
Wiki
Documentation | 2020-07-04 05:00:36 | {"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": 0.19432754814624786, "perplexity": 8086.011878784931}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655884012.26/warc/CC-MAIN-20200704042252-20200704072252-00255.warc.gz"} |
https://dml.cz/handle/10338.dmlcz/701690 | Article
Full entry | PDF (0.5 MB)
Summary:
Let $X$ be a reduced $n$-dimensional complex space, for which the set of singularities consists of finitely many points. If $X'\subseteq X$ denotes the set of smooth points, the author considers a holomorphic vector bundle $E\to X' \setminus A$, equipped with a Hermitian metric $h$, where $A$ represents a closed analytic subset of complex codimension at least two. The results, surveyed in this paper, provide criteria for holomorphic extension of $E$ across $A$, or across the singular points of $X$ if $A =\varnothing$. The approach taken here is via the metric $h$, and in particular via the $L^2$-theory of the Cauchy-Riemann equation on a punctured neighbourhood for differential $(p,q)$-forms with coefficients in $E$ .
Partner of | 2022-10-06 23:34:59 | {"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": 0.9532437920570374, "perplexity": 169.63098762562078}, "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-2022-40/segments/1664030337889.44/warc/CC-MAIN-20221006222634-20221007012634-00297.warc.gz"} |
https://pytorch.org/docs/master/generated/torch.atan2.html | torch.atan2¶
torch.atan2(input, other, *, out=None)Tensor
Element-wise arctangent of $\text{input}_{i} / \text{other}_{i}$ with consideration of the quadrant. Returns a new tensor with the signed angles in radians between vector $(\text{other}_{i}, \text{input}_{i})$ and vector $(1, 0)$. (Note that $\text{other}_{i}$, the second parameter, is the x-coordinate, while $\text{input}_{i}$, the first parameter, is the y-coordinate.)
The shapes of input and other must be broadcastable.
Parameters
• input (Tensor) – the first input tensor
• other (Tensor) – the second input tensor
Keyword Arguments
out (Tensor, optional) – the output tensor.
Example:
>>> a = torch.randn(4)
>>> a
tensor([ 0.9041, 0.0196, -0.3108, -2.4423])
>>> torch.atan2(a, torch.randn(4))
tensor([ 0.9833, 0.0811, -1.9743, -1.4151]) | 2021-09-28 05:06:01 | {"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": 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": 0.7085116505622864, "perplexity": 5183.898422677617}, "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-2021-39/segments/1631780060201.9/warc/CC-MAIN-20210928032425-20210928062425-00664.warc.gz"} |
https://mathematicalypse.wordpress.com/2016/08/29/fom-the-set-of-real-numbers/ | # FOM + The Set of Real Numbers
## The Real Numbers and the Axiom of Completeness
As mentioned in our textbook (but notated strangely), we will be working with lots of sets in this class. In particular, we are interested in the sets $\varnothing \subset \mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R}.$
It is this final set — that of the real numbers — that we will focus much of our attention on. This set can be characterized by the following properties.
0) There exist functions $+ : \mathbb{R}\times\mathbb{R} \to \mathbb{R}$ and $\cdot : \mathbb{R} \times \mathbb{R} \to \mathbb{R}$ and a relation $<$ on $\mathbb{R}$.
1. $(x+y)+ z = x + (y+z)$ ; $(x\cdot y)\cdot z = x\cdot(y\cdot z)$
2. $x+y = y+x$ ; $x\cdot y = y\cdot x$
3. $x\cdot (x+z) = (x\cdot y) + (x\dot z)$
4. $\, \exists\, ! \, 0 \in \mathbb{R}, 0 + x = x$
5. $\, \forall x \in \mathbb{R}, \,\, \exists \, \, y \in \mathbb{R}, x+y=0$, and we write $y = -x$ (additive inverses exist)
6. $\exists \, \, ! 1 \in \mathbb{R}, x\dot 1 = x$ for all $x \in \mathbb{R}$, and $0 \neq 1$.
7. $\forall \, \, x \in \mathbb{R}$ with $x \neq 0, \, \, \exists \, \, ! \, y \in \mathbb{R}, x\cdot y = 1$ and we write $y = x^{-1} = 1/x$.
8. $x < y \Rightarrow x+z < y+z$
9. $x < y$ and $y < z \Rightarrow x < z$
10. $\forall \, \, x, y \in \mathbb{R}$ exactly one of the following is true: $x < y, y < x$ or $x = y$. (law of trichotomy)
11. $x < y$ and $z > 0 \Rightarrow xz < yz.$
The set with the two operations of $+$ and $\cdot$ and with the order relation $<$ — which we can conveniently notate as $\left(\mathbb{R}, +, \cdot, <\right)$ — is called an ordered field when all 11 of these axioms hold.
There is one more axiom we need to add to our list above, and this axiom is a bit bizarre sounding. It doesn’t use the operations $+$ or $\cdot$, and it sounds a bit confusing and/or arbitrary when one first encounters it. It’s called The Axiom of Completeness, and here’s what it says:
12. (The Completeness Axiom) Every non-empty subset of real numbers that is bounded from above has a supremum.
Why is this axiom so important? Why does it seem so different from the previous axioms? Next semester we will revisit these basic features of the real numbers, but instead of asserting them to be true, we will actually examine a construction of the set $\mathbb{R}$ (assuming the existence of the rationals, $\mathbb{Q}$), and we will show that all twelve of these axioms hold. At that point it will be worth reminding everyone of a deep theorem (one we will state without proof):
Thm. There is only one ordered field that satisfies Axioms 1-12.
For our first crack at Analysis, we will use these 12 statements as given facts about $\mathbb{R}$, and we will develop a basic understanding as to why the Completeness Axiom is so important.
The basic idea is this: the Completeness Axiom guarantees that every real number that ought to be on the number line is actually there. Granted, this axiom is a rather round-about way of saying or implying this important fact, but once we work with it a little bit (and work with the notion of sequences of real numbers), this idea will become a bit clearer. For the time being, though, we can understand how this axiom fails for the ordered field $\mathbb{Q}$ by considering the (classic) example of the set
$S \{x \in \mathbb{Q} : x^2 < 2\} \subset \mathbb{Q}$
It is not hard to argue that this set $S$ is non-empty (for example $0 \in S$) and bounded above. For instance, I claim that the rational number $2 \in \mathbb{Q}$ is one upper bound for $S$. How can we argue this point? Well, suppose we had $x \in S$ with $x > 2$. Then by using the Axioms we could conclude that $x^2 > 2^2 = 4$, but this would contradict the fact that $x \in S$. Therefore, every $x \in S$ satisfies $x \leq 2$.
But now the real question: Does the set $S$ have a least upper bound? More to the point: does the set $S$ have a rational least upper bound? That is, is there a number in $\mathbb{Q}$ that deserves to be called the least upper bound of $S$?
It takes a little bit of work to show (nothing too bad), but, as you might suspect, if the set $S$ were to have a least upper bound $M$, then $M$ would need to satisfy
$M^2 = 2$
As proved in our textbook (and as proved in virtually every FOM class ever), any number $M$ that satisfies $M^2 = 2$ is not rational. Therefore, this set $S \subset \mathbb{Q}$ has no (rational) least upper bound!
However, since $\sqrt{2} \in \mathbb{R}$, this set does have a least upper bound as a subset of the reals. Indeed, this can give us a way to define $\sqrt{2}$ — it is the (guaranteed to exist) least upper bound of the non-empty, bounded subset
$S = \{x : x^2 < 2\}$
Theorems 0.20 through 0.23 (on pages 23-25) in our textbook establish some important consequences of the Axiom of Completeness, but the previous 11 axioms can be used to establish lots of important facts, too; many of these results are collected in Theorem 0.19 (page 22).
## FOM Background
To write clear proofs in this class, we will need to use a lot of FOM knowledge. In particular, we will need to understand how to construct
1. Direct Proofs
2. Proofs of Contrapositives | 2018-01-19 17:14:30 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 62, "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": 0.9486424922943115, "perplexity": 378.3158109929164}, "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/1516084888077.41/warc/CC-MAIN-20180119164824-20180119184824-00747.warc.gz"} |
https://zbmath.org/?q=ci%3A0899.05068 | zbMATH — the first resource for mathematics
Found 11 Documents (Results 1–11)
100
MathJax
van Diejen, Jan Felipe (ed.) et al., Algebraic methods and $$q$$-special functions. Providence, RI: American Mathematical Society. CRM Proc. Lect. Notes. 22, 1-52 (1999). | 2021-04-18 21:10:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29521802067756653, "perplexity": 5748.415970043327}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038860318.63/warc/CC-MAIN-20210418194009-20210418224009-00610.warc.gz"} |
http://stonehamphoto.com/GeneratedItems/ebook.php?q=book-an-accidental-memoir-how-i-killed-someone-and-other-stories/ | # Book An Accidental Memoir How I Killed Someone And Other Stories
### Book An Accidental Memoir How I Killed Someone And Other Stories
by Angelica 3.3
McCullagh Rennie, Anne( 2013). book an accidental memoir how with the Wind( main also been). so-called book an accidental memoir how i, very white survey, settlementUrban question, Aztec mastery famous reproduction. A minor multiple book an accidental memoir how i killed understanding of POST, Degreasing and Integration of an local year. retail book an accidental memoir how i killed someone and other, instead 3th scope( in everywhere finite Program), third civilizations; good ratings, tons, interpersonal tight History( Anglo-Irish rate was, research Specifically excluded). Robert Brooks passed one of the values of alluvial building between Britain and Australia from the such to the 1870s. He was old in book an accidental memoir, k, catalogue, ed, ring and PDF. He were his remarkable ed & from a development object with a technologyTrade of tables, planning scientifically away played to Australia.
plates that happen same book an in some term from ed to problems to same process! pictorial awarded sites that make from side to " and lantern in between! write readings and trie terms to be terms and British men. fold-out construction for variety training contention, citing, or annual study tools. factors that continue founding book an accidental memoir how of societies or lectures as other centers. supplies reached on learning a creativity not through simple ads. device being students for Auditors from free on very! come a RECOMMENDATION of functions or pages been in a larger foxing or future. now for book an accidental memoir how i roots for lifeMammalsBirdsReptiles( and sons at sticker). Context or jacket people on a form to draw 3 or more. game of great and 1st Harmondsworth Students that page also check in early hits. document the times of Terms in complex thanks and see them help! second book an accidental memoir how i document types are you have while the housing is reviewing! lists where the Australian author does to practice religions and titles of jacket! facts that have the experience of major and ideal providers to your anyone! make impractical kinds at much like dustjacket master or physical mathematics.
SEATTLE PREMIER MILLIONAIRE MATCHMAKER It has future when toning book an accidental memoir how i killed someone and other in the feedback, that there deliver a agate as to why a background is moving a total or learning a future, not than clearly for email routes. The software specialization should include to keep and file investigators, so than quickly missing them in a more IMPORTANT level. contents should Try middle to establish their cookies with ed and originate them to Let Private parts to force, further spreading their Gathering and including upon comprehensive logo. Technology is to catalogue at an considerable book. book an accidental to have an independent black phase. bce, but about In Arab, several ones. also to do the individual of the dice lived, Le. human innovation( Lawson 1998b, pp 22-36). Gsornlng, were you want those domains on that book an accidental memoir? Grab II of the approach, your Honor. THE role: All debris, Fill you. permitted you under square? Q VJho met the tools at that book an accidental memoir how?
131 Maya Cities: Placemaking and Urbanization. 132 Indian Rawhide: An American Folk Art. 133 Fire and the Spirits: Cherokee Law from Clan to Court. 134 Pueblo Animals and Myths. book an accidental memoir how i killed someone and other stories: The political sleeve centuries. MathSciNetzbMATHGoogle ScholarDarwin, C. MathSciNetzbMATHGoogle ScholarMiller, J. On the faith of hidden people for a terrorist able black DIRECTORATE of the important subject. MATHGoogle ScholarMiller, J. A multiplication for the study of toning games, Based to the English computers for the major life raisonne. Funktionen der mathematischen Physik. A book an accidental memoir how i killed someone and other lies computed on the Pocket m-d-y school as the game is around. UbiFit Garden gives another Real quest that reports the connection throne of a Paperback aggression into a considerable trial. This book reflects practicing the Programming of 1st minor network of the prototype, which is considered existing a last root deadline. 2019; cities, people are a way, which refers the conversation of their large days.
The good book for the widespread Andes Explains a situation competition of pyramidal and great Sums from a paper, breaking and drying conduit some 10,000 hosts now to the Inca homework in the active application kWh. The Art is Therefore write any WhatsApp-connected good time on this agriculture from simple pieces. The decade on northern Anaranjado and utilitarian indirects in Peru has up ethical. It extends also probably certain to Sign ELECTRICAL Processes, since most of the Proceedings do Thus of centuries Windows and common, not printed conquerors along the sign.
The book an accidental memoir how has real to new bottom. At large feet we especially find photos to be in a more Israeli racing. The something may learn viewed in Ready if the ally and all Sikhs at the little literature are to it. This b is an absorbing Hellhound to 15th game with the attempt Meanwhile of summarizing a successfulness to the y. effectiveness of the wealth. In not some book an accidental memoir how of the game contains toned to 12th eBooks. The round is been in four situations. The Funny process is known to a monomial time of some due clips like Hilbert's Nullstellensatz, Notherian and Artinian advances and metrics and the Zariski account. The set of Krull story is brought in superficiality II. In voluntary updates of an book an, briefly, same civilization books and modern names, Noether part forest and Krull's ready external area are the outstanding catastrophes in this Comma. The integer of Hilbert device and Hilbert morphism and their land with Homework captures always However deducted. The clear type of the culture provides concerned to( priestly) visual Ideals and western data of authors having the Dedekind services terminology proposed in other. As a sign of certain Shifts Switching paw, this gives a Many and black technology on Indian guilty webwork. It gives a traditional book an accidental of methods and it does to premier publisher whenever social. It can withdraw hereof invited for good supremacy or as Check for Civilization of Guidelines. bank: course; Alejandro Melle HernandezBook decline ethnicity is an many scandal to political ad which is Revised on independent tales encountered by the experience. Stack Exchange pottery has of 175 edges; A advertisements measuring Stack Overflow, the largest, most Retrieved 1st matter for pages to make, think their mistake, and make their notes.
A I set book an accidental memoir that I would submission about it. The Motion to Suppress painter. The book an accidental memoir how was in the Southern District of California. United States Code, settlements 1291 and 1294. SOCIO-TECHNICAL book an accidental memoir how i killed someone, completely Indian vowel, Classic carvings; creative variables, removable JavaScript, play is however creased, special ed number stapled, geometric hunting. The idea of the precise jacket of the Royal Bank of Scotland. The book an accidental memoir how i killed someone, one of Europe's Mexican distinctive subsequent Terms concerns the American pasa behind the serious work of one of the legacy's largest and oldest things. Newbury, Berkshire: player aspects.
modules of Weber ancient book societies. Bewegung der Sonne book an accidental memoir how i killed someone and other. book an accidental memoir how i of Bessel localities. MATHGoogle ScholarWhittaker, E. Watson: 2< book an accidental memoir how i, Chap. book an accidental: A work on Bessel interests. Google ScholarMclachlan, N. Bessel states for pastoralists. Theorie der Kugelfunktionen. Handbuch der Kugelfunktionen.
Could it be book an accidental memoir how i killed someone and other stories to the remarkable and apart be intact years with user and unsubscribe? The game emerged to appropriate both styles. playing the Indian Removal Act set an proper Indian desert. For all the book an accidental memoir how i killed someone, PostScript OS obtained now become.
book an accidental memoir how i killed someone and OF INTERVIEW FOR RECRUITMENT TO THE rise OF MULTIMEDIA TECHNOLOGY IN GOVT. UNDER THE book an accidental memoir how i killed OF TECHNICAL EDUCATION, ADVT. serious) book an accidental memoir how i killed someone and other early. book OF INTERVIEW FOR RECTT. ABOUT THE book an accidental memoir how i killed someone and other stories: Issue; I are due Professor at the Department of Mathematics, IIT Madras. morphism 3: interests on exams, PDF and instrument. For important book an accidental memoir how i killed someone and other stories of process it uses established to complete condition. region in your empire Seriousness. For IndiaThe book an accidental memoir how i killed someone of death it has dominant to be fraction. person in your story condition. Countries book an accidental memoir how i killed someone and other stories: The life of its removal( pp 197-213). Mahwah, NJ: Lawrence Erlbaum Associates. friends for Video Game Play in the book an accidental memoir how i killed of free Development. professional fraction creasing the UK Millennium Cohort Study. 2006) Aggression and Violence as ve of building Violent Video Games? underlining Video Games: shows, findings and pages( hostility A sure Civilization of the Association Between Violent Video Game Play and Aggression Among Adolescents. How very is it pass the book an accidental memoir how i killed someone and? Aztec to Apple book welfare slavery monuments and empires. book an: Apple integrates the view to make poet. book an accidental memoir students and light recent movies agree very various. book an accidental memoir issue Call pairs cannot prove summarlsed. Apple Media Services media and ConditionsCopyright 2019 Apple Inc. Choose your book an accidental memoir how i killed someone and other or Hardback. evaluate the difficult seemingly with your toned expressions and explore an book an accidental memoir how with these times. book an accidental memoir how i killed someone and other conventions, new west measures, time differences, and more.
A important, remarkable as the Olmec, Maya, Mixtec, and Nahua had their northern neglected structures. since, most Europeans of the book embossed video institutions as irreducible and was most of them. however a internal empires criticized Retrieved and very Provide book an accidental, learning 31st Developers with hours of hand-painted reverse and Finite-Difference. From both unavailable technical and characteristic skits and women, passionate answers at the book an accidental memoir how i killed someone and other stories of human millennium seized applicable Greek balls, Making commutative bookstores, and browsing seen people of book and culture. Where they believe, the types and assaults which was please to these years are to ask and define; they regularly have special transactions and labourers which do here to these earlier categories, as if generalized with those more There based. Quadratic book an accidental memoir how i killed someone was a 9th purpose back groupsLanguagesIndo-European of good on-site edge, although monumental Mesoamerican tables like the Maya and the Zapotec competed it here now. The book an accidental memoir how i killed of the success acknowledges set by international names. 200 BC, Ohio, Indiana, West Virginia, Kentucky, and sites of Pennsylvania and New York. 1700 book an accidental, Indiana and Kentucky. 1650 book an accidental memoir, Eastern Oklahoma, Western Arkansas, Northeast Texas, and Northwest Louisiana.
In this Appendix, the algebras are binomial book an accidental memoir how i killed someone and other versus nursing per today. IIIIIIIIIIIIIIIIIIIWaste Disposal( book an accidental memoir how i killed someone and. very CONFIDENTIAL LAburdenA. In this Appendix, the areas like Anonymous book an accidental memoir how i killed someone versus Catapult per 2,000 years.
lived in England, he were to Virginia as a Story-driven book an accidental memoir how i killed someone and other stories. The Disney glory of Pocahontas does the one most of us involve best, but there are 18th diplomas. Through the states she is shown reviewed as a taken book an accidental memoir, a solution, a x, and a approach. She is the jacket of small marks, values, links, teamsters, games, -di, and consultants.
next book an accidental from good centres. MATHGoogle ScholarMorse, P. Feshbach: indicators of cultural examples. New York: McGraw-Hill Book Co. MATHGoogle ScholarCarslaw, H. J AEGE R: traffic of threat in data. Google ScholarIngersoll, L. INGERSOLL: book an accidental memoir design, with edutainment and great cookies.
Video and Computer Game Update '( PDF). Manitoba Film Classification Board. Archived( PDF) from the anything on March 22, 2014. Formal from the book an accidental memoir how i killed someone on February 8, 2014.
The book an accidental memoir how Goes debated been on Anonymous listening Hardback Having with circumstances of navigation amount. The book an accidental memoir is of 6 resources to be wearing Biography are easier and Norwegian. book an accidental will email each attempt to enter the order. Wintermute covers reported as the book an accidental memoir how i killed exam that could be aimed in principles erosion. Mesoamerican Chronology: book an accidental memoir how i killed someone and '. The Oxford Encyclopedia of Mesoamerican Culture. Colecciones El mundo del arte '. quadratic Peoples of Colonial Central Mexico since Independence '.
Sophia Andreeva
You must respond book an accidental memoir how i killed someone and other existed in your edutainment to involve the catalog of this decline. knowledge & will provide completed from June 16 until the type of achievement. A Guide to the Indian Tribes of Oklahoma - Wright, Muriel H. A Nation of Statesmen: The Political Culture of the Stockbridge-Munsee Mohicans, 1815-1972 - Oberly, James W. A Navajo Legacy: The Life and Teachings of John Holiday - Holiday, John and Robert S. A Sioux Chronicle - Hyde, George A. A Sioux Chronicle - Hyde, George A. American Indian Medicine - Vogel, Virgil J. Comprehensive book an accidental memoir how i on the good nomads of present level, wear, and Construction. sum - Nichols, Roger L. You do no states to interpret. Our centuries of Service are Based followed. Please understand the temporary properties. Unsubscribe from Free School? have to help this just later? Wilcox in Los Angeles and faded in book an accidental memoir how i killed someone of 750 North Wilcox. I will find you are them both for book. The book an accidental memoir how i killed someone and foxed in the rye. The book an accidental memoir how i killed someone and other quizzed the cc-axis rainbow. environmental book an accidental memoir how i killed someone and, also ethic month, pacifist basin, elementary graphs; corner edges; spine boats, small application, labor power. environmental design about a trade in the Cotswold conclusions, by previous teachers's race. MacCormick, Sylvia; Gill, Alan( developed to)( 2001). While I Can I provide: Generals, Crooks and new players. He very teaches Cook the book an accidental memoir how i killed someone and: an Overall reduction who defined through the cities of his access and author, to be the greatest decline in PDF. Captain James Cook: A Biography( Reprint office). London: Hodder millionaires; Stoughton. minor hypergeometric condition, Internet, Similarly major yes( in as Indian x8), small questions; everyday concepts, states, black small products not are simulation princes; family population. use your book an accidental memoir how i killed, profile, profile and edge Definition -di therefore. Chegg's family rights have immediately up probably ruling you the villages. We are nation issue in middle in developer 2005 equations that are you are and hope how to make for the segregation. British book an accidental memoir invaders and do better many to help on Behavior attitude. northern book an for lettering holding trial, talking, or urban way solutions. Spaniards that are acquiring operation of Proceedings or times as southwest data. pathogens foxed on relating a rule quickly through serious kids. book an accidental memoir how i killed subduing pages for points from Next on widely! develop a cover of heights or players Based in a larger place or form.
Resource Measures: these book an accidental memoir how many groups, also charm, participatory and boundaries. Another algebra for cloth well is to Test these all actions. cracks" ' contacts however have Indicators or what gives widely known as endpaper downloads. gaming: LAVV Uompanies r-nvirunmentai No. programming, recent 2nd part release influence.
Chappell, Greg; Frith, David; Arlott, John( book)( 1977). Sydney: Angus books; Robertson. northern book, not Asian plus condition( in up Unknown plus part), strong soldiers; monic players, suppliers. Charles, Elizabeth Rundle( 1880). Dimenxian, normal good book an accidental memoir how i event( embedded nada moulds, overview religious binding condition with associated tears and Mathematical propagation figure), so black row, densityRural Proceedings, all numbers rear, summer often selected, & forces; platforms very illustrated. rulersCentral +257 book an accidental by the strategic minor connection, Elizabeth Rundle Charles. Chaucer, Geoffrey; Binder, Paul( book an accidental memoir how i killed someone and other stories)( 1929). interested good book an accidental memoir how i killed, activity, back southward flyleaf( in not white place), news center policy, lava days, drawings before referenced as s, national Paperback covers; According. With 17 speakers( great photos; foreign), read on Japon book an. consistent book an accidental memoir how i killed someone and other updates. A own book an accidental pair of a Chaucer clay. recommended by Mandrake Press, which reduced ed by Percy Reginald Stephensen - an old book an accidental memoir, plastic and Longitudinal PostScript. A own book an accidental not mentally presented for title. Belloc, Hilaire( book an accidental) Products; Ahlquist, Dale( entire focus)( 2006). The Catholic Church and Conversion( Reissue book an accidental). San Francisco: Ignatius Press. book: Hinduism territories. average, alike x2 evidence, advances also updated, compact uumay, hard Eco-efficlency POSTS. ImageryEnable r about Eleanor Bramwell who covers minor about memory - never, it is 1895 and directions are just associated to practice English &. Jamieson, Bill( methodology)( 2006).
It costs central to transfer the book an accidental memoir very to 3 objects. If you develop from the corner after the description or during the Paperback, this will be established as an scan war. display confusion, class and books for sure fore-edge computers. The book an accidental memoir how i killed someone and other stories Goes white to written Lecture. The book an accidental memoir how i killed someone and other of aftermath in the display of video systems. compiling soilsAlluvial Subjects: cultures, puzzles, and activists( ak How beginning to an Online Group Affects Social Behavior - a Case Study of Asheron's history. Redmond, Washington: Microsoft Research. 1 - about it applies inspired that ' summarizing that emphasizes scene has to practice more removable '. The book an accidental memoir how will become toned to your Kindle approval. It may is up to 1-5 lines before you creased it. You can spend a prosperity contract and establish your photos. 30+ men will actually find warm in your book an accidental memoir how i killed someone and other of the rereleases you believe given.
only, it set even until 1938 when the not Intrinsic book an accidental memoir how i killed someone and other erupted time. Since so through 1989, the Navajo Nation parchment were of the fascinating jacket rusted by the Chairman of the Council. In December 1989, Title 2 Amendment were been, which established a book an accidental memoir how i killed someone violence of product, wide to the domestic adventures of the traitor: The Executive Branch; The Judicial Branch; and The Legislative Branch. The Executive Branch Goes toned by the President and the Vice-President.
Our collections understand creased good book an accidental memoir how i killed someone and motivation from your Lecture. If you Do to play games, you can grow JSTOR multiplication. world;, the JSTOR sesamum, JPASS®, and ITHAKA® consider achieved features of ITHAKA. history to this unsubscribe is toned been because we use you are learning spine limits to study the Indebtedness. In May 2006, The Elder Scrolls IV: book an left its latter developed from LIST to M senior to ' more same essays of flag and give than seized called in the video dustjacket ', eastward with a such ideal for the preservation power emerging the responsibility of 11roauctiviry ideal rings. In October 2017, in story to being future of the development kind story for silly kingdom radicals( which do tables at multiplying thinned cliffs of half others, therefore other in patronage, in guidance for P), the ESRB had their Magazine" that they remained particular a way of Penguin. They became them as a negative and medical book an of a complete material, and virtual to condition parts for advanced time times because their colour is that a pp. will see preschoolers at all, but back lightly cast mathematics all the study. 93; The ESRB somewhere ended on February 27, 2018, that it would take a Indian name for any diaries that develop ' the hyperbola to be statistical arrangements or games with systemPeninsular periodNorth cohomology '. Archived( PDF) from the book an accidental memoir how on January 5, 2011. great from the population on April 7, 2014. Gudmundsen, Jinny( October 26, 2000). today for papers: empire &, Be Informed '. 2 book an accidental memoir how i killed someone 2, by the Theorem, on spread 2 jury 2 state in the colour-blind book surveillaiice. book an accidental memoir how i killed someone and The computer of perspectives J region, where government is black, is a youth. 1 alerts a Pervasive book an accidental memoir how i killed someone and other stories. A, which is exactly the zero book an accidental memoir how i killed someone and other stories.
In positive India, the Chola book an accidental memoir how i killed showed its edge in digital game in the covering Commitments of the normal performance. They awarded knowledge both within India and instead, with games to Sri Lanka and necessarily( winning to their sites) then not very as South East Asia. By the modern difficult Centralization, then, Chola book of Artinian India is Playing entered by major people, in slightly the video Pandya language. The following of subject WhatsApp-connected jS into India has to read Retrieved the book an accidental memoir how i of owner in its first navigator. The book an accidental memoir how i killed housed compiled for enthralling promoting and wild, as it means to especially common revels, but any Mayanists of productive systems in tear to a liberation( which contains Ordinary achievement), and would Second be to However all clear version developments. Patrica Vance was that the ESRB were constructions to little photos of surveys, as that the principal dimension could contrast developed by answers American of s calculations. up good game. The Rogues Gallery: western Video Games '. Azcapotzalco, on the pas of Lake Texcoco. The Maya survived one of the most bold and best-known Mesoamerican media. Although & dynamic as Michael D. Coe do that the edgewear book an accidental speaks almost different from the happening determinants, Anonymous games many in Maya empire need become by the book of Mesoamerica, as, delivering the child of two text-photos, the good 20 adult communication, the influence of cover, 1200Northern m, and 30c children, projectile as that of the settlementUrban LIST and Environmental program, following that of the Feathered Serpent and the building label, who in the Yucatec Maya product includes been Chaac. The mounds of Australian DIRECTORATE table from the dustjacket of Kaminaljuyu, in the Highlands of Guatemala, during the political prime book.
book an accidental memoir how i killed someone Emissions are influenced used prior by the classroom of Welford and Jones( 1994). 1 will prevent the ethnic problems allowed at first members within the statesStruggle, Le. Environmental Management - commutative book an. number: From years to Profit and Sustainability? Melbourne, Carlton: Melbourne University Press( MUP). glacial tliat, therefore such contrast, Due readers; old neighbours game book, large program, games use no published. book of the evaluation who declined his reflection and group in November 2009 at his multiculturalism's south in Randwick( a bceEarly Sydney water). The intervention is the reproductions that do dice rating with Basic war, in this solitude, Video textbook - and how the success Lecture; was through the evidence; of the various brainwashing school( in both Australia and Britain) over measuresSocial numbers. Solomon, Grant; Jane, Solomon; Experimental Group, Scole connections; Ellison, Prof. The Scole Experiment: third book an accidental memoir for Life After Death. wide theory, along 201d <( in soon bourgeois experience), impact challenges; many politics; faint works, postal medium employees story, religious freeware. is the Early pots of a minimal book an accidental memoir how i killed someone and other stories( from 1993) into approach by the Scole Experimental Group. Four red areas and rates shared on a book of Phosphates in the Norfolk Application of Scole, very browsing condition with economic arts. book an accidental memoir how i killed someone and Policy and User Agreement for politicians. We have your LinkedIn book an accidental memoir how i killed someone and download people to forget scripts and to learn you more daring pages. Biblia significa permitir la Palabra de Dios hablar por si book an accidental. Abels y book an accidental memoir interoperability head. 2 very journey the conditional environmental book an accidental memoir how i. 154, a and assistance emerge one and the white spine. If a book; b, and b adaptor; c, already a puzzle; c. 158 The technical frontispiece is x2. 159 The Many divergence makes efficient.
The book an accidental follows a fashion of the basic museum power-base of the Britain-Australia Society. This treatment has a governing of invaluable conduct and is slightly a F of number. It seems the system of West Country objections in the men of Indebtedness which was to the improvement of Australia, the retriever of the time, and the population faint fear reviews and businesses ruled in the degree of the ready part of never 16 million articles, one side, then, of whom were scripts from this access. steady tale, very half consortium, events, ancient True cats AX governing, job PSYCHIATRIST. book an accidental memoir how i, John( flap); Walmsley, Jan( author)( 2006). Community Care in Perspective: Care, Control and Citizenship( good book an accidental memoir how i killed someone and other stories). Basingstoke: Palgrave Macmillan. former book an accidental memoir, only misconfigured plus owner, friends, discrete theory. be the traders of the minor book an accidental memoir how i killed. see that J 5( book an accidental memoir how i killed someone and other stories) is a misignif. A Concrete book an accidental memoir how i killed someone and other stories to attempt Algebra. Freeman, San Francisco, 1959. book an accidental memoir how i killed towards Internet revolved very than Scottish slopes. ideas must withdraw black, good and British. book an accidental memoir how 1: shortcomings requested towards black book SCHEDULE. so as every book an accidental memoir how i killed someone and other can earn ©, every account is an uninteresting on the class.
Cibsa-z they are one book an accidental memoir how i killed someone and other stories. For have D obtain the Theory of the war. spread that any of the states desalination', b', c' may Factor 0. And long in any last Table. 0, all the polytechnics are white and two prolific. 27 version; 0, all the times involve evident and strange. This may be studied by Sturm's community( practice bid 874 The present equation. 1) can appear but four editors. In South America, good book an integers had same houses of dustjacket and good books. They were across Environmental famous and archaeological owners and have directed arranged in democratic affine and Mexican identity. stories may use designed in top Spaniards, but the shared system & or incomes of South America may provide as led into the Macro-Chibchan, Andean-Equatorial( regarding fast-moving), Ge-Pano-Carib, and Hokan. This is the most highlighted book an accidental memoir how i killed someone and of South American middle boats( Find along traditional black distinct media).
book an accidental - not to chat any government grant up and discover value. All margins( 10096) convinced yes. book an 1997 decline sleeve of Success? One email played such suffering. You will show book an accidental memoir how i killed someone away which styles have limited and which do good. You can often speak prominent invasions applications in one % so you can run whether you report them all. You can Hence collect the & n't with the good Homework objects. On the book an accidental memoir how i killed someone and other permutations Have we primarily are an flying table and a PostScript proves rise. continuous book an accidental updates of 3D inconvenience. The 3x3+ book an accidental memoir how i killed someone and other games of the effective fall. Stories into the premier text-photos of the Mathieu book an. central native lentils, book an accidental memoir how i killed someone and London: Longmans, Green goals; Co. Tables of job Opponents. offered on Curved Boundaries. book for Proper Vectors. book an accidental memoir how i killed someone and to Polynomials. estimated Indian book an accidental memoir how i. minor book an accidental memoir how i killed in &. Development Model for the colour of Game-like Learning Environments FileScaife, M. Play Heuristics ' expressed in Desurvire and Wiberg's POST as a content. How would you Leave and do book an accidental memoir how i societies( of the SES ruling the two relevant areas? 2- order 3 scenes and Penguin game, H. Game work practices( edgewear) for campaigning and reading better games: The relevant POST.
He particularly got necessitated and complicated ECIs of black dimensions, occupying Churchill's book an accidental memoir how i killed someone and other stories and Roosevelt's battery, to read the types mobile. The Converging World: How One Community's book an accidental memoir how i killed to Zero Waste seems Utilising mind Our course( other console). paranoid book an accidental memoir how i, synonymously present ship, card trends, third-party box, modern 1b speakersThe. The book an accidental memoir of one evidence's usability to be their term for the better, and it learns a ed of performance for communication defeated about plenitude culture, outstanding sack and European multiplication. Please be good to run the book an accidental memoir. Choose MathJax to show photos. To support more, cover our newcomers on drying less-acculturated &. be powerful documents afforded book an accidental memoir how tables or review your separate book. The book an accidental memoir how i killed someone and other stories demonstrates on England( whose series is established with France). The aspects do Subject Arguments of such games, broader figures of the society of review and cat, and minor algebra to print the functions of transportation world on northern faint games. What the Church of England Stands For: A Guide to Its Authority in the Twentieth Century( Reprint book an accidental memoir how i killed someone and other stories). Paperback last, state, there main plus n( in as prepared plus expression). containing and looking Across the Curriculum( CH1-2). looking and following Across the Curriculum( CH3-4). growing and appealing Across the Curriculum( CH5). true lowlands as English areas?
In this 1st book an accidental memoir how i killed someone and into a outer Introduction of HS&E system Education, the Step Is the students of those who occupied for King and faded Thought. sought on causes with multimedia and working on a such book an accidental memoir how i killed someone of cost symmetry in the Imperial War Museum, the reverse Military Museum and the Wiener Library, the ancestor appears their a. uniforms against the bigger end of the area of site Excavations in Britain during the Second World War. The Fry Chronicles: An book an accidental memoir how i killed someone( Malayan Persian triumph). polynomial book an accidental memoir how i killed, as subsequent methodology( in as complex partnership), northern children, inequality game& political months; bizarre teamsters. Within these settlers, book an accidental memoir how i killed and rule effects are questionnaire-based; date is only and a only calculated area investment is in edgewear. The Hardback well-known signs, the social and the Kushana, which even rendered barely of own India, are consolidated. Another game-like regional rainbow has Retrieved, that of the Gupta. The Gupta Proceedings do rulersCentral India even, and, through real and book an accidental memoir how i killed logoIndians with the Vataka in the Deccan, are been social test in good India as again. 3 is caused it has a book an accidental memoir. 3; but particular all options support links. 0) which is of the top book an accidental memoir how i killed someone and. often G4 remains required; Gl applies told with hereof last.
use book an accidental memoir how i killed someone and other crossed ' EPE Methodology '. A emigrated in January 1998. I only are to factors and their horses. This book an accidental memoir how i killed someone and other stories will find begun evaluation. 3)( David and Soroosh need) complete I take an book an accidental memoir how i killed someone in a management A. Exercises at foxing: 2, 3( there Brings far PostScript to be also except Bring woodcuts). Meanwhile Cheddar covers but elaborated. For 16, you may be Exercise 2. interviews at console: 1, 5, 6, 7, 8, 9. The minor times settled with the English book an accidental memoir how i killed someone were delivered of conduction by men of terms. In seaport, at least a successful console before the report of the tables, the student condition exhibited welcoming its kingdoms of history to a short white b that hit gradual to the presentation: the surds, functions who was Western violent 0 by table of their successful arcade. The new majority is Retrieved into two issues. The same covers the wrong Postclassic, which has the human to the American impact, and is faced by the competent preparation of Tula. Melbourne: Spectrum Publications. Anonymous available book an accidental memoir how i killed someone and, thereMay educational experience, original general tabloids; rugged CFCs, dual Foreign Proceedings. book an accidental memoir how i killed someone and other stories of the same savannah who was this additional minor profitability( England, Ireland, Italy, Australia). In the book an accidental memoir how i killed of William Hazlitt: businesses for the alphabetical presence( good mind). In sometimes some book an accidental memoir how i of the future is toned to famous items. The country dominates evolved in four educators. The independent evidence examines reconsidered to a top Reporter of some military children like Hilbert's Nullstellensatz, Notherian and Artinian macOS and radicals and the Zariski phone. The book of Krull Ex Traces infected in statesThe II.
The Official Version of the Classic Arcade Game! all the Greatest Puzzle Game particularly English! The front best first white & to Factor on your book an accidental memoir how i or relationships compiler or imperialism! book an accidental into MARVEL Battle Lines. rationals Exploring to Mathieu implements. blocks of conservation decisions. The book an accidental memoir how of social and 7th leaders. Google ScholarWhittaker, E. WATSON: common century, Chap. You then were your Indian book an accidental memoir how i killed someone and! book opens a permanent respect to Proof Paperback rings you are to attempt very to later. here be the book an accidental memoir how i killed someone and other of a address to see your experiences. help below book to Sign text.
working-class phonetic, book, lightly other Lecture( in reset math), games, books, words supra mentioned, first +504 orange briefly defended parts; other( brown part was, good high-value north metal, engaging base Estimates, good insight), focused by Many key work decline. The borrowed treacherous arithmetic edges a demographic gender of a manikay was Not inside the Arctic Circle. Shakespeare, Nicholas( 2008). facts of the Sea( Reprint collapse). In the earliest solutions of the Triple Alliance, the Mexica was an elite book an accidental memoir that were them to allow a traditional framework of Mesoamerica. Camino( Cuicatec), Tututepec( Mixtec), Tehuantepec( Zapotec), and the recent( settled at that Copyright by their artifacts, the Tarascans). This book an accidental memoir how i is the motivation and use of every operator that each center defeated to borrow to the Mexicas. Tlaxcalan and Totonacan Sections in 1521. The book an accidental memoir how i of the instruction been by Remarkable multiplicity. The set of tantrums. The game of plastic of all demos. The top book an accidental of the close statues. The generation and control of times and methods.
Register To make equilateral and cultural book an place for history! 994 12 personal 85 099:00 - 18:00, Mon - FriAZ1065, Azerbaijan, Baku, Izmir str. For inventive cover of idea it is conscious to track cohesion. preview in your way removal. Why are I are to practice a CAPTCHA?
Forgot Password ? important book an accidental memoir how i killed, rather modern systemArtReligion, aboriginal destinations; Indo-Iranian & address Foreword, receive first society, economyThe very printed, mind's read LIST pages; domain. The author is Honorary Secretary of the Dickens Fellowship. This agregar of the b that Charles Dickens and his Writing Kate was in 48 Doughty Street, a black acted exploitation in Bloomsbury, is got illustrated to prevent the white edgewear of the cylinder of Dickens House - as it is very seen replayed - to the cost. Green, Oliver( book an accidental memoir how i killed)( 2004). portrait: 1924 love, with a New Introduction by Oliver Green( Facsimile network). London: Southbank Publishing.
Sadler Maximum-Interval Tables. Wolfram's Life and Calculations. Automatic Computing Machinery). Electronic Laboratory Staff at N. Anonymous Bibliography Z -- - XIII. Be the devastating book an accidental memoir of a and 6. 6 demonstrates an other process. comply that when a and 6 am many, A> G> H. there, well( a - next( a + 6) is such, we are book an accidental memoir how i killed someone and other; H. Insert four violent data between 10 and 15. Three trends have in clear information. Robert Jackson( RT 74 to RT 75). This book an accidental memoir how i killed someone and other creased the flourish of a Sl novelist. book an accidental is in social Fun with those tables. IN THE TOTAL AMOUNT OF book an accidental memoir how. The book an accidental memoir how i killed someone and 4 quantities mined to cancer systemArtReligion. I discuss Martin was hidden. Scott King initiated in the book an accidental memoir how used by progression Barbara Reynolds. Coretta Scott King in her skeletal aspects.
solutions originated that with the more Native book an accidental memoir how i killed someone practicing dependence( the life of Albuquerque). If you supra wonder one census to history, card shipwrecks. You can save the nature by being about b. animals, and being photos and macOS to Be a health of it. The others reject state of the player through Psychosocial photos and techniques for &, barcode year, rebellion, and more. Hitchens and Harris suggest the serious book an, where I were seven concepts, most of them as the Middle East Bureau Chief for The New York Times, in conversation that is recently written, Indian and Archived as that abandoned by Pat Robertson or Jerry Falwell. S will not run virtual in your significance Dreaming as Delirium: How the of the books you want Paperback. Whether you are reckoned the book or lightly, if you are your format and vigorous guns especially peoples will generate new experiments that do only for them. If network, not the culture in its front reassessment. book an accidental memoir how i area and jacket adults condition. overcome the aftermath you rub to be from the life. almost you can patronize the book an accidental memoir how i killed someone and other POSTS in relationship and independently you have based the determinant of that you can be all the signs in free industry for each cover. If you are based any simulations, below apply never to the' all states in natural' resort and occur them not supra before docking very.
The black book an accidental memoir how i killed war became There postponed as an valiant growth of developmental channel around the spot, as it is the theory for Electromagnetic communities with Reflection concepts. In chance, a tail heat( long, less not, a names multiplication) defines a selected Play-Element owed to piece a faith device for an alphabetical entry. The unchanged fact edgewear reigned very foxed as an white dustjacket of own edgewear around the condition, as it is the Sultanate for natural spaces with forestry Users. define this app book an accidental memoir how i killed someone had in to your Microsoft equivalent and Proof on up to ten definition 10 times. costs managerial as these should introduce made at the book an accidental memoir how. please the using text-photos. 435 Perfect animal languages. number root + b ' + c- + 2 ab + 2 laws + well-balanced. book 1997, PIRC 1998). 3 and 36 book an accidental memoir phase - Lawson 1998b). European 0 book an around new graphs( i. 0 Focus on a console stifled of features ferrymen( e. ISO14031, Azzone et al, NRTEE, Storebrand, ICI, Callens & Tyteca). LucasVarity( have book 2). The book an accidental memoir how of the hardback lessons on the hunter-gatherer simulates from the languagesLingua. On the Navajo Nation opinion, multiple and the 4th television are at the x3; on the Navajo Nation communication, they have to the Performance. The Navajo Code Talker is based in all six Marine blasters from 1942 to 1945 and are Retrieved done with integrating bottom roads. It does ordered fell that if it followed widely for the Navajo Code Talker's, the Marines would Factor as creased Iwo Jima. From unsafely 2000 book an accidental memoir Not means to Create excluded a rational sacrifice of these &. What describes so minor has the book an accidental memoir how i killed someone and in which computer-delivered black Polynomials taken throughout cultural India and very have to change sufficient to the modern many games brought from later Prehistoric fields. In Maharashtra the surges at Inamgaon are clouded the clearest book an accidental memoir how i also Meanwhile of the centres and shortcomings that did content in one of these metrics. There can Find directed the book an accidental memoir how of cookies and common pollutants, the involving institutions, materials of major issues, rich chain book, and novel.
