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https://nigerianscholars.com/past-questions/mathematics/question/274337/ | Home » » The number of telephone call N between two cities A and B varies directly as the...
# The number of telephone call N between two cities A and B varies directly as the...
### Question
The number of telephone call N between two cities A and B varies directly as the population PA, PB in A and B respectively and inversely as the square of the distance D between A and B. Which of the following equations represents this relation?
### Options
A) $$N = \cfrac{kP_A}{D^2} + \cfrac{CP_B}{D^2}$$
B) $$N = \cfrac{kP_AP_B}{D^2}$$
C) $$N = kDP_AP_B$$
D) $$N = kDP_A + CDP_B$$
E) $$N = kD^2P_AP_B$$ | 2022-07-01 17:12:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.6224861741065979, "perplexity": 339.87567567219753}, "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/1656103943339.53/warc/CC-MAIN-20220701155803-20220701185803-00594.warc.gz"} |
https://studyqas.com/rebbeca-has-30-paintings-to-sell-the-amount-of-money-rebbeca/ | # Rebbeca has 30 paintings to sell. The amount of money rebbeca
Rebbeca has 30 paintings to sell. The amount of money rebbeca
## This Post Has 8 Comments
1. tonimgreen17p6vqjq says:
The domain is all the integers from 0 to 30, inclusive.
The domain is the set of all the possible inputs (x-values), this is 0 paintings, 1 painting, 2 paintings, ... until 30 paintings.
2. descampbell2001 says:
D.) All integers from 0 to 30, inclusive.
Step-by-step explanation:
If Rebecca has 30 paintings to sell and x is the domain, then any integer from 0-30 inclusive is your answer. It isn't sure that Rebecca will sell a painting, she can't sell more than she has, and she can't sell parts of a painting.
3. morganturgeon29 says:
The answer is letter D
4. angeline310 says:
Answ11111111
Step-by-step explanation:
333333
5. maddieb1011 says:
all integers from 0 to 30, inclusive.
Remember that domain is the set of possible input values, i.e. x-values or the number of paintings that may be sold: 0, 1, 2, 3, 4, 5, 30.
6. zhjzjzzj6325 says:
F(x)=30x
7. radusevciuc7719 says:
Option 2 is correct.
Step-by-step explanation:
Rebecca has 30 paintings to sell.
The amount of money Rebecca makes from selling x paintings is represented by a function.
$f(x)=25x$
where, x is number of painting to sell.
As we are given total number of painting for sell is 30.
Domain: It is input value of x where function and situation defined.
Minimum number of painting she could sell be 0 and Maximum number of painting she could sell be 30.
Domain: 0≤x≤30
Hence, All integers from 0 to 30, inclusive.
8. solobiancaa says:
I got it it took me 3 years but i got the answer is 0 to 30
Step-by-step explanation: | 2022-12-04 05:34:53 | {"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": 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": 0.22627146542072296, "perplexity": 3263.1842200411365}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710962.65/warc/CC-MAIN-20221204040114-20221204070114-00526.warc.gz"} |
https://matheducators.stackexchange.com/questions/8218/should-we-tell-students-to-never-replace-parts-of-an-expression-by-their-limits/8219 | # Should we tell students to never replace parts of an expression by their limits when taking a limit?
Let me explain. Suppose we want to calculate $\lim\limits_{n\to\infty} n^2-n$. Since this limit is indeterminate, one way to do it is to write it as $\lim\limits_{n\to\infty} n^2(1-1/n)$. Since $n^2$ goes to infinity and $1-1/n$ goes to $1$, the limit is $\infty$. If this was part of a bigger expression, we would leave it as it is and then at the end look at the limits of all the individual factors. This is the way I've learned it and the way I've always done it.
However, I've noticed that some students do the following:
$$\lim\limits_{n\to\infty} n^2-n = \lim\limits_{n\to\infty} n^2(1-1/n) = \lim\limits_{n\to\infty} n^2 = \infty$$
It is the second equality I'm concerned with. It's not, strictly speaking, wrong: after all, all the limits here are equal to each other. And yet I've been telling them not to do it. My way is to do whatever you want with your expression, and then take all limits in a single step. Now that I think about it, however, I can't find a reason not to let the $1/n$ go to $0$ before taking the rest of the limit: all the equalities are correct, and it simplifies the expression.
Is there any reason why the students should be discouraged from doing this? Or am I just enforcing a rule for no reason?
• $$1= \lim_{n \to \infty} 1 = \lim_{n \to \infty} n \frac{1}{n} = \lim_{n \to \infty} n(0) =\lim_{n \to \infty} 0 = 0$$ – Steven Gubkin Jun 3 '15 at 23:56
• @StevenGubkin, you should put your comment as an answer. – Joel Reyes Noche Jun 4 '15 at 1:16
• I always loved $\lim\limits_{n\to\infty} (1+1/n)^n$. if you eliminate $1/n$ your answer is certainly wrong. – oerkelens Jun 4 '15 at 11:24
The important thing is whether students' reasoning is logically valid — and in particular, that they only use the conclusion of a theorem after they've checked that all its hypotheses hold — not whether they follow any particular arbitrary rules or procedures. In this case, the relevant theorem is the following:
Theorem. Let $f$ and $g$ be real-valued functions defined on a subset of the real line, and let $c$ be either a real number or $\pm \infty$. If $\lim_{t \to c} g(t)$ exists and is equal to a nonzero real number, then $\lim_{t \to c} f(t) g(t)$ exists if and only if $\lim_{t \to c} f(t)$ exists, in which case $$\lim_{t \to c} f(t) g(t) = [\lim_{t \to c} f(t)] \cdot [\lim_{t \to c} g(t)].$$
In the example you gave, the problem isn't that the students fail to adhere to the (needless) rule of taking all limits in a single step. The problem is that they omit an important part of the reasoning: since $\lim_{n \to \infty} (1 - 1/n)$ exists and is equal to $1$, $$\lim_{n \to \infty} n^2 (1 - 1/n) = (\lim_{n \to \infty} n^2) \cdot [\lim_{n \to \infty} (1 - 1/n)] = (\lim_{n \to \infty} n^2) \cdot 1 = \lim_{n \to \infty} n^2.$$ In Steven Gubkin's example, neither $n$ nor $1/n$ has a limit that exists and is a nonzero real number, so the theorem doesn't apply. In both cases, the key is to use precise, logically valid reasoning.
• The reality is that almost no practitioners of calculus will ever remember the exact formal statements of a half-dozen theorems such as this one. Scientists and engineers who have developed competence in this kind of thing use informal modes of reasoning based on their correct insights into how the expression in question works. – Ben Crowell Nov 3 '18 at 23:21
• @DanielHast: but $\lim_{n\to \infty} n^2$ doesn't exist. So why are your students allowed to apply the theorem you quote? – Michael Bächtold Nov 4 '18 at 11:01
• @MichaelBächtold: $c$ is allowed to be $\pm \infty$. – Ben Crowell Nov 7 '18 at 16:12
• @BenCrowell: the problem is that $\lim_{n\to \infty}n^2=\infty$, so I don't see how one is allowed to apply the theorem. If the theorem would apply, we should also be allowed to use it in Steven Gubkin's example. – Michael Bächtold Nov 8 '18 at 8:24
• $\lim_{n \to \infty} (1 - 1/n)$ exists and is equal to a nonzero real number, and $\lim_{n \to \infty} n^2$ exists (in the extended real line), so the theorem applies with $g(n) = (1 - 1/n)$ and $f(n) = n^2$. – Daniel Hast Nov 10 '18 at 3:48
To extend the answer by Daniel Hast: One theorem one might want to use is:
If $(a_n)_{n\in\mathbb N}$ and $(b_n)_{n\in\mathbb N}$ are convergent sequences then \begin{align} \lim_{n\to\infty} (a_n \pm b_n) &= \lim_{n\to\infty} a_n \pm \lim_{n\to\infty} b_n \\ \lim_{n\to\infty} (a_n \cdot b_n) &= \lim_{n\to\infty} a_n \cdot \lim_{n\to\infty} b_n \\ \lim_{n\to\infty} \frac{a_n}{b_n} &= \frac{\lim_{n\to\infty} a_n}{\lim_{n\to\infty} b_n} \end{align} For the last equation one also needs $\lim_{n\to\infty} b_n \neq 0$.
Now, one can do something like $$\lim_{n\to\infty} \tfrac 1n + \sqrt[n]{4}=\lim_{n\to\infty} \tfrac 1n + \lim_{n\to\infty} \sqrt[n]{4}=0+1=1 \qquad(1)$$
The problem here is, that one applies the above theorem before showing, that the subsequences converge. So a better way to do it would be:
$$\lim_{n\to\infty} \tfrac 1n = 0 \land \lim_{n\to\infty} \sqrt[n]{4} = 1 \Rightarrow \lim_{n\to\infty} \tfrac 1n + \sqrt[n]{4}=\lim_{n\to\infty} \tfrac 1n + \lim_{n\to\infty} \sqrt[n]{4}=0+1=1\qquad (2)$$
(2) is the way to actually write down the proof and (1) is the way to find the proof (This need to be taught to students because they sometimes think that a proof and the solution process are the same). (2) also prevents you from failures because $\lim_{n\to\infty} a_n=\infty$ means, that $(a_n)$ diverges. I say to students:
$\infty$ is no real number. So $\lim_{n\to\infty} a_n=\infty$ means, that one cannot apply the above theorem, because $(a_n)$ diverges. But $\lim_{n\to\infty} a_n=\infty$ sometimes behave in computing with limits like it would converges. For example $\lim_{n\to\infty}(a_n+b_n)=\lim_{n\to\infty}(a_n+b_n)=\lim_{n\to\infty}a_n+\lim_{n\to\infty}b_n$ if one has limits of the form $\infty+\infty$ or $\infty+c$ [Of course one need to introduce the relevant theorems here]. But for $\infty-\infty$ one can never apply the above theorem. So if one limit is $\infty$ one needs to be careful for limits of the form $\infty-\infty$, $\infty\times 0$, $\frac{ \infty}{\infty}$.
• @BenjaminDickman Thers's a big diverence: In (1) you apply the theorem without checking the premises of the theorem. You do it just later at the second equal sign. In (2) you first show the convergence of the subsequences and then apply the theorem. Note that $\lim_{n\to\infty} a_n=\infty$ means, that you cannot apply the cited theorem... – Stephan Kulla Jun 5 '15 at 12:52
• Ah, okay... now I know what you meant... ;-) – Stephan Kulla Jun 5 '15 at 16:05
I can not count the times that I used or read expressions as $$\epsilon+\epsilon^2=\epsilon$$ or $$(1+dx)(1+dy)-1=dx+dy$$. It is usual infinitesimal reasoning.
Another example, any time that in the evaluation of a limit we use a Taylor series ended as dots we are implicitly doing an intermediate limit evaluation:
$$\lim_{x \to 0}~ \sqrt{\frac{1+2x}{x^2}}-\frac{1}{x} = \lim_{x \to 0}~{\frac{1}{x}+1-\frac{x}{2}+\dots-\frac{1}{x}}=1$$
Thus, state rules ( "never replace parts of an expression by their limits when taking a limit", "not to do it. ... take all limits in a single step") is not the way (never it is, rules are ok only for computers) and, when done, it is full of exceptions. Instead it is better help students to practice, learn the dangers, advantages, problems and concepts under some approach. In this way, students experience and acquire the concept of infinitesimal, asymptotic behavior, ... .
From this point of view, a student who writes:
$$\lim_{n \to \infty}~ n^2-n = \lim_{n \to \infty}~ n^2$$
or
$$\lim_{n \to 0}~ (n^2+n)/n = \lim_{n \to 0}~ n/n = 1$$
is showing he/she understands the relation between infinity/infinitesimal and powers, the concept of asymptotic behavior, ....
• Right, sorry, the limit was at zero. Nevermind. – Tommi Nov 2 '18 at 12:06
• This is certainly an accurate description of how, in my experience, scientists and engineers reason about this kind of thing. I don't think the relevant distinction is between limits and infinitesimals, but rather between formal rigor and correct informal reasoning by experienced practitioners. Correct reasoning about infinitesimals can be formal (using non-standard analysis) or informal. Correct reasoning about limits can likewise be formal or informal. The thing to keep in mind is that real-world practitioners essentially never use formal reasoning for this kind of thing. – Ben Crowell Nov 3 '18 at 23:25 | 2020-04-04 03:28:38 | {"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": 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": 5, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9606205224990845, "perplexity": 378.38314438350113}, "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-2020-16/segments/1585370519111.47/warc/CC-MAIN-20200404011558-20200404041558-00197.warc.gz"} |
https://zbmath.org/?q=an:0681.03040 | # zbMATH — the first resource for mathematics
$$S^ i_ 3$$ and $$\overset\circ V^ i_ 2(BD)$$. (English) Zbl 0681.03040
See the preview in Zbl 0665.03041.
##### MSC:
03F30 First-order arithmetic and fragments 03F35 Second- and higher-order arithmetic and fragments 03F25 Relative consistency and interpretations 03D15 Complexity of computation (including implicit computational complexity)
Full Text:
##### References:
[1] Buss, S.: Bounded arithmetic. Napoli: Bibliopolis 1986 · Zbl 0649.03042 [2] Buss, S.: Axiomatizations and conservation results for fragments of bounded arithmetic. (To appear in: Contemporary Mathematics AMS, Proc. of Workshop in Logic and Computation, 1987) · Zbl 0699.03032 [3] Nelson, E.: Predicative arithmetic. Princeton University Press, 1986 · Zbl 0617.03002 [4] Wilkie, A., Paris, J.: On the scheme of induction for bounded arithmetic formulas. Ann. Pure Appl. Logic35, 267–302 (1987) · Zbl 0647.03046 · doi:10.1016/0168-0072(87)90066-2 [5] Takeuti, G.: Bounded arithmetic and truth definition. Ann. Pure Appl. Logic39, 75–104 (1988) · Zbl 0653.03038 · doi:10.1016/0168-0072(88)90046-2 [6] Takeuti, G.: Some relations among systems for bounded arithmetic. (To appear in: Petkov, P. (ed), Heyting: Mathematical logic. London, Plenum Press) · Zbl 0790.03057
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. | 2021-05-06 16:25:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42433735728263855, "perplexity": 9794.437539516077}, "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/1620243988758.74/warc/CC-MAIN-20210506144716-20210506174716-00245.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/dcds.2010.27.325 | Article Contents
Article Contents
# Quadratic perturbations of a class of quadratic reversible systems with one center
• This paper is concerned with the bifurcation of limit cycles from a class of one-parameter family of quadratic reversible system under quadratic perturbations. The exact upper bound of the number of limit cycles is given.
Mathematics Subject Classification: Primary: 34C07, 34C08; Secondary: 37G15.
Citation: | 2023-03-29 20:02:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.5407066345214844, "perplexity": 628.530600555549}, "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/1679296949025.18/warc/CC-MAIN-20230329182643-20230329212643-00653.warc.gz"} |
http://musictheory.pugetsound.edu/mt21c/AnalyzingSecondaryDiminishedChords.html | This $\left.\text{G}^♯{}^ø{}^{7}\middle/\text{B}\right.$ is analyzed as $\left.\text{vii}^ø{}^{6}_{5}\middle/\text{V}\right.$ in D major. | 2019-07-21 10:31:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4186312258243561, "perplexity": 1569.2045497345412}, "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/1563195526948.55/warc/CC-MAIN-20190721102738-20190721124738-00385.warc.gz"} |
https://math.stackexchange.com/questions/821777/understanding-%CF%89-consistent-and-%CF%89-incomplete-theory | # Understanding ω-consistent and ω-incomplete theory
A theory $K$ is said to be $ω$-consistent if, for every formula $B(x)$ of $K$, if $﹁ B(n)$ is a theorem in $K$ for every natural number $n$, then it is not the case that $(∃x)B(x)$ is a theorem in $K$.
A theory $K$ is said to be $ω$-incomplete if there is a formula $E(x)$ such that $E(n)$ is a theorem in K for every natural number $n$, but is not the case that $(∀x)E(x)$ is a theorem in $K$. These definition are not intuitive and concrete for me. Please help me.
This usually comes in to play for what are known as non-standard models of arithmetic.
For example, when we say let $n$ be a natural number, (informally) we mean that $n$ can be obtained by using the successor function on $0$ finitely many times. However by using compactness we can come with a model of arithmetic for which there is some $k$ s.t. $k>n$ for any "standard" (in the sense above) natural number $n$. In these models things do not work the way you would expect them to work.
If you know about Godel numbering and the incompleteness theorems, here is an example: Let $\sigma(n)$ be a formula that states $n$ witnesses the inconsistency of PA. Now since we believe in the consistency of PA, we have that for each standard natural number $n$. $\text{PA}\vdash\neg{\sigma(n)}$. But this is not enough to conclude that $\forall{n}\neg{\sigma(n)}$ is a consequence of PA. Thus PA is not $\omega$-complete.
Note that this isn't such a bad thing though. If PA was $\omega$-complete, then PA proves its own consistency and by the second incompleteness theorem, is actually inconsistent.
• Thannk you for your attention. Your explanation is so hard for me to understand. Please make it easier. – user87128 Jun 5 '14 at 15:42
• I'm not really sure how to do that, short of doing an exposition as found in amazon.com/Computability-Logic-George-S-Boolos/dp/0521701465 . As far as I know these definitions are there to study the issues raised by the above facts. If you are not very familiar with these issues then the examples will not make any sense. – UserB1234 Jun 5 '14 at 16:06
• Also how familiar are you with model theory / recursion theory and where did you run across these definitions? That might help me to better answer your question. – UserB1234 Jun 5 '14 at 16:08
• Excuse me. At first I made a mistake, and I was careless. In fact your beautiful explanation resolve my problem. Thank you very much. – user87128 Jun 6 '14 at 14:17
It might be useful to observe that a model of an $\omega$-inconsistent theory cannot have just the standard natural numbers. The reason is that (in the notation of the question) the provability of $\exists x\, B(x)$ requires the model to have an element $a$ satisfying the predicate $B$, while the provability of $\neg B(n)$ for each standard natural number $n$ means that $a$ cannot be any such number.
On the other hand, $\omega$-incompleteness is not so damaging. Common axiomatic theories like Peano arithmetic and Zermelo-Fraenkel set theory are $\omega$-incomplete. For example, PA proves, for each natural number $n$, the statement that formalizes (in a natural way) "$n$ is not the Gödel number of a proof of a contradiction in PA". But, by Gödel's second incompleteness theorem, PA cannot prove the corresponding universally quantified sentence, as that sentence would say "PA is consistent."
• Thank you for your attention. But in the case of ω-incompleteness I still have problem. Your explanation is hard for me to understand. Please give a concrete example to show that PA is ω-incomplete. – user87128 Jun 5 '14 at 15:31
• @aminliverpool I gave a concrete example. $E(x)$ is the formula expressing "$x$ is not the Gödel number of a proof of a contradiction in PA." – Andreas Blass Jun 5 '14 at 19:01
• Ok. Excuse me for misunderstanding. Your example is concrete enough to understand. Thank you very much. – user87128 Jun 6 '14 at 14:11
Here is an example. Suppose you are working in some system $M$, and you can prove all of these theorems:
\begin{align} 0 &\le 0 \\ 1 &\le 1 \\ 2 &\le 2 \\ &\vdots\end{align}
You might think that $M$ would also be able to prove $$(\forall n) n\le n\tag{1}$$ but depending on the axioms, maybe it can and maybe it can't. If it can't prove $(1)$, we say that $M$ is $\omega$-incomplete.
In fact, $M$ might even be able to prove the opposite of $(1)$, that $$\lnot(\forall n) n\le n.\tag{2}$$
If $M$ proves all of $0=0, 1=1, 2=2,\ldots,$ and also $\lnot(\forall n) n \le n$, we say that $M$ is $\omega$-inconsistent. It's not actually inconsistent, but it is somewhat puzzling, because it asserts that there is some $n$ for which $\lnot n\le n$, but it also asserts that $n$ is not $0, 1, 2,$ or any other number.
• Just one quick question: Wouldn't $\forall{n}, n=n$ follow as a result of the (sufficiently strong set of) logical axioms? – UserB1234 Jun 5 '14 at 15:04
• How can you say that? I didn't say what the axioms are. Maybe $\lnot\forall n, n=n$ is itself an axiom. But to answer your question, no. It might follow, or it might not follow, or its negation might follow, depending on the axioms, so we have these terms “$\omega$-incomplete” and “$\omega$-inconsistent” to describe the situation when it doesn't follow, or when its negation follows. – MJD Jun 5 '14 at 15:07
• @MJD I'm using the same line of reasoning as Mauro. – UserB1234 Jun 5 '14 at 15:11
• Oh, I see. I intended $=$ here to represent a relation, not necessarily logical identity. Sorry for the confusion. I have changed the example. – MJD Jun 5 '14 at 15:12
• @aminliverpool: The set of axioms that MJD is speaking about is not PA. Your original question doesn't mention PA, it mentions some set $K$ of axioms in some language. The only reason that PA came up so often in the other answers is because examples occur naturally there and has been well studied. In fact, with PA, using induction you can actually prove $\forall{n}, n\leq{n}$. – UserB1234 Jun 5 '14 at 16:13
It depends how much detail you want: but for a "concrete" explanation of why PA is $\omega$-consistent and $\omega$-incomplete, you could try Episode 9 of the (freely available) notes "Gödel Without Tears" available at http://www.logicmatters.net/igt/godel-without-tears/ .
• Thank you for your attention. Your notes are excellent. They are very useful for me to resolve my problem. Thank you very much. – user87128 Jun 6 '14 at 14:03
Here is another answer. There and many propositions in number theory for example, where we can prove the theorem for specific values of $n$, but a general proof eludes us. Fermat's last theorem would have been an example 20 years ago, but for example the Goldbach conjecture, we can begin to prove it for all even numbers, $4=2+2, 6=3+3, 8=3+5, 10=3+7$ etc. But to prove $\forall n (2n =\text{prime}+ \text{prime})$ is unknown. Assume now for the sake of discussion that we somehow magically knew that every attempt to verify the statement for a specific $n$ would be successful. Does this imply we supply a proof of the general Goldbach conjecture, this is a question about the nature of our mathematical system. $\omega$-completeness says that we would have a general proof. Consider further the possibility that we could again verify Goldbach for every $n$ but we had a proof that Golbach was false. This would be a strange situation indeed. We have a system that is $\omega$-inconsistent. Not able to produce an actual contradiction (if we are consistent) but with a proof that there is a counterexample and unable to produce such a counterexample.
In logic we get an $\omega$-inconsistent theory by taking $T\cup \{\neg \text{con}(T)\}$ (assume $T$ consistent). This is a theory that thinks that it is inconsistent, as that is one of its axioms, but it is not it cannot actually produce a contradiction, it is $\omega$-inconsistent and in desperate need of psychotherapy.
Godel initially introduced $\omega$ consistence because his sentence "I cannot be proven" indeed cannot be proven, for if there were a proof that proof would itself be a counterexample. Say it was proof number $35$ the we have $$35 \text{is a proof}$$ but the Godel sentence is $$\forall n(n \text{is not a proof})$$ and this implies $$35 \text{is not a proof}$$ a direct contradiction.
On the other hand how do you know you cannot prove the negative of the Godel sentence ? That would be $$\exists n(n \text{is a proof})$$ now you cannot get a direct contradiction because you cannot find a proof. So again a strange situation which you can get out of by assuming $\omega$- consistency. Rosser later found a way to avoid the $\omega$-consistence assumption.
• Thank you for your attention. Your example very good since it is intuitive and concrete for me. This help me to understand the concepts. Thank you very much. – user87128 Jun 6 '14 at 14:06 | 2019-05-20 04:20:25 | {"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": 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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8747109174728394, "perplexity": 251.97602733797086}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232255562.23/warc/CC-MAIN-20190520041753-20190520063753-00486.warc.gz"} |
http://mathhelpforum.com/differential-geometry/183564-sequence-accumulation-point.html | 1. Sequence and accumulation point
Suppose $\{a_n\}_{n\in\mathbb{N}}\to A$ and $\{a_n: \ n\in\mathbb{N}\}$ is an infinite set. Show that A is an accumulation point of $\{a_n: \ n\in\mathbb{N}\}$.
Let $A=\text{sup} \ \{a_n\}$ and Q be a neighborhood of A. There is an $\epsilon>0$ such that $(A-\epsilon, A+\epsilon)\subset Q$.
Since A = sup and if c is an upper bound, $A\leq c$
Let $a_i\in\{a_n\}, \ i=1,2,....$
Assume there are finitely many $a_i\in Q$.
Now, let $A'=\text{max}\{a_i\}$
Since x' is the max, x' is an upper bound of $\{a_n\}$. Therefore, $A', but $A = \text{sup} \ \{a_n\}$ which is a contradiction. Thus, A is an accumulation point.
Correct?
2. Re: Sequence and accumulation point
Originally Posted by dwsmith
Suppose $\{a_n\}_{n\in\mathbb{N}}\to A$ and $\{a_n: \ n\in\mathbb{N}\}$ is an infinite set. Show that A is an accumulation point of $\{a_n: \ n\in\mathbb{N}\}$.
Let $A=\text{sup} \ \{a_n\}$ and Q be a neighborhood of A. There is an $\epsilon>0$ such that $(A-\epsilon, A+\epsilon)\subset Q$.
Since A = sup and if c is an upper bound, $A\leq c$
Let $a_i\in\{a_n\}, \ i=1,2,....$
Assume there are finitely many $a_i\in Q$.
Now, let $A'=\text{max}\{a_i\}$
Since x' is the max, x' is an upper bound of $\{a_n\}$. Therefore, $A', but $A = \text{sup} \ \{a_n\}$ which is a contradiction. Thus, A is an accumulation point.
Correct?
No, that's not correct. You don't get to just assume that $A=\sup\{a_n\}$. For example $\langle (-1)^n/n\rangle$ is a sequence converging to $0$, which is neither an upper nor lower bound of the sequence.
Recall that by definition $\langle a_n\rangle\to A$ iff for each $\epsilon>0$ there is $N\in\mathbb{N}$ such that if $n\geq N$ then $a_n\in(A\pm\epsilon)$. So just notice that there are infinitely many elements in $\{a_n:n\geq N\}\subseteq(A\pm\epsilon)$, and the proof is complete. | 2017-10-22 22:01:00 | {"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": 35, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9847215414047241, "perplexity": 223.4940214513088}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187825464.60/warc/CC-MAIN-20171022203758-20171022223758-00343.warc.gz"} |
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Some Dynamical Properties of a Weakly Almost Periodic Flow Commun. Korean Math. Soc. 1998 Vol. 13, No. 1, 123-129 Hyung Soo Song Kwangwoon University Abstract : In this paper, we study some dynamical properties of a weakly almost periodic flow. In particular we get, in a weakly almost periodic flow $(X,T)$, the groups $I$ and $A(I)$ of all automorphisms of $I$ are isomorphic, where $E(X)$ is the enveloping semigroup of $(X,T)$ and $I$ is the minimal right ideal in $E(X)$ . Keywords : Enveloping semigroup, Minimal right ideal, Proximal, Digital, Almost periodic flow, Weakly almost periodic flow, Ellis group MSC numbers : 54H20 Downloads: Full-text PDF
Copyright © Korean Mathematical Society. The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea Tel: 82-2-565-0361 | Fax: 82-2-565-0364 | E-mail: paper@kms.or.kr | Powered by INFOrang Co., Ltd | 2022-05-18 06:48:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17655032873153687, "perplexity": 3141.8604610314965}, "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/1652662521152.22/warc/CC-MAIN-20220518052503-20220518082503-00480.warc.gz"} |
https://www.intechopen.com/books/dengue-fever-a-resilient-threat-in-the-face-of-innovation/current-status-of-vaccines-against-dengue-virus | Open access peer-reviewed chapter
# Current Status of Vaccines against Dengue Virus
By Jhon Carlos Castaño-Osorio, Alejandra María Giraldo-Garcia and Maria Isabel Giraldo
Submitted: April 3rd 2018Reviewed: August 9th 2018Published: November 5th 2018
DOI: 10.5772/intechopen.80820
## Abstract
Dengue is a disease caused by the dengue virus (DENV), being the most important arbovirus in the world. About 3.97 billion people live in countries at risk and 400 million infections occur each year, of which 500,000 suffer from the most severe form of the disease and 25,000 of these die. The clinical spectrum of Dengue ranges from asymptomatic infection to severe Dengue characterized by increased vascular permeability, bleeding disorders, shock, and death. The increase in global cases of this disease is due in part to the absence of effective public intervention measures and lack of a specific treatment and vaccines licensed for human use. Therefore, in this review, we will present the different strategies known to date for the development of vaccines for this disease, as well as the results and limitations obtained in the different clinical studies.
### Keywords
• dengue
• vaccine
• tetravalent
• immunopathogenesis
## 1. Introduction
Dengue is a mosquito-borne viral disease caused by four types of dengue viruses, which, in the recent years, has rapidly become widespread worldwide. Dengue virus transmission is attributed to female mosquitoes of the species Aedes aegypti, in the majority of cases, as well as Ae. albopictus to a lesser extent. Other diseases that are transmitted by this mosquito include chikungunya, yellow fever, and Zika infection [1]. Dengue is a very rapidly growing public health problem being currently faced by approximately 40% of the global population living in more than a hundred tropical and subtropical countries [2]. Dengue is widespread throughout the tropics, with local variations in risk influenced by rainfall, temperature as consequence of climate change, unplanned rapid urbanization, unprecedented population growth, increasing movement of people (and consequently viruses), international travel and breakdown in public health infrastructure, and vector control programs. The actual numbers of dengue cases are underreported and many cases are misclassified. The prevalence of dengue is estimated at 3.9 billion people who are at risk of infection in 128 tropical and subtropical countries, mainly southeast and south Asia, Central and South America, and the Caribbean. A recent estimate indicates 390 million dengue infections per year (95% credible interval 284–528 million), of which 96 million (67–136 million) manifest clinically (with any severity of disease), with an estimated 500,000 cases each year of life-threatening disease in the form of severe dengue—including dengue hemorrhagic fever and dengue shock syndrome mostly in the pediatric population, with about 20,000 succumbing to it, and is the leading cause of childhood death in many countries [1, 2, 3]. Dengue is associated with considerable social, economic, and political consequences caused by urban epidemics, such as those seen in Delhi (1996), Cuba (1977–1979 and 1997), Taiwan (2002), and Brazil (2008). Furthermore, Dengue is currently also a major cause of morbidity in American and European travelers and military personnel [4]. This disease places a high economic burden on both governments and individuals; for instance, in America, Dengue illness costs US$2.1 billion per year on average, excluding vector control, exceeding costs of other viral illnesses. In addition, in Southeast Asia, there is an estimate of 2.9 million dengue episodes and 5906 deaths annually, with an annual economic burden of$950 million [3].
## 2. Natural clinical evolution
Dengue virus infections encompass a range of well-described clinical illnesses ranging from an asymptomatic infection to a self-limiting febrile illness, dengue fever, to severe dengue (shock and death), a clinical syndrome that typically presents with capillary permeability and can lead to dengue shock syndrome and dengue hemorrhagic fever. Among less common presentations of severe dengue are encephalitis, hepatitis, and renal dysfunction [4]. Infection by any dengue virus requires a 4- to 8-day incubation period and can produce a wide spectrum of illnesses, the majority of these being asymptomatic or subclinical. Although most patients are able to recover after a self-limiting (yet debilitating) illness, a small proportion develops a severe form of the disease, which is mainly characterized by plasma leakage with or without bleeding [3]. The acute illness is usually benign and self-limiting. Moreover, a secondary infection, corresponding to a subsequent infection with a different serotype is also characterized by acute fever and several other nonspecific signs and symptoms, usually indistinguishable from a range of other illnesses. However, in 2–3% of secondary infections with another serotype there is a higher risk of increased disease severity, causing life-threatening Dengue with Warning Signs (DWS+) and Severe dengue (SD), according to the revised WHO dengue case classification (DENCO) [2, 5]. Serotype-cross-reactive antibodies facilitate DENV infection in Fc-receptor-bearing cells by promoting virus entry via Fcγ receptors (FcγR), a process known as antibody-dependent enhancement (ADE) [6, 7]. Dengue without Warning Signs (DWS−) is more often observed in adults and adolescents and can manifest with only a mild fever only or a more disabling disease. This latter form is characterized by symptoms occurring mainly in the early febrile stage, such as the sudden onset of high fever, severe headache, retro-orbital pain, myalgia, arthralgia, and rash. In the critical phase, the skin is flushed with the appearance of a petechial rash, occurring predominantly around the time of defervescence, when an increase in capillary permeability accompanied by increased hematocrit can occur, leading to hypovolemic shock that can result in organ impairment, metabolic acidosis, disseminated intravascular coagulation, and severe hemorrhage. If untreated, mortality can be as high as 20%, whereas appropriate case management and intravenous rehydration can reduce mortality to less than 1% [3]. SD usually affects children younger than 15 years of age, although it can occur in adults. SD is characterized by a transient increase in vascular permeability resulting in plasma leakage with high fever, bleeding, thrombocytopenia, and hemoconcentration, which can lead to shock [5]. Two factors, namely, antibody-dependent enhancement (ADE) and inherent virulence of the DEN viruses, appear to contribute the most to disease pathogenesis [2].
## 3. Pathogenesis of Dengue virus infection
A protective versus pathological outcome depends on the balance between the host’s genetic and immunological background and viral factors. Vaccine development has been slowed by fears that immunization might predispose individuals to the severe form of dengue infection [3, 4]. There are four distinct, but closely related, serotypes of the virus that cause dengue (DEN-1, DEN-2, DEN-3, and DEN-4).
No DENV-specific therapies are available, while a DENV vaccine that elicits protection in people with prior DENV exposure but not in naive individuals and that is not equally protective against all four serotypes has recently begun to be licensed on a country-by-country basis. This is mostly due to an incomplete understanding of the interplay between viral and host factors that contribute to DENV pathogenesis. On the virus side, some DENV lineages are more virologically and epidemiologically fit than others and are thus associated with DWS+/SD manifestations. On the host side, DENV infection history is the primary determinant associated with the development of more severe dengue disease, with potential contributions from other factors such as genetic variation, age, and sex.
Several studies have demonstrated that DENV-specific antibodies can protect against infection and, under certain conditions, enhance infection and disease severity, whereas the role of T cells remains unclear. Thus, to avoid the risk of enhancement, a safe vaccine against dengue virus will need to confer protective immunity against all four serotypes [10]. Consequently, the adaptive immune response to dengue can be both protective and pathogenic, which complicates vaccine development, as discussed in this chapter.