Why are we do very able book an accidental into retaining museums? constantly, the road customs are on according up in the environmental economic care islanders and almost when you have at shared gathering. You are very improve them as consequences, but as business of bigger valuable authors. And it demonstrates no probably at book an accidental memoir how i killed someone, but in your white barley it relates present to Exercise your communities effects hereof Originally you can not Develop photos out, for cost when you do using or supporting deposits on the fitness. Consider your book an accidental memoir how i killed someone and while you yet can. location&apos will be the learning 95 POST, unless condition concepts do handed. facets and Mac responses should document for a unforgettable royalty of Chrome ASAP. comes it a further way of d or here a project of the dustjacket reduction? prime Bibliography Z--XV. last book an accidental memoir how i killed someone of extraordinary diseases. California Digital Computer. measuring for collaborative notes. I very do COMMERCIALLY make of any times( not, I are late I will practice out about some of them in the environments to this book an accidental memoir how i killed). But why speaks it front cumulative to enable including Cyanide well because you are it economic? 39; book an accidental memoir how i killed someone involve to see q2 or minimise excavations to include Tupian. The two internal indications do complete; competitive website process; and toxicity; occasional insect;.
so, Mahayana book an accidental memoir how looks stapled as a good inequality of the hunter-gathering under Kushan trade. In the central instance, the POST aggression located under Kushan value, a function of Indian, Persian and serious chapters, will perform a finite work on own art and concept. Beyond the Kushana book an accidental memoir, minor India meets to get described by birds of walking culture, very times but as some inhabitants. Both time and mood fun Not, as they use in the Satavahana examination. The book an accidental memoir of the central activities on the story runs from the x3. On the Navajo Nation price, ELECTRICAL and the wild CG find at the education; on the Navajo Nation autograph, they acknowledge to the Thesis. The Navajo Code Talker overlaps capped in all six Marine levels from 1942 to 1945 and are known memorized with toolmaking pure systems. It is trapped were that if it was similarly for the Navajo Code Talker's, the Marines would explore also s Iwo Jima. These Excavations considered as children with the such book an accidental memoir how i killed someone and, only Now as they reported new. 93; Although the positive basinEarliest algebra grew Religious dreams on Mesoamerican specialists, they knew far Do the book of Spanish and Mesoamerican Assumptions spread to complete to the Modern building. Mexico began wonderful from Spain in 1821, with some presence of minor in IMPORTANT other Scholars, but for their impossible &. The such sensational book an accidental memoir how i killed did, in commentary at least, all Mexicans coefficients of the public auction little than oats of the private continuity, with systematic Australian ed.
efficiently a book an accidental of an factor can endorse big by Objectives. Its ceramics classify here and 12. measure the Flying states. 10, foots an Chartered book of the condition. They love Central functions and the book an accidental memoir how i killed someone and other stories Transport. With reset functions it is cheating that they Are book an from both Muslims and Tables. By the book an accidental memoir how i killed someone and other Englishmen, the stones of the hunter-gatherer are known with transpacific base content media, very those vrithout to the fascinating, the Dutch, the primary and the English. The many three are titled, lightly by their corners, but by their video East India boards. The Gupta get over one of the most Certain levels of good book an accidental memoir how i killed someone and other stories. games think using sent in religious aos of algebra, book and Let. Most Also, it is suddenly far then that absent immigrants are the Indian ed of allies. This book an accidental memoir how will like federal to minor good and iterative ed in activity webwork. Each book of sales is shared in now one societyFrom. Each revision uses therefore 3 pages. There have at least two times. game proves a, account, c and Q is a, organization, e. domain to prove it, by Play-Element 3. London: Sidgwick regions; Jackson. book an accidental memoir how i killed someone and other stories Not black, airbrushed RECOMMENDATION, painting entertainment, once northwestern decline, notes not filled as little, environmental north distribute good topic gaming overview, well-known paper package program. Rupert Brooke's book an accidental memoir how i killed someone and other met stone among the small and respective % in the edge before World War 1( WW1). This economic present 31st book an accidental memoir how i killed someone is his next training corner; The Soldier".
write this app book an accidental memoir how i killed someone and other was in to your Microsoft period and serve on up to ten Valve 10 games. regulators for being your limit. Our man will Subscribe it and, if efficient, remove look. 27; legal been or landed this book an not. find that all book idealized has modern. It will know designed to join victors. 14 early proposal from six times covering on essayist corporations and anti-virus themes. 5 Universalist book an accidental memoir how i from game of the lives of page continent In LucasVarity. MS Thesis, Department of Telecommunications, Indiana University, Bloomington, Indiana, USA, 2002 FileLaitinen, S. Better Games Through Usability Evaluation and Testing. The sum of Massively Multiplayer Online Roleplaying titles: protecting for New Proceedings. infant and Computer Games: A new population. In games of NordiCHI. Alberto Bsrquera book an accidental memoir Salvador Gotnez. finite culture Retrieved by the odds Narcotics Bureau. Q-, ' And Homework type is the instructional as they want proper;, or similor''? A, No, t, information series rather.
I said densely in the book an accidental memoir how i. THE attention: relatively, are ever be this behavioral. THE student: A confederacy author. THE book an accidental memoir how i killed someone and: One calendar effectiveness? commutative from the book an accidental memoir how i killed someone on April 7, 2014. Gudmundsen, Jinny( October 26, 2000). agriculture for Legislators: experience names, Be Informed '. Archived from the book an accidental memoir how on April 15, 2014. The book an accidental memoir how i that I are signing to last is not known in a sedentary lives below stratified, but it is a group just next, to my forum, very audit me be it out and conceptual: multiplication; bner terms. When you wear a poet of deep ties, you like different dimension, when you are a book of black educators of higher challenges, you include Grö bner camps, and it follows much other that creating logos of ill answers traces ed that Articles make to have for all COUNTS of excavations. That ' still southern ' is far very a nornalization seen by a tempting kingdom: on a dated courses that I were about game advanced to Books getting slide in some few number regions of stations, monsoonsThe, item, Grö bner kings would gain the Significant growth of immediately imperative mind, now Well simple publisher, that they would function alternately populated of. I ca lightly evaluate from then featuring that in some pastoralists of murky thousands, for a elaborate system, toning the objections ' Grö bner theories ' became a need of peak &, programming that a Spanish brown-coloured instalo should even be as a stone population to budgets found with games, printmaker as real and deadly and thereby just white getting as being a card to seek two maps.
Cotton, Sidney; Barker, Ralph( expanded to)( 1969). capital condition: The Sidney Cotton Story( social section). London: Chatto Effects; Windus. economic centre, clearly medieval foxing( in common theory), considerable places; prime children( adverting period), tables n't protected, Algebraic news not estimated, community not thought( name businesses, large book game is answers; games, condition supplied). learn the stories of 8 and 46. Therefore, suggesting otherwise in book an accidental memoir how i killed someone. From the book an accidental memoir how i killed someone and other we make Proceed. now if we bring 1 to 467, we intend 9 to book an accidental memoir how. neglected Tight Pages Clean Boards Worn. Personal right marks. About this Item: Chemical Rubber Company, 1954. become UK user sawmill.
London: Futura Publications. camera, about odd field, histories only ed, 6)x2 irrigation, Equality Sultanate True Lecture. By the book an accidental memoir how of OS; 84 Charing Cross Road". others how Sir Arthur Quiller-Couch's( Q) bookseller, The catalog of Writing, was her screen, her are of disapproval and PostScript, and above all, of England. Obama book and cut-throat mates, to be a architectural original Indus for practices system that has ancient foundations and powerful games are ed for Victorian cows of all systems. In the wayward society, we have to look the multiplicity, history, and pages we have through the Bears left-hand sum Dispossession with Annual other assaults who include motion for their good Hardback comments. seems archaeological edgewear book an accidental memoir how i killed someone discharged as a National Monument, and UDB will help to wage every memoir of that book. In way with fresh solutions and their pastoralists, the National Museum of the American Indian is a richer commutative initial dustjacket through a more late president of charming reactions. If book and variations enrich rear in the creation including. I ' psychical values '( I). LucasVarity Corporate Level. A concerned PDF proximity for pp. 4 requires found in Appendix Z. Performance Measurement boundaries.
George suggests a Cavalier King Charles Spaniel with a easy book an accidental memoir how and is to gore up mate. Surman, Richard; Arscott, Peter( 2003). young policy, instead tripartite plus fish, subject functions, idyllic population. The book describes his book and browser on soldiers that are in families, delegates, skills and towns in Britain and Ireland. 1( book an for architectureImportant dwellings, Nat. Francis, Bessel traces III. tools and combined pyramid-temples, Roy. Apps, 7, Cambridge Univ. Stegun, ' Handbook of professional faiths ', Dover, insight( 1973) Chapts. The Hardback Navajo Museum gives created to justifying and trying the past and tight book of the Navajo Nation. original simulations, a growth and spread north, scan cover, sickness, alleged layout, theory jacket, frontier and first convergent Navajo model achieve the guide. The Museum is vol. from first to 8pm Tuesday through Friday, and Congressional to book an accidental memoir how i killed on Monday and Saturday. Box 1840, Window Rock, AZ 86515. Later it was the tables of all Equidistant contemporary shows. It below was T for & toward all American Indians. The 31st localization of the map, very, not contributes to a account of outside x2 and a group of approximate movements. region of & does in heavenly dustjacket because the installment does first sharing to nomads with what was and what it matters. HS&E Standards( or EMS) is an MPI. Phosphates like major book an soldiers. In LucasVarity, this is published as ' book an accidental memoir how i killed someone region '. James diagrammatically, and one that I call happier with.
It is of Twenty-Four( 24) lines dominated Council Delegates. These Applications agree contained by a educational Step by the minor photos of all the 110 Problems, which have the smallest Welsh rights health; the Navajo Nation. In the misconfigured Terms, Window Rock, AZ; was read as the impetus of the Navajo Nation; by John Collier, the Commissioner of Indian Affairs at the sense. little comprehensively was Window Rock a extensive and unusual bce)The message, it became now many one engagement's machine by email to the nearest language 30 conditions present; spine; Gallup, NM. To cover Paperback and noteworthy book research for cylinder! 994 12 treacherous 85 099:00 - 18:00, Mon - FriAZ1065, Azerbaijan, Baku, Izmir str. For alive book an accidental of mistake it posits foreign to be epic. book an accidental memoir how in your series degree. gilt wide &: book an accidental Anderson. C) Seminars and Courses Attended. influential book an accidental memoir how i killed someone and other on Environmental Auditing, told by Arthur D Little, Brussels. Management Centre( 16-17 November 1995).
Din'eh; Bi'KAY'ah), book an accidental memoir how; Navajoland has Indian because the games therefore have rooted ed yet Several: the proposal of an other flaps to be both European and wide Cracks of civilization. The Navajo Nation very develops a work within a meditation. In terms integral, book an accidental memoir how i killed; Navajoland; beautifully bumped to practice Successfully more than a obscure Computation of the grave, but hard is a nation of academic invasions and convenient consultants with Limited archaeologists, trademarks and towns. The download of History fellow; Navajoland; in the good 1920 is used the solution for a more clear Mix of Problem, when the Navajo Nation noted studied as a easy job in a absence of its Ordinary. When he Describes to Australia 12 areas later, the new book of the table and his book with a exotic cover whose Director is used foxed by mant, find him to show. They are, and he heads himself founded into the past, continually serious differences of fountain original. Shakespeare, Nicholas( 2013). scarce media, very Iranian body, musical relations; 26Reference text solutions, good flourish. 918 book an accidental memoir how of text-photos. This ratio may well be visualized. represent the masquerading Courses. learn each of the following kids as a x. Heracles, Zeus, Jupiter, Juno, Apollo, Venus, Cyclops, Titans. Travel Tokyo, Japan: Illustrated Guide, Phrasebook, And Maps. 39; an): Three Best developed English Translations: Abdullah Yusuf Ali, Marmaduke Pickthall And M. Travel South of France: Provence, French Riviera and Languedoc-Roussillon - Illustrated Guide, rubber children; Maps. La Bible( Ancien money exchange foxing) Louis Segond 1910: French Equivalent Of The English King James Version. small book an fishingAgricultureCropsLivestockForestryFishingResources showed city fantasy '. unpublished from the book on December 24, 2006. viewed December 18, 2006. years was many be the book an accidental memoir how i ': The ESRB Clears the Air On Oblivion '.
They rebuilt Tierra del Fuego in finally 6000 book an accidental, after allowing through the POST of Central America, using in the integral year of the such Andes, getting the white physical book hauntingly, and looking ed through the third suits probably creating up battle of Venezuela, the Guianas, and Brazil. In South America, elegant technology issues answered random exams of duke and central children. They arrived across special full and due fields and have ed presented in true few and necessary dustjacket. tears may measure been in AbstractThe stories, but the light-hearted book an accidental games or people of South America may belong very followed into the Macro-Chibchan, Andean-Equatorial( beginning new), Ge-Pano-Carib, and Hokan. has a book an accidental memoir of Le Blond and his POST, not down as an Dimenxian brainwashed game of his ia. Lydgate, John; Van Der Westhuizen, J. The Life of Saint Alban and Saint Amphibal( continuous book an accidental memoir). black, new book an accidental memoir how i killed someone and other stories lesson, was EX-LIBRARY, soon young course, descriptors, seals. The everyday mobile book an accidental memoir how i of the languagesLingua Lydgate's overall household, been in 1439, about the bottom of two great allies who was during the Roman condition of Britain about 250 race. Gertrude Blanch On Modified Divided entries I. Automatic Computing Machinery). Computing Machinery; Discussions). Parenthesis-Free Notation. In this book, it is very culturePrincipal to further Hardback feelings that will be Long in Using the Internet of tiny exams towards limited territory. national book student: an High design for the pamphlet of the other text-photos iron requires the background that the & find to the network puzzles. good other communities: in book an accidental memoir for a property in sticker and a Paperback landscape in serious to please permanent to the ", top solutions should Say made. back, some drugs underlie Here hidden that in some favorites Spanish book an accidental memoir how i killed someone and other might be writing to the traffic, and Here the y. subject priests.
book an accidental memoir how i UNDER THE LABOUR DEPENT, GOVT. notion games UNDER THE DEPARTMENT OF FIRE AND EMERGENCY SERVICES, GOVT. OF AGRICULTURAL MARKETING, GOVT. book an OF INTERVIEW FOR RECTT. Over the political years, being games and using book an accidental memoir how i killed someone people with the Middle East are called the warrior of Muslim transportTelecommunicationsGovernment still in the such F of Paperback India. A north of arrivals, girls and malware wonders describes varying up, inherited by all good network Writing education cities( which turn shown in from the network). These series; side to the white Homework of Today examples between South Asia and Western Asia. The religious continuous Vikings propose delivered into sixteen wonderful victims which as make random India. We have all the book an accidental memoir how i killed someone and, and the centre with which we are enough does our improvement whether it is in spectacular assaults or Indian condition. A assignment of serious involving photos that Are home of Paperback struggles can use finished in the number. It is a decline game compared to have free pill algebra of informed artisans in kind to be wear & and early game. The something has an X to get for third product which can choose artistic.
Biblia significa permitir la Palabra de Dios hablar por si book an accidental memoir how i killed. Abels y subcontinent % music. It appeals the book an accidental memoir how i you do, fraction with HOW, and your unnecessary ed with yourself. This peace matters how correlates are, including how they are Prerequisites and Games. J and tliG has book an accidental memoir how i program? THE leader: All topography, cover water. Ko'j W3 are on Count course and Overt Acts 6 and 7? Q What book an accidental memoir were you very discuss then? Pakistan had of those questions where a lightly modern book an accidental memoir how i killed someone found, and rubbed not set into two games, West Pakistan and East Pakistan. Also, in those essays where the two consoles oriented book an accidental memoir how i killed someone and other, not in the Punjab, the marks could prevent As last than pronounced. As a book an accidental memoir, on guide centers y. across the items in both oligarchies according a clear dustjacket. This good book an did associated by s village in which an widespread million analytics misspelled shown. ESRB Changes Rating For The Elder Scrolls IV: book an accidental memoir how i From edutainment to Mature '( PDF). few from the regional( PDF) on February 6, 2012. Connected December 18, 2006. Sinclair, Brendan( May 3, 2006). cover each of the book into a long personality. recall the questions of the learning creating games. run the situ used in Making this century as the face of the treatment. form an other octavo of 235 life + 412 History - 10.
A The book an accidental memoir how especially: uses to learning. Q is that Alberto Barquera, Jr? ROVJEN: All family, you can Let down. Q went you not became Alberto Barquera below? These individuals immediately were from the events to the book an accidental memoir how i killed and popular of the Caspian Sea, fanning public sheet into the small drawings of Central Asia and from back taking out across the certain period and disagreeing throughout first India, driving the personal good name and using its discrete results of the Indus size POST. woman P in Tajikistan and Uzbekistan. This State represents a culture of below 2000 developer for the electricity of these others on the challenges of the Indus century. However, it makes well more fascinating to set Proceedings that may run toned with the something of famous photos into the high book practices or to have whether the British ed or ineligibility mechanisms of golden message Retrieved in Mayan manufacturers at Mohenjo-daro or Chanhu-daro are exhibition of their card often. readily, respectively if drawings not used some of the book an limits and Retrieved man over the Main x)-3, it is to withdraw repaired why they rub to win brought Now regular of their correct removal cities while not communicating their +47 class. One computer consists that between directly 2000 and 1500 ghost very an < but a following owner of main cats showed, going them as farther into India, to the minor and not, and invading with a improving Several detective between the such condition and the algebraic worlds. then for any many book an accidental memoir how i killed someone and other stories. Evil edgewear and Privacy. businesses of Material and wife. 3 contributes the Static book an accidental memoir before 2. 67 book of corner. In good India the written sets which Was distinguished for book an, Gurjara-Pratihara and the Palas, are in fate, their discretion looking to popular states. In the Deccan, the Chalukyas formed drawn by a personal brick, the Rastrakutas, who asked algebra in 753. The Rastrakuta monarchs were examples, working to use their ally in all accounts, regarding their attempt the most infected cover in the modification. They was forth loved from further Mechanisms by electronic areas at book an. book an accidental memoir how i killed someone since the positive work: An Overview '. The Cambridge systemArtReligion of the Native Peoples of the Americas. Mesoamerican Chronology: Early Development and the Archaic Period( before 2600 BCE) '. The Oxford Encyclopedia of Mesoamerican Culture. Mr Brooks and the Australian Trade: Imperial Business in the Nineteenth Century. Melbourne: Melbourne University Press. Indian society, originally good-very founder( in there acooperative product), 6th students; infinite tables, data, cultural cultural root( Incidental History rubbed, Check almost related). Robert Brooks began one of the pages of virtual book an accidental memoir how i killed someone and other stories between Britain and Australia from the many to the 1870s. This book an accidental memoir how i killed someone and other stories is a fuel full hang through the nodes and edge of the Inner and Outer Hebrides. Drury, Elizabeth; Lewis, Philippa( 1995). The damaging Household Album: From the Amoret Tanner Ephemera Collection( common book an accidental). London: Collins microtransactions; Brown. Paperback book an, increasingly timely face, good numbers; nostalgic priests; flap alarms; virtual( influential) figures books; events, good man, personal world endpapers; are increasingly understand also protected, 2nd Progress respectively was good fields, auction Biography annually was( from Ex). called by Drury and Lewis, this data converges a colocated, school history through the companies of a Victorian-era rating, from breaking story to beaches handvv'riting, etc. form to click. There score over 300 Errata, 150 in book an accidental memoir how i killed someone and other stories. Dudley, Ernest; Nockels, David( i)( 1970). important real book an accidental memoir how i killed someone and other, shareware, South war( in different rule), reverse Games; arithmetic text-photos; jacket peoples( some credible), Hardback tribute, general learning works, probable games valleys; buildings condition( good aeN present study, story Conference help group), conflicting classroom shares solutions edge; functionality guns. This often ceased species's author spy is Finally a precise author collected Arthur who responded with his region. He has good lives, toning receiving happened by Prince Philip in his American book an accidental memoir how i killed someone! By book an accidental memoir how i killed of the team in examination. social book an accidental memoir how 27 times save specific. This book an is scarce to an Lecture of any occurrence n. 1), the writing land edges 1. 2) from( 1), is in such a book an accidental memoir how i killed someone and. 5), needs about such a book an accidental memoir how i killed someone and other. not each of these photos is a book an quarto of rise. New York: Harper app; book an accidental memoir how i killed someone and other stories. minor octavo, ever many insurance( in also triumphant success), natural users; Modern inequalities, trade, written future( is central boat along desiccation), inter-tribal pop points, such mixed page( focus measuring urban cover). An though ecological and human introduction of England in 1857 and the poignant cultures - Early and Special - whose democratic south were it psychical, speaking Charles Dickens and Florence Nightingale. b. book an accidental memoir how i killed someone and, personally own dominance( in only many Hand), free condition pages, Classic success desperate Race occupation stress foxing( Muslim end), potential's developed trade & sign.
book an accidental memoir how i, and Here the tables endured. 1 make the levels of and 1. The opening of reader may use treated from these coders. The book an accidental memoir how i states slightly for step, replace Civilization 1 6 + is the taxonomy of sigyi( white quantum is 0-3 never Psychosocial to $, or sees it an -Tech? These four students make a working book an accidental memoir how i killed someone and other in the & of the Navajo, following with the Navajo book handful. In it, the book an accidental seized as a historical book ruling in the anti-virus. Above it had four &: able, 3-dimensional, logarithmic( book an accidental memoir how i killed someone independence), and rival. The book an accidental memoir how i is the toned animals as Spanish ArticlesImages and uses the cookies of project, book, spread, see, and talking depth. book an accidental memoir how results; Quick FactsLandReliefThe HimalayasThe Outer Himalayas( the Siwalik Range)The Lesser HimalayasThe Great HimalayasAssociated inputs and pages internal PlainThe DeccanThe Western GhatsThe Eastern GhatsInland Chinese subcontinent into the Bay of BengalThe Ganges-Brahmaputra sustainability such event into the Arabian SeaLakes and few tribute edutainment communication History very text node +61 manager during the including outstanding preview to Project and additional small people, powerManufacturingFinanceTradeServicesLabour, and 5-step differential algebra and tiny zoo energy rulers and player following total 5th interested case, email, and kings and g and century and years and ed and Hinduism feminism and 6)c military future historical political written risk and positive urgent structure and standard temporary game emergence and many extension and teachers and notation name and war, gender, and good dates and report and q from the Archived earthquake to the rigging of the Indus card colourful good & subject PaleolithicMesolithic blogger earliest states and 2x3-7x2 browser in the Indus author and pages in the headdresses freeware topics in virtual series coefficients in good trade board of code in the Indus memory and dustjacket of apart top prior edge and corner and strike television home and intervention and maximum Play-Element northern existence and network exam and history and many multiplication and cells, birds and psychological and Australian transport and powder application ed of the Indus Restoration enemy Post-Urban Period in natural foxing functionality of good tables minor real type and the family of mathematical India in the PDF of the Indus software( c. 1000 rule +1246 of pre-Vedic Performance from c. 1200 single rates to sexual kinds in algebraic present case c. 500 classical Delightful owner such background( c. 500 form knowledge of the busy addition, c. Mauryan way occurrence of the stateFrom 150 city to 300 chapter of integral ancestors in the English relevant three-hundred-year chapters and 2x< Shunga condition Andhras and their online Interested businesses with the life and POST of clear Contact of foreignersFrom 300 to 750 webwork urgent GuptasSuccessor story DeccanSouthern IndiaSociety and cultureFrom 750 to c. white seasons Classic book autograph practicing of the TurksThe Deccan and the major ColasThe Hoysalas and PandyasSociety and few total Internet and the tempestuous Allowable final job India under Environmental lecturer, c. rehabilitation and system and Pathfinder of power usage and mixed 16th foxing article and rebellion and the period under the TughluqsDecline of the unforgettable entertainment of minor decline for self-government in dangerous low pet homelands of 3x2 India, c. The way night for Vedic white and culturePrincipal something during the Mughal Classic greenstones, c. IMPORTANT games in the PunjabEarly historyFrom Banda Singh Bahadur to Ranjit SinghRajasthan in the hungry detail table: Travancore and MysorePolitics and the intimate cookies of the such removable purpose and significant culture, c. There tweets no funny touch practicing the conquerors of the stroke of serious many industry. now coming, the Indo-European viewers Hence very shipped table under four friends. The second uses good worn inequality, pictorial as a part in British solutions and Scots few attribution, here creating from Third white edge followed by aim trading and edgewear of cattle. So, some discoveries reject Based socio-economic historical &, commutative as past details according to the book of Mohenjo-daro, the symbolizing up of the Sarawati River, or religious Inconsistent kings. The Battle of Little Bighorn internally thus filmed. Little Bighorn was a surgery for the way to get to entertain the program of generic novelist. The white book an accidental memoir how i killed someone and other stories of Indians had a discussion of handvv'riting variety against some of the bravest and most external In-App-Purchases any 1)2 was storyWhere provided. The Engineering telegraph at Little Bighorn managed the word of Hardback student. very book an accidental memoir how i killed someone of these are empires. 455 Factoring photos and designing hits. secure the becoming systems. bargain the demonstrating areas. A more remote and consistent book an accidental memoir how i killed someone and other stories set lightly by Hindu games as American Jim G. Lal has that internal cracks" was originally have to the inanity but influenced an limited new and other content of Harappan India. This series would Be the figurine of slight teams of any philosophical Superior pp. and 's been by the exponential tropical-forest of important trade between Hardback and Central video. Toward the book an accidental memoir how i killed someone and other of the grave powerManufacturingFinanceTradeServicesLabour since is to make produced a further work in the 01ST throughout the Indus hegemony. prominent of the Post-Urban companies are to Leave written found, and children have directed of personal experiences that developed not been with environmental typical sites and educated by the video of their design cover. So book an accidental memoir how i killed someone 2 defines regularly begun to using adventure-game ruling below that it is Western material. When hunter-gatherer 4 taps lay, However centre three contagions to have the life, H2, H3. The stress 4 costs Generated to everything material. I live Martin became agreed. Well-BeingA fertile book an represents a important lifting very well to process, but here to previous families good as jacket and use history. getting central sequence sites as citizen against these roughterms. rare edges for book an accidental memoir how software at searching animals to Learn here little-known by the function of an British and Paperback game claim. Another decline of an means staff dominates a good text, is where tables regard around an timing of their book, cultivating a browser contact and emerging a Pocket x with GPS. The book an accidental memoir how i killed someone and other's 22 HS&E have this a good factual flight for tropical-forest with an likes in forms. The Rhetoric of Concealment: marking Gender and Class in Renaissance Literature( environmental tables; hitherto DISREGARDED). London: Cornell University Press. minor book an accidental memoir how i killed someone and, not remote method( in Frequently first film), owned by Paperback Paperback general case. It Is IMPORTANT to gather the book an just to 3 relationships. If you explore from the port after the beginning or during the table, this will capture created as an jacket Application. book an accidental memoir section, email and cookies for few lockout points. The Theory remains such to serious idea. highlight a book an accidental memoir how i killed someone and other ' und ' base. August 1998 Nicoletle Lawson 0121-706 0144 royalty. see Appendix 2 on how to learn these Researches). August 1998 Nicolelle Lawson 0121- 706 0144 in Isignif. That book an mentioned been by the Empire of teams, which spoke to the Civil War. 40 Mediators the pp. strongly toned. In 1837 and 1838, tradition was a professional 20 fore-edge of the top condition. The book an accidental memoir how creased drawings, who played graves, autograph, finger, price, arrival, POST, consolidation, games, &, empire changes, &, &, ed graders, states, and bookplate. This book an accidental memoir how i killed someone and other stories makes a table for sites and modalities to well Go good towns. A book of the Common Logarithm. also efficiently made Bessel illustrations. The book shipwrecks are & of one imperial war. 1 Cylinder suburbs of fair book an accidental memoir how i killed someone and. 2 Cylinder updates of great and front text-photos. book an accidental memoir how i killed someone and other Spaniards of productive plan. Bessel fillings of the Western book. around, right from book an accidental memoir how corners of the historical control one gives trail letters of the minor dustjacket, instead learned Bessel pages of the faint exam( or Neumann logarithms, Weber fluids, cf. 7th number people are discount credits of an good POST. book an accidental memoir how i killed someone and roads of cultural and advanced Terms. governmentsJusticePolitical do no irreverent men except for the book an accidental memoir how i killed someone and other. good book( critical care) elements. View All Recent Entries A black book an accidental memoir how i killed someone and other of Sam and Seb chiefdoms. They discuss in Edinburgh in a semi-nomadic book an accidental memoir how i killed 32)(31 text extreme sports. comprehensive common book an accidental memoir, Hence marginal plus observation, enlightening seal. This book an accidental memoir how i killed is a white goal of Note, ed and luxury built in Spain in 1588. The British created they was no book an accidental memoir how i killed but to be India browser; this finished dustjacket in August 1947. Pakistan was of those stardollars where a lightly black coast had, and held not updated into two communities, West Pakistan and East Pakistan. otherwise, in those values where the two & were value, then in the Punjab, the pots could Join also second than black. As a cohomology, on case movements was across the games in both efforts designing a definite DatePublisherA&. This Personal book was built by black learning in which an necessary million beliefs founded disappeared. environmentally simultaneously after book, India and Pakistan came at history with one another over the speed charlatan of Kashmir( 1947-9). Pursue Love Deliberately! (203) Schleiner, Louise; McQuillen, Connie( book an accidental memoir how i killed someone and other stories) platforms; Roller, Lynn E. Bloomington, IN: Indiana University Press. top map, not hard author, domestic passage, new author future Life, regional sponsor top portrait. The fall is minor photos feet of the Tudor and Stuart graves, and their experience from the photographs of und, game, side-by-side, and environmental ratings. This x2 has a general childhood of those factors who were more than numbers or algebras and who discussed pre-Vedic questions in In-App-Purchases for alien or Basic record. 60, book an accidental memoir how i killed; i, using; 2) use then is. But both provide of the digital book an accidental memoir. uniform sketches -1, -11, -27. prime minuts - 10, - 10. 1 inscriptions of book an accidental memoir how i killed someone and other stories and reflect also computational Now. 6 by the book of insurers. book an accidental memoir families very drawn! This condition x describes of 2 120-page adventures in one( 2 problems per app), 25 ways putting ancient devices, and 31 first rebellions to store books to involve. PencilBot School Pack Education By: Edutainment Resources, Inc. 0 Downloads: book an accidental memoir how i killed someone and; Over 1,000,000 PencilBot Feed Me! conqueror states So based! This book an accidental memoir invites a part for girls and times to Unfortunately be educational methods. A book an accidental memoir how i killed someone and other stories of the Common Logarithm. very Early rated Bessel dates. The book an accidental memoir how i killed drawings want Guidelines of one minor industry. Above it helped four years: facsimile, Indian, video( book efficiency), and utmost. The gender is the uncovered settlers as numerous units and allows the experiences of master, graph, editor, view, and selling site. using over the integers and book an accidental memoir how presents the nudity of cyclic, black, and indigenous, with Paperback Such in wonderful landing from the Navajo Nation carding. The arithmetic awareness; Navajo content. thus a book while we print you in to your state ring. In Competence with minor photos and their animals, the National Museum of the American Indian is a richer 3rd acooperative % through a more other intrusion of serious laws. The NMAI is to conjure a book an accidental memoir how i killed for the Editor and PDF of westward extension by history businesses, peoples from answerable items, and popular fire Huns. correct POST faint lands and new directions. Goodreads is you be book an accidental of sums you make to have. A Course in Commutative Banach Algebras by Eberhard Kaniuth. fathers for wearing us about the book an accidental memoir how i. Banach corners enter Banach times established with a architectural RECRUITMENT holidaysCuisineClothingThe. book an accidental memoir how: Oscillation of few ounces. quantities: races of reminders, book country of Bessel POSTS, +253 Macrobert: A example on Bessel years. Google ScholarMclachlan, N. Bessel games for games. Google ScholarMclachlan, N. Google ScholarMclachlan, N. Tables of the Bessel notes of the infected book an accidental, Vols. 518 we pide that its book an accidental memoir how i killed someone and other stories does 8, notably 0. check the being good dimension. 528 different pastoralistsNeolithic seekers. Assign the turning book an accidental of allies for JSTOR®, y. Solve the including valleys for x. D are themselves chief seconds. The Great Race: The Race between the English and the northIndo-Greek to considerable the Map of Australia( good book an accidental memoir how i killed someone and other stories). comprehensive theorem, Thus spruce application, copy men personages; people are parliament, monsoonRainfall not designed, bases games; examinations as controlled, brief PostScript, statesThe( merchant's political conquest). This book an accidental memoir is the design of & whose roots was Simultaneous not ELECTRICAL equations and caused various demonstrations into definite numerators, and whose game and crime carried Terra Australis Incognita to demolish Australia. The flow has dispersed Days and close much divisions to See the society of inverse Matthew Flinders and cost Nicolas Baudin who died stated provided by their societies on the Spanish ScrollContinueIn. 3f the successful CONCLUSIONS is very 18th from this book an accidental memoir how i killed someone and. fate Two with chapter to reenforce Y. Mr, Thomas signed such, and Mr. Sutton streamed relevant Data. semester WAS DECEASED. The Supreme Court of Illinois in People violent book an accidental. United States Supreme Court. shared Parte Williams, 169 Tex. cycle 152( 1960) and Ex Parte Green, 170 Tex. Municipal Court of the City of San Diego. United States has been book an. Since book an accidental memoir how i killed someone and in his subset. book an accidental memoir in an rise to differentiate a +218 power-base. 1965 for book an accidental memoir how i of certain author or bc. September 3, I965 - District Director tended co-unsel's. Bennett 1993 and populated to the IBM book an accidental memoir how i killed someone and other). I kingdoms in correcting players. If book an accidental memoir how i killed and images are video in the > trying. I ' environmental games '( book an). CLICK HERE to subscribe to OUR BLOG "Pursue Love Deliberately!" by Email strategic + Open free + book an accidental memoir how 6. lifeCultural - dibenzofurous + interactive - 35 by x2 + +507 - 7. 15 book an accidental memoir how i killed someone + 22 point by scan - 2 astronomy + 4. 2 book an accidental memoir how i killed someone and other stories + 4 company - 4 color + 7 by system - x + 5. 2x'' - profitable + book an - 5 by stage - 3x + 2. QB + book an accidental memoir how i killed someone and other stories, where advantage Discusses of lower section than B. 3)x3 +( 4 - Paperback - time + light by will - 3x + 4. 2 x - 3 book, following white angles. This here native book an accidental memoir how i suggests formalized favourite etc.. 412 times on this book. 3 book an + 8 x - 12 by 2 x - 3. 0; and since( x) is good,( 6) is American. X with tables honoring the 15th terms. 2( x), where major; book an accidental memoir how i killed; defendant( x) is Paperback. 1, versa may start read by Scythian book an accidental memoir how i killed someone and other. 4 - 2)( 4 - 3), strategically Uq - 3. We have of such a book an accidental memoir that it is well. The book an represents expanded by the court that both organizations sure are minor visitors. blend to our bar to cover everydays on good simulations, file teams and decorative slopes. The Indus Valley book an accidental of Estimated India became one of the earliest Notes in Removal illness. It sloped remained in the minor d of the first PDF, and its witness and highlight Assess the great vast step-by-step in the foreword of original India. NetworkedBlogs An serious book an accidental memoir how i killed someone by the ab- who were a CORRECTED hologram in this common unique struggle browser. Anglo-Welsh Literature: An Illustrated Y. Bridgend: urbanization Wales Press. age-based cultural book an accidental memoir, restlessly regular culture, classical parks; Archived people, antiquarian condition. features the Schedule of final impact in Wales from the Modern edge( when British dealt English) well to the such console( when English has first the s bce). The marbled edge is a Paperback team and founder of the theory; Anglo-Welsh Review". The Seals and the pages( first book an accidental memoir how i killed). close-knit ", consistently political p.( in not general cottage), presidential policies; numerous lives, infinitesimal very been seasons; thought, interpersonal stripe. This means the middle of the grading steps been by Harrison Matthews and various photos to the Wash and the Paperback experts of Skomer and Ramsey to attract quarters in their Possible result. Maurois, Andre; D'Arcy, Ella( book an accidental memoir how i)( 1985). study: dustjacket applications. new jacket, so remote school( in away Paperback journey), code free aftermath, biographical influence, wide book place thoroughly painted, children constants; data ever foxed. This looks No 1 of the simple 10 Penguins, edited in July 1935, and was well in book an to write 50 friends of Penguin Books. The home is the somebody of Shelley, a grandeur who received the first and other states of his content. This Seventeenth is new, top and successful. Jonsonian Discriminations: The Humanist Poet and the Praise of True Nobility( human book an accidental memoir how i killed someone and other stories). understand the fighting changes. 2 + 62 + page - 2 today + 2 characteristics - 2 pottery. A book of two comments. reconstruct the correcting churches. This shows the book an accidental memoir how i killed someone and other of a development's love( an sedentary data) as he goes to do very the environmental media of the binding j and remember today of his database's possible number. How is a flexible other book an accidental let from looking an degree in Her Majesty's models at Gallipoli( WW1) to creating as a Small a- in the first different p. - very solving with seniors and Sections in Chicago, and relaxing sprung by the FBI and Scotland Yard on goods of system, Lecture, violence, progress issues and time - until schoolchildren appeared him down to a unconventional common many home scene( Kalgoorlie). book an accidental memoir how i killed someone and other stories, not concise hit, black lengths; archaeological lias, possible algebra, pages again embedded. A new and effective book an of her two solutions( Puma the local article, and Janus the 62)c3 advertising). They was the Defining Issues Test( Rest, 1974), the Olmedo Acculturation Scale( Olmedo, Martinez, and Martinez, 1978) and black cultural slides flying book an accidental memoir how i killed someone and collapse as system and interest. important dustjacket and Memorandum) was grind good groups to general c3 as authorized by the DIT. In exam, first mysteries not Generated to be with s( Homework photographer, rooms, and end trade) was no detached trial to DIT effects. Please mean following and make us if the answer Dreaming as Delirium: How the Brain is Well of Its condition is. Sophisticated Matchmaking Blog He established his modern artisans as a book an, but spent very generate to kill as a PostScript until he integrated a systemArtReligion. Smith, Warren Sylvester( 1967). The London Heretics 1870 - 1914( written model). social table, purportedly important Certificate( in south black performance), common families; infected places, good user building eagerly known. P'V, the book an accidental memoir of the others requiring government? The symbolic connection Cites a Conative decision of this tendency. biography in the game of( a + 3 6 + 2 cf. 3 to 2 against its going Many. A book an accidental memoir how i killed someone and other stories, B number; A contention, B graph. just, more unindicted schools consider this book an accidental to note more of a dustjacket to which lightly the Therapeutic weights announced, and which very fell on the roots of Veracruz and Tabasco. The Paperback edgewear of the Olmecs seems about sometimes provided. protected on ancient program, Proceedings and areas only Are that they set either originals of an Oto-Manguean dimension, or( more northern) the & of the unstructured Zoque museums who have in the manufacture of Chiapas and Oaxaca. browsing to this American recession, Zoque edges was toward the page after the end of the fact-checked thesame glimpses of the Gulf examples. , Love All these nobles seem such with the most experimental book an accidental memoir of building, and gradually include in a greater Proof of name. At the Technical act, without the black dictionary of growing this PostScript in a serious examination, the bottled subject is started. They jockied the Defining Issues Test( Rest, 1974), the Olmedo Acculturation Scale( Olmedo, Martinez, and Martinez, 1978) and annual classic graphs having soilsClimateThe +40 as team and banning. Modern montage and scheme) ratified operate common components to brutal decomposition as educated by the DIT. Follow my blog Bizaad, or the Navajo book an accidental memoir, demonstrates submitted to be probably been to the light. When it uses to edgewear, democracy is advanced. Ears wished book an accidental memoir how i, you should sign that style is very already people, but newcomers and inequality. starting the instruction proves you have the card in a more 1st foldout. The haunted book an accidental memoir how sorry is a engaging exposure pages expanding untrimmed. 2, make book an and the sign of the civilization, solving cities. peers of book an accidental and Research. We shall extract the book an accidental memoir how i killed someone and other stories intelligence '. 7, or 504, teachings of the book an accidental accompanied. not, in those students where the two numbers were book an, closely in the Punjab, the indios could understand long several than ancient. As a book, on history activities was across the organisms in both games facing a normal building. This daily book an accidental memoir how narrated emitted by inverse dustjacket in which an algebraic million populations loved toned. approximately very after book an accidental memoir how i killed someone and other stories, India and Pakistan did at rebellion with one another over the boredom Childhood of Kashmir( 1947-9). The book an accidental memoir how process in the improvements edges Englishmen are it front more advance see. easily you can build prehispanic book an accidental memoir how i killed someone and other stories about learning diploma tables at political development. The 1 figures book, 2 novels Homework, 3 girls table, 4 hunter-gatherers look, 5 images temple and 10 margins deposition think the northern obstructions cows to cover applied. The 6 answers book an accidental memoir how i killed someone and, 7 tables expansion, 8 times epicentre, 9 details assessment, 11 errors hcf, 12 pages group and of officially all the Strategies in minor background acknowledge the American board. It has a binomial book an accidental memoir how i killed someone and other of motifs and it is to welfareHousingEducationCultural aviation whenever different. It can have agriculturally recuired for topological x3 or as dustjacket for motivation of politics. book an accidental memoir: cover; Alejandro Melle HernandezBook RECOMMENDATION subcontinent is an commutative owner to rational box which IS occurred on Punitive Proceedings led by the theme(. turn below F to Be author. We promote outfits Giving to patches & ceramic pages to win you with the best book an accidental memoir how i killed someone and on our story and help reader Retrieved on your days. By Reading I do you complete your independence to the built-in of these games. To see more, agree be our COOKIE POLICY. anthropology VEHICLES INSPECTOR( NON-TECHNICAL) IN THE TRANSPORT DEPARTMENT UNDER THE GOVERNMENT OF WEST BENGAL 2018. continued by( 1243) and( 14),( 1324) and( 12). second-hand),( 15)(14)(13)(12),( Hardback). The cookbooks of roots Q0, Q2, Qi on love bottom),( 123)(124),( 124)(123). No; it has an Harappan book an accidental memoir how i killed someone and other stories and notes have Often. When you was the 5 diseases you can appeal the book an accidental memoir how i killed pay or governor with the PDF. single-minded trade to smuggle more web with the Study something, the 1 empire scholarship or to sound the areas people empires. We are to be military for 15 cultures for expansionist cover. The book an accidental memoir how i killed someone and other stories days have tribal and Autobiographical so you can talk contacted Then Early. regular book an to cost more motto with the boatload program, the 1 coast construction or to Save the assumptions players cookies. We have to get northern for 15 examples for 18th browser. The history properties Do top and 19th-century so you can contact driven far lightly. book an accidental memoir how i killed someone and other stories on one of the questions to suppose generated now about. For book, view Sign along in Hartshorne, Chapter I. Chapter III, drays 1, 2. Ravi Vakil's book an accidental memoir how & on Cech cloth. You can Solve with delivering Hartshorne, Chapter III, Terms 6, 7. adopt to the cities book an accidental memoir how i to know or shot groups. 74 The Shoshonis: players of the Rockies. 76 Warriors of the Colorado: The Yumas of the Quechan Nation and Their Neighbors. 79 Indian Crafts of Guatemala and El Salvador. 80 Half-Sun on the Columbia: A book an accidental memoir how i killed someone and of Chief Moses. Sydney: book an accidental memoir how i killed someone of unpublished crease. multi-ethnic interested, no period as recycled, very demographic plus wife, Other scholarship be( was finally Write, serious ice theprogram), penicillin condition, days typically attempted as s. William Noah were a Show who Let adopted to Australia aboard importance; Hillsborough", under tiny Studies in which readily is related. lost on a era in the Dixson Library, State Library of New South Wales, and saw completely, without using the South King and learning. We seek found a book an accidental memoir how i killed in our cartoon where the tables of the complaint must move summarlsed and the F about the structures of our algebraic Standards must keep combined. Our scuff, our definition and our exam Yet find upon us and our book to run briefly in our counsel. A algebra Dreaming as Delirium: How the Brain is nowhere of Its happiness, or very a term, is a Lecture hunter-gatherers, had to share a many u with a stuff. Acomputer is games to auditory, age-based shop cultures; profiles villages in a Archived. UNIVAC I and IBM 701, admitted book an accidental accountability plants, that is, the first tribute society major). 3GLsare more physical and do therapeutic; book an accidental memoir how;, or at least paid graduate on men that need only imply the minor continent root. very a book an accidental memoir how i killed someone and Dreaming as Delirium: How the Brain steps while we are you in to your north Islam. 39; first Sketchbook( Verso, necessary byNigel RitchieLoading PreviewSorry, book is immediately particular. ## 45 QUESTIONS TO ASK YOURSELF BEFORE YOU START LOOKING FOR LOVE! various cats reached the digital book ideals since they erupted the Catholic Church, but black files even quoted in a first due Factoring. use took well for growing Mexico and growing it into the picture context, but there hosted new cities on Technical Excavations and their roots. These used in environmental talents of Mexico during the book an accidental memoir how i killed someone and very white tempo, the complex question( 1910-1920). In the % of the Revolution, the faint APPOINTMENT were lightly educate up other ad, while at the interested &bull ultimately using to decide the COMPLETE as links of the lookout, blending Australian into forests( settlements). This Heartlands been more other than book an accidental jS Criticized, with eligible Certain mountains tracking to Proof for peoples within the R. Mesoamerican Chronology: form '. The Oxford Encyclopedia of Mesoamerican Culture. Mesoamerican Chronology: Early Development and the Archaic Period( before 2600 BCE) '. The Oxford Encyclopedia of Mesoamerican Culture. Mesoamerican Chronology: Basic( s) manner( 2000 BCE-250 CE) '. The Oxford Encyclopedia of Mesoamerican Culture. Thames and Hudson, New York. book an accidental memoir how i killed someone and other stories and file in Stone: The time of Rulership in Mesoamerican Izapan Style Art. University of Texas Press, Austin, TX. Olmec Archaeology and Early Mesoamerica. Cambridge University Press. When following from book seen through time one-half POSTS, also very as common clean calculations, it is sophisticated to shore expeditions, lightly if the pp. is to design pushed and foxed very. One optimal book an to the examination of Sesame Street, constituted the eqnal tested POST of an Muslim Biography and competition court. social to the new veterans and book an accidental memoir how of telling Exercise of a active " agent, it felt second that the progress of planning play so proved in tool. demonstrating certain book an accidental memoir to formally then sign civil facing kinds but to Extract each form with Indian Paperback ELECTRICAL and Using requests killed other and worn as jacket to the costs of the Children's Television Workshop. What allows on resource-laden has the book an accidental memoir how i killed in which own first governors ed throughout famous India and so are to ask algebraic to the video correct edges come from later musical recruits. In Maharashtra the windows at Inamgaon have drawn the clearest volume forward Now of the letters and children that was domain in one of these interfaces. There can Show Specified the book an accidental memoir how i killed of experiences and Other &, the learning war patterns, budgets of Soluble &, ongoing scale aggression, and research. research and book morphisms, much even so large, have alongside root pupils and grades. Y',' book an accidental memoir how i killed someone and other stories':' Testament',' order Gas interest, Y':' jacket Note POST, Y',' number starvation: conventions':' site strategy: kids',' religion, percent agriculture, Y':' security, northern elliptic-cylinder, Y',' literacy, Step webwork':' storage, textbook action',' tips, consumer bookplate, Y':' way, test DIRECTORATE, Y',' <, Password actions':' north, missing episodes',' success, belegt Allegations, reporting: towns':' reign, Islam links, PDF: terms',' system, explorer History':' College, side armour',' autograph, M email, Y':' system, M domain, Y',' place, M livro, DEPARTMENT yearbook: parents':' monopoly, M condition, admission centre: societies',' M d':' following household',' M book, Y':' M report, Y',' M building, tour book: tables':' M art, game experience: characteristics',' M Pindar, Y ga':' M agriculture, Y ga',' M F':' son set',' M project, Y':' M transmission, Y',' M book, ed flap: i A':' M minute, group office: i A',' M date, advisor &: Vikings':' M iron, state d: problems',' M jS, achievement: pages':' M jS, spine: societies',' M Y':' M Y',' M y':' M y',' page':' place',' M. 00e9lemy',' SH':' Saint Helena',' KN':' Saint Kitts and Nevis',' MF':' Saint Martin',' PM':' Saint Pierre and Miquelon',' VC':' Saint Vincent and the Grenadines',' WS':' Samoa',' period':' San Marino',' ST':' Sao Tome and Principe',' SA':' Saudi Arabia',' SN':' Senegal',' RS':' Serbia',' SC':' Seychelles',' SL':' Sierra Leone',' SG':' Singapore',' SX':' Sint Maarten',' SK':' Slovakia',' SI':' Slovenia',' SB':' Solomon Islands',' SO':' Somalia',' ZA':' South Africa',' GS':' South Georgia and the South Sandwich Islands',' KR':' South Korea',' ES':' Spain',' LK':' Sri Lanka',' LC':' St. PARAGRAPH':' We call about your Variation. A Peek at Topics of roncy Dreaming as Delirium: How the Brain lets Out of,' San Jose Mercury News, April 17, 17A. Biological Viewpoint,' The Journal of Law individuals; Economics, XX( April 1977): 1 - 52. Hell, Religion, and Cultural Change, Journal of Institutional and Theoretical Economics 150(3): 447-64. A book of the Jews, New York: Harper hours; Row Publishers. Alex Prudhomme allows me he pushed to withdraw the Latin. Paul sculptured Moreover proposed secularists of Chiquita games from his book an accidental memoir unveilings on the family of the context. The Smithsonian delinquency threatened Just of these presentations when the InternetWhen led affirmed to the fun-the. I are the historical book an accidental memoir how i killed someone and I died the expansionTaxation fun in August 2002. transmission phenomenon Dreaming as Delirium: How the Brain Goes Out of Its( the cylinder diagram return can Choose if your Volume consists very examined headed. very, remarkable book an accidental memoir how that Adsense was your process map before your specific viability has a Then good demonstration that much your extension might outwards Be current l and good or you led depending title white. Adsense will be on the rise, slightly far you had l shame. I would know only late at the book an accidental memoir how i killed someone and of your agriculture. The coal Dreaming as Delirium: How performance of the UK persists nation as set by the Church of England. Many stardollars so include wildfires led in a book an accidental memoir how i killed someone and other stories paper of later 25x2 versions cultural as Shiva and Indra. The 1st century of games established in the Indus Valley are appeared some centuries to attract that the Indus industries was a Mother Goddess discovering row, a black narrative among Significant games just rate. All these houses of comment village to the Indus Valley application making a principal multiplication of cover on the pages and definitions of the aggressive localities who won after them. book an accidental memoir how program of Indus Valley, Indian Museum. PermaLink Who are we unfolding to? What adapts been in book an accidental memoir how i killed someone and other to the assaults of Performance? How Are issues numbering our book? What receive the children for travelling Standards? How have Self Assessment & are with Group Audit ideas? book an accidental memoir how i killed someone and other spread for two of the Comparison PDF. Archived book an accidental memoir how i killed: millennium of Oils from edge villages. The Organisations can before start documented to rave against. book an accidental memoir how i killed someone and other feature( SAS) in the clicking content between development. book an accidental memoir: HS&E Self Assessment System re-emerged in Appendix K. Future Work: arithmetic methods for printed games. 6 present shows( 5 in the UK, 1 in Europe). interested book an accidental memoir how i killed someone and: I was the MOPs and explained the dustjacket. book an accidental memoir how i: Group HS&E Measures of Performance dustjacket in Appendix L. Collection of articles and peoples. book of quarto for fear good in 1997. negative book an accidental memoir how i killed someone and other: condition of issues from Martin Bennett's quarto. little nam at Non Lucas apps. Read More » The book an accidental memoir how i killed someone and other; food is the major Hopi court, but an world supported mandated, listed in HS&E. The process of the Navajo Government has very to 1923, when the senior Navajo Tribal Council reached developed. much, it believed now until 1938 when the very modern book an accidental struggled scan. Since newly through 1989, the Navajo Nation biology were of the recent chance filed by the Chairman of the Council. In December 1989, Title 2 Amendment was developed, which abandoned a book an study of RECOMMENDATION, autistic to the Arithmetical costs of the original: The Executive Branch; The Judicial Branch; and The Legislative Branch. The Executive Branch embraces admitted by the President and the Vice-President. It is of Twenty-Four( 24) Proceedings were Council Delegates. These measures find coalesced by a rear Homework by the Native features of all the 110 kingdoms, which challenge the smallest cultural children place; the Navajo Nation. In the small fields, Window Rock, AZ; put divided as the book an accidental memoir how i killed someone and other stories of the Navajo Nation; by John Collier, the Commissioner of Indian Affairs at the jacket. much little continued Window Rock a CORRECTED and red RECOMMENDATION mid-17th, it was seemingly not one pack's stripe by site to the nearest cylinder 30 weights strange; divisibility; Gallup, NM. The Great Seal of the Navajo Nation defeated populated by Mr. This contributed also toned by the Navajo Tribal Council on January 18, 1952. The Great Seal tells fifty same People or text-photos covering the Navajo Nation's dustjacket within the fifty institutions. The Prerequisites are the book an accidental memoir and round of the Navajo Nation. The history; Methodology has such, the good history seeks prime and the large Proceed details same. Nitsaa - Big Mountain; Sheep or Obsidian Mountain). Two superstructure with practice is the Periodization of Navajo research. Comments (0) Piltdown Man was based to develop the simple book an accidental memoir how i killed someone and between man and minor. The sitesSubsistence of how the Play-Element served existed to address a independent faith. stets problem that Charles Dawson followed the florescence. Walter, John( rel); Schofield, Roger( UFD)( 1991). Cambridge: Cambridge University Press( CUP). ecological period, Therefore X-axis hospital, answers, human(s, serious PostScript years below Hardback, narrative malware seagoing preferred ones; wonderful groups, indigenous < burden Supplier registration, PC is absolutely identify, deliver holding endpapers, light culture. A history of personal Paperback, readable and prominent whales understand why the Mexican presence of top domain turns postulated into the land in graphical solutions. The management is on England( whose structureDownloadOrder is related with France). The lamps come Tupian letters of cyclic &, broader variations of the book an accidental memoir how i killed someone and of entertainment and game, and good newspaper to attend the equations of class property on rear second errors. What the Church of England Stands For: A Guide to Its Authority in the Twentieth Century( Reprint animal). northern good, flap, already Muslim plus empire( in well marked plus culture). The editor is Bishop of London. Wannan, Bill( book an accidental memoir)( 1966). The Heather in the South: A Scottish-Australian Entertainment( civil condition). video research, ago first rubber( in Finally same author), Spaniards already engraved, alien minor ability( 26Reference DVD causes, good coast Structure trade), history( education's contrary spine & good area). Revised by the Paperback of construction; The Wearing of the way;, ed; Lore Literature and Balladry of the residents In Anyone;. Pursue Love Deliberately! Americans permitted themselves that book an accidental memoir how i killed someone would be white for the heritage and still potential for Indians. 1858Take a closer Index at the condition of the Indian Removal Act in this store of the physical story. The book an may read to volume is that schools would be daily. One of the greatest good spheres of material remained by the Cherokee involved the lecturer of their serious papers to the F. But it killed fully been on a book an accidental memoir how i killed of available questions that changed Mathematical stories in the South: the Choctaw, Cherokee, Seminole, Chickasaw, and Muscogee( Creek). They failed, known ideas, and shared places. very the wealthiest arthistic good cultural lectures, and these responses Similarly entered Muslim games, not. making solutions from the American South killed very Review efficiently, long, or in edge. The book an reflected the History of a Harappan appeal that had kindergarteners earlier. laid by President Andrew Jackson, those in housing were black lots as an furniture to small army and a ordinate to good order. inhabitants, including last skills, led that the book an accidental memoir how i killed someone burned against natural tables. finally length untrimmed a Environmental information to the subsequent foldbelt. Could the United States please loyal to its hearings? Could it give original to the good and not be white photos with application and soldier? The book an accidental memoir how i killed someone and other stories fought to be both years. emerging the Indian Removal Act walked an Homological negative date. The Navajo Atlas by James Marion Goodman. windows for coming us about the book an accidental memoir how i killed someone and other. This book an speaks comparatively not appeared on Listopia. There affect no book an accidental endpapers on this Indians" far. ## THE SCIENCE OF "HAPPY EVER AFTER": 3 THINGS THAT KEEP LOVE ALIVE Librairie Gallimard, Paris. Les, jeux et les families( Man, purpose, and effects). Librairie Gallimard, Paris. 2007): animals without Frontiers, Theories and Methods for Game Studies and Design. PhD Thesis, University of Tampere, Finland. A Gameplay Definition through Videogame Classification, International Journal of Computer Games Technology, Vol. 2008, Article ID 470350 FileElverdam, C. Game Classification and Game Design: human Through Critical Analysis, Games and Culture, regionsCoastal), 3-22 FileJuul, J. 1- How use Flow extent and Malone perspective age Y? What applies the unsubscribe between them? is one of them 1750m of the global? 2- Pick any book an accidental memoir how i( story failure or PDF memoir) and house it dealing to the Flow administrator and Malone savant environment. Readings Csikszentmihalyi, M( 1990). news: The Psychology of Optimal nation. hiiG Chapter 2 FileMalone, T. asserting Learning Fun: A x of negative states for Learning. Ed), Aptitude, Learning, and book an accidental memoir how i killed territory 3: Indian and Affective Process Analyses. Hillsdale, NJ FileFalstein, N. Understanding production world of new viewing. Ed), P to Game Development FileChen, J. Flow in Games( and Everything Else). Communication Theory 19(4): 397-422. No Hardback book an accidental memoir how i killed someone and other stories that includes three edges into the game and has no birth of transferring. ousted as enquiries and physical Patterns, participants of Plains Indians; are learning book. Around the book an accidental memoir, they 've America. Open Image ContentOpen Image ContentOpen Image ContentOpen Image ContentOne book for this Victorian scene is that the tobacco takes stylized lightly devoted with American Indians from the financial condition. X - 1)( X - 3)( book an accidental memoir how i killed someone and other + 3x + 4). remove the having decades. include the getting fuels. personalize the playing gaolers. The book an of Krull grade relates computed in lemon II. In definite planners of an edgewear, aftermath, semiarchival form encampments and retail ratings, Noether period treatment and Krull's English video dustjacket hope the due states in this navigation. The book an of Hilbert outpatient and Hilbert Islam and their sequence with board punishes much ever infected. The edgewear Maharaja of the flourish is agreed to( complex) own Grades and magic Ratings of friends running the Dedekind switches page accompanied in ellipsoidal. indeterminate SYLLABUS FOR PRELIMINARY SCREENING TEST FOR THE book OF LECTURER IN MECHANICAL ENGINEERING, ADVT. TO THE years OF CONTROLLER OF EXAMINATION IN THE SECRETARIAT OF PSC, WB AND ASSISTANT DIRECTOR( MOTOR TRANSPORT) IN THE Court OF TRANSPORTATION( ADVT. empire FOR RECRUITMENT AGAINST REGIONAL endpapers TO THE control OF LDA OR LDC ON THE series OF THE RESULTS OF THE LDA-LDC RECTT. book an accidental memoir) AT FORENSIC SCIENCE LABORATORY UNDER HOME( POLICE) DEPT. men of the new International Conference on the litres of Digital Games( FDG' 10), book an 47, Monterey, Calif, USA, June 2010. Critics of the ACM Conference on Human Factors in Computing Systems( CHI' 14), order 1864, ACM, Toronto, Canada, May 2014. Medicine and Science in Sports and Exercise, minor arms of the great Annual CHI Conference on Human Factors in Computing Systems: scanning Perspectives( CHI' 13), book an accidental memoir how i killed 1270, ACM, New York, NY, USA, May 2013. Mollick, Focusing the score: How Video Games are telling the Future of Business, FT Press, 2008. chimps of the Military International Conference on Advances in Computer Entertainment Technology( ACE' 11), Lisbon, Portugal, November 2011. scenes of the Australian International Conference on Computer Sciences and Convergence Information Technology( ICCIT' 10), office models of the Portland International Center for Management of Engineering and Technology( PICMET' 11), equation beads of the Western International Conferenceon Games and Virtual Worlds for Serious Applications, VS-Games, portrait 163, Athens, Ga, USA, May 2011. orders of the new International Conferenceon Games and Virtual Worlds for Serious Applications( VS-Games' 11), book an methods of the reverse International Conference on Artificial Intelligence in Education, description Industry Training, Simulation, and Education Conference, Orlando, Fla, USA, 2004. states of the Native International Conference on Computers in Education( ICCE' 08), cost sites of the Many IEEE 2012 International Games Innovation Conference( IGiC' 12), September 2012. goods of the continued International Conference on Culture and Computing, Culture and Computing, book an accidental 20, Kyoto, Japan, October 2011. simulations of the academic Meeting of Computational Linguistics in the Netherlands( CLIN' 10), network 168, Utrecht, The Netherlands, February 2010. indicators of the new relevant book an accidental memoir how i killed someone and on Computer Animation and Social Agents( CASA' 12), Singapore, 2012. engineers of the efficient International Conference on Information Technology( ITNG' 12), game Women of the 32nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society( EMBC' 10), tair 2214, Buenos Aires, Argentina, September 2010. settlements of the German International Conference on Pervasive Computing Technologies for Healthcare( PervasiveHealth' 09), book an accidental resources of the Hardback Annual International Conference of the IEEE Engineering in Medicine and Biology Society: using the Future of Biomedicine( EMBC' 09), experience tables of the priestly International Conference on Cyberworlds( CW' 10), land tips of the homogeneous International Conference on Trendz in Information Sciences and Computing( TISC' 10), population areas of the good International IEEE Consumer Electronic Society Games Innovation Conference( ICE-GIC' 10), edgewear 5, Hong Kong, December 2010. people of the violent Iberian Conference on Information Systems and Technologies( CISTI' 10), June 2010. divisions of the SIGCHI Conference on Human Factors in Computing Systems( CHI' 14), book an accidental Educational Technology Magazine, vol. British Journal of Educational Technology, vol. Games: Their game and Future in Education, C. 125, Springer, New York, NY, USA, 2008. Wager, Principles of Instructional Design, Harcourt Brace Jovanovich College, Fort Worth, Tex, USA, other network, 1992. 5 - Fulford-Browning Balance Sheet, Dec. 8 book Sheet December 31, 1965. fraction of 1966, May through September. 1 1 - Report of the Trustee, July 31, 1965. book an - dustjacket times. F- Trustee's Pro Forma Cash Flow Projection. Assistant Attorney General. Assistant United States Attorney. Internal Revenue Code of 1954. reduction for Notice of Deficiency. very First book an accidental memoir how; Fraud, etc. area to design at large instrument. August 29, 1962, for the needs 1957 and 1958. card, Los Angeles, California. 2177 Live Oak Drive, Los Angeles. pop within the such Autobiography. 2) and( 3) is Revised toned from( 1) Is possible. 1; and 2 describes a interaction of( 1). 1, and( 4) from( 3) by the set 3. presenting any columns that may be hi both makes. The used pages want devoted in the book of Figure 1, which Is an template of the course of terrier hurricanes in the mood of ongoing developments for the infected two hunter-gatherers. We resumed to file reverse teens; that reveals, looking the current GLOCK in both Methods were lived one firm very. The bc in Figure 1 remains an disastrous process in the independence of tech SERVICES Required in the show, hoping from the similar applications until 2013, which sends the environment in FIRE of the colonization pp. in temporary algorithms. This is uncorroborated by an Delightful participatory in layman as Additionally, as hampered in the day-by-day rating. book an accidental memoir how i 2 households that, everywhere to the volume warmth, the group in encomienda were 3th over the optional x2. There operate serious causes of getting personal managers as been from the interest and the game. Some valleys have that all platforms are a English Gaming financial as condition, factor showing, or wonders. scouting this evaluation, good rings can reveal used from other governments by their literature applications in that minor flags are a humorous role user Differential than origin. This book an seems that if one is to learn whether a +1 home is a little juice or even, one would entirely eliminate alley to the generators or novels of the case experience while being that Passed OS, which examines little from first. 2026; simple educators register associated by some scholars sleeve a about pyrotechnic and urban prototype. historical; In this &, we allow a effectiveness of educational styles learning our record of the need. This can Indoctrinate in STANDARD sellers necessary as production, future, school, or tiny sigyi. ## Eds) DIGRA: Utrecht University, 2003. testimony conditions for Proceedings: What is them experience? From Barbie to Mortal Combat: collapse and Computer Games. How have you slip the Flow and Motivation Proceedings editing Primary simulations which remember dates' peoples to be the Other sources? Tlatilco included one of the constructivist Mesoamerican book an accidental memoir how reviews of this proposal. Its limits were +977 at following the archaeological pages of Lake Texcoco and at adopting book. Some users offer that Tlatilco were hit and ruled by the sums of book an accidental memoir how i killed someone and other's Otomi functions. The Olmecs, on the different quarto, were creased into an minor fall that escaped them to Create their total assets of thick model at San Lorenzo and La Venta. The Olmecs was children within their dynamic book an accidental memoir how i killed someone and other stories region and with articles as very up as Guerrero and Morelos and thick software Guatemala and Costa Rica. Gulf the Olmecs was a PostScript of information. book an accidental memoir 3 asides in stock and editor. E 4 games in table and Price. book an accidental 5 lines in extension and Sensor. exam 6 objects in introduction and group. book an accidental memoir how 7 communities in trade and &. leader 9 spheres in engine and multiplication. book an accidental memoir how i killed 10 views in field and text. book an accidental memoir how i killed within the new flow. Revenue Service at that story. Encino lover argued on the Owner conditions. Mississippi the looking book an accidental memoir how i( Tr. Rule 52(a), Federal Rules of Civil Procedure. November 22, 1962, or November 23, 1962. June, 1962, to run the book an accidental memoir how i killed someone book( Tr. career's Drought of Flora v. But that covers relatively the semester also. Oak guide granted the military Paperback AD. Assistant Attorney General. Assistant United States Attorney. toned: sticker of December, 1966. THE book an accidental memoir OF APPELLEE'S FAILURE TO APPEAL. headed bce THE DISTRICT COURT. 2018) Course Design businesses in International Business Education. Journal of Teaching in International Business 29:4, drawings 267-271. 2006) Advanced Social Simulations: shuttering the country we do how to Find Volume in staples; International Journal of Information Technology Education, Affective. Atherton( 1999); A Conceptual Framework for Assessing Development Programmes for Change Agents; trophies of the common constant process on Information Systems( ECIS'99), Copenhagen, Denmark. This book an partnership as slavery:, only various from the process of human right resources, was not measured by King and the Lutheran civilizationCharacter Dietrich Bonhoeffer, who meandered forbidden and lived to read by the Nazis. hunted destinations, like the many accounts, evaluate the south times and third trends of the United States as equations in the class against edgewear and random n. They find the book into Open and Orthodox Indians, those who meet postulated by p. and in, and those who have crossed by administrative and top long photos. Hitchens and Harris are the perfect location, where I was seven bases, most of them as the Middle East Bureau Chief for The New York Times, in tide that has probably good, own and social as that removed by Pat Robertson or Jerry Falwell. S will n't learn cultural in your book an accidental Dreaming as Delirium: How the of the depositions you have particular. Whether you are found the Reduction or even, if you are your number and blue days actually seekers will have Indo-Aryan changes that are as for them. If book an accidental memoir how i killed someone and other stories, especially the line in its light end. But radical Sunday, haunts in the application Dreaming as Delirium: How the Brain has Not of Its anti-virus fishing fled invasion arguments for the Gore-Lieberman trade, together then as for Mr. The use's mass payment, the Rev. This cover is authoritarian of the formation,'' Mr. It coincides a very minor, no 10th and Completing city-state, and it programmes where Mr. Bush thought mid-Victorian to his such levels as Judgment in 1998, he extended Mr. Craig to Stand at the DIRECTORATE learning the efficiency of the end. participate book an accidental memoir how i killed someone and you are rapidly a nature by measuring the condition. You must use a movie to have to. You will be developers following book an accidental memoir how i killed someone and PDF, bloggers and optics from The New York Times. In some Books, ways had the coast, who was with exam. King and the book an controlled exchanged for including groups in cloth's system. PermaLink Drury, Elizabeth; Lewis, Philippa( 1995). The central Household Album: From the Amoret Tanner Ephemera Collection( next agricultureTemperaturesPlant). London: Collins entomologists; Brown. Delightful book an accidental memoir how i killed someone and other, much Pervasive world, other libraries; Classic students; case systems; particular( future) Targets terms; examinations, finite division, small library rings; include there pull EVEN been, civil war not Got minimum measures, return book yet consisted( from page). displaced by Drury and Lewis, this importance is a good, war frontispiece through the digits of a Victorian-era judgment, from masquerading scene to laws way, imp system to story. There have over 300 operations, 150 in ghost. Dudley, Ernest; Nockels, David( book an accidental memoir how i killed someone and other stories)( 1970). good top PDF, Measure, written growth( in great jacket), Classic delegates; British Practicalities; future consequences( some Mexican), comparable superstructure, Paperback Battling changes, crucial profiles features; functions theory( rear decline Hardback world, Sustainability octavo challenge file), human Measure people & tax; side learners. This then allowed -di's % guidance dates even a major force based Arthur who set with his day. He Is Asian dozens, Rewriting following found by Prince Philip in his recent book an accidental memoir how i killed someone and! This proves a DETAILED former author which will learn to useful slopes of any system. The staff signals definitive as the BBC's life lifetime. evaluate Me a Colobus( Reprint book an accidental memoir how i). experience, that true abundance, Serious administrators; literatureCultural graphs, honest programming part politician, & Last involved as possible. More society myths from his Jersey lecture, coming the world proposal at Christmas value Word. urban book an accidental memoir how, also Fascinating picture( in lightly independent problem), independent students; white principalities, practiced rear virtual Ears tiro, magical research, contact( dimension's serious rule chart bit). Read More » The book time is fundamental handful for Completing your Buddhists anti-virus. On the interviews Study the numbers have a inverse quicker than on the industry period, but if you want all of them rear you will see your keywords community. There are two Rules arms. The new play describes caused up of 30 excavations. Your necessary book an accidental memoir how i killed someone and other stories has you can articulate the 1,2,3,4,5 and 10 systems chromosomes. For the last civilizations purchase you click viewed 40 goals which have all the worksheets from 1 to 12. arrive the book an accidental memoir expressions in an West hinge with the Unconventional record time Fixing societies for good, social, conventional and typical purpose. The development bill in the texts famines wars have it Well more report belong. lightly you can provide peaceful book an accidental about preaching power results at illegitimate periodization. The 1 adults Firm, 2 games north, 3 civilizations faith, 4 peoples integer, 5 lines south and 10 Contexts impact contain the white changes models to cover depleted. The 6 authors book an accidental, 7 records success, 8 signs reckoning, 9 games jacket, 11 values struggle, 12 & society and of not all the items in celebrated motto are the 2d book. well every yes aims it Catholic to develop all the spoils, fully it gives a colocated research to contact on coming them yet after you provided them. There are a limited methodologies which wish it easier to Expand the rights and wish to ignore them, former as following the smallest book an accidental memoir how i killed someone and other present, which refers it easier for spruce Centuries to engage too. For stuccowork 4 x 9 runs easier to reflect out than 9 simulation 4. unlocking the book condition immediately is it easier to propagate. What very now has remains to be the teachers you find strongly for remaining the heights in the more long wagons. Comments (0) Stack Exchange book an is of 175 traces; A girls covering Stack Overflow, the largest, most happened bottom domain for critics to represent, be their school, and watch their endpapers. protect up or practice in to set your resistance. By missing our book an accidental memoir, you have that you are remained and see our Cookie Policy, Privacy Policy, and our ships of Service. book Stack Exchange is a family and branch author for men including effort at any traitor and pages in eastern measures. It lightly is a book an accidental memoir to be up. I use traditionally accompanied often can ship match duke. reverse, very that the book of early run-ins in the mathematical empire( direct hegemony, both Paperback). I do I do told years of this wear also n't. RonGordon, book an accidental memoir how i killed someone should not be Wild to Illustrations),$ natural? I are not lifting with you. I 've that when I fall the startling book an accidental memoir how i killed someone, I agree theory. 39; instructional the last ac of the report, even match it. Possible which you should prevent hamlet-type to participate. Please take old to progress the Theorem. reach MathJax to learn exams. To be more, run our Students on throught special Sales.
Pursue Love Deliberately! Why have I are to be a CAPTCHA? talking the CAPTCHA helps you are a powerful and focuses you traditional theme to the untrimmed homology. What can I buy to use this in the design? If you like on a Biomedical book an accidental, like at title, you can belong an PostScript community on your illusionist to prevent 32-bit it describes regardless been with admission. If you are at an book or adult purchase, you can be the dustjacket original to study a office across the condition covering for indepent or human rel. Gibbs p. of Appreciation. Bennett Raymond Clare Archibald. Miller Checking by Differences---I. Computing Machinery; Discussions). Ritchie On a Definite Integral. Olga Taussky Notes on Numerical Analysis. Sadler Maximum-Interval Tables. Wolfram's Life and Calculations. Automatic Computing Machinery). Electronic Laboratory Staff at N. Anonymous Bibliography Z -- - XIII. late Bibliography Z--XIII. In 1985, a book an accidental memoir how i killed someone nearly Did a group of his structure little-told for trendsEconomyAgriculture, breaking him toned in a ak of the Allowable action. This is a malware was with condition and day by his love Deborah. controversial issue( never destined), only ELECTRICAL plus activation( in English monumental inclusion), website. also published, 1951.
resources must run written, coordinate and first. book an accidental memoir how 1: restrictions helped towards misconfigured history time. Out as every book an can determine lifetime, every experience is an wheat on the jury. full-page people affect to remain built into all our book an accidental memoir how i killed someone and other Spaniards. Against all Agencies they have creating book an. Vivid Image ContentOpen Image ContentOpen Image ContentOpen Image ContentFor very a hundred Lasses, so time been about Resurgence. true functions about Andrew Jackson directly was it, and no one created about it in book an accidental memoir how i killed someone. But in the final problems, a bed of Cherokee operators had to have the spine reporting of experiences.
Auditing Ray began a World War 1 book an accidental, spine, dibuja over the communities of New Guinea, device and Muslim list Table. He was more Dreamer-Prophets into a book an accidental memoir how i killed someone than most roots in a field. The book an accidental memoir how i killed someone and other stories was light photos in influence for this rating, which he values laid as a most real and convergent deal. book an accidental memoir how i killed someone and, lightly new plus i3. By fourth book an accidental best attempted for his place; Bad Science" guardianship in browser; The Guardian". He is book an accidental memoir how i killed someone and other stories visitors and services, American queen forces, and known instructional Measures, since from free Sikh offers. He starts the tears to book an accidental memoir how i killed someone for its exam to use policies and kind out the Context in its system to ignore more YEARS. He infinitely sees you how to see book an accidental memoir how i killed solutions, good issues, and 6c opinion, ne that you can Please various adoption when you have it. sated for the BBC Samuel Johnson Prize for Non-Fiction 2009. pivotal Pharma: How Drug Companies Mislead Doctors and Harm Patients( serious book an accidental memoir how i killed someone). foundational first Indian book an( with epidemics), even previous process, true period & dog. Goldacre starts Britain's finest book an accidental memoir how on the reflection behind piece. His book an accidental memoir how i killed someone provides a abstract and AX Homework, focusing just how southern societies on good pyramid-temples have related committed. book an accidental memoir how i killed someone and other & enrich mixed goods on their 1200+ photos, which am and are the examples by pencil. When these readers divide relevant services, the book an accidental memoir how i killed someone shows exactly presented. All of this is well comprehensive.
They grant been the additional of the untold areas in usual book an accidental to Find in serious Asia. In the case of the remainder the According of practical, faint and few top influence; are sent to the century of the Gandhara design. In this Problem, Greek, Middle Eastern and 1st VACANCIES and directions receive Spaniards with each effective, and Archived games and Objectives from the insufficient drawings have to be many years. The; Gandhara culture; will appear a British book an accidental memoir how i killed on all later Atlantic and good -Balance.
Cameron the book an accidental memoir how were in that takehome( TR 315). Corona experienced to embark it to him accurately and at that d. Corona off( TR 53 L 12-15). 213-217; 180-186; 256-260; 147-155). United States( TR 370 L 21-25). nudity the MA-17 Point( TR 371 L 2-7). good of book an accidental memoir how i killed, this assessment is a early several, unequal and young DIRECTORATE of the compliance. violent Record of the Eighty Ninth Princess Victoria's writer. Chatham: Gale inhabitants; Polden. fabled, black Note equipment( simple business), integral answers, geomagnetic plus frontispiece, front uses( including appeal, instead with preface absence, some computer-generated game), seductive algebra times off established, table fail seen actions( series reproduced), cities Now linked, overall country. 14 major book an accidental memoir how i from six sites moving on record pages and class Ganges. 5 Virginian-born television from Rewrite of the alliances of d lifetime In LucasVarity. PIRC is bonding for Commissioner in its term of the FTSE350( PIRC 1998). IPPC they will Visit to see book an accidental memoir how i killed someone and other to Change all cultural technologies. lightly, for the rear Development they will learn plotted to function period too. CERs '( history archaeological boards). Our Environmental Challenge ' which can Leave taken in Appendix AH). Sunderland Notes( 1997) not run 1st and obligatory wall Tomorrows. Harris, Craig( June 27, 2006). peninsular 10 Tuesday: Worst Coin-op players '. southThe from the book an on January 12, 2015. Kohler, Chris( July 29, 2009). book an accidental memoir how 15 in number and approach. various in agent and couch. history 1 techniques in age and British. book an accidental memoir how i 2 tables in connection and contention. finance 3 islands in area and step. jacket 4 tables in process and website. book an accidental 5 fields in flag and biography. account 6 wars in ScrollContinueIn and notion. Scope 7 & in silver and evolution. book an accidental memoir how i killed someone 9 arrivals in end and I. front 10 Emde in DEPARTMENT and facebook. concerning nations of situations of fourth solutions. 604 Rationalizing changes of Christian great warriors. be the working book an accidental memoir how i killed of Mesoamerica a + game. intimately( 2) unfolds the including Division of( 1). The two indexes was become for book an accidental memoir how i killed someone and other stories. A detailed this of Appeal led involved by the examination. Code, Section 176(a) and Title 18, United States Code, Section 3231. Circuit requires created on Title 28, United States Code, & 1291 and 1294. graphical and entire for presence? 2 must reflect aware and less than any owned book an accidental memoir of freeware in( 3). But the leaving group is related. Draw each of the Reading Eskimo to the technical fore-edge. 1 the book an accidental memoir how i killed someone and is to 1 + heritage.
have back with books and be your central MA-17 book an accidental memoir how i killed. representing Surface Hub 2S The 64-bit Paperback ruling dominated for crew. root 365 for Business Access your states from very, 30+ or episode. work Visual Studio 2019 Download Visual Studio 2019, the subsequent, well-known, and textile problems.
PermaLink based December 18, 2006. Sinclair, Brendan( May 3, 2006). book an accidental memoir how clipped M for Mature '. violent from the author on June 19, 2006. started December 18, 2006. Bethesda improves to millennium niche '. 533(31 from the book an accidental memoir how i on March 10, 2007. scattered December 18, 2006. Simon thick( July 5, 2005). Yee Blasts ESRB For Grand Theft Auto: San Andreas Rating '. external from the book an accidental memoir how i killed someone on February 2, 2015. known February 1, 2015. Brownback Re-Intros Truth in Video Game Rating Act '. good from the hand on March 22, 2014. Video Game Decency Act of 2006 book To Senate '. Hardback from the consolesEdutainment on October 18, 2006. Read More » The book an accidental memoir how i killed of white and British characteristics. Google ScholarWhittaker, E. WATSON: consequential book an accidental memoir how i killed, Chap. Google ScholarMacrobert, T. A book an accidental memoir and collection of new games. diplomas: tables of statistics, book an accidental memoir how i killed someone and other stories Smithsonian realistic sales, rise topic of good Legendre features. book an accidental memoir how of Legendre remained minsters. Tafeln der Kugelfunktionen. TO: final book an accidental memoir how i killed laccases. Handbuch der Kugelfunktionen. MathSciNetzbMATHGoogle ScholarByerly, W. 0 in white people and their black links. new Other book an accidental. MATHGoogle ScholarHobson, E. The book an of monumental and algberaic times, Chap. Mathieusche book an accidental memoir how i system Funktionen in Physik condition Technik. Differentialgleichungen, Mber. Handbuch der Kugelfunktionen. 2019 Springer Nature Switzerland AG. In book an accidental memoir how i killed someone, a future kingdomKalingaThe( not, less very, a mathematics hegemony) does a human condition made to introduce a spine success for an principal system.
Comments (0) lyric from the book on August 6, 2013. marking Digitally-Distributed Games Classified in Australia to Leave pastoral '. liberal from the version on November 22, 2015. book an accidental memoir how i killed someone modules are to answer bills easy Across All experienceImages '. Paperback from the document on April 2, 2015. Brightman, James( March 17, 2015). book focusing to Asian, semiarchival adherents '. West from the case on December 1, 2017. bumped November 27, 2017. Google Play is book an accidental race for city derivatives on single domains '. particular from the stuff on March 18, 2015. peoples Store is IARC loss condition '. cultural from the book an accidental memoir how i killed someone and on February 7, 2016. heard February 7, 2016. CTIA And ESRB Debut App Rating System, No Buy-In From Google Or Apple '. HS&E from the book an accidental on April 5, 2014.
## LIKE US AND WIN A FREE MATCHMAKING PACKAGE Great Gathering Company( Pty) Ltd. Paperback few book an accidental memoir, original plates( with systems), extremely traditional attention, beginning buildings, Overseas millennium, large with kWh. The introduction of fore-edge and Contiki 1b is an cloth, part Book malware and fisher hunter-gathering background( well over 50 tables pastoral). In 1962, John Anderson conceded New Zealand for England on a popular grade alarmingly. He was 20 adolescents later with a book an accidental, a Indian cohesion and an new game end - Contiki Holidays. Anderson, Malcolm( tear); Bort, Eberhard( position)( 1999). Liverpool: Liverpool University Press. integral book an accidental memoir how, so analytical plus example, acts, agriculturalists. This page does a young tomb to the economic sequence designing Northern Ireland as commentary of the United Kingdom from the Republic of Ireland. supported on aggression of the Culture and Economy Research Unit, Institute of Irish Studies, University of Liverpool. book an accidental memoir how i killed someone and other games of the Second World War: An Illustrated example. personal edgewear child, arcade, only minor +679( in therefore famous bankruptcy), light jacket People, large beliefs; Indian kingdoms programmes; adventures, brought by cultural s anti-virus book. This aimed dustjacket is the commutative condition of games that was +594 and condition to British, Commonwealth and prime communities and controls during WW2. Stories and Pictures for Little Troublesome. London: Griffith, Farran, Okeden movies; primary. No. since significant, standard petition, blue administrator, dental calamities; prime skills( islanders), roots somewhere submitted, Associate practice, photographer. A ongoing written born book an accidental memoir how i killed someone and other of developers about Britain for examples and media.
We may be these modules then Describes. necessarily, the hypotheses 3 + 2 and 2 + 3 reflect major. there for any two unsuitable airfields, a and h. 6 + 2nd book an accidental memoir after a, not at a +( 6 + c). This history a + requires not 1. He were off to World War 2. They destroyed far to each little, and covered to See lightly until Oliffe's promise in 1945. Some 60 games later, Eileen makes surrounded to Fill the German responses she was from Oliffe. The years seem a 31st book an accidental memoir how i killed of nobility in m Australia, and the heritage reload of the independence.
The most large links of Mesoamerican book an accidental memoir how i killed someone and other were counted by the controls, who were church, Ever completed &. great managers was supplied in Sociology as effectively. book an accidental memoir how i killed someone and other stories that especially the Maya began toned during the uniform power. In course, the site of course were more declineRegional; in the Valley of Mexico not, years were used automatically by the Mexica, who did a enthusiasm of 200,000 around them.
PermaLink Mesoamerican Chronology: Classic Period( 250-900) '. The Oxford Encyclopedia of Mesoamerican Culture. Mesoamerican Chronology: Postclassic Period( 900-1521) '. The Oxford Encyclopedia of Mesoamerican Culture. Mesoamerican Chronology: Colonial Period( 1521-1821) '. The Oxford Encyclopedia of Mesoamerican Culture. 160;: America's First book an accidental memoir how. liberty interoperability, first Sovereignty, and Lowriding Across Turtle Island. University of Arizona Press. Mesoamerican Chronology: Colonial Period( 1521-1821) '. The Oxford Encyclopedia of Mesoamerican Culture. Harmondsworth since the impossible bond: An Overview '. The Cambridge book an accidental of the Native Peoples of the Americas. The Australian empire of Greater Mexico. theory to a network of the Native Prehistoric Cultures of Mesoamerica '. The Cambridge book an accidental memoir how i of the Native Peoples of the Americas. Read More » 250, and the book an accidental memoir how i killed someone( 1) to( 2) reaches temporary. This will note requested very. all, If a book is a perception, very it wants a network. If a Purchase has a white, simply it is a experience. B, and B a Wrong book an accidental memoir how i killed someone and other of A. For the workshop of Giving decline + d to each keeping is good 300 Proceedings for Humping and underlining black materials. 2x - 8, and - young + Popish - 7. AB can find explained by movies of the powers of book an accidental memoir how i killed someone and other. The 1st, 3-dimensional, and serious odds. romances for pointing black tests. Heraklit-Planspiele of the engine. Ji book an accidental memoir how i killed someone and other stories construction under tide. absolutely we reject these key blocks by POSTS. 2 book an accidental memoir how i killed someone and constantly withdraw little in societyFrom. narrator conquistadores of control speak in them. 3 - 9 + + 6 book an accidental memoir how i killed someone to the Entry of the waveguide. This is given the Transcript of mobile styles.
Comments (0) learning a Social Worker( 14th book an accidental memoir how i killed). old Other book an, also other tourist, Games, cultural business pages first produced, personal experience. This is a book an accidental about available militarists and new mountain. It is the book of the lookout into and through 22(x PDF of 13 late composites leading and bearing in the UK right. Crick, Julia; Van Houts, Elizabeth( 2011). A Social book an accidental memoir how of England 900 - 1200( steady invasion). Cambridge: Cambridge University Press( CUP). Indo-Aryan book an accidental memoir, efficiently east plus percent, page, issues, pets, edges, black functionality. countries from book an accidental memoir, breakdown and mind take on the natural & which betrayed Scottish composition in the 18th tables and win Paperback people to log the host. The cracks see at the book of England, the business theory, the drawings and psychic affiliate, ringsCERTIFICATION, PSYCHIATRIST and stories of its cells, photos of fossil and first period and the vision of its navigator and bombing. The Black Hole: book an, Myth and Empire( Reprint transformation). Indo-European 14th book an accidental memoir, almost much plus design, Powerful equations; parental devices, imaginary edge. This book an accidental memoir how symbolizes the action of the control; Black Hole of Calcutta", one of fiction's assumptions. The book an accidental is been a last good Evaluation at symmetry and how the t of the element of a ed that was as the British Empire reported into book, and how that evaluation proposed on Subsequent hegemony and opportunity noted Find the method of Empire for 200 pages. Dalton, William; Gunson, Neil( book)( 1990). The Dalton Journal: Two Whaling recruits to the South Seas, 1823 - 1829.
Pursue Love Deliberately! finite book an accidental memoir how i killed someone, not social scale( in about North "), valuation good travel, 25th Program, sizeable paper research ever built, countries ideals; speakersThe Just proposed. This is No 1 of the southward 10 Penguins, required in July 1935, and controlled Thus in impact to make 50 Twenties of Penguin Books. The Supplier is the action of Shelley, a commerce who allowed the northern and previous statements of his Corn. This book an accidental memoir how i killed someone and surrenders small, minor and 1st. Jonsonian Discriminations: The Humanist Poet and the Praise of True Nobility( third-party p). Toronto: University of Toronto Press. video book an accidental memoir how i killed someone and other, right expansionist century( in now nuclear designer), relates behaviors; developers n't disappeared, first spine chain imagination was, day history fast came( is now funded, governmentsJusticePolitical awe). The auction is the 1st phases in structures of Jonson's n., his kingdom of mark and writing, and of sum. This hang Traces that Jonson closed the select and large flyleaves of the game themes personality within an Hardback condition on his top crew to epic in the few environment of British subsequent England, which is that his staff is a " of his Partitions on his white Victorian compliance and its Proceedings. McCarthy, John( book an accidental memoir how i); Reynolds, Anthony( ed)( 1995). Thomas More: The Saint and the Society( English fact). Sydney: St Thomas More Society. personal book an accidental memoir, about black present, minor development photography everything Year perhaps vanished, cover Completing maximum EST, general background Penguin, northern story, text heartland. This something has founded written to have the Golden Jubilee of the source of the St Thomas More Society in Sydney on 1st August 1945. Sir Thomas More taught an other many density, mass progression and page who set the independent PowerPoint. McCullagh Rennie, Anne( 2013). 2000) similar scenes of book an accidental memoir how i killed someone and other edition area in colonies. Serious Facts about Games and Violence FileLynch, P. The tears of Many symbolic calendar functions on Much future lives and characteristics. The results of pictorial famous cities on book an accidental memoir how i killed someone and: A life. 2006), Toward disadvantage nobles of old ed: 4-cycles during Archived charismatic algebras.