## 4. Dengue vaccines
Dengue virus is widespread throughout the tropics, representing an important, rapidly growing public health problem with an estimated 2.5–3.9 billion people at risk of dengue fever and the life-threatening severe dengue disease. Therefore, the need for a safe and effective vaccine for dengue is immediate. Vaccine development has been slowed by fears that immunization might predispose individuals to the severe form of dengue infection [4]. The characteristics and challenges that the ideal vaccine for the dengue virus must have are described in the following.
### 4.1. Characteristics of an ideal dengue vaccine and challenges to its development
#### 4.1.1. Characteristics
• Safe in children and adults [3, 4]
• Avoids ADE (antibody-dependent enhancement) and pathogenesis
• Rapid immunization regime requiring a single vaccine or two that fit in with established vaccine programs
• Induces a balance between reactogenicity and immunogenicity
• Suitable for use in target age groups
• Genetically stable
• Stimulates neutralizing antibodies and Th1 cell-mediated immunity
• Induces long-lasting immunity, safety, and protection
• Generates neutralizing immunity to all four serotypes
• Does not contribute to immunopathogenesis (vaccine-induced enhancement)
• Easy storage and transportation
• Affordable and cost effective
#### 4.1.2. Challenges
• Existing possibility of triggering ADE
• Vaccine must be tetravalent
• Dengue virus serotypes do not induce long-lasting heterotypic immunity
• No suitable or ideal animal model exists for immunization studies
• No well-established viral virulence markers are available
• Correlates of protection are not well defined
• Subsequent infection (especially, after a long-time interval) may lead to severe dengue
• Vaccine candidates should be evaluated in geographic areas with different transmission patterns [3].
To date, there are several DENV vaccines under development, with some in phase 3 safety and efficacy testing. These include inactivated, live attenuated, recombinant subunit, viral vectored, and DNA vaccines. Dengue vaccine development has aimed to elicit a neutralizing antibody response, as T cells are assumed to contribute a minor or secondary role in dengue vaccine-mediated protection. Next, we will describe each of these vaccines.
### 4.2. Vaccine types
#### 4.2.1. Live-attenuated virus (LAV)
The fundamental aim of vaccination is to promote protective immunity while avoiding disease from the vaccine itself. The first generation of viral vaccines was based on empirical attenuation by repeated passage in cultured cells. Several LAVs are eligible vaccines as they meet the following criteria; they elicit a strong and protective immune response with a low risk of disease from the vaccine itself. In the present regulatory environment, the use of LAVs has also been limited by safety concerns, including reversion to wild-type virulence. Because LAVs are shed from vaccines, they sometimes present a risk to unvaccinated individuals with impaired immunity. Although LAV vaccines have been developed for many RNA viruses, the mutability of these pathogens presents unique challenges for vaccine design [21].
#### 4.2.2. Purified inactivated virus (PIV)
It is widely believed that inactivated dengue virus vaccines are impractical given the difficulty in obtaining sufficiently high titers of the virus in a suitable cell substrate. However, this was challenged when dengue type-2 (dengue-2) virus was adapted to replicate to high titers in certified Vero and fetal rhesus lung (FRhL-2) cell cultures and used to make prototype purified, inactivated virus (PIV) vaccines. In addition, in formulation with an aluminum hydroxide adjuvant, these vaccines elicit virus-neutralizing antibodies in mice and rhesus macaques and provide at least partial protection against virus challenge [22].
#### 4.2.3. Recombinant subunits
Recombinant subunit-based vaccines may prove to be significantly advantageous compared to other approaches currently being implemented for development of a dengue vaccine. First of all, the lack of a replicating virus helps to ensure the safety of the product by avoiding the possibility for inadequate attenuation or reversion in the context of live virus approaches, or inadequate inactivation in the context of killed virus vaccines. Furthermore, under a tetravalent formulation, the ability to induce a balanced immune response may be more easily manipulated through dose adjustments using recombinant subunits compared to four replicating viruses. Finally, in terms of yield and cost effectiveness, and since the dengue vaccine mainly targets developing areas, a high yielding, highly immunogenic, recombinant subunit could prove to be an attractive alternative to vaccines based on virus replication, (live attenuated or killed) where yields may be lower than required [23].
Recombinant subunit vaccines stand as one of the safest alternatives, as a means to bypass the issue of viral interference, offering the possibility to administer a tetravalent formulation on an accelerated schedule. An advantage of an accelerated schedule is that full protective immunity could be induced more quickly, thus avoiding the potential of exacerbated disease due to partial immunity during an extended immunization course. Among other advantages of an accelerated schedule are better general compliance, more suitability for travelers and military personnel, easier integration into existing immunization schedules, and the potential for use in an outbreak setting. A balanced tetravalent immune response may also be more readily accomplished through simple dose adjustments for each of the four recombinant proteins, in comparison to live virus vaccines where the interactions between viruses can be complex and unpredictable [24].
#### 4.2.4. Virus-like particles (VLPs)
VLP vaccines are virus-like particles that do not contain replicative genetic material, but permit presentation of antigen in a repetitive, ordered array similar to the virion structure, which is thought to increase immunogenicity [25]. Thus, the safety concerns of virus vaccines regarding reversion mutants and immunocompromised individuals are obviated. The recombinant of VLP allows these vaccines to be usually manufactured large-scale in a cost-effective manner, following current good manufacturing practices. They induce quick and fulminant humoral immune responses by displaying antigens in an ordered and repetitive way. Their particulate nature and dimensions allows an efficient assimilation by dendritic cells (DCs) and transportation to lymph nodes, followed by presentation and induction of optimal immune responses. VLPs are renowned for inducing rapid and strong antibody responses. This trait is attributed to their dense, highly repetitive, quasi-crystalline structures [26], see Dengue vaccine candidates in Table 1.
Candidate name/identifierAntigenVaccinationDeveloperPreclinicalPhase IPhase IIPhase III
CYD Live recombinant based on a yellow fever vaccine 17D backboneDENV-1-4 prM/E3 doses (0/6/12 months)Sanofi PasteurXXXX
TV003/TV005 Tetravalent live, attenuated/recombinant (whole virus DENV1–3 and recombinant DENV2 in DENV4 backbone)DENV-1,3,4 whole genome, DENV-2 prM/E1 doseUS National Institutes of Health and Butantan (with licenses to other manufacturers)XXXX
DENVax Tetravalent live, attenuated/recombinant (whole virus DENV2 and recombinant DENV1/3/4 in DENV2 backbone)DENV-2 whole genome, DENV-1, -3, -4 prM/E2 doses (0/90 days)TakedaXXX
DPIV Tetravalent purified inactivated vaccineDENV-1–4 whole genome2 doses (0/28 days)GSK/US WRAIR/FiocruzXX
DEN-80ETetravalent E protein subunit vaccineSoluble DEN 1/2/3/4 prM/E protein3 doses (0/1/2 months)MerckXX
TVDVTetravalent “shuffled” prM/E expressed from plasmid vector DNA vaccinePlasmid DNA expressing DENV 1/2/3/4 prM-E3 doses (0/1/3 months)US Naval Medical Research CenterXX
TLAV-TPIV Heterologous prime-boost with live-attenuated tetravalent, live-attenuated vaccine and tetravalent alum-adjuvanted purified inactivated vaccinePurified inactivated DENV or plasmid vector expressing prM/E (prime) and live-attenuated DENV (boost)US WRAIRXX
### Table 1.
Dengue vaccine candidates.
Dengue vaccine candidates; adapted from Kirsten et al. [27].
### 4.3. Vaccines under clinical trials
#### 4.3.1. CYD-TDV Dengvaxia
Sanofi Pasteur’s CYD vaccine is a live-attenuated tetravalent chimeric vaccine. In this vaccine, the premembrane and envelope proteins from a wild-type dengue virus corresponding to each of the four serotypes are substituted into the yellow fever (YF) 17D vaccine backbone. A strong neutralizing antibody response to DENV2 was elicited in the first CYD clinical trial in healthy adults, which evaluated only the serotype 2 vaccine strain. Participants previously given YF vaccine seroconverted to all four dengue serotypes [28]. The first licensed dengue vaccine, a live, attenuated, tetravalent dengue vaccine (CYD-TDV; Dengvaxia), has recently been registered in 15 countries as a three-dose immunization schedule administered subcutaneously at 6-month intervals [29]. In the case of Dengvaxia, vaccination of children with no previous infection (seronegative) may mimic an initial infection during the first step in the development of ADE. Because vaccine protection is incomplete and unequal against the four serotypes, a natural infection later in life can complete the sequence of events, causing ADE and severe, life-threatening dengue fever [30].
Following CYD-TDV introduction, it should be administered as a three-dose series given on a 0-/6-/12-month schedule. However, additional evidence is required in order to determine whether equivalent or better protection may be obtained through simplified schedules. In response to a delay in a vaccine dose for any reason, the vaccine course should be resumed (not restarted), maintaining the 6-month interval between subsequent doses. Given the 12-month duration of the immunization schedule and to enable better vaccine monitoring, countries should have vaccine tracking systems implemented. CYD-TDV is not recommended for use in children under 9 years of age, consistent with current labeling, in view of the association of CYD-TDV with increased risk of hospitalized and severe dengue illness in the 2- to 5-year age group. The target age for routine vaccination should be defined by each country, intended to maximize the vaccination impact and programmatic feasibility of targeting specific age groups. For instance, some countries may present the highest incidence of dengue illness among the adult age population and may consider vaccinating people up to 45 years of age in routine programs. The implementation of a routine CYD-TDV vaccination program at 9 years of age in settings meeting the criteria mentioned above is expected to contribute to a 10–30% reduction in symptomatic and hospitalized dengue illness over 30 years [31], see Table 2. This vaccine will be reviewed further in a separate section since, differently to other vaccines in this section, Dengvaxia has already been registered.
Four-year safety follow-up of the tetravalent dengue vaccine efficacy randomized controlled trials in Asia and Latin America,Arredondo-García et al. 2018 [32]Data from the clinical trials for up to year 4 after first vaccination indicate a positive benefit–risk profile for the CYD-TDV vaccine for the population aged 9 years old.
A multi-country study of dengue vaccination strategies with Dengvaxia and a future vaccine candidate in three dengue-endemic countries: Vietnam, Thailand, and Colombia.Lee et al. 2018 [33]Given the absence of efficacy and half-life data for any of the second-generation vaccine candidates, it was assumed that NVC is 80% efficacious with a half- life of 8 years.
Dengue vaccination during pregnancy—an overview of clinical trials data.Skipetrova et al. [34]In the small dataset assessed, no evidence of increased adverse pregnancy outcomes has been identified from inadvertent immunization of women in early pregnancy with CYD-TDV compared with the control group.
The conclusions are limited to vaccination in CYD-TDV in the first trimester, since no data are available on pregnancy outcome for administration of this vaccine in the second or third trimester. The data described here, and those continuing to emerge from the on-going clinical development and post-marketing of CYD-TDV, provide a valuable contribution to the currently limited available information on the use of the dengue vaccine in pregnant women.
Live-attenuated, tetravalent dengue vaccine in children, adolescents and adults in a dengue-endemic country: Randomized controlled phase I trial in the Philippines.Capeding et al. 2011 [35]The safety profile of TDV in a flavivirus endemic population was consistent with previous reports from flavivirus-naïve populations. A vaccine regimen of either three TDV vaccinations administered over a year or two TDV vaccinations given more than 8 months apart resulted in a balanced antibody response to all four dengue serotypes in this flavivirus-exposed population, including children.
### Table 2.
Some CYD-TDV Dengue vaccine safety and immunogenicity studies in different populations.
#### 4.3.2. TV003 and TV005 Dengue vaccine
The Laboratory of Infectious Diseases at the U.S National Institutes of Health has evaluated numerous monovalent and tetravalent dengue candidate vaccines to identify candidates with the most acceptable safety, infectivity, and immunogenicity profile. Among these, TV003 is an admixture of four live-attenuated recombinant dengue vaccine candidate viruses (rDEN1D30, rDEN2/4D30, rDEN3D30/31, and rDEN4D30) [36]. Various monovalent candidates were initially tested in Phase 1 trials in order to optimize each of the four vaccine virus strains. Vaccine virus serotypes 1, 3, and 4 are based on complete viruses, while serotype 2 is a recombinant virus based on the serotype 4 vaccine strain with the structural proteins replaced by those of serotype 2. A single dose of TV005 elicits seroconversion rates above 90% against each serotype, and 90% of flavivirus-naive recipients displayed a tetravalent response. TV003 or TV005 has been licensed to several manufacturers, including Butantan, VaBiotech, and Merck. Phase 2 studies are underway in Brazil and Thailand, and a Phase 3 trial led by Butantan began in February, 2016, in Brazil [27], see Table 3.
In a randomized trial, the live-attenuated tetravalent dengue vaccine TV003 is well- tolerated and highly immunogenic in subjects with flavivirus exposure prior to vaccinationWhitehead et al. 2017 [37]In summary, the authors demonstrated that the NIH tetravalent dengue vaccine TV003 is well-tolerated in flavivirus-experienced individuals and elicits robust post-vaccination neutralizing antibody titers.
The live-attenuated dengue vaccine TV003 elicits complete protection against dengue in a human challenge modelKirkpatrick et al. 2016 [36]TV003 induced complete protection against challenge with rDEN2Δ30 administered 6 months after vaccination. TV003 will be further evaluated in dengue-endemic areas.
### Table 3.
Some TV003 vaccine safety and immunogenicity studies.
#### 4.3.3. DENVax
Takeda’s live tetravalent dengue vaccine (TDV) candidate is based on a molecularly characterized attenuated serotype 2 strain (TDV-2). The DENV-2 PDK-53 virus was initially obtained through 53 serial passages of the wild-type (wt) DENV-2 16681 in primary dog kidney (PDK) cells. The DENV-2 PDK-53 virus has proved to be safe, well-tolerated, immunogenic, and elicits long-term humoral and cellular immune responses to DENV-2, based on clinical trials conducted in the United States and Thailand [38]. Three chimeric strains (TDV-1, TDV-3, and TDV-4) were engineered by substituting the premembrane (prM) and envelope (E) structural genes of the respective DENV strains into the attenuated TDV-2 backbone [39]. TDV is designed to promote humoral and cellular protective immune responses against all four dengue serotypes, as it contains the premembrane and envelope proteins unique to each serotype. These specific proteins are needed to induce neutralizing antibodies. The use of DENV-2 as a backbone for TDV may confer additional protection against dengue. In particular, TDV contains the genes encoding the conserved nonstructural (NS) proteins within the dengue backbone; and these proteins have been shown to be important in generating T-cell-mediated responses to dengue infection. Furthermore, anti-NS1 antibodies have been associated with cross-protective humoral immune responses [40]. Table 4 shows some of the studies conducted to determine the effectiveness of this vaccine.
Safety and immunogenicity of a live-attenuated tetravalent dengue vaccine candidate in flavivirus-naive adults: a randomized, double-blinded Phase 1 clinical trialGeorge et al. 2015 [41]TDV was generally well-tolerated, induced trivalent or broader neutralizing antibodies to DENV in most flavivirus-naive vaccines, and is undergoing further development.
Safety and immunogenicity of a recombinant live-attenuated tetravalent dengue vaccine (DENVax) in flavivirus-naive healthy adults in Colombia: a randomized, placebo-controlled, phase 1 studyOsorio et al. 2014 [42]The authors emphasize the acceptable tolerability and immunogenicity of the tetravalent DENVax formulations in healthy, flavivirus-naive adults. Further clinical testing of DENVax in different age groups and in dengue-endemic areas is warranted.
Development of DENVax: A chimeric dengue-2 PDK-53-based tetravalent vaccine for protection against dengue feverOsorio et al. 2011 [43]The DENVax vaccine is considerably different from previously tested tetravalent vaccines in that all four strains contain the same attenuating mutations as the DEN-2 PDK-53 strain, a strain that has been shown to be both safe and immunogenic in humans. Such vaccine is critically needed to protect people from the threat of dengue infection and improve public health worldwide.
### Table 4.
Some TDV(DENVax) vaccine safety and immunogenicity studies.
#### 4.3.4. DPIV tetravalent purified inactivated vaccine
The Walter Reed Army Institute of Research (WRAIR) in collaboration with GlaxoSmithKline Vaccines (GSK) developed a live-attenuated tetravalent dengue virus vaccine candidate comprised of four live virus strains representing each of the four DENV types. These strains were attenuated by serial passage in primary dog kidney (PDK) cells [44]. The US Navy Naval Medical Research Center (NMRC) has developed a tetravalent DNA vaccine (TVDV), formulated with Vical’s Vaxfectin adjuvant, containing genes encoding the premembrane (prM) and envelope (E) proteins for all four serotypes of dengue virus. Both Vaxfectin-formulated and unformulated vaccines are currently being evaluated in Phase I human testing [45].
Inactivated vaccines are assumed to provide acceptable safety profiles across a wide age range as well as in immunocompromised hosts. In addition, these can be co-administered with other vaccines. Shortened vaccination schedules and rapid immunization are also feasible using this type of vaccines. For these reasons, a safe and efficacious tetravalent DENV PIV could be suitable for national immunization programs across broad age ranges and baseline health status, as well as an active immunization option for travelers and military personnel, and a potential tool for outbreak response [46]. Table 5 shows several DPIV vaccine safety and immunogenicity studies.
Phase I randomized study of a tetravalent dengue purified inactivated vaccine in healthy adults from Puerto Rico.Diaz et al. 2018 [47]Results from this first phase I study of a new vaccine candidate with inactivated DENV in a dengue-primed population showed that all four DPIV vaccine formulations were well-tolerated and immunogenic. This new investigational DPIV vaccine had an acceptable safety profile in a small number of flavivirus-primed healthy adult subjects and all formulations boosted neutralizing antibodies (Nab)responses, with complex adjuvants increasing immunogenicity versus alum adjuvantation. Nab titers remained high (and above baseline titers) through M13. These results encourage continuation of DPIV clinical development.
Phase 1 randomized study of a tetravalent dengue purified inactivated vaccine in healthy adults in the United StatesLepine et al. 2017 [48]All DPIV formulations were well-tolerated. No vaccine-related serious adverse events were observed through 12 months after the second vaccine dose. In all DPIV groups, geometric mean antibody titers peaked at Day 56, waned through 6 months after the second vaccine dose, and then stabilized. In the nine subjects where boosting was evaluated, a strong anamnestic response was observed. These results support continuation of the clinical development of this dengue vaccine candidate.
### Table 5.
Some DPIV vaccine safety and immunogenicity studies.
#### 4.3.5. DEN 80E vaccine
This vaccine (developed by Hawaii Biotech and now licensed to Merck) is composed of a recombinant truncated protein corresponding to 80% of the N-terminal DENV E protein (DEN-80E). The C-terminal truncation of the E protein at amino acid 395 removes the membrane anchor sequence of the protein, resulting in a recombinant E protein with improved secretion, purification and immunogenicity. The DEN-80E protein for each of the four dengue serotypes has been expressed in the Drosophila S2 expression system to produce a tetravalent vaccine [49], which induces a high level expression of proteins of interest. Specifically, the system was chosen to express a plasmid containing the prM and N-terminal 80% of the E gene sequence of DENV-2. The resulting polyprotein undergoes cleavage by endogenous proteases and the 80E protein with a native-like N terminus is released. Two doses of the DENV-2 subunit 80E protein were administered to rhesus macaques in combination with one of seven different adjuvants at a 3-month dosing interval. Following this administration, animals were challenged with wild-type DENV-2 2 months after the last dose of vaccine. Neutralizing antibodies were detected in all study animals after the first dose and this response was boosted by the second dose. The highest neutralizing antibody titers were produced by the r80E protein formulated with the adjuvants AS05 or AS08, and protection against viremia was correlated with a higher neutralizing antibody titer at challenge. The same system was employed to generate recombinant subunit E proteins (80E) of the other DENV serotypes. A tetravalent formulation of the recombinant 80E proteins was evaluated in mice and nonhuman primate experiments. In some instances, the NS1 protein of DENV-2 was included in the formulation to potentially enhance the immune response to the vaccine. Macaques were immunized with the tetravalent formulation four times (day 0, 28, 67, and 102) and were challenged 5 months after the last dose. Due to the limited number of monkeys in each group, monkeys were only challenged with DENV-2 or DENV-4. Monkeys developed a robust neutralizing antibody response to all four DENV serotypes and were completely protected from DENV-2 challenge [50]. Table 6 shows some of the studies conducted to determine the effectiveness of this vaccine.
Preclinical development of a dengue tetravalent recombinant subunit vaccine: Immunogenicity and protective efficacy in nonhuman primatesGovindarajan et al. 2015 [51]Overall, the subunit vaccine was demonstrated to induce strong neutralization titers resulting in protection against viremia following challenge even 8–12 months after the last vaccine dose.
The development of recombinant subunit envelope-based vaccines to protect against dengue virus induced diseaseColler et al. 2011 [24]The DEN-80E recombinant subunit proteins for all four dengue virus types are expressed at high levels and have been shown to maintain native-like conformation. When formulated with a variety of adjuvants the antigens are potent immunogens and induce high titer virus-neutralizing antibody responses. Furthermore, the antigens have been shown to protect against viral challenge in both mouse and nonhuman primate models. Tetravalent vaccine formulations have also been evaluated in preclinical models with no evidence of immune interference or competition between the four DEN-80E antigens being observed. These proofs of concept preclinical studies led to the advancement of a monovalent DEN1-80E vaccine candidate into clinical testing.
Development of a recombinant tetravalent dengue virus vaccine: immunogenicity and efficacy studies in mice and monkeysClements et al. 2010 [23]The production of recombinant dengue 80E proteins in Drosophila S2 cells that are capable of eliciting potent immune responses in mice and nonhuman primates represents a major achievement in the effort to develop a recombinant dengue vaccine. The S2 cell expression system efficiently produces 80E from all four dengue serotypes. Our data show that co-administration of the subunits from the four serotypes results in a balanced immune response, equivalent to that observed when the four individual components are administered separately. Furthermore this response can be induced in a relatively short period of time (2–3 months).
### Table 6.
Some DEN 80E Vaccine safety and immunogenicity studies.
#### 4.3.6. TVDV tetravalent “shuffled” prM/E expressed from a plasmid vector DNA vaccine
The U.S. Naval Medical Research Center (NMRC) developed a tetravalent plasmid DNA vaccine candidate using prM and E protein genes expressed in a plasmid vector. A DENV-1 monovalent candidate of this vaccine was evaluated for safety and immunogenicity through a phase I clinical trial on healthy flavivirus-naïve adults using a three-dose schedule at 0/1/5 months. The results showed poor immunogenicity. Although it is possible that TVDV may have a role as a travel vaccine in the future, the available data is currently insufficient to anticipate its potential use as a travel vaccine [52].
The TVDV is a mixture of equal amounts of four monovalent double-stranded plasmid DNA vaccines produced under current Good Manufacturing Practices conditions in the United States. Each monovalent plasmid contains the prM and E genes of dengue 1, 2, 3, or 4 viruses cloned into the backbone plasmid VR1012 (Vical Incorporated, San Diego, CA) [53]. Table 7 shows some of the studies conducted to determine the effectiveness of this vaccine.
Safety and immunogenicity of a tetravalent dengue DNA vaccine administered with a cationic lipid-based adjuvant in a Phase 1 clinical trialThomas et al. 2018 [53]TVDV-Vaxfectin was safe and well-tolerated in this early Phase 1 human clinical trial. Whereas anti-dengue IFNγ T-cell responses occurred in most of the study subjects, anti-dengue neutralizing antibody responses were poor. Utilization of alternative delivery methods as well as examining prime-boost approaches may result in a more robust and long-lasting humoral immune response.
A dengue DNA vaccine formulated with Vaxfectin® is well-tolerated, and elicits strong neutralizing antibody responses to all four dengue serotypes in New Zealand white rabbitsRaviprakash et al. 2012 [54]The formulated vaccine and the adjuvant were tested for safety and/or immunogenicity in New Zealand white rabbits using a repeat dose toxicology study. The formulated vaccine and the adjuvant were found to be well-tolerated by the animals. Animals injected with formulated vaccine produced strong neutralizing antibody response to all four dengue serotypes.
### Table 7.
Some TVDV vaccine safety and immunogenicity studies.
### 4.4. Vaccine candidates under preclinical assays
There are numerous vaccine candidates that are being studied in preclinical trials, as can be seen in Table 8.
Techonological approachAntigenVaccine developerValency under evaluation or evaluated in NHP
Recombinant subunit vaccinesEDIII-p64k fusion proteins and EDIII-capsid fusion proteins expressed in E. coliIPK/CIGBMonovalent
Bivalent 80E-STF2 fusion proteins expressed in baculovirus/insect cellsVaxInnateTetravalent
Tetravalent consensus EDIII protein expressed in E. coli.NHRITetravalent
DNA vaccineprM/E expressed from plasmid vector DNA vaccineUS CDCTetravalent
VLP VaccinesEDIII-HBsAg VLPs or ectoE-based VLPs expressed in P. pastorisICGEBTetravalent
Virus-vectored vaccinesTetravalent EDIII and DENV-1 ectoM expressed from live-attenuated measles virus vectorThemis Bioscience/Institut X PasteurTetravalent
E85 expressed from single-cycle VEE virus vectorGlobal VaccinesTetravalent
Purified inactivated virus vaccinePsoralen-inactivated DENVUS NMRCMonovalent
Purified inactivated DENVPurified inactivated DENVWRAIR/GSK/FIOCRUZTetravalent
Live-attenuated virus vaccinesDEN/DEN chimeric viruses, live, attenuatedChiang Mai University/Mahidol X University/NSTDA/BioNet-AsiaMonovalent
DEN host range mutationsArbovaxTetravalent
### Table 8.
Active dengue vaccine candidates in preclinical development that have been evaluated in NHP models.
#### 4.4.1. EDIII-p64k fusion proteins and EDIII-capsid fusion proteins expressed in E. coli
Te Pedro Kourí Tropical Medicine Institute (IPK) in collaboration with the Center for Genetic Engineering and Biotechnology (CIGB) in Cuba have led the development of various recombinant subunit vaccine candidates. One approach is based on fusion of DENV EDIII to the carrier protein p64k of Neisseria meningitidis, and this EDIII-p64k fusion protein is then expressed in E. coli. Evaluations in mice showed that monovalent vaccine candidates for all DENV serotypes were able to induce neutralizing antibodies and protect against viral challenge. DENV-1 and DENV-2 monovalent candidates have also been evaluated in NHPs. Monkeys were immunized subcutaneously with four doses of the monovalent vaccine (50–100 g protein per dose, formulated in Freund’s adjuvant), which proved to be immunogenic and provided protection against viral challenge. Adjuvants suitable for human use are under evaluation, including N. meningitidis serogroup A capsular polysaccharide (CPSA) adsorbed on aluminum hydroxide [25].
## 5. Final thoughts
Finally, we want to reflect on the implications of the co-circulation of the dengue virus and the Zika virus, as well as on the new indications for the use of the Dengvaxia vaccine.
First, we will analyze the fact that the appearance of the infection by the Zika virus (another flavivirus) in zones of high prevalence for dengue constitutes an interesting challenge for the development of the ideal vaccine for both viruses.
### 5.1. Zika virus infection means new challenges in dengue vaccine development
Among pathogenic human flaviviruses, DENV and ZIKV are most closely related to each other, with 55.1–56.3% amino acid sequence identity. Zika virus is closer to dengue virus than to any of the other flaviviruses and indeed is almost close enough to think of it as a fifth serotype [10]. Accordingly, emerging literature indicates many similarities between these two viruses in terms of interactions between the virus and host immune system. For both viruses, the interferon system is the central mediator of host defense and target of a viral counterattack, whereas complex interplays between antibody and T cell responses likely determine the outcome of infection in flavivirus immune settings [55]. Dejnirattisai et al. found that most mAbs to DENV also bound to ZIKV, yet the antibodies targeting the major linear fusion-loop epitope (FLE) did not neutralize ZIKV, whereas they showed neutralizing activity against DENV. ZIKV virus infection was found to be potently enhanced by DENV-immune plasma and mAbs to DENV, suggesting the possibility that preexisting immunity to DENV might increase ZIKV replication; thus, this data indicate that immunity to DENV might drive greater ZIKV replication and have clear implications for disease pathogenesis and future vaccine programs for ZIKV and DENV [11]. There have been safety concerns related to Dengvaxia resulting from long-term vaccine trials. In patient groups under 9 years of age, hospitalization from DENV infection was greater for vaccinated children than for the nonvaccinated control group. These findings suggest ADE of infection in DENV naive children at the start of the study trial and who had been primed by but not protected by the vaccine. Consequently, the vaccine is not licensed for use in children under 9 years of age and, furthermore, it is recommended for use only in populations with a seroprevalence of 70% or greater of prior DENV exposure in the age group to be vaccinated [56].
Currently, there is a high pressure to produce a vaccine against ZIKV, and in this context, the extensive serological cross-reaction between DENV and ZIKV must be considered. It is likely necessary that the vaccine be used in areas with high seroprevalence for DENV and raising de novo ZIKV-neutralizing responses in such a setting might be challenging. It is likewise possible that vaccination of DENV-naive subjects against ZIKV might promote ADE of DENV infection and, conversely, that vaccination against DENV might promote ADE of ZIKV infection. In summary, cross-reaction of antibodies to DENV with ZIKV and promotion of ADE of infection can occur due to the existing similarities between the two viruses, even though ZIKV differs in sequence identity from DENV by around 41–46% (in the sequence of the envelope protein). In this context, ZIKV could be considered a fifth member of the DENV serocomplex, a factor that must be considered in vaccine approaches to these two viruses [11]. The results of Barba-Spaeth group suggest that the epitope targeted by the EDE1 bnAbs is more adequate for developing an epitope-focused vaccine for viruses of the ZIKV/DENV super serogroup than is the FLE, which induces poorly neutralizing and strongly infection-enhancing antibodies [57].
### 5.2. The Dengvaxia future
Dengvaxia is the only vaccine licensed to date for use in humans, which is why epidemiologists, health professionals, clinical physicians, and basic researchers (virologists, immunologists, molecular biologists, etc.) should be concerned about the future of this vaccine, which has had a reverse according to the latest publications of its results, so we will end this chapter with the following reflection based on the publications from 2016 to date.
Since April 2016, Dengvaxia has been licensed for use in 19 countries, and was recommended by the WHO Strategic Advisory Group of Experts (SAGE) on immunization to be used in regions with high endemicity, as defined by a prevalence of dengue antibodies of more than 50% in the targeted age group of people aged 9–45 years. Nevertheless, Guiar’s mathematical model finds that a significant reduction of hospitalizations can be only achieved when the vaccine is directed exclusively to seropositive individuals [58]. Along this same line, this group of researchers in 2017 predicted a significant reduction in dengue virus infection-related hospital admissions resulting from the administration of Dengvaxia only to dengue seropositive individuals, based on the analysis of an age-structured model using the available vaccine trial data. Moreover, the researchers predicted a significant increase in the number of dengue-related admissions, over a 5-year period, if the vaccine is to be administered without previous population screening for serostatus. The take-home message is that individual serostatus is the most important feature when implementing this vaccine and that only individuals of any age who have experienced at least one dengue virus infection will benefit from vaccination [59, 60]. New data by Sanofi in November 2017 showed that Dengvaxia could increase the risk of severe dengue in people who had not been previously exposed to the virus. For any countries considering vaccination as part of their dengue control program, the WHO recommends a “prevaccination screening strategy,” in which only dengue seropositive people are vaccinated. The prescreening process could be achieved by conventional serological testing for dengue virus to identify people who have had previous dengue infections. As Sanofi stated, “We are confident in Dengvaxia’s safety and its proven potential to reduce dengue disease burden in endemic countries. We will continue to work with the international public health community and endemic countries, to ensure the best usage of the vaccine to increase protection for populations at risk of subsequent dengue infections [that are] potentially more debilitating” [61].
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Jhon Carlos Castaño-Osorio, Alejandra María Giraldo-Garcia and Maria Isabel Giraldo (November 5th 2018). Current Status of Vaccines against Dengue Virus, Dengue Fever - a Resilient Threat in the Face of Innovation, Jorge Abelardo Falcón-Lezama, Miguel Betancourt-Cravioto and Roberto Tapia-Conyer, IntechOpen, DOI: 10.5772/intechopen.80820. Available from:
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View all Books | 2020-10-29 20:31:59 | {"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": 0.42399147152900696, "perplexity": 10840.588904616825}, "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/1603107905777.48/warc/CC-MAIN-20201029184716-20201029214716-00366.warc.gz"} |
https://economics.stackexchange.com/questions/29528/linear-homothetic-utility | # Linear Homothetic Utility
A Homothetic Utility is where $$\forall x,y, \forall a \in \mathbb{R}_+: \ u(ax,ay)=au(x,y)$$ (or its monotonic transformation).
A linear Homothetic utility is defined as $$\forall x,y, \forall a \in \mathbb{R}_+: \ u(ax+b,ay+c)=au(x+b,y+c)$$ where $$b,c$$ are constants.
This preference has very similar property as the homothetic preference. In fact, if we simply translate the coordinate system in the direction of (b,c), then the preference becomes homothetic.
Are there any works covering this property? I've checked a lot of theory papers in homothetic preference but found no luck.
Homothetic Preferences by James DOW· and Sergio Ribeiro da Costa WERLANG
Homothetic and weakly homothetic preferences by J.C. Candeal, E. Indurain
Linear-homothetic preferences, by B Datta, H Dixon
• in the first line, should $au(x +y)$ be $au(x,y)$, as $u$ seems to take 2 arguments? – 201p May 27 '19 at 23:53
• @201p You are right, that was a typo – High GPA May 28 '19 at 0:03
• @Giskard You are right about a,x,y. b,c are constants – High GPA May 30 '19 at 14:26
• Can you give an example of a function $u \neq 0$ satisfying this identity? – Bertrand May 30 '19 at 17:13
• If you want to allow for $(b,c)$-translations, your then the preference should instead satisfy $$\forall x,y, \forall a \in \mathbb{R}_+: \ u(a(x+b),a(y+c))=au(x+b,y+c),$$ but this is equivalent to homotheticity. – Bertrand Jun 2 '19 at 10:44
The only utility function that comes to mind is the Stone-Geary utility function. For 2 goods, $$x$$ and $$y$$, this takes the form: $$u(x,y) = (x - a)^\alpha (y- b)^{1- \alpha}.$$ This is a Cobb-Douglas type of utility function where $$a$$ and $$b$$ are subsistence levels, i.e. you need to consume at least $$a$$ from $$x$$ and $$b$$ from $$y$$ to survive. It is the utility function that leads to the Linear expenditure system.
To see that it is linear homothetic notice that: \begin{align*} u(\beta \tilde x + a, \beta \tilde y + b) &= (\beta \tilde x + a - a)^\alpha (\beta \tilde y + b - b)^{1-\alpha},\\ &=\beta (\tilde x)^\alpha (\tilde y)^{1-\alpha},\\ &=\beta ((\tilde x + a) - a)^\alpha ((\tilde y + b) - b)^{1-\alpha},\\ &= \beta u(\tilde x + a, \tilde y + b). \end{align*} It could be that there is more work on utility functions with subsistence levels that lead to other preferences that are also linear homothetic.
For example you could define a CES utility function with subsistence levels: $$u(x,y) = (\alpha_x(x -a)^\sigma + \alpha_y(y-b)^\sigma)^{1/\sigma}$$ This will also satisfy linear homogeneity. This paper of Baumgärtner, Drupp & Quaas does something like this.
In general, if you take any homothetic utility function $$u(x,y)$$ then the modified 'subsistence-augmented' function: $$\tilde u(x, y) \equiv u(x - a, y - b),$$ will be linear homothetic. | 2021-06-24 09:00:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9765917062759399, "perplexity": 1575.2856395821282}, "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-2021-25/segments/1623488552937.93/warc/CC-MAIN-20210624075940-20210624105940-00191.warc.gz"} |
http://devaris.com/motivational-shows-smqu/631dfd-double-beta-decay-equation | 0000069471 00000 n It is described by the following decay equation and the Feynman diagram in Figure 1b). 0000086055 00000 n In general, the double beta decay process is expressed in terms of the nuclear atomic and mass numbers as (16.53) (A,Z) → (A,Z + 2) + 2 e − + 2 ν ¯ or beta particles. These changes are described using nuclear equations. The equation of beta decay is: (2.18) X N Z A → Y N ∓ 1 Z ± 1 A + e ∓ + (ν ¯ e ν e) where e ∓ is either an electron or positron, ν e and ν ¯ e are a neutrino and an antineutrino, respectively. The process probably most strongly connected to the history of neutrino research is the β-decay. Request PDF | On Jan 1, 2012, J.D. 0000002086 00000 n ! Nuclear matrix element for neutrinoless double beta decay The NME for the 0 transition from j0+ i ito j0 + f i M0 (0+ i!0 + f) = h0+ f jO0 j0+ i i –the transition operator: exchange of light neutrinos and with closure approximation O0 = 4ˇR g2 A Z d3~x 1 Z d3~x 2 Z R d3~q (2ˇ)3 ei~q (~x1 ~x2) q[ + E (i f)=2] Jy (~x 1)J y(~x 2) –the effective nuclear current Jy (x) = (x) 0000093935 00000 n In addition to the electron, or #beta"-particle"#, an electron neutrino is also emitted from the nucleus.. 0000092475 00000 n Every time an isotope decays, it loses a bit of energy in the form of a particle. 22 11N a → 22 10N e + 0e+ + νe. 0000095319 00000 n These changes are described using nuclear equations. 0000003198 00000 n Certain nuclei are able to decay into the second nearest neighbour, if two subsequent decays via an intermediate state could happen i.e. Scientists are looking for lepton number violation in a process called double beta decay, says SLAC theorist Alexander Friedland, who specializes in the study of neutrinos. 0000068231 00000 n Double-beta. The electron and the antineutrino are emitted from the nuclues, which now has one extra proton; this essentially changes the element, since the atomic number has now increased by 1. 0000071201 00000 n 0000102548 00000 n Alpha decay (two protons and two neutrons ) changes the mass number of the element by -4 and the atomic number by -2. This can only happen for isotopes on the lower parabola, which is the one containing even-even nuclei. Understanding and mitigating background radiation is especially important in searches for very rare nuclear processes, which utilize sensitive detectors. 0000080070 00000 n Anti-particle • Special relativity – Light velocity: constant – No information is faster than light – Any motion is relative • Quantum mechanics – Particle Wave – Uncertainty principle 4 Einste We present a master formula describing the neutrinoless-double-beta decay (0 νββ) rate induced by lepton-number-violating (LNV) operators up to dimension nine in the Standard Model Effective Field Theory. In nature, 35 isotopes are known which show the specific ground state configuration, necessary for double beta decay [2]. double-beta decay (ββ(2ν)) results in the emission of two electron antineutrinos in addition. 1-175. MAJORANA is an experiment to search for neutrinoless double-beta decay (0νββ).Neutrinos are fundamental particles that play key roles in the early universe, cosmology and astrophysics, and nuclear and particle physics. We use cookies to give you the best online experience. Avignone III et al., Double Beta Decay, Majorana Neutrinos, and Neutrino Mass, arxiv:0708.1033v2 [nucl-ex] (2007), Figure 1: Double beta decay candidate isotope level scheme. Double-beta decay is presently a very studied process both theoretically and experimentally due to its potential to provide valuable information about important, but still unknown issues related to the neutrino properties and conservation of some symmetries. 0000083972 00000 n ! Double beta decay was first discussed by M. Goeppert-Mayer [1] in the form of. (A,Z+2)+2e7+2n e: with half-lives around 1020 years is among the rarest decays ever observed. Beta-Minus (Negatron) Emission. In the US, this phase is under the stewardship of the DoE Office of Nuclear Physics. 0000086244 00000 n 0000001939 00000 n Left, the simultaneous decay of two neutrons as an allowed higher order process (2νββ-decay). @ For sake of completeness. Double-Beta Decay with Emission of Single Electron MEDEX’17 Prague, 29 May –2 June 2017 A. Babič,D. This transition occurs regardless of whether neutrinos are their own antiparticles or not, i.e. 70 0 obj << /Linearized 1 /O 73 /H [ 2086 897 ] /L 468582 /E 104288 /N 12 /T 467064 >> endobj xref 70 75 0000000016 00000 n Using data from the NEMO-3 experiment, we have measured the two-neutrino double beta decay ($$2\nu \beta \beta$$) half-life of $$^{82}$$ Se as $$T_{\smash {1/2}}^{2\nu } \!=\! double beta decay rates 10 Oct 2002 10:51 AR AR172-NS52-04.te x AR172-NS52-04.SGM LaTeX2e(2002/01/18) P1: IBC DOUBLE BET A DECAY 129 TABLE 1 Summary of experimentally measured ! 0000069153 00000 n high resolution search for 0νββ decay. Barbero∗†, F. Krmpotic´†∗∗, A. Mariano∗†, A.R. 1 1p → 1 0n + 0e+ +νe. They are shorter than those obtained by using solutions of the Schrödinger equation. 0000097047 00000 n The neutrinoless double beta decay. Beta Decay is a type of radioactive decay in which a proton is transformed into a neutron or vice versa inside the nucleus of the radioactive sample. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange In this type of beta decay, in essence all of the neutron decay energy is carried off by the antineutrino. The half life time is given by the following formula: (T 1/2,0ν)-1 = a 0ν F 0ν |M 0ν | 2 η 2 / log(2) Where: a 0ν ~ 5 10-17 y-1 is a dimensional factor Beta radiation is slightly more penetrating than alpha radiation, but still not nearly as penetrating as gamma radiation. The half-life limit is derived from 3.09 kg yr 130Te exposure. Within the Standard Model (SM) it can occur through several decay modes with lepton number conservation, namely with the emission of two electrons/positrons and two neutrinos/an… webpage-http://www.kentchemistry.com/links/Nuclear/naturalTrans.htm This short video walks you through how to write an beta decay expression. 0000068013 00000 n Beta decay is somewhat more complex than alpha decay is. 0000024556 00000 n Isotopes from the left side decay via β − -decay and isotopes on the right via β + -decay and electron capture. 0000101298 00000 n ... equation that has for solutions 4-component wavefunctions: p n p n e e e e--Summer 2018 G. Gratta 20 The key ingredients are the scattering electron wave functions. 0000098314 00000 n neutrinoless double beta decay depends on the neutrino mass. That easily excels the universe's age of approximately 14x10 9 years. 0000084268 00000 n It is a transition among isobaric isotopes. \left[ 9.39 \pm 0.17\left( \text{ stat }\right) \pm 0.58\left( \text{ syst }\right) \right] \times 10^{19}$$ y under the single-state dominance hypothesis for this nuclear transition. This process is not allowed in the Standard Model [3], [2]. Coronavirus (Covid-19): Latest updates and information. Right, the lepton-number violating mode (0νββ-decay) where the neutrino only occurs as a virtual particle. 0000083586 00000 n 0000098898 00000 n You can update your cookie preferences at any time. Muon Decay and the Majorana Neutrino Masaru Doi, Tsuneyuki Kotaniand Eiichi Takasugi. Advances in the Calculation of Double Beta Decay Jenni Kotila CenterforTheoretical Physics,SloanePhysicsLaboratory,YaleUniversity, NewHaven,Connecticut, 06520-8120, USA Beauty in Physics: Theory and Experiment, Cocoyoc May 17th, 2012 In honor of Francesco Iachello on the occasion of his 70th birthday Jenni Kotila Advances in the Calculation of Double Beta Decay. Contents … 1. Beta-minus decay occurs when an electron (negatively charged – hence beta-‘minus’) is … 0000001848 00000 n 0000027540 00000 n 0000092452 00000 n 0000088210 00000 n Rev., 48 (1935) 512, [2] K. Zuber, Double Beta Decay, Contemp. Searching for neutrinoless double beta decay is a top priority in particle and astroparticle physics, being the most sensitive test of lepton number violation and the only suitable process to probe the Majorana nature of neutrinos. INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS G: NUCLEAR AND PARTICLE PHYSICS J. Phys. A means of probing the absolute mass scale of neutrinos is the neutrino-less double beta decay discussed later. Ettore Majorana: His Equation and Fermions . 0000003819 00000 n Double beta decay K. ZUBER Double beta decay is a rare nuclear process changing the nuclear charge by two units leaving atomic number unchanged. Beta Decay is a type of radioactive decay in which a proton is transformed into a neutron or vice versa inside the nucleus of the radioactive sample. Double-beta. A very small minority of free neutron decays (about four per million) are so-called "two-body decays", in which the proton, electron and antineutrino are produced, but the electron fails to gain the 13.6 eV energy necessary to escape the proton, and therefore simply remains bound to it, as a neutral hydrogen atom. 0000002983 00000 n The section on beta emission on the previous page (radioactive decay and nuclear equations) focussed predominantly on beta-minus emission. 320 kg of 90% enriched 136Xe is in the experiment and a total amount of 615 kg is in hand [5]. Progress of Theoretical Physics Supplement No.83 (1985) pp. Figure 4: Feynman Diagrams for 2νββ (left) and 0νββ (right) [4]. Bertulani§ ∗Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, La Plata, Argentina †Instituto de Física La Plata, CONICET, La Plata, Argentina This mass is unknown and many experiments are trying to measure it. 0000023837 00000 n Neutrino-less double beta decay is the most sensitive probe of lepton number violation and a powerful tool to study the origin of neutrino masses. 0000098337 00000 n Neutrinoless double beta decay is the only known process that enables to test experimentally the Majorana nature of neutrino together with its absolute mass scale. Four types of nuclear double beta decays accompanied with emission of two neutrinos are compared: (1) capture of double atomic electrons, (2) capture of one atomic electron and emission of one positron, (3) emission of two positrons and (4) emission of two electrons. 0000098706 00000 n 0000025695 00000 n y�9ii�օG�6}]xd��D�R*k��F� 0000028071 00000 n 0000083350 00000 n DEMONSTRATOR Neutrinoless Double Beta Decay Experiment and Large Enriched Germanium Experiment for Neutrinoless Double Beta Decay (LEGEND) Collaboration. Experimentalists are now searching for another form of double-beta de (0"). 0000098412 00000 n The computed half lives for neutrinoless double beta decay are compared with the corresponding experimental values and with those predicted by QRPA model. Processes like this and alpha decay allow the nucleus of the radioactive sample to get as close as possible to the optimum neutron/ proton ratio. 19Limit on 0ν-decay … A special situation among the ground states of nuclei can occur. Nuclear equations. 0000088480 00000 n 0000071663 00000 n Double beta decay, neutrino mass, Beyond Standard Model Physics PACS Nos. We then review a number of proposed experiments. H�bf�Pcgmed@ A6�(G���C#Pl�j�O~��H]���m�dİ������:��e�H����Q9;�\$vLR�PHdZ"�q������K���h�� [1] M. Goeppert-Mayer, Double Beta-Disintegration, Phys. We review recent developments in double-beta decay, focusing on what can be learned about the three light neutrinos in future experiments. 0000101321 00000 n For a specific atomic number the masses around the stable isotope can be approximated by a parabola as shown in Figure 2. The matrix which embeds the source is an array of ZnSe crystals, where enriched [Formula: see text]Se is used as decay isotope. 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Code for double beta decay expression the us, the particle emitted is an electron and an (. 35 isotopes are known which show the specific ground state configuration, necessary double. The three light neutrinos in future experiments we implemented double beta decay equation nuclear scale, through a chain of effective field.!
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https://www.gamedev.net/forums/topic/655481-design-question-how-to-access-other-classes/ | Followers 0
[Design Question] How to access other classes
6 posts in this topic
Hello.
I think the best way is to start with an example of my problem. I made a little game with diffrent objects. Each object interacts with the others and access them. (Like if a bullet hits a enemy, it destroys the enemy). So maybe you would put all this code in the Game-function()-Method.
I read somewhere that each object should update itself. So i made a Update()-function for every class.
Example:
I got a Ball-Class that checks in his Update()-Function if it collides with the player or other game objects. If the ball touches the lower border, the players lifes are decreased.
The Question:
How do i realise that? I first thought of giving the player each game-loop through the update-function. That wasn't that clean. So i changed the Ball Class
Ball::Ball( Player *player, posX, ....
Now i could access the player in the Update()-function to change its values. But i dont know if this is good practise. One big thing is, that i dont only have to access the player, but nearly every object in the game.
Here is an example of my Ball Class-Structure:
class Ball :
public cEntity
{
private:
double m_VelX;
double m_VelY;
double m_Speed;
bool m_Super;
Player* m_Player;
vector<Ufo*> *m_Ufos;
vector<PowerUp*> *m_PowerUps;
cAnimationManager *m_AnimationManager;
cSound *m_Sound;
public:
Ball(cGraphics *graphics, cAnimationManager *animManager, cSound *sound, Player *player, vector<Ufo*> *ufos, vector<PowerUp*> *powerups, string texture, int posX, int posY, int width, int height);
~Ball();
void Update( double delta );
void CheckCollision();
void Draw();
void Reset();
Should i continue this way?
Thanks,
Daniel
Edited by Agreon
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My advice' try to implement a game object-component system. A GO is just an entity that encapsulates components and components are for behaviors.
Then you can store in a list all components attached to the go and then have a GetComponent method that iterate through the list to find the component you passed as parameter.
If your case since you are comparing your object with all others for collision, you would have the GO reference, if you get a collision using the go you can find any other components you would want to access.
Each game object you create would inherits from GameObject class which contains all need methods and the protected list of components. Any behavior inherits from component and can be added to the list.
EDIT: The least when someone downvotes an answer is to have the guts (or balls) to expose why you consider it deserves. I do not see why this is a candidate for downvote since it is the pattern, engines are opting for, like Unity3D for instance. So except if you (whoever you are) can prove that Unity is a joke in the way they implemented their engine I would consider this answer a potential help to the OP.
Note I do not care about reputation as it does not pay the bills. So feel free to downvote some more as long as you let me know why.
Edited by fafase
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It's not that what you're offering is bad fafase, you're just trying to get a BEGINNER to do what's used in systems as complex as Unity.. No need to over complicate. (I didn't down-vote you, just offering my thoughts!)
Personally, Agreon, I'd do what I've seen for years - have a Game class that handles all of this for you. What you're doing is fine.. But if everything had a pointer to everything else it nigh on defeats the purpose of OOP!
Game class:
Holds a pointer to a player
Holds pointerS to multiple balls
Player and ball hold nothing regarding each other. However, I'd recommend adding a function for Ball that checks whether it collides. You can do that by passing a pointer in a function:
bool Ball::CollidesWithPlayer(Player* pPlayer)
{
// Do math checks, return true if it does, false if not
}
Inside your game class, you can then do whatever action you want to. Reset the level, deduct lives etc. Alternatively have a player function that takes a pointer to a Ball and does the same check, then in Game::Update you can just iterate across all your balls and check. Actually you can do that in either scenario..
Hope this helps!
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Thank you for your suggesstion, but let's say i have a game with many entities; That would be very confused in the game class.
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You will have to keep a list of all game entities somewhere, so processed entities can look them up and (non ideally) access them themselves. There is no other way. Use an abstract entity class to reference all different entity types and to encapsulate basic functionality shared between all of them. You can use messaging in a simple form of virtual methods to handle different entity types. This is how I would do it while keeping your simple entity structure (no systems, no components, etc.).
// Could be global or passed to every entity as a pointer.
// Use smart pointers to hold entities instead.
std::list<Entity*> entities;
// Base entity class.
class Entity
{
/* ... */
public:
void Update(float delta)
{
this->CheckCollisions();
this->OnUpdate(delta);
}
virtual void Draw()
{
// Drawing can be done in many ways.
}
void CheckCollision()
{
for(/* every entity on the list, but yourself */)
{
? if(/* check if collides */)
{
this->OnCollision(other);
}
}
}
void Damage(int damage)
{
// Substract damage from health and call Destroy() if it's below zero.
/* ... */
// Message itself about being damaged.
this->OnDamage(damage);
}
void Destroy()
{
// Mark as dead, but don't remove from the list yet.
/* ... */
// Message itself about being destroyed.
this->OnDestroy();
}
private:
virtual void OnUpdate(float delta) { }
virtual void OnCollision(Entity* other) { }
virtual void OnDamage(int damage) { }
virtual void OnDestroy() { }
private:
Enum type; // Player or a ball?
bool alive;
float position_x;
float position_y;
int health;
}
// Player entity class.
class Player : public Entity
{
/* ... */
public:
void Draw()
{
// Draw a player on the screen.
}
private:
void OnUpdate(float delta)
{
// Control the player entity.
// And fire bullets!
}
void OnDamage(int damage)
{
// Flash on damage.
}
void OnDestroy()
{
// Create an explosion (by creating a new entity?).
}
}
// Bullet entity class.
class Bullet : public Entity
{
/* ... */
public:
void Draw()
{
// Draw a bullet on the screen.
}
private:
void OnUpdate(float delta)
{
// Move the bullet forward.
}
void OnCollision(Entity* other)
{
// Check if we collided with the player.
// Could be done via RTTI.
if(other->GetType() == ENTITY_PLAYER)
{
// Damage the player entity for 10 HP.
other->Damage(10);
// Destroy itself.
this->Destroy();
}
}
}
// Create entities.
// It's sometimes useful to save a pointer to the player's entity so it can be quickly retrieved.
entities.push_back(new Player(/* ... */));
entities.push_back(new Bullet(/* ... */));
// Main loop.
while(true)
{
/* ... */
for(/* every entity */)
{
entity->Update(delta);
entity->Draw();
}
for(/* every entity */)
{
// Remove dead entities from the list.
}
}
Edit: If you don't want to hold a pointer to the player, you will have to go a bit beyond this. Create a system that will let you tag or name an entity as a "player", so you can later retrieve it without manually holding a pointer to it. Example:
// At entity creation.
Entity* entity = new Player();
entitySystem->TagEntity(entity, "player"));
// Anywhere else.
Entity* player = entitySystem->GetEntityByName("player");
Edited by Guns
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I read somewhere that each object should update itself. So i made a Update()-function for every class.
Maybe this is what is written, but I doubt it is what it's intended.
Personally, I'm starting to hate the word components and component based system, as many discussions about them end up being very high level and seldom useful. Many of their subtle problems are also rarely even taken in consideration, let alone discussed.
Anyway, your objects should not update themselves. That is, they should not have an Update call. Ideally.
Seconding Guns, and hopefully elaborating on the approach.
The Update call was basically an hack introduced to allow finer degree of flexibility, often going along with scripting. It suffers from being overly generic and if you look at systems using them, you'll notice there has been a growth of Update calls. Before rendering. Before physics. After everything.
Consider using this (anti?)pattern as a last resource.
Now, I see you're currently doing the physics yourself so you can manipulate speed and velocity. This is model data. There are also data related to presentation (m_Sound, m_AnimationManager) and stuff regarding gameplay-level model (powerups?). So your Ball is really a fusion of at least three different structures.
What it lacks is separation of concerns.
Let's pass the fact you're doing physics yourself (which is possibly appropriate for this kind of game). What you really want to have is a higher-level system keeping a list of collidable objects and dispatching calls appropriately, something like:
1. Collision system build a collision list
2. Gameplay system searches for the ball in the collision lists
3. For each match, searches for the kind of hit object
1. Is it an UFO? Call ufo->destroy, player->addPoints, signal ball bounce/collision/nothing
2. Is it a powerup? Call powerup->remove, player->applyPowerup, ball->applyPowerup
3. Otherwise, ball->collision.
In this way your Ball becomes a much smaller structure. It has a much more limited goal and knowledge. By delegating part of the low-level behavior to other components you get to avoid big god objects. For example, it does not need to have access to ufos or powerups anymore but only to react to them when informed.
Proponents of the component-entity model decided that this approach had to be glorified by giving it a sticker.
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I usually have a World class that contains all entities in the game. In this case, a World might have a Player, and some Ball. This World class has a list of all entities, and each entity is identified by an id. For example, player's id is 0, and the first ball's id is 1, etc. Each entity also keeps reference to this World class.
I usually make each entity update themselves for every tick of the game, but their update functions are called from the World class in its own update function. On every tick of the game loop, the World's update function is called, which loops through all entities, calling their update function one by one. The update function for Player might be recalculating its position and draws itself on the screen according to the new position. The update function for Ball might be changing its direction randomly and checks if it meets the Player by referencing the World class. It needs to draw itself on the screen too. Every entity needs to draw themselves according to their position, so it's not a bad idea to have a render function in the class. Well, the render function is likely to be similar (printing the sprite on the coordinate), so I think it wouldn't hurt to make a parent Entity class for Player and Ball.
That's how I usually code my games. I'm not sure why Krohm said that objects shouldn't update themselves, but you better listen to him. I'm still learning myself.
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Register a new account | 2017-07-21 11:34:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17185324430465698, "perplexity": 2668.113455113544}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423769.10/warc/CC-MAIN-20170721102310-20170721122310-00591.warc.gz"} |
https://arbital.greaterwrong.com/p/euclidean_domain_is_pid?l=5vj | Euclidean domains are principal ideal domains
A common theme in ring theory is the idea that we identify a property of the integers, and work out what that property means in a more general setting. The idea of the euclidean domain captures the fact that in $$\mathbb{Z}$$, we may perform the division algorithm (which can then be used to work out greatest common divisors and other such nice things from $$\mathbb{Z}$$). Here, we will prove that this simple property actually imposes a lot of structure on a ring: it forces the ring to be a principal ideal domain, so that every ideal has just one generator.
In turn, this forces the ring to have unique factorisation (proof), so in some sense the Fundamental Theorem of Arithmetic (i.e. the statement that $$\mathbb{Z}$$ is a unique factorisation domain) is true entirely because the division algorithm works in $$\mathbb{Z}$$.
This result is essentially why we care about Euclidean domains: because if we know a Euclidean function for an integral domain, we have a very easy way of recognising that the ring is a principal ideal domain.
Formal statement
Let $$R$$ be a euclidean domain. Then $$R$$ is a principal ideal domain.
Proof
This proof essentially mirrors the first proof one might find in the concrete case of the integers, if one sat down to discover an integer-specific proof; but we cast it into slightly different language using an equivalent definition of “ideal”, because it is a bit cleaner that way. It is a very useful exercise to work through the proof, using $$\mathbb{Z}$$ instead of the general ring $$R$$ and using “size” noteThat is, if $$n > 0$$ then the size is $$n$$; if $$n < 0$$ then the size is $$-n$$. We just throw away the sign. as the Euclidean function.
Let $$R$$ be a Euclidean domain, and say $$\phi: \mathbb{R} \setminus \{ 0 \} \to \mathbb{N}^{\geq 0}$$ is a Euclidean function. That is,
• if $$a$$ divides $$b$$ then $$\phi(a) \leq \phi(b)$$;
• for every $$a$$, and every $$b$$ not dividing $$a$$, we can find $$q$$ and $$r$$ such that $$a = qb+r$$ and $$\phi(r) < \phi(b)$$.
We need to show that every ideal is principal, so take an ideal $$I \subseteq R$$. We’ll view $$I$$ as the kernel of a homomorphism $$\alpha: R \to S$$; recall that this is the proper way to think of ideals. (Proof of the equivalence.) Then we need to show that there is some $$r \in R$$ such that $$\alpha(x) = 0$$ if and only if $$x$$ is a multiple of $$r$$.
If $$\alpha$$ only sends $$0$$ to $$0$$ (that is, everything else doesn’t get sent to $$0$$), then we’re immediately done: just let $$r = 0$$.
Otherwise, $$\alpha$$ sends something nonzero to $$0$$; choose $$r$$ to be nonzero with minimal $$\phi$$. We claim that this $$r$$ works.
Indeed, let $$x$$ be a multiple of $$r$$, so we can write it as $$ar$$, say. Then $$\alpha(ar) = \alpha(a) \alpha(r) = \alpha(a) \times 0 = 0$$. Therefore multiples of $$r$$ are sent by $$\alpha$$ to $$0$$.
Conversely, if $$x$$ is not a multiple of $$r$$, then we can write $$x = ar+b$$ where $$\phi(b) < \phi(r)$$ and $$b$$ is nonzero. noteThe fact that we can do this is part of the definition of the Euclidean function $$\phi$$. Then $$\alpha(x) = \alpha(ar)+\alpha(b)$$; we already have $$\alpha(r) = 0$$, so $$\alpha(x) = \alpha(b)$$. But $$b$$ has a smaller $$\phi$$-value than $$r$$ does, and we picked $$r$$ to have the smallest $$\phi$$-value among everything that $$\alpha$$ sent to $$0$$; so $$\alpha(b)$$ cannot be $$0$$, and hence nor can $$\alpha(x)$$.
So we have shown that $$\alpha(x) = 0$$ if and only if $$x$$ is a multiple of $$r$$, as required.
The converse is false
There do exist principal ideal domains which are not Euclidean domains: $$\mathbb{Z}[\frac{1}{2} (1+\sqrt{-19})]$$ is an example. (Proof.)
Parents: | 2019-12-05 20:36:38 | {"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": 0.9627111554145813, "perplexity": 1818.093600953065}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540482038.36/warc/CC-MAIN-20191205190939-20191205214939-00248.warc.gz"} |
https://www.physicsforums.com/threads/vaccum-fluctuations.207958/ | # Vaccum fluctuations?
1. Jan 9, 2008
### quantumfireball
Vaccum fluctuations???
How to understand vaccum fluctuations mathematically without getting into the virtual particles that is so stereotypical of POP sci articles???
Am i right in saying that the vaccum expectation value of the square of electric field is inversely proportional to the fourth power of l.
where l is the lenght of the cube in where you are measuring the vev????
2. Jan 9, 2008
### olgranpappy
here's a simple way to put it in terms of creation/annihilation operators (with all indices/sums suppresed).
In QED the electric field operator is given by (suppressing a bunch of indices and constants, etc):
$E\sim (a+a^\dagger)$
where 'a' annihilates and 'a^\dagger' creates.
then if <whatever> indicates the vacuum expectation value of 'whatever'
$$<E>=0$$
but
$$<E^2>\ne 0$$ | 2017-08-18 20:56:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8378022909164429, "perplexity": 1462.4159616927202}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105108.31/warc/CC-MAIN-20170818194744-20170818214744-00347.warc.gz"} |
http://clay6.com/qa/3267/y-ae-be-satisfies-which-of-the-following-differential-equation- | Browse Questions
# $y=ae^{mx}+be^{-mx}$ satisfies which of the following differential equation?
$(A)\;\frac{dy}{dx}+my=0 \quad (B)\;\frac{dy}{dx}-my=0\quad(C)\;\frac{d^2y}{dx^2}-m^2y=0 \quad (D)\;\frac{d^2y}{dx^2}+m^2y=0$
Toolbox:
• The general solution of a differential equation is a relation between dependent and independent variable having n arbitary constant.
• The general solution may have more than one form but the arbitary constants must be the same in numbers
Given $y=ae^{mx}+be^{-mx}$
On differentiaiting w.r.t x we get
$\large\frac{dy}{dx}$$=mae^{mx}+(-m)be^{-mx} =mae^{mx}-mbe^{-mx} Again differentiating w.r.t. x we get \large\frac{d^2y}{dx^2}$$=m^2ae^{mx}-m(-m)be^{-mx}$
$=m^2ae^{mx}+m^2be^{-mx}$
$=m^2[ae^{mx}+be^{-mx}]$
But $ae^{mx}+be^{-mx}=y$
$\large\frac{d^2y}{dx^2}$$=m^2y =>\large\frac{d^2y}{dx^2}$$-m^2y=0$
Hence the correct option is $C$ | 2016-12-08 20:08:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "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": 0.959820032119751, "perplexity": 1186.6380330579054}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542655.88/warc/CC-MAIN-20161202170902-00164-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://stats.stackexchange.com/questions/34008/how-does-ties-method-argument-of-rs-rank-function-work/34010 | # How does ties.method argument of R's rank function work?
I am using rank(a, ties.method="max") to rank a. But I am not quite sure what does ties.method="max" do. Can you please help?
Ties.method specifies the method rank uses to break ties. Suppose you have a vector c(1,2,3,3,4,5). It's obvious that 1 is first, and 2 is second. However, it's not clear what ranks should be assigned to the first and second 3s. Ties.method determines how this is done. There are a few options:
• average assigns each tied element the "average" rank. The ranks would therefore be 1, 2, 3.5, 3.5, 5, 6
• first lets the "earlier" entry "win", so the ranks are in numerical order (1,2,3,4,5,6)
• min assigns every tied element to the lowest rank, so you get 1,2,3,3,5,6
• max does the opposite: tied elements get the highest rank (1,2,4,4,5,6)
• random breaks ties randomly, so you'd get either (1,2,3,4,5,6) or (1,2,4,3,5,6).
• Thank you very much! Your answer helped me solve my problem! Thank you again! – Joy Aug 9 '12 at 18:24
• No problem. You may already know this, but ?command will print the help for a command. – Matt Krause Aug 12 '12 at 3:52 | 2019-12-09 13:11:37 | {"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": 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": 0.5886164903640747, "perplexity": 1820.6779883834627}, "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-2019-51/segments/1575540518882.71/warc/CC-MAIN-20191209121316-20191209145316-00155.warc.gz"} |
http://www.starlink.ac.uk/devdocs/sun95.htx/sun95ss131.html | ### OUTLINE
Draws an outline of a two-dimensional NDF
#### Description:
This application draws an outline of a two-dimensional NDF on the current graphics device, aligning it with any existing plot.
Annotated axes can be produced (see Parameter AXES), and the appearance of the axes and curve can be controlled in detail (see Parameter STYLE). The axes show co-ordinates in the current co-ordinate Frame of the supplied NDF.
This command is a synonym for contour mode=bounds penrot=yes clear=no.
outline ndf
#### Parameters:
TRUE if labelled and annotated axes are to be drawn around the plot, showing the current co-ordinate Frame of the supplied NDF. The appearance of the axes can be controlled using the STYLE parameter. [TRUE]
The plotting device. [current graphics device]
Specifies the position at which to place a label identifying the input NDF within the plot. The label is drawn parallel to the first pixel axis. Two values should be supplied for LABPOS. The first value specifies the distance in millimetres along the first pixel axis from the centre of the bottom-left pixel to the left edge of the label. The second value specifies the distance in millimetres along the second pixel axis from the centre of the bottom-left pixel to the baseline of the label. If a null (!) value is given, no label is produced. The appearance of the label can be set by using the STYLE parameter (for instance "Size(strings)=2"). [current value]
##### MARGIN( 4 ) = _REAL (Read)
The widths of the margins to leave around the outline for axis annotation. The widths should be given as fractions of the corresponding dimension of the current picture. The actual margins used may be increased to preserve the aspect ratio of the DATA picture. Four values may be given, in the order bottom, right, top, left. If fewer than four values are given, extra values are used equal to the first supplied value. If these margins are too narrow any axis annotation may be clipped. If a null (!) value is supplied, the value used is 0.15 (for all edges) if annotated axes are being produced, and zero otherwise. [current value]
NDF structure containing the two-dimensional image to be outlined.
A group of attribute settings describing the plotting style to use for the outline and annotated axes.
A comma-separated list of strings should be given in which each string is either an attribute setting, or the name of a text file preceded by an up-arrow character "^". Such text files should contain further comma-separated lists which will be read and interpreted in the same manner. Attribute settings are applied in the order in which they occur within the list, with later settings overriding any earlier settings given for the same attribute.
Each individual attribute setting should be of the form:
$<$name$>$=$<$value$>$
where $<$name$>$ is the name of a plotting attribute, and $<$value$>$ is the value to assign to the attribute. Default values will be used for any unspecified attributes. All attributes will be defaulted if a null value (!)–-the initial default–-is supplied. To apply changes of style to only the current invocation, begin these attributes with a plus sign. A mixture of persistent and temporary style changes is achieved by listing all the persistent attributes followed by a plus sign then the list of temporary attributes.
See Section E for a description of the available attributes. Any unrecognised attributes are ignored (no error is reported).
The appearance of the outline is controlled by the attributes Colour(Curves),
Width(Curves), etc. [current value]
#### Related Applications
KAPPA: WCSFRAME, CONTOUR, PICDEF; CCDPACK: DRAWNDF. | 2022-07-06 22:07:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 9, "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": 0.2438683807849884, "perplexity": 1963.9110734791311}, "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/1656104678225.97/warc/CC-MAIN-20220706212428-20220707002428-00259.warc.gz"} |
https://underthehood.meltwater.com/blog/2019/08/26/enriching-450m-docs-daily-with-a-boring-stream-processor/ | # Enriching 450M Docs Daily With a Boring Stream Processor
For our fairhair.ai platform we enrich over 450 million documents such as news articles and social posts per day, with a dependency tree of more than 20 NLP syntactic and semantic enrichment tasks. We ingest these documents as a continuous stream of data and guarantee delivery of enriched documents within 5 minutes of ingestion.
This technical feat required tight collaboration between two specialised teams: data science and platform engineering. Enabling both teams to efficiently work together around a common workflow execution engine was another problem we needed to solve. Hopefully that description fully piqued your interest because our solution (Benthos) is totally boring.
## Too Many Cooks
Some components of fairhair.ai are owned by individual teams. Data science teams have ownership of the enrichments, written as HTTP services in order to allow easy deployment and granular horizontal scaling. Platform engineering teams have ownership of the production stream pipelines, using Kafka as a message bus.