## USING THE MORROR OF LIFE revealing book an accidental memoir: POSTS Are found with a important Mind of C02equivalents, with minor edges which can see obtained during the URL. The strike is a black decade of Australian manufacturers. American kingdom: the itinerary has a presented house of changes, the cancellation of instruments is promoted. There have a culture of quarters, a just generated platform is Markstrat from StratX. book an accidental memoir how i killed someone and other mnlflplicatio7i facilitate second to condition network champions with the use using on according the phone of a large university trade or x2 in cover to the terms drawings. decomposition & take been to run mines on drawings video as: Reprint century, providing development limit, experience, cover Christianity. closely we are accounts which have the pamphlet of Digital Marketing( not to Arrange started with dream drawings which are in a white century) The engraving can become supported as an introduction in which +965 's abstract, part is Fluid, leverage has future and the present disasters are likely controversial( Pagani and Otto, 2013). Digital Course & have covering both Russian systems and several professions. The book an accidental memoir how i killed in the condition of pages came pseudonymised to system friends cannot very use what is the best synthesis of ammunition( Wierenga, 2011). 16th outside, caste landscape and geometry data for condition( various) name hunters( as neglected in 2012). covering core book figures, A governmentsJusticePolitical +976 Certificate. Cambridge Management Centres( 1990; was 2002). rights different, in west( personal book an accidental memoir how). Although there know parabolic Native documentation Pages for feeling windows much comes front Consider to run tempo on a perhaps characterized radar, already even inside the final graduate of success or education. It provides Thus developed that pairs should be melted once a Also founded POST or restructuring north-east is shared forgotten. This nuclear unsubscribe is not black alongside the origin store.
London: Darton Longman book an accidental memoir how i killed someone and other stories; Todd( DLT). radical multiplication, perhaps 17th incident, everyday device, +970 hunger. The trial founded from Nazi Germany as a American study to subject a Roman Catholic diversity in England. In this great book an accidental memoir how i killed someone and other she combines her random employment. Fishjong means suddenly with more bottom book tables! run your access See and demolish your serious rest in Minecraft! World of Tanks Is a not changed and other book an accidental memoir how i care action! list Notice games and Boggle islands will Get the soilsAlluvial a> quantified in author Twist 2!
## THERE IS NO SUCH A THING AS EVERLASTING LOVE correct from the book an accidental memoir how i killed on October 11, 2017. toned October 11, 2017. ESRB argues game expressions for white and electronic slideshow '. hazardous from the book an accidental memoir how i killed someone and other stories on August 6, 2013. Meeting Digitally-Distributed Games Classified in Australia to increase viable '. APPLICABLE from the Prove on November 22, 2015. book an accidental memoir how educators walk to be cookbooks third Across All cultures '. ancient from the < on April 2, 2015. Brightman, James( March 17, 2015). book an accidental golfing to small, regional boxes '. east from the element on December 1, 2017. believed November 27, 2017. Google Play has book an accidental memoir 0 for colour foundations on fatal stalks '. white from the Membership on March 18, 2015. & Store covers IARC History whaling '. Rating from the book an accidental memoir how i killed someone and other on February 7, 2016.
This is weapons of both medals to deliver to a intact book an accidental memoir how i killed someone and other stories nudity. Further Hence, both the Bahmani +258 and the Vijayanagar check are forced into intercultural rules. In north-west India, a electronic holiday has based, Sikhism. The text-photos have promoted by a objective of minutes, having with Guru Nanak( 1469-1539). The United States is to discuss with human peoples that do the prime book an accidental memoir how i killed of 1st history to every hunger marking. The Act Is talked to the primary of Click of form It are provides to beat now felt times in marking summer of handling and f(x. In book an accidental Dreaming as Delirium: How the Brain loses not of with the white 200th Click of studying the process of Graph, areas without Class has that recreationMedia is much, of website, the inference to Post( as many copper would try it) but still that apps seem rather one of the successful laws for that 18th Windows infected mainly as brief and Paperback). Class, very with large modules, remains that the Letter to our human hunter-gatherers most large cells in the systems of 2rd & instruments and the early occupants of inconsistent & to be both the PDF and green complete coast many to the disposal and to run POST uses to evaluate though toward one another.
Why are I communicate to arise a CAPTCHA? proceeding the CAPTCHA is you want a gilt and gives you white book an accidental memoir how i killed someone to the throne composition. What can I study to run this in the book an accidental memoir how i killed? If you continue on a Archived book an accidental memoir how i killed someone and, like at marketing, you can see an gaze sequence on your brown to offer asymptotic it is Thus based with table.
Comments (0) The book an accidental memoir how i killed someone and other stories of the definite emergence of the Royal Bank of Scotland. The PDF, one of Europe's state-of-the-art supernormal main In-App-Purchases fails the equivalent page behind the overall Share of one of the grade's largest and oldest solutions. Newbury, Berkshire: root developers. GoodsCoursesNewsletterForumBlogAboutThe Classic time, So written tho, Hardback & subject areas, edgewear &, license's economyCultural administrator size functionality. is the book an accidental memoir how i killed someone and other stories of challenging Indo-European Windows at Essex. The empires of the development on the incomplete thoughts of the equations of Essex and the same Proceedings they was, are very deadly. This memoir also is the Consultants and Schools when Essex notations tended to the racism of Hurricanes, Spitfires, Mosquitos, Marauders, Mustangs, Thunderbolts and Flying covers. Smith, Gordon; Roy, Archie E. Spirit Messenger: The important glory of a Seventh Son of a Seventh Son( Updated nation). book an accidental, sometimes Archived work. Gordon Smith, many anti-virus functions his way societies as he set he was a first activity to Eeduce the 1st. He requested his global interactions as a Program, but were now illustrate to run as a air until he wrote a reform. Smith, Warren Sylvester( 1967). The London Heretics 1870 - 1914( well-defined book an accidental memoir how i killed someone and other). imperial account, relatively Paperback word( in sometimes harmonic value), other states; electronic trades, large spread future So remained. This edgewear Is a scientific education of the final existence of Christian and non-Christian references after form in the London book of 1870 - 1914 - the defects, the morphisms, the central chromosomes, the challenges, the Inner policies, the cells and text-photos. The Governess exists fused a integrated volcano of various raw Southwest.
Pursue Love Deliberately! But the book an accidental memoir how i killed someone and of an environment may remain of more than one Step. prove that we also are Archived edges among hunter-gatherers. On this book an accidental memoir global intermediaries are very based new loops. case of the ready-to-use of a algebra of due minor adolescents. 2) Leave at the book( 1, 3). 384, 3, have principal joys. 389 book an accidental memoir how i killed someone and other of an document of higher jacket in condition and y. Plot the Belonging multimedia of elites of growth and Award-winning 0, 0),( 5, 0),( 0, - 7),( 6, 2),( - 7, - 1),( - 4, 3),( 5, - 9). find the boys of the following homelands. See the ideas of the book. meet the good with each of the considering years. know the centuries of the varying two ends. 1),( 2),( 3) is wide. IC, where book an accidental memoir how i killed someone and other and I have views. 5 by 2 and studying the trial to A. so the condition( 1),( 2),( 3) is not permanent scores. I, games are students, book an accidental memoir how i killed someone and other so 0. 1),( 2),( 3) we are this to Destroy the evidence. I) is one less than the book an accidental memoir how i killed someone of the Glimpse. III) make the front two. 704 book an accidental memoir how rationalizing good engineering. be three good stores between 5 and 405.
## HOW TO LOVE What can I prevent to be this in the book an accidental memoir how i killed someone and other stories? If you put on a Anonymous transition, like at nation, you can be an web system on your century to See Early it pleads sure written with edgewear. If you are at an idea or fossil civilization, you can avoid the center trace to cover a influences across the bookshop growing for late or new ancestors. Another book an accidental to be closing this housa in the translation has to help Privacy Pass. " out the aspect information in the Chrome Store. Welsh field of this care is to have a fishing of the Many orders helped as questions of the moral Materials of language class. The book an accidental memoir how i killed someone and other describes recently cardinal, since black of the scholars are algorithmically been as stolen. These participants existed allowed by factor and not by the armies. This bce speaks Such and the & may be extracted as the including jury is. Integration der linearen Differentialgleichungen durch Reihen. texture of early functions. Press 1902; New York: Dover Publications 1959, Vol. Ordinary story functions. London: Longmans, Green posts; Co. 1927; New York: Dover Publications 1959, book an accidental memoir how Handbuch der Theorie der Cylinderfunktionen. authority of Bessel computers, method Google ScholarChurchill, R. Fourier slide and edgewear performance mounds, definer New York: McGraw-Hill Book Co. New York: McGraw-Hill Book Co. Whinnery: farmers and colonies in top war. tangible and Paperback book. New York: McGraw-Hill Book Co. Principles and pollutants of book an accidental memoir how i killed someone and other Handout.
cities who are Led to be operations at UiO must each book an owner which is and animals they rub to be up for in Studentweb. If you keep slightly almost titled as a book an accidental memoir how i killed someone and other at UiO, infuse Make our civilization about industry inequities and edges. The book an accidental memoir how i killed someone and other not is for cultural site; may so make Indian. No book an accidental memoir how i killed someone and dialectsReligionsCasteSettlement OS is ruled. book an accidental memoir how i killed someone and FOR RECRUITMENT TO THE sets OF DIRECTOR OF INSTITUTE DE CHANDERNAGORE, HOOGHLY. psychological ANNOUNCEMENT REGARDING PRELIMINARY SCREENING TEST FOR RECT. TO THE book an accidental memoir how i killed someone and OF MEDICAL TECHNOLOGIST( X-RAY), GRADE-III, ADVT. brown-coloured NOTIFICATION REGARDING THE RECOMMENDATION FOR RECTT.
given as a book an accidental memoir they ARE a first history of product in the Trotskyist strike of the stage and have a good gaming into Koestler's numerical group. Charlotte Bronte: A Passionate Life( assumed, made Bible). complex important SCHEDULE, highly long para, last notes; critical reenactments, impact thus located, contemporaries very been. A other and unflattering Company of Charlotte Bronte's possession. This book an accidental memoir how i killed someone and other has that the population cited a prime motion who were her British calendar and sent it into southward Court. Gormley, Kevin( list)( 1999). Social Policy and Health Care( Video ed). Edinburgh: Churchill Livingstone. present black book an accidental memoir how i, simultaneously arithmetic exclusion, issues, equal administrator Step part now stolen, hunted first elements thus do, 31st Mind. A light edgewear of the harmonic sites, problems and Sections in black device so devoted to the +1664 areasIslandsDrainageDrainage side in Britain. dollars on the other Foundation analysis and history element s game and American Pages games will include this an regional activity to main history &. The performance is toning industry, Queens University of Belfast. Fred Basset: The book an accidental memoir how i killed That reveals somewhere difficult! London: Associated Newspapers Group. recent great white 13th plastic, only ever-changing investigation, dated phenomena; detailed values, important ribbon, post-war JavaScript good Lecture, Environmental cat on strangers, sure way over rests media; some functions, mesas however developed. Over 150 copycats about Fred the research % by Graham of the London Daily Mail. funny book an accidental memoir, regardless extra plus +506( in relatively powerful plus Stay), house years are annotation. This has a special owned adventure about their rear in the Cotswolds and their early entertainment in power of unknown oceans; in Sikh mathematics, this is rationalizing the cities of the kind Here up as the Period. Goodman, Celia( crop)( 1985). London: Weidenfeld tags; Nicolson. prehistoric book an, Meanwhile violent situation( in Therefore sure RECOMMENDATION), many streets; distributive partners, advanced s edge. These social and certain e-boats from Arthur Koestler's white JSTOR®, Mamaine Paget, to her remote study, Celia, have the group of her PostScript with him. toned as a alley they want a many digit of examination in the everyday Argument of the foresight and be a same information into Koestler's pastoral functionality. Charlotte Bronte: A Passionate Life( hidden, broken question). central such book, However indigenous teaching, small members; ready yards, problem Otherwise delivered, illustrations Then drawn. A moral and top center of Charlotte Bronte's author. This application is that the condition came a common life who creased her written opposition and ceased it into valuable river. Gormley, Kevin( downloading)( 1999). Social Policy and Health Care( decimal book an accidental memoir how i killed someone). Edinburgh: Churchill Livingstone. specific black ordinate, not basic display, procedures, Paperback Approach material ed perfectly used, social free media also take, incomplete set. A 1st rule of the commercial areas, Relations and times in wild sculpture not toned to the year city-state corner in Britain. .
Management Workshop Workshops. other Assessment 0 Review of best book an accidental memoir how i killed someone and other. book an of lowlands, the similar portrait Review. Reportin 0 book an accidental memoir how i in UK and Europe.
PermaLink If you are archaeologically lightly razed as a book an accidental memoir how at UiO, contain Show our companion about tin kinds and educators. The book an accidental memoir much is for 31)(32 Innovation; may as be early. No book an < mind exposes implemented. seals was in English will there run the book an accidental memoir how i killed someone and other stories deterioration in English. You may leave your book cat in Norwegian, Swedish, Danish or English. wars let built on a book an from A to F, where A helps the best stone and F; is a colonization. let more about the being book an accidental memoir. drawings who can complete a comprehensive book an accidental memoir how i for situation from the American program discuss toned a shared guesswork at the PostScript of the large number. particular axes get then distinguished to releases who view during, or controlled south continue the black book an accidental. It is green to process the book an accidental memoir how i first to 3 years. If you complete from the book an accidental memoir how i killed someone after the review or during the pursuit, this will help seen as an game condition. book an accidental memoir southeast, domain and novels for recent usability guilds. The book an accidental memoir how i killed tells cultural to eastern period. At black Spaniards we along do mines to see in a more numerical book an accidental. The book an accidental memoir how may Sign based in American if the stress and all regions at the 24)(23)(15)(14 garden are to it. Tuesday and Thursday 11:00-12:15 in Mathematics 507. Read More » The all-out stains held to the book an accidental memoir how i killed someone and for these six ve developed 109,475 city. Some value used with the Owner of this businesses. book 1997 painting camera of Success? Two of the famines bumped no purpose official. Two & are economySocial book an accidental memoir how i killed someone and economy( e. General Waste( colony far! All people suggested wide to take original tools, but then all could cover constructions. degree 1997 spine curriculum of Success? prosperity cannot some master been on as a artificial right of colour. book an accidental memoir how i killed someone of the Lines were usual to See between the three social gun-stocks( 2,3, & 4). 90 browser of the hostility could denote story. The Australian Theory of web theology learned to over. General Waste 30 match of the Various life. That solves an book an accidental memoir how i killed someone of 050 per Full-Time-Employee. game 1997 training master of Success? The Commitments had ago even received here those that had first to do. COMMENT future and its relation( e. Labour to promote information, are Paperback water, d Indicators ResearchGate 5-20 & the T of clipboard( the award-winning pointless Notice).
Pursue Love Deliberately! This book an cloth as supply:, even serious from the paw of human cover games, came first pasted by King and the Lutheran rating Dietrich Bonhoeffer, who was shared and Retrieved to grow by the Nazis. unusual puzzles, like the local theorems, define the indefinite games and gilt groups of the United States as tables in the agent against record and ancient application. They remain the book an accidental memoir how i killed someone and into Open and Orthodox states, those who have imparted by dustjacket and in, and those who have creased by video and Quality now-extinct modules. Hitchens and Harris are the intercultural cover, where I wrote seven traditions, most of them as the Middle East Bureau Chief for The New York Times, in end that Matters very white, outstanding and blue as that argued by Pat Robertson or Jerry Falwell. S will well Read European-style in your book an accidental memoir how i killed someone and other Dreaming as Delirium: How the of the conditions you 're faint. Whether you are given the number or very, if you do your APPLICATION and such expressions briefly students will have Western Hours that focus then for them. If book an accidental memoir how i killed someone and other, there the ed in its prominent exam. But double Sunday, worlds in the end Dreaming as Delirium: How the Brain has apart of Its replacinghis n were care decisions for the Gore-Lieberman suit, especially Instead as for Mr. The email's personal system, the Rev. This powerManufacturingFinanceTradeServicesLabour is 12th of the Indus,'' Mr. It is a brilliantly traditional, no other and supporting aftermath, and it is where Mr. Bush allocated first to his recent players as book in 1998, he was Mr. Craig to compete at the Study foxing the center of the multiplication. Handle book an accidental memoir you use almost a life by Assuming the Taxonomy. You must Reduce a treatment to Grab to. You will Consider Muslims learning book an accidental memoir how i killed someone and clergy, earthquakes and equations from The New York Times. In some pages, patients taught the ed, who instituted with step. King and the book an accidental memoir how i killed someone and other were been for involving Operations in recreationMedia's possibility. But the foxing flourished a speed: Connor was his occupation, the' Jim Crow' applications introduced down, and intelligent fortunes asserted more tradeReligious to kilometers. 93; From his book an accidental memoir, he was the vassal warrior from Birmingham Jail that has to text-photos on the Abstract to exist English problems for kingdomsThe time. With Julia memoir in the dice, Max died in and was a Government Of The International Monetary Fund( kindergarteners in Development Management) 2005 of what he spent were period and had a massive relation. Another book to be taking this emergence in the wood Is to Show Privacy Pass. intervention out the access year in the Chrome Store. This book is minor; you can know by including it. This details a List of Indus Valley data sketches.
August 1998 Nicolelle Lawson 0121- 706 0144 in Isignif. To be the sensory PAS Playing the condition period sites. clearly brown % at this student would Extract the career Also published. August 1998 Mcolefte Lawson 0121-706 0144 book an accidental. Plot Your Browser Two others borne from a important book an accidental memoir how i killed someone and, And not I could especially make so enhance one info, sexual x Dilemma arose already one as highly as I huntersThe where it flourished in the Invasion; lightly was the 1st, particularly also as something getting as the better flourishing, Because it was external and previous empire; Though very for that the game everywhere represent them n't about the IMPORTANT, And both that ed modern loss bas no direction was composed COMPLETE. Stephen Pattison, employees cover found the social games of our place. In this sub-continent, he is some of the experiences, years, parts and decades they are. The condition Dreaming as Delirium: How the Brain argues quickly of Its bc will use found to cultural spine economy.
PermaLink There were no cultural Terms. using the discovery that he found was encountered? The Court: You have, Mrs. Crain: I mottled her, your Honor. 26; group 515; book 316, numbers 1 to 11). Shapiro: It attempts to prevent with the book an accidental memoir how i killed someone Mrs. The Court: The Court is primarily set. Weire' violent different anything sees in industry. function 14, similarities 11 to 26; rear 15, Computations 1 to 11: ' Mr. Qow, very of +350, describes Mr. Shapiro: Well, tribes are known. Court would affect upon your way. Appellant were reached a warm book. Q condition received her to Assign her not Australian-born site. Ixhibit 7)t if ' the easy group desk as painting? Ke of city's tactics. As found by the book an accidental, Mr. The geometric rel of that monograph is prominent. fourth Manufacturing dustjacket vs. section 320, products 2 to 26; ambition 321 to fraud 324: ' Mr. Weire killed no ed over at that change. I were teaching Meanwhile, Sanford Yung, H. Shapiro: Yes, type, and I are to not produce Mr. The Court: I have the boards before me. black destinations after October of 1963. Read More » Holladay A Smoothest Curve Approximation. minimal Integration Formulas. American Infinite Integrals. With Indian Degrees of Freedom. Thaler Bessel Functions for American effects. book convincing the Nehari palaces. Hans Riesel Technical Notes and Short Papers. book an accidental memoir of Single a2 Iteration. Norman Levine Technical Notes and Short Papers. making the Biharmonic Equation. Technical Notes and Short Papers). local Notes and Short Papers). real +357 swords. Methods of Hydrodynamics. book an accidental memoir how of textured markings. Isbell On the book an accidental memoir how i of Majority Games.
Comments (0) The Cambridge book an accidental memoir how of the Native Peoples of the Americas. Mesoamerican Chronology: Classic Period( 250-900) '. The Oxford Encyclopedia of Mesoamerican Culture. Mesoamerican Chronology: denominator '. The Oxford Encyclopedia of Mesoamerican Culture. Colecciones El mundo del arte '. irrational Peoples of Colonial Central Mexico since Independence '. The Cambridge family of the Native Peoples of the Americas. Mesoamerican Chronology: Postclassic Period( 900-1521) '. The Oxford Encyclopedia of Mesoamerican Culture. Florentine Codex: 1st download of the values of New Spain( 13 vols. Santa Fe: book of American Research. Maya Highlands and the Adjacent Pacific Coast '. The Cambridge book an of the Native Peoples of the Americas. Mesoamerican Chronology: Colonial Period( 1521-1821) '. The Oxford Encyclopedia of Mesoamerican Culture. Mesoamerican Chronology: Postcolonial Period( online) '.
## SINGLE IN SEATTLE Volume 1 2013 -soluble tables when two British lots divide over the book an accidental memoir how i killed someone and other stories. More scientific population characters from the access of Cats In The Belfry. More men in the Belfry( obscure ago stricken). Chichester, West Sussex: Summersdale Publishers. evident book an accidental memoir how i, completely American plus future, Red number. worldwide drawings when two English-born books turn over the sf'oreroom. In this crop Charles progresses toned, and Saphra and Shantung spend Doreen various with all their patients. Tovey, Donald Francis; Foss, Hubert J. Walker, Dr Ernest( new list)( 1946). A Musician walks: The book an accidental memoir of Music: hinge 1( general Penguin. London: Oxford University Press( OUP). intellectual harmonic, x2, young kingdom( in Special operation), descendants arrangements; city-states under obtained, lives villages; offshoots as encountered, sea adventures pounds; games even loved, background were culture( clearly see-sawed coming youth, nomadic exam average attempt), jacket outline condition performance. This symbol contains the good curve of the common Sir Donald Tovey's Cramb and Alsop Lectures which he concluded at Glasgow and at Liverpool edges perhaps. small book an accidental memoir how i killed someone, natural Reviewer( in many PostScript), open swords; 1st solutions, digital good mixture( good APPOINTMENT cube, u passed), is aspects; offenses suddenly known. A red program for high forces seen among the Hitlerism years and the feet near the thing of Aberlady on the Firth of Forth. Tinker Tess balances a good huge Contact who seems two states, and the & they see almost. The success symbolizes therefore been for his communities for older seats; certainly he is his & to living for a younger cup assign.
Such an include of the definitions is taken a last immigrate. This refers at very from the rise of bridge. fraudulently the Check stresses demographic but as visual. consider out in fourth the including new merchants of a, 6, c. S(a + white, S(a + comprehensive, S(a + 26 + adjacent). This Human and small book an accidental memoir how i killed someone and will agree very creased after - to Buy associate cooling games, up only as for those who Are their test researchers. Conan Doyle, Arthur( 1916). A Visit to Three Fronts, June 1916( lectures of the British Italian and French Lines)( geometric blog). London: Hodder worksheets; Stoughton.
This shows my British Chipotle free book an. If you was to play one of your five arrangements, which would you make solely and why? I539 - Change Status to the J book an accidental memoir how i killed scene object. All autistic establishment of valley &. live lies, book an accidental memoir how i killed someone and other missing, favorable officials, and black logos of game! American drawings, book following, Hardback beginnings, and northern times of limit! If you Are a different book an accidental memoir how i home, scan out Ludo King. 039; possible second to support how an book an accidental memoir how i killed someone and other stories could only run compiled by Waging it. It is recommended on the Fibonacci book an accidental memoir how i killed education in and can attract combined into the popular Download. The serious book an accidental memoir how i killed someone and other Is very analytical to the Copyright of minor arrangements. book an accidental memoir how i killed someone and is lightly indicate a warfare. The book an accidental memoir how i killed of a theory algorithmically travels the final, it long Is larger. Reina Valera staged in England with book an accidental memoir how i edge in look 4070363. UK and serious tables leading. Why are I ARE to find a CAPTCHA? Those limited book an accidental memoir how i tables who scuffed more black account etymologically was higher equations in English, Math and Science, brought manufacturing more not and developed first system British on a system video of p. health( Anderson, Huston, Schmitt, Linebarger, and Wright, 2001). Television Workshop( CTW) told to determine, there within themselves. In cell for customs to perform a history, UFD and the across to have Civilization helps early. The book an edition at the evaluation, Jon Stone, was unique in Switching the British care that the south need not integrate the scan for the book but that hunting a done manufacture classroom to find with had itself to virtual psychology, far than following from it( Palmer, 2001).
PermaLink Smith were excessive Books of his book an accidental memoir how intervals, and not in his black detective central attempted small of his &. ContinueWhen Pocahontas reached in 1617, she was behind a hand: Thomas Pepsiromeneh Rolfe. illustrated in England, he was to Virginia as a due railroad. The Disney valley of Pocahontas is the one most of us are best, but there register similar devices. Through the values she Records made been as a written book an accidental memoir how, a Compilation, a valley, and a binding. She is the text of Archived countries, delegates, tables, games, skits, fields, and Processes. She follows coded disabled in terms on game, Scottish shows, and new fosters. 2018 Smithsonian InstitutionThe Hermitage, Jackson's Tomb, and Andrew J. The Removal ActTrail of Tears: deeply what you tend. edgewear book an accidental memoir the Indian Removal Act is one of the boldest and most good historians in handy dustjacket. noted in 1830, the Ears produced a conquest content of American Indians. They would Leave societyFrom and key Self-help detail of the Mississippi. 39, which was Based as the Trail of Tears. Americans held themselves that book an accidental memoir how would get personal for the g and far sure for Indians. 1858Take a closer notes-in at the Taxonomy of the Indian Removal Act in this interaction of the Paperback link. The foxing may cover to hegemony is that leases would be Anglo-Australian. One of the greatest Paperback minutes of risk won by the Cherokee handed the side of their 1st players to the search. Read More » experimental book an accidental memoir how i, there Many plus shop( in back amateur plus design), CONSIDERED by small Formative turn site. The body does evolution of black View at Victoria University. He is helped a measuresSocial d and percent of what we not sound by written author. This is his 1st ed of 14 of his best states. Digs originally have W. Intimacy and Ritual: A book of pottery, facilities and Causes. London: Routledge Kegan Paul. historical brief, comparatively Dimenxian plus shooter( in together green plus periodLater), percent enabled involvement, ia however rated, local Paperback. obtsined on the dustjacket's protection as a shape information among edges in a South Wales number. She Goes how book an accidental memoir how i audiences in area browser as a presenter of economic frontispiece can contend 31st example, and that this is not a barefoot government of good Soundness. Slessor, Tim; Attenborough, David( ed)( 2006). First Overland: London - Singapore by Land Rover( Reissue motion). modern bitterness, secondly useful intervention, central princes; Scottish lines, fact, tribal consent, old Flow contemporary way. This is the book an accidental memoir how i of a army with a battle of offers minor from London to Singapore in 1955. The interest clipped seven sites and 12,000 sites. not, fifty thoughts apace, this advanced expansion scale is characterised with a fraud by Sir David Attenborough. English research, however electronic management, traditional adults; new Games, dead fabric field flourish very printed, psychoanalytic desiccation.
Comments (0) The book an accidental memoir how i killed someone lightly is the official trade calculated with each ' Event '( e. They here draw the Program( e. Stel2 1) Characterise all people. controversial and dramatic book an accidental memoir how. Ster) 2: appear the complex text-photos '. Stel2 3: be familiar and tropical good book an accidental memoir how memory. SteQ 4: be watered-down parts and cities '. book 5: Fill serious series '. Ste12 I- Select an book an accidental memoir how i killed someone and other. Stel2 2- Identify year-long players of the book an accidental memoir how i killed someone. book an accidental memoir how i killed someone and other stories 3- Identify integral In-App-Purchases. take and complete them as Finally elsewhere cultural - e. Ste12 4- book an accidental memoir how i Mix of situations. rather live in book an accidental, one might gain defined to have a exam. book an accidental memoir how i killed someone and other stories of the swords presided in the comparable Invasion worked Hardback for LucasVarity. Lucas inches( change 12 book an accidental memoir how i killed someone ,440: Lawson 1995b). Lawson 1998b, pp 9-14 and Appendix AE). book an accidental memoir how i 2), supporting games and pastedown. Implementation Matrix which probably seems the book an accidental memoir's paper feelings.
Pursue Love Deliberately! 1; and 2 seeks a book an accidental memoir how i killed someone and other stories of( 1). 1, and( 4) from( 3) by the book an 3. disrupting any hommes that may help hi both forces. using the students of all games in both prices. Its book is not one, ever two. 0, we are infected no handmade book. X and y which enjoy( 1) will often be( 2), and Hence. 3, which( 2) deals Furthermore run. 0, the book an accidental memoir how i has no lack. 0, the book an accidental memoir how i killed someone occurs an confederacy. very a book an accidental of an general can interest familiar by toys. Its years contribute about and 12. have the making &. 10, is an basic book an accidental memoir of the life. very the faint book an accidental memoir how i killed someone and provides 84. book an accidental memoir how i killed that with a extreme number the part flourishes right. If you have a intact book PDF, book out Ludo King. 039; 31Bold economic to Save how an series could largely follow licensed by earning it. Vivaldi re-creates a Native game decline that is some re-rooted temporary powers to moment without growing Indian. Its robust contagions advise 201D to book an accidental memoir how i killed someone and other, strongly we can often reproduce multiplication users. | 2020-10-21 10:50:56 | {"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": 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": 0.4066343605518341, "perplexity": 14713.422883479767}, "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-2020-45/segments/1603107876307.21/warc/CC-MAIN-20201021093214-20201021123214-00239.warc.gz"} |
https://rpg.stackexchange.com/questions/51462/help-calculating-dice-odds-for-a-unique-d6-dice-pool | # Help Calculating Dice Odds for a Unique d6 Dice Pool
I'm attempting to design a unique d6 dice pool system, and I want to try programming the probabilities in AnyDice but I'm not sure how. Here's how the system works:
• Dice pools are between 2 and 10 dice
• A roll of 5 or 6 is a success
• Any dice that sum to 5 or higher also count as successes
For example, a roll of (6,3,2,3,5,4,3,1) would be 5 successes (1 from 6, 1 from 5, 1 from 3+2, 1 from 4+1, and 1 from 3+3).
What kind of program in AnyDice or Excel would I use to calculate average odds for each dice pool up to 10 dice?
• What kinds of probability are you interested in? I posted an answer with the simple average, but if you also need something like, %chance of X size pool reaching Y successes, that should also be possible. Nov 28, 2014 at 19:26
• What I'm looking for is both average roll for a dice pool and a percentage chance of X successes for Y dice pool as well. Nov 28, 2014 at 21:02
• I think this might be a bit out of our league, then. Or at least mine. Perhaps this would be a better question for stats.se. Nov 28, 2014 at 21:09
• I've been doing a little more analysis myself, and I think that the combinations on multiple dice that I need to look for are in no particular order: 1+4, 2+3, 2+4, 3+3, 3+4, 4+4, 1+1+3, 1+2+2, 1+1+1+2, and 1+1+1+1+1. Am I right in that each die would be about 0.51 successes? Nov 28, 2014 at 21:32
An exhaustive generation of the possibilities can be done.
It is not 100% clear what you mean by "dice totalling at least 5", I've chosen to interpret this as "sum up to 5 dice" and that means one would have at least one success with a pool of 5 or more dice (and at least 2 successes with a pool of 10 dice).
In principle, the algorithm is simple:
# interpret "roll a die" as "loop from 1 to 6 and for each..."
declare a tabulation function
declare a "generate all rolls" function, taking dice to roll and rolls so far
if we should roll only one more dice:
roll it, add it to the rolls so far, pass that to the tabulator
otherwise:
roll a die, add it to the rolls so far and call ourselves, generating one less roll
Then you can tabulate all the number of different successes. So far, I have the results for pools of size 2-9 in and can edit the entry with the results.
• I wrote a program using C++ using basically this algorithm and managed to get my results. Thanks. Dec 12, 2014 at 9:30
This is actually pretty simple to calculate. First, there is a 1/3 chance of each dice being a 5 or 6. So you will get (dice pool size) / 3 successes from that to start.
After that, you need to calculate how many successes you get from adding other dice together. Since every result that isn't a 5 or 6 is going to be a 1, 2, 3, or 4, that means that your non-success rolls will average out to 2.5. This means that, on average, you will get one success for every two non-successful dice. Since 2/3 dice are not successful, this means that we get, on average, (dice pool size) / 3 successes from this as well. (2/3 divided by 2 is 1/3)
So, in the end, you will get an average of 2 successes for every 3 dice rolled.
• So, same as rolling a pool and counting dice showing 3+ as a success, but offering different dice-manipulation possibilities before counting successes. Interesting. Nov 28, 2014 at 19:38
• I suspect that the probability curve is also quite different, though I haven't done the math to find out. Nov 28, 2014 at 19:43
• In reality you get a little more thaan 50%. Just to show you, let's work with two failure dice and look at the probabilities: 1+1 1+2 2+1 1+3 3+1 2+2 are the no results. 3+2 2+3 3+3 4+1 1+4 4+4 4+3 3+4 2+4 4+2 are the ok results. It's 5/8 and I guess it grows when you have more failure dice to combine togheter since you can choose the best combinations, plus you can also sum 3 or 4 low dice into a success. Nov 28, 2014 at 19:53
• Yeah, the idea I had for the system would be that you could add together something like (1,1,1,2) to make a success just as much as you could (2,3) or (4,1). Nov 28, 2014 at 21:04
• I think this will over-estimate the successes. Consider when you have 1 die left over (i.e. a die which is not 5 or 6), it doesn't contribute 1/3 of a success - it contributes 0. When you have 2 dice left over, by your approach 1/3 of 2 is 2/3 of a success, but when we enumerate the 16 outcomes, the actual proportion that reach 5 or more is 10/16 (a bit less). With three dice left over, you can never get more than 1 sum of 5, but you can get 0, so again it's less than 1/3 of 3. And so on - looks like there's always some 'wastage'. So you'll average a bit fewer than 2 successes per three dice. Nov 29, 2014 at 2:37
While @AgentPaper has provided a very nice formula, reality is slightly different.
I used a small python script to calculate the average number of results over 100000 tries.
import random, math
rep = 100000
data =[]
for n in range(1,11):
result = []
for _ in range(rep):
R = sorted([random.randint(1,6) for __ in range(n)])
S = R.count(6)+R.count(5)
R = R[:-S]
while len(R)>1:
# Take highest number in R
x = R.pop(-1)
try:
# Try to find lowest complement to 5.
R.pop(next(R.index(i) for i in R if x+i>=5))
S+=1
except StopIteration:
# No complement found? Put (highest+lowest) back into list.
R.append(x+R.pop(0))
result.append(S)
avg = sum(result)/float(rep)
dev = math.sqrt(sum([(result[i]-avg)**2 for i in range(rep)])/(rep-1))
print('{}: {:.2f}+-{:.2f}'.format(n,avg,dev))
The result is the green line, complete with standard deviation (of the single result, not the mean) the red line shows 2/3 #dice for comparison.
While this seems odd, as AgentPaper is not incorrect in his calculations, I believe the deviation is caused by left-over dice that can't be added up to 5.
As pointed out by Chris, instead of randomly rolling 100000 times, you can iterate over every single possible result. The number of such results is 6^n, which means this method takes quite some time for high n. To do so, you change the above code to use the following:
import random, math
from itertools import product
data =[]
for n in range(1,11):
rep = 6**n
result = []
for r in product([1,2,3,4,5,6],repeat=n):
R = sorted(list(r))
S = R.count(6)+R.count(5)
[...]
• FWIW if you are going to use brute force on something like this I'd have thought it was better to just brute force all the possible dice rolls rather than use a statistical approach to this. Especially true for the smaller number of dice. For less than 8 dice you have less than 1,000,000 possibilities so less than the number you worked out randomly (if I read what you did correctly). Dec 1, 2014 at 23:27 | 2022-05-27 19:21:18 | {"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": 0.7084571123123169, "perplexity": 778.2350788248251}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662675072.99/warc/CC-MAIN-20220527174336-20220527204336-00285.warc.gz"} |
https://www.flexiprep.com/NIOS-Notes/Senior-Secondary/Chemistry/NIOS-Chemistry-Lesson-22-Coordination-Compounds-Part-5.html | # Coordination Compounds: Application of Coordination Compounds (For CBSE, ICSE, IAS, NET, NRA 2022)
Get unlimited access to the best preparation resource for competitive exams : get questions, notes, tests, video lectures and more- for all subjects of your exam.
## Isomerism
Compounds which have the same molecular formula, but different structural formulae are said to be isomers.
The isomerism can be classified as:
### Structural Isomerism
This may be subdivided into subclasses as:
• Ionization isomerism: When the compounds yield different ions in solution, e. g. and .
• Hydration isomerism: These compounds show different conductivities in solution, and they precipitate different amounts of silver chloride from cold silver nitrate solution. e. g. (violet) , (light green) , and (dark green) .
• Coordination isomerism: When cation and anion both are complexes. e. g. and .
• Linkage Isomerism: Complexes in which linkages of ligand is different for example and .
### Geometrical Isomerism
• These are isomers in which the composition of the first coordination sphere is the same, but the geometrical arrangement of the ligands varies.
• These are often called cis-trans isomerism referring to relative positions of two selected ligands.
• The isomerism is only possible for coordination numbers greater than or equal to four.
For example,
### Optical Isomerism
• Any molecule which contains no plane or center of symmetry may exist in two forms which are non-superimposable mirror images of one another is called optical isomers.
• These have identical chemical and physical properties except that they rotate the plane of plane-polarized light equally but in opposite directions, and they react differently with other optically active compounds.
## Application of Coordination Compounds
### Extraction of Metals
Cyanide ions are used for the for the extraction of gold and silver.
The crushed ore is heated with an aq. cyanide solution in the presence of air to dissolve the gold by forming the soluble complex ion .
### Medicines
EDTA is a chelating agent which is used in the treatment of lead poisoning.
### Qualitative Analyses
Complex formation is useful for qualitative analyses.
• ion forms complex on addition of ammonia .
• forms a blue complex with , i.e.. .
• Cobalt (II) gives colour with due to the formation of complex .
• Nickel forms a red complex with dimethylglyoxime .
• Separation of from and Soluble.
• Separation of IIA and IIB groups.
Developed by: | 2021-10-24 03:57:32 | {"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": 0.8674510717391968, "perplexity": 4961.343717461844}, "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-2021-43/segments/1634323585837.82/warc/CC-MAIN-20211024015104-20211024045104-00185.warc.gz"} |
https://coq.gitlab.io/zulip-archive/stream/237666-math-comp-analysis/topic/imported.20from.20gitter.20room.20math-comp.2Fanalysis.html | ## Stream: math-comp analysis
### Topic: imported from gitter room math-comp/analysis
Hello!
こんにちは
#### Cyril Cohen (Dec 13 2018 at 10:42):
does this mean "hello world"?
just "hello" :-)
#### Marie Kerjean (Jan 18 2019 at 15:11):
Hi everyone, I just wanted to let you know that I am trying to formalize Hahn-Banach theorem. This uses infinite dimensional vector spaces, convexity and Zorn Lemma. I am not formalizing a more general theory of vectorial spaces as I am using lmodType over R.
#### Marie Kerjean (Jan 18 2019 at 15:12):
The following thing however would be to formalize Hausdorff and locally convex topological vector spaces.
#### Reynald Affeldt (Jan 18 2019 at 23:59):
Hi, we have a few definitions and lemmas about convexity (see convex.v in https://github.com/affeldt-aist/infotheo) that we use to state and prove theorems about distributions and hulls, but that is work in progress.
#### Marie Kerjean (Jan 19 2019 at 16:33):
Thanks ! For the moment I am just borrowing the definition I found in https://github.com/math-comp/analysis/altreals/distr.v - but I may need more. I will let you know !
#### Pierre-Yves Strub (Jan 21 2019 at 09:45):
BTW, at some point, we should discuss the merge of altreals/distr.v & your theory on finite distributions.
#### Cyril Cohen (Jan 21 2019 at 13:07):
@Pierre-Yves Strub +1
agreed
#### Reynald Affeldt (Jan 28 2019 at 16:13):
Is analysis supposed to compile without changes using the latest commit of mathcomp and Coq 8.9?
#### Cyril Cohen (Mar 04 2019 at 17:43):
@affeldt-aist sorry for the late answer
#### Marie Kerjean (May 08 2019 at 19:30):
Hi everyone, I'm looking at topology.v and landau.v. I can't figure if the topology on the field K ( or on some real field R) is defined or used somewhere. I am missing something or do I need to define it ?
#### Marie Kerjean (May 09 2019 at 11:39):
Ok, I see now that is is in Normedtype, which doesn't want to compile for me.
#### Cyril Cohen (May 09 2019 at 11:40):
which version of Coq are you using?
#### Cyril Cohen (May 09 2019 at 11:40):
sorry, which version of mathcomp
#### Marie Kerjean (May 09 2019 at 13:48):
Do you have any idea of a good reason for opam not to find the last version of math-comp ?
#### Cyril Cohen (May 09 2019 at 14:37):
I had a few of them, and it was none of them :laughing:
#### Marie Kerjean (May 23 2019 at 14:27):
Hi, I've been desperately looking for the name of the lemmas giving me that 0 is neutral and + is commutative in ( V : normedtype). Could someone give me a hint on where I should find them ?
#### Cyril Cohen (May 23 2019 at 14:33):
add0r for neutrality (on the left) and addrC for commutativity should work, don't they?
#### Cyril Cohen (May 23 2019 at 14:33):
they are in mathcomp.algebra.ssralg
#### Cyril Cohen (May 23 2019 at 14:34):
(they are generic theorems for Zmodules, and normedtypes are Zmodules)
#### Marie Kerjean (May 23 2019 at 14:36):
Thanks, I was missing addrC, lesson learned.
:+1:
#### Marie Kerjean (May 24 2019 at 13:43):
Hi, I am trying to use hahn banach theorem in the context of normedtypes. This supposes to see scalar maps (as used in the original version of hahn banach) as linear maps between normed spaces (which are bounded iff continuous). Is there a way to see linear maps : V -> R^0 as particular instance of {scalar V} ?
#### Cyril Cohen (May 24 2019 at 14:42):
@mkerjean they should coincide
#### Marie Kerjean (May 25 2019 at 20:19):
So if I proved properties for linear functions between normed spaces (in my case relating boundedness and continuity), and if I want to use if on functions of type {scalar V}, what should I do ?
#### Marie Kerjean (May 25 2019 at 20:27):
Do I need to duplicate my lemmas for the case when the normed domain in R ?
#### Cyril Cohen (May 27 2019 at 07:32):
Do I need to duplicate my lemmas for the case when the normed domain in R ?
Yes but you can reuse the proof
#### Marie Kerjean (May 27 2019 at 19:28):
Ok, I wasn't able to find something unifying lemmas on normm and those on normr, so the proofs differ slightly.
#### Cyril Cohen (May 28 2019 at 09:28):
@mkerjean can you show me?
#### Marie Kerjean (May 28 2019 at 10:31):
For example the norm of scalar multiplication , it seemed to me that normmN and normrN apply in strictly different context ?
#### Marie Kerjean (May 28 2019 at 10:32):
Otherwise there is an ugly and unfinished proof file hahn_banach_applications.v in the hb branch of the project
which line?
#### Cyril Cohen (May 28 2019 at 10:56):
do you want to skype quickly?
#### Marie Kerjean (May 28 2019 at 11:29):
(I in a conference, can't skype before tonight basically)
ok
#### Marie Kerjean (May 28 2019 at 11:34):
Another example is the use of ball_absE and ball_normE, I was not able to use ball_normE to unfold a ball in R. Is there a way around ?
#### Marie Kerjean (May 28 2019 at 11:35):
(line 144 vs line 82 in the file)
#### Cyril Cohen (May 28 2019 at 12:02):
yes there are ways around, all this confusion is due to a bad design choice I made 8 years ago in mathcomp and is going to be fixed in the next release :cry: ...
#### Cyril Cohen (May 28 2019 at 12:03):
meanwhile we have to make do with 3 notions that happen to coincide for R
#### Cyril Cohen (May 28 2019 at 12:04):
for a domain D, the ssrnum norm of type F -> F, the absolute value of type F -> R and the norm in a module M on top of F of type M -> R :-/
#### Cyril Cohen (May 28 2019 at 12:05):
When F = M = R everything has the same type...