This division of responsibility provided some autonomy. However, the logic of the workflow execution engine would need to be shared by multiple teams. Enrichments are often selected based on the result of other enrichments (e.g. type of sentiment analysis chosen based on language detection), and some have flavours tailored to certain categories of document (e.g. long form editorial text versus social), making it a large and cumbersome system to manage.
Our data scientists were in the best position to describe the evolving dependency tree between components, and the logic for determining which enrichment flavours are appropriate for each document type. Our platform engineers had the expertise needed for tuning the workflow to maximize performance, observability and resiliency.
We also needed multiple deployments of the engine, each tailored to a specific teams’ requirements. Our platform engineers were ultimately responsible for running the production engine as a stream processing component, from Kafka to Kafka. However, our data science teams would also need to run it regularly for their model improvements, metrics evaluation and integration testing, often on custom training and gold standard datasets and usually from S3 to S3.
We therefore needed a workflow engine that was simple enough to enable contributions from anyone regardless of their programming skills, and powerful enough to satisfy our complex workflows. It also needed to be flexible enough for any team to deploy it however they required, with the performance needed to meet our scaling and resiliency requirements in production.
## The Workflow Engine
Our solution to this problem was to use Benthos, which is a stream processor focused on solving complex tasks by breaking them down into simple stateless operations, expressed in a YAML file. Its goal is to be a solid and boring foundation for stream processing pipelines.
You can read a full guide on Benthos workflows at docs.benthos.dev/workflows. In summary, it has the ability to automatically resolve a Directed Acyclic Graph (DAG) of our workflow stages provided they are expressed as process_map processors.
For each stage we define a map that extracts parts of the source document relevant to the target enrichment, followed by the processing stages that execute the enrichment. Finally, we also define a map that places the enrichment result back into the source document. We may also choose to define conditions that determine whether a document is suited for the stage.
Here’s an example of one of our enrichment targets expressed as a step in our flow:
basics:
premap:
id: id
language: tmp.enrichments.language.code
title: body.title.text
body: body.content.text
processors:
- http:
parallel: true
request:
verb: POST
Content-Type: application/json
backoff_on: [ 429 ]
drop_on: [ 400 ]
retries: 3
postmap:
tmp.enrichments.basics: .
From this definition Benthos is able to determine that any stages that change part of the path tmp.enrichments.language.code are a dependency of basics, and will ensure that they are executed beforehand. Similarly, any stage that premaps a value within the namespace tmp.enrichments.basics will be considered dependent on this stage.
These stages in the workflow are organised by Benthos into tiers at runtime, where stages of a tier are only dependent on tiers that come before them. Each tier is executed only after the tier beforehand is finished and stages of a tier are executed in parallel.
This guarantee allows authors of these workflow stages to ignore the overall flow and focus only on the enrichment at hand. It also allows readers of this stage to understand it outside of the context of other stages.
Finally, it clearly outlines the relevant technical behaviour of the stage. In the above example we can see at a glance that documents of a batch are sent in parallel HTTP requests to the target enrichment, and that we retry it a maximum of three times for a document (unless we receive a status code 400.) Updating this stage is easy thanks to the power of Benthos processors, here’s a diff that instead sends batched documents as a JSON array in a single request:
@@ -5,4 +5,6 @@ basics:
body: body.content.text
processors:
+ - archive:
+ format: json_array
- http:
parallel: true
@@ -15,4 +17,6 @@ basics:
drop_on: [ 400 ]
retries: 3
+ - unarchive:
+ format: json_array
postmap:
tmp.enrichments.basics: baz
After enrichments are aggregated into the tmp namespace we have a separate process that maps them into their final structure using another Meltwater technology called IDML.
### Unit Testing
A small subset of our workflow steps were complicated enough that making changes to them carried a significant risk. Benthos has support for defining unit tests for our processors in this case.
However, although this provided us with a degree of protection it was considered an exception. The main benefit of using Benthos was to keep these steps simple and easy to reason about. Whenever workflow stages reached a level of complexity we weren’t comfortable with we took a step back and tried to simplify the enrichment instead.
## Hosted and Custom Deployments
Keeping all of this logic in configuration files allowed us to use all the same source control and collaboration tools as our regular codebase. These configurations live in a central repository, and using config references we are able to import them into our team-specific deployment configs, let’s take a look at how that works.
Importing our enrichments config into a simple Kafka to Kafka pipeline looks like this:
input:
kafka_balanced:
- exampleserver:9092
topics:
- example_input_stream
consumer_group: benthos_consumer_group
max_batch_count: 20
pipeline:
processors:
# Import our entire enrichment flow.
- $ref: ./enrichments.yaml#/pipeline/processors/0 output: kafka: addresses: - exampleserver:9092 topic: example_output_stream For our data scientists, who wish to test against datasets stored in S3 as .tar.gz archives of JSON documents, it might look like this: input: s3: region: eu-west-1 bucket: example-bucket pipeline: processors: - decompress: algorithm: gzip - unarchive: format: tar -$ref: ./enrichments.yaml#/pipeline/processors/0
- archive:
format: tar
- compress:
algorithm: gzip
output:
s3:
region: eu-west-1
bucket: another-example-bucket
# Upload with the same key as the source archive.
path: ${!metadata:s3_key} It’s even possible to deploy our enrichment flow as an HTTP service, which makes it easy for solutions engineers to test against custom documents in a one-off request: http: address: 0.0.0.0:4195 input: http_server: path: "/post" pipeline: processors: -$ref: ./enrichments.yaml#/pipeline/processors/0
output:
# Route the resulting payloads back to the source of the message.
type: sync_response
Benthos supports a wide range of inputs and outputs, including brokers for combining them at both the input and output level. This has proven extremely useful as often we have teams that wish to share data feeds but rely on differing services, in such cases Benthos was easily able to bridge and occasionally duplicate feeds across queue systems.
### Observability
Benthos automatically reports metrics for the components you have configured and sends them to an aggregator of your choice. Here’s an example of what some of our enrichment dashboards look like in Grafana, showing latencies, throughput, status codes, etc:
This gave us a birds-eye view of enrichment performance and allowed us to build alerts on events such as a drop in 200 status rates, a spike in latencies, etc.
### Error Handling
When something goes wrong and enrichments fail Benthos has plenty of error handling mechanisms on offer, which allowed teams to choose how they wish to deal with them. In production we configured a dead-letter queue for failed documents, but during integration tests our data science teams chose to simply log the errors.
## Conclusion
Innovation in data insights is often stunted by failing to establish a strong coupling between data science and engineering, resulting in awkward deployments and a lack of collaboration. However, getting this coupling right requires a common framework that enables everyone to focus on their specialities.
We found that Benthos was highly effective at bridging that gap. It democratised the deployment of our common workflow, allowing teams to hack away on their own test environments without impacting others, thus enabling continuous innovation. It also accommodated all of the technical requirements we had for our production environment. Finally, and most importantly, it was easy for all teams to work with.
This is because it is able to expose the simple processes that made our pipelines unique, whilst solving the more complex stream problems that aren’t specific to us out of the box. As a result Benthos has had a dramatic impact on the productivity of our teams and the quality of our platform.
benthos enrichments stream processing stream processor data science | 2019-10-22 14:30:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28150489926338196, "perplexity": 2938.9843639753517}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987822098.86/warc/CC-MAIN-20191022132135-20191022155635-00472.warc.gz"} |
https://math.stackexchange.com/questions/1005186/high-school-math-questions-algebra | # High school math questions, algebra.
the difference between a positive integer, n, and its cube is 4896. Compute n. Please give solution and detailed explanation! Thank you ver much! I tried and got 17, but what i did is to try numbers one by one, so i would really appreciate if anyone can tell me the right and systematic way to tackle this question??
• What if someone asks "Product of three successive integers is $4896$. What is the middle number?"? Hint: Prime factorization of $4896$. – Alistair Nov 4 '14 at 2:15
• You can factor 4896 but since (n-1)n(n+1) is close to the cube root of 4896 and started from that. Rounded 16.5+ to 17 and showed that 16*17*18 equals 4896. Although I guessed n = 17 it was an easy and fast guess to fit the three successive factors formula. – K7PEH Nov 4 '14 at 2:18
$\textbf{HINT-}$ you have to solve $n^3-n-4896=0$. $n=17$ is the only real solution to this cubic. So there are none other. | 2019-11-22 02:15:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7772303819656372, "perplexity": 529.955182804784}, "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-2019-47/segments/1573496671106.83/warc/CC-MAIN-20191122014756-20191122042756-00222.warc.gz"} |
http://www.physicsforums.com/showthread.php?p=3775966 | # Holomorphic on C
by fauboca
Tags: holomorphic
P: 159 Suppose $f : \mathbb{C}\to \mathbb{C}$ is continuous everywhere, and is holomorphic at every point except possibly the points in the interval $[2, 5]$ on the real axis. Prove that f must be holomorphic at every point of C. How can I go from f being holomorphic every except that interval to showing it is holomorphic at that interval? I am assuming it has to be due to continuity. But there are continuous functions that aren't differentiable every where.
Sci Advisor HW Helper P: 2,020 One approach is to use Morera's theorem.
P: 159
Quote by morphism One approach is to use Morera's theorem.
I haven't learned that Theorem yet. Is there another approach.
HW Helper
P: 2,020
## Holomorphic on C
Yes, but it's tricky. The key idea is that if you can find a holomorphic function $g \colon \mathbb C \to \mathbb C$ that agrees with f everywhere except possibly on [2,5], then g must in fact agree with f on [2,5] too (why?), so f must be holomorphic on all of C because g is. But now, how does one find such a g? Do you have any ideas?
P: 159
Quote by morphism Yes, but it's tricky. The key idea is that if you can find a holomorphic function $g \colon \mathbb C \to \mathbb C$ that agrees with f everywhere except possibly on [2,5], then g must in fact agree with f on [2,5] too (why?), so f must be holomorphic on all of C because g is. But now, how does one find such a g? Do you have any ideas?
This is just a guess but let g be a primitive of f.
Sci Advisor HW Helper P: 2,020 That's not a bad idea. Could you spell it out a bit more?
P: 159
Quote by morphism That's not a bad idea. Could you spell it out a bit more?
If g is a primitive of f, then $g' = f$. As long as f is on an open set which is the case here.
Sci Advisor HW Helper P: 2,020 But how is g defined on [2,5]? I have to run so I'll leave you with a hint: Let $C = \{ z \in \mathbb C \mid |z-3.5| < 1 \}$ and define $g(z) = \frac{1}{2\pi i} \int_C \frac{f(w)}{w-z} dw$ in C. Try to show that f and g agree off of [2,5].
P: 159
Quote by morphism But how is g defined on [2,5]? I have to run so I'll leave you with a hint: Let $C = \{ z \in \mathbb C \mid |z-3.5| < 1 \}$ and define $g(z) = \frac{1}{2\pi i} \int_C \frac{f(w)}{w-z} dw$ in C. Try to show that f and g agree off of [2,5].
I am not sure why you center your circle at 3.5.
With our definition of g, I have a theorem from class that show f and g agree but it was only stated for one point not a set of points. We call it the Integral Transform Theorem:
Let $\gamma$ be any path and $g:\gamma\to\mathbb{C}$ be continuous. Define for all $z \notin \gamma$
$$G(z) = \int_{\gamma}\frac{g(u)}{u-z}du$$.
Then $G(z)$ is analytic at every point $z_0\notin\gamma$.
Then our corollary to it
If $f:\gamma\to\mathbb{C}$ is holomorphic and $\gamma$ is inside a disc on which f is holomorphic and which $\gamma$ is a circle, then for all z we get
$$f(z) = \frac{1}{2\pi i}\int_{\gamma}\frac{f(u)}{u-z}du$$
and so f is analytic for all z inside gamma.
HW Helper
P: 2,020
Quote by fauboca I am not sure why you center your circle at 3.5.
The radius should have been 1.5 and not 1. I basically wanted a circle centered on the real axis with [2,5] as a diameter. (Now that I think about it a bit more, the radius should probably be 1.5+0.01 (the small increment is to ensure that [2,5] is contained in the interior of C). But this doesn't matter much.)
With our definition of g, I have a theorem from class that show f and g agree but it was only stated for one point not a set of points. We call it the Integral Transform Theorem: Let $\gamma$ be any path and $g:\gamma\to\mathbb{C}$ be continuous. Define for all $z \notin \gamma$ $$G(z) = \int_{\gamma}\frac{g(u)}{u-z}du$$. Then $G(z)$ is analytic at every point $z_0\notin\gamma$. Then our corollary to it If $f:\gamma\to\mathbb{C}$ is holomorphic and $\gamma$ is inside a disc on which f is holomorphic and which $\gamma$ is a circle, then for all z we get $$f(z) = \frac{1}{2\pi i}\int_{\gamma}\frac{f(u)}{u-z}du$$ and so f is analytic for all z inside gamma.
You will need to modify the corollary a bit to conclude that f and g agree for all points inside C but not on [2,5].
P: 159
Quote by morphism The radius should have been 1.5 and not 1. I basically wanted a circle centered on the real axis with with [2,5] as a diameter. (Now that I think about it a bit more, the radius should probably be 1.5+0.01 (the small increment is to ensure that [2,5] is contained in the interior of C).) You will need to modify the corollary a bit to conclude that f and g agree for all points inside C but not on [2,5].
I am not sure how to alter the corollary besides saying we can run this process for all real numbers in [2,5] where each f* agrees with f.
Also, we were told today that we have proven Morera's Theorem but just didn't name it before. So we could use that as well then.
HW Helper
P: 2,020
Quote by fauboca I am not sure how to alter the corollary besides saying we can run this process for all real numbers in [2,5] where each f* agrees with f.
The corollary requires f to be holomorphic inside $\gamma$. But if $\gamma=C$, we run into problems, because we don't know if f is holomorphic on [2,5].
P: 159
Quote by morphism The corollary requires f to be holomorphic inside $\gamma$. But if $\gamma=C$, we run into problems, because we don't know if f is holomorphic on [2,5].
For now, can we say by the Integral Transform Theorem, we know g and f agree on all the points out side of C?
I am still not sure then how to get the points inside C but not on [2,5]
Sci Advisor HW Helper P: 2,020 Let's not even concern ourselves with points outside of C. All that matters is stuff inside of C. The problem with your corollary is that it requires that $\gamma$ be a circle, but really any simple closed curve works.
P: 159
Quote by morphism Let's not even concern ourselves with points outside of C. All that matters is stuff inside of C. The problem with your corollary is that it requires that $\gamma$ be a circle, but really any simple closed curve works.
The definition of C you provided is a circle. Since $\mathbb{C}$ is open, there is an open disc around C. So using that definition, we would have inside C is analytic.
HW Helper
P: 2,020
Quote by fauboca The definition of C you provided is a circle. Since $\mathbb{C}$ is open, there is an open disc around C. So using that definition, we would have inside C is analytic.
Yes, g is analytic inside C. But we don't know that f is. And your corollary doesn't show that f=g inside C (but off of [2,5]), which is really what we want to show. So the corollary has to be tweaked to show that f=g inside C (but off of [2,5]).
P: 159
Quote by morphism Yes, g is analytic inside C. But we don't know that f is. And your corollary doesn't show that f=g inside C (but off of [2,5]), which is really what we want to show. So the corollary has to be tweaked to show that f=g inside C (but off of [2,5]).
Does it have to do with the winding number?
Not really. It has to do with allowing more general $\gamma$ instead of just circles. | 2014-03-12 01:21:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8933208584785461, "perplexity": 292.75564191203745}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394020561126/warc/CC-MAIN-20140305115601-00011-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://mymathforum.com/calculus/346877-minimal-value.html | My Math Forum Minimal value
Calculus Calculus Math Forum
August 4th, 2019, 12:28 PM #1 Senior Member Joined: Dec 2015 From: somewhere Posts: 592 Thanks: 87 Minimal value Find the minimal value of $\displaystyle f(x)=e^{x} +|x|\cdot e^{x} .$ Last edited by idontknow; August 4th, 2019 at 12:39 PM.
August 4th, 2019, 01:12 PM #2 Global Moderator Joined: May 2007 Posts: 6,806 Thanks: 716 $f(x)\gt 0$ for all $x$. $f(x)\to 0$ as $x\to -\infty$. That is the minimum. Thanks from idontknow
August 4th, 2019, 07:14 PM #3 Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 Isn't 0 a limiting value (and greatest lower bound) rather than a minimum value? Thanks from idontknow
August 5th, 2019, 12:34 PM #4 Global Moderator Joined: May 2007 Posts: 6,806 Thanks: 716 It depends on a precise definition of minimum. Greatest lower bound is precise, minimum is not. Thanks from idontknow
August 5th, 2019, 11:57 PM #5
Senior Member
Joined: Dec 2015
From: somewhere
Posts: 592
Thanks: 87
Quote:
Originally Posted by mathman It depends on a precise definition of minimum. Greatest lower bound is precise, minimum is not.
My mistake on the question.
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Contact - Home - Forums - Cryptocurrency Forum - Top | 2019-08-19 02:04:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.7756049036979675, "perplexity": 11410.666358435668}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314638.49/warc/CC-MAIN-20190819011034-20190819033034-00201.warc.gz"} |
https://kullabs.com/classes/subjects/units/lessons/notes/note-detail/9472 | Notes on Binomial Distribution | Grade 12 > Mathematics > Probability | KULLABS.COM
• Note
• Things to remember
Random Variable and Probability Distributions
A variable that takes different probability in a random way so that the outcomes are not known is called a random variable. Hence, X is called a random variable if it takes values X1 , X2 , X3. . .Xn randomly. There are several types of probability distribution such as the binomial distribution, Poisson, Normal etc. They differ according to the nature of the random variable.
Bernoulli Process:
An experiment consisting only two outcomes is known as “Bernoulli Process”. Generally, the two outcomes are called success and failure. For example, tossing a coin, result of an examination, throwing a dice, production of bulbs etc.
Binomial Distribution:
The discrete probability distribution derived from the Bernoulli process is known as Binomial distribution. The following are the basic assumptions under which Binomial Distribution can be used:
• Random experiment should be performed for a fixed number of times.
• The experiment should only have two events known as success or failure.
• All the experiments performed should be independent of one another.
• The probability of success denoted by p should be constant per every experiment.
When the probability of a success in one trial is known, the probabilities of success of exactly once, twice, thrice, . . . etc. in n trials can also be known.
Let a trial be repeated so as to make a set of n trials. We denote the occurrence of an event known as success by S and the non-occurrence, a failure by F. Let p and q be the probabilities of a success and a failure in one trial respectively be such that p + q = 1. Let us assume that the trials are independent and the probability of success in every trial is the same. Now, we find the probabilities of 0, 1, 2 , . . . .,n success in n trials. Thr probabilities of a success and a failure be denoted by P(S) and P(F) respectively. Then the probability of r success and (n-r) failure in a set of n trials in any specified order say S.S.S.S …S (r times) F.F.F.F.F.F…F.(n-r times).
=P(S).P(S)… P(S) P(F).P(F).P(F)….. p(F)
=(p.p.p……r times) (q.q.q.q…. (n-r)times)
= pr . qn-r
But the number of orders of occurring r success out of n trials is same as the number of combination of n things taken r at a time i.e. nr. These are all equally probable and mutually exclusive hence by the theorem of total probability of r success; i.e. P(r) in a set of n independent trials is given by:
$$\;P(r)\;$$=^nC_r\;p^r\;q^_{n-r}\;\;$$……\;(0\leq\;r\leq\;n)\;$$
Thus if n = number of trials performed
p = probability of success in a trial
q = probability of a failure in a trial such that p + q = 1
r = number of success \;in trials
then P(r) = P(x = r) = probability of r success in n trials
$$\;=\;^nC_r\;p^r\;q^_{n-r}\;$$
The probabilities of 0, 1, 2, 3, . . . . . . n successes obtained by putting r = 0, 1, 2, 3, . . . . n in the above equation is listed below:
No of successes (r) Probability of r success i.e. P(r) 0 P(0) = qn 1 P(1) = C(n,1)p1qn-1 2 P(2) = C(n,2) P2qn-2 3 P(3) = C(n,3) P3qn-3 n P(2) = C(n,n) Pnqn-n = pn
Mean and Standard deviation of Binomial Distribution:
If p be the probability of a success and q that of a failure in one trial, then the probabilities of 0,1,2,3, . . . . n successes in n trials are listed above which are the successive terms of the binomial expansion of (p+q)n . Hence the distribution is known as binomial distribution. The mean and the standard deviation of the binomial distribution and np and (npq)-1/2 respectively.the two independent constants n and p (or q) are known as parameters.
• Mean of the distribution is given by np
• Variance of the distribution is given by npq
• $$Standard\;deviation\;of\;the\;distribution\;is\;given\;by\;\sqrt{npq}\;$$
Taken reference from
( Basic mathematics Grade XII and A foundation of Mathematics Volume II and Wikipedia.com )
• P(r) = P(x = r) = probability of r success in n trials
$$\;=^nC_r\;p^r\;q^_(n-r)\;$$
• Mean of the distribution is given by np
• Variance of the distribution is given by npq
• $$Standard\;deviation\;of\;the\;distribution\;is\given\;by\;\sqrt{npq}\;$$
.
0%
## ASK ANY QUESTION ON Binomial Distribution
No discussion on this note yet. Be first to comment on this note | 2020-02-27 18:12:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8981722593307495, "perplexity": 621.7830124946258}, "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-2020-10/segments/1581875146744.74/warc/CC-MAIN-20200227160355-20200227190355-00390.warc.gz"} |
http://www.solutioninn.com/a-precision-instrument-is-checked-by-making-12-readings-on | # Question
A precision instrument is checked by making 12 readings on the same quantity. The population distribution of readings is normal.
a. The probability is 0.95 that the sample variance is more than what percentage of the population variance?
b. The probability is 0.90 that the sample variance is more than what percentage of the population variance?
c. Determine any pair of appropriate numbers, a and b, to complete the following sentence: The probability is 0.95 that the sample variance is between a% and b% of the population variance.
Sales0
Views28 | 2016-10-27 13:28:24 | {"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": 0.9376091957092285, "perplexity": 305.65121117008397}, "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/1476988721278.88/warc/CC-MAIN-20161020183841-00546-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/integrating-function-of-force-with-respect-to-angle.910078/ | I Integrating function of force with respect to angle
1. Apr 3, 2017
Brian
I have a function of force with respect to a certain angle, θ. I also have the angle of the force, Ψ, with respect to the same angle. Plug in θ, get the force and Ψ. This function is determined by a table of data: F(θ) and Ψ(θ)
This force is acted upon a beam at a distance L from a pivot at one end. The beam has a skew angle of Φ. If I find the force that is normal to the skew angle, Φ, the resultant force is: Fr(θ) = F(θ) ⋅ cos(Ψ(θ)) ⋅ sin(Φ). Note: The force always points vertically (see top view below) The angle Φ changes as a result of the force on the beam.
I need to find the angular displacement of Φ as a function of θ.
Using Newtons second law, I know that Fr ⋅ L = I ⋅ α
If mass moment of intertia is constant, Fr(θ) ⋅L = I ⋅ α(θ)
Thus α(θ) = (Fr(θ) ⋅L) / I
Now my next thought was to integrate α(θ) with respect to the angle θ to find ω(θ), as I know my initial ω is zero. Once I find ω(θ), I can integrate again with respect to θ to find Φ(θ), as I know my initial Φ and that the rotation only takes place around a single axis, the pivot point.
First, I have doubts that this is the correct way to find Φ(θ). I'm unsure whether the pivot can be considered a single axis of rotation.
Second, I am having trouble integrating:
(F(θ) ⋅ cos(Ψ(θ)) ⋅ sin(Φ)⋅L)/I.
with respect to θ, as F(θ) and Ψ(θ) are tables of values, not equations. I could use the trapezoidal method to find the integrals of both tables, call them F'(θ) and Ψ'(Φ), but how would these fit into integrating the equation above?
Finally, I realize that I will have Φ on both sides of the equation, and thus Φ will be a function of itself. This reflects on my assumption that the pivot is a "single" axis.
Below is a rough sketch of the "beam" to which the force is being applied.
http://imgur.com/aKniN5Z
http://imgur.com/a/hsBoT (if embed isnt working)
The angle θ, for all intents and purposes, could be thought of as time, as it is the independent variable. I could convert this angle into time (as it is determined by a different rod rotating at a known angular speed) but I need to solve for the skew angle as a function of the given angle and the functions F(θ) and Ψ(θ) are different during different angular speeds.
If integrating the angular velocity is incorrect, could I integrate the regular velocity to find the displacement of the point at which the force is contacting the beam, and then use trig to find the resultant change in angle?
Major Edit: Was using F = ma instead of τ = Iα
Last edited: Apr 3, 2017
2. Apr 8, 2017
PF_Help_Bot
Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better. | 2018-03-22 22:27:53 | {"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": 0.9270533323287964, "perplexity": 783.9233914152177}, "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-2018-13/segments/1521257648003.58/warc/CC-MAIN-20180322205902-20180322225902-00613.warc.gz"} |
https://stats.stackexchange.com/questions/254525/chi-squared-test-of-independence-with-one-binary-dependent-variable | # Chi-squared test of independence with one binary dependent variable
I am given a sample with n = 100 of patients with risk factor information for all of them (binary variable, yes/no) and the disease status (also binary). I have to find the association between each individual risk factor and the disease and supply the result as a p-value and $\chi^2$ value.
I thought I would make a 2×2 contigency table for each risk factor, where one variable was presence of disease and the other the presence of a risk factor. After that I simply used the formula $\chi^2 = \sum{\frac{(O - E)^2}{E}}$ and obtained the $\chi^2$ and p values. Is this a correct or wrong way to do this? If not then how should I have done it?
• Welcome to the site. If this is a homework question, please add the self-study tag and read its wiki. To answer your other question, if you are tasked with bivariate analysis of the association between your outcome and the risk factor variables, then your approach is correct – Marquis de Carabas Jan 4 '17 at 15:24
• Maybe you should consider logistic regression with risk factor as predictor. – Mur1lo Jan 5 '17 at 1:37
You could do a $\chi^2$ test, but you could also just note that, in a 2-by-2 table, the rows and columns are independent iff the OR = 1. The standard error of the log odds ratio is the sum of the reciprocals of the cell counts. Checking whether log of the OR divided by that standard error is greater than 1.96 (in absolute value) is an approximate $\alpha=.05$ test of independence. | 2020-09-27 07:49:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6754445433616638, "perplexity": 366.97594883644507}, "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/1600400265461.58/warc/CC-MAIN-20200927054550-20200927084550-00729.warc.gz"} |
https://www.techwhiff.com/issue/tony-bought-12-identical--541518 | # Tony bought 12 identical
###### Question:
tony bought 12 identical
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### Read the excerpt from Roll of Thunder, Hear My Cry. "This here's an important decision, Cassie, very important—I want you to understand that—but I think you can handle it. Now, you listen to me, and you listen good. This thing, if you make the wrong decision and Charlie Simms gets involved, then I get involved and there'll be trouble." Why is Cassie’s father stressing the importance of the decision Cassie must make? He thinks it will cause problems between himself and Cassie. He thinks it will
Read the excerpt from Roll of Thunder, Hear My Cry. "This here's an important decision, Cassie, very important—I want you to understand that—but I think you can handle it. Now, you listen to me, and you listen good. This thing, if you make the wrong decision and Charlie Simms gets involved, the... | 2022-11-30 00:29:41 | {"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": 0.2635102868080139, "perplexity": 1628.2673910597582}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710712.51/warc/CC-MAIN-20221129232448-20221130022448-00645.warc.gz"} |
http://computerklinika.com/standard-error/fixing-confidence-interval-standard-error.php | Home > Standard Error > Confidence Interval Standard Error
# Confidence Interval Standard Error
in order to estimate the standard error; there is sufficient information within a single sample. Thus with only one sample, and no other information about the population parameter, we error of 2%, or a confidence interval of 18 to 22. The graphs below show the sampling distribution of theto express the variability of data: Standard deviation or standard error of mean?".JSTOR2340569. (Equation 1)
Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement 120 people operated on for appendicitis 37 were men. Some of these are error http://computerklinika.com/standard-error/repairing-90-confidence-standard-error.php of such observations occurring is 5% or less. confidence Hypothesis Testing Standard Error very close to the mean of the population. And Keeping, E.S. (1963) Mathematics of Statistics, van Nostrand, p. error when the sample size n is equal to the population size N.
The smaller standard deviation for age at first marriage vary depending on the size of the sample. This is the 99.73% confidence interval, and the chance of the true score is called the error score. Thus the variation between samples depends partly on the amount interval Standard deviations and standard errors.This probability is small, so the observation probably did not that samples are not unique.
However, the concept is that if we were to take repeated random samples from patients with appendicitis, described in Chapter 3, was 4.46. These areand the result is a higher SEM at 1.18. Confidence Interval Standard Error Calculator These come from a distribution known as the t distribution,the 95% limits.Or decreasing standard error by a factor ofis represented by the symbol σ x ¯ {\displaystyle \sigma _{\bar {x}}} .
The estimated standard deviation for the sample mean is 0.733/sqrt(130) = 0.064, http://www.bmj.com/about-bmj/resources-readers/publications/statistics-square-one/4-statements-probability-and-confiden become more narrow, and the standard error decreases.Economic less certain guide to the population from which it was drawn than a large sample.
For the purpose of this example, the 9,732 runners whothe 20,000 sample means) superimposed on the distribution of ages for the 9,732 women.The difference between the observed score and Confidence Interval Standard Deviation Does this number lie The researchers report that candidate A is expected to receive 52%the Evidence3.
In the diagram at the right theis the Standard Deviation.The standard error for the percentage of maleIn other words, the student wishes to estimate the true meanAssume that the following five numbers are sampled from a normal distribution: 2, the JSE Dataset Archive.
However, the concept is that if we were to take repeated random samples from 0.90, and (1-C)/2 = 0.05.The smaller the standard deviation the closer the scoresof the boiling temperatures to be 101.82, with standard deviation 0.49. Scenario learn this here now standards that their data must reach before publication.This common mean would be expected to lieintervals on the two percentages: These confidence intervals exclude 50%.
Thus with only one sample, and no other information about the population parameter, we in the standard deviation. the mean to contain a given proportion of the area.The mean ageblood pressure of men aged 20-44 differs between printers and farm workers.Statistical
Then we will show how sample data confidence If we now divide the standard deviation by the square root of the number of regarded as the normal (meaning standard or typical) range. Because these 16 runners are a sample from the population of 9,732 runners, Confidence Interval Standard Error Of The Mean sampling distribution of a statistic,[1] most commonly of the mean.The standard error of the risk difference is obtained by dividing Square One, 10 th ed.
(101.82 + (1.96*0.49))) = (101.82 - 0.96, 101.82 + 0.96) = (100.86, 102.78).The confidence interval is then computed https://en.wikipedia.org/wiki/Standard_error than 3.92; for 99% confidence intervals divide by 5.15.With this standard error we can get 95% confidence intervals on the two percentages: 60.8 standard a confidence interval as between the standard deviation and the standard error. confidence literature, and some authors attach them to every estimate they make.
For a 95% confidence interval, the area in Confidence Interval Standard Error Of Measurement is somewhat greater than the true population standard deviation σ = 9.27 years.Correction for correlation in the sample Expected error in the mean ofintervals on the two percentages: These confidence intervals exclude 50%.As the sample size increases, the sampling distribution estimate of a risk difference of 0.03 (P = 0.008).
a margin of error equal to 0.5 with 95% confidence.The sample mean x ¯ {\displaystyle {\bar {x}}} = 37.25 is greaterthe mean for N=9.Dividing the difference by theof the correction factor for small samples ofn<20.the ink color of the word "blue" written in red ink.
The 95% limits are often In the example above, the student calculated the sample meanan empirical normal range.As an example of the use of the relative standard error, consider two Confidence Interval Standard Error Or Standard Deviation also on the size of the sample.
In the first row there is a empirical normal range . However, the mean and standard deviation are descriptive statistics, whereas theof the probability attached to confidence intervals.It can only be calculated if 95% probability, that the mean from another sample is in this interval. These levels correspond to percentages ofSEM and Observed Score what the confidence interval would be.
For a sample of size n, the sample mean is the standard error divided by the mean and expressed as a percentage. Confidence interval for a proportion In a survey of(1.96 x 4.46) = 52.1 and 69.5 39.2 (1.96 x 4.46) = 30.5 and 47.9. error This is expressed P Value Standard Error probability is very close to 0.0027. standard As a result, you have to extend farther from error investigators the confidence interval will include the population mean interval.
C are 0.90, 0.95, and 0.99. If we take the mean plus or minus three timesof the sampling distribution of the sample statistic. When should one Standard Deviation Standard Error ± (1.96 × 0.87), giving a range of 0.48 to 3.89.new drug lowers cholesterol by an average of 20 units (mg/dL).
If you had wanted to compute the 99% confidence interval, you would have possible sample means is equal to the population mean. The sample mean will very rarely confidence is regarded as abnormal. The points that include 95% of the observations are 2.18so even if the observations from which they were obtained do not. Since the samples are different, of the probability attached to confidence intervals.
A better method would be to use a chi-squared this interval excluding the population mean is 1 in 370. However, to explain how confidence intervals are constructed, we are going more variation there is in the scores. This would be the amount of consistency in the
Greek letters indicate that
Some of these are a more precise measurement, since it has proportionately less sampling variation around the mean. The standard deviation of the age for the 16 runners is 10.23, which is investigating acute appendicitis in people aged 65 and over. Thus in the 140 children we might choose
A t table shows the critical value of t for 47 - the population, this is how we would expect the mean to vary, purely by chance.
© Copyright 2018 computerklinika.com. All rights reserved. | 2018-08-18 00:21:48 | {"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": 0.8034529089927673, "perplexity": 911.4206609874734}, "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-2018-34/segments/1534221213247.0/warc/CC-MAIN-20180818001437-20180818021437-00047.warc.gz"} |
https://homework.cpm.org/category/CC/textbook/cc2/chapter/7/lesson/7.1.1/problem/7-14 | ### Home > CC2 > Chapter 7 > Lesson 7.1.1 > Problem7-14
7-14.
Sao can text $1500$ words per hour. He needs to text a message with $85$ words. He only has $5$ minutes between classes to complete the text. Can he do it in $5$ minutes? Homework Help ✎
Convert ''words per hour'' to ''words per minute.''
There are $60$ minutes in $1$ hour, so you need to divide $1500$ by $60$ to find out how many words he can type per minute.
$\frac{1500}{60}=25$ words per minute
How many words can he type in $5$ minutes if he can type $25$ words per minute?
$(25)(5)=?$
Does he have enough time to complete the $85$ word text? | 2020-02-25 06:50:42 | {"extraction_info": {"found_math": true, "script_math_tex": 13, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4373505115509033, "perplexity": 1627.6268704882239}, "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-2020-10/segments/1581875146033.50/warc/CC-MAIN-20200225045438-20200225075438-00023.warc.gz"} |
https://itprospt.com/num/1938600/field-f-1-marks-0-0-to-shoy-4-that-along-1-vector-1-field | 5
# Field F 1 marks) (0,0) to (Shoy: 4 that along 1 vector 1 field 1 conservative conservative. then curI(F)Use this factshow that { Ce...
## Question
###### Field F 1 marks) (0,0) to (Shoy: 4 that along 1 vector 1 field 1 conservative conservative. then curI(F)Use this factshow that { Ce
field F 1 marks) (0,0) to (Shoy: 4 that along 1 vector 1 field 1 conservative conservative. then curI(F) Use this fact show that { Ce
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##### 302520 Percent 15 105561 67 73 Height (Inches)79What percent of students are between 61 and 64 inches tall?
30 25 20 Percent 15 10 55 61 67 73 Height (Inches) 79 What percent of students are between 61 and 64 inches tall?... | 2022-09-28 15:20:18 | {"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": 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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.762423574924469, "perplexity": 6718.351489410784}, "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/1664030335257.60/warc/CC-MAIN-20220928145118-20220928175118-00692.warc.gz"} |
https://astronomy.stackexchange.com/questions/43552/working-with-stellar-spectra-in-fits-format-in-python/43554#43554 | # working with stellar spectra in fits format in python
Hey I am new to working with astronomical data in Python. I wanted to start working with stellar spectra and I am having trouble with the data. To get a first look I just wanted to plot a spectra (flux over wavelength). I downloaded the Miles library (http://research.iac.es/proyecto/miles/pages/stellar-libraries/miles-library.php) and started working with a single fits file. My first steps where as follows :
import numpy as np
import matplotlib.pyplot as plt
from astropy.io import fits
hdul = fits.open('s0013.fits')
data = hdul[0].data
I read the header using print(repr(h1)) and know I wanted to plot the spectrum. The data has shape (1, 4367) and I am not sure how to proceed to achieve 2 arrays one with the wavelength and one with the flux to plot the data. I am sorry if this question is stupid but I can not figure it out.
Cheers
The information you need to recreate the wavelength array is in the World Coordinate System (WCS) of the header, specifically:
CRPIX1 = 1.00
CRVAL1 = 3500.0000 / central wavelength of first pixel
CDELT1 = 0.900000 / linear dispersion (Angstrom/pixel)
which lists the starting/reference pixel of the wavelength array (1.0), the wavelength value at the start point (3500 angstroms (assumed)) and the step per pixel (0.9 Angstrom/pixel). To read this information, it is best to use a WCS library rather than trying to interpret them directly as they can be more complicated and there are many subformats of FITS WCS.
Fortunately astropy has a module to make this easy (starting from your code above and extending it):
import numpy as np
import matplotlib.pyplot as plt
from astropy.io import fits
from astropy.wcs import WCS
hdul = fits.open('s0013.fits')
data = hdul[0].data
obj_name = h1.get('OBJECT', 'Unknown')
flux = data[0]
w = WCS(h1, naxis=1, relax=False, fix=False)
lam = w.wcs_pix2world(np.arange(len(flux)), 0)[0]
plt.plot(lam, flux)
plt.ylim(0, )
plt.xlabel('Wavelength (Angstrom)')
plt.ylabel('Normalized flux')
plt.savefig(obj_name + '.png')
This will produce the following plot:
If you want to do more extended manipulation of spectra, particularly with the bewildering variety of wavelength and flux units, it might be worth looking at synphot and specutils which build on Astropy and add more direct support for spectra beyond simple numpy arrays. For example, you could make a synphot SourceSpectrum from the above by doing:
from astropy import units as u
from synphot import units, SourceSpectrum
from synphot.spectrum import Empirical1D
source_spec = SourceSpectrum(Empirical1D, points=lam*u.AA, lookup_table=flux, | 2022-01-27 20:57:19 | {"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": 0.3563366234302521, "perplexity": 2142.380449252518}, "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-2022-05/segments/1642320305288.57/warc/CC-MAIN-20220127193303-20220127223303-00384.warc.gz"} |
https://ncatlab.org/nlab/show/Mostowski+set+theory | foundations
# Contents
## Idea
Mostowski set theory is a well-founded material set theory which is equivalent in strength to the structural set theories of ETCS and bounded SEAR with choice.
## Definition
### In classical logic
We assume that we are working in full classical logic. Mostowski set theory has the following axioms and axiom schemata:
1. Extensionality: for any set $x$ and $y$, $x = y$ if and only if for all $z$, $z \in x$ if and only if $z \in y$.
2. Empty set: there is a set $\varnothing = \{\}$.
3. Pairing: for all sets $x$ and $y$, there is a set $\{x, y\}$
4. Union: for all sets $x$, there is a set $\{z \vert \exists y \in x.z \in y\}$
5. Schema of $\Delta_0$-separation: for any $\Delta_0$-formula $\phi(x)$ and for any set $a$, there is a set $\{x \in a \vert \phi(x)\}$
6. Schema of limited $\Delta_0$-replacement: for any $\Delta_0$-formula $\phi(x, y)$, for all sets $a$ and $b$, if for any set $x \in a$ there is a unique set $y$ such that $\phi(x, y)$, and for all $z \in y$, $z \subseteq b$, then there is a set $\{y \vert \exists x \in a.\phi(x, y)\}$
7. Power sets: for any set $x$, there is a set $\mathcal{P}(x) = \{y \vert y \subseteq x\}$
8. Infinity: there is a set $\omega$ such that for all sets $x$, $x \in \omega$ if and only if $x = \emptyset$ or there exists a set $y \in \omega$ such that $y \cup \{y\} = x$.
9. Choice: for any set $a$, if for all $x \in a$ there is a set $y \in x$, then there is a function $f$ from $a$ to $\bigcup a$ such that $f(x) \in x$ for all $x \in a$.
10. Regularity: if there is a set $y \in x$, then there is a set $y \in x$ such that $x \cap y = \emptyset$
11. Transitive closure: every set is a subset of a smallest transitive set
12. Mostowski's principle: every well-founded extensional relation is isomorphic to a transitive set equipped with the relation $\in$.
This implies that Mostowski set theory is equivalent in strength to ETCS, a well-pointed topos with natural numbers object and the axiom of choice.
#### Variations of Mostowski set theory in classical logic
By removing axiom 9 from Mostowski set theory, one gets Mostowski set theory without choice, which is equivalent in strength to a well-pointed Boolean topos with natural numbers object and the axiom of well-founded materialization.
By removing axiom 7 from Mostowski set theory, one gets predicative Mostowski set theory, which is equivalent in strength to a well-pointed Boolean pretopos with natural numbers object and the axiom of choice.
By removing axiom 8 from Mostowski set theory, one gets weakly finitist Mostowski set theory, which is equivalent in strength to a well-pointed Boolean topos with the axiom of choice.
If one replaces axiom 8 with the axiom of finiteness (for any formula $\phi$, if $\phi(\emptyset)$ and for all sets $x$, $\phi(x)$ implies that $\phi(x \cup \{x\})$, then for all sets $x$, $\phi(x)$), one gets strongly finitist Mostowski set theory, which is equivalent in strength to the category FinSet. Axioms 7 and 9 are redundant in this formulation, since both are implied by the axiom of finiteness.
Thus, the most general variation of Mostowski set theory in classical logic is weakly finitist predicative Mostowski set theory without choice, which consists of axioms 1-6 and 10-12, and is equivalent in strength to a general well-pointed Boolean pretopos with the axiom of well-founded materialization.
### In intuitionisitc logic
Now, we assume that we are working in intuitionistic logic. Then $\Delta_0$-classical Mostowski set theory has the following axioms and axiom schemata:
1. Extensionality: for any set $x$ and $y$, $x = y$ if and only if for all $z$, $z \in x$ if and only if $z \in y$.
2. Empty set: there is a set $\varnothing = \{\}$.
3. Pairing: for all sets $x$ and $y$, there is a set $\{x, y\}$
4. Union: for all sets $x$, there is a set $\{z \vert \exists y \in x.z \in y\}$
5. Schema of $\Delta_0$-separation: for any $\Delta_0$-formula $\phi(x)$ and for any set $a$, there is a set $\{x \in a \vert \phi(x)\}$
6. Schema of limited $\Delta_0$-replacement: for any $\Delta_0$-formula $\phi(x, y)$, for all sets $a$ and $b$, if for any set $x \in a$ there is a unique set $y$ such that $\phi(x, y)$, and for all $z \in y$, $z \subseteq b$, then there is a set $\{y \vert \exists x \in a.\phi(x, y)\}$
7. Power sets: for any set $x$, there is a set $\mathcal{P}(x) = \{y \vert y \subseteq x\}$
8. Infinity: there is a set $\omega$ such that for all sets $x$, $x \in \omega$ if and only if $x = \emptyset$ or there exists a set $y \in \omega$ such that $y \cup \{y\} = x$.
9. Choice: for any set $a$, if for all $x \in a$ there is a set $y \in x$, then there is a function $f$ from $a$ to $\bigcup a$ such that $f(x) \in x$ for all $x \in a$.
10. Regularity: if there is a set $y \in x$, then there is a set $y \in x$ such that $x \cap y = \emptyset$
11. Transitive closure: every set is a subset of a smallest transitive set
12. Mostowski's principle: every well-founded extensional relation is isomorphic to a transitive set equipped with the relation $\in$.
This implies that Mostowski set theory is equivalent in strength to ETCS in intuitionistic logic, a constructively well-pointed topos with natural numbers object and the axiom of choice.
The name $\Delta_0$-classical Mostowski set theory comes from the fact that the law of excluded middle is only valid for $\Delta_0$-formulas in the theory, being a consequence of the axiom of choice, rather than for all formulas in the theory, as in the case for Mostowski set theory in classical logic.
#### Variations of Mostowski set theory in intuitionistic logic
By removing axiom 9 from $\Delta_0$-classical Mostowski set theory, one gets intuitionistic Mostowski set theory or constructive Mostowski set theory, which is equivalent in strength to a constructively well-pointed topos with natural numbers object and the axiom of well-founded materialization.
By removing axiom 7 from $\Delta_0$-classical Mostowski set theory, one gets predicative $\Delta_0$-classical Mostowski set theory, which is equivalent in strength to a constructively well-pointed Heyting pretopos with natural numbers object and the axiom of choice.
By removing axiom 7 from intuitionistic Mostowski set theory, one gets strongly predicative constructive Mostowski set theory, which is equivalent in strength to a constructively well-pointed Heyting pretopos with a natural numbers object and the axiom of well-founded materialization.
By replacing axiom 7 by the axiom of exponentiation (for all sets $a$ and $b$, the set $b^a$ of functions from $a$ to $b$ exists) in intuitionistic Mostowski set theory, one gets weakly predicative constructive Mostowski set theory, which is equivalent in strength to a constructively well-pointed ΠW-pretopos with the axiom of well-founded materialization.
By removing axiom 8 from any $X$ Mostowski set theory, with $X$ being one of ($\Delta_0$-classical, intuitionistic, predicative $\Delta_0$-classical, weakly predicative constructive, strongly predicative constructive), one gets weakly finitist $X$ Mostowski set theory, which is equivalent in strength to a constructively well-pointed $C$, where $C$ is one of (Boolean topos with the axiom of choice, elementary topos with the axiom of well-founded materialization, Boolean pretopos with the axiom of choice, Π-pretopos with the axiom of well-founded materialization, Heyting pretopos with the axiom of well-founded materialization).
If one replaces axiom 8 in any of the above with the axiom of finiteness (for any formula $\phi$, if $\phi(\emptyset)$ and for all sets $x$, $\phi(x)$ implies that $\phi(x \cup \{x\})$, then for all sets $x$, $\phi(x)$), one gets strongly finitist Mostowski set theory, which is equivalent in strength to the category FinSet. Axioms 7 and 9 are redundant in this formulation, since both are implied by the axiom of finiteness.
Thus, the most general variation of Mostowski set theory in intuitionistic logic is weakly finitist, strongly predicative, constructive Mostowski set theory, which consists of axioms 1-6 and 10-12, and is equivalent in strength to a general constructively well-pointed Heyting pretopos with the axiom of well-founded materialization.
Given any material set theory $V$ which satisfies axioms 1-6. Then one could construct the category $\mathbb{Set}(V)$ of sets and functions in $V$, and $\mathbb{Set}(V)$ is a constructively well-pointed Heyting pretopos.
Given any constructively well-pointed Heyting pretopos $\mathcal{E}$, we can construct the type $\mathbb{V}(\mathcal{E})$ as the type of well-founded extensional accessible pointed graph objects in $\mathcal{E}$. $\mathbb{V}(\mathcal{E})$ is a model of material set theory satisfying axioms 1-6 and 10-12. | 2023-02-08 09:56:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 136, "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": 0.9196527004241943, "perplexity": 339.8806302100221}, "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/1674764500758.20/warc/CC-MAIN-20230208092053-20230208122053-00841.warc.gz"} |
http://en.wikipedia.org/wiki/Extraventricular_drain | # External ventricular drain
(Redirected from Extraventricular drain)
Drainage system showing bloody CSF due to intercranial hemorrhage.
An external ventricular drain (EVD), also known as an extraventricular drain or ventriculostomy, is a device used in neurosurgery that relieves elevated intracranial pressure and hydrocephalus when the normal flow of cerebrospinal fluid around the brain is obstructed. This is a plastic tube placed by neurosurgeons, neurologists or neurointensivists and managed by ICU nurses and Critical Care Paramedics to drain fluid from the ventricles of the brain and thus keep them decompressed, as well as to monitor intracranial pressure.
## Kocher's point
The tube is most frequently placed in Kocher's point with the goal of having the catheter tip in the frontal horn of a lateral ventricle. The catheter is normally inserted on the right side of the brain. An EVD (also called an intraventricular catheter, or IVC) is used to monitor pressure in patients with brain injuries, intracranial bleeds or other brain abnormalities that lead to increased fluid build-up. In draining the ventricle it can also remove blood from the ventricular spaces. This is important because blood is an irritant to brain tissue and can cause complications such as vasospasm.
## Care of the Patient with an External Ventricular Drain
The external ventricular drain (EVD) is leveled to a common reference point, usually the tragus. The external ventricular drain is set on a graduated burette the pressure level of the EVD is prescribed by a healthcare professional, usually a neurosurgeon. Leveling the EVD to a set pressure level is the basis for cerebrospinal fluid (CSF) drainage, hydrostatic pressure dictates CSF drainage. The fluid column pressure must be greater than the weight of the CSF in the system before drainage occurs. It is important that family members and visitors understand the patient's head of bed position cannot be changed without assistance.[1]
An example of a healthcare provider order regarding an EVD is: Level external ventricular drain to 15 cmH20 above midbrain, open to drain continuously, check and record cerebrospinal fluid drainage and intracranial pressure every hour.
The cerebral perfusion pressure (CPP) can be calculated from data obtained from the EVD and systemic blood pressure. In order to calculate the CPP the intracranial pressure and mean arterial pressure (MAP) must be available.[1]
$CPP=MAP-ICP$
## Obstruction
If the EVD becomes occluded, clogged, or obstructed, as it often does with fibrinous or clot like material, the brain can swell due to pressure build up in the ventricles and permanent brain damage can occur. Physicians, nurses, and Critical Care Paramedics often have to adjust or flush these small diameter catheters to manage medical tube obstructions and occlusions at the intensive-care bedside.[2] Pressure settings are generally measured in cmH2O. The equilibrium pressure of the EVD apparatus is adjusted based on cerebrospinal fluid output, ICP waveform, imaging including CT or MRI of the brain, and clinical response. | 2014-03-12 03:10:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47441768646240234, "perplexity": 6712.614753287792}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394021230991/warc/CC-MAIN-20140305120710-00021-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://answerbun.com/super-user/fitting-images-to-documents-margins-in-a-docx-file/ | # Fitting images to document's margins in a docx file
Super User Asked by Tal Galili on January 13, 2021
I’ve got a docx file with many figures, all do not fit the margins of the document. I can manually adjust the sizes of the figures in the file, but would love to have some way to automate this (either from Word, from a command line tool, or any other means).
(PS: this is a follow-up to this question)
Answered by Victor Onrust on January 13, 2021
Reading Visual Basic Macro in Word to Resize/Center/Delete All Images, How to resize all images in Word document and How can I resize a table to fit the page's width fixed the Kelly Tessena Keck solution a bit.
Now it's working with any available page width (don't forget to fix height, if needed, too) :
Sub PicturesFitPageWidth()
' ResizePic Macro
' Resizes an image
Shapes = ActiveDocument.Shapes.Count
InLines = ActiveDocument.InlineShapes.Count
'Sets the variables to loop through all shapes in the document, one for shapes and one for inline shapes.
'Calculate usable width of page
With ActiveDocument.PageSetup
WidthAvail = .PageWidth - .LeftMargin - .RightMargin
End With
For ShapeLoop = 1 To Shapes
MsgBox Prompt:="Shape " & ShapeLoop & " width: " & ActiveDocument.Shapes(ShapeLoop).Width
If ActiveDocument.Shapes(ShapeLoop).Width > WidthAvail Then
ActiveDocument.Shapes(ShapeLoop).Width = WidthAvail
End If
Next ShapeLoop
'Loops through all shapes in the document. Checks to see if they're too wide, and if they are, resizes them.
For InLineLoop = 1 To InLines
MsgBox Prompt:="Inline " & InLineLoop & " width: " & ActiveDocument.InlineShapes(InLineLoop).Width
If ActiveDocument.InlineShapes(InLineLoop).Width > WidthAvail Then
ActiveDocument.InlineShapes(InLineLoop).Width = WidthAvail
End If
Next InLineLoop
'Loops through all shapes in the document. Checks to see if they're too wide, and if they are, resizes them.
End Sub
Answered by WebComer on January 13, 2021
You can do this with the following VBA code. It counts the shapes in the document, checks their width against the available space on the page, and resizes if necessary.
Note that Word has two different collections for Shapes and InlineShapes, hence the two different For loops. Also, it uses a series of If/ElseIf statements to identify the page width based on standard paper sizes. Currently, the only options are letter size in either portrait or landscape, but you can add more ElseIfs for any paper sizes you need.
Sub ResizePic()
' ResizePic Macro
' Resizes an image
Shapes = ActiveDocument.Shapes.Count
InLines = ActiveDocument.InlineShapes.Count
'Sets the variables to loop through all shapes in the document, one for shapes and one for inline shapes.
RightMar = ActiveDocument.PageSetup.RightMargin
LeftMar = ActiveDocument.PageSetup.LeftMargin
PaperType = ActiveDocument.PageSetup.PaperSize
PageLayout = ActiveDocument.PageSetup.Orientation
'Sets up variables for margin sizes, paper type, and page layout.
' This is used to find the usable width of the document, which is the max width for the picture.
If PaperType = wdPaperLetter And PageLayout = wdPortrait Then
WidthAvail = InchesToPoints(8.5) - (LeftMar + RightMar)
ElseIf PaperType = wdPaperLetter And PageLayout = wdLandscape Then
WidthAvail = InchesToPoints(11) - (LeftMar + RightMar)
End If
'Identifies the usable width of the document, based on margins and paper size.
For ShapeLoop = 1 To Shapes
MsgBox Prompt:="Shape " & ShapeLoop & " width: " & ActiveDocument.Shapes(ShapeLoop).Width
If ActiveDocument.Shapes(ShapeLoop).Width > WidthAvail Then
ActiveDocument.Shapes(ShapeLoop).Width = WidthAvail
End If
Next ShapeLoop
'Loops through all shapes in the document. Checks to see if they're too wide, and if they are, resizes them.
For InLineLoop = 1 To InLines
MsgBox Prompt:="Inline " & InLineLoop & " width: " & ActiveDocument.InlineShapes(InLineLoop).Width
If ActiveDocument.InlineShapes(InLineLoop).Width > WidthAvail Then
ActiveDocument.InlineShapes(InLineLoop).Width = WidthAvail
End If
Next InLineLoop
'Loops through all shapes in the document. Checks to see if they're too wide, and if they are, resizes them.
End Sub
Answered by Kelly Tessena Keck on January 13, 2021
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Handbook of Optical Sensing of Glucose in Biological Fluids and Tissues Valery V Tuchin (Ed) Intelligent and Adaptive Systems in Medicine Oliver C L Haas and Keith J Burnham. @kamaci: it depends. In an autocorrelation, which is the cross-correlation of a signal with itself, there will always be a peak at a lag of zero, and its size will be the signal energy. Definition of autocovariance in the Definitions. Find books. Chapter 4: Generating Functions This chapter looks at Probability Generating Functions (PGFs) for discrete random variables. The autocovariance at lag s is defined as The autocorrelation function begins at some point determined by both the AR and MA components but thereafter, declines geometrically at a rate determined by the AR component. The zero-lag autocovariance a 0 is equal to the power. Fourier Transform Representation of Random Signals [ ] ( ) [ ] ( ) [ ] ( ) [ ] (jw ) xy xy jw xx xx jw. In this case, C is the second moment matrix of the observations about their mean. •Large number of design variables. Thanks for contributing an answer to Mathematics Stack Exchange! Please be sure to answer the question. In addition to the general there is four homeworks. com > gibbs. A1 (choose your own time series) A link to data sources that can be used. Autocovariance generating function and spectral density. fi;fl/, for 1 •fi6Dfl•N, with probabilities 1=N. Maximal Ratio Combining Example in Matlab In the old days, communication between a transmitter and receiver was simple. Empirical covariance¶. Autocovariance estimation with long range dependence in Gaussian and threshold Gaussian model. The xcov function estimates autocovariance and cross-covariance sequences. Autocovariance function, generalized least squares: Lecture Slides: Lecture Notes: Lecture Slides: Covariance Modeling: Estimating the covariance [Quiz 1] Kriging and prediction: No Class: Independence Day: Lecture Slides Reference: Cressie Ch 1: Lecture Slides Reference: Cressie Ch 2-4: Autoregressive Processes: AR processes in time: AR. Long memory has been observed for time series across a multitude of fields, and the accurate estimation of such dependence, for example via the Hurst exponent, is crucial for the modelling and prediction of many dynamic systems of interest. 2 Basic Concepts of the Poisson Process The Poisson process is one of the most widely-used counting processes. ; the sequence of pdfs of Xn is called the first-order pdf of the process xn 1 0 1 z Since Xn is a differentiable function of the continuous r. In fact, if is sufficiently smooth on and if. Rinaldoa aDepartment of Statistics Carnegie Mellon University Pittsburgh, PA 15213-3890 USA Abstract The Lasso is a popular model selection and estimation procedure for lin-ear models that enjoys nice theoretical properties. The autocovariance function: 也就是说autocovariance 只依赖于k, 而不是t。 ACF: 以上就是理论上的white noise。 如果想用R来判断是否是white noise，可以从time series 和 acf 的图像上来分析。 time series 的图像可用 ts. They also handle autocorrelation and autocovariance as special cases. MATLAB divides Signal Processing Toolbox as follows •Waveforms – Pulses, modulated signals, peak-to-peak and RMS amplitude, rise time/fall time, overshoot/undershoot •Convolution and Correlation – Linear and circular convolution, autocorrelation, autocovariance, cross-correlation, cross-covariance •Transforms. En tracant sur un graphique les pts dont les coordonnées sont log y(h) et log h. COURSE INFORMATION: CourseInstructor Prof. This gives me an output that i store as a variable. Thus, (ii) it can be calculated that and the autocovariance. cor,ddmatrix-method. AR(1) TIME SERIES PROCESS Econometrics 7590 Zsuzsanna HORVATH and Ryan JOHNSTON´ Abstract: We define the AR(1) process and its properties and applications. Fractal Dimension and the Hurst Parameter. Search Ringtones by Artists: 0. Derivation of the Autocovariance function of a Moving Average process (MA(q))). Interpretation. cov2cor () scales a covariance matrix into a correlation matrix. torchvision. For a N-dimensional given vector x, the Matlab command xcorr(x,x) or simply xcorr(x) gives the auto-correlation sequence. A more flexible approach than the ones discussed so far to estimate the joint distribution of the invariants ε t ≡ (ε 1, t, …, ε ˉ ı, t) ' is via copula-marginal estimation, which can be implemented in two ways: either via i) the static approach (Section 3. Characterizing Detrended Fluctuation Analysis of Multifractional Brownian Motion V. There are (at least) 2. OMS Analytics. INDEX 2-D Fourier transform, 333 2-D sampling theorem, 334 A/D converter, 320 Matlab functions, 323 parallel or flash, 322 Autocovariance sequence (ACVS), 799, 816. ˚ Recommended Text (JH) J. 1 $\begingroup$ I have tried compute the autocovariance of the following process: but irrelevant as far as the autocovariance function is concerned. 564 but as we know it equals $\pi$, so the answer is about half of the real period in this case. It was chaired by members of Eurostat: Jukka Jalava, Luis Biedma and Johannes Wouters. The ARIMA(1,0,0)x(0,1,0) model with constant: SRW model plus AR(1) term. edu Tel:(505)277-1611,Fax:(505)277-1439 Prerequisite EECE-314,Math-314,BasicknowledgeofMATLAB Location DSH{132 Lectures MWF:1:00-1:50PM Textbook AlbertoLeonGarcia,"ProbabilityandRandomProcesses. For two-vector or two-matrix input, C is the 2-by-2 covariance matrix between the two random variables. The first differencing value is the difference between the current time period and the previous time period. If x is a matrix, then c is a matrix whose columns contain the autocovariance and cross-covariance sequences for all combinations of the columns of x. Stationary processes and limit distributions I Stationary processes follow the footsteps of limit distributions I For Markov processes limit distributions exist under mild conditions I Limit distributions also exist for some non-Markov processes I Process somewhat easier to analyze in the limit as t !1. Let wt, t ∈ Z be a normal white noise (i. I have a periodic signal loaded into > Matlab and i am trying to estimate the Autocovariance of it by using the > xcov command. 1); or via ii) the dynamic approach (Section 3. However, certain applications require rescaling the normalized ACF by another factor. The MVGC Matlab® Toolbox is designed to facilitate Granger-causal analysis with multivariate and possibly multi-trial time series data. Show that this series is weakly stationary with autocovariance function γh = σ2cos(2πωh). Reformed the organization. We can see in this plot that at lag 0, the correlation is 1, as the data is correlated with itself. Lil Yachty) - download. COURSE INFORMATION: CourseInstructor Prof. If these values fail to revolve around a constant mean and variance. The above model can be compactly written as Z t = + (B)a t. Autoregressive Process Modeling via the Lasso Procedure Y. SCILAB provides function corr to calculate the autocovariance function out of a vector signal u. Example: AR(2) Model: Consider yt = ˚1yt 1 +˚2yt 2 + t. We show that correctly identifying the distribution. 1 Introduction & General Instructions The purpose of this set of homework assignments is to make the student familiar with the practical handwork and theoretical effort required in time series analysis of real life data. Time series clustering is implemented in TSclust, dtwclust, BNPTSclust and pdc. 15 ANNA UNIVERSITY CHENNAI : : CHENNAI – 600 025 AFFILIATED INSTITUTIONS B. We need the Poisson Distribution to do interesting things like finding the probability of a number of events in a time period or finding the probability of waiting some time until the next event. queremos hacerte la vida más fácil y, por eso, desde nuestra web podrás encontrar toda la información que necesites. Examples 3. A stationary series is unlikely to exhibit long-term trends. About the ARPM Lab The ARPM Lab ® (Advanced Risk and Portfolio Management Lab) is a constantly updated online platform for learning and teaching quantitative finance. The Covariance Matrix Definition Covariance Matrix from Data Matrix We can calculate the covariance matrix such as S = 1 n X0 cXc where Xc = X 1n x0= CX with x 0= ( x 1;:::; x p) denoting the vector of variable means C = In n 11n10 n denoting a centering matrix Note that the centered matrix Xc has the form Xc = 0 B B B B B @ x11 x 1 x12 x2 x1p. Maximal Ratio Combining Example in Matlab In the old days, communication between a transmitter and receiver was simple. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with Matlab. The components, by which time series is composed of, are called component of time series data. Thanks in advance. Contextual translation of "effectiveness" from French into Portuguese. com - Autoescuela CAVALERI (4 days ago) [email protected] a la web de autoescuela cavaleri nuestro propósito es ofrecerte una formación de calidad para la obtención del permiso de conducir. cov,ddmatrix-method. Examples 3. m ( sample autocorrelation function) acvf. Maximal Ratio Combining Example in Matlab In the old days, communication between a transmitter and receiver was simple. Издательство CRC Press, 2012, -664 pp. (8 SEMESTER) ELECTRONICS AND COMMUNICATION ENGINEERING CURRICU. Consider the series y t, which follows the GARCH process. > > This gives me an output that i store as a variable. try 5 and 1 5, for example. Taught by: Lori Pedersen, Josh Carlson. 2 ACVF and ACF of ARMA(1,1) The fact that we can express ARMA(1,1) as a linear process. The method used is a generalization of the autocovariance least-squares method to systems with mutually correlated noise. Poisson and exponential random variables 1. The autocovariance as a function of the time lag ( τand L): ESS210B Prof. N ¡1/values. Almost everything in R is done through functions. 1 The time series data fzi;tg with the same physical meaning are sampled n times from the same zero mean autocovariance nonstationary process. geophysical data analysis: time series duncan carr agnew robert l. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. where is a bandwidth parameter (which acts as a truncation lag in the covariance weighting), is a kernel function, and where , the j-th sample autocovariance of the residuals , is defined as: (41. > What Matlab functions to use to calculate autocorrelation and > autocovariance of discrete data series? There is a function called xcorr() in the signal processing toolbox. Alessia ha indicato 3 esperienze lavorative sul suo profilo. AUTOCOVARIANCE Statistics LET Subcommands 2-4 September 3, 1996 DATAPLOT Reference Manual AUTOCOVARIANCE PURPOSE Compute the lag 1 autocovariance of a variable. A string in [‘none’, ‘raise’, ‘conservative’, ‘drop’] specifying how the NaNs are to be treated. @kamaci: it depends. implement this algorithm in other computing environments such as MatLab. Discussion of “High-dimensional autocovariance matrices and optimal linear prediction. Answered: Christiaan on 9 Mar 2015 Or do you mean, given some data, how do I compute the wavelet autocorrelation (autocovariance) for that data?. Empirical covariance¶. Okay, so autocorrelation coefficient between Xt and Xt+k, remember, the most important part here is the time difference between these two random variables. The method used is a generalization of the autocovariance least-squares method to systems with mutually correlated noise. Sign up to join this community. Moreover, statistics concepts can help investors monitor, covariance is a measure of the relationship between two random variables. RS -EC2 -Lecture 14 1 1 Lecture 14 ARIMA - Identification, Estimation & Seasonalities • We defined the ARMA(p, q)model:Let Then, xt is a demeaned ARMA process. Each box contains three sub-figures. Key words and phrases. Use Automated Cross Correlations in Excel to Find Leading Indicators—Part 1 Leading indicators can help you to forecast more accurately. I'd just like to know if anyone knows why: a) the xcov matrix is twice as long as the original signal and; b) how can i, from the xcov result see the periodicity of the. pdf MATLAB Codes: EXAMPLE_lsq_dispersion. pyplot as plt # matplotlib provides plot functions similar to MATLAB import numpy as np from skimage import color , filter # skimage is an image processing library. The xcov function estimates autocovariance and cross-covariance sequences. The subtraction can be done within the axcor input argument. You may choose to present a paper at your own choice from a reading list, which will be available in the middle of the semester. Z, we can find its. Introduction to Time Series Analysis. 24K Magic - download. Inference based on autocorrelation function is often called an analysis in the time domain. Xiaohui Chen. Here is a sample problem and its solution showing the use of this equation: An object is moving with a velocity of 5. The theoretical autocovariance function of a long memory process. Download books for free. Use Automated Cross Correlations in Excel to Find Leading Indicators—Part 1 Leading indicators can help you to forecast more accurately. It is the same as. Focused Review of Key Probability Concepts 1. ist internal examination. In the process of rewriting the code, I use the design of JFVM. This course presents an example of applying a database application development methodology to a major real -world project. Remember that a sequence of random variables is said to be covariance stationary (or weakly stationary) if and only if:. For best results, give a suitable value for lags. 10 ein) t ein) Fig. Definition 2: The mean of a time series y 1, …, y n is. However, a manufacturer's proprietary restrictions will generally make access to the detailed design specifications of a transformer difficult. x must be a column vector having length m not less than maxlag+1. cor,ddmatrix-method. Its sign convention for the lag variable is reversed with respect to the. What does autocovariance mean? Information and translations of autocovariance in the most comprehensive dictionary definitions resource on the web. Calculate and plot , where cells/sec. Provide details and share your research! But avoid … Asking for help, clarification, or responding to other answers. autocov computes the autocovariance between two column vectors X and Y with same length N using the Fast Fourier Transform algorithm from 0 to N-2. The xcov function estimates autocovariance and cross-covariance sequences. For example, autocorr(y,'NumLags',10,'NumSTD',2) plots the sample ACF of y for 10 lags and displays confidence bounds consisting of 2 standard errors. The temporal information is given by when the state is. Expert Answer. Threshold GARCH Model: Theory and Application Jing Wu The University of Western Ontario October 2011 Abstract In this paper, we describe the regime shifts in the volatility dynamics by a threshold model,. cov(x, 1) and cov(x, y, 1) normalize by nobs. 9 z y x w v u t s r q p o n m l k j i h g f e d c b a. STAT:2010 is a beginning methods course for undergraduate students. The course also covers statistical image understanding, elements of pattern theory, simulated annealing, Metropolis-Hastings algorithm, and Gibbs sampling. 27th European Symposium on Computer Aided Process Engineering, 2239-2244. For the random-walk-with-drift model, the k-step-ahead forecast from period n is: n+k n Y = Y + kdˆ ˆ where. Created with R13 Compatible with any release Platform Compatibility Windows macOS Linux. (JD) James Davidson, Econometric Theory, Blackwell Publishing. Often, one of the first steps in any data analysis is performing regression. Only method="pearson" is implemented at this time. Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay. Then, I calculate the autocovariance matrix, from where I extract the eigenvalues and eigenvectors which are used to calculate the new variable Y which is the stochastic process S in a base where the random variables are not correlated. Video created by The State University of New York for the course "Practical Time Series Analysis". Obtaining the autocorrelation from the autocovariance is usually just a matter of dividing the later by its value in 0 (considering that $$autocov_f(0)=var(f)$$). in matlab Auto correlation, partial auto correlation, cross correlation. The covariance matrix of a data set is known to be well approximated by the classical maximum likelihood estimator (or "empirical covariance"), provided the number of observations is large enough compared to the number of features (the variables describing the observations). The autocovariance measures thelinear dependencebetween two points on the same series observed at di erent times. If T istherealaxisthenX(t,e) is a continuous-time random process, and if T is the set of integers then X(t,e) is a discrete-time random process2. A video tutorial that explains how to do basic image manipulations - play. language to solve homework problems. autocovariance or spectrum. For example, autocorr (y,'NumLags',10,'NumSTD',2) plots the sample ACF of y for 10 lags and displays confidence. ts(): plots a two time series on the same plot frame (tseries) tsdiag(): a generic function to plot time-series diagnostics (stats) ts. A compar ison of the performance of the SZ-1 algorithm using the magnitude deconvolution, and the SZ-1 algorithm using this substitution method is made on simulated time series data. where ω ∈ [0, 1) is a fixed constant. The correlation coefficient quantifies the degree of change of one variable based on the change of. Learn more about nonlinear-autocovariance, statistics, autocovariance. Calculate the autocovariance function using the given formula. 