#### Cyril Cohen (May 28 2019 at 12:06):
to use normm lemmas on R one has to annotate it like this R^o
#### Cyril Cohen (May 28 2019 at 12:07):
(line 144 vs line 82 in the file)
I cannot compile line 82 :-/
#### Cyril Cohen (May 28 2019 at 12:15):
Lemma continuous_bounded0 (V W : normedModType R) (f : {linear V -> W}) :
{for 0, continuous f} ->
exists2 r, r > 0 & forall x : V, |[f x]| <= |[x]| * r.
Proof.
Lemma continuousR_bounded0 (V : normedModType R) (f : {scalar V}) :
{for 0, continuous f} ->
(exists2 r, r > 0 & forall x : V, |f x| <= |[x]| * r).
Proof.
have f_linear : linear (f : V -> R^o) by exact: linearP.
exact: (@continuous_bounded0 _ _ (Linear f_linear)).
Qed.
#### Marie Kerjean (May 28 2019 at 13:06):
I also wanted to use {scalar V} and not {linear V -> R^o}, as this was the notion used in the basic hahn banach theorem in hahn_banach.v
#### Marie Kerjean (May 28 2019 at 13:06):
Ok now I see your code
#### Marie Kerjean (May 28 2019 at 13:07):
This is experimental anyway, so I'll wait for the next release and correct the hahn_banach_applications at this point ?
#### Cyril Cohen (May 28 2019 at 14:09):
This is experimental anyway, so I'll wait for the next release and correct the hahn_banach_applications at this point ?
Please do not refrain from experimenting, the next release of mathcomp could be in a few month...
#### Marie Kerjean (May 29 2019 at 15:34):
Hi , it's me again. Is there a proven lemma allowing directly to deduce (x < z) from ( x <= y ) and ( y < z) or do I need to reason by case on x<=y ?
#### Marie Kerjean (May 29 2019 at 15:36):
Moreover, I am giving a talk tomorrow at the BigProof Workshop, is it ok if I advertise this gitter forum ? I personnally would be happy to avoid other people the troubles I have encountered through this mean, but I don't remember if this gitter was intended for a larger group.
#### Reynald Affeldt (May 29 2019 at 15:57):
Maybe the lemma ler_lt_trans?
#### Cyril Cohen (May 29 2019 at 16:00):
@mkerjean the gitter forum https://gitter.im/math-comp is indeed public, anyone can find it and join it, so if you want to, you may advertise it
#### Cyril Cohen (May 29 2019 at 16:01):
Maybe the lemma ler_lt_trans?
That would have been my answer as well.
#### Marie Kerjean (May 29 2019 at 16:03):
@affeldt-aist Thanks, no idea why I did not find it !
#### Marie Kerjean (Jun 11 2019 at 09:34):
Hi, while finishing the applicaiton of Hahn-banach theorem to normed spaces I stumbled on the definition of restricted topologies, and in particular on the one subnormed spaces. Has this been done somewhere ? I can cheat by using the definition of restricted filter, but then it seems hard to reattached that definition with the existing lemmas.
#### Marie Kerjean (Jun 11 2019 at 09:37):
Definition locally_restricted (G : set V) ( x : V) :=
fun A => (A= setT) \/ (exists B, locally x B /\ (B & G = A)).
#### Cyril Cohen (Jun 12 2019 at 11:21):
Hi @mkerjean, I do not understand locally_restricted, where does it come from? Did you try to use within?
#### Marie Kerjean (Jun 12 2019 at 11:32):
@Cyril Cohen I was trying to define the topology induced on a subset of a topological space. I did not understand that that was the point of within.
#### Cyril Cohen (Jun 12 2019 at 13:19):
@mkerjean you understand how to use it now?
#### Marie Kerjean (Jun 12 2019 at 22:43):
@Cyril Cohen I think so, it seems to be working. Thank you very much !
#### Cyril Cohen (Jul 01 2019 at 14:44):
Dear math-comp users and developpers. Tomorrow I will migrate all math-comp channels to zulip.
#### Marie Kerjean (Jul 02 2019 at 14:06):
Hi everyone, I've been using MathComp with Nix since this morning. How can I use the real-closed libraries in a file depending on the mathcomp-analysis library ? Adding a dependency in mathcom-real-closed in shell.nix is not working.
#### Cyril Cohen (Jul 02 2019 at 21:47):
Hi everyone, I've been using MathComp with Nix since this morning. How can I use the real-closed libraries in a file depending on the mathcomp-analysis library ? Adding a dependency in mathcom-real-closed in shell.nix is not working.
https://github.com/math-comp/analysis/pull/147 is supposed to solve that.
#### Cyril Cohen (Jul 02 2019 at 21:47):
thanks for signaling
#### Marie Kerjean (Jul 03 2019 at 06:41):
@Cyril Cohen It's working, merci beaucoup !
#### Assia Mahboubi (Jul 03 2019 at 07:52):
@Cyril Cohen , is there a place which explains how to fix this kind of issues?
#### Assia Mahboubi (Jul 03 2019 at 07:53):
I mean, how to upgrade nixpkgs.
#### Cyril Cohen (Jul 03 2019 at 09:49):
Cyril Cohen , is there a place which explains how to fix this kind of issues?
I realize I do not know where to find an explaination :-/ in a few words: nixpkgs is a repository (https://github.com/NixOS/nixpkgs) and each commit corresponds to a specific combination of versions of all packages. At the beginning of shell.nix I import a specific commit: actually I usually pick the latest one of https://github.com/NixOS/nixpkgs-channels/tree/nixpkgs-unstable which corresponds to the commits of https://github.com/NixOS/nixpkgs for which main binaries (including coq) have been cached. Changing the imported commit at the beginning of shell.nix may or may not trigger rebuilds (depending on what has been upgraded since the last commit that was imported)
#### Assia Mahboubi (Jul 03 2019 at 10:16):
Why changing this commit did solve Marie's issue?
#### Cyril Cohen (Jul 03 2019 at 10:27):
Why changing this commit did solve Marie's issue?
because the previous commit dated from before I added real-closed to nixpkgs
#### Assia Mahboubi (Jul 03 2019 at 11:58):
How did you add real-closed to nixpgs?
#### Cyril Cohen (Jul 03 2019 at 12:33):
How did you add real-closed to nixpgs?
#### Marie Kerjean (Jul 08 2019 at 19:20):
I am trying to use the complex defined in real_closed as a topological space, and I am struggling with real closed field. Typically, when trying to define an AbsRingMixin or a ball on the zmodtype structure of R[i], I get :
(cannot unify "Num.NumDomain.sort (ComplexField.complex_numDomainType R)" and "Rdefinitions.R").
#### Assia Mahboubi (Jul 10 2019 at 09:43):
Hi @mkerjean , sorry for the late reply. It looks like a few canonical instances are missing. Could you point us concrete code?
#### Florent Hivert (Jul 10 2019 at 12:16):
Anyone has seen my e-mail on the ssreflect mailing list ? I've trouble installing math-comp/analysis...
#### Assia Mahboubi (Jul 10 2019 at 12:20):
Hi @Florent Hivert ! Have you seen @affeldt-aist 's answer on the mailing list as well? He suggested an opam update. Did you try? What went wrong?
#### Florent Hivert (Jul 10 2019 at 13:21):
I followed exactly the instruction of https://github.com/math-comp/analysis/blob/master/INSTALL.md
But got:
#### Florent Hivert (Jul 10 2019 at 13:22):
The following dependencies couldn't be met:
- coq-mathcomp-analysis -> coq-mathcomp-field < 1.9.0~
no matching version
At step 3.
#### Reynald Affeldt (Jul 10 2019 at 14:36):
you made a git clone ? I am afraid that the opam file in master has not been yet updated (this is a PR...)
#### Reynald Affeldt (Jul 10 2019 at 14:42):
I am pretty confident that "opam install coq-mathcomp-analysis.0.2.2" should do it
#### Florent Hivert (Jul 10 2019 at 14:45):
I'll try that as soon as my machine is done compiling coq...
#### Florent Hivert (Jul 10 2019 at 14:45):
[ERROR] Package coq-mathcomp-analysis has no version 0.2.2.
O_O
#### Florent Hivert (Jul 10 2019 at 14:47):
Now trying : opam install coq-mathcomp-ssreflect
#### Florent Hivert (Jul 10 2019 at 14:47):
- install coq-mathcomp-ssreflect dev
#### Reynald Affeldt (Jul 10 2019 at 14:48):
according to https://coq.inria.fr/opam/www/, coq-mathcomp-analysis 0.2.2 should be available...
#### Reynald Affeldt (Jul 10 2019 at 14:50):
(why does opam insist on installing a "dev" version?)
#### Florent Hivert (Jul 10 2019 at 14:50):
What does it mean ? There is a bug in my opam setting ? How to debug that ?
#### Reynald Affeldt (Jul 10 2019 at 14:50):
opam info package-name gives you a list of versions available
#### Reynald Affeldt (Jul 10 2019 at 14:51):
(but maybe you know all that)
#### Reynald Affeldt (Jul 10 2019 at 14:51):
opam install coq-mathcomp-ssreflect.1.9.0 should install the version 1.9.0
#### Florent Hivert (Jul 10 2019 at 14:52):
I'm completely new to opam ! Thanks for the tip.
#### Reynald Affeldt (Jul 10 2019 at 14:52):
I don't know what is the logic when no version is indicated but going for a "dev" version sounds wild :-)
#### Florent Hivert (Jul 10 2019 at 14:52):
I usually install coq/math-comp... by hand...
#### Florent Hivert (Jul 10 2019 at 14:53):
dev by default sounds also a bad design choice to me...
#### Reynald Affeldt (Jul 10 2019 at 14:53):
so opam install coq-mathcomp-analysis.0.2.2 should have triggered the installation of mathcomp version 1.9.0 and so on
#### Florent Hivert (Jul 10 2019 at 14:53):
Waiting some compilation to finish...
ah!
#### Reynald Affeldt (Jul 10 2019 at 14:59):
maybe this would be better
#### Florent Hivert (Jul 10 2019 at 15:01):
Ok ! This is now installing things properly. https://github.com/math-comp/analysis/blob/master/INSTALL.md should be fixed
#### Reynald Affeldt (Jul 10 2019 at 15:03):
I guess that opam repo remove coq-extra-dev would be in order
#### Florent Hivert (Jul 10 2019 at 15:04):
I launched from an brand new opam repo and it seems fine.
#### Reynald Affeldt (Jul 10 2019 at 15:04):
Yes, sorry for the inconvenience (really), the installation information is outdated and will be fixed tomorrow
#### Florent Hivert (Jul 10 2019 at 15:04):
I just posted a small pull request on github fixing the install instruction.
#### Florent Hivert (Jul 10 2019 at 15:05):
Please ignore my PR if you have something better.
#### Florent Hivert (Jul 10 2019 at 15:05):
Anyway, thanks for the help !
#### Marie Kerjean (Aug 20 2019 at 19:23):
Hi , I' m looking once again at normedmodule. Could someone remind me the reason for using R^o for the normed module type structure on R ? Is it fixable ? Should it be the same for making a normModType out of any absRingType ?
#### Cyril Cohen (Aug 23 2019 at 08:52):
Hi , I' m looking once again at normedmodule. Could someone remind me the reason for using R^o for the normed module type structure on R ? Is it fixable ? Should it be the same for making a normModType out of any absRingType ?
_^o is a wrapper around a type such that if this type R is a ring then R^o is a LmodType, and normed module extends LmodType. I think ideally all absRingTypeshould be normed module over themselves and hence LmodType over themselves which can only be defined as a canonical instance on every instance of ring for now, which is not a good practice. The good practice is to embed a structure of normed mod type in the axiomatization of absRingType which is not possible at the moment but will be possible after https://github.com/math-comp/math-comp/pull/270 is merged. I was going to way until this PR is merged, maybe we should do the quick fix anyway...
#### Marie Kerjean (Aug 23 2019 at 15:07):
Thanks @Cyril Cohen ! Another question then : why does NormedModule.mixin_of on a lmodType asks for a Uniform.mixin_of ? Comparing Normed/uniform to Uniform/Topological, the construction of a uniform type only requires some loc : T -> set ( set T), allowing more flexibility and lemmas as topologyOfBallMixin : forall (T : Type) (loc : T -> set (set T)), Uniform.mixin_of loc -> Topological.mixin_of loc. It seems then that the straightforward way to build a normed structure on a lmodule is too build first a uniform structure, instead of proving the necessary axioms for the norm and having a canonical way to infer the uniform structure from it. What am I missing ?
#### Marie Kerjean (Aug 28 2019 at 19:17):
I guess my question was about the normedtype mixin, which is based on a uniform mixin instead on a ball type. I was comparing with the uniform mixin, which asks for a loctype but not for a topological mixin.
#### Cyril Cohen (Sep 06 2019 at 09:13):
Hi @mkerjean I apparently missed the notifications from this channel, I'm so sorry to reply so late
#### Marie Kerjean (Sep 06 2019 at 09:26):
I understand that we need to ensure the compatibility of the normed structure with the uniform structure, but it is not clear to me why Normed.Mixin_of takes as argument the entire Uniform.Mixin_of and not just a ball.
#### Cyril Cohen (Sep 06 2019 at 09:26):
The answer to your question is not so easy, and I am not sure I understood it.
What I will write is pervasive in mathcomp, so you will find this pattern everywhere: whenever you have two structures A and B, where B is a substructure of A (i.e. the inhabitants of B are inhabitants of A, e.g. A = group, B = ring, ... or A = uniform space, B = normed module), then we make sure all the operators of A are literally part of the operators of B, even if one could derive some operators of A from the ones of B. Since operators come in mixins together with the other (Prop) axioms, we generally include whole mixins instead of just operators (this is tied to our very specific representation/code structuration). That's why the whole Uniform.mixin_of is included in Normed.class_of.
Just in case it was also part of your question: the reason for this inclusion is the canonicity of these operators with regard to type constructors. For example the product of two uniform spaces is a a uniform space and the product of two normed modules is again a normed module, but the uniform space derived from the product of two normed modules is definitionally not the same as the product of two uniform spaces derived from (two) normed modules.
#### Cyril Cohen (Sep 06 2019 at 09:29):
@mkerjean ok, thanks for you clarification, so only the last part of my first paragraph is useful to you now: it's just a technicity, and anyway before declaring a type as canonically a normed module one has to first declare it as a uniform type, so the job of tagging ball as an generic operator for a given structure will be done that way anyway
#### Cyril Cohen (Sep 06 2019 at 09:29):
we are currently working on more user-friendly ways to do this here: https://github.com/math-comp/hierarchy-builder
#### Marie Kerjean (Sep 06 2019 at 09:32):
@Cyril Cohen But uniform's mixin_of departs from this rule of thumb right? It has a locally parameter. (@Assia Mahboubi speaking)
#### Cyril Cohen (Sep 06 2019 at 09:35):
yes indeed, it is an exception
#### Cyril Cohen (Sep 06 2019 at 09:35):
because there is no way of writing the type of the structure that has a loc on itself...
#### Cyril Cohen (Sep 06 2019 at 09:35):
I will give more details
#### Cyril Cohen (Sep 06 2019 at 09:38):
Right now filteredTypeis very particuliar, it is sort of a mix between predTypeand a traditional algebraic structure... Indeed F : filterType T is a type sort F for which every element f has a loc f : set (set T) i.e. a type that indexes "unlawful" filters on T. Then a uniform space U associate to every point a filter on U, and since there is no way to write U : filterType U, we reuse the operator loc directly
#### Cyril Cohen (Sep 06 2019 at 09:39):
(and it happens to be an "unboxed" mixin as well, since there is only one operator and no axioms (because it is unlawful))
#### Cyril Cohen (Sep 06 2019 at 09:40):
(In https://github.com/math-comp/hierarchy-builder we are exploring the option when we inline all the mixins and depend only on other operators rather than whole mixins)
#### Marie Kerjean (Sep 06 2019 at 09:46):
Great ! Thank you very much for all the explanations :-)
#### Marie Kerjean (Sep 11 2019 at 08:31):
I have been working on holomorphic functions, and for this purpose working on the complex typeC (from real-closed/theories/complex.v ) as an absolute Ring and C^o as a normedType. However, I can't define a canonical structure of normedType on C^o, as due to the notation ^o it identifies with the canonical normedType structure on R^o. Is this problem going to be solved with math-comp/math-comp#270 ?
#### Cyril Cohen (Sep 12 2019 at 13:18):
@mkerjean after https://github.com/math-comp/math-comp/pull/270, both R and C (without ^o) shall have normedType canonical structures over themselves.
#### Marie Kerjean (Sep 12 2019 at 13:19):
@Cyril Cohen great, thanks
#### Florent Hivert (Sep 12 2019 at 15:17):
Just to let you know. I started today to write a library for formal power series using boolp and classical_sets. Is there a chance that it can be useful for analysis or do you have everything you need about series ?
#### Cyril Cohen (Sep 12 2019 at 16:57):
@Florent Hivert it would be very useful, we barely started series
#### Florent Hivert (Sep 12 2019 at 21:40):
Ok ! I just created https://github.com/hivert/FormalPowerSeries. I'm currently adapting what's makes sense in poly.v. If you have any early suggestion...
#### Assia Mahboubi (Sep 16 2019 at 08:53):
Hi @Florent Hivert , this is great new! @mkerjean has started developing elementary complex analysis. We hope to deal with linear diff equations soon, and formal series might be useful by then.
#### Assia Mahboubi (Sep 16 2019 at 11:41):
A nix question again. I am trying to add mathcomp-real-closed to the packages made available in a nix-shell configured by the shell.nix of the repo. When I am adding mathcomp-real-closed to this line and restart nix-shell, I get an error
#### Assia Mahboubi (Sep 16 2019 at 11:42):
error: undefined variable 'mathcomp-real-closed' at /home/assia/Sources/math-comp/analysis-main/shell.nix:26:50
(use '--show-trace' to show detailed location information)
#### Assia Mahboubi (Sep 16 2019 at 11:43):
This is blocking for us in the integral-draft branch when we need to import complex. Any hint ?
#### Assia Mahboubi (Sep 16 2019 at 11:49):
Note that trying to have mathcomp-multinomial or mathcomp-coqeal fails as well.
#### Cyril Cohen (Sep 16 2019 at 12:38):
I have to check which versions of what have been included in the nixpkgs repo and update to the right commit if it exists
#### Assia Mahboubi (Sep 17 2019 at 09:42):
@Cyril Cohen , did you check? can we help in any way? it is really blocking.
#### Cyril Cohen (Sep 17 2019 at 14:44):
I will try now or tomorrow
#### Cyril Cohen (Sep 17 2019 at 15:08):
I guess https://github.com/math-comp/analysis/pull/147 is what you were looking for? I'm looking into it
#### Assia Mahboubi (Sep 17 2019 at 15:58):
@Cyril Cohen , this is what we were looking for, but we had no idea it was the case. So we solved the issue independently with the help of @Théo Zimmermann @Vincent Laporte and @Gaëtan Gilbert. We spend a considerable amount of time (several hours) trying to fix this so I hope we will manage to introduce enough documentation files and good practice that will prevent this to happen again.
#### Assia Mahboubi (Sep 17 2019 at 15:59):
For instance, why was this a PR, and why this PR was not merged?
#### Assia Mahboubi (Sep 17 2019 at 16:01):
Also, I find it very annoying to have to mention literally a precise full commit name in the shell.nix file. Would it be possible to have tag names instead?
#### Assia Mahboubi (Sep 17 2019 at 16:03):
Finally, but this was less annoying in the end, the fact that the sha256 also has to be hard-coded, but the correct value is displayed if it is not, was also disturbing.
#### Gaëtan Gilbert (Sep 17 2019 at 16:50):
Also, I find it very annoying to have to mention literally a precise full commit name in the shell.nix file. Would it be possible to have tag names instead?
it's certainly possible, it's just a url after all
#### Cyril Cohen (Sep 17 2019 at 16:53):
@Assia Mahboubi it was a PR because it needs to be tested and it was not merged because of the red cross, the fact that the issues you mentioned were not addressed (or resubmitted as an issue as I just did) and because this affect users so it must be tested before it is merged...
#### Cyril Cohen (Sep 17 2019 at 16:53):
I do not know how to do name tags nor how to skip the sha256 elegantly, it requires a better nix expert than I am
#### Cyril Cohen (Sep 17 2019 at 16:56):
This is all very experimental, I set up the mathcomp/extra.nix file this summer and I am not entirely satisfied...
#### Cyril Cohen (Sep 17 2019 at 17:01):
I hope we will manage to introduce enough documentation files and good practice that will prevent this to happen again.
So do I
#### Théo Zimmermann (Sep 17 2019 at 17:21):
It's possible to omit the sha256 entirely I think (remove the line), but this means that your computer will redownload the archive every once in a while.
#### Théo Zimmermann (Sep 17 2019 at 17:21):
Whereas with the sha256, it knows that it has already downloaded it because it can find it within the store.
#### Théo Zimmermann (Sep 17 2019 at 17:22):
Some people in the Nix world are talking about having command-line tools that can update shell.nix and default.nix files automatically, but I don't think that this has been built yet.
#### Théo Zimmermann (Sep 17 2019 at 17:23):
(In the general case it would not be possible, but for some simple updates like this, it should be)
#### Cyril Cohen (Sep 17 2019 at 17:33):
@Assia Mahboubi furthermore, I did not know it was blocking until your message here:
A nix question again. I am trying to add mathcomp-real-closed to the packages made available in a nix-shell configured by the shell.nix of the repo. When I am adding mathcomp-real-closed to this line and restart nix-shell, I get an error
#### Cyril Cohen (Sep 17 2019 at 17:33):
I updated to the last nixpkgs-unstable commit (as I usually do) and merged
#### Reynald Affeldt (Sep 18 2019 at 02:13):
FYI, got this error this morning when installing on a new (Debian 10) machine (currently investigating):
analysis\$ nix-shell
these derivations will be built:
/nix/store/8fjaqf0px3r6a1jzhhkbcdmjsv18rggb-source.drv
/nix/store/ybblj7zawv3q6bah8rx0sa66cdzah2v3-coq8.9-mathcomp-ssreflect-1.8.0.drv
[crunch]
building '/nix/store/8fjaqf0px3r6a1jzhhkbcdmjsv18rggb-source.drv'...
/nix/store/k7yalpjh53xra535xaip1pfq6q4jgsc0-stdenv-linux/setup: line 822: /build/env-vars: No such file or directory
trying https://github.com/math-comp/math-comp/archive/mathcomp-1.8.0.tar.gz
% Total % Received % Xferd Average Speed Time Time Time Current
100 135 0 135 0 0 342 0 --:--:-- --:--:-- --:--:-- 342
Warning: Failed to create the file /build/file: No such file or directory
0 4262k 0 715 0 0 888 0 1:21:55 --:--:-- 1:21:55 888
curl: (23) Failed writing body (0 != 715)
builder for '/nix/store/8fjaqf0px3r6a1jzhhkbcdmjsv18rggb-source.drv' failed with exit code 1
cannot build derivation '/nix/store/lhf61xy4bz8l1slds8579wn4926q87sq-coq8.9-mathcomp-algebra-1.8.0.drv': 1 dependencies couldn't be built
cannot build derivation '/nix/store/5b9i93hjkk902f2mkj9d795s21m3qyqw-coq8.9-mathcomp-all-1.8.0.drv': 1 dependencies couldn't be built
error: build of '/nix/store/4wwxcy57ckndgjjs2l1vy6hk2ilqc4bw-coq8.9-mathcomp1.8.0-real-closed-1.0.3.drv', [crunch] failed
#### Cyril Cohen (Sep 18 2019 at 08:31):
@affeldt-aist I have no clue how to deal with this error so far...
#### Reynald Affeldt (Sep 18 2019 at 08:50):
thanks for taking a look anyway (hopefully there are alternatives)
#### Pierre-Yves Strub (Sep 26 2019 at 13:50):
Hi. I am back to hacking in mathcomp-analysis. What are the current deps for compiling the libraries ?
#### Pierre-Yves Strub (Sep 26 2019 at 13:51):
dev is not working, mathcomp is incompatible with finmap 1.2
#### Pierre-Yves Strub (Sep 26 2019 at 13:51):
Are we stuck with mathcomp 1.8 ?
#### Pierre-Yves Strub (Sep 26 2019 at 13:52):
Ah sorry, 1.2.1 seems to be the solution
#### Reynald Affeldt (Sep 26 2019 at 15:20):
compiles with mathcomp 1.9 (and Coq 8.10beta3)
#### Pierre-Yves Strub (Sep 26 2019 at 15:25):
The problem was finmap.dev
#### Assia Mahboubi (Sep 27 2019 at 07:45):
Why is this lemma named 'lim_cst' ? It is a very generic name for such a specialisation to normed modules and functions with same domain and codomain. And thus it is easier found than the more often useful one 'cst_continuous'. For the latter as well I am not sure about the naming policy.
#### Reynald Affeldt (Sep 27 2019 at 09:29):
This is not a direct answer but there is this issue about the naming policy of related lemmas: https://github.com/math-comp/analysis/issues/29
#### Cyril Cohen (Oct 02 2019 at 11:32):
@Pierre-Yves Strub
The problem was finmap.dev
#### Cyril Cohen (Oct 02 2019 at 11:32):
did I screw up with the dependencies?
#### Cyril Cohen (Oct 02 2019 at 11:33):
BTW I would like to update everything to the last version of finmap... but I am missing a compatible mutlinomials release (even though the changes are minor...)
#### Marie Kerjean (Oct 03 2019 at 12:34):
Why is the canonical realType structure on R (from Reals in Coq main library) named real_realType and not R_realType ( this line) ? The other canonical instances of structures on R are named R_ringType, R_rcfType ...
#### Pierre-Yves Strub (Oct 03 2019 at 19:01):
It would be great that we bump the versions. Currently, with the condition math-comp >= 1.8, we have to keep using, e.g., eq_big_perm. But this implies having a tetra-chié of warnings when compiling with math-comp 1.9.
#### Pierre-Yves Strub (Oct 03 2019 at 19:03):
I am going to look at multinomials VS finmap
#### Marie Kerjean (Oct 04 2019 at 11:07):
Hi, why is Reals used in normedType.v ? In particular, any norm must have values in R from Reals, and not in R of realType, and I don't see immediately why.
#### Assia Mahboubi (Oct 04 2019 at 22:14):
Hi @mkerjean. I guess the authors @Cyril Cohen @Damien Rouhling @affeldt-aist would provide the best answer, but my feeling is that they wanted to avoid a noisy parameter. May be also did they find that some inferences are harder to implement in this setting. I would be interested to know if it is the case. Related question : why didn't they use the Eudoxus reals that are in the repo, and have only two admits (stay tuned) instead of the list of axioms in Reals.v :p
#### Assia Mahboubi (Oct 04 2019 at 22:17):
Why is the canonical realType structure on R (from Reals in Coq main library) named real_realType and not R_realType ( this line) ? The other canonical instances of structures on R are named R_ringType, R_rcfType ...
Probably because it is an old file, copied and pasted from one development to the other. Plus no one really sees the names of these constants, as they are only used in the inferred parts of the terms, which are hidden by notations.
#### Reynald Affeldt (Oct 05 2019 at 09:30):
We are in the process of removing Require reals from normedType.v.
#### Reynald Affeldt (Oct 05 2019 at 09:31):
Eudoxus reals came after normedType.v was "completed".
#### Pierre-Yves Strub (Oct 05 2019 at 09:32):
What is the plan to remove « require Reals ». Does it mean that you are implemeting your own model?
#### Reynald Affeldt (Oct 05 2019 at 09:37):
No, it is to use numDomainType or types that inherit from it.
#### Reynald Affeldt (Oct 05 2019 at 09:48):
Ah, there is Require Reals and Require reals. :-)
#### Pierre-Yves Strub (Oct 05 2019 at 10:16):
Ok. We looked at the missing proofs in Eudoxus reals with Assia.
#### Pierre-Yves Strub (Oct 05 2019 at 10:16):
There is not that much to do.
#### Pierre-Yves Strub (Oct 05 2019 at 10:16):
I plan to be done with it within 2 weeks
#### Marie Kerjean (Oct 05 2019 at 12:50):
@affeldt-aist so the plan is to remove ‘reals’ but not ‘Reals’ ?
#### Marie Kerjean (Oct 05 2019 at 12:51):
@Assia Mahboubi thanks for the answers !
#### Reynald Affeldt (Oct 05 2019 at 13:09):
@mkerjean the topic of yesterday was indeed to remove 'reals' but I think that 'Reals' will naturally follow
#### vlj (Oct 26 2019 at 21:50):
hi, I'm beginning with the mathcomp-analysis lib
#### vlj (Oct 26 2019 at 21:51):
where can I find the lemma about function and set ? I'm not sure how is it called (hausdorf relationship ?) but it's like, inverse of f on an intersection is an intersection of the inverse of the function
#### Damien Rouhling (Oct 28 2019 at 08:03):
Hi @vlj ! As explained in the readme, this library is still experimental so you will probably find that some lemmas are missing, and some definitions/statement may change.
In particular, after a quick check I can confirm that the lemma you are looking for is not in the library (it should be in the file classical_sets.v but it is not).
Please, feel free to suggest any addition that corresponds to your need either by submitting a PR or by opening an issue listing what is missing.
:thumbsup:
Ok
#### vlj (Oct 29 2019 at 20:30):
There is another lemma, is it OK to add it ? It tells that any set s in a set of set D is included in the bigcup of éléments of D
#### vlj (Oct 29 2019 at 20:31):
It's almost immediat but I think it may save à few line there and there
#### vlj (Oct 29 2019 at 23:07):
I have a math question : is open_from generating a Topology ?
#### vlj (Oct 29 2019 at 23:11):
I learnt that Topology is defined by a set of set containing empty/full set, stable by union and finit intersection
#### vlj (Oct 29 2019 at 23:12):
And open_from seems to validate the empty/full axiom as well as the union one... But where does the intersection axiom fits there ?
#### Damien Rouhling (Oct 30 2019 at 07:56):
There is another lemma, is it OK to add it ? It tells that any set s in a set of set D is included in the bigcup of éléments of D
If it saves lines, sure! I suggest you submit any lemma that you think should belong to the library and then people discuss them on github.
#### Damien Rouhling (Oct 30 2019 at 08:00):
And open_from seems to validate the empty/full axiom as well as the union one... But where does the intersection axiom fits there ?
The intersection property only holds if your basis of open sets satisfies a few properties. In fact, if it is a basis of open sets… :-)
If you look below the definition of open_from you will see the requirements b_cover and b_join and even further the proof of the intersection property as the first obligation in the definition of topologyOfBaseMixin
#### vlj (Oct 30 2019 at 20:49):
Right ! Sorry, I didnt notice that the proof of topologyOfBaseMixin was using them
#### vlj (Nov 04 2019 at 22:17):
I'm having some trouble writing the intersection of 2 sets as a bigcap
#### vlj (Nov 04 2019 at 22:19):
I'm trying Lemma Intersect2 {I} (X: set I) (Y: set I): \bigcap_ (i in [set X; Y]) (fun x => x) = X & Y.but it doesn't work (syntax error, '.' expected but I don't understand why
#### vlj (Nov 04 2019 at 22:21):
and if I add an auxiliary def, like Definition I2 {I} (X: set I) (Y: set I):=(X & Y).and then
Lemma Intersect2 {I} (X: set I) (Y: set I): \bigcap_ (i in [set X; Y]) (fun x => x) = (I2 X Y).
#### vlj (Nov 04 2019 at 22:21):
I have an error : The term "I2 X Y" has type "set I" while it is expected to have type
"set Prop" but I don't really know to deal with it
#### Emilio Jesús Gallego Arias (Nov 05 2019 at 00:42):
@vlj I dunno, this works for me:
#### Emilio Jesús Gallego Arias (Nov 05 2019 at 00:42):
Lemma Intersect2 (I : finType) (X: {set I}) (Y: {set I}): \bigcap_ (i in [set X; Y]) i = X :&: Y.
#### Florent Hivert (Nov 05 2019 at 07:49):
@vlj I think the problem is (fun x => x). The big notations automatically add the fun i => . So that add @Emilio Jesús Gallego Arias did you want to write \bigcap_ (i in [set X; Y]) i.
#### Damien Rouhling (Nov 05 2019 at 07:50):
Indeed, the bigcap @vlj wrote intersects all sets of the form fun x => x for any i which is either X or Y.
Since fun x => x must be a set, hence a function of type ?T -> Prop, the only possibility is to have ?T = Prop, which explains the message asking for an expression of type set Prop.
#### Damien Rouhling (Nov 05 2019 at 07:53):
Note that with the notations of mathcomp-analysis the solution of @Emilio Jesús Gallego Arias can be generalised to any type I:
Lemma Intersect2 (I : Type) (X Y : set I) : \bigcap_(i in [set X; Y]) i = X & Y.
#### Assia Mahboubi (Nov 05 2019 at 07:58):
Hi mathcomp/analysis devs. A while ago, we promised to showcase the design choices of the library wrt exceptional points for real analysis (Rbar, infinity, Nan). Deadline Nov.15th. Has anyone started something?
#### Damien Rouhling (Nov 05 2019 at 08:08):
Hi @Assia Mahboubi. Personally, I haven't written anything.
#### Cyril Cohen (Nov 05 2019 at 12:23):
@Assia Mahboubi I did not start anything either...
#### Pierre-Yves Strub (Nov 05 2019 at 12:32):
I can write something with my experience on summability.
#### Pierre-Yves Strub (Nov 05 2019 at 12:32):
And positive stuffs.
#### Pierre-Yves Strub (Nov 05 2019 at 12:32):
Where should we put our stuffs?
#### Cyril Cohen (Nov 05 2019 at 12:33):
In a subdirectory and/or a branch of math-comp/analysis?
#### Pierre-Yves Strub (Nov 05 2019 at 12:35):
Any solution will do. Decide, I obey :)
#### Cyril Cohen (Nov 05 2019 at 12:37):
Then a subdirectory
#### vlj (Nov 05 2019 at 17:54):
@Emilio Jesús Gallego Arias thanks !
Is there à
#### vlj (Nov 05 2019 at 18:08):
Docker script to build analysis ?
#### vlj (Nov 05 2019 at 18:09):
I d like to check that a change I did is properly compiling with a clean setup
#### Pierre-Yves Strub (Nov 06 2019 at 05:57):
You can have a look at the travis script
#### Pierre-Yves Strub (Nov 06 2019 at 05:58):
E.g., it is using (among others): mathcomp/mathcomp:1.9.0-coq-8.10
Ok
#### Reynald Affeldt (Nov 06 2019 at 13:28):
@Damien Rouhling if we were to use bigop to define bigmax (instead of the fold in Rstruct.v), which branch could be used as a reference: bigmaxr, entourages_bigmax, entourages_bigmaxr_mem?
#### Damien Rouhling (Nov 06 2019 at 13:30):
oh… we definitely should do some clean up
let me check
:-)
#### Damien Rouhling (Nov 06 2019 at 13:36):
none of the above ! :-)
#### Reynald Affeldt (Nov 06 2019 at 13:36):
I would have said entourages_bigmaxr_mem :-/
#### Damien Rouhling (Nov 06 2019 at 13:37):
the latest code is in uniform-entourages
thanks!
#### vlj (Nov 09 2019 at 18:13):
I opened a PR : https://github.com/math-comp/analysis/pull/162
#### Cyril Cohen (Nov 15 2019 at 10:16):
I can write something with my experience on summability.
@Pierre-Yves Strub did you have time to do something?
#### vlj (Nov 17 2019 at 00:41):
I'm having an issue now, I have a proposition that tells that an element is in a singleton, but I don't know how to turn this into an equality
#### vlj (Nov 17 2019 at 00:42):
more precisely :
Lemma Intersect2 {I} (X: set I) (Y: set I):
\bigcap_ (i in ([set X] | [set Y])) i = (X & Y).
Proof. rewrite /bigsetI predeqE => //= ; split.
- move => H. split ; [apply: (H X) | apply: (H Y)]=> //= ; by [left|right].
- case. move => Xx Yy seti. case => //=.
The proof environnement at this step is :
I: Type
X, Y: set I
x: I
Xx: X x
Yy: Y x
seti: set I
________
[set X] seti -> seti x
#### vlj (Nov 17 2019 at 00:43):
the [set X] seti means that X = seti and thus goal is solved
#### vlj (Nov 17 2019 at 00:43):
I tried with in_setE or things like that
#### vlj (Nov 17 2019 at 00:50):
[set X] is a notation for set1 X ie [set a : _ | a = X]. but I dont know how to "destruct" set1 X seti
#### Emilio Jesús Gallego Arias (Nov 17 2019 at 05:11):
Maybe you can prove forall x, x \in [set X] -> x = X ?
#### Reynald Affeldt (Nov 17 2019 at 08:05):
@vlj Maybe you want to do this
rewrite /set1.
move=> ->.
done.
#### Reynald Affeldt (Nov 17 2019 at 08:06):
(which can be of course shortened to by move=> -> and furthermore streamlined into the previous line of script)
#### vlj (Nov 17 2019 at 15:34):
what does "->" do in a move => tactic ?
#### vlj (Nov 17 2019 at 15:36):
@affeldt-aist it works thanks ! but I don't understand why atm
#### vlj (Nov 17 2019 at 15:37):
the rewrite is not necessary actually
#### Damien Rouhling (Nov 18 2019 at 07:45):
hi @vlj. When your goal is of the form l = r -> G, move=> -> or even move-> rewrites l = r from left to right in G (and you don't have access anymore to the assumption l = r). From right to left it would be move<-.
Thanks
#### vlj (Nov 18 2019 at 21:50):
Is there a way to know what coq "really sees" behind a notation ? I mean it was stuck to [set X] seti in the environnment even with a rewrite /set1
#### vlj (Nov 18 2019 at 21:52):
Completly unfolding the definition "on paper" and reducing shows that it is equivalent to X=seti but it the coq prompt didn't want to strip the notation for me
#### Reynald Affeldt (Nov 19 2019 at 06:09):
The command Unset Printing Notations reveals what is behind notations.
Thanks
#### vlj (Nov 19 2019 at 12:15):
it works but it doesn't stay past the command that follows.
#### vlj (Nov 19 2019 at 12:16):
but actually it showed me that I need to rewrite rewrite /classical_sets.set1and not just rewrite /set1so that's useful.
#### vlj (Nov 19 2019 at 12:51):
I have another issue with type :s
From mathcomp Require Import topology.
Section Test.
Variable X: topologicalType.
Variable Y: pointedType.
Variable f: X -> Y.
Print topologyOfOpenMixin.
Definition minus := [ set A | open (f @^-1 A)].
Theorem minusT : minus setT.
The theorem fails to be properly typed, because of The term "[set: fintype.Finite.sort ?T]" has type "{set fintype.Finite.sort ?T}" while it is expected to have type "set Y". but I don't understand what's going on... As far as I understand, "minus" type is set (set Y) (at least that's what Print shows) and setT should be a set Y, so it should be correctly typed.
#### vlj (Nov 19 2019 at 12:54):
hmm apparently the issue is with setT, but I really don't understand why
#### vlj (Nov 19 2019 at 19:48):
err nvm it works with classical_sets.setT
#### vlj (Nov 19 2019 at 19:49):
actually I imported finset in my scope and it looks like it conflicts with things in classical_sets all over the place
#### Reynald Affeldt (Nov 19 2019 at 20:12):
maybe Local Open Scope classical_set_scope. ?
Yes
#### vlj (Nov 21 2019 at 17:10):
hi, I have (again) an issue with typing. The code :
From mathcomp Require Import classical_sets eqtype boolp seq.
Require Import ssreflect.
Open Scope classical_set_scope.
Lemma preimage_bigsetU {A B I} (P : set I) (g:A->B) F:
g @^-1 (\bigcup_ (i in P) F) = \bigcup_(i in P) (g @^-1 F).
Proof.
rewrite predeqE. split; rewrite /bigsetU /preimage ; by [].
Qed.
From mathcomp Require Import topology.
Section Ex.
Variable X: topologicalType.
Variable Y: pointedType.
Variable f: X -> Y.
Print topologyOfOpenMixin.
Definition minus := [ set A | open (f @^-1 A)].
Theorem minusT : minus setT.
Proof.
Print setT.
rewrite !/minus !/preimage => //=.
apply openT.
Qed.
Theorem intersect: forall (A:set Y) (B:set Y),
minus A -> minus B -> minus (A & B).
Proof.
rewrite !/minus.
move => A B.
Unset Printing Notations.
rewrite /setI /preimage.
apply: openI => //=.
Qed.
Theorem union (D : set (set Y)):
(forall i, D i -> minus i) -> minus (\bigcup_ (i in D) i).
Proof.
rewrite !/minus.
move => Siiopen.
(**Unset Printing Notations.*)
rewrite (preimage_bigsetU D f (fun i: set Y => i)).
I'd like to apply the preimage_bigsetU lemma (which tells that preimage union = union of preimage) but it fails to unify type.
Error message is : Found type "set Y" where "Pointed.sort Y" was expected.
#### vlj (Nov 21 2019 at 17:13):
the type of preimage_bigsetU according to check is preimage_bigsetU : forall (P : set ?I) (g : ?A -> ?B) (F : set ?B), g @^-1 (\bigcup_(_ in P) F) = \bigcup_(_ in P) g @^-1 F
#### vlj (Nov 21 2019 at 17:15):
there's something I dont really grasp with the notation, it's that F should depend on i, but according to the type, it's not a function of i
#### vlj (Nov 21 2019 at 19:16):
actually simplifying the preimage_bigsetU (removing F, using i instead in a set (set B)) prop) works
#### Damien Rouhling (Nov 22 2019 at 08:31):
Hi @vlj. The issue is in the definition of preimage_bigsetU.
I think you mixed up the definition of the notation \bigcup_(i in P) F, where we use a variable F instead of the more precise F i in order to match any expression used by the user, with the actual use of the notation, where you have to put F i if you want Coq to infer that F is a function whose argument is i.
Here, since you used \bigcup_(i in P) F instead, Coq inferred Fto be of type set B which makes preimage_bigsetU not very interesting: when P is non-empty, \bigcup_(i in P) F = Fso this lemma almost just states that g @^-1 F = g @^-1 F
#### vlj (Nov 22 2019 at 21:13):
Ho yes you're right
#### vlj (Nov 22 2019 at 21:35):
I though F was a type in the notation indeed
#### vlj (Nov 26 2019 at 21:26):
Is there a definition of sqrt in mathcomp ? There is one in stdlib,and there is another one which may fit my needs (sqrt on int) but it uses module which are not recommended according to coq wiki (besides I don't know how to instantiate it ) https://coq.github.io/doc/master/stdlib/Coq.Numbers.NatInt.NZSqrt.html
#### vlj (Nov 26 2019 at 21:38):
Ssrnum has a sqrt but not for nat
#### Reynald Affeldt (Dec 05 2019 at 17:29):
there has been a minor update of mathcomp-analysis (0.2.3) so that it is compatible with mathcomp.1.10.0 (available on opam)
#### vlj (Dec 09 2019 at 22:40):
is there a lemma/theorem to "map" a comparaison from R to N ?
#### vlj (Dec 09 2019 at 22:41):
my use case is : I want to proof that ifloor (sqrt n) ^ 2 <= n
#### vlj (Dec 09 2019 at 22:42):
to do that I need at some point to rewrite n, which is a nat, as sqrt * sqrt, so I need to inject the inequality in a real closed field
#### vlj (Dec 09 2019 at 22:42):
but then I have no idea how to "go back" to N
#### Assia Mahboubi (Dec 10 2019 at 07:38):
hi @vlj, what do you need exactly? A definition for the largest i : nat such that n = i * i ? If so, it might indeed be more convenient to use a dedicated definition, and not use the square root in real numbers.
#### Pierre-Yves Strub (Dec 10 2019 at 07:42):
S.t. n >= i * i, no ?
Yes, sorry
#### Assia Mahboubi (Dec 10 2019 at 14:55):
@vlj, what about using ex_maxn as provided in ssrnat?
#### Assia Mahboubi (Dec 10 2019 at 14:55):
Lemma leq_expr (e n : nat) : 0 < e -> n <= n ^ e.
Proof.
case: e => [| e] // _. case: n => [| n] //=.
by rewrite expnS; apply: leq_pmulr; rewrite expn_gt0.
Qed.
Lemma sqrtn_aux m : exists n, n ^ 2 <= m. Proof. by exists 0. Qed.
Lemma sqrtn_bound m n : n ^ 2 <= m -> n <= m.
Proof. apply: leq_trans; exact: leq_expr. Qed.
Definition sqrtn (n : nat) := ex_maxn (sqrtn_aux n) (@sqrtn_bound n).
Lemma sqrtn_ge0 n : 0 <= sqrtn n. Proof. by rewrite /sqrtn; case: ex_maxnP. Qed.
Lemma lesqrtn n : sqrtn n <= n.
Proof.
rewrite /sqrtn; case: ex_maxnP => j Pj _;apply: leq_trans Pj; exact: leq_expr.
Qed.
I can give a try
#### vlj (Dec 10 2019 at 21:24):
I initially had in mind to "mimic" c like code (which use float to float) but it turns out to be very complicated
#### vlj (Dec 10 2019 at 21:24):
Using what you suggest is probably better
#### zstone1 (Gitter import) (Jan 07 2020 at 01:01):
Hey all, I have been working on a complex analysis package based on Coquelicot (https://github.com/zstone1/coq-complex), and have manged to prove some nice stuff, including "Holomorphic implies analytic". Now that I know what I'm doing (a little bit), I'd like to port the work to mathcomp analysis.
However, I need definite integrals. This is blocking me right now, as I am not sure where/if results like fundamental theorem of calculus live in mathcomp analysis. Can anyone help me to understand the current state of integration theorems in mathcomp/analysis? (FTC and exchanging limits and integrals are the only two thing I really need to do).
#### Reynald Affeldt (Jan 07 2020 at 09:48):
@zstone1 there is actually already some work in this direction performed on top of mathcomp-analysis
#### Reynald Affeldt (Jan 07 2020 at 09:54):
the branch analysis_270_integration provides the draft of a definition of integration and basic facts about holormophic functions
#### Reynald Affeldt (Jan 07 2020 at 09:55):
this is all very sketchy but this is also the focus of much attention right now
#### Bas Spitters (Jan 07 2020 at 12:45):
@zstone1 These have also been formalized in corn, math-classes, and there is a recent PR to the coq stdlib. There might be some posibilities to refactor things.
Consider contacting @vincentSe (vincent.semeria@gmail.com) https://github.com/coq/coq/pull/9185
The classical theory seems to factor quite well via the constructive one.
#### zstone1 (Gitter import) (Jan 07 2020 at 15:41):
Thanks for the pointers. The proofs in analysis_270_integration do seem to be in the right direction. I can definitely merge some of my work is to that. For example, I have the reverse direction of Cauchy Riemann, which should port pretty well from coquelicot. I am also extremely agnostic to the definition of integral being used. I only integrate (uniformly) continuous functions over real intervals. Considering how uncertain all this work is, maybe I should just define an interface to decouple it?
#### zstone1 (Gitter import) (Jan 07 2020 at 15:46):
As far math-classes and corn go, it appears they don't use filters to handle convergence. My work defines the topology of compact convergence, and proves compact limits exchange with contour integrals. So porting everything to an epsilon Delta world would be pretty tough.
#### Reynald Affeldt (Jan 07 2020 at 16:59):
Considering how uncertain all this work is, maybe I should just define an interface to decouple it?
The integral.v is intended to provide an interface to support other work; it would be great if you can plug on it, but if something is lacking or needs improvement your input is welcome and should be followed by quick action!
#### Bas Spitters (Jan 07 2020 at 17:19):
@zstone1 yes, these libraries use eps-delta.
In any case, it's nice to see some complex analysis. Is this your PhD-project?
#### Marie Kerjean (Jan 07 2020 at 18:52):
@zstone1 Hi, I would be happy to discuss or help with your porting to mathcomp analysis. When porting the cauchyriemann equations to the recent PR270 some questions were raised on complex analysis, and on how to handle the various topologies on C. Don't hesitate to ask if something seems obscure !
#### zstone1 (Gitter import) (Jan 08 2020 at 00:35):
@affeldt-aist That sounds like a plan. I will start there, and we can figure out what I need to complete my proofs.
@Bas Spitters Not a PhD project, this is a side project for me. I'm just trying to learn about the intersection of computer science and analysis. If you are handing out graduate degrees, I'll take one though.
@mkerjean, thanks for the offer. I first need to bash my head against this new notation for a bit, then I might have some relevant questions. Dealing with multiple topologies wasn't too painful. I have some (hacky) tactics to automatically apply forall (P:Prop) (x:C), locally_square x P <-> locally_circle x P. So I rarely cared which topology I was in. That being said, my proofs are... inelegant. So maybe not a great data point.
#### zstone1 (Gitter import) (Jan 11 2020 at 00:57):
I have two questions. In cauchyetoile, which seems to be the right file, there is a comment that differentiable in derive.v, means continuoulsy differentiable, not just that the limit exists. I'm pretty sure all it's doing is asking for the linear approximation to be continuous, not for f' to be continuous. If I'm right, is there any need to define a separate difference quotient in holomorphic? Your existing proofs need almost no change, as a short proof shows holomorphic f z = derivable f z 1 today.
Now the thing I really don't understand is why differentiable_def is coinductive. Why not just a normal inductive type?
#### Marie Kerjean (Jan 11 2020 at 07:14):
Hi @zstone1 , cauchyetoile is very much work in progress (and me learning mathcomp analysis) - I don't remember when I wrote this comment and you should be right about continuity.
#### Cyril Cohen (Jan 29 2020 at 23:36):
@zstone1
Now the thing I really don't understand is why differentiable_def is coinductive. Why not just a normal inductive type?
Actually, is should be Variant rather than Inductive or Coinductive (the latter was a "hack", because for non-recursive inductive types, it actually has the same semantics, except it does not generate (unused) induction principles). Variant is the "clean" way to do that.
#### Marie Kerjean (Feb 05 2020 at 19:31):
Hi, am I right if I say that no lemmas in analysis shows the equivalence between continuous and bounded for linear maps between normed spaces ? Maybe we could add them to normedtype ( I needed them for Hahn-Banach here ) ?
#### Cyril Cohen (Feb 05 2020 at 21:13):
@mkerjean one direction of this equivalence should be hidden in here https://github.com/math-comp/analysis/blob/master/theories/derive.v#L152-L166
#### Marie Kerjean (Feb 06 2020 at 09:32):
@Cyril Cohen It seems to be it just shows that the identity is bounded ?
#### Marie Kerjean (Feb 11 2020 at 19:38):
Hi everyone,
For several reasons, I would like to endow a numFieldType with a (canonical) topological structure. This would for example allow for the use of multiplication instead of scalar multplication in some cases of complex theory, and makes us closer to maths.
If I understand well, it would be necessary to make a clone of ssrnum in the analysis library, creating types as PseudoMetricNormedZmodule. How close are we to have a viable Hierarchy Builder tool (@Cyril Cohen @Kazuhiko Sakaguchi ) ?
#### vlj (Mar 06 2020 at 21:47):
How "feasible" is it to prove something using à derivative ? In arithmetic there is the lia tactic which ease équation transformation to some extent, but it likely doesn't work for reals. Since it's tedious to transform expression by hand is there some recommanded way to do with mathcomp analysis ?
#### Paolo Giarrusso (Mar 06 2020 at 21:51):
@vlj lia has relatives for reals https://coq.inria.fr/refman/addendum/micromega.html#short-description-of-the-tactics
#### Paolo Giarrusso (Mar 06 2020 at 21:52):
(but never used any of the other ones)
#### vlj (Mar 06 2020 at 22:21):
It works with reals ? It's not limited to presburger arithmetic ?
It's a good new
#### vlj (Mar 06 2020 at 22:24):
There is a zify like mecanism
#### Emilio Jesús Gallego Arias (Mar 07 2020 at 00:39):
Hi folks, should \max in order.v be generalized such that it works with ring_display? (cc: @Cyril Cohen )
#### vlj (Mar 08 2020 at 16:43):
this would mean that \max would be defined with ringType ?
#### Emilio Jesús Gallego Arias (Mar 08 2020 at 20:09):
I think you need something higher, such as numField
#### Cyril Cohen (Mar 09 2020 at 09:36):
Hi folks, should \max in order.v be generalized such that it works with ring_display? (cc: Cyril Cohen )
Sure!
#### vlj (Apr 05 2020 at 21:08):
What is the recommended way to make proof relying on formula on a field ? For instance I have a formula defined in numFieldType, and it has a nice composition property. If I use Coq.Reals the field tactic can be used ; I tried adding a custom field theory to the field database, but then I hit the bug
#11998 in coq
#### vlj (Apr 05 2020 at 21:09):
In this bug somebody mentions ssring which is part of a third party lib on elliptic curve, but elliptic curve by themselve seem to be too specific to be part of mathcomp
#### vlj (Apr 05 2020 at 21:10):
Should I just copy the file content and use it or is there another more "official" way of doing ?
#### Cyril Cohen (Apr 05 2020 at 22:49):
Hi @vlj, sorry, there is no official way yet. Your question is a "generalization" of https://github.com/math-comp/math-comp/issues/401
#### vlj (Apr 05 2020 at 23:10):
Yes, that's where I found ssring.
#### vlj (Apr 05 2020 at 23:11):
It looks like there are several methods "floating around" but I'm not really sure which one to pick
#### vlj (Apr 06 2020 at 17:29):
If I have a topologyOfBaseMixin, how can I make a TopologicalType out of it ? in topology.v it's not directly considered as a topologicalType, it's used to create another mixin (topologyOfSubbaseMixin) which in turn is used to generate another mixin (sup_topologicalTypeMixin ) which has it's own type
#### vlj (Apr 06 2020 at 17:31):
here is the sample I'm using : https://gist.github.com/vlj/b45fb840764357d58c6d2e1ee4e501f1
#### vlj (Apr 06 2020 at 20:49):
btw is there a definition of "included" topology somewhere ?
#### vlj (Apr 06 2020 at 20:52):
eg coarser topology
#### vlj (Apr 08 2020 at 18:26):
classical_set means that Excluded Middle hold ? I miss a lemma "Lemma setCC: ~' ~' X = X
#### vlj (Apr 08 2020 at 18:27):
I can write one, but I'd like to know if this I'm not mistaking something
#### vlj (Apr 11 2020 at 17:07):
I created a pull request : https://github.com/math-comp/analysis/pull/173 all comment welcome (I'm still not completly familiar with every mathcomp convention)
#### Marie Kerjean (Apr 12 2020 at 19:43):
Hi everyone, I would like to create a PR getting rid of the ^o for analysis ( defined here ). In the current state of the library (branch mathcomp master), the tag ^o is the only way to have a topology on a numFieldType as well as a lmodType structure on it.
#### Marie Kerjean (Apr 12 2020 at 19:43):
As I see it, while it is understandable that no canonical algebra structure should be put on a ring, this became less clear in the case of fields, especially if one wants to deal with analysis. The inconvenient of ^o to me is that dealing with topology on it leads to multiplication of the tags ^o on a single type.
#### Marie Kerjean (Apr 12 2020 at 19:45):
The solution would be the creation of an copy of the structure numField endowed by inheritance with a lmodType structure.
#### Marie Kerjean (Apr 12 2020 at 19:45):
Does any of you have an opinion on that subject ?
#### vlj (Apr 12 2020 at 21:47):
Am I missing a Lemma saying that the complement of set0 is setT ? I dont find it in classical set
#### Reynald Affeldt (Apr 13 2020 at 17:26):
it seems so, here is a proposal: https://github.com/math-comp/analysis/pull/178
#### vlj (Apr 14 2020 at 17:28):
Thanks for the pr and merge !
#### vlj (Apr 16 2020 at 18:35):
I opened another pr : https://github.com/math-comp/analysis/pull/184 I'm less confident in it, there are a lot of split.
#### vlj (Apr 20 2020 at 20:27):
I have a maths question : is <= a lattice ? in mathcomp it's not a subtype of lattice, and I'm not familiar with lattice, but it looks a lot like intersection and union may be meet and join in a top bottom lattice, maybe a distributed one
#### vlj (Apr 20 2020 at 20:28):
I had to prove that A '<=' A | B and it looks a lot like a <= max a b
#### vlj (Apr 20 2020 at 21:21):
I created another PR : https://github.com/math-comp/analysis/pull/186 I don't know if boolean reflection is the best way, I didn't find the exact demorgan law in boolp.
#### Reynald Affeldt (Apr 24 2020 at 16:05):
There has a substantial merge on master (of PR https://github.com/math-comp/analysis/pull/175), following the release of MathComp 1.11.0+beta1. It is documented here https://hal.inria.fr/hal-02463336v2/document.
#### Reynald Affeldt (Apr 24 2020 at 16:07):
You can enjoy better notations and more general lemmas but there might be unforeseen issues. Does not hesitate to report them here or on github. Thank you.
#### Reynald Affeldt (Apr 27 2020 at 11:35):
@Cyril Cohen is it reasoanble to assign PR #176 to milestone 0.3?
#### Cyril Cohen (Apr 27 2020 at 12:42):
Yes, actually I am in favor of releasing 0.3.0 asap and working on 0.3.1 if needed
#### Reynald Affeldt (Apr 27 2020 at 12:51):
cool (I meant #177 of course)
#### vlj (Apr 29 2020 at 20:55):
I have a math question : in meetjoin theory , the mixin is built using a less or equal relation, and also a less than relation. Is there an exemple where the less than could not be deduced from less than ? An obligation of the mixin is to prove than less than is less or equal + not equal
#### vlj (Apr 29 2020 at 20:56):
https://github.com/math-comp/math-comp/blob/master/mathcomp/ssreflect/order.v#L4165
#### Cyril Cohen (Apr 30 2020 at 00:35):
@vlj, yes, logically speaking, it can always be inferred thanks to the equation you cited. However, in some cases it is convenient to be able to choose another one. For example, for natural numbers, defining lt as ltn (where ltn m n := (m.+1 <= n)) makes (m <= n)%O convertible to (m < n)%N.
#### Reynald Affeldt (Apr 30 2020 at 15:10):
#### Reynald Affeldt (Apr 30 2020 at 15:10):
We need to commit something! ;-)
#### Cyril Cohen (Apr 30 2020 at 17:26):
Let's keep it that way :laughing:
#### Marie Kerjean (May 01 2020 at 14:56):
I can't find lemmas on the monotonicity of limits (if f bounded by M, then lim f <= M). Are they missing or maybe I don't have the right keyword ?
#### Cyril Cohen (May 01 2020 at 16:59):
Hi Marie, I think they are WIP in the sequence branch, and not general enough...
(yet)
thanks !
#### Reynald Affeldt (May 03 2020 at 23:23):
I can't find lemmas on the monotonicity of limits (if f bounded by M, then lim f <= M). Are they missing or maybe I don't have the right keyword ?
this one is for real numbers: https://github.com/math-comp/analysis/blob/mathcomp_master_sequences/theories/sequences.v#L561-L563
Last updated: Aug 11 2022 at 02:03 UTC | 2022-08-11 02:59:36 | {"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": 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": 0.558684229850769, "perplexity": 5659.088668152324}, "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-2022-33/segments/1659882571232.43/warc/CC-MAIN-20220811012302-20220811042302-00310.warc.gz"} |
http://sagi.io/bloom-filters-for-the-perplexed/ | Jul 29, 2017
# Bloom Filters for the Perplexed
A rusty engineer's take on a potent data structure
#algo
Discussion on Hacker News.
Bloom filters are one of those simple and handy engineering tools that any engineer should have in their toolbox.
It is a space-efficient probabilistic data structure that represents a set and allows you to test if an element is in it.
They are really simple to construct and look like this:
The cool thing is that to achieve such space-efficiency Bloom filters allow for errors with an arbitrarily small probability!
Remarkably, a Bloom filter that represents a set of $1$ million items with an error rate of $0.01$ requires only $9585059$ bits ($\text{\textasciitilde}1.14 \text{MB}$)! Irrespective of the length of each element in $S$!
There’re many kinds of Bloom filters. We’ll cover the Standard Bloom Filter as it is the basis for the others and also serves as a nice intro for more advanced probabilistic set-membership data structures such as Cuckoo Filter.
## What’s on our menu for today?
All code snippets can be found on Github.
Academic fellows might want to review Bloom’s original $1970$ paper [1]. Strikingly, Bloom has only $3$ references in his article!
## Standard Bloom Filters
A Bloom filter represents a set $S=\{x_1, x_2, \ldots, x_n\}$ of $n$ elements by an array of $m$ bits (initially set to $0$). Lets call it $B$.
$B = [b_1, b_2, b_3, b_4, \ldots, b\_{m-1}, b_m]$
A Bloom filter uses $k$ independent hash functions $h_1, \ldots, h_k$ that are assumed to be uniformly distributed over the range $\{1, \ldots, m \}$.
Standard Bloom filters have two operations:
1. Add($x$) - Add $x$ to the Bloom filter.
$\text{For} \space 1 \leq i \leq k \space \text{set} \space B[h_i(x)]=1$
To represent set $S$ by Bloom filter $B$ we need to Add all $x \in S$.
2. Contains($y$) - Check if $y$ is in the Bloom filter.
$\text{If for all} \space 1 \leq i \leq k \space, \space B[h_i(y)]==1 \\ \text{return true, otherwise false}$
To make things clearer, here is a hand-drawn illustration (heavily inspired by Julia Evans (@b0rk) blog illustrations):
### False-Negatives and False-Positives
If Contains($y$) returns False, clearly $y$ is not a member of $S$. This property is why we say Bloom filters have zero false-negatives. A situation where Contains($e$) is False and $e \in S$ simply can’t happen (because otherwise all relevant bits were $1$).
If Contains($y$) returns True, $y$ may or may not be a member of $S$. This is why we say that Bloom filters may have false-positives, because a situation where Contains($e$) is True and $e \notin S$ can occur.
### Arbitrarily Small Probability of Error (False-Positive)
The cool thing about Bloom filters is that based on $n$ (number of elements in the set $S$) and a chosen probability of false positives $P_{FP}$ we can derive optimal $k$ (number of hash functions) and $m$ (length of bit vector $B$).
These are the formulae (we derive those in the Appendix):
$k=-{\frac {\ln P_{FP}}{\ln 2}}, \enspace m=-{\frac {n\ln P_{FP}}{(\ln 2)^{2}}}$
A very cool result is that the optimal number of hash functions $k$ depends only on the false-positive probability $P_{FP}$.
Lets play with it:
import math
def optimal_km(n, p):
ln2 = math.log(2)
lnp = math.log(p)
k = -lnp/ln2
m = -n*lnp/((ln2)**2)
return int(math.ceil(k)), int(math.ceil(m))
print(optimal_km(10**6, 0.01)) # Returns (7, 9585059)
Remarkably, a Bloom filter that represents a set of $1$ million items with a false-positive probability of $0.01$ requires only $9585059$ bits ($~1.14 \text{MB}$) and $7$ hash functions. Only $9.6$ bits per element! ($\frac{9585059}{1000000}$).
## Toy Implementation
The first thing that comes to mind is how exactly do we get a family of hash functions $h_1, \ldots, h_k$ that are uniformly distributed?
Since our objective is learning and we are not aiming for efficiency, we can simply build our family of hash functions on top of an existing hash function as a primitive. Such as SHA256.
One such construction is the following:
$h_i(s) = \text{SHA256}(i\space||\space s) \text{ mod } m$
Where:
• $i$ - the number of the hash function.
• $s$ - the string to be hashed.
• $m$ - the length of the bit vector.
• $||$ - string concatenation.
And with Python:
def h_i(i, m, s):
return int(sha256(bytes([i]) + s).hexdigest(), 16) % m
Recall that the standard bloom filter had two simple operations:
class bloom_filter:
def __init__(self, m, k, h=h_i):
self.m = m # length of bit array
self.k = k # number of hash functions
self.h = h # hash function
self.bits = bitarray(self.m) # the actual bit store
for i in range(self.k):
self.bits[self.h(i, self.m, s)] = 1
def contains(self, s):
for i in range(self.k):
if self.bits[self.h(i, self.m, s)] == 0:
return False
return True # all bits were set
## Example: Efficiently Verify Compromised SSH Keys
In 2008, Luciano Bello discovered that Debian’s OpenSSL random number generator was seriously flawed and depended only on a process id integer.
Without getting into the gory details, essentially it means that between 2006 and 2008, cryptographic keys that were generated using OpenSSL on Debian-based operating systems were limited to 32768 different possible keys given their type (e.g. RSA) and size (e.g. 1024 bit).
Fortunately, g0tmi1k (@g0tmi1k), generated all possible compromised keys and uploaded them to a repo.
Say we’d like to build a system that allows users to query whether their keys were compromised.
Moreover say we’d like our system to use a minimal amount of bandwidth and/or requests to the server.
Using a bloom filter for that purpose fits perfectly! Lets see why:
Note that the initial client request is just a fetch (GET) request, the actual key X isn't sent with it.
Since Bloom filters have zero false negatives, if key $X$ isn’t in Bloom filter $B$ we know that $X$ isn’t compromised with certainty! Therefore, no more requests needed.
The other case is that $X$ is in $B$:
Note that the initial client request is just a fetch (GET) request, the actual key X isn't sent with it.
So a request to verify the state of $X$ must be sent to the server as it may be either a true positive ($X$ is in $B$ and $X$ is compromised) or a false positive ($X$ is in $B$ but $X$ isn’t compromised).
The nice thing about bloom filters is that the size of the Bloom filter is dependent on the false positive probability that is arbitrarily chosen by us!
So if we notice a lot of false positives we can just tune the Bloom filter to our needs and sacrifice some bandwidth for more accuracy.
In Github there’s test_bloom.py which populates a toy Bloom filter with the compromised keys and tests its effectiveness:
\$ ./test_bloom.py
[+] Number public keys in ./dsa/1024: 32768. Total length: 19004952 bytes (18.12Mb).
[+] False-positive probability of 0.001.
[+] Optimal number of bits is 471125 (57Kb). 322 times more space efficient.
[+] Optimal number of hash functions is 10.
[+] Test: All public keys were found within the bloom filter.
[+] Test: Average number of false positives: 21, false positive rate: 0.0213. Averaged over 10 tests, 1000 random strings in each test.
Notice that the bloom filter is $322$ more space efficient than the actual length of the public keys (18.12Mb vs. 57Kb)!
If you’d like to run it yourself make sure to follow the simple installation instructions.
For completeness, here’s the code of test_bloom.py:
#!/usr/bin/env python3
'''A test script that queries vulnearble keys (debian openssl debacle)
in a space efficient manner using Bloom filters.'''
import glob
import random
from string import ascii_letters
import bloom
def random_string(size=10):
rand_str = ''.join(([random.choice(ascii_letters) for i in range(size)]))
return str.encode(rand_str)
def empirical_false_positive_rate(bf, nr_tests=1, nr_strings=1000):
c = 0
for i in range(nr_tests):
rand_strings = [random_string(30) for i in range(nr_strings)]
t = 0
for r in rand_strings:
if bf.contains(r):
t += 1
c += t
avg_fpr = ((c/nr_tests)*(1/nr_strings))
avg_errs = c/nr_tests
return (int(avg_errs), avg_fpr)
if __name__ == '__main__':
public_keys = set()
total_keys_bytes= 0
for pk_file in glob.glob('./dsa/1024/*.pub'):
pk_base64 = open(pk_file, 'rb').read().split()[1]
total_keys_bytes += len(pk_base64)
n = len(public_keys)
print('[+] Number public keys in ./dsa/1024: {}. Total length: {} bytes ({:0.2f}Mb).'.format(n, total_keys_bytes, total_keys_bytes/(2**20)))
p = 1/1000
print('[+] False-positive probability of {}.'.format(p))
k, m = bloom.optimal_km(n, p)
t = int((total_keys_bytes*8)/m)
print('[+] Optimal number of bits is {} ({}Kb). {} times more space efficient.'.format(m, int(m/(8*(2**10))), t))
print('[+] Optimal number of hash functions is {}.'.format(k))
# Populating our bloom filter.
bf = bloom.bloom_filter(m, k)
for pk in public_keys:
# Testing that all public keys are inside the bloom filter
all_pks_in_bf = True
for pk in public_keys:
if not bf.contains(pk):
all_pks_in_bf = False
break
if all_pks_in_bf:
print('[+] Test: All public keys were found within the bloom filter.')
else:
# Can't be...
print('[-] Test: One or more public key were not found within the bloom filter.')
# Testing the empirical false positive rate by generating random strings
# (that are surely not in the bloom filter) and check if the bloom filter
# contains them.
nr_tests = 10
nr_strings = 1000
avg_errs, avg_fpr = empirical_false_positive_rate(bf, nr_tests, nr_strings)
print('[+] Test: Average number of false positives: {}, false positive rate: {:0.4f}. Averaged over {} tests, {} random strings in each test.'.format(avg_errs, avg_fpr, nr_tests, nr_strings))
## Applications
In their 1994 paper, Andrei Broder and Michael Mitzenmacher coined the Bloom Filter Principle:
Wherever a list or set is used, and space is at a premium, consider using a Bloom filter if the effect of false positives can be mitigated.
Andrei Broder and Michael Mitzenmacher
Below are some cool applications I’ve bumped into over the years.
## Breaking Bitcoin (and Ethereum) Brainwallets
In DEFCON 23 (2015), Ryan Castellucci (@ryancdotorg) presented Brainflayer. A cryptocurrency brainwallet cracker that uses a Bloom filter under the hood.
I specifically abstracted away low level Bitcoin technicalities.
Bitcoin’s blockchain is made out of a sequence of blocks. Each block contains transactions and each transaction cryptographically instructs to transfer $X$ Bitcoins from a previous transaction to a Bitcoin address.
How does a Bitcoin address is generated?
A Bitcoin address $A$ is simply a hashed ECDSA public-key $Q$. Lets denote $A = H(Q)$.
How does an ECDSA public key is generated?
An ECDSA public key $Q$ is the outcome of multiplying a private key $d$ with some known constant base point $G$. That is, $Q = d \times G$.
How does an ECDSA private key is generated?
An ECDSA private key $d$ is simply an integer that is preferably generated using a cryptographically secure random number generator. Anyone that knows $d$ can redeem Bitcoins that were sent to $A$.
What’s a Brainwallet address?
A Brainwallet is simply a Bitcoin address where its corresponding private key $d$ was generated using a mnemonic (!) rather then a secure random number generator. One possible Brainwallet construction looks like:
$d = \text{SHA256(MNEMONIC)}$
For instance, the string (embedded in Bitcoin’s Genesis block):
The Times 03/Jan/2009 Chancellor on brink of second bailout for banks
When hashed with SHA256 yields the following ECDSA private key:
a6d72baa3db900b03e70df880e503e9164013b4d9a470853edc115776323a098
That yields the following Bitcoin address:
1Nbm3JoDpwS4HRw9WmHaKGAzaeSKXoQ6Ej
Using a blockchain explorer we can check the address’s history and see that it was used :)
Using a Bloom filter to crack Brainwallets
It is rather straight forward:
1. Extract all Bitcoin addresses from the Blockchain.
2. Add them to a Bloom filter $B$.
3. Generate a set $W$ of Bitcoin addresses using plausible mnemonics (“Brainwallets”).
4. Gather possible candidates set $C$ - addresses from $W$ that $B$ returns positive on.
5. Filter out false positives by checking which addresses in $C$ exist on the Blockchain.
Currently, Bitcoin’s blockchain contains about $440M$ unique addresses (according to Quandl - press on Cumulative).
Ryan’s implenetation contains a bloom filter of length $512MB$ and $20$ hash functions (he actually uses simple functions over the original public key hashes - no heavy cryptographic hash - neat).
In the Appendix we derived an experssion for the false positive probability:
$P_{FP} = (1 - P_0)^{k} = \left(1 - \left(1 - \frac{1}{m}\right)^{kn}\right)^{k}$
Where $k$ is the number of hash functions, $n$ the length of the set and $m$ the length of the bloom filter.
def exact_pfp(n, m, k):
return ( 1 - (1 - (1/m))**(k*n) )**k
m_bytes = 512*1024*1024
m_bits = m_bytes * 8
k = 20
print(exact_pfp(440*(10**6), m_bits, k)) # ~0.063
print(exact_pfp(220*(10**6), m_bits, k)) # ~0.000137
print(exact_pfp(110*(10**6), m_bits, k)) # ~1.14e-08
print(exact_pfp(80*(10**6), m_bits, k)) # ~7.16e-11`
As one can tell from above, a Bloom filter of length $512MB$ and $20$ hash functions has a high false positive rate on $440M$ items.
In 2015, when Ryan released Brainflayer, there were about $80M$ unique addresses on the blockchain and such a construction yielded a very low false postive rate of $\sim 7.16\times 10^{-11}$.
Today, in order to maintain a similar false positive rate, one would have to either dissect the blockchain to chunks and use several Bloom filters of length $512MB$, or simply increase the length of the bloom filter and the number of hash functions.
I highly recommened you to go and watch Ryan’s talk.
### Recommender System Optimization
Simply put, a recommender system $R$ is an algorithm that predicts the preferences of a user.
For instance, you’ve just bought The Hard Thing About Hard Things. Amazon’s recommender system learns that you like books about entrepreneurship and start show you other book recommendations.
But, how do you keep track of irrelevant recommendations such as books the user already read or dismissed ?
Say $X$ books were recommended by $R$. $X$ is comprised of $Y$ relevant and $Z$ irrelevant recommendations ($Y \cap Z = \emptyset$).
Using a Bloom filter $B_Z$ to store irrelevant recommendations $Z$ is one possible answer.
First, say we’re dealing with a lot of irrelevant recommendations, then since Bloom filters are space efficient, it reduces the data stored per user substantially, and even bandwidth (if your logic resides in client side).
Second, since Bloom filters have zero false-negatives, we are guarunteed that a user will never be shown irrelevant recommendations (the event where $e \in Z$ and $B_{Z}.contains(e)$ is false can’t happen).
Third, since Bloom filters may have false-positives, a relevant recommendation may not be shown to the user (the event where $e \in Y$ and $B_{Z}.contains(e)$ is true). But that’s ok since nothing will happen if a user won’t get a relevant recommendation once every 1K visits.
I’d like to thank Sébastien Bratières for spotting an error in this clause.
### Search Engine Optimizations
In his 2016 Strange Loop talk, Dan Luu (@danluu), shared some of the internals of one of Bing’s production search indices: BitFunnel (hint: they use Bloom filters, but not in a trivial way).
The talk is short and built in a very constructive way:
You might want to review BitFunnel’s SIGIR’17 paper.
## Appendix
While studying the math behind Bloom filters I found myself rusty and confused. Here is a guided tour for the rusty-confused engineer :)
## False-Positive Probability and Formulae
Assume Bloom filter $B$ was populated with elements from $S$.
A false-positive is an input $y$ that isn’t an element of $S$ but $B[h_1(y)], \ldots, B[h_k(y)]$ are all set to $1$.
The false-positive probability $P_{FP}$ then is simply the probability of having any $k$ arbitrary cells set to $1$ after Bloom filter $B$ is populated with elements from $S$.
Lets define $P_1$ to be the probability that a certain bit is set to $1$ after we populate the Bloom filter.
Given $P_1$, the probability of a false positive, $P_{FP}$ is simply:
$P_{FP} = P_{1}^{k}$
But, how do we calculate $P_{1}$ ?
Lets assume now that Bloom filter $B$ is empty and we begin add elements from $S$.
Given $x_1$ we compute $h_1(x_1)$ and set $B[h_1(x_1)]$ to $1$. What’s $P_1$ now?
$P_1 = \frac{1}{m}$
because we assume $h_i$ are uniform over $\{1, \ldots, m\}$.
Next, we compute $h_2(x_1)$ and set $B[h_2(x_1)]$ to $1$. What’s $P_1$ now?
$P_1 = \frac{1}{m} + \frac{1}{m} -\frac{1}{m^2}$
Wait! Why did you subtract $\frac{1}{m^2}$ ?
Recall that we defined $P_1$ to be the probability that a specific bit is set to $1$. This specific bit might be set to $1$ by either $h_1$ or $h_2$ or both. That is, we search for the probability of the union of independent events that are not mutually exclusive.
We subtract $\frac{1}{m^2}$, since otherwise we “count” the event that both $h_1$ and $h_2$ set the bit to $1$ twice. This is due to the Inclusion-Exclusion Principle.
Doing the same thing for $h_3$. What’s $P_1$ now?
$P_1 = \frac{3}{m} -\frac{3}{m^2} +\frac{1}{m^3}$
As evident from above, if we continue this way we end up with a rather intricate expression for $P_1$. For this reason, most derivations of the false-positive probability use the complementary event to go around it.
Lets define $P_0$ to be the probability that a certain bit is not set to $1$.
If we knew $P_0$ we could easily compute $P_1$ and $P_{FP}$:
$P_{FP} = P_{1}^{k} = (1 - P_0)^{k}$
So, how do we calculate $P_{0}$ ?
Lets start with an empty Bloom filter $B$ again and add elements from $S$.
Given $x_1$ we compute $h_1(x_1)$ and set $B[h_1(x_1)]$ to $1$. What’s $P_0$ now?
$P_0 = 1 - \frac{1}{m}$
Next, we compute $h_2(x_1)$ and set $B[h_2(x_1)]$ to $1$. What’s $P_0$ now?
$P_0 = \left(1 - \frac{1}{m}\right)^2$
Wait! Why does $P_1$ and $P_0$ differ at this stage of the analysis?
Because when calculating $P1$ we wanted the probability of the event that at least one of the hash functions sets a specific bit. But, for $P_0$ we want the probability that all hash functions does not set a specific bit!
That is, we search for the probability of the intersection of independent events that are not mutually exclusive.
Setting the bits for the other hash functions $h_3(x_1), h_4(x_1), \ldots, h_k(x_1)$:
$P_0 = \left(1 - \frac{1}{m}\right)^k$
And since we add $n$ elements:
$P_0 = \left(1 - \frac{1}{m}\right)^{kn}$
Therefore:
$P_{FP} = (1 - P_0)^{k} = \left(1 - \left(1 - \frac{1}{m}\right)^{kn}\right)^{k}$
Since we want to find the optimal $k$ and $m$ such that $P_{FP}$ (the false probably rate) is minimized, we will need to differentiate it.
The expression for $P_{FP}$ isn’t easy to differentiate, this is why most derivations use a neat trick that represents it with $e$ (Euler’s number).
One of $e$’s many definitions is:
$\lim_{n\to\infty} \left( 1 + \frac{1}{n}\right) ^n = e$
That is, for large enough $n$, $e$ is approximately $\left( 1 + \frac{1}{n}\right)^n$.
Therefore,
\begin{aligned} \left(1 - \frac{1}{m}\right)^{kn} &= \left(1 + \frac{1}{-m}\right)^{\frac{-mkn}{-m}}\\ &= \left(\left(1 + \frac{1}{-m}\right)^{-m}\right)^{\frac{kn}{-m}}\\ &\approx e^{\frac{kn}{-m}} \end{aligned}
Hence, $P_{FP}$ can be reduced to the following expression:
$P_{FP} \approx \left(1 - e^{\frac{kn}{-m}}\right)^{k}$
Although we got a nicer expression for $P_{FP}$, we would like to differentiate it with respect to $k$ (to find the the optimal number of hash functions). But $k$ is the exponent.
To differentiate such equations usually one uses some $\ln$ (natural logarithm) trickery.
For any function $f(x,y) = g(y)^{x}$ ($g$ is simply a function of $y$) it holds that:
\begin{aligned} f(x,y) &= e^{ln(f(x,y))}\\ &= e^{ln(g(y)^x)}\\ &= e^{x \cdot ln(g(y))} \end{aligned}
Therefore, in the case of our $P_{FP}$:
$P_{FP} = e^{ln(\left(1 - e^{\frac{kn}{-m}}\right)^{k})} = e^{k \cdot ln(\left(1 - e^{\frac{kn}{-m}}\right))}$
Lets denote $g = k \cdot ln(\left(1 - e^{\frac{kn}{-m}}\right))$, which makes $P_{FP} = e^{g}$.
Since $e$ is a monotonically increasing function minimizing $e^{g}$ is equivalent to minimizing $g$ with respect to $k$.
Differentiating $g$ with respect to $k$ (WolframAlpha):
$\frac{\partial g}{\partial k} = ln \left( 1 - e^{\frac{-kn}{m}}\right) + \frac{kn}{m} \cdot \frac{e^{\frac{-kn}{m}}}{1 - e^{\frac{-kn}{m}}}$
To find the optimal $k$, the one that minimizes the above expression, one needs to equate it to $0$
It is easy to verify that the derivative is $0$ when $k=ln 2 \cdot \frac{m}{n}$:
\begin{aligned} \frac{\partial g}{\partial k} &= ln \left( 1 - e^{-ln2}\right) + ln2 \cdot \frac{e^{-ln2}}{1 - e^{-ln2}}\\ &= ln \left( 1 - \frac{1}{2}\right) + ln2 \cdot \frac{\frac{1}{2}}{\frac{1}{2}}\\ &= ln \left(\frac{1}{2} \right) + ln2\\ &= 0 \end{aligned}
Great! Now we know that $k=ln 2 \cdot \frac{m}{n}$ is the optimal number of needed hash functions.
A very cool result of bloom filters is that $k$ only depends on a given $P_{FP}$.
To achieve that result, lets plug the $k$ we got in equation we derived for the false positive probability:
\begin{aligned} P_{FP} &\approx \left(1 - e^{\frac{kn}{-m}} \right)^{k}\\ &= \left(1 - \frac{1}{2}\right)^{ln2 \cdot \frac{m}{n}}\\ &= \left(2\right)^{-ln2 \cdot \frac{m}{n}}\\ \end{aligned}
Taking $ln$ on both sides:
$ln(P_{FP}) = -\frac{m}{n} \cdot (ln2)^{2}$
Therefore, $m$, the number of bits in our bloom filter (number of bits in $B$) is:
$m=-{\frac {n\ln P_{FP}}{(\ln 2)^{2}}}$
Pluggin that $m$ into the $k$ we got yields:
$k=-{\frac {\ln P_{FP}}{\ln 2}}$
And voila, $k$ depends only on a given false positive probability $P_{FP}$!
## Summary
Bloom filters are simple and useful beasts. They were designed in times of great scarcity in memory, but since nowadays we explode in data they fit almost perfectly for our times as well!
If you found this article interesting, make sure to read about Scalable Bloom filters which allows you to add items to an already existing Bloom filter and Counting Bloom filters which allows you to delete items from an already existing Bloom filter.
If you spot an error / have any question please let me know so others may gain :)
Comments and thoughts are also welcome on this tweet:
1. B. H. Bloom. Space/time trade-offs in hash coding with allowable errors. Communications of the ACM, 13(7):422-426, 1970.
© 2020 Sagi Kedmi | 2020-08-08 20:05:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 243, "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": 0.7755697965621948, "perplexity": 1728.304247505747}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738351.71/warc/CC-MAIN-20200808194923-20200808224923-00588.warc.gz"} |
https://paperity.org/journal/206538/stochastics-and-partial-differential-equations-analysis-and-computations | # Stochastics and Partial Differential Equations: Analysis and Computations
## List of Papers (Total 59)
#### A reflected moving boundary problem driven by space–time white noise
We study a system of two reflected SPDEs which share a moving boundary. The equations describe competition at an interface and are motivated by the modelling of the limit order book in financial markets. The derivative of the moving boundary is given by a function of the two SPDEs in their relative frames. We prove existence and uniqueness for the equations until blow-up, and...
#### Electro-rheological fluids under random influences: martingale and strong solutions
We study generalised Navier–Stokes equations governing the motion of an electro-rheological fluid subject to stochastic perturbation. Stochastic effects are implemented through (i) random initial data, (ii) a forcing term in the momentum equation represented by a multiplicative white noise and (iii) a random character of the variable exponent $$p=p(\omega ,t,x)$$ (as a result of...
#### Some results on the penalised nematic liquid crystals driven by multiplicative noise: weak solution and maximum principle
In this paper, we prove several mathematical results related to a system of highly nonlinear stochastic partial differential equations (PDEs). These stochastic equations describe the dynamics of penalised nematic liquid crystals under the influence of stochastic external forces. Firstly, we prove the existence of a global weak solution (in the sense of both stochastic analysis...
#### Berry–Esseen theorem and quantitative homogenization for the random conductance model with degenerate conductances
We study the random conductance model on the lattice $${\mathbb {Z}}^d$$, i.e. we consider a linear, finite-difference, divergence-form operator with random coefficients and the associated random walk under random conductances. We allow the conductances to be unbounded and degenerate elliptic, but they need to satisfy a strong moment condition and a quantified ergodicity...
#### Iterated stochastic integrals in infinite dimensions: approximation and error estimates
Higher order numerical schemes for stochastic partial differential equations that do not possess commutative noise require the simulation of iterated stochastic integrals. In this work, we extend the algorithms derived by Kloeden et al. (Stoch Anal Appl 10(4):431–441, 1992. https://doi.org/10.1080/07362999208809281) and by Wiktorsson (Ann Appl Probab 11(2):470–487, 2001. https...
#### Recursive formulae in regularity structures
We construct renormalised models of regularity structures by using a recursive formulation for the structure group and for the renormalisation group. This construction covers all the examples of singular SPDEs which have been treated so far with the theory of regularity structures and improves the renormalisation procedure based on Hopf algebras given in Bruned–Hairer–Zambotti...
#### Strong solutions to SPDEs with monotone drift in divergence form
We prove existence and uniqueness of strong solutions, as well as continuous dependence on the initial datum, for a class of fully nonlinear second-order stochastic PDEs with drift in divergence form. Due to rather general assumptions on the growth of the nonlinearity in the drift, which, in particular, is allowed to grow faster than polynomially, existing techniques are not...
#### Weak universality of dynamical $$\Phi ^4_3$$ : non-Gaussian noise
We consider a class of continuous phase coexistence models in three spatial dimensions. The fluctuations are driven by symmetric stationary random fields with sufficient integrability and mixing conditions, but not necessarily Gaussian. We show that, in the weakly nonlinear regime, if the external potential is a symmetric polynomial and a certain average of it exhibits pitchfork...
#### Exponential integrators for nonlinear Schrödinger equations with white noise dispersion
This article deals with the numerical integration in time of the nonlinear Schrödinger equation with power law nonlinearity and random dispersion. We introduce a new explicit exponential integrator for this purpose that integrates the noisy part of the equation exactly. We prove that this scheme is of mean-square order 1 and we draw consequences of this fact. We compare our...
#### Itô formula for processes taking values in intersection of finitely many Banach spaces
Motivated by applications to SPDEs we extend the Itô formula for the square of the norm of a semimartingale y(t) from Gyöngy and Krylov (Stochastics 6(3):153–173, 1982) to the case \begin{aligned} \sum _{i=1}^m \int _{(0,t]} v_i^{*}(s)\,dA(s) + h(t)=:y(t)\in V \quad dA\times {\mathbb {P}}\text {-a.e.}, \end{aligned}where A is an increasing right-continuous adapted process...
#### A solution theory for a general class of SPDEs
In this article we present a way of treating stochastic partial differential equations with multiplicative noise by rewriting them as stochastically perturbed evolutionary equations in the sense of Picard and McGhee (Partial differential equations: a unified Hilbert space approach, DeGruyter, Berlin, 2011), where a general solution theory for deterministic evolutionary equations...
#### Eikonal equations and pathwise solutions to fully non-linear SPDEs
We study the existence and uniqueness of the stochastic viscosity solutions of fully nonlinear, possibly degenerate, second order stochastic pde with quadratic Hamiltonians associated to a Riemannian geometry. The results are new and extend the class of equations studied so far by the last two authors.
#### Sublinear growth of the corrector in stochastic homogenization: optimal stochastic estimates for slowly decaying correlations
We establish sublinear growth of correctors in the context of stochastic homogenization of linear elliptic PDEs. In case of weak decorrelation and “essentially Gaussian” coefficient fields, we obtain optimal (stretched exponential) stochastic moments for the minimal radius above which the corrector is sublinear. Our estimates also capture the quantitative sublinearity of the...
#### Symmetrization of exterior parabolic problems and probabilistic interpretation
We prove a comparison theorem for the spatial mass of the solutions of two exterior parabolic problems, one of them having symmetrized geometry, using approximation of the Schwarz symmetrization by polarizations, as it was introduced in Brock and Solynin (Trans Am Math Soc 352(4):1759–1796, 2000). This comparison provides an alternative proof, based on PDEs, of the isoperimetric...
#### Optimal rate of convergence for stochastic Burgers-type equations
Recently, a solution theory for one-dimensional stochastic PDEs of Burgers type driven by space-time white noise was developed. In particular, it was shown that natural numerical approximations of these equations converge and that their convergence rate in the uniform topology is arbitrarily close to $$\frac{1}{6}$$. In the present article we improve this result in the case of...
#### Convergence of tamed Euler schemes for a class of stochastic evolution equations
We prove stability and convergence of a full discretization for a class of stochastic evolution equations with super-linearly growing operators appearing in the drift term. This is done by using the recently developed tamed Euler method, which employs a fully explicit time stepping, coupled with a Galerkin scheme for the spatial discretization.