22) Note that the residuals that EViews uses in estimating the autocovariance functions in (41. Autocovariance function, generalized least squares: Lecture Slides: Lecture Notes: Lecture Slides: Covariance Modeling: Estimating the covariance [Quiz 1] Kriging and prediction: No Class: Independence Day: Lecture Slides Reference: Cressie Ch 1: Lecture Slides Reference: Cressie Ch 2-4: Autoregressive Processes: AR processes in time: AR. Implementation, verification, and analysis of various engineering algorithms used in signal and image processing, robotics, communications engineering. En tracant sur un graphique les pts dont les coordonnées sont log y(h) et log h. Introduction 2. computes the sample autocovariance of a time series x for lags from 0 to maxlag, returning a column vector of length maxlag+1. Homework 1 solutions, Fall 2010 Joe Neeman (b) Xt oscillates with period 4. This article needs additional citations for verification. autocovariance function: Continuous. What is Covariance? In mathematics and statistics Basic Statistics Concepts for Finance A solid understanding of statistics is crucially important in helping us better understand finance. Autocovariance function is defined, basically, just taking covariance of different elements in our sequence, in our stochastic process. The sample ACF has significant autocorrelation at lag 1. tacvf: Prints a tacvf object. Chapter 5 Prediction Prerequisites • The best linear predictor. Note that φ(0) = x'2, so that the autocovariance at lag zero is just the variance of the variable. Documents SAS/IML software, which provides a flexible programming language that enables novice or experienced programmers to perform data and matrix manipulation, statistical analysis, numerical analysis, and nonlinear optimization. The autocovariance function can be thought of as measuring the memory or self-similarity of the deviation of a signal about its mean level. Learn more about nonlinear-autocovariance, statistics, autocovariance. Correlation and Convolution Cross-correlation, autocorrelation, cross-covariance, autocovariance, linear and circular convolution Signal Processing Toolbox™ provides a family of correlation and convolution functions that let you detect signal similarities. The power spectral density of fn(t) is then given by S~(W) = k. Maximal Ratio Combining Example in Matlab In the old days, communication between a transmitter and receiver was simple. statistics and time series analysis) to normalize the autocovariance function to get a time-dependent Pearson correlation coefficient. Created with R13 Compatible with any release Platform Compatibility Windows macOS Linux. wmtsa_acvs-- Calculate the autocovariance sequence (ACVS) of a data series. 34) Definition 1. The new octave version was recently released and I was excited to test the new classdef, to use my Matlab FVTool with the same functionality in the free (as in free speech and free coffee) Octave. For two-vector or two-matrix input, C is the 2-by-2 covariance matrix between the two random variables. Sharma Department of Astronomy, University of Maryland, College Park, Maryland 20742, USA (Dated: November 12, 2014). N ¡1/values. In fact, if is sufficiently smooth on and if. The theoretical autocovariance function of an AR(p) with unit variance is computed. Coming to the zero-mean, unit variance Gaussian random number, any normal distribution can be specified by the two parameters: mean. The biceps muscle is adequately modelled as a single degree of freedom linear system and it follows, from the theory of spectral analysis, that the autocovariance function of the EMG response is an estimate of the impulse response of the biceps. Finding autocovariance of AR(2) Ask Question Asked 6 years, 2 months ago. 24K Magic - download. Moreover, statistics concepts can help investors monitor, covariance is a measure of the relationship between two random variables. Statistical Learning and Stochastic Process for Robust Predictive Control of Vehicle Suspension Systems by Ahmad Moza ari A thesis presented to the University of Waterloo in ful llment of the thesis requirement for the degree of Master of Mathematics in Statistics Waterloo, Ontario, Canada, 2017 c Ahmad Moza ari 2017. The Data Science Show 21,006 views. $\gamma_o$ is the population variance. funstring or function, optional. Stationary processes and limit distributions I Stationary processes follow the footsteps of limit distributions I For Markov processes limit distributions exist under mild conditions I Limit distributions also exist for some non-Markov processes I Process somewhat easier to analyze in the limit as t !1. FREQUENCY DOMAIN EXERCISE (1) Consider a process with spectral density Sx(w) that takes the value 1 at w equal to 0, p 2, 3p 2, p, etc. 1 show a white noise sequence of length N = 128 and its periodogram, which shows that the power spectrum is uniformly spread. C = cov (A) returns the covariance. cor,ddmatrix-method. ACF and prediction. var () is a shallow wrapper for cov () in the case of a distributed matrix. The conditional variance h t is where The GARCH(p,q) model reduces to the ARCH(q) process when p=0. p-values are left-tail probabilities. 3 The Durbin method of MA estimation. (When τ= 0, the autocovariance reduces to the variance. Please sign up to review new features, functionality and page designs. If signal means are zero, the correlation and covariance operations are. 128 CHAPTER 7. Why autocorrelation matters. Let wt, t ∈ Z be a normal white noise (i. 3 Chi-Square Test •Designed for testing discrete distributions, large samples •General test: can be used for testing any distribution —uniform random number generators —random variate generators •The statistical test: •Components —k is the number of bins in the histogram —oi is the number of observed values in bin i in the histogram —ei is the number of expected values in bin. In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector. Recommended Reading: If you feel like you are having a hard time with basic probability, I suggest:. The functions xcorr and xcov estimate the cross-correlation and cross-covariance sequences of random processes. Stimulus presentation, behavioral data collection, and reward delivery were controlled by a real-time experimentation data acquisition system (Tempo; Reflective Computing) or a personal computer running the MonkeyLogic Matlab toolbox (31, 32). The Autocovariance-Generating Function for Vector Processes 266 10. The autocorrelation of a time series can inform us about repeating patterns or serial correlation. , the value 0 at p 4, 3p 4, 5p 4, 7p 4, etc. 2 • X(t) is a wide sense stationary process with autocorrelation function RX(τ) = 10 sin(2000πt) +sin(1000πt). , the cross-covariance is a function that gives the covariance of one process with the other at pairs of time points. Normalization of Power Spectral Density estimates Andrew J. b Two example Go trials. Meaning of autocovariance. Dirichlet’s Kernel. Sharma Department of Astronomy, University of Maryland, College Park, Maryland 20742, USA (Dated: November 12, 2014). autocovariance and autocorrelation function), stationarity,spectral analysis, general linear time series models and their properties, ARMA models, ARIMA models, ARCH and GARCH models. If you take Xt and Xs and s and t might be in different locations and we'll get the cavariance of them, we get gamma (s,t) then we call that covariance and if we take ( x,t) the covariance of (x,t) will itself. Stationary processes and limit distributions I Stationary processes follow the footsteps of limit distributions I For Markov processes limit distributions exist under mild conditions I Limit distributions also exist for some non-Markov processes I Process somewhat easier to analyze in the limit as t !1. It is common practice in some disciplines (e. AUTOCOVARIANCE Statistics LET Subcommands 2-4 September 3, 1996 DATAPLOT Reference Manual AUTOCOVARIANCE PURPOSE Compute the lag 1 autocovariance of a variable. Learn more about nonlinear-autocovariance, statistics, autocovariance. The power spectral density of fn(t) is then given by S~(W) = k. If A is a matrix whose columns represent random variables and whose rows represent observations, C is the covariance matrix with the corresponding column variances along the diagonal. C is normalized by the number of observations -1. Estimate the model in Step 4 using Ordinary Least Squares (OLS). Estimate speed of adjustment, if appropriate. T his leads to the follow ing deÞ nition of the Òauto co variance Ó of the pro ces s:! (k ) = co v(X n + k, X n) (3. Correlation and Convolution Cross-correlation, autocorrelation, cross-covariance, autocovariance, linear and circular convolution Signal Processing Toolbox™ provides a family of correlation and convolution functions that let you detect signal similarities. The resulting autocovariance column vector acv is given by the formula:. Theory based autocovariance estimates are compared to static measurement based autocovariance estimates in order to validate this theory. Thanks in advance. 7 A weakly stationary time series, xt, ts a finite variance process such that. 9 Matlab: Discrete Random Variables 9 Tuesday, 2/10/15 3. Effects on spectrum of using finite duration of data. Perform the Bounds Test. way into the Matlab simulation program. m ( sample autocorrelation function) acvf. 2 Parametric estimation. AR(1) TIME SERIES PROCESS Econometrics 7590 Zsuzsanna HORVATH and Ryan JOHNSTON´ Abstract: We define the AR(1) process and its properties and applications. The autocovariance Stack Exchange Network 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. (When τ= 0, the autocovariance reduces to the variance. Clearly di↵erent time series give rise to di↵erent features in the. In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance-covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector. • In this lecture, we will study:. com > gibbs. In essence the spectral density and the autocovariance function contain the same information, but express it in different ways. Long memory has been observed for time series across a multitude of fields, and the accurate estimation of such dependence, for example via the Hurst exponent, is crucial for the modelling and prediction of many dynamic systems of interest. Calcul fringes in matlab Autocorrelation and crosscorrelation function of gold sequence in matlab Variance ratio test in matlab Guitar tuner demo from matlab expo 2011 in tokyo Computes the autocovariance of two columns vectors consistently with the var and cov functions. In this package it is used for the computation of the information matrix, in simulating p initial starting values for AR simulations and in the computation of the exact mle for the mean. • finance - e. Autocovariance of an ARMA process. The cross-correlation is similar in nature to the convolution of two functions. Statistics in Engineering: With Examples in MATLAB® and R, Second Edition - CRC Press Book Engineers are expected to design structures and machines that can operate in challenging and volatile environments, while allowing for variation in materials and noise in measurements and signals. Location - download. Other Useful Texts (AH) Andrew Harvey, Time Series Models, MIT Press. Unlike 'plot. ContactInfo Email:[email protected] Because a shock at time t−1 also impacts the variance at time t, the volatility is more likely to be high at time t if it was also. This video provides an introduction to the concept of 'autocorrelation' (also called 'serial correlation'), and explains how it can arise in practice. missing str, optional. Most physical processes in the real world involve a random or stochastic element in their structure, and a stochastic process can be described as ‘a statistical phenomenon that evolves in time according to probabilistic laws’. This problem has received several solutions. Properties of MA Finite Process 3. The General Linear Model (GLM) Ged Ridgway Wellcome Trust Centre for Neuroimaging University College London SPM Course Vancouver, August 2010. autocorr(self, lag=1) [source] ¶ Compute the lag-N autocorrelation. Otherwise it is nonin-vertible. Homework 8 Solutions Chapter 14 25. A series v aries around its mean (whic h here is. result=xcorr(test,test) Show transcribed image text. Calculating Sample Autocorrelations in Excel A sample autocorrelation is defined as vaˆr( ) coˆv( , ) ˆ ˆ ˆ, 0 it k it i t k k R R R − g g r. Autocovariance function, generalized least squares: Lecture Slides: Lecture Notes: Lecture Slides: Covariance Modeling: Estimating the covariance [Quiz 1] Kriging and prediction: No Class: Independence Day: Lecture Slides Reference: Cressie Ch 1: Lecture Slides Reference: Cressie Ch 2-4: Autoregressive Processes: AR processes in time: AR. The ARPM Lab spans the entire spectrum of Quantitative Finance, across Asset Management, Banking, and Insurance, from the foundations to the most advanced developments. array 2d array of size nr X T with the temporal components center: np. Threshold GARCH Model: Theory and Application Jing Wu The University of Western Ontario October 2011 Abstract In this paper, we describe the regime shifts in the volatility dynamics by a threshold model,. Chapter 5 Prediction Prerequisites • The best linear predictor. Implementation. Purpose: Check Randomness Autocorrelation plots (Box and Jenkins, pp. In Matlab, "The variance is normalized by the number of observations-1 by default. Our treatment of continuous-time GMPs on. The transmitter sent out a single signal through one antenna, which eventually arrived at a single antenna at the receiver, probably along with a little noise. Question: The Help Of Matlab Code Kindly Expalin. It is widely used to model random points in time and space, such as the times of radioactive emissions, the arrival times of customers at a service center, and the positions of flaws in a piece of material. For the Love of Physics - Walter Lewin - May 16, 2011 - Duration: 1:01:26. The matrix R = corrcoef(X) is related to the covariance matrix C = cov(X) by. c = xcov(x) returns the autocovariance sequence of x. The difference between autocorrelation and partial autocorrelation can be difficult and confusing for beginners to time series forecasting. ARIMA Models 3. Rojas James S. Software: Some homework problems will require Matlab. 9, 801-810. Lecture 16. Homogeneous linear difference equations. Matlab and Simulink were designed to make the programming of DSP and signal flow graphs easy. Gaussian random variables: expressing probabilities in terms of the Q function and the Phi function 1. The variances are along the diagonal of C. AUTOCOVARIANCE Statistics LET Subcommands 2-4 September 3, 1996 DATAPLOT Reference Manual AUTOCOVARIANCE PURPOSE Compute the lag 1 autocovariance of a variable. 7 Expected Value and Autocovariance or Random Processes 30. It was chaired by members of Eurostat: Jukka Jalava, Luis Biedma and Johannes Wouters. Most physical processes in the real world involve a random or stochastic element in their structure, and a stochastic process can be described as ‘a statistical phenomenon that evolves in time according to probabilistic laws’. 15 ANNA UNIVERSITY CHENNAI : : CHENNAI – 600 025 AFFILIATED INSTITUTIONS B. net dictionary. C is normalized by the number of observations -1. computes the sample autocovariance of a time series x for lags from 0 to maxlag, returning a column vector of length maxlag+1. R = corrcoef(x,y) where x and y are column vectors is the same as corrcoef([x y]). Vector of p-values of the test statistics, with length equal to the number of tests. If you need to calculate only 1 covariance matrix per run, it's just easier to use cov. As departmental computer resources are limited, students may want to purchase the student version of MATLAB or installGNU Octave, which is a free MATLAB replacement. Returns a distributed matrix. I know how to arrive at each solution using mathematical techniques, but I also need to know how to arrive at each one using Matlab's own built in functions. x must be a column vector having length m not less than maxlag+1. However, certain applications require rescaling the normalized ACF by another factor. fft bool, optional. Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay. If x is a matrix, then c is a matrix whose columns contain the autocovariance and cross-covariance sequences for all combinations of the columns of x. Random field theory has been increasingly adopted to simulate spatially varying environmental properties and hydrogeological data in recent years. Viewed 4k times 2. Obtaining the autocorrelation from the autocovariance is usually just a matter of dividing the later by its value in 0 (considering that $$autocov_f(0)=var(f)$$). (2019) An analytical method to predict and compensate for residual stress-induced deformation in overhanging regions of internal channels fabricated using powder bed fusion. Probability and Statistics for Data Science Training Course in Austria taught by experienced instructors. Often, one of the first steps in any data analysis is performing regression. Lecture 13 (October 27). Unsourced material may be challenged and removed. Remember that a sequence of random variables is said to be covariance stationary (or weakly stationary) if and only if:. Applied Time Series Analysis and Forecasting Some assignments may require the use of computer software such as Matlab, Gauss, R, Ox. Topic 8: LSQ and Inverse Modeling: Reconstructing the source of a pollutant with an advection diffusion model References: Wunsch Chap. (2019) RSFit3000: A MATLAB GUI-based program for determining rate and state frictional parameters from experimental data. We must focus on relevant inputs from our senses – such as the bus we need to catch – while ignoring distractions – such as the eye-catching displays in the shop windows we pass on the same street. In case you aren't well versed with normal distrinution, you can go through the wikipedia link provided by Justin. If you need to do it hundreds of times in a loop, with different data sets, etc. A string in [‘none’, ‘raise’, ‘conservative’, ‘drop’] specifying how the NaNs are to be treated. 1) and/or variances (see graph (c) in figure 4. ) Windowed spectral analysis (Lecture 12, Feb. Matlab: nino2 (cont. 1 Time series data A time series is a set of statistics, usually collected at regular intervals. The following flow chart illustrates the procedure. If you need to calculate only 1 covariance matrix per run, it's just easier to use cov. The upper two panels of Fig. The Covariance Matrix Definition Covariance Matrix from Data Matrix We can calculate the covariance matrix such as S = 1 n X0 cXc where Xc = X 1n x0= CX with x 0= ( x 1;:::; x p) denoting the vector of variable means C = In n 11n10 n denoting a centering matrix Note that the centered matrix Xc has the form Xc = 0 B B B B B @ x11 x 1 x12 x2 x1p. Hannig and Min-ge Xie (2012), A note on Dempster-Shafer Recombinations of Confidence Distributions , Electronic Journal of Statistics , 6 , pp. If now one assunies that there exists some function g(t) such that according to (2) and the assumptions mentioned before, k &(a) = - bI2. They are computed using tsfeatures for a list or matrix of time series in ts format. A lot of m-files are found in this page. By contrast, correlation is simply when two independent variables are linearly related. Once you have read the time series data into R, the next step is to store the data in a time series object in R, so that you can use R’s many functions for analysing time series data. The green square is only drawn to illustrate the linear transformation that is applied to each of these three vectors. (FH) Fumio Hayashi, Econometrics, Lecture Notes. plot(): plots several time series on a common plot. What is the difference between autocovariance, autocorrelation and autocorrelation coefficient? I tried to google it, but most of them don't really make sense to me. 1 Estimation from the autocovariance function 9. If x is an M × N matrix, then xcorr(x) returns a (2M – 1) × N 2 matrix with the autocorrelations and cross-correlations of the columns of x. For each of the following, state if it is a stationary process. I'd just like to know > if anyone knows why: > > a) the xcov matrix is twice as long as the original signal and;. Making statements based on opinion; back them up with references or personal experience. Thanks for contributing an answer to Mathematics Stack Exchange! Please be sure to answer the question. Part 1: White Noise and Moving Average Model In this chapter, we study models for stationary time series. 13 is displayed in Figure 3. Here is a Matlab code and experimental and theoretical autocorrelations Autocovariance - expectation across all time indices? 3. Autocovariance Least Squares Package ALS is an Octave package for determining noise covariances from routine operating data, written for. The autocovariance is the covariance of a variable with itself at some other time, measured by a time lag (or lead) τ. Digital signal processing and control engineering has been widely used in many areas of science and engineering today 1,2. (1개의 변수의 이산정도를 나타내는 분산과는 별개임) 만약 2개의 변수중 하나의 값이 상승하는 경향을 보일 때, 다른 값도 상승하는 경향의 상관관계에 있다면, 공분산의 값은 양수가 될 것이다. Spectral Factorization; Lecture 18 (November ). Chapter 4 Variances and covariances Page 5 This time the dependence between the Xi has an important effect on the variance of Y. More precisely, let g() be the autocovariance function of a time series X. Vector autoregressive Moving Average Process Presented by Muhammad Iqbal, Amjad Naveed and Muhammad Nadeem. Proofs of Chapter 10 Propositions 285 Exercises 290 References 290 257 11 Vector Autoregressions291 11. In the nonparametric framework, the literature has concentrated on banding and tapering the sample autocovariance matrix. cov () forms the variance-covariance matrix. 1To make it easier for researchers to apply these estimators, we have posted Matlab code for both estimators on our websites. Remember if you have two random variables x and y, covariance is basically measuring the linear dependence in those two random variables. Answered: Christiaan on 9 Mar 2015 Or do you mean, given some data, how do I compute the wavelet autocorrelation (autocovariance) for that data?. 2 User's Guide. Goosebumps - download. m-- generate time series and corresponding training and testing matrices. ist internal examination. (2017) Region of attraction estimation using invariant sets and rational Lyapunov functions. 1: Introduction. It is the same as. The mission of the Department of Management Science and Statistics is to offer both undergraduate and graduate educational programs that are of high quality and meet the changing needs of the global community, to provide a supportive learning environment for students, to foster the success of our students in their professional careers, and to create an academic environment. Stationary processes and limit distributions I Stationary processes follow the footsteps of limit distributions I For Markov processes limit distributions exist under mild conditions I Limit distributions also exist for some non-Markov processes I Process somewhat easier to analyze in the limit as t !1. In fact, i. cov$(Y_t, Y_{t-j}). Chapter 4 Variances and covariances Page 5 This time the dependence between the Xi has an important effect on the variance of Y. Purpose: Check Randomness Autocorrelation plots (Box and Jenkins, pp. White Noise, Power Spectral Density; Lecture 15 (October 29). For single matrix input, C has size [size(A,2) size(A,2)] based on the number of random variables (columns) represented by A. The following flow chart illustrates the procedure. It ha een found, however, that certain observed time series, although apparently stationary, seem to violate t i the central limit theorem in that the variance of xd seems to go to zero more slowly than 1/n. , the average increase from one period to the next. 1 After intravenous injection, ICG is bound to plasma proteins, mainly α-lipoproteins. In locits: Test of Stationarity and Localized Autocovariance. The APARCH Model The APARCH model exhibits several stylized properties of finan-cial time series. In the book of Brockwell and Davis follows a disk with their time series program PEST. Use MathJax to format equations. 本书以易于理解的方式讲述了时间序列模型及其应用，主要内容包括：趋势、平稳时间序列模型、非平稳时间序列模型、模型识别、参数估计、模型诊断、预测、季节模型、时间序列回归模型、异方差时间序列模型、谱分析入门、谱估计、门限模型. 1) Questi ons : 1. Nonlinear autocovariance in Matlab. A Methodology for Determining Statistical Performance Compliance for Airborne Doppler Radar with Forward-Looking Turbulence Detection Capability Roland L. a Each state is defined as having its own distinct temporal, spatial and spectral characteristics. Gaussian Random Variable Definition A continuous random variable with pdf of the form p(x) = 1 p 2ˇ˙2 exp (x )2 2˙2; 1. The xcov function estimates autocovariance and cross-covariance sequences. • First-order pdf of the process: For each n, Xn = Zn is a r. If x is an M × N matrix, then xcorr(x) returns a (2M – 1) × N 2 matrix with the autocorrelations and cross-correlations of the columns of x. Sharma Department of Astronomy, University of Maryland, College Park, Maryland 20742, USA (Dated: November 12, 2014). The transmitter sent out a single signal through one antenna, which eventually arrived at a single antenna at the receiver, probably along with a little noise. This function has the same options and evaluates the same sum as xcorr , but first removes the means of x and y. Autocorrelation Function Properties and Examples ρ x( )= γ x( ) γ x(0) γ x( ) σ2 x The ACF has a number of useful properties • Bounded: −1 ≤ ρ x( ) ≤ 1 • White noise, x(n) ∼ WN(μ x,σ2 x): ρ x( )=δ( ) • These enable us to assign meaning to estimated values from signals • For example, - If ρˆ x( ) ≈ δ( ), we can conclude that the process consists of. Use MathJax to format equations. torchvision. The stationarity condition is: two solutions of x from ˚(x) = 1 ˚1x ˚2x2 = 0 are outside the unit circle. Since the autocorrelation function (ACF) is each lag's autocovariance divided by the variance, that spike will always be 1 for a stationary series, no matter whether the se. Contextual translation of "effectiveness" from French into Portuguese. 2 • X(t) is a wide sense stationary process with autocorrelation function RX(τ) = 10 sin(2000πt) +sin(1000πt). Then, I calculate the autocovariance matrix, from where I extract the eigenvalues and eigenvectors which are used to calculate the new variable Y which is the stochastic process S in a base where the random variables are not correlated. Use Automated Cross Correlations in Excel to Find Leading Indicators—Part 1 Leading indicators can help you to forecast more accurately. This course utilizes Matlab and a programming language (C/Fortran). Returns a distributed matrix. There is no GUI, but rather a set of functions designed to be used in your own Matlab® programs. , and Jeon, Y. You can prove the Cauchy-Schwarz inequality with the same methods that we used to prove | ρ(X, Y) | ≤ 1 in Section 5. The Poisson process is one of the most important random processes in probability theory. En tracant sur un graphique les pts dont les coordonnées sont log y(h) et log h. The distinct cutoff of the ACF combined with the more gradual decay of the PACF suggests an MA(1) model might be appropriate for this data. The autocorrelation of a time series can inform us about repeating patterns or serial correlation. @kamaci: it depends. Variance and covariance are frequently used in statistics. 2 Parametric estimation. Wh at is the variance of the pro ces s in terms. Note that γ 0 is the variance of the stochastic process. Derivation of the Autocovariance function of a Moving Average process (MA(q))). C = cov (A) returns the covariance. The MVGC Multivariate Granger Causality Matlab® Toolbox. For example, some students may write Cov(x t k;x t) = (t k)˙ w 2. For two-vector or two-matrix input, C is the 2-by-2 covariance matrix between the two random variables. Okay, so autocorrelation coefficient between Xt and Xt+k, remember, the most important part here is the time difference between these two random variables. 13 is displayed in Figure 3. Location - download. The correlation coefficient quantifies the degree of change of one variable based on the change of. What is more surprising is that the computation of the sample autocovariance function is. Here I'm only refering to numeric and character functions that are commonly used in creating or recoding variables. The moving average is extremely useful for forecasting long-term trends. Then observe that z ph j(1 ˚ 1z j ˚ 2z 2 ˚ pz j) = 0 In general, any linear combination of the zeros of ˚(z) is a solution. 2 • X(t) is a wide sense stationary process with autocorrelation function RX(τ) = 10 sin(2000πt) +sin(1000πt). This course presents an example of applying a database application development methodology to a major real -world project. Autocorrelation function (ACF) Learn more about Minitab 18 The autocorrelation function is a measure of the correlation between observations of a time series that are separated by k time units (y t and y t-k). 1 VAR process For a covariance stationary kdimensional vector process {x t}, let E(x t) = µ, then the autocovari- ance is defined to be the following kby kmatrix. TEACHING EXPERIENCE. A video tutorial that explains how to do basic image manipulations - play. This is one of the 100+ free recipes of the IPython Cookbook, Second Edition, by Cyrille Rossant, a guide to numerical computing and data science in the Jupyter Notebook. 564 but as we know it equals$\pi\$, so the answer is about half of the real period in this case. If none is passed, all are used. When I want to calculate the autocovariance and cross covariance function the simulation lasts maybe 5 minutes because of my loops. ) Windowed spectral analysis (Lecture 12, Feb. Autocorrelation and partial autocorrelation plots are heavily used in time series analysis and forecasting. Al Nosedal University of Toronto The Autocorrelation Function and AR(1), AR(2) Models January 29, 2019 5 / 82 Durbin-Watson Test (cont. Finally, incorporate your code which computes autocorrelation or autocovariance coe cients with the code which takes speech input and compare the results seen on the oscilloscope to those generated by MATLAB. 0 m/s/s, (2 m/s 2 ), for a time period of 3. , daily exchange rate, a share price, etc. For single matrix input, C has size [size(A,2) size(A,2)] based on the number of random variables (columns) represented by A. The transmitter sent out a single signal through one antenna, which eventually arrived at a single antenna at the receiver, probably along with a little noise. Moreover, statistics concepts can help investors monitor, covariance is a measure of the relationship between two random variables. Unlike 'plot. Guarda il profilo completo su LinkedIn e scopri i collegamenti di Alessia e le offerte di lavoro presso aziende simili. The autocovariance Stack Exchange Network 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. This video is part of the Udacity course "Machine Learning for Trading". Review: Causality, invertibility, AR(p) models 2. b Two example Go trials. MATLAB Release Compatibility. We typically measure or calculate slope, curvature, power spectrum and autocovariance with this instrument. Follow 6 views (last 30 days) Santino M on 5 Mar 2015. Autocorrelation is a type of serial dependence. The resulting autocovariance column vector acv is given by the formula:. m, utl_sincos. Ensure residuals from Step 5 are serially uncorrelated and homoskedastic. For further promoting patient motivation and engagement, the selected task is reproduced and updated according to the patient behavior in a virtual reality environment (VR) developed in Matlab. %TACF = theoretical (Yule-Walker) autocovariance function (given in assignment). Since the success of the fast Fourier transform algorithm, the analysis of serial auto- and cross-correlation in the frequency domain has helped us to understand the dynamics in many serially correlated data without necessarily needing to develop complex. Calculate and plot , where cells/sec. in matlab Auto correlation, partial auto correlation, cross correlation. Eigenvectors (red) do not change direction when a linear. The autocovariance least-squares method is revised for a general linear stochastic dynamic system and is implemented within the publicly available MATLAB toolbox Nonlinear Estimation Framework. title str, optional. The following points are noteworthy so far as the difference between covariance and correlation is concerned: A measure used to indicate the extent to which two random variables change in tandem is known as covariance. sim(), which works for all forms and subsets of ARIMA models. By Deep Climate Today I continue my examination of the key analysis section of the Wegman report on the Mann et al "hockey stick" temperature reconstruction, which uncritically rehashed Steve McIntyre and Ross McKitrick's purported demonstration of the extreme biasing effect of Mann et al's "short-centered" principal component analysis. The Partial Autocorrelation Function Brian Borchers April 4, 2001 Suppose that our ARMA process is purely autoregressive of order k. In fact, if is sufficiently smooth on and if. Active 4 years, 5 months ago. rar > momentg. Function Pacf computes (and by default plots) an estimate of the partial autocorrelation function of a (possibly multivariate) time series. A1 (choose your own time series) A link to data sources that can be used. 13 is displayed in Figure 3. For example, autocorr(y,'NumLags',10,'NumSTD',2) plots the sample ACF of y for 10 lags and displays confidence bounds consisting of 2 standard errors. Then observe that z ph j(1 ˚ 1z j ˚ 2z 2 ˚ pz j) = 0 In general, any linear combination of the zeros of ˚(z) is a solution. array 2d array of size nr X T with the temporal components center: np. X is said to be long-memory if there exists , 0 < <1, such that g(t) is asymptotically equivalent to jtj when t!+1(see [5] and references therein). The autocovariance is the covariance of a variable with itself at some other time, measured by a time lag (or lead) τ. Consider the image below in which three vectors are shown. The covariance of X and Y is defined by: where E is the expectation. VARMA (p,q) process 5. Notice that power at a frequency f0 that does not repeatedly reappear in xT(t) as T → ∞ will result in Sx(f0) → 0, because of the division by T in Eq. title str, optional. , it is a repeated sequence of “tents” of height one and base p 2. Contextual translation of "effectiveness" from French into Portuguese. array 2d array of size nr x 2 [ or 3] with the components centroids Author: Eftychios A. 19), that is. We must focus on relevant inputs from our senses – such as the bus we need to catch – while ignoring distractions – such as the eye-catching displays in the shop windows we pass on the same street. It has the formula: (EQ 2-2) SYNTAX LET = AUTOCOVARIANCE 0 it generates p ositiv ely auto-correlated time series, = 1 is a random w alk, < 1 represen ts stationary time series. (When τ= 0, the autocovariance reduces to the variance. The sample autocorrelation function for the data in Table 3. Matlab is quite popular in Economics/Econometrics/Finance, while R is popular in Statistics. MATLAB divides Signal Processing Toolbox as follows •Waveforms – Pulses, modulated signals, peak-to-peak and RMS amplitude, rise time/fall time, overshoot/undershoot •Convolution and Correlation – Linear and circular convolution, autocorrelation, autocovariance, cross-correlation, cross-covariance •Transforms. The subtraction can be done within the axcor input argument. The APARCH Model The APARCH model exhibits several stylized properties of finan-cial time series. Note: CD-ROM/DVD and other supplementary materials are not included as part of eBook file. 1 The time series data fzi;tg with the same physical meaning are sampled n times from the same zero mean autocovariance nonstationary process. Similarly, the cross-covariance function is a measure of the similarity of the deviation of two signals about their respective means. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying. Xiaohui Chen. Time Series Analysis of GPS Observables Kai Borre, Aalborg University Christian Tiberius, Delft University of Technology BIOGRAPHY Kai Borre is a Professor of Geodesy at the Aalborg Univer-sity since 1976. The metric evaluates how much - to what extent - the variables change. (c) Xt oscillates more-or-less with period 4, but there is quite a bit of noise. We compute the outer product of each, and the average all samples to get an estimate of the autocovariance matrix. Learn more about nonlinear-autocovariance, statistics, autocovariance. Some assignments may require the use of computer software such as Matlab, Gauss, R, Ox. autocov computes the autocovariance between two column vectors X and Y with same length N using the Fast Fourier Transform algorithm from 0 to N-2. Matlab: nino2 (cont. So, the long-term forecasts from the random-walk-with-drift model look like a trend line with slope. The autocovariance approach is a sequence-based variant of Chou’s pseudo-amino-acid composition, which extracts a set of pseudo-amino-acid-based features (extracted by the MATLAB code shared by the original authors) from a given protein as the concatenation of the 20 standard amino-acid composition values and values reflecting the effect of. It has the formula: (EQ 2-2) SYNTAX LET = AUTOCOVARIANCE 0 it generates p ositiv ely auto-correlated time series, = 1 is a random w alk, < 1 represen ts stationary time series. tacvf: Prints a tacvf object. The first differencing value is the difference between the current time period and the previous time period. Successfully applied the technique to operating data in collaboration with industrial partners such as Shell, ExxonMobil and Eastman Chemicals. Stationarize the series, if necessary, by differencing (& perhaps also logging, deflating, etc. fi;fl/, for 1 •fi6Dfl•N, with probabilities 1=N. Corequisite: MATH 152 and MATH 232. (2020), Sparse Graphical Models via Calibrated Concave Convex Procedure with Application to fMRI Data, Journal of Applied. The School has a flexible licence for all Versions. where , ; , and are the characteristic scales of the medium along the 3-dimensions and , and are the wavenumber components. autocavaleri. m-- calculate sample auto-correlation or autocovariance lags using rectangular window or triangular window. MATLAB Release Compatibility. For two-vector or two-matrix input, C is the 2-by-2 covariance matrix between the two random variables. Okay, so autocorrelation coefficient between Xt and Xt+k, remember, the most important part here is the time difference between these two random variables. 1 Models for time series 1. cov(x, 1) and cov(x, y, 1) normalize by nobs. More precisely, let g() be the autocovariance function of a time series X. Autocovariance estimation with long range dependence in Gaussian and threshold Gaussian model. Sharma Department of Astronomy, University of Maryland, College Park, Maryland 20742, USA (Dated: November 12, 2014). Assume the channel vector and the noise are uncorrelated, it is derived that Equation 5 Equation 6 Equation 7. It only takes a minute to sign up. The difference between autocorrelation and partial autocorrelation can be difficult and confusing for beginners to time series forecasting. 13 Downloads. , anisotropic). Location - download. parker sio 223b class notes, spring 2011. It is the same as. (2019) An analytical method to predict and compensate for residual stress-induced deformation in overhanging regions of internal channels fabricated using powder bed fusion. Autocorrelation and partial autocorrelation plots are heavily used in time series analysis and forecasting. ; the sequence of pdfs of Xn is called the first-order pdf of the process xn 1 0 1 z Since Xn is a differentiable function of the continuous r. Introduction to Time Series Analysis. Down - download. Feldman's Badges sets the state for Matlab's normal (Gaussian) random number generator compute sample autocovariance of a time series (vector). If A is a row or column vector, C is the scalar-valued variance. ni0w6ylw53, d2bgshmcdh, d0ul00p9iy, dcy1zh53gt, bq9tzoavb6133, uebt0yvkf5mn, unb03adxmva, snzwz1z4qc, kfrmm1oatame0t5, ji1d9jr75w0, cutzamuy3f90, t3xdel0e4ocuvi, m5crkzn42zls53x, mhbasabzpnyc, pib0lavqtr9, i2lnyyd6nev01, haz4co0pyjshi, xrvad0bir3, un9fpv986apdn, jnexmv35xi, bp83oi0yd3q, gmfx61qv6ys, 95wvd92ongf, 903pktkhlb, ound5wi9j8po, d1be9sobnx82wmx, rckum1f9zxe0l, g4dbkl0dlgofwp8, etbtle39lcj, mkjfljxhngr, fu842y6rqrejz9, pb9cur5m8b, y5u2vkb55xu, u9xmswinjdvk8, gn7486v089 | 2020-06-03 15:22:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.6241816282272339, "perplexity": 1986.113245732812}, "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-2020-24/segments/1590347435238.60/warc/CC-MAIN-20200603144014-20200603174014-00208.warc.gz"} |
https://docs.plasmapy.org/en/stable/api/plasmapy.formulary.parameters.kappa_thermal_speed.html | # kappa_thermal_speed¶
plasmapy.formulary.parameters.kappa_thermal_speed(T: Unit("K"), kappa, particle: plasmapy.particles.particle_class.Particle, method='most_probable') -> Unit("m / s")
Return the most probable speed for a particle within a Kappa distribution.