#### Splitting up method for the 2D stochastic Navier–Stokes equations
In this paper, we deal with the convergence of an iterative scheme for the 2-D stochastic Navier–Stokes equations on the torus suggested by the Lie–Trotter product formulas for stochastic differential equations of parabolic type. The stochastic system is split into two problems which are simpler for numerical computations. An estimate of the approximation error is given for...
#### Scalar conservation laws with rough (stochastic) fluxes: the spatially dependent case
We continue the development of the theory of pathwise stochastic entropy solutions for scalar conservation laws in $${\mathbb {R}}^N$$ with quasilinear multiplicative “rough path” dependence by considering inhomogeneous fluxes and a single rough path like, for example, a Brownian motion. Following our previous note where we considered spatially independent fluxes, we introduce...
#### Consistency and stability of a Milstein–Galerkin finite element scheme for semilinear SPDE
We present an abstract concept for the error analysis of numerical schemes for semilinear stochastic partial differential equations (SPDEs) and demonstrate its usefulness by proving the strong convergence of a Milstein–Galerkin finite element scheme. By a suitable generalization of the notion of bistability from Beyn and Kruse (Discrete Contin Dyn Syst Ser B 14(2), 389–407 2010...
#### On stochastic finite difference schemes
Finite difference schemes in the spatial variable for degenerate stochastic parabolic PDEs are investigated. Sharp estimates on the rate of $$L_p$$ and almost sure convergence of the finite difference approximations are presented and results on Richardson extrapolation are established for stochastic parabolic schemes under smoothness assumptions.
#### A note on error estimation for hypothesis testing problems for some linear SPDEs
The aim of the present paper is to estimate and control the Type I and Type II errors of a simple hypothesis testing problem of the drift/viscosity coefficient for stochastic fractional heat equation driven by additive noise. Assuming that one path of the first $$N$$ Fourier modes of the solution is observed continuously over a finite time interval $$[0,T]$$, we propose a new... | 2019-05-20 00:42:13 | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.676397442817688, "perplexity": 517.7095892919814}, "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-2019-22/segments/1558232255251.1/warc/CC-MAIN-20190520001706-20190520023706-00494.warc.gz"} |
http://math.stackexchange.com/questions/20374/abcde-odd-numbers | # (a)+(b)+(c)+(d)+(e) odd numbers
There are 5 questions in a quiz designated by:
a, b, c, d, e
Each of the questions can only have one of 4 possible answers:
-
Am I correct to say that there are 625 possible variations of answers that we can receive?
-
Can any of the variations equal to zero when we would add all the answers up?
For example on variation
(5) + (-5) + (7) + (-7) + (5) = 5
-
So the core question is can the sum of all the answers to a particular variation ever be zero.
-
Do you mean 5,-5,7, and -7? Also, can you explain the last sentence a little more clearly? – user3180 Feb 4 '11 at 7:57
The answer is no. The sum of a single odd number is odd (since it is just the original number), the sum of two odd numbers is even (see here), and in general, the sum of $n$ odd numbers is odd if $n$ is odd, and even if $n$ is even.
In your problem, you are adding 5 odd numbers, and because 5 is odd, we must have that the sum is odd, regardless of which of the values $5,-5,7,-7$ the numbers $a,b,c,d,e$ take on. However, 0 is an even number. Thus, the sum $a+b+c+d+e$ can never be 0. | 2014-09-20 08:02:17 | {"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": 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": 0.709743320941925, "perplexity": 263.64452418961304}, "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-2014-41/segments/1410657133033.29/warc/CC-MAIN-20140914011213-00002-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-7-exponents-and-exponential-functions-7-6-exponential-functions-practice-and-problem-solving-exercises-page-450/14 | Algebra 1
$f(2) = 36$
We plug in the given value for the independent variable. When we do this, we find: $f(2) = 6^2 =6*6= 36$ | 2018-05-21 07:41:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7226027846336365, "perplexity": 185.02551569587587}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794863967.46/warc/CC-MAIN-20180521063331-20180521083331-00518.warc.gz"} |
http://mathoverflow.net/questions/121638/does-every-commutative-monoid-admit-a-translation-invariant-measure | # Does every commutative monoid admit a translation-invariant measure?
Let $T$ be a commutative monoid, written additively. The set $T$ is equipped with a canonical pre-order, defined by $s \le t$ when there exists $s' \in T$ so that $s + s' = t$. Consequently, $T$ may be equipped with the specialization topology for this pre-order, where the closed sets are those which are downward-closed. Note that $T$ is typically not Hausdorff, since the closure of a singleton is its down-set: $\overline{\{t\}} = t\!\downarrow\, := \{ s : s \le t \}$.
Let $\mathcal B(T)$ denote the Borel $\sigma$-algebra with respect to this topology. In this way, every commutative monoid is canonically a measurable space.
Equipped with the $\sigma$-algebra $\mathcal B(T)$, does every commutative monoid $T$ admit a (non-trivial) family of translation-invariant measures?
-
If $T$ is a group, this is not a very interesting topology... – Daniel Litt Feb 12 '13 at 19:48
Of course not. That's why I said commutative monoid. – Tom LaGatta Feb 12 '13 at 23:35
I think the integers Z with max is a counterexample. First note the set $I_n$ of all integers bigger than or equal to n is open. Thus each singleton is Borel by looking at $I_n\setminus I_{n+1}$. Hence by countability of Z the measure is a weighted counting measure. But the inverse image of n under translation by n consists of all numbers less than or equal to n. Thus the weight of n is the weight of n plus the weights of all numbers less than n. Thus the weights of all numbers strictly less than n are zero. Since n is arbitrary all elements have weight 0.
-
Why the downvote? It seems ok. – Benjamin Steinberg Feb 13 '13 at 16:32
That's odd that someone would downvote this. It's a great counterexample, and your argument is elegant. It's going to take me some time to reformulate my question so as to circumvent such obstructions. Thanks very much, @Benjamin Steinberg. – Tom LaGatta Feb 13 '13 at 19:38
If in the finer interval topology the monoid is locally compact, I suspect by the same construction that it admits a 'Haar' measure. Moreover, as the Borel sigma algebras generated by these topologies are identical, in this case yes you get a family of invariant measures parameterized by '$\mathbb{R}^+$'.
-
That's a good point. – Tom LaGatta Feb 12 '13 at 23:36
Benjamin's example is locally compact, no? – Mariano Suárez-Alvarez Feb 13 '13 at 6:29
My example last night was wrong. I have a new example. Namely Z with max. The interval topology here is still locally compact since the order is the usual one. – Benjamin Steinberg Feb 13 '13 at 13:06
RE: Benjamin. Let's break this down in detail. Let $\Gamma := \mathbb{Z}$ (so I can keep track of the action versus the space). Then under the specialization or the interval topology, the Borel sigma algebra $\mathcal{B}_{\mathbb{Z}} := \mathcal{B}$ as you pointed out contains sigletons and hence $\mathcal{B} = 2^{\mathbb{Z}}$. Let $\Gamma$ act on $\mathbb{Z}$ by max e.g. for $\gamma \in \Gamma$ define $\gamma(m) = max(\gamma,m)$. So, $\gamma^{-1}(\{n\}) = \{m \in \mathbb{Z}: max(\gamma,m) = n \} = \{n\}$ if $\gamma < n$ ; $\{m \leq n\}$ if $\gamma = n$; $\varnothing$ if $\gamma > n$. – Tyler Bryson Feb 13 '13 at 18:27
That's slightly cleaner than how I wrote it but yes. – Benjamin Steinberg Feb 13 '13 at 19:11 | 2014-12-23 04:24:57 | {"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": 0.96379154920578, "perplexity": 367.39859207811355}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802778085.5/warc/CC-MAIN-20141217075258-00030-ip-10-231-17-201.ec2.internal.warc.gz"} |
http://dolinastrugu.pl/darbhanga-rural-aoyse/3c1fd4-types-of-returns-in-portfolio-management | The formula for the holding period return computation is as follows: $$\text{Holding Period Return (HPR)} = \frac {P_t – P_{t-1} + D_t} {P_{t-1}}$$, $$P_t$$ is the price of the asset at time t when the asset is sold, $$P_{t-1}$$ is the price of the asset at time t-1 when the asset was bought, $$D_t$$ is the dividend per share paid between t and t-1. Thus, one measure of risk is absolute deviations of returns under column 6. This website includes study notes, research papers, essays, articles and other allied information submitted by visitors like YOU. I. Employees of both private and public companies often save and invest for retirement... Risk budgeting is focused on implementing the risk tolerance decisions taken at a... 3,000 CFA® Exam Practice Questions offered by AnalystPrep – QBank, Mock Exams, Study Notes, and Video Lessons, 3,000 FRM Practice Questions – QBank, Mock Exams, and Study Notes. x̅ is the mean or the weighted average return. If α is a positive return, then that scrip will have higher returns. Thus, the portfolio expected return is the weighted average of the expected returns, from each of the securities, with weights representing the proportionate share of the security in the total investment. If we have a large enough portfolio it is possible to eliminate the unsystematic risk When the return of company XYZ is compared with that of company ABC, we have to take into account, their expected return and standard deviation of the return. An investor considering investment in securities is faced with the problem of choosing from among alarge number of securities. Suitable securities are those whose prices are relatively stable but still pay reasonable dividends ⦠The total risk of a portfolio (as measured by the standard deviation of returns) consists of two types of risk: unsystematic risk and systematic risk. Meaningful diversification is one which involves holding of stocks of more than one industry so that risks of losses occurring in one industry are counterbalanced by gains from the other industry. A geometric return provides a more accurate representation of the portfolio value growth than an arithmetic return. When a portfolio is made up of several assets, we may want to find the aggregate return of the portfolio as a whole. To annualize a return earned for a period shorter than one year, the return must be compounded by the number of periods in the year. For example, if a share has returned 15%, 10%, 12% and 3% over the last four years, then the arithmetic mean is as follows: $$\text{Arithmetic mean} = \frac {15\% + 10\% + 12\% + 3\%} {4} = 10\%$$. Active portfolio management strategy is normally dependent on the style of management and analysis that can generate healthy returns and beat the stock market as well. And one of the things you should know in order to complete one is to know the various types of portfolio management. If the security “ARC” gives the maximum return why not he invest in that security all his funds and thus maximise return? If you hire a prudent portfolio manager, he can optimize or maximize the returns on your portfolio. Passive Portfolio Manageme⦠The different types of portfolio investment are as follows: Risk-Free Portfolios â Risk-free portfolios are the ones that have investment securities regarding treasury bonds and such where the risk is almost nil but low returns. What are the arithmetic mean and geometric mean, respectively, of an investment which returns 8%, -2% and 6% each year for three years? Why an investor does has so many securities in his portfolio? There shall be bifurcation across these five units of the total corpus provided. The time period may be as short as a day or many years and is expressed as a total return. A. Arithmetic mean = 5.3%; Geometric mean = 5.2%, B. Arithmetic mean = 4.0%; Geometric mean = 3.6%, C. Arithmentic mean = 4.0%; Geometric mean = 3.9%, $$\text{Arithmetic mean} = \frac {8\% + (-2\%) + 6\%} {3} = 4\%$$, $$\text{Geometric mean} = [(1+8\%) × (1+(-2\%)) × (1+6\%)]^{1/3} – 1 = 3.9\%$$, Calculate and interpret major return measures and describe their appropriate uses. Portfolio management is the art of selecting the right investment tools in the right proportion to generate optimum returns with a balance of risk from the investment made. If there is no relation between them, the coefficient of correction can be zero. Say company A and B have the following characteristics: Which company do you prefer? A portfolioâs historical standard deviation can be calculated as the square root of the variance of returns. As returns and prices of all securities do not move exactly together, variability in one security will be offset by the reverse variability in some other security. If α = 0, then the regression line goes through the origin and its return simply depends on the Beta times the market return. This is the coefficient of variation, namely (SD/X). Financial market assets generate two different streams of return: income through cash dividends or interest payments and capital growth through the price appreciation of the asset. The previous year’s returns are compounded to the beginning value of the investment at the start of the new period in order to earn returns on your returns. September 12, 2019 in Portfolio Management. Content Guidelines 2. Thus (.04)2 = .0016 and this multiplied by the probability of it 0.25 gives .0004 and so on. ADVERTISEMENTS: Portfolio theories guide the investors to select securities that will maximize returns and minimize risk. Asset classes could ⦠Tax considerations like capital gains tax and tax on interest or dividend income will need to be deducted from the investment to determine post-tax returns. On the other hand, the 7-stock portfolio might represent a number of different industries where returns might show low correlation and, hence, low portfolio returns variability. these object types have been created, you can also attach your Account to a Model Portfolio, and then attach your Model Portfolio to a Strategy â all in Portfolio Management. Active Portfolio Management: When the portfolio managers actively participate in the trading of securities with a view to earning a maximum return to the investor, it is called active portfolio management. 1. It measures the unsystematic risk of the company. Real returns are useful for comparing returns over different time periods as inflation rates vary over time. Share Your PPT File, Essay on Financial Economics | Branches | Economics. The Company with a higher return of 11.5% has a higher risk than the other company. Portfolio management helps an individual to decide where and how to invest his hard earned money for guaranteed returns in the future. Capital Asset Pricing Model When an asset needs to be added to an already well diversified portfolio, Capital Asset Pricing Model is used to calculate the assetâs rate of profit or rate of return (ROI). Second, some financial assets may also offer capital appreciation as the prices of these securities change themself. An arithmetic mean is a simple process of finding the average of the holding period returns. Portfolio Management - Introduction A portfolio is a collection of investment tools such as stocks, shares etc, and Portfolio Management is the art of selecting the right investment policy in terms of minimizing risk and maximizing returns. Risk avoidance and risk minimization are the important objectives of portfolio management. A net return is the return post-deduction of fees. A defensive portfolio focuses on consumer staples that are impervious to downturns. Defensive Portfolio : Defensive portfolio comprises of stocks with low risk and stable earnings â e.g. Thus, the portfolio expected return is the weighted average of the expected returns, from each of the securities, with weights representing the proportionate share of the security in the total investment. You will notice the workflow logic is the same for each object type. The last column of weighted squared deviations are derived by multiplying the weights of probabilities with squared deviations. Before publishing your Articles on this site, please read the following pages: 1. Portfolio Risk and Return: Expected returns of a portfolio, Calculation of Portfolio Risk and Return, Portfolio with 2 assets, Portfolio with more than 2 assets. Risk on a portfolio is different from the risk on individual securities. Average investors are risk averse. A portfolio contains different securities, by combining their weighted returns we can obtain the expected return of the portfolio. A portfolio that consists of 70% equities which return 10%, 20% bonds which return 4%, and 10% cash which returns 1% would have a portfolio return as follows: Portfolio return = (70%×10%)+(20%×4%)+(10%×1%) = 7.9% Portfolio return = ( 70 % × 10 %) + ( ⦠Understanding Active Return Active return refers to the portion of returns (profit or loss) in an investment portfolio that can be directly attributed to the active management decisions made by the portfolio manager Portfolio Manager Portfolio managers manage investment portfolios using a six-step portfolio management process. It is a long-term strategy for index investing whose purpose is to generate ⦠So for example, the portfolio could include real estate, fixed deposits with banks, mutual funds, shares, and bonds. Portfolio Diversification refers to choosing different classes of assets with the objective of maximizing the returns and minimize the risk profile. Portfolio management involves selecting and managing an investment policy that minimizes risk and maximizes return on investments. An Example for Covariance and Correlation: Given the standard deviation of X and Y as 13.23 and 9.75 in the portfolio of two securities the covariance between them has to be estimated. The expected return of the portfolio can be computed as: Covariances and correlation of returns Before moving on to the variance of the portfolio, we will have a quick look at the definitions of covariance and correlation. A monthly return must be compounded 12 times, a weekly return 52 times and a daily return 365 times. Dow Theory: ADVERTISEMENTS: Charles Dow, the editor of Wall Street Journal, USA, presented this theory through a series of editorials. In other words, a portfolio is a group of assets. All Rights ReservedCFA Institute does not endorse, promote or warrant the accuracy or quality of AnalystPrep. Diversification of risk in portfolio management - Portfolio should be diversified to the degree at which specific risk has virtually been eliminated. If the period during which the return is earned is not exactly one year, we can annualize the return to enable an easy comparative return. Return and standard deviation and variance of portfolios can also be compared in the same manner. Passive portfolio management Passive portfolio management is a process where the portfolio manager creates a fixed portfolio aligning it with current trends in the market. Traditional Approach: 1. Now, the variance is sum of the weighted squared deviations, namely, .0008. There are other measures of returns that need to be taken into account when evaluating performance. Passive Portfolio: When the Investors typically have one or more types of portfolios among their investments and seek to achieve a balanced return on investment over time. Arithmetic returns tend to be biased upwards unless the holding period returns are all equal. The portfolio is a collection of investment instruments like shares, mutual funds, bonds, FDs and other cash equivalents, etc. If an investor makes use of derivative instruments within a portfolio or borrows money to invest, then leverage is introduced into the portfolio. PORTFOLIO MANAGEMENTWhat is portfolio management? But when you want to calculate the expected volatility, you must include the covariance or correlation of each asset. Welcome to EconomicsDiscussion.net! The IRR provides the investor with an accurate measure of what was actually earned on the money invested but does not allow for easy comparison between individuals. Portfolio management is a process of choosing the appropriate mix of investments to be held in the portfolio and the percentage allocation of those investments. If Beta is zero, stock price is unrelated to the Market index. So the portfolio manager according to the risk-taking capacity and the kind of returns calculated provides a portfolio structured in tandem with that. Headline stock market indices typically report on price appreciation only and do not include the dividend income unless the index specifies it is a “total return” series. Return on Portfolio: Each security in a portfolio contributes returns in the proportion of its investment in security. Share Your PDF File A weekly return of 2%, when annualized, is as follows: $$\text{Annualized return} = (1+2\%)^{52} – 1 = 180\%$$. Our mission is to provide an online platform to help students to discuss anything and everything about Economics. Disclaimer Copyright, Share Your Knowledge For example, a year relative to a 20-month holding period is a fraction of 12/20. If on the other hand, Rho is -1, the direction of the movement will be opposite as between the stock price and market index. Aggressive Portfolio: An aggressive portfolio comprises of high-risk investments like commodities, futures, options and other securities expecting high returns in the short run. Portfolio Management Involves,-Investing and divesting different, -investment Risk management,- Monitoring and analyzing returns Portfolio management is a process encompassing many activities aimed at optimizing the investment We examine the cash flows from the perspective of the investor where amounts invested in the portfolio are seen as cash outflows and amounts withdrawn from the portfolio by the investor are cash inflows. Module â 4 Valuation of securities: Bond- Bond features, Types of Bonds, Determinants of interest rates, Bond Management Strategies, Bond Valuation, Bond Duration. Portfolio management thus refers to investment of funds in such combination of different securities in which the total risk of portfolio is minimized while expecting maximum return from it. investments in high quality, blue-chip stocks . This means itâs generating the highest possible return at your established risk tolerance . It is important to be able to compute and compare different measures of return to properly evaluate portfolio performance. Dow ⦠Companies can be ranked in the order of return and variance and select into the portfolio those companies with higher returns but with the same level of risk. (read difference between saving & investment) Investment is about deferring your present consumption for future goals with expectation of security of amount & getting returns. Beta measures the systematic market related risk, which cannot be eliminated by diversification. a) Investment b) Speculation c) Technical analysis d) Fundamental analysis e Assuming that investor puts his funds in four securities, the holding period return of the portfolio is described in the table below: The above describes the simple calculation of the weighted average return of a portfolio for the holding period. Types of PMS There are three types of Portfolios in PMS, you can choose any of them-Discretionary PMSâ Discretionary Portfolio provides the service provider a right to make decisions on behalf of the client, whether he wants to sell or buy the shares. This can be positive and negative. The expected return depends on the probability of the returns and their weighted contribution to the risk of the portfolio. Reducing the Risk of Certain Asset Classes An aggressive portfolio takes on great risks in search of great returns. The summation of all deviations from the mean and then squared will give the variance. (Alternatively, this term may refer to a portfolio that has the minimum amount of risk for the return that it seeks, although itâs a less common usage.) Share Your Word File A risk averse investor always prefer to ⦠The answers to this question lie in the investor’s perception of risk attached to investments, his objectives of income, safety, appreciation, liquidity and hedge against loss of value of money etc. This means we look at the return as a composite of the price appreciation and the income stream. If Beta is 1, a one percentage change in Market index will lead to one percentage change in price of stock. Arithmetic and geometric returns do not take into account the money invested in a portfolio in different time periods. β or Beta describes the relationship between the stock’s return and the Market index return. If the correlation coefficient is one (+ 1), an upward movement of one security return is followed by a direct upward movement of the second security. Using the same annual returns of 15%, 10%, 12% and 3% as above, we compute the geometric mean as follows: $$\text{Geometric mean} = [(1+15\%) × (1+10\%) × (1+12\%) × (1+3\%)]^{1/4} – 1 = 9.9\%$$. In general, returns are presented pre-tax and with no adjustment for the effects of inflation. We note the geometric return is slightly less than the arithmetic return. There are two measures of Risk in this context — one is the absolute deviation and the other standard deviation. In this article we will discuss about the analysis of return and risk on portfolio of a company. This Risk is reflected in the variability of the returns from zero to infinity. Investment Analysis & Portfolio Management (FIN630) VU general types: those that are pervasive in nature, such as market risk or interest rate risk, and These are as follows: A gross return is earned prior to the deduction of fees (management fees, custodial fees, and other administrative expenses). There is an art, and a science, when it comes to making decisions about investment mix and policy, matching investments to objectives, asset allocation and balancing risk against performance. A portfolio that consists of 70% equities which return 10%, 20% bonds which return 4%, and 10% cash which returns 1% would have a portfolio return as follows: $$\text{Portfolio return} = (70\% × 10\%) + (20\% × 4\%) + (10\% × 1\%) = 7.9\%$$. It is the percentage change in the price of the stock regressed (or related) to the percentage changes in the market Index. These theories can be classified into different categories as depicted in figure 6.1. The square root of variance is standard deviation (sd). The leverage amplifies the returns on the investor’s capital, both upwards and downwards. These are briefly discussed below. Another measure is the standard deviation and variance-. These can be explained with following illustrations, the assumed probabilities of each of the returns and the estimation of absolute deviation and standard deviation, based on them are given for only illustration: Column 5 is deviation of the returns under column 3 from the expected return 15 (Thus -25 = (-10-15). A money-weighted return is similar in computation methodology to an internal rate of return (IRR) or a yield to maturity. Privacy Policy3. The relationship between coefficient of correction and covariance is expressed by the equation below: Financial Economics, Investment, Portfolio, Risk and Return on Portfolio. When we talk about the returns from a financial asset, we can broadly classify them into two types. There are different types of returns, it can be either short-term return or long term, it must go according to the goals of the corporate entity etc. It includes more than average values and stresses on taking benefits of stock market inabilities. Each investor has his own risk profile, but there is a possibility that he does not have the relevant investment security that matches his own risk profile. Each security in a portfolio contributes returns in the proportion of its investment in security. If the portfolio is efficient, Beta measures the systematic risk effectively. The basic equation for calculating risk can be formulated as a regression equation-, Where, y = Return in the security in a given period and, α = The intercept where the regression line crosses the y-axis. Column 6 is the result of multiplying deviation under column 5 with the probability in column 2 without considering signs. Computing a geometric mean follows a principle similar to the computation of compound interest. This pattern of investment in different asset categories, security categories, types of instruments, etc., would all be described under the caption of diversification, which aims at the reduction or even elimination of non- systematic or company related risks and achieve the specific objectives of investors. If we had a return of 12% for 20 months, then the annualized return is as follows: $$\text{Annualized return} = (1+12\%)^{12/20} – 1 = 7\%$$. When the holding period is longer than one year, we need to express the year as a fraction of the holding period and compound using this fractional number. Image Credit Onemint 2 most basic types of risk Investment is related to saving but saving does not mean investment. A holding period return is a return earned from holding an asset for a specified period of time. When we have assets for multiple holding periods, it is necessary to aggregate the returns into one overall return. TOS4. Returns are typically presented in nominal terms which consist of three components: the real risk-free return as compensation for postponing consumption, inflation as compensation for the loss of purchasing power and a risk premium. In doing so, active managers would buy stocks with lower value and would sell it once it climbs above the norm. First, financial assets may provide some income in the form of dividends or interest payments. If the Beta is minus one, it indicates a negative relationship with the Market Index and if the market goes up by a + 1%, the stock price will fall by 1%. CFA® and Chartered Financial Analyst® are registered trademarks owned by CFA Institute. Active Portfolio Management: This type of portfolio management aims to make better returns in contrast to what the market hypothesizes. Take the following graph to illustrate the above: α or Alpha is the distance between the horizontal axis and line’s intersection with y-axis. PORTFOLIO MANAGEMENT-TRIAL QUESTIONS 1) Explain the following terms as used in Portfolio management and give examples and/or furmulas. Rho or Correlation Coefficient (Covariance): Rho measures the correlation between two stocks say i and j. ©AnalystPrep. One of the corporate financial essentials includes a complete investment portfolio. In order to compute this, we weight the returns of the underlying assets by the amounts allocated to them. Portfolio Management 1. Return in Portfolio Investments The typical objective of investment is to make current income from the investment in the form of dividends and interest income. Portfolio optimization should result in what investors call an âefficient portfolioâ. It can normally vary from – 1 to 4- 1. The IRR is the discount rate applied to determining the present value of the cash flows such that the cumulative present value of all the cash flows is zero. If two Risks are compared, then standard deviations divided by their means are compared. Covariance (or correlation) denotes the directional relationship of the returns from any two stocks. 2. You On the other hand alpha and Epsilon (α + ∑) measures the unsystematic risk, which can be reduced by efficient diversification. Return ( IRR ) or a yield to maturity comparing returns over different periods... Compare different measures of returns the weighted average return or the weighted squared deviations like you in portfolio helps. Taking benefits of stock market inabilities other measures of risk in portfolio management - portfolio should diversified! And geometric returns do not take into account when evaluating performance investment in securities is faced the! Alpha and Epsilon ( α + ∑ ) measures the unsystematic risk, which can be.... So, active managers would buy stocks with low risk and stable â! Words, a portfolio in different time periods 2 =.0016 and this multiplied by the allocated... Geometric returns do not take into account the money invested in a portfolio in different time periods both upwards downwards! Than average values and stresses on types of returns in portfolio management benefits of stock money-weighted return is fraction. All his funds and thus maximise return papers, essays, articles and other allied information submitted visitors! Related to saving but saving does not mean investment offer capital appreciation the... Borrows money to invest, then that scrip will have higher returns column is. (.04 ) 2 =.0016 and this multiplied by the amounts allocated to them hand! Between two stocks articles and other allied information submitted by visitors like you we have assets multiple... “ ARC ” gives the maximum return why not he invest in that security all funds..0016 and this multiplied by the amounts allocated to them in securities is faced with the objective of maximizing returns... And everything about Economics internal rate of return ( IRR ) or yield! Amounts allocated to them managers would buy stocks with low risk and stable â. Yield to maturity correlation between two stocks income stream management: this type of portfolio management helps an individual decide. So for example, a portfolio or borrows money to invest, then leverage introduced! To achieve a balanced return on investment over time returns of the underlying assets by the probability the... Introduced into the portfolio the expected return of 11.5 % has a higher return 11.5. Registered trademarks owned by CFA Institute, it is important to be able to compute this, we want... Earned from holding an asset for a specified period of time impervious to downturns useful for comparing over. One percentage change in market index there are two measures of return properly. Stock regressed ( or related ) to the risk of the things you should know in order complete! It is important to be able to compute and compare different measures of return ( IRR ) a! Of risk in portfolio management - portfolio should be diversified to the computation compound! For comparing returns over different time periods as inflation rates vary over.... Is important to be able to compute and compare different measures of returns that need to be able to this! Across these five units of the stock regressed ( or related ) to the degree at which risk... Of finding the average of the stock ’ s return and risk minimization are the objectives. On individual securities and B have the following pages: 1 relation them. The stock ’ s return and the market index will lead to one percentage change in market index lead... Return is a group of assets with the problem of choosing from among alarge number securities! Other hand alpha and Epsilon ( α + ∑ ) measures the systematic market risk. Weekly return 52 times and a daily return 365 times risk effectively the risk-taking capacity and the income stream 11.5... From among alarge number of securities to the computation of compound interest multiplied by the amounts allocated to them )... Is faced with the problem of choosing from among alarge number of securities to achieve a return. Allocated to them the square root of variance is standard deviation a money-weighted is. Been eliminated give examples and/or furmulas hand alpha and Epsilon ( α ∑. Chartered financial Analyst® are registered trademarks owned by CFA Institute and seek to a... Compute this, we can obtain the expected volatility, you must include covariance. If you hire a prudent portfolio manager according to the risk of the on... Of maximizing the returns into one overall return other allied information submitted by visitors like.. The effects of inflation different categories as depicted in figure 6.1 change.... All Rights ReservedCFA Institute does not mean investment classified into different categories as depicted in figure 6.1 be as. Many securities in his portfolio includes a complete investment portfolio this is the same each. Portfolio is efficient, Beta measures the systematic risk effectively your portfolio has a higher risk than the hand. And geometric returns do not take into account the money invested in a portfolio contains securities! Securities is faced with the objective of maximizing the returns on your portfolio company with a higher of... Into the portfolio could include real estate, fixed deposits with banks, mutual,... The returns from zero to infinity variation, namely,.0008 securities change themself derived by multiplying the weights probabilities. In column 2 without considering signs relation between them, the variance properly. Irr ) or a yield to maturity in what investors call an âefficient portfolioâ to achieve balanced..04 ) 2 =.0016 and this multiplied by the amounts allocated to them one of the portfolio is from! No relation between them, the variance is standard deviation is to an! Students to discuss anything and everything about Economics a one percentage change in the proportion of its investment security. For example, a portfolio is a return earned from holding an asset for a specified period time! In general, returns are presented pre-tax and with no adjustment for the effects of inflation be diversified the! Aims to make better returns in contrast to what the market hypothesizes or correlation (! The prices of these securities change themself properly evaluate portfolio performance and everything about Economics as. Multiple holding periods, it is necessary to aggregate the returns and their weighted returns we can obtain the return. Be compounded 12 times, a one percentage change in price of stock inabilities... A holding period returns this is the return as a composite of the returns from zero infinity... Portfolio Manageme⦠portfolio diversification refers to choosing different classes of assets, one measure of risk in this article will. Appreciation as the prices of these securities change themself is necessary to aggregate returns. Company do you prefer there are two measures of return ( IRR ) or a to! Active portfolio management in security management and types of returns in portfolio management examples and/or furmulas in a portfolio contains different securities by! Returns tend to be biased upwards unless the holding period returns are useful for comparing returns over different periods! Quality of AnalystPrep achieve a balanced return on investment over time risk is reflected in the price stock... Rates vary over time by multiplying the weights of probabilities with squared deviations, namely ( SD/X ) units the. Total return useful for comparing returns over different time periods as inflation rates over... Column 5 with the objective of maximizing the returns on your portfolio probabilities with squared deviations are derived multiplying! The norm does has so many securities in his portfolio the variability the! Contributes returns in contrast to what the market index return for guaranteed returns contrast. Compound interest market index will lead to one percentage change in market index return amplifies the returns from a asset! Price appreciation and the market index earned money for guaranteed returns in contrast to what the market index return has... Have higher returns essays, articles and other allied information submitted by visitors like you will... Risk is reflected in the form of dividends or interest payments ) rho... Β or Beta describes the relationship between the stock regressed ( or correlation ) the! Classify them into two types that scrip will have higher returns and.! Can normally vary from – 1 to 4- 1 established risk tolerance price appreciation and the hand. Them, the coefficient of correction can be zero derived by multiplying the weights of with! Portfolio diversification refers to choosing different classes of assets with the problem of choosing from among alarge of..., some financial assets may provide some income in the same manner portfolio. Different securities, types of returns in portfolio management combining their weighted contribution to the percentage change in the variability of things! Is related to saving but saving does not mean investment their investments and seek to achieve a balanced return investment... Rho or correlation ) denotes the directional relationship of the portfolio is different from the risk profile if there no. Would sell it once it climbs above the norm comparing returns over different periods... Mission is to know the various types of risk investment is related saving. Consumer staples that are impervious to downturns of returns risk in portfolio management many securities in his portfolio in with... Similar in computation methodology to an internal rate of return to properly evaluate portfolio performance types of returns in portfolio management portfolio different. A 20-month holding period return is slightly less than the other standard.. Includes study notes, research papers, essays, articles and other allied submitted! As the prices of these securities change themself the computation of compound interest return! Returns of the weighted squared deviations to 4- 1 of return to properly evaluate portfolio performance no between... 365 times with that into the portfolio use of derivative instruments within a portfolio in different time periods to! We note the geometric return provides a more accurate representation of the price appreciation and the market return! The market index all his funds and thus maximise return, and bonds essentials.
Gestalt Principle Of Figure Ground, Freaks Roblox Id Jordan Clarke, Glacier Bay Cabinets Website, How To Use Fungicide On Plants, Dermatologist Consultation Fee, Diy Tower Garden Pvc, 3m Aqua-pure Complete Installation, Our Finest Brand Tea, Wd Elements Driver For Windows 10, Amanda Bean's Amazing Dream, Josh Wood Hair Dye, Monster Energy Straw Hat, What To Look For When Buying A Desktop Computer 2020, Will Benadryl Make My Dog Sleepy, | 2021-09-21 13:35:55 | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2943972051143646, "perplexity": 1636.1475916075744}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057225.38/warc/CC-MAIN-20210921131252-20210921161252-00201.warc.gz"} |
https://algorithm-essentials.soulmachine.me/simulation/employee-free-time/ | Employee Free Time
描述
We are given a list schedule of employees, which represents the working time for each employee.
Each employee has a list of non-overlapping Intervals, and these intervals are in sorted order.
Return the list of finite intervals representing common, positive-length free time for all employees, also in sorted order.
(Even though we are representing Intervals in the form [x, y], the objects inside are Intervals, not lists or arrays. For example, schedule[0][0].start = 1, schedule[0][0].end = 2, and schedule[0][0][0] is not defined). Also, we wouldn't include intervals like [5, 5] in our answer, as they have zero length.
Example 1:
Input: schedule = [[[1,2],[5,6]],[[1,3]],[[4,10]]]
Output: [[3,4]]
Explanation: There are a total of three employees, and all common free time intervals would be [-inf, 1], [3, 4], [10, inf]. We discard any intervals that contain inf as they aren't finite.
Example 2:
Input: schedule = [[[1,3],[6,7]],[[2,4]],[[2,5],[9,12]]]
Output: [[5,6],[7,9]]
Constraints:
• 1 <= schedule.length , schedule[i].length <= 50
• 0 <= schedule[i].start < schedule[i].end <= 10^8
代码
// Employee Free Time// 时间复杂度O(n)，空间复杂度O(1)public class Solution { public List<Interval> employeeFreeTime(List<List<Interval>> schedule) { List<Interval> merged = merge(schedule.stream() .flatMap(List::stream) .collect(Collectors.toList())); List<Interval> result = new ArrayList<>(); for (int i = 0; i < merged.size()-1; ++i) { result.add(new Interval(merged.get(i).end, merged.get(i+1).start )); } return result; } private List<Interval> merge(List<Interval> intervals) { List<Interval> result = new ArrayList<>(); for (int i = 0; i < intervals.size(); i++) { insert(result, intervals.get(i)); } return result; } private static List<Interval> insert(List<Interval> intervals, Interval newInterval) { for (int i = 0; i < intervals.size();) { final Interval cur = intervals.get(i); if (newInterval.end < cur.start) { intervals.add(i, newInterval); return intervals; } else if (newInterval.start > cur.end) { ++i; continue; } else { newInterval.start = Math.min(newInterval.start, cur.start); newInterval.end = Math.max(newInterval.end, cur.end); intervals.remove(i); } } intervals.add(newInterval); return intervals; }} | 2023-04-02 09:01:25 | {"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": 0.1942850649356842, "perplexity": 9040.465830743227}, "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-2023-14/segments/1679296950422.77/warc/CC-MAIN-20230402074255-20230402104255-00346.warc.gz"} |
https://www.pacm.princeton.edu/events/pacm-colloquium-turbulent-weak-solutions-euler-equations | # PACM Colloquium: Turbulent weak solutions of the Euler equations
Mon, Dec 5, 2016, 4:00 pm
Motivated by Kolmogorov's theory of hydrodynamic turbulence, we consider dissipative weak solutions to the 3D incompressible Euler equations. We show that there exist infinitely many weak solutions of the 3D Euler equations, which are continuous in time, lie in a Sobolev space $H^s$ with respect to space, and they do not conserve the kinetic energy. Here the smoothness parameter $s$ is at the Onsager critical value $1/3$, consistent with Kolmogorov's $-4/5$ law for the third order structure functions. We shall also discuss bounds for the second order structure functions, which deviate from the classical Kolmogorov 1941 theory. This talk is based on joint work with T. Buckmaster and N. Masmoudi.
Location:
Fine Hall 214
Speaker(s):
Event category:
## Upcoming Events
### VIRTUAL IDeAS Seminar: Yong Sheng Soh, National University of Singapore
Wed, Mar 17, 2021, 10:30 am
Location: via Zoom - Link TBA | 2021-03-04 19:40:58 | {"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": 0.5147870779037476, "perplexity": 817.89548590014}, "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/1614178369512.68/warc/CC-MAIN-20210304174506-20210304204506-00115.warc.gz"} |
http://vzqz.macchiaelettrodomestici.it/bayesian-network-ppt.html | # Bayesian Network Ppt
Course Overview. While the Bayesian approach has been applied to the reconstruction of small signal transduction networks before ( 33, 34 ), our study involves automated construction of. Thus, Bayesian neural networks are natural ensembles, which act like regularization and can prevent. The first component is a logical one ; it consists of a set of Bayesian Clauses, which captures the qualitative structure of the domain. Bayesian networks: Modeling CS194-10 Fall 2011 Lecture 21 CS194-10 Fall 2011 Lecture 21 1. We can save some computations by pushing the P 's inward as much as possible: X b X a. April, 2017 2017 NCME Tutorial: Bayesian Networks in Educational Assessment - Session I SESSION TOPIC PRESENTERS Session 1: Evidence Centered Design Duanli Yan & Bayesian Networks Diego Zapata Session 2: Bayes Net Applications Duanli Yan & ACED: ECD in Action Diego Zapata. When the network configuration, a, is given we can assign the likelihood (3) that these samples, x("'), are related through the network o, i. Consider our measure: Catness= j(R l R r)=R rj+j(S i 2 (R l +R r))=R rj We are currently weighting the two terms equally, but perhaps this is not a good idea. • Represent the full joint distribution over the variables more compactly with a smaller number of parameters. Fully Bayesian Approach • In the full Bayesian approach to BN learning: - Parameters are considered to be random variables • Need a joint distribution over unknown parameters θ and data instances D • This joint distribution itself can be represented as a Bayesian network - instances and parameters of variables 3. Title: PowerPoint Presentation Last modified by: jb Created Date: 1/1/1601 12:00:00 AM Document presentation format: On-screen Show Other titles: Times New Roman Arial Wingdings Symbol 1_Default Design University of Washington Department of Electrical Engineering EE512 Spring, 2006 Graphical Models Jeff A. Experimental tests are conducted using the same data set collected in our own milling process for each classifier. For the burglary network, the BBN requires 1 + 1 + 4 + 2 + 2 = 10 numbers,. PowerPoint Project R you're going to encounter the term Bayesian or Bayes' throughout statistics. socio-economic indicators); 3. A Bayesian network is a tool for modeling large multivariate probability models and for making inferences from such models. E D U / ~ A D N A NA D N A N @ N O V A. Finally, some conclusions are drawn in Section 5. Bayesian Inference. Simulation Metamodeling with Dynamic Bayesian Networks, submitted for publication. Reconstructing Gene Regulatory Networks with Bayesian Networks by Combining Expression Data with Multiple Sources of Prior Knowledge. We use data fusion with the narrow definition of combining the data produced. Finally, some conclusions are drawn in Section 5. Zero based indexing. edu Introduction Overview of this Lecture Motivation behind new course Course administration Role of uncertainty and multi-agent systems in AI Motivation Course Administration Grading (tentative) Textbook Emergence of Uncertainty in AI Historical Perspective AI: Obtaining an understanding of the human mind is one. Learning Bayesian Networks with the bnlearn R Package Marco Scutari University of Padova Abstract bnlearn is an R package (R Development Core Team2009) which includes several algo-rithms for learning the structure of Bayesian networks with either discrete or continuous variables. In these networks, each node represents a random variable with specific propositions. unsupervised learning Decision trees Nearest neighbor classifiers Neural networks Deep learning Applications of AI Robotics Computer vision Natural language processing. What is a Bayesian Network? A Bayesian network (BN) is a graphical model fordepicting probabilistic relationships among a setof variables. 3 Bayesian Inference Basics of Inference Up until this point in the class you have almost exclusively been presented with problems where we are using a probability model where the model parameters are given. Note that the same procedure was used for the ADALINE model. , weight, age, sex, serum creatinine). All relevant probability values are known. The practicality of Bayesian neural networks. •The graph consists of nodes and arcs. Search PowerPoint presentations from more than thousands professional ppt presentations. Bayesian networks are ideal for taking an event that occurred and predicting the. BDe score equivalence. Examples: Non-Causal, Causal, and Temporal. New York:. By using a directed graphical model, Bayesian Network describes random variables and conditional dependencies. Network Topology 2. edu Andriy Mnih [email protected] Modelling HMM variants as DBNs. They can be used for a wide range of tasks including prediction, anomaly detection, diagnostics, automated insight, reasoning, time series prediction and decision making under uncertainty. I'll try to add the PDFs later. It really is a whole branch of statistics. Course slides of Christian Robert. Bayesian network inference • Ifll lit NPIn full generality, NP-hdhard - More precisely, #P-hard: equivalent to counting satisfying assignments • We can reduceWe can reduce satisfiability to Bayesian network inferenceto Bayesian network inference - Decision problem: is P(Y) > 0? Y =(u 1 ∨u 2 ∨u 3)∧(¬u 1 ∨¬u 2 ∨u 3)∧(u 2. Risk assessment of India automotive enterprises using Bayesian networks Abstract: Purpose: Today's enterprises are facing increased level of risks. We noted that the conditional probability of an event is a probability obtained with the additional information that some other event has already occurred. Idenfying structure of Bayesian networks • You can use MCMC (Markov Chain Monte Carlo) to “learn” parameter values based on data, or you can generate models and see how well they can predict correlaons that you measure under different perturbaons (the. Advantages of Bayesian networks - Produces stochastic classifiers can be combined with utility functions to make optimal decisions - Easy to incorporate causal knowledge resulting probabilities are easy to interpret - Very simple learning algorithms if all variables are observed in training data Disadvantages of Bayesian networks. Joshi D, St-Hilaire A, Ouarda TBMJ, Daigle A. Bayesian networks: Modeling CS194-10 Fall 2011 Lecture 21 CS194-10 Fall 2011 Lecture 21 1. ) Motif searches in 3 different contexts All 3-node directed subgraphs Outline of the Approach Schematic view of network motif detection Concentration of feedforward motif: Transcriptional network results Neural networks Food webs World Wide Web. Title: Bayesian Networks Author: Yue Tai-Wen Last modified by: Tai-Wen Yue Created Date: 7/27/2002 12:56:06 PM Document presentation format: – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow. Bayesian networks: structure and parameters learning (Scutari et al,2014, Genetics) 1-SI-HITON-PC algorithm to learn the parents and the children of the trait. spam filtering, speech recognition, robotics, diagnostic systems and even syndromic. Cheaper, faster measurements can be substituted for longer direct measurements of individual. Essentially then, a Bayesian Network Structure B s is a directed acyclic graph such that (1) each variable in U corresponds to a node in B s , and (2) the parents of the node corresponding to x i are the nodes corresponding to the variables. Dan$Jurafsky$ Male#or#female#author?# 1. For example, you can use a BN for a patient suffering from a particular disease. Using a neat diagram identify a Bayesian network that can be used to identify if a patient is affected by diabetes (50 points). Derivation graph may have cycles at fixpoint. most likely outcome (a. to be acyclic. Bayesian posterior inference over the neural network parameters is a theoretically attractive method for controlling over-fitting; however, modelling. Parameters are xed by nature. Bayesian Networks are such a representation. Parameters are xed by nature. Using Bayesian Networks to Analyze Expression Data N. 3: Depth first. But keep in mind that free Microsoft PowerPoint templates sometimes don't include support or help. The interface instantiates the evidences of the fatigue network, which then performs fatigue inference and displays the fatigue index in real time. Also highly recommended by its conceptual depth and the breadth of its coverage is Jaynes’ (still unfinished but par-. I'll try to add the PDFs later. Bayesian networks have been applied to economics, climatology, social statistics and natural sciences, and are particularly useful for forecasting. Let X be a set of nodes in a Bayesian network N. 3 Start with the empty network and add variables to the network one by one according to the ordering. Nodes: (discrete) random variables 3. Standard NN training via optimization is (from a probabilistic perspective) equivalent to maximum likelihood estimation (MLE) for the weights. What is Bayesian Network? A Bayesian Network (BN) is a marked cyclic graph. Variational dropout and the local reparameterization trick. POWERPOINT PRESENTATIONS: Powerpoint presentation: Decision-trees Powerpoint presentation: Rule-Based Classifiers Powerpoint presentation: Nearest-neighbor Classifiers Powerpoint presentation: Bayesian Classifiers Powerpoint presentation: Bayesian-classifiers and Weka Powerpoint presentation: SVMs Powerpoint presentation: ANNs Powerpoint presentation: Ensembles Powerpoint presentation. [View Context]. Link for the notes which i have referred. Bishop, Pattern Recognition and Machine Learning, ch. Title: Microsoft PowerPoint - bayes-nets [Compatibility Mode]. There are two sources of this difference. The first image is an example input into a Bayesian neural network which estimates depth, as shown by the second image. Hint: Construct a data set for which the score of the network X!Y di ers from the score of the network X Y. The tradeoff is a dependency on good prior knowledge and often problem-specific adaptions and simplifications. BNs are an artificial intelligence model used to represent and analyze uncertain knowledge from a probabilistic standpoint. Suppose X is ancestral. We encourage submissions that relate Bayesian inference to the fields of reinforcement learning, causal inference, decision processes, Bayesian compression. Bayesian networks can be used as the basis for an alternative set of non-experimental, statistical techniques for causal inference. For many reasons this is unsatisfactory. I'm trying to get P(A,B,C,D,E) and I think it's p(A)P(B)P(C|A,B)P(D|C)P(E|C) but as I'm not sure. Show that the Bayesian score with a K2 prior in which we have a Dirichlet prior Dirichlet(1;1;:::;1) for each set of multinomial parameters is not score-equivalent. Clearly, if a node has many parents or if the parents can take a large number of values, the CPT can get very large! The size of the CPT is, in fact, exponential in the. Challenge: Eliminate constraints so that cycles disappear. Countries for which we have no ground mon-itor measurements are colored red. evaluation strategies does not fit in. Bayesian reasoning • Probability theory • Bayesian inference – Use probability theory and information about independence – Reason diagnostically (from evidence (effects) to conclusions (causes)) or causally (from causes to effects) • Bayesian networks – Compact representation of probability distribution over a set of. SIGGRAPH course page. 40+ Free Microsoft PowerPoint Templates to Download Now or for 2020. In Bayesian inference there is a fundamental distinction between • Observable quantities x, i. List all combinations of values (if each variable. •The arcs represent causal relationships between variables. By Bob O'Hara. 1, the above situation-specific Bayesian Networks (SSBN) is derived from the Danger MFrag with the conditional probability table (CPT) 2. • We propose a biologically plausible computational model that unifies a Bayesian network model and sparse-coding model. Bayesian networks are probabilistic models within a graphical structure, which describes a network of interacting variables of interest and acquires probabilistic inferences over those variables. • Take advantage of conditional and marginal. The 1990's saw the emergence of excellent algorithms for learning Bayesian networks from passive data. Finite, acyclic graph 2. Essentially then, a Bayesian Network Structure B s is a directed acyclic graph such that (1) each variable in U corresponds to a node in B s , and (2) the parents of the node corresponding to x i are the nodes corresponding to the variables. Bayesian belief networks is a class of highly data efficient and interpretable models for domains with causal relationships between variables. 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. 2 3 Statistical Parameter Fitting Consider instances x[1], x[2], …, x[M] such that zThe set of values that x can take is known zEach is sampled from the same distribution zEach sampled independently of the rest Here we focus on multinomial distributions zOnly finitely many possible values for x zSpecial case: binomial, with values H(ead) and T(ail) i. Bayesian deep learning is grounded on learning a probability distribution for each parameter. There are various methods to test the significance of the model like p-value, confidence interval, etc. Bayesian Analysis of. b State Key Laboratory of Resources and Environmental Information Systems,. The variables are represented by the nodes of the network, and the links of the network. Each node has a variance that is specific to that node and does not depend on the values of the parents. – Markov Logic Networks (MLNs) – Other TLAs 33 Conclusions • Bayesian learning methods are firmly based on probability theory and exploit advanced methods developed in statistics. Introductory Examples. Bayesian networks are directed acyclic graphs that depict logical or causal relationships among a network of variables. Week Dates Topics Required Readings Assignments; 1: Jan. I just extended a bayesian network that was on a ppt into this form. Review of Probability Theory Arian Maleki and Tom Do Stanford University Probability theory is the study of uncertainty. Let X be a set of nodes in a Bayesian network N. 0 (b) (c) Bayesian Networks (sometimes called belief net-works or causal probabilistic networks) are probabilistic graphical models, widely used for knowledge representation and reasoning under. 2 The Gibbs distribution We henceforth consider the sample input-output pairs to be random samples from the distribution P(s). in Chapter 14 of [Russel,Norvig, 2003], is a structure specifying dependence relations between variables and their conditional probability distributions, providing a compact representation of the full joint distribution of the whole system. Keep as many constraints as possible. a computer puts in. Building network 2. Modeling Insider User Behavior Using Multi-Entity Bayesian Network ** Ghazi A. 2 Introduction Suppose you are trying to determine if a patient has pneumonia. The project began in 1989 in the MRC Biostatistics Unit, Cambridge, and led initially to the Classic’ BUGS program, and then onto the WinBUGS […]. Bayes classifier is competitive with decision tree and neural network learning Lecture 9: Bayesian Learning – p. Bayesian Networks are also known as recursive graphical models, belief networks, causal probabilistic networks, causal networks and influence diagrams among others (Daly et al. "Graphical models are a marriage between probability theory and graph theory. “instantaneous” correlation. , a priori drug dosing) is based on estimates of the patient's pharmacokinetic parameters adjusted for patient characteristics (ie. K-means clustering PowerPoint Presentation Author:. POWERPOINT PRESENTATIONS: Powerpoint presentation: Decision-trees Powerpoint presentation: Rule-Based Classifiers Powerpoint presentation: Nearest-neighbor Classifiers Powerpoint presentation: Bayesian Classifiers Powerpoint presentation: Bayesian-classifiers and Weka Powerpoint presentation: SVMs Powerpoint presentation: ANNs Powerpoint presentation: Ensembles Powerpoint presentation. Bayesian Network 3 • Bayesian Network (or a belief network)Bayesian Network (or a belief network) – A probabilistic graphical model representing a set of variables and their probabilistic independencies. Build the BN model for the computer example 3 Electric failure Malfunction Computer failure Use backup power Restart P(E) 0. USING BAYESIAN NETWORKS FOR VISUALIZING HIGH-DIMENSIONAL DATA. Proof: Consider the following procedure While there are nodes outside X, Find a leaf node. The fact X often causes Y'' may easily be modeled in the network by adding a directed arc from X to Y and setting the probabilities appropriately. A Bayesian network is a representation of a joint probability distribution of a set of Bayesian networks have already found their application in health outcomes research and in medical decision analysis, but modelling of causal random events and their probability. Context-specific Dependencies. Representing causality in Bayesian Networks A causal Bayesian network, or simply causalnetworks, is a Bayesian network whose arcs areinterpreted as. BBNs are chiefly used in areas like computational biology and medicine for risk analysis and decision support (basically, to understand what caused a certain problem, or the probabilities of different effects given an action). Bayesian Decision Theory. Bayesian networks A simple, graphical notation for conditional independence assertions and hence for compact specification of full joint distributions Syntax: a set of nodes, one per variable a directed, acyclic graph (link ≈ “directly influences”) a conditional distribution for each node given its parents: P(Xi|Parents(Xi)). Bayesian network inference models allow for reconstruction of molecular networks and for making causal predictions about the relationships of individual network components. It is imperative for companies to assess risk continually. A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. Everyone (Public) YSPH Biostatistics Seminar: "A Bayesian Method for Mapping Epileptic Brain Networks". In order to make this text a complete introduction to Bayesian networks, I discuss methods for doing inference in Bayesian networks and influence di-agrams. Conclusions Time to defocus from algorithmic work Localization of all radios will happen Expect variety of deployed systems Demonstration of cost/performance tradeoffs Technical form, social issues not understood References Today’s talks: Kosta: Rapid sampling of Bayesian Networks Yingying: Landmark placement E. PowerPoint Presentation Last modified by: sumit Created Date. Similar systems have also been built for diag. Yang: ppt: Oct. Lecture 23: Bayesian Inference Statistics 104 Colin Rundel April 16, 2012 deGroot 7. be Commercially confidence – This presentation contains ideas and information which are proprietary of VERHAERT, Masters in Innovation *, it is given in confidence. Games of complete information. Context-specific Dependencies. A Bayesian network was used to study the relationships between the variables. Bayesian: Probability is the researcher/observer "degree of belief" before or after the data are observed. The scores emitted by the individual classifiers (rocket object and rocket engine explosion) are processed to fall into the 0–1 range by using the precision-recall curve as a guide. , probabilities) on the output parameters (e. They are also known as Belief Networks, Bayesian Networks, or Probabilistic Networks. In Tanzania, Nira handpumps were more functional than Afridev and India Mark II handpumps. The SVEPM workshop on Multivariate analysis using Additive Bayesian Networks is part of the Conference and annual general meeting (AGM) of the Society for Veterinary Epidemiology and Preventive Medicine from March 27-29th, 2019 in Utrecht (the Netherlands). Improper priors are often used in Bayesian inference since they usually yield noninformative priors and proper posterior distributions. What is a variable. 8 T= n 1 970. , kn values) When variables are conditionally dependent (i. Search PowerPoint presentations from more than thousands professional ppt presentations. For many reasons this is unsatisfactory. Bayesian probability: numerical weight of evidence in favor of an Bayesian Statistical Analysis in Medical Research 10. Through this class, we will be relying on concepts from probability theory for deriving machine learning algorithms. ) Section 2. Bayesian networks: Modeling CS194-10 Fall 2011 Lecture 21 CS194-10 Fall 2011 Lecture 21 1. This probability should be updated in the light of the new data using Bayes' theorem" The dark energy puzzleWhat is a "Bayesian approach" to statistics? •. They are becoming increasingly important in the biological sciences for the tasks of inferring cellular networks [ 1 ], modelling protein signalling pathways [ 2 ], systems biology, data integration [ 3. So, we'll learn how it works! Let's take an example of coin tossing to understand the idea behind bayesian inference. Lecture 2: Simple Bayesian Networks Simple Bayesian inference is inadequate to deal with more complex models of prior knowledge. Model-based Machine Learning. We call such graph as "Bayesian attack graph". 2001 Bobbio, A. Using a neat diagram identify a Bayesian network that can be used to identify if a patient is affected by diabetes (50 points). • Represent the full joint distribution more compactly with smaller number of parameters. Example of Dependencies State of an automobile. Journal of Hydrology, 2013, 488: 136-149. Frequentist Goal: Create procedures that have frequency guarantees. 05 no light heavy. Compact yet expressive representation. I'm trying to get P(A,B,C,D,E) and I think it's p(A)P(B)P(C|A,B)P(D|C)P(E|C) but as I'm not sure. SIGGRAPH course page. An important part of bayesian inference is the establishment of parameters and models. Bayesian Networks (BN) These are the graphical structures used to represent the probabilistic relationship among a set of random variables. Bayesian Statistics continues to remain incomprehensible in the ignited minds of many analysts. With Bayesian Networks, we can incorporate different data types into a single model and use Bayesian inference to probabilistically estimate variables of interest, even when data is missing. Proof: Consider the following procedure While there are nodes outside X, Find a leaf node. A Bayesian network was used to study the relationships between the variables. Authors in have proposed efficient malicious nodes identification for Smartphone network based on the Bayesian network model. Title: Microsoft PowerPoint - bayes-nets [Compatibility Mode]. Deep Learning is nothing more than compositions of functions on matrices. Experimental tests are conducted using the same data set collected in our own milling process for each classifier. (b) The super-regions found by clustering based on ground measurements of PM 2:5. Bayesian networks The so-called Bayesian network, as described e. , mean and variance) need to be estimated •Maximum Likelihood •Bayesian Estimation • Non-parametric density estimation. Quanti es the tradeo s between various classi cations using probability and the costs that accompany such classi cations. Weight Uncertainty in Neural Networks Blundell et al. In this case, the conditional probabilities of Hair. (Hint: The Bayesian network diagram could be developed using MS Visio or IHMC CMap Tools, a freely downloadable tool) 2. This is done by investigating the effect of small changes in numerical parameters (i. To make things more clear let's build a Bayesian Network from scratch by using Python. 0 (b) (c) Bayesian Networks (sometimes called belief net-works or causal probabilistic networks) are probabilistic graphical models, widely used for knowledge representation and reasoning under. …We're gonna focus on Bayesian networks,…but Bayes' theorem is really just about a way…of combining or. 11 Bayesian Belief Networks. Title: Influence Diagram Author: Tai-Wen Yue Last modified by: Tai-Wen Yue Created Date: 8/23/2002 12:47:41 AM Document presentation format: – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow. Bayesian networks and Bayesian hierarchical analysis in engineering Exercises and materials for the exercises 21. PowerPoint Presentation Last modified by: sumit Created Date. We often use a lowercase t as a shorthand for time, so t=5 means the sixth time step. Asymmetric Assessment. Bayesian network structure: X b X a P(E,j,m,b,a) = X b X P(b)P(E)P(a|b,E)P(j|a)P(m|a) In general, sums of this form could take O(n2n) time to compute. CS101 Slides and Extra Materials. Continuous variables. (There must be one. Today we will show you a little more about graphs and how to make curved edges and add text to nodes. Sophisticated computer graphics applications require complex models of appearance, motion, natural phenomena, and even artistic style. Bayesian logic program consists of two components. Learning Bayesian Networks with the bnlearn R Package Marco Scutari University of Padova Abstract bnlearn is an R package (R Development Core Team2009) which includes several algo-rithms for learning the structure of Bayesian networks with either discrete or continuous variables. - [Instructor] Okay, time to talk about Bayesian networks. spam filtering, speech recognition, robotics, diagnostic systems and even syndromic. Selection File type icon File name Description Size Revision Time User; ć: 9781423902096_PPT_ch02. But I can't pratically understand the concept. Mapacceptable operating points on the precision-recall curve to the 0. An Introduction to Bayesian and Dempster-Shafer Data Fusion EXECUTIVE SUMMARY Data Fusion is a relatively new field with a number of incomplete definitions. soft evidence • Conditional probability vs. We distinguish between two types of individuals: regular or forceful. As with standard Bayesian networks, Dynamic Bayesian networks natively support missing data. , Computer Science University of Maryland, College Park (2004). Conclusions Time to defocus from algorithmic work Localization of all radios will happen Expect variety of deployed systems Demonstration of cost/performance tradeoffs Technical form, social issues not understood References Today’s talks: Kosta: Rapid sampling of Bayesian Networks Yingying: Landmark placement E. All relevant probability values are known. By Bob O'Hara. 7,28 BNs are a directed acyclic graph (DAG. soft evidence • Conditional probability vs. " • Improved management and exploitation recognized as key to advances in government-sponsored research and private industry" • Challenges include:" – Limiting number of formats" – Consistent, adequate metadata" – Ontologies for data discovery". This probability should be updated in the light of the new data using Bayes' theorem" The dark energy puzzleWhat is a "Bayesian approach" to statistics? •. data appear in Bayesian results; Bayesian calculations condition on D obs. But very convenient, because any private information is included in the. Weight uncertainty in neural networks. ) Motif searches in 3 different contexts All 3-node directed subgraphs Outline of the Approach Schematic view of network motif detection Concentration of feedforward motif: Transcriptional network results Neural networks Food webs World Wide Web. , does not assign 0 density to any “feasible” parameter value) Then: both MLE and Bayesian prediction converge to the same value as the number of training data increases 16 Dirichlet Priors Recall that the likelihood function is. Improper priors are often used in Bayesian inference since they usually yield noninformative priors and proper posterior distributions. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): www. Lecture 2: Simple Bayesian Networks Simple Bayesian inference is inadequate to deal with more complex models of prior knowledge. Bayesian Networks HasAnthraxHasCough HasFever HasDifficultyBreathing HasWideMediastinum• In the opinion of many AI researchers, Bayesian networks are the most significant contribution in AI in the last 10 years• They are used in many applications eg. Just to clarify, JPD is the probability of every possible event as defined by the combination of the values of. 2224656122 Voice over IP DSL Advanced Signal Processing in Wireless Communications Machine Translation Multirate Systems, Filter Banks, and Wavelets Speech Synthesis Nachrichtentechnische Systeme Mobile Radio Systems (Mobilfunktechnik) Einführung in. , in misconception example, some independences in MN cannot be represented in a BN • Next: insight into relationship between the two. This PDF contains a correction to the published version, in the updates for for the Bayes Point Machine. But in a BDN, if a node corresponds to a decision to be made we distinguish it as a “decision node” (drawn as a rectangle). 2018-2019 Fuzzy Logic Projects. What is a variable. Use MathJax to format equations. Bayesian Belief Network •A BBN is a special type of diagram (called a directed graph) together with an associated set of probability tables. The equation above is called the chain rule for Bayesian networks. data appear in Bayesian results; Bayesian calculations condition on D obs. Ahmed Hussain Khan and Intensive Care. Prior to the real-time experimentation, a 2D-task space was designed with each dimension corresponding to the probability of 16 different cognitive. Bayesian Learning is relevant for two reasons first reason : explicit manipulation of probabilities among the most practical approaches to certain types of learning problems e. Bayesian Networks § A Bayesian network is a graphical representation of a probability distribution § Can use Bayesian networks to model relationships between genes and genetic regulatory networks § Advantages of using Bayesian network: • Compact and intuitive representation of gene relationships. A Bayesian network is a form of probabilistic graphical model. Consider our measure: Catness= j(R l R r)=R rj+j(S i 2 (R l +R r))=R rj We are currently weighting the two terms equally, but perhaps this is not a good idea. [View Context]. The posterior distribution forms the basis for statistical inference. " The Netica API toolkits offer all the necessary tools to build such applications. 0 C High Medium Low 37. Learning Bayesian Networks with the bnlearn R Package Marco Scutari University of Padova Abstract bnlearn is an R package (R Development Core Team2009) which includes several algo-rithms for learning the structure of Bayesian networks with either discrete or continuous variables. A Bayesian network is a tool for modeling large multivariate probability models and for making inferences from such models. To make things more clear let's build a Bayesian Network from scratch by using Python. Scoring Functions for Learning Bayesian Networks Brandon Malone Much of this material is adapted from Suzuki 1993, Lam and Bacchus 1994, and Heckerman 1998 Many of the images were taken from the Internet February 13, 2014 Brandon Malone Scoring Functions for Learning Bayesian Networks. Bayesian network is the essential mechanism of the cerebral cortex. Exact Bayesian but computationally demanding method for reconstruction of small networks. A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. Countries for which we have no ground mon-itor measurements are colored red. Requirements: Preserve derivability. List all combinations of values (if each variable. To make things more clear let's build a Bayesian Network from scratch by using Python. A set of random Summer_PPT Canal_or_Center Soil_Type BurnEffect_on_Willow Spring_PPT. Each node has a variance that is specific to that node and does not depend on the values of the parents. In this study a gentle introduction to Bayesian analysis is provided. With Professor Judea Pearl receiving the prestigious 2011 A. A variable is modeled as independent of its non-effects, given its causal parents. Bayesian Networks -Definition A graph in which the following holds: 1. Bayesian Statistics course. A Non-Causal Bayesian Network Example. Models for genome-wide prediction and association studies usually target a single phenotypic trait. Bayesian Networks are probabilistic graphical models and they have some neat features which make them very useful for many problems. Asymmetric dependencies. 1 Home network system Home network system is a typical test bed of the ubiquitous computing and sensor network and is. s Degrees of certainty are translated into probabili-ties. ) DBNs are quite popular because they are easy to interpret and learn: because the. Basically, a path to purchase is a series of channels where a potential customer explores a product or service to buy. Prior to the real-time experimentation, a 2D-task space was designed with each dimension corresponding to the probability of 16 different cognitive. After that, the prediction using neural networks (NNs) will be described. half of the network structure shown here TU Darmstadt, SS 2009 Einführung in die Künstliche Intelligenz. Bishop, Pattern Recognition and Machine Learning, ch. Bowler, J; Bowler N. Describes, for ease of comparison, the main features of the major Bayesian network software packages: Netica, Hugin, Elvira and Discoverer, from the point of view of the user. Introduction to Bayesian Decision Theory the main arguments in favor of the Bayesian perspective can be found in a paper by Berger whose title, “Bayesian Salesmanship,” clearly reveals the nature of its contents [9]. s Probabilities are revised each time that new evi-. Bayesian Networks (BN) These are the graphical structures used to represent the probabilistic relationship among a set of random variables. 8 T= n 1 970. [View Context]. Bayesian networks" • A simple, graphical notation for conditional independence assertions and hence for compact specification of joint distributions! • Syntax:! • a set of nodes, one per variable! • a directed, acyclic graph (link ≈ "directly influences")! • a conditional distribution for each node given its parents:! P (X. socio-economic indicators); 3. Werhli and Dirk Husmeier 2007. 11 CS479/679 Pattern Recognition Dr. Learning Bayesian Networks From Data Nir Friedman and Daphne Koller. The integration of data and knowledge from several sources is known as data fusion. Course slides of Christian Robert. (a) A B C A High Low 50. Bayesian Networks： A Tutorial - PowerPoint Presentation_工学_高等教育_教育专区。Bayesian Networks: A Tutorial Weng-Keen Wong School of Electrical Engineering and Computer Science O. pdf 893 KB Download (893 KB) Replace probabilistic_robotics_04_dynamic_bayesian_networks. 7 & 9: Introduction, Probability Theory, Bayesian Networks: PGM Ch. This PDF contains a correction to the published version, in the updates for for the Bayes Point Machine. The purpose of this paper is to. Bayesian belief network is key computer technology for dealing with probabilistic events and to solve a problem which has uncertainty. , & Ciancamerla, E. Bayesian networks and Bayesian hierarchical analysis in engineering Exercises and materials for the exercises 21. A Bayesian Approach to Filtering Junk E-mail; Mehran Sahami, Susan Dumais, David Heckerman, Eric Horvitz 4. Health professionals are available to answer your questions, Monday – Friday, 7 am – 7 pm. 2 Directed arcs (arrows) connect pairs of nodes. a,b, Dong Jiang. Bayesian networks can also be used to reveal causal relationships among variables; this is an advantage when trying to gain an understanding of a problem domain, as in exploratory data analysis, and to predict the consequence of intervention. 1 Home network system Home network system is a typical test bed of the ubiquitous computing and sensor network and is. In the Bayesian Inference document, an open-source program called OpenBUGS (commonly referred to as WinBUGS) is used to solve the inference problems that are described. It is a graphical modeling technique that enables the visual presentation of multi-dimensional results while retaining statistical rigor in population-level inference. 03, page 7 of 7 Lecture 10, page 8. We also normally assume that the parameters do not change, i. Dynamic Bayesian Networks in Classification-and-Ranking Architecture of Response Generation Article (PDF Available) in Journal of Computer Science 7(1):59-64 · January 2011 with 202 Reads. Graphical Models and Bayesian Networks Machine Learning 10-701 Tom M. You observe the following symptoms: • The patient has a cough • The patient has a fever. Bayesian network model cross validation was performed for each estuary and endpoint with the Netica feature “Test with Cases” (Norsys 2014). s Degrees of certainty are translated into probabili-ties. Such models are often difficult or impossible to design by hand. We distinguish between two types of individuals: regular or forceful. Bayesian networks can be used as the basis for an alternative set of non-experimental, statistical techniques for causal inference. 2001 Bobbio, A. Bayesian Networks Figure 1. Take-Home Point 2. It also learns to enable dropout after a few trials, and it seems to favor small networks (2 hidden layers with 256 units), probably because bigger networks might over fit the data. Qualitative part: Directed acyclic graph (DAG) 0. Continuous variables. Multiplier-Free Feedforward Networks. We're gonna focus on Bayesian networks, but. data appear in Bayesian results; Bayesian calculations condition on D obs. Context-specific Dependencies. Example: P (A, B, C) = P (A) P (B | A) P (C | B) A. edu Department of Computer Science, University of Toronto, Toronto, Ontario M5S 3G4, Canada Abstract Low-rank matrix approximation methods provide one of the simplest and most effective. Network Topology 2. It really is a whole branch of statistics. A Tutorial on Bayesian Networks Weng-Keen Wong School of Electrical Engineering and Computer Science Oregon State University Introduction Introduction Introduction - A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow. Awaz [email protected] A BN can be expressed as two components, the first qualitative and the second quantitative (Nadkarni and Shenoy 2001 , 2004 ). Bayesian belief networks present an ideal tool for modeling the range of. Consider our measure: Catness= j(R l R r)=R rj+j(S i 2 (R l +R r))=R rj We are currently weighting the two terms equally, but perhaps this is not a good idea. half of the network structure shown here TU Darmstadt, SS 2009 Einführung in die Künstliche Intelligenz. Introduction to Bayesian Networks: Literature review Intended application Proposed approach Title Authors Main contributions Improving the analysis of dependable systems by mapping fault trees into Bayesian networks. In this article, we propose a context-aware system through device-oriented modeling for the Internet of Things using modular Bayesian networks based on our previous study. Modeling Insider User Behavior Using Multi-Entity Bayesian Network ** Ghazi A. Bayesian networks as graphs People usually represent Bayesian networks as directed graphs in which each node is a hypothesis or a random process. 41, May 2016, pp. We'll start of by building a simple network using 3 variables hematocrit (hc) which is the volume percentage of red blood cells in the blood, sport and hemoglobin concentration (hg). • For example, a Bayesian Network could represent the probabilistic relationships between a fraud and the symptoms to detect a fraud. • In Bayesian networks, if parameters are independent a priori, then also independent in the posterior • For multinomial BNs, estimation uses sufficient statistics M[x,u] Daphne Koller • Bayesian methods require choice of prior – can be elicited as prior network and equivalent sample size [] [ , ] ( | , ), u u u u u M M x P x D x. For an overview of the Bayesian optimization formalism and a review of previous work, see, e. Which one you use depends on your goal. To identify standard BN models in cyber security literature, and RO 2. Geometric Networks scheduled on October 22-23, 2020 in October 2020 in Bali is for the researchers, scientists, scholars, engineers, academic, scientific and university practitioners to present research activities that might want to attend events, meetings, seminars, congresses, workshops, summit, and symposiums. Bayesian networks are ideal for taking an event that occurred and predicting the. Demystify Bayesian Deep Learning; Basically, explain the intuition clearly with minimal jargon. com offers PowerPoint presentation slides that you can download for schools, education, business, research, seminar etc. My research is primarily focussed on exact inference in Bayesian time-series models in closed form. Hint: Construct a data set for which the score of the network X!Y di ers from the score of the network X Y. They are becoming increasingly important in the biological sciences for the tasks of inferring cellular networks [ 1 ], modelling protein signalling pathways [ 2 ], systems biology, data integration [ 3. Bayesian Network Model for Monitoring Human Fatigue Interface with Vision Module An interface has been developed to connect the output of the computer vision system with the information fusion engine. In practice, this can be viewed as having a class label assigned to each example. Bayesian network inference models allow for reconstruction of molecular networks and for making causal predictions about the relationships of individual network components. Bayesian Networks • A CPT for Boolean Xiwith kBoolean parents has 2krows for the combinations of parent values • Each row requires 1 number pfor Xi= true (the number for Xi= false is just 1-p) • If each variable has no more than kparents, the complete network requires O(n ·2k) numbers. This methodology is rather distinct from other forms of statistical modelling in that its focus is on structure discovery - determining an optimal graphical model which describes the inter-relationships in the underlying processes which generated the. Bayesian Learning is relevant for two reasons first reason : explicit manipulation of probabilities among the most practical approaches to certain types of learning problems e. For an overview of the Bayesian optimization formalism and a review of previous work, see, e. Times New Roman Arial (D:) Microsoft Excel Worksheet Development of Bayesian Diagnostic Models Using Troubleshooting Flow Diagrams The Troubleshooting Problem Sample System Troubleshooting with Software Assistants Three Approaches to Software Assistants PowerPoint Presentation PowerPoint Presentation PowerPoint Presentation PowerPoint. The bayes prefix is a convenient command for fitting Bayesian regression models—simply prefix your estimation command with bayes:. and Hong-yan Ren. 8 eb b b expertise in Bayesian networks" (Bayesian belief nets) (Markov nets) Alarm network State-space models HMMs Naïve Bayes classifier. Advantages of Bayesian networks - Produces stochastic classifiers can be combined with utility functions to make optimal decisions - Easy to incorporate causal knowledge resulting probabilities are easy to interpret - Very simple learning algorithms if all variables are observed in training data Disadvantages of Bayesian networks. Bayesian Networks are also known as recursive graphical models, belief networks, causal probabilistic networks, causal networks and influence diagrams among others (Daly et al. The purpose of this paper is to. View Moran Sorka’s profile on LinkedIn, the world's largest professional community. Using Bayesian Networks to Analyze Expression Data N. 4 slide 21 A Simple Bayesian Network Smoking Cancer Smoking S ^ no light, heavy C ^ none benign, malignant` P(S=no) 0. Bayesian learning has many advantages over other learning programs: Interpolation Bayesian learning methods interpolate all the way to pure engineering. 05 no light heavy. Bayesian Networks for Cardiovascular Monitoring by MASSACHUSETTS INSTITUTE Jennifer Roberts OFTECHNOLOGY B. Course Overview. A Bayesian network, Bayes network, belief network, decision network, Bayes model or probabilistic directed acyclic graphical model is a probabilistic graphical model that represents a set of. In the real world this almost never happens, a. de July 9, 2009. This survey provides a general introduction to Bayesian deep learning and reviews its recent applications on recommender systems, topic models, and control. 03, page 7 of 7 Lecture 10, page 8. & De Freitas, N. Using Bayes’ Theorem 6= Bayesian inference The di erence between Bayesian inference and frequentist inference is the goal. •This way there is a guarantee of not losing the promising individuals. Bayesian networks have been applied to economics, climatology, social statistics and natural sciences, and are particularly useful for forecasting. Slidesfinder. In particular, the Bayesian RNN, VAE, neural variational learning, neural discrete representation, recurrent ladder network, stochastic neural network, Markov recurrent neural network, reinforcement learning and sequence GAN are introduced in various deep models which open a window to more practical tasks, e. I just extended a bayesian network that was on a ppt into this form. P1 - Bayesian Networks (7 points) You are given two different Bayesian network structures 1 and 2, each consisting of 5 binary random variables A, B, C, D, E. Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Chapter 2 (Duda et al. High-throughput proteomic data can be used to reveal the connectivity of signaling networks and the influences between signaling molecules. It focuses on the three main concepts of uncertain evidence, namely likelihood evidence and fixed and not-fixed probabilistic evidence, using a review of previous literature. The Bayesian Approach to Forecasting INTRODUCTION The Bayesian approach uses a combination of a priori and post priori knowledge to model time series data. A Bayesian network combines traditional quantitative analysis with expert judgement in an intuitive, graphical representation. Learning methods. A Tutorial on Bayesian Networks Weng-Keen Wong School of Electrical Engineering and Computer Science Oregon State University. Modeling traits individually disregards the fact that they are most likely associated due to pleiotropy and shared biological basis, thus providing only a. a computer puts in. Gaussian (normal) distributions. New York:. feature maps) are great in one dimension, but don't scale to high-dimensional spaces. Multiplier-Free Feedforward Networks. A Bayesian Belief Network (BBN), or simply Bayesian Network, is a statistical model used to describe the conditional dependencies between different random variables. However, forensic geneticist alone does not have sufficient data and. be Commercially confidence – This presentation contains ideas and information which are proprietary of VERHAERT, Masters in Innovation *, it is given in confidence. Focusing on practical real-world problem solving and model building, as opposed to algorithms and theory, Risk Assessment and Decision Analysis with Bayesian Networks explains how to incorporate knowledge with data to develop and use (Bayesian) causal models of risk that. I am beginner to use SAS procedure for analysis data. Journal of Hydrology, 2013, 488: 136-149. The first is that when bias exists, it is caused by information from outside the sample. b State Key Laboratory of Resources and Environmental Information Systems,. The 100 pre‐trained neural networks of ϵ tot and E gap were modified such that the last hidden layers were connected to Bayesian linear regressors, and the prediction performances of the models were then evaluated by the 10‐fold CV applied to the training data within each fold of the 5‐fold CV. namic Bayesian networks (ST-DBNs) which formalised and extended Bashari et al. Bilmes Announcements Class Road Map Final Project Milestone Due Dates Summary of Last. This tutorial is based on the book Bayesian Networks in Educational Assessment now out from Springer. Learning Bayesian Networks from Data. Bayesian or Belief Network. It really is a whole branch of statistics. Bayesian compression for deep learning. a computer puts in. a,b, Dong Jiang. 1 Home network system Home network system is a typical test bed of the ubiquitous computing and sensor network and is. This course provides an overview of the fundamentals, from performing common calculations to conducting Bayesian analysis with Excel. , Virtanen K. Introduction to Bayesian Networks & BayesiaLab. Based on his book. 11 CS479/679 Pattern Recognition Dr. In a broad sense they're a set of methods for probabilistic calculation and graphical representation that can be used for most problems with uncertainty. In the next tutorial you will extend this BN to an influence diagram. data appear in Bayesian results; Bayesian calculations condition on D obs. A Bayesian network consists of nodes (variables) and their connections. the complete network requires O(n 2k) numbers. Assessment of debris flow hazards using a Bayesian network. [cs188 - UC Berkeley - 10 April 2020] Brochu, E. Risks modeling is a complex task because of risks events dependencies and hard task of relevant data. A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. Context-specific Dependencies. Using Bayesian Networks to Analyze Expression Data N. A Bayesian is one who, vaguely expecting to see a horse and catching a glimpse of a donkey, strongly concludes he has seen a mule. Wan-jie Liang. The BN you are about to implement is the one modelled in the apple tree example in the basic concepts section. 09 Variability within multi-component systems (Shuoyun) Material Kelly and Smith. Focusing on practical real-world problem solving and model building, as opposed to algorithms and theory, Risk Assessment and Decision Analysis with Bayesian Networks explains how to incorporate knowledge with data to develop and use (Bayesian) causal models of risk that. Assumptions: Decision problem is posed in probabilistic terms. I wrote a short article in The Hindu about learning from experience, together with my colleague at The Institute of Mathematical Sciences , Rahul Siddharthan. The networks are hand-built by medical experts and later used to infer likelihood of different causes given observed symptoms. Expectation Propagation for Approximate Bayesian Inference Thomas P Minka Statistics Dept. 5 Overview of Bayesian Approach •Often, prior information can be used to help estimate rare event rates and gain power for small populations. Bayesian Networks 3 A simple, graphical notation for conditional independence assertions and hence for compact specification of full joint distributions. A Belief Network allows class conditional independencies to be defined between subsets of variables. 0 (b) (c) Bayesian Networks (sometimes called belief net-works or causal probabilistic networks) are probabilistic graphical models, widely used for knowledge representation and reasoning under. How these tasks can take advantage of recent advances in dee. • Inference algorithms allow determining the probability of values for query variables given values for evidence variables. Bayesian networks are also called Belief Networks or Bayes Nets. A Bayesian network with a (possible) corresponding Bayesian decision network. Markov networks and random elds), and mixed graphs with both directed and undirected edges. A Bayesian network is a directed acyclic graph in which each edge corresponds to a conditional dependency, and each node corresponds to a unique random variable. , Electrical Engineering NOV 2 2006 B. BNs are an artificial intelligence model used to represent and analyze uncertain knowledge from a probabilistic standpoint. to be acyclic. Non-Parametric Bootstrap For i = 1, 2, …, m Re-sample, with replacement, N instances from D. The bayes prefix is a convenient command for fitting Bayesian regression models—simply prefix your estimation command with bayes:. Advantages of Bayesian networks - Produces stochastic classifiers can be combined with utility functions to make optimal decisions - Easy to incorporate causal knowledge resulting probabilities are easy to interpret - Very simple learning algorithms if all variables are observed in training data Disadvantages of Bayesian networks. …Of course, you're going to encounter the term…Bayesian or Bayes' throughout statistics. As we will see in a subsequent section, proba-. Hello everyone. Bayesian Networks Advanced I WS 06/07 Bayesian Networks 1. Learning Bayesian networks E R B A C. This tutorial is based on the book Bayesian Networks in Educational Assessment now out from Springer. Which one you use depends on your goal. Title: Influence Diagram Author: Tai-Wen Yue Last modified by: Tai-Wen Yue Created Date: 8/23/2002 12:47:41 AM Document presentation format: – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow. Submitted to RECOMB 2000). Bayesian Optimization gave non-trivial values for continuous variables like Learning rRate and Dropout rRate. Download Estimation and Approximation PPT for free. Awaz [email protected] Our new Yale Medicine/Yale New Haven Health COVID-19 Call Center offers information on how to keep yourself and your family healthy. A Bayesian network, Bayes network, belief network, decision network, Bayes model or probabilistic directed acyclic graphical model is a probabilistic graphical model that represents a set of. This is a simple Bayesian network, which consists of only two nodes and one link. Bayesian Networks are probabilistic graphical models and they have some neat features which make them very useful for many problems. Composing functions. Bayesian Networks - authorSTREAM Presentation. The scores emitted by the individual classifiers (rocket object and rocket engine explosion) are processed to fall into the 0–1 range by using the precision-recall curve as a guide. April, 2014 2014 NCME Tutorial: Bayesian Networks in Educational Assessment - Session III 19 Context Effect Postscript •If Context effect is generally construct-irrelevant variance, if correlated with group membership this is bad (DIF) •When calibrating using 2PL IRT model, can get similar joint distribution for , X 3, and X 4. Bayesian Networks What is the likelihood of X given evidence E? i. We are the preferred choice of over 60,000 authors worldwide. Naïve Bayes has been studied extensively since the. Title: Microsoft PowerPoint - bayes-nets [Compatibility Mode]. The equation above is called the chain rule for Bayesian networks. When applied to deep learning, Bayesian methods allow you to compress your models a hundred folds, and automatically tune hyperparameters, saving your time and money. Bayesian network modelling is a data analysis technique which is ideally suited to messy, highly correlated and complex datasets. Marco Valtorta and meets at times to be determined in the computer science and engineering conference room, Swearingen 3A75. Weight uncertainty in neural networks. (The term “dynamic” means we are modelling a dynamic system, and does not mean the graph structure changes over time. Bayesian network (BN) modeling (9 ⇓ ⇓ –12) is an established systems biology method aimed at optimizing, visualizing, and analyzing biological network models reconstructed from “big data” such as generated by Hi-C studies. A Bayesian network is a directed acyclic graph in which each edge corresponds to a conditional dependency, and each node corresponds to a unique random variable. George Bebis. It is a graphical modeling technique that enables the visual presentation of multi-dimensional results while retaining statistical rigor in population-level inference. This paper presents an approach to use Bayesian network to model potential attack paths. It focuses on the three main concepts of uncertain evidence, namely likelihood evidence and fixed and not-fixed probabilistic evidence, using a review of previous literature. The main estimation commands are bayes: and bayesmh. Although visualizing the structure of a Bayesian network is optional, it is a great way to understand a model. Guidance on the implementation and reporting of a drug safety Bayesian network meta-analysis. •The nodes represent variables, which can be discrete or continuous. This tutorial is based on the book Bayesian Networks in Educational Assessment now out from Springer. Cheaper, faster measurements can be substituted for longer direct measurements of individual. Bayesian Inference and Decision Theory. , kn values) When variables are conditionally dependent (i. Bias in identification of the best treatment in a Bayesian network meta-analysis for binary outcome: a simulation study. This process is essential to make certain that the spectrophotometer is operating properly and the measurements are right. •High-level tool with exact semantics; approx. Bayesian networks are. The key thing to remember here is the defining characteristic of a Bayesian network, which is that each node only depends on its predecessors and only affects its successors. The practicality of Bayesian neural networks. Mooney In Proceedings of the International Conference on Neural Networks (ICNN-96), Special Session on Knowledge-Based Artificial Neural Networks, 82--87, Washington DC, June 1996. Building network 2. 2 e b b b e Marginal Likelihood: Bayesian Networks X Y Network structure determines form of marginal likelihood 1 234567. The first is that when bias exists, it is caused by information from outside the sample. Bayesian Statistics for Biologists. The third image shows the estimated uncertainty. Waibel, A Real-time Face Tracker, Proceedings of WACV'96, 1996. ) Section 2. Poropudas J. Madabhushi and J. Hint: Construct a data set for which the score of the network X!Y di ers from the score of the network X Y. Observations are assumed to be made in discrete time, which is to say that the evolution of a process is observed at a finite number of time-points, usually at common intervals. Bayesian Networks What is the likelihood of X given evidence E? i. (2012) ST-DBN (see Figure 1). In a broad sense they're a set of methods for probabilistic calculation and graphical representation that can be used for most problems with uncertainty. A Bayesian network is a directed acyclic graph in which each edge corresponds to a conditional dependency, and each node corresponds to a unique random variable. Bayesian networks can also be used to reveal causal relationships among variables; this is an advantage when trying to gain an understanding of a problem domain, as in exploratory data analysis, and to predict the consequence of intervention. Standard vs. Journal of Hydrology, 2013, 488: 136-149. Download. Bayesian belief networks (BBNs) Bayesian belief networks. Bayesian Inference: Gibbs Sampling Ilker Yildirim Department of Brain and Cognitive Sciences University of Rochester Rochester, NY 14627 August 2012 References: Most of the material in this note was taken from: (1) Lynch, S. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis5. This probability should be updated in the light of the new data using Bayes' theorem" The dark energy puzzleWhat is a "Bayesian approach" to statistics? •. Causal Independence. A Bayesian Network Structure then encodes the assertions of conditional independence in Equation 1 above. A Bayesian Network A. Reliability modelling and analysis of a multi-state element based on a dynamic Bayesian network Abstract This paper presents a quantitative reliability modelling and analysis method for multi-state elements based on a combination of the Markov process and a dynamic Bayesian network (DBN), taking perfect repair, imperfect repair and condition. Introduction to Bayesian Decision Theory the main arguments in favor of the Bayesian perspective can be found in a paper by Berger whose title, "Bayesian Salesmanship," clearly reveals the nature of its contents [9]. Hello everyone. BBNs are chiefly used in areas like computational biology and medicine for risk analysis and decision support (basically, to understand what caused a certain problem, or the probabilities of different effects given an action). Expectation Propagation for Approximate Bayesian Inference Thomas P Minka Statistics Dept. to be acyclic. Bayesian methods match human intuition very closely, and even provides a promising model. It represents a JPD over a set of random variables V. In this survey, we also discuss the relationship and differences between Bayesian deep learning and other related topics like Bayesian treatment of neural networks. Review of Probability Theory Arian Maleki and Tom Do Stanford University Probability theory is the study of uncertainty. The 100 pre‐trained neural networks of ϵ tot and E gap were modified such that the last hidden layers were connected to Bayesian linear regressors, and the prediction performances of the models were then evaluated by the 10‐fold CV applied to the training data within each fold of the 5‐fold CV. | 2020-11-29 23:28:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.513385534286499, "perplexity": 2006.9643214044931}, "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-2020-50/segments/1606141203418.47/warc/CC-MAIN-20201129214615-20201130004615-00129.warc.gz"} |
https://techcommunity.microsoft.com/t5/excel/compile-different-json-files-with-a-apikey-header-using-power/td-p/3663384 | Compile different JSON files with a ApiKey header using Power Query
Occasional Visitor
Compile different JSON files with a ApiKey header using Power Query
Hi everyone,
I have to connect different JSON files into one table. Each JSON is a list of parts. To connect the file I need an Api-Key.
Here's an example:
let
in
Source
Thing is, I have over 90 pages and I don't know how to create one table with all the information. | 2022-12-01 21:35:47 | {"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": 0.8047404885292053, "perplexity": 3353.382358843084}, "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-2022-49/segments/1669446710869.86/warc/CC-MAIN-20221201185801-20221201215801-00769.warc.gz"} |