Aliases: vth_kappa_
Parameters: T (Quantity) – The particle temperature in either kelvin or energy per particle kappa (float) – The kappa parameter is a dimensionless number which sets the slope of the energy spectrum of suprathermal particles forming the tail of the Kappa velocity distribution function. Kappa must be greater than 3/2. particle (Particle) – Representation of the particle species (e.g., ‘p’ for protons, ‘D+’ for deuterium, or ‘He-4 +1’ for singly ionized helium-4). If no charge state information is provided, then the particles are assumed to be singly charged. method (str, optional) – Method to be used for calculating the thermal speed. Options are ‘most_probable’ (default), ‘rms’, and ‘mean_magnitude’. V – Particle thermal speed Quantity TypeError – The particle temperature is not a ~astropy.units.Quantity. astropy.units.UnitConversionError – If the particle temperature is not in units of temperature or energy per particle. ValueError – The particle temperature is invalid or particle cannot be used to identify an isotope or particle. RelativityWarning – If the particle thermal speed exceeds 5% of the speed of light, or ~astropy.units.UnitsWarning – If units are not provided, SI units are assumed.
Notes
The particle thermal speed is given by:
$V_{th,i} = \sqrt{(2 \kappa - 3)\frac{2 k_B T_i}{\kappa m_i}}$
For more discussion on the mean_magnitude calculation method, see [1].
Examples
>>> from astropy import units as u
>>> kappa_thermal_speed(5*u.eV, 4, 'p') # defaults to most probable
<Quantity 24467.87... m / s>
>>> kappa_thermal_speed(5*u.eV, 4, 'p', 'rms')
<Quantity 37905.47... m / s>
>>> kappa_thermal_speed(5*u.eV, 4, 'p', 'mean_magnitude')
<Quantity 34922.98... m / s>
References
[1] PlasmaPy Issue #186, https://github.com/PlasmaPy/PlasmaPy/issues/186 | 2021-02-27 19:07:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.652044951915741, "perplexity": 5800.70155318203}, "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-2021-10/segments/1614178359082.48/warc/CC-MAIN-20210227174711-20210227204711-00348.warc.gz"} |
http://dec41.user.srcf.net/exp/global_analysis/sect0009.html | Global AnalysisProof of local elliptic regularity
# A Proof of local elliptic regularity
We fill in the details of the proof of local elliptic regularity. We fix $L$ a differential operator of order $k \geq 1$ on $\mathbb {R}^n$, $U \subseteq \mathbb {R}^n$ precompact and $L$ elliptic over $\bar{U}$.
Lemma
If $L$ has constant coefficients, i.e.
$L = \sum _{|\alpha | \leq k} a^\alpha \mathrm{D}_\alpha ,$
then there is an $A$ such that for all $u \in C_c^\infty (U)$,
$\| u\| _{s + k} \leq A(\| u\| _s + \| Lu\| _{s}).$
Proof
Observe that we have
$\widehat{Lu}(\xi ) = p(\xi ) \hat{u}(\xi ).$
for some polynomial $p$ of degree at most $k$. By ellipticity, for some $R \gg 0$ and constant $A > 0$, we have
$A |p(\xi )| \geq (1 + |\xi |^2)^{k/2}.$
So in the decomposition
$\int |\hat{u}(\xi )|^2 (1 + |\xi |)^{s + k} \; \mathrm{d}\xi = \left(\int _{|\xi | \leq R} + \int _{|\xi | \geq R}\right) |\hat{u}(\xi )|^2 (1 + |\xi |)^{s + k} \; \mathrm{d}\xi ,$
we can bound the first term by $(1 + R^2)^k \| u\| _s$, and we can bound the second term by
$\int _{|\xi |\geq R} |\widehat{Lu}(\xi )|^2 (1 + |\xi |^2)^s\; \mathrm{d}\xi \leq \| Lu\| _s.$
Proof
Lemma
For any fixed $L$ and $x_0 \in U$, there is some neighbourhood $V \subseteq U$ of $x$ and $A > 0$ such that for all $u \in C_c^\infty (V)$, we have
$\| u\| _{s + k} \leq A(\| u\| _s + \| Lu\| _{s}).$
Proof
Let $L_0$ be the differential operator with constant coefficients that agree with $L$ at $x_0$. Then $L_0$ is also an elliptic operator, and the above applies. So for any $u$, we have
$\| u\| _{s + k} \leq A_1(\| u\| _s + \| L_0u\| _s) \leq A'(\| u\| _s + \| (L - L_0) u\| _s + \| Lu\| _s).$
So we have to control the term $\| (L - L_0)u\| _s$. For a tiny $\delta \ll 1$, pick a neighbourhood $V$ of $x_0$ such that the coefficients of $L - L_0$ are bounded by $\delta$. Then
$\| (L - L_0)u\| _s \leq \delta A_2 \| u\| _{s + k} + A_3 \| u\| _{s + k- 1},$
where $A_2, A_3$ are fixed, independent of $u$ and $V$. By the next lemma, for any $\varepsilon > 0$, we can bound
$A_1 A_3 \| u\| _{s + k - 1} \leq \varepsilon \| u\| _{s + k} + A_4(\varepsilon ) \| u\| _s.$
We then deduce that
$\| u\| _{s + k} \leq A_1 \| Lu\| _s + (\delta A_1 A_2 + \varepsilon ) \| u\| _{s + k} + (A_1 + A_4(\varepsilon )) \| u\| _s.$
Picking $\delta$ and $\varepsilon$ to be small enough, we are done.
Proof
Lemma
For any $r < s < t$ and $\varepsilon > 0$, there exists $C(\varepsilon )$ such that
$(1 + |\xi |^2)^s \leq (1 + |\xi |^2)^t \varepsilon + (1 + |\xi |^2)^r C(\varepsilon )$
for all $\xi$. Hence
$\| u\| _s \leq \varepsilon \| u\| _t + C(\varepsilon ) \| u\| _r.$
Proof
The claim is the same as
$1 \leq (1 + |\xi |^2)^{t - s} \varepsilon + (1 + |\xi |^2)^{r - s} C(\varepsilon ).$
Observe that for any $y$, we always have
$1 \leq y^{t - s} + (1/y)^{s - r}.$
Then take $y = (1 + |\xi |^2) \varepsilon ^{1/(t - s)}$.
Proof
Theorem
For any $L$, there exists $A$ such that
$\| u\| _{s + k} \leq A (\| u\| _s + \| Lu\| _s).$
Proof
Pick $W \supseteq \bar{U}$ such that $L$ is elliptic on $W$, and cover $W$ (and hence $\bar{U}$) with finitely $V_i$ where we have a bound as above, say
$\| u\| _{s + k} \leq A (\| u\| _s + \| Lu\| _{s - k})$
for any $u$ supported in the $V_i$'s. Now pick a partition of unity $\{ \mu _i\}$ subordinate to $\{ V_i\}$. Then
$\| u\| _{s + k} \leq \sum \| \mu _i u\| _{s + k} \leq \sum C(\| \mu _i u\| _s + \| L \mu _i u\| _s) \leq \sum C(\| \mu _i u\| _s + \| \mu _i Lu\| _s + \| [L, \mu _i] u\| _s).$
We can bound the first two by a constant multiple of $\| u\| _s$ and $\| Lu\| _s$. To bound the last term, we use that $[L, \mu _i]$ is a differential operator of order $k - 1$, and hence
$\| [L, \mu _i] u\| _s \leq C \| u\| _{s + k - 1} \leq \varepsilon \| u\| _{s + k} + C(\varepsilon ) \| u\| _s.$
Proof | 2022-09-29 23:39:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 78, "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": 0.9606075286865234, "perplexity": 97.79675751083303}, "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/1664030335396.92/warc/CC-MAIN-20220929225326-20220930015326-00553.warc.gz"} |
https://www.numerade.com/questions/find-each-double-integral-over-the-rectangular-region-r-with-the-given-boundaries-iint_r-y-exy2-d-x-/ | Enroll in one of our FREE online STEM bootcamps. Join today and start acing your classes!View Bootcamps
02:59
Problem 27
# Find each double integral over the rectangular region $R$ with the given boundaries.$$\iint_{R} y e^{x+y^{2}} d x d y ; \quad 2 \leq x \leq 3,0 \leq y \leq 2$$
## Discussion
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## Video Transcript
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http://archive.numdam.org/item/CM_1989__72_2_237_0/ | Erratum for “Generalized dirichlet series and $B$-functions”
Compositio Mathematica, Volume 72 (1989) no. 2, p. 237-239
@article{CM_1989__72_2_237_0,
author = {Lichtin, Ben},
title = {Erratum for Generalized dirichlet series and $B$-functions''},
journal = {Compositio Mathematica},
publisher = {Kluwer Academic Publishers},
volume = {72},
number = {2},
year = {1989},
pages = {237-239},
zbl = {0679.32002},
mrnumber = {1030143},
language = {en},
url = {http://www.numdam.org/item/CM_1989__72_2_237_0}
}
Lichtin, Ben. Erratum for “Generalized dirichlet series and $B$-functions”. Compositio Mathematica, Volume 72 (1989) no. 2, pp. 237-239. http://www.numdam.org/item/CM_1989__72_2_237_0/ | 2020-07-09 12:33:24 | {"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": 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": 0.44810423254966736, "perplexity": 11759.849812316928}, "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-2020-29/segments/1593655899931.31/warc/CC-MAIN-20200709100539-20200709130539-00221.warc.gz"} |
https://www.physicsforums.com/threads/pressure-in-branching-pipes-when-diameters-are-not-equal.1015116/ | # Pressure in branching pipes when diameters are not equal
fraggordon
TL;DR Summary
Trying to solve pressure in branching pipes with non-equal diameters. Inlet flow parameters are given.
Electrical engineer here hi!
I'm little bit out of my comfort zone trying to figure out the following fluid mechanics problem. I have a branching pipe similar to schematic below...
...and I'm trying to find the pressures in branches 1 (p1) and 2 (p2). The d1 and d2 are not equal (d1 = 0.1*d and d2 = 0.5*d) but the lengths l1 and l2 are equal. The inlet diameter (d), flow rate (Q), velocity (v) and pressure (p) are given.
Is it even possible to figure out the p1 and p2 with this little information? If so, where should I start? I imagine that at least following equations will be needed, but I guess I would need something else as well?
1) Conservation of flow rate: Q = Q1 + Q2
2) Conservation of energy (no losses or height difference): 0.5*density*v^2 + p = 0.5*density*v1^2 + p1 + 0.5*density*v2^2 + p2
Homework Helper
Gold Member
Welcome!
Pressure along each branch will change from P1 to P2 values.
That equal delta pressure is what drives each flow.
Naturally, each branch will self-balance its flow percetage according to its own restriction.
Last edited:
Mentor
Is this a homework problem? If so, we can move it to the homework forum.
You can find the pressure drop from p1 to p2, then p2 if you know p1 (or vice versa).
You know the diameters, lengths, and total flow. The next step is to calculate the flow rates in the two branches subject to the conditions that the sum of those two flow rates is equal to the total flow and the pressure drops are equal. This is an iterative calculation using a Moody chart (search the term).
Gold Member
Electrical Engineer, no problem.
The pressure ## P_i ## is analogous to the Voltage at node ## i ##
The loss of pressure in the pipe between nodes is given by ## \frac{f}{lD}\frac{v^2}{2g} ##
You'll want to convert from velocity to volumetric flow rate ## Q ## for each branch, assuming uniform velocity distribution across each branch.
Then you will have to find the Reynolds Number, and as others have pointed out, using it determine an initial estimate for the friction factor ## f ##
From there you are going to get a system of equations that looks something like this:
$$Q = Q_1 + Q_2$$
$$Q_1 = Q_2 k \sqrt{ \frac{f_2}{f_1} }$$
Where ## k ## is a constant comprised of several parameters tied to each branch geometry.
You are going to assume a flow distribution, find the friction factors ## f ## from the Moody Diagram, solve and re-evaluate ## f ## based on the solutions until its change is negligible.
It appears that you are going to need some more information if you are going to actually find the pressure drop between 1 and 2. Namely one of the pressures or the total flow rate should get you there as others have pointed out.
EDIT:
Looking more carefully at your information (2) conservation of energy. Are you really to assume, no losses between section 1 and 2? If that's the case the pressure drop is trivial.
I believe you should have this instead:
$$\frac{P_1}{\gamma} + z_1 + \frac{v_1^2}{2g} = \frac{P_2}{\gamma} + z_2 + \frac{v_2^2}{2g} + \sum_{1 \to 2 } h_l$$
Also, I'm not sure on this, but if there is no friction (inviscid flow) then the flow just splits 50/50 in each branch... regardless of actual branch diameter.
and I'm trying to find the pressures in branches 1 (p1) and 2 (p2).
The pressures in each branch will vary along their length linearly from the common pressure at their junction. So, when you say you are trying to find the "pressure in each branch", the answer is "where" not exactly a "what".
Last edited:
Lnewqban | 2023-03-25 14:03:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.6672577857971191, "perplexity": 819.7008651339964}, "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/1679296945333.53/warc/CC-MAIN-20230325130029-20230325160029-00350.warc.gz"} |
https://datascience.stackexchange.com/questions/93510/different-training-method-for-encoder-decoder-model | # Different training method for encoder-decoder model
Trying to learn the encoder-decoder model for some NLP problems.
I am referring to this Keras tutorial.
During the model training phase, this tutorial just uses the following:
model.fit([encoder_input_data, decoder_input_data], decoder_target_data,
batch_size=batch_size,
epochs=epochs)
I understand this logic. But the confusion is in some other tutorials for EXACTLY THE SAME PROBLEM. For example, in Tensorflow's documentation for NMT with Attention the training_phase is very different where they use custom training loops with a custom train step and calling the step for every batch manually.
The question is are these 2 different training methods which should be used in particular cases OR its the same training method with 2 different forms of implementation? | 2021-07-28 02:01:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4917806386947632, "perplexity": 1552.6441946137911}, "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/1627046153515.0/warc/CC-MAIN-20210727233849-20210728023849-00466.warc.gz"} |
https://www.esaral.com/q/if-x-1-x-3-calculate-x2-92124 | # If x + 1/x = 3, calculate x2
Question:
If $x+1 / x=3$, calculate $x^{2}+1 / x^{2}, x^{3}+1 / x^{3}, x^{4}+1 / x^{4}$
Solution:
Given, $x+1 / x=3$
We know that $(x+y)^{2}=x^{2}+y^{2}+2 x y$
$(x+1 / x)^{2}=x^{2}+1 / x^{2}+(2 * x * 1 / x)$
$3^{2}=x^{2}+1 / x^{2}+2$
$9-2=x^{2}+1 / x^{2}$
$x^{2}+1 / x^{2}=7$
Squaring on both sides
$\left(x^{2}+1 / x^{2}\right)^{2}=7^{2}$
$x^{4}+1 / x^{4}+2^{*} x^{2} * 1 / x^{2}=49$
$x^{4}+1 / x^{4}+2=49$
$x^{4}+1 / x^{4}=49-2$
$x^{4}+1 / x^{4}=47$
Again, cubing on both sides
$(x+1 / x)^{3}=3^{3}$
$x^{3}+1 / x^{3}+3 x^{*} 1 / x(x+1 / x)=27$
$x^{3}+1 / x^{3}+\left(3^{*} 3\right)=27$
$x^{3}+1 / x^{3}+9=27$
$x^{3}+1 / x^{3}=27-9$
$x^{3}+1 / x^{3}=18$
Hence, the values are $x^{2}+1 / x^{2}=7, x^{4}+1 / x^{4}=47, x^{3}+1 / x^{3}=18$ | 2023-02-08 05:00:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.926626980304718, "perplexity": 5713.836023834172}, "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/1674764500671.13/warc/CC-MAIN-20230208024856-20230208054856-00005.warc.gz"} |
https://math.stackexchange.com/questions/404995/is-this-problem-in-p-or-np-complete | # Is this problem in P or NP-Complete?
I need to determine if the following problem is in P or NP-Complete:
$\mathrm{2-IS} = \{\left< G, k\right > | G \text{ is a graph which every node in it has a degree 2 AND there is an independent set of size$k$in$G$}\}$
My intuition says it's in NP-Complete but I can't find another NP-Complete problem to reduce it to... any help?
• Hint: Think about how graphs where every node has degree 2 look like. – sdcvvc May 28 '13 at 18:32
• If every node has degree 2, then it must be the union of cycles of length $k_i$. There is an independent set of size $\sum\lfloor \frac{k_i + 1}{2} \rfloor$. – Calvin Lin May 28 '13 at 18:32
• @Calvin: Of course $\left\lfloor\frac{k_i+1}2\right\rfloor=\left\lceil\frac{k_i}2\right\rceil$. – Rahul May 28 '13 at 18:36
• @CalvinLin what is ki? please further explain – DanielY May 28 '13 at 18:40
• The main idea is that the graphs in which every vertex has degree 2 are very simple. So simple that one can actually find the size of their maximum independent set in polynomial time. Calvin hinted that such graphs are just composed of one or more disjoint cycles -- so it might be a good idea to look at what can we say about independent sets in a cycle (clearly, if the graph consists of more than one cycle, they can be treated... independently) – Peter Košinár May 28 '13 at 19:12
• Checking if every node in a graph has degree $2$ is easy.
• A graph in which every node has degree $2$ is a disjoint union of one or more cycles.
• The size of maximum independent set of a cycle on $n$ nodes is $\lfloor\frac{n}{2}\rfloor$. | 2019-11-19 08:47:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5975550413131714, "perplexity": 250.52883692559251}, "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-2019-47/segments/1573496670036.23/warc/CC-MAIN-20191119070311-20191119094311-00060.warc.gz"} |
https://tex.stackexchange.com/questions/439449/how-do-i-make-break-in-chronology | # How do I make break in chronology?
This is my code
\documentclass[10pt]{beamer}
\usetheme[progressbar=frametitle]{metropolis}
\usepackage{appendixnumberbeamer}
\usepackage{chronology}
\begin{frame}{Timeline}
\begin{center}
\begin{chronology}[10]{1810}{2020}{63ex}[\textwidth]
\event{\decimaldate{}{}{1812}}{\small Beginnings of Gerrymandering}
\event{\decimaldate{26}{3}{1962}}{\small Baker v. Carr}
\event{\decimaldate{15}{12}{1964}}{\small Reynold v. Sims}
\event{\decimaldate{2}{10}{1985}}{\small Bandermer v. Davis}
\event{\decimaldate{}{}{1991}}{\small Third Criterion}
\event{\decimaldate{}{}{2004}}{\small Vieth v. Jubelirer}
\event{\decimaldate{31}{12}{2006}}{\small LULAC v. Perry}
\event{\decimaldate{}{}{2015}}{\small Efficiency Gap}
\event{\decimaldate{}{}{2018}}{\small Gill v. Whitford}
\end{chronology}
\end{center}
\end{frame}
\end{document}
Since the events go from 1812-2018, the timeline get so small you cant see them on my frame. I want there to be a break in between the first two events. Does anyone know how to do this?
• Hello and welcome to TeX.SX. Could you provide a MWE - minimal working example? This begins with \documentclass and includes the packages you use. That way we can compile your code and see what we can do.
– nox
Jul 5, 2018 at 23:17
• \documentclass[10pt]{beamer} Jul 5, 2018 at 23:19
• You can use the 'edit' link at the bottom left of your question to edit your post and make the snipped compilable.
– cfr
Jul 5, 2018 at 23:20
After having a lot of fun (this package is !#\$&), adjusting the very internals by copying and improving the code, you can use the code below. This is far from perfect, e.g. the label from long events aren't shifted, spacing is not optimal etc. But at least something you can work with. You could still add sub-ticks and do more fancy stuff. But in general I would recommend to use another package. This is not general enough, well documented enough, ...
\documentclass[10pt]{beamer}
\usetheme[progressbar=frametitle]{metropolis}
\usepackage{appendixnumberbeamer}
\usepackage{chronology}
\newlength{\myunit}
\makeatletter%
\newif\ifchronology@star%
\renewenvironment{chronology}{%
\@ifstar{\chronology@startrue\chronology@i*}{\chronology@starfalse\chronology@i*}%
}{%
\end{tikzpicture}%
\end{lrbox}%
\usebox{\timelinebox}
}%
\def\chronology@i*{%
\@ifnextchar[{\chronology@ii*}{\chronology@ii*[{5}]}%
}%
\def\chronology@ii*[#1]#2#3#4#5{%
\newif\ifflipped%
\ifchronology@star%
\flippedtrue%
\else%
\flippedfalse%
\fi%
\setcounter{step}{#1}%
\setcounter{yearstart}{#2}\setcounter{yearstop}{#3}%
\setcounter{deltayears}{\theyearstop-\theyearstart}%
\setlength{\timelinewidth}{#4}%
\setlength{\myunit}{#5}%
\pgfmathsetcounter{stepstart}{\theyearstart-mod(\theyearstart,\thestep)}%
\pgfmathsetcounter{stepstop}{\theyearstop-mod(\theyearstop,\thestep)}%
\begin{lrbox}{\timelinebox}%
\begin{tikzpicture}[baseline={(current bounding box.north)}]%,x=\timelinewidth,y=\p@]%
\draw [|->] (0,0) -- (\timelinewidth, 0);%
%\foreach \x in {1,...,\thedeltayears}%
%\draw[xshift=\x/\thedeltayears*\timelinewidth] (0,-.5\myunit) -- (0,.5\myunit);%
\foreach \x in {\thestepstart,\thestep,...,\thestepstop}{%
\pgfmathsetlength\xstop{(\x-\theyearstart)/\thedeltayears*\timelinewidth}%
\draw[xshift=\xstop] (0,-\myunit) -- (0,\myunit);%
\ifflipped%
\node[chrontickslabel] at (\xstop,0) [above=\myunit] {\x};%
\else%
\node[chrontickslabel] at (\xstop,0) [below=\myunit] {\x};%
\fi%
}%
}%
\makeatother%
\RenewDocumentCommand{\event}{o m m}{%
\pgfmathsetlength\xstop{(#2-\theyearstart)/\thedeltayears*\timelinewidth}%
\IfNoValueTF {#1} {%
\ifflipped%
\draw[chronevent]%
(\xstop, 0) circle (.7\myunit);%
\draw[chronevent]
(\xstop,-.5\myunit+2pt) node[flippedeventlabel] {#3};%
\else%
\draw[chronevent]%
(\xstop, 0) circle (.7\myunit);%
\draw[chronevent]
(\xstop,.5\myunit-2pt) node[eventlabel] {#3} ;%
\fi%
}{%
\pgfmathsetlength\xstart{(#1-\theyearstart)/\thedeltayears*\timelinewidth}%
\ifflipped%
\draw[chronevent,rounded corners=.7\myunit]%
(\xstart,-.7\myunit) rectangle%
node[flippedeventlabel] {#3} (\xstop,.7\myunit) [below=\myunit];%
\else%
\draw[chronevent,rounded corners=.7\myunit]%
(\xstart,-.7\myunit) rectangle%
node[eventlabel] {#3} (\xstop,.7\myunit);%
\fi%
}%
}
\begin{document}
\begin{frame}{Timeline}
\vspace*{-5ex}
\begin{chronology}[50]{1800}{2020}{.9\linewidth}{1ex}
\event{\decimaldate{}{}{1812}}{\small Beginnings of Gerrymandering}
\event[\decimaldate{}{}{1960}]{\decimaldate{}{}{2020}}{}
\end{chronology}
\par
\begin{chronology}[10]{1960}{2020}{.9\linewidth}{1ex}
\event{\decimaldate{26}{3}{1962}}{\small Baker v. Carr}
\event{\decimaldate{15}{12}{1964}}{\small Reynold v. Sims}
\event{\decimaldate{2}{10}{1985}}{\small Bandermer v. Davis}
\event{\decimaldate{}{}{1991}}{\small Third Criterion}
\event{\decimaldate{}{}{2004}}{\small Vieth v. Jubelirer}
\event{\decimaldate{31}{12}{2006}}{\small LULAC v. Perry}
\event{\decimaldate{}{}{2015}}{\small Efficiency Gap}
\event{\decimaldate{}{}{2018}}{\small Gill v. Whitford}
\end{chronology}
\end{frame}
\end{document}
• What would you recommend? Thanks! Jul 6, 2018 at 3:02
• I don't know any such package and would have to search myself, so up to you, sorry I can't help here. Maybe it might be best to write a small script yourself, there are heaps of sources on that in the internet. Search for e.g. latex create figure timeline or something. Or be happy having finished this timeline and forget about it =P
– nox
Jul 6, 2018 at 10:53 | 2022-08-13 15:49:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.7170382738113403, "perplexity": 5779.2332032782315}, "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-2022-33/segments/1659882571959.66/warc/CC-MAIN-20220813142020-20220813172020-00214.warc.gz"} |
https://chem.libretexts.org/Courses/University_of_California_Davis/UCD_Chem_002A/UCD_Chem_2A/Worksheets/Worksheet_2C%3A_Stoichiometry | # Worksheet 2C: Stoichiometry
## Q1.
$$Na_2SiO_3 (s) + 8 HF_{(aq)} \rightarrow H_2SiF_{6\; (aq)} + 2 NaF_{(aq)} + 3 H_2O_{(l)}$$
1. How many moles of $$HF$$ are needed to react with 0.300 mol of $$Na_2SiO_3$$?
2. How many grams of $$NaF$$ form when 0.500 mol of $$HF$$ reacts with excess $$Na_2SiO_3$$?
3. How many grams of $$Na)2SiO_3$$ can react with 0.800 g of $$HF$$?
## Q2.
$$C_6H_{12}O_{6\; (aq)} \rightarrow 2 C_2H_5OH_{(aq)} + 2 CO_{2\; (g)}$$
1. How many moles of $$CO_2$$ are produced when 0.400 mol of $$C_6H_{12}O_6$$ reacts in this fashion?
2. How many grams of $$C_6H_{12}O_6$$ are needed to form 7.50 g of $$C_2H_5OH$$?
3. How many grams of $$CO_2$$ form when 7.50 g of $$C_2H_5OH$$ are produced?
## Q3.
$$Fe_2O_{3\; (s)} + CO_{(g)} \rightarrow Fe_{(s)} + CO_{2\; (g)}$$ (unbalanced!)
1. Calculate the number of grams of $$CO$$ that can react with 0.150 kg of $$Fe_2O_3$$
2. Calculate the number of grams of $$Fe$$ and the number of grams of $$CO_2$$ formed when 0.150 kg of $$Fe_2O_3$$ reacts
## Q4.
$$2 NaOH_{(s)} + CO_{2\;(g)} \rightarrow Na_2CO_{3\; (s)} + H_2O_{(l)}$$
1. Which reagent is the limiting reactant when 1.85 mol NaOH and 1.00 mol $$CO_2$$ are allowed to react?
2. How many moles of $$Na_2CO_3$$ can be produced?
## Q5.
$$C_6H_6 + Br_2 \rightarrow C_6H_5Br + HBr$$
1. What is the theoretical yield of $$C_6H_5Br$$ in this reaction when 30.0 g of $$C_6H_6$$ reacts with 65.0 g of $$Br_2$$?
2. If the actual yield of $$C_6H_5Br$$ was 56.7 g, what is the percent yield?
Worksheet 2C: Stoichiometry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts. | 2023-03-31 09:26:53 | {"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": 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": 0.9154980778694153, "perplexity": 1303.4162333547274}, "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/1679296949598.87/warc/CC-MAIN-20230331082653-20230331112653-00222.warc.gz"} |
https://chemistry.stackexchange.com/questions/126109/polymers-which-are-miscible-in-oil/126134 | # Polymers which are miscible in oil
Can someone suggest me a list of polymers or some paper where I may find polymers that are soluble in oils like silicon oil, mustard oil, coconut oil, bean oil or petroleum ether, etc.?
• There are many types of polymers, from elemental sulfur to polyborazylenes. Be more specific. – DrMoishe Pippik Jan 5 '20 at 2:35
• Can you suggest to me how to look for these types? I don't want to single out some properties, since my research demands a holistic picture of things, rather than just simply looking at a certain set of polymers! I would be very grateful if you would share some of your knowledge with me! Thank you – Anshuman Sinha Jan 5 '20 at 12:23
Plastics Design Library series include tabulated parameters for the variety of polymers. One of such parameters is a PDL number rating from 0 to 9:
0: solvent dissolved disintegrated
1: decomposition
2: severe distortion; oxidizer and plasticizer deteriorated
9: highest resistance, no change
In the table below I assembled data on thermoplastics chemically unstable towards various oils with PDL numbers below 3:
$$\begin{array}{lrcll} \hline \textbf{Polymer} & \boldsymbol{T/\pu{°C}} & \textbf{PDL} & \textbf{Oil} & \textbf{Resistance Note} \\ \hline \text{CAB} & 20 & 0 & \text{spearmint oil} & \text{Limited Resistance} \\ \hline \text{LDPE} & 20 & 1 & \text{aniseed oil} & \text{Not resistant; tensile strength at yield and elongation at break greatly reduced} \\ \hline \text{HDPE} & 20 & 2 & \text{camphor oil} & \text{Not resistant} \\ \hline \text{PP} & 100 & 2 & \text{two-stroke engine oils} & \text{Unsatisfactory/severe effect} \\ & 20 & 2 & \text{turpentine oil} & \text{Not resistant} \\ & 100 & 2 & \text{vaseline oil} & \text{Unsatisfactory/severe effect} \\ \hline \text{LLDPE} & 20 & 1 & \text{aniseed oil} & \text{Not resistant; tensile strength at yield and elongation at break greatly reduced} \\ \hline \text{PS} & 22 & 2 & \text{clove oil} & \text{Not resistant; plastic severely crazed; softened or dissolved} \\ & 22 & 2 & \text{lemon peel and oil} & \text{Not resistant; plastic severely crazed; softened or dissolved} \\ & 22 & 2 & \text{orange peel and oil} & \text{Not resistant; plastic severely crazed; softened or dissolved} \\ & 22 & 2 & \text{pine needle oil} & \text{Not resistant; plastic severely crazed; softened or dissolved} \\ & 22 & 2 & \text{spearmint oil} & \text{Not resistant; plastic severely crazed; softened or dissolved} \\ \hline \text{SAN} & 23 & 2 & \text{citronella oil} & \text{Severe attack; softened in few hrs} \\ & 23 & 2 & \text{clove oil} & \text{Severe attack; softened in few hrs} \\ & 22 & 2 & \text{lemon peel and oil} & \text{Not resistant; plastic severely crazed; softened or dissolved} \\ & 52 & 2 & \text{pine needle oil} & \text{Severe attack; softened in few hrs} \\ & 23 & 2 & \text{spearmint oil} & \text{Severe attack; softened in few hrs} \\ \hline \text{ABS} & 52 & 2 & \text{pine needle oil} & \text{Severe attack; softened in few hrs} \\ & 23 & 2 & \text{spearmint oil} & \text{Severe attack; softened in few hrs} \\ \hline \end{array}$$
### Acronyms
$$\begin{array}{ll} \text{CAB} & \text{Cellulose Acetate Butyrate} \\ \text{LDPE} & \text{Low Density Polyethylene} \\ \text{HDPE} & \text{Polyethylene} \\ \text{PP} & \text{Polypropylene} \\ \text{LLDPE} & \text{Linear Low Density Polyethylene} \\ \text{PS} & \text{Polystyrene} \\ \text{SAN} & \text{Styrene Acrylonitrile Copolymer} \\ \text{ABS} & \text{Acrylonitrile Butadiene Styrene} \end{array}$$
### References
1. Chemical Resistance of Thermoplastics; Woishnis, W. A., Ebnesajjad, S., Eds.; Plastics Design Library; William Andrew: Norwich, N.Y, 2012.
• I'm very thankful for your guidance! I will surely be referring to this book from now onwards! You may want to look at this question, which I did post before, in case you need some more insights towards the research I'm working on! chemistry.stackexchange.com/questions/126078/… – Anshuman Sinha Jan 5 '20 at 15:52
• Hey, I find an Alphabetical List of Exposure Media at the end of the book. What should be my strategy to detect which of these media are immiscible in water and will tend to float on water (i.e lower density)? Does this follow any trend, or are they only a few which would follow any such rule, or else I have to look at all of them individually? Thank you for all the help! – Anshuman Sinha Jan 8 '20 at 2:39
• @AnshumanSinha I suspect you have to look it up (miscibility) or even determine the density yourself experimentally for your samples as it might slightly deviate from one manufacturer to another. – andselisk Jan 8 '20 at 6:06 | 2021-06-15 20:29:02 | {"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": 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": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4187615215778351, "perplexity": 2179.7091246058567}, "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/1623487621519.32/warc/CC-MAIN-20210615180356-20210615210356-00391.warc.gz"} |
http://mathhelpforum.com/geometry/98152-another-geometry-question-print.html | # Another Geometry Question
• Aug 15th 2009, 11:50 AM
Voluntarius Disco
Another Geometry Question
The ratio of two sides of a right triangle is 3:4. What are the sides of the triangle if the hypoteneuse of the triangle is 20?
• Aug 15th 2009, 12:03 PM
masters
Quote:
Originally Posted by Voluntarius Disco
The ratio of two sides of a right triangle is 3:4. What are the sides of the triangle if the hypoteneuse of the triangle is 20?
Hi Voluntarius Disco,
Try this:
$(3x)^2+(4x)^2=20^2$
Solve for x. Then, 3x and 4x. | 2017-01-21 00:35:39 | {"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": 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": 0.8423342704772949, "perplexity": 1509.013094602003}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280891.90/warc/CC-MAIN-20170116095120-00528-ip-10-171-10-70.ec2.internal.warc.gz"} |
http://www.mathynomial.com/problem/2028 | # Problem #2028
2028 Each vertex of a cube is to be labeled with an integer $1$ through $8$, with each integer being used once, in such a way that the sum of the four numbers on the vertices of a face is the same for each face. Arrangements that can be obtained from each other through rotations of the cube are considered to be the same. How many different arrangements are possible? $\textbf{(A) } 1\qquad\textbf{(B) } 3\qquad\textbf{(C) }6 \qquad\textbf{(D) }12 \qquad\textbf{(E) }24$ This problem is copyrighted by the American Mathematics Competitions.
Note: you aren't logged in. If you log in, we'll keep a record of which problems you've solved.
• Reduce fractions to lowest terms and enter in the form 7/9.
• Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
• Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
• Exponents should be entered in the form 10^10.
• If the problem is multiple choice, enter the appropriate (capital) letter.
• Enter points with parentheses, like so: (4,5)
• Complex numbers should be entered in rectangular form unless otherwise specified, like so: 3+4i. If there is no real component, enter only the imaginary component (i.e. 2i, NOT 0+2i). | 2017-10-19 02:02:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5744293928146362, "perplexity": 674.1394332205195}, "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-2017-43/segments/1508187823214.37/warc/CC-MAIN-20171019012514-20171019032514-00423.warc.gz"} |
https://welchemmeinung-gruppe.com/physic8u81px22309-vhb61 | Home
# Universal gas law
Ideal Gas Law. The Universal Gas Constant. The ideal gas constant is a Universal constant that we use to quantify the relationship between the properties of a gas Temperature, kinetic theory, and the ideal gas law: ThermodynamicsSpecific heat and heat transfer: ThermodynamicsLaws of thermodynamics: Thermodynamics
A eudiometer is a device that measures the downward displacement of a gas. The apparatus for this procedure involves an inverted container or jar filled with water and submerged in a water basin. The lid of the jar has an opening for a tube through which the gas to be collected can pass. As the gas enters the inverted container, it forces water to leave the jar (displacing it downward). To fill the entire container with gas, there must enough gas pumped into the container to expel all of the water. As the result of many different science experiments, several gas laws have been discovered. These laws relate the various state variables of a gas. Template:Text Box These gas laws can be used to compare two different gases, or determine the properties of a gas after one of its state variables have changed. Daily Universal Register. Briefing. UK: The deadline for applications for the post of general secretary of the Law firms have long been regarded as the soft underbelly of British business in relation to..
### Gas laws - Wikipedi
1. Gas Law in United Kingdom. Table of Contents. This entry about Gas Law has been published under the terms of the Creative Commons Attribution 3.0 (CC BY 3.0) licence, which permits unrestricted..
3. At low temperature or high pressure, the size of the individual molecules and intermolecular attractions becomes significant, and the ideal gas approximation becomes inaccurate.
### Universal and Individual Gas Constant
• Highlights, press releases and speeches..
• Start studying Universal Gas Law. Learn vocabulary, terms and more with flashcards, games and What states: Gases are composed of tiny particles called molecules that move in rapid, random..
• Calculations involving gas constituents can include either the universal gas constant. involves dividing by the atomic mass of the gas (or gas mixture) in question. Using USC units as an example..
• Values of R (Gas Constant). Value. Units (V.P.T
• Ideal Gas Calculations. Dalton's Law of Partial Pressures. Gas law problems often ask you to predict what happens when one or more changes are made in the variables that describe the gas
• Achieves increased incentive for universal compliance than possible with recommendations Performance-Based Standards (examples: toy safety, greenhouse gas emissions, food safety)
## Video: General Chemistry/Gas Laws - Wikibooks, open books for an open worl
### Gas Laws
• Gay-Lussac’s Law is also know as Amontons’ law. It states that if the volume of a given mass of a gas (V) is kept constant, then the pressure of the gas (P) is directly proportional to its absolute temperature (T).
• ate from the equation anything that will remain constant.
• In an ideal gas, there are no intermolecular attractions, and the volume of the gas particles is negligible. However, there is no real gas that can perfectly fits this behavior, so the Ideal Gas Law only approximates the behavior of gases. This approximation is very good at high temperatures and low pressures.
As you can see there are a multitude of units possible for the constant. The only constant about the constant is that the temperature scale in all is KELVIN. At Big Bottle Co., we make the best ejuice that won't break the bank. We ship everything free & fast. If you think we could improve in someway, let us know! WARNING: Products are not for use by persons.. The ideal gas law is an equation of state that is very important and fundamental in thermodynamics. R is a constant of proportionality called the universal gas constant, and in accordance with its name it.. The gas constant (also known as the molar, universal, or ideal gas constant) is a physical constant that is featured in a number of fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation
LoveToKnow. www.yourdictionary.com/universal-gas-law. APA Style The viscosity of gases increases as temperature increases and is approximately proportional to the square root of temperature. This is due to the increase in the frequency of intermolecular collisions at.. Ideal gas behavior furnishes an extremely good approximation to the behavior of real gases for a wide variety of aerospace applications. It should be remembered, however, that describing a substance as.. BSE (formerly Bombay Stock Exchange) - LIVE stock/share market updates from Asia's premier stock exchange. Get all the live S&P BSE SENSEX, real time stock/share prices, bse indices, company.. The ideal gas law combines four empirical simple gas laws discovered by several scientists who Note that historically, the empirical gas laws described below led to the derivation of the ideal gas law
### Universal Gas Law ( Read ) Physics CK-12 Foundatio
1. Gas Laws Practice. Gap-fill exercise. Fill in all the gaps, then press Check to check your answers. 2) At a pressure of 100 kPa, a sample of a gas has a volume of 50 liters. What pressure does it exert..
2. As the pressure goes up, the temperature also goes up, and vice-versa. Also same as before, initial and final volumes and temperatures under constant pressure can be calculated.
3. A 0.1000 g sample of a compound with the empirical formula CHF2 is vaporized into a 256 mL flask at a temperature of 22.3 oC. The pressure in the flask is measured to be 70.5 torr. What is the molecular formula of the compound? Quantity Raw data Conversion Data with proper units P 70.5 torr x 1 atm / 760 torr = 0.0928 atm V 256 mL x 1 L / 1000 mL = 0.256 L g 0.1000 g sample 0.1000 g R 0.0821 L-atm / mole-K 0.0821 L-atm / mole-K T 22.3 oC + 273 = 295.3 K FW ? ?
4. The combined gas law is also known as a general gas equation is obtained by combining three gas laws which include Charle's law, Boyle's Law P = pressure of the gas. R = universal gas constant
5. Universal Gas Constant Versus Gas Constant Click to view movie (31k). The relationship between pressure and temperature for most gases can be approximated by the ideal gas law
6. Oil & Gas Laws and Regulations covering issues in USA of Overview of Natural Gas Sector As a matter of law, neither the federal government nor individual state governments have an ownership..
The ideal gas equation (PV=nRT) provides a valuable model of the relations between volume, pressure, temperature and number of particles in a gas. As an ideal model it serves as a reference for the behavior of real gases. The ideal gas equation makes some simplifying assumptions which are obviously not quite true. Real molecules do have volume and do attract each other. All gases depart from ideal behavior under conditions of low temperature (when liquefaction begins) and high pressure (molecules are more crowed so the volume of the molecule becomes important). Refinements to the ideal gas equation can be made to correct for these deviations. Wedding photographer alters mum-in-law's dress in pics after she wore WHITE gown. Off the wall. Savvy mum transforms daughter's bedroom with 99p Home Bargains wrapping paper
### Combined Gas Lawedit
The volume of a given amount of gas is proportional to the ratio of its Kelvin temperature and its pressure. Same as before, a constant can be put in: PV / T = C The Combined Gas Law. Now we can combine everything we have into one proportion Where n is the number of moles of the number of moles and R is a constant called the universal gas constant..
### Derivation of Ideal Gas Lawedit
57 IDEAL GAS LAW When we make these assumptions, we can create a universal IDEAL GAS LAW PV = nRT. 58 VARIABLES P = pressure (must be in the units of atm) V = volume.. Gas Laws explain the behavior of an ideal gas in terms of temperature, pressure, volume. They are Boyles, Charles, Gay-Lussacs, Avogadros, Universal gas Law
### Universal gas law - definition of universal gas law by The Free
1. ..Gas Law, and how the ideal gas equation allows you to find out pressure, volume, temperature or of Boyle's law, Charles law and Avogadro law.Also derive an ideal gas equation, also known as the..
2. R = universal gas constant = 8.3145 J/mol K N = number of molecules The ideal gas law can be viewed as arising from the kinetic pressure of gas molecules colliding..
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4. As the result of many different science experiments, several gas laws have been discovered. These laws relate the various state variables of a gas. Template:Text Box These gas laws can be used to compare two different gases..
5. When Avogadro's Law is considered, all four state variables can be combined into one equation. Furthermore, the "constant" that is used in the above gas laws becomes the Universal Gas Constant (R).
6. When using the Ideal Gas Law to calculate any property of a gas, you must match the units to the gas constant you choose to use and you always must place your temperature into Kelvin.
### Universal Gas Law Flashcards Quizle
1. Gas Laws explain the behavior of an ideal gas in terms of temperature, pressure, volume. The following are the some of the important gas laws:
2. ed empirically: Molecule a (liters2-atm / mole2) b (liters / mole) H2 0.2444 0.02661 O2 1.360 0.03183 N2 1.390 0.03913 CO2 3.592 0.04267 Cl2 6.493 0.05622 Ar 1.345 0.03219 Ne 0.2107 0.01709 He 0.03412 0.02370
3. Boyle's Law - states that the volume of a given amount of gas held at constant temperature varies inversely with the applied pressure when the temperature and mass are constant.
4. When pressure goes up, volume goes down. When volume goes up, pressure goes down. From the equation above, this can be derived:
5. Gas Laws. The content that follows is the substance of lecture 18. The addition of a proportionality constant called the Ideal or Universal Gas Constant (R) completes the equation
### The Gas Laws: Pressure Volume Temperature Relationships
You are using an outdated browser that is no longer supported by Ontario.ca. Outdated browsers lack safety features that keep your information secure, and they can also be slow. Learn about the.. Combined gas law is a result of unification of Charles's law, Boyle's law and Gay-Lussac's gas laws. In isolation each of these laws relate one thermodynamic variable to another while holding everything.. nH2 = PH2V / RT ; nH2 = (0.9503 atm)(0.456 L) / (0.0821 L-atm / mole-K)(295 K) = 0.0179 mole H2. The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between pressure, volume and temperature of a sample of gas could be obtained which.. Gases and gas law. 19. Kinetic theory of gases. Where R is proportionality constant and is defined as universal gas constant i.e. the constant used when 1gram mole of each gas is taken under..
Covering geo-political news and current affairs across Asia Asia Times is a pan-Asia online news platform covering politics, economics, business and culture from an Asian perspective. It is one of the.. There are 4 general laws that relate the 4 basic characteristic properties of gases to each other. Each law is titled by its discoverer. While it is important to understand the relationships covered by each law, knowing the originator is not as important and will be rendered redundant once the combined gas law is introduced. So concentrate on understanding the relationships rather than memorizing the names.
### Other Forms of the Gas Law
The units of pressure that are used are pascal (Pa), standard atmosphere (atm), and torr. 1 atm is the average pressure at sea level. It is normally used as a standard unit of pressure. The SI unit though, is the pascal. 101,325 pascals equals 1 atm. Use the free DeepL Translator to translate your texts with the best machine translation available, powered by DeepL's world-leading neural network technology. Currently supported languages are.. the law that the product of the pressure and the volume of one gram molecule of an ideal gas is equal to the product of the absolute temperature of the gas and the universal gas constant Use the ideal gas law, PV-nRT, and the universal gas constant R = 0.0821 L*atm. to solve the following problem Gives the universal gas law, gives the commonly used values for R, and works through examples The universal gas law relates temperature, pressure, volume and moles of a gas in a single equation
### Notes on Gas Laws ~ ME Mechanical Universal Gas Law
• Gas laws. Concept. Gases respond more dramatically to temperature and pressure than do the Most of the gas laws were derived during the eighteenth and nineteenth centuries by scientists whose..
• The addition of a proportionality constant called the Ideal or Universal Gas Constant (R) completes the equation.
• A gas that would obey Boyle's , Charle's law and Avogadro's law under the conditions of temperature and pressure is called an ideal where R is the constant of proportionality or universal gas constant
If this problem persists please contact customer support Dalton's Law of Partial Pressures states that the total pressure of a mixture of nonreacting gases is the sum of their individual partial pressures.
### Laws of Gas Properties
Combined gas law: Graham's law of effusion gases behave than when the gas laws were first invented. Explain why we continue to use these laws even though we V = nRT / P ; V = (1300 mole)(0.0821 L-atm/mole-K)(294 K) / (0.9868 atm) = 31798.358 L = 3.2 x 104 L. Partial pressures are useful when gases are collected by bubbling through water (displacement). The gas collected is saturated in water vapor which contibutes to the total number of moles of gas in the container.
By combining Boyle's and Charles' laws, an equation can be derived that gives the simultaneous effect of the changes of pressure and temperature on the volume of the gas Guy-Lussac's Law or the Pressure Law is one of the gas laws. Gay-Lussac studied the relationship between the pressure and the temperature of a gas at constant volume
Download all files as a compressed .zip. Title. Pressure, Volume, Temperature=Combined Gas Law. Description. Have students complete during class on their own This law is named after Joseph Louis Gay-Lussac as he made the observation in 1802. For this reason, R is called universal gas constant (or molar gas constant)
Here are some problems for the other gas laws that you can derive from the combined gas law: Practice and KEYThe reduction in the volume of the gas means that the molecules are striking the walls more often increasing the pressure, and conversely if the volume increases the distance the molecules must travel to strike the walls increases and they hit the walls less often thus decreasing the pressure.456 mL of gas was collected at 22.0 oC. The total pressure in the flask was 742 torr. How many moles of H2 were collected? The vapor pressure of H2O at 22.0 oC is 19.8 torr. Quantity Raw data Conversion Data with proper units Ptotal 742 torr PH2O 19.8 torr PH2 742 torr - 19.8 torr = 722.2 torr x 1 atm / 760 torr = 0.9503 atm V 456 mL x 1 L / 1000 mL = 0.456 L n ? ? R 0.0821 L-atm / mole-K 0.0821 L-atm / mole-K T 22 oC + 273 = 295 K PASCO's Adiabatic Gas Law Apparatus can be used with our 850 Universal Interface. The computer functions as a 3-channel storage oscilloscope, generating graphs for pressure, temperature, and..
### Related Posts on Law tag(s)
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions.. Density and pressure/temperature. The Ideal Gas Law for dry air: pV = RT. p = air pressure (hPa) (kg m-1 s-2) V = air volume (m3) R = universal gas constant for dry air (287 J kg-1 K-1) T = air.. The ideal gas law is the most important gas law for you to know: it combines all of the laws you The four conditions used to describe a gas—pressure, volume, temperature, and number of moles.. Law 3 The Universal Gas Law—pressure and volume are directly related to temperature. The hotter the fire, the higher the pressure it develops. Confining the pressure (like in a dead end or in a roof..
As seen in this diagram, the downward displacement involves water. Therefore, in the container where the gas is collected, there is unwanted water vapor. To account for the water vapor, subtract the pressure of water vapor from the pressure of the gases in the container to find the pressure of the collected gas. This is simply a restatement of Dalton's Law of Partial Pressure: Military & Law Enforcement Simulation. ECA Group (Euronext Paris: ECASA) has filed its 2019 Universal Registration Document including.. This equation states that the product of the initial volume and pressure is equal to the product of the volume and pressure after a change in one of them under constant temperature. For example, if the initial volume was 500 mL at a pressure of 760 torr, when the volume is compressed to 450 mL, what is the pressure? Plug in the values: Boyle’s law states that the volume of a given mass of gas (V) is inversely proportional to its absolute pressure (P), provided the temperature of the gas (T) remains constant.
## Universal Gas Law - Big Chemical Encyclopedi
'ME Mechanical' is an online portal for mechanical engineers and engineering students. Published hundreds of articles on various engineering topics. Visit our about section to know more. So the only equation you really need to know is the combined gas law in order to calculate changes in a gas' properties. Services and information. Benefits. Includes eligibility, appeals, tax credits and Universal Credit. Crime, justice and the law. Legal processes, courts and the police
## The Universal Gas Constan
By applying the well-known IDEAL GAS LAW, I REACH THE FINAL PRESSURE BY. R is Universal Ideal Gas Constant, that is 0.0821 atm * L / (mol * K). T is Temperature in Kelvin Scale.. From the Universal Gas Law: PV/T = a constant, where P = gas pressure, V = gas volume, and T Boyle's law describes the fact that, at constant temperature, the pressure and volume of a particular.. There are three ways of writing the ideal gas law, but all of them are simply algebraic rearrangements of each other. Combined Gas Law Practice Problem. The initial temperature of a 1 L sample of O2 is 20ºC. The only variable we haven't discussed is R, the universal gas constant, which has a value of 0.082 atm L..
The Perfect Gas Law relates temperature, pressure, and density of gases in the atmosphere. We seem like we've made things more complicated, because we no longer have a universal gas constant The gas laws are a set of laws that describe the relationship between thermodynamic temperature Three of these laws, Boyle's law, Charles's law, and Gay-Lussac's law, may be combined to form the.. As the volume goes up, the temperature also goes up, and vice-versa. Also same as before, initial and final volumes and temperatures under constant pressure can be calculated. npower is a leading supplier of gas and electricity for residential and business customers. Compare our cheap energy tariffs online and find out more
According to Charles law, the volume of a given mass of gas (V) is directly proportional to its absolute temperature (T), when its pressure remains constant. The gas laws deal with how gases behave with respect to pressure, volume, temperature, and Where n is the number of moles of the number of moles and R is a constant called the universal gas.. In 1873 J. D. van der Waals proposed his equation, known as the van der Waals equation. As there are attractive forces between molecules, the pressure is lower than the ideal value. To account for this the pressure term is augmented by an attractive force term a/V2. Likewise real molecules have a volume. The volume of the molecules is represented by the term b. The term b is a function of a spherical diameter d known as the van der Waals diameter. The van der Waals equation for n moles of gas is: Calculations using Charles' Law involve the change in either temperature (T2) or volume (V2) from a known starting amount of each (V1 and T1):If you heat a gas you give the molecules more energy so they move faster. This means more impacts on the walls of the container and an increase in the pressure. Conversely if you cool the molecules down they will slow and the pressure will be decreased.
## Ideal Gas Law
The ideal gas law is the most useful law, and it should be memorized. If you know the ideal gas law, you do not need to know any other gas laws, for it is a combination of all the other laws. If you know any three of the four state variables of a gas, the unknown can be found with this law. If you have two gases with different state variables, they can be compared. which includes the gas laws postulated by Charles, Boyle and Avogadro. In Eq. (1), is the molar volume (m3/mol), V is the volume (m3), N is the number of moles and is the Universal Gas Constant, J/(mol K) Combined Gas Law. Other gas laws can be constructed, but we will focus on only two more. The combined gas lawThe gas law that relates pressure, volume, and absolute temperature. brings.. Along with the University of Groningen, the University of Oslo, and the University of Copenhagen, the school runs the part-time North Sea Energy Law program as well
To use the equation, you simply need to be able to identify what is missing from the question and rearrange the equation to solve for it. Deadly gas leak in India A grim wakeup call - UN expert says chemical industry must step up on human rights to prevent more Bhopal-like disasters. Deadly gas leak in India A grim wakeup call..
Scotland has repealed an arcane blasphemy law, only to replace it with a modern-day heresy act Op-ed For Example, If a question said that a system at 1atm and a volume of 2 liters, underwent a change to 3.5 liters, calculate the new pressure, you could simply eliminate temperature from the equation and yield: Universal Gas Law. The kinetic energy of gases is directly proportional to the temperature of the gas. The intermolecular forces between the gas molecules are negligible
(760 torr)(500 mL) = P2(450 mL) 760 torr x 500 mL/450 mL = P2 844 torr = P2 The pressure is 844 torr after compression. Gas laws, Laws that relate the pressure, volume, and temperature of a gas. where n is the number of gram-moles of a gas and R is called the universal gas constant CHARLES'S LAW states that the volume of a gas is directly proportional to its Kelvin temperature. We replace k with the universal gas constant R and get V = nRT/P. This can be rearranged to give.. The Gas Laws. All gases generally show similar behaviour when the conditions are normal. Boyle's law states the relation between volume and pressure at constant temperature and mass A typical question would be given as 6.2 liters of an ideal gas are contained at 3.0 atm and 37 °C. How many of this moles of the gas are present?
Gas Gas Gas is a 2007 Eurobeat song by Italian musician Manuel Karamori that gained During portions of the stream, the songs Remove Kebab and Gas Gas Gas could be heard playing in the.. Gas Laws - . gas pressure. gas pressure is the result of gas particles colliding with the walls of the Universal (Ideal) Gas Equation • Based on the previous laws there are four factors that define the.. units of universal gas constant-. Posted 4 years ago by Saroj Bhatia. According to Avogadro's law, the volume of one mole of a gas at NTP is 22.4 litre Avogadro’s law states that equal volumes of different perfect gases, at the same temperature (T) and pressure (P), contain equal number of molecules (n).
## Gas Laws - Five Gas Laws, Formula, Problems, Ideal Gas
The content that follows is the substance of lecture 18. In this lecture we cover the Gas Laws: Charles',Boyle's,Avagadro's and Gay Lussacs as well as the Ideal and Combined Gas Laws. The Ideal Gas Law Formula. A gas may be completely described by its makeup, pressure R is always the same Universal Gas Constant. If we are considering the same gas only at two different.. Definition: The Universal or Ideal Gas Law describes the relationship between all four properties (pressure, volume, number of moles, and temperature) as well as a gas constant called R Universal Gas Law: Closed System. Science PLIX of the Week! http...Why do canisters of compressed gas get cold when you allow the gas to escape quickly? http..
## Ideal gas law derivation:pv=nrt general gas equatio
R is the universal gas constant. The ideal gas law was first articulated by Émile Clapeyron in 1834 as a synthesis of the experimentally derived Charles's law and Boyle's law This law states that the volume of a given amount of gas held at constant pressure is directly proportional to the Kelvin temperature. Units: Matter · Atomic Structure · Bonding · Reactions · Solutions · Phases of Matter · Equilibria · Kinetics · Thermodynamics · The Elements The balloon used by Charles in his historic flight in 1783 was filled with about 1300 mole of H2. If the outside temperature was 21 oC and the atmospheric pressure was 750 mm Hg, what was the volume of the balloon? Quantity Raw data Conversion Data with proper units P 750 mm Hg x 1 atm / 760 torr = 0.9868 atm V ? ? n 1300 mole H2 1300 mole H2 R 0.0821 L-atm / mole-K 0.0821 L-atm / mole-K T 21 oC + 273 = 294 K universal gas law. Also found in: Encyclopedia, Wikipedia. Related to universal gas law: Gas laws, Boyle's law, universal gas constant
Gay Lussac's Law - states that the pressure of a given amount of gas held at constant volume is directly proportional to the Kelvin temperature. CNBC is the world leader in business news and real-time financial market coverage. Find fast, actionable information Gives the relationship between volume and amount when pressure and temperature are held constant. Remember amount is measured in moles. Also, since volume is one of the variables, that means the container holding the gas is flexible in some way and can expand or contract.
Because the units of the gas constant are given using atmospheres, moles, and Kelvin, it's important to make sure you convert values given in other temperature or pressure scales. For this problem, convert °C temperature to K using the equation: Ideal gas law is a generalization containing both Boyle's law and Charles's law as special cases and states that: In such a gas, all the internal energy is in the form of kinetic energy and any change in.. It is intimately related to the universal gas constant (R) which converts from degrees to conventional The easiest way to explain osmotic pressure is to connect it to Dalton's law of partial pressures, as.. Like Charles' Law, Boyle's Law can be used to determine the current pressure or volume of a gas so long as the initial states and one of the changes is known: Also called perfect-gas laws, ideal-gas laws. gas scrubbing. The contacting of a gaseous mixture with a liquid for the purpose of removing gaseous contaminants or entrained liquids or solids
Charles' Law- gives the relationship between volume and temperature if pressure and amount of gas are held constant. Key Difference - Universal Gas Constant vs Characteristic Gas Constant. However, the ideal gas law gives us an equation that can be used to explain the behavior of a normal gas Principle All gases may be considered, to a first approximation, to obey the ideal gas equation which relates the pressure p, volume V, temperature Determination of molar mass using the ideal gas law
7. The gas constant (also called the universal gas constant, molar gas 8. Boyle's Law describes the inverse proportional relationship between pressure and volume at a constant temperature and a fixed.. Since the question never mentions a temperature we can assume it remains a constant and will therefore cancel in the calculation. You should also think about the answer you get in terms of what you know about the gases and how they act. We increased the volume so the pressure should go down. Checking our answer, this appears to be correct since the pressure went from 1atm to 0.6atm.
## Gas laws physics Britannic
Tags: Boyles law , charles law , Gas laws , Gay-lussacs law , universal gas law. Every once in a while we hear about the law of attraction or universal law of attraction it must be know that the low of.. The Gas Law. Card 1: State Boyle's law. In case (a), the pressure of the gas trapped in the capillary is equal to the atmospheric pressure + the pressure caused by the mercury thread Laws written by Congress provide the authority for EPA to write regulations. Regulations explain the technical, operational, and legal details necessary to implement laws
Search the U.S. News-Best Lawyers® Best Law Firms rankings for firms near you by using our advanced search engine. National Tier 1 in Oil & Gas Law. No. of National Rankings: 25 To better understand the Ideal Gas Law, you should first see how it is derived from the above gas laws. Alibaba.com offers 380 universal lighter gas products. About 74% of these are Lighters. A wide variety of universal lighter gas options are available to you, such as usage, type, and style In air pollution literature ppm applied to a gas, always means parts per million by volume or by mole. These are identical for an ideal gas, and practically identical for most gases of air pollution interest at.. Where n is the number of moles of the number of moles and R is a constant called the universal gas constant and is equal to approximately 0.0821 L-atm / mole-K.
## Gas Laws: Boyle's Law, Charle's Law, Gay-Lussac's Law
Gas Pressure and Atmospheric Pressure (5 Questions). Combination of Logic Gate. NAND gate as the universal gate 2021 edition of Oil & Gas Law Conference will be held at Hilton Houston North, Houston starting on 18th February. It is a 2 day event organised by The Center for American and International Law and.. Basic laws of chemistry. Classes of inorganic substances. Theoretical methods based on the laws of thermodynamics and quantum mechanics is the foundation of natural science
The law of the triads takes us one step closer. As early chemists began to experiment with and make notes of properties of elements some interesting observations would soon be made To calculate a change in pressure or temperature using Gay Lussac's Law the equation looks like this: Different Ideal Gas Law Equations for different unknown (our PV=nRT calculator is based on the The gas constant also well-known as the molar, universal, or ideal gas constant, represented by the.. The combined gas law allows you to derive any of the relationships needed by combining all of the changeable peices in the ideal gas law: namely pressure, temperature and volume. R and the number of moles do not appear in the equation as they are generally constant and therefore cancel since they appear in equal amounts on both sides of the equation. The ideal gas law $pV=m\mathcal RT$ can obviously be used to solve for mass. First you need the assumption that laws of equilibrium thermodynamics apply to a manifestly non-equilibrium case such..
The combined gas law is not a new law but a combination of Boyle's and Charles' laws, hence the The constant R in this equation is known as the universal gas constant. It arises from a combination.. Although oil and gas laws vary by state, the laws regarding ownership prior to, at, and after extraction are practically universal. An owner of real estate also owns the minerals underneath the surface.. If the amount of gas in a container is increased, the volume increases. If the amount of gas in a container is decreased, the volume decreases.
Gas Laws. Gas Laws. Experiment 1: Boyle's Law The combined gas law is a gas law which combines Charles's law, Boyle's law, and Gay-Lussac's law. There is no 'official' founder for this law because it is a consolidation of the three other laws
This law explained Gay-Lussac Law that noted that volumes of gases reacting are related by small whole number where koverall turns out to be the Ideal gas constant (or universal gas constant) high-grade marijuana, usually strains that emit strong odor that lingers in an aroma much like gasoline. That pizza was GAS man, soooo good! Mr. McCormic's test sucked, not gas
Appendices: Periodic Table · Units · Constants · Equations · Reduction Potentials · Elements and their Properties • In most combustion systems, thermally ideal gas law is valid • Even for high pressure combustion this is a sufficiently accurate walls of the vessel the partial pressure. • Universal gas constant equal to If the amount of gas in a container is increased, the volume increases. If the amount of gas in a container is decreased, the volume decreases. This is assuming of course that the container has expandible walls.
The gas constant is equivalent to the Boltzmann constant, just expressed in units of energy per temperature It is the universal gas constant divided by the molar mass (M) of a pure gas or mixture Are you having troubles with understanding the laws of physics? Or maybe you have to solve a complicated homework from physics classes? The Omni Calculators might be exactly what you're.. The Universal Gas Constant - Ru - appears in the ideal gas law and can be expressed as the product between the Individual Gas Constant - R - for the particular gas - and the Molecular Weight - Mgas..
I said above that memorizing all of the equations for each of the individual gas laws would become irrelevant after the introduction of the laws that followed. The law I was referring to is the Combined Gas Law: And within this Universe, there are seven major Universal Laws or Principles that explain how To understand the Law of Attraction, let's first understand its underlying counterpart, the Law of Vibration The pressure in a flask containing a mixture of 1 mole of 0.20 mole O2 and 0.80 mole N2 would be the same as the same flask holding 1 mole of O2. FW = gRT / PV ; V = (0.1000 g)(0.0821 L-atm / mole-K)(295.3 K) / (0.0928 atm)(0.256 L) = 102 g / mole
With an increase in temperature, the pressure will go up. Also same as before, initial and final pressures and temperatures under constant volume can be calculated. The Combined gas law or General Gas Equation is obtained by combining Boyle's Law, Charles's law, and where the proportionality constant, now named R, is the universal gas constant with a value of.. for gene synthesis, only 2 days and \$49. GenCRISPR™..
Avagadro's Law- Gives the relationship between volume and amount of gas in moles when pressure and temperature are held constant.This means that the volume-amount fraction will always be the same value if the pressure and temperature remain constant. For laboratory work the atmosphere is very large. A more convient unit is the torr. 760 torr equals 1 atm. A torr is the same unit as the mmHg (millimeter of mercury). It is the pressure that is needed to raise a tube of mercury 1 millimeter. n = number of moles (quantity of gas particles). R = universal gas constant. It is given that at a constant temperature of 1 K, the pressure and volume of 1 mole of gas vary inversely
At high temperature the molecules have high kinetic energy, so intermolecular attractions are minimized. At low pressure the gas occupies more volume, making the size of the individual molecules negligible. These two factors make the gas behave ideally. Boyle's law or the pressure-volume law states that the volume of a given amount of gas held at constant temperature varies inversely with the applied pressure when the temperature and mass are constant. Each molecule, on average, travels a distance of 2 s {\displaystyle 2s} between two consecutive collisions with wall A. Therefore, it will collide u / 2 s {\displaystyle u/2s} times per second with wall A. But the ideal gas law, and the chemical laws of definite proportions and multiple proportions, which . This is the same dimensionality as the universal gas constant R, which means that the heat capacity.. Descubre y compra online: electrónica, moda, hogar, libros, deporte y mucho más a precios bajos en Amazon.es. Envío gratis con Amazon Prime
In this gas law worksheet, students use the Universal Gas Law and van der Waals equation to calculate volume and molar mass of gases The Ideal Gas Law was first written in 1834 by Emil Clapeyron. What follows is just one way to Sometimes it is referred to as the universal gas constant. If you wind up taking enough chemistry.. These two laws interact to determine the actual market prices and volume of goods that are traded on a market. Several independent factors can affect the shape of market supply and demand, influencing.. Ideal Gas Law - Thermodynamics. Thermodynamics Directory | Heat Transfer Directory. The individual gas constant (R) may be obtained by dividing the universal gas constant (Ro) by the.. The Kinetic Molecular Theory attempts to explain the gas laws. It describes the behavior of microscopic gas molecules to explain the macroscopic behavior of gases. According to this theory, an ideal gas is composed of continually moving molecules of negligible volume. The molecules move in straight lines unless they collide into each other or the walls of their container.
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• Kuinka monella suomalaisella on älypuhelin. | 2021-02-27 04:19:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6283023953437805, "perplexity": 1084.1895512766484}, "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/1614178358064.34/warc/CC-MAIN-20210227024823-20210227054823-00262.warc.gz"} |
https://www.physicsforums.com/threads/why-we-only-consider-group-symmetry-but-not-general-symmetry.552990/ | # Why we only consider ''group'' symmetry but not general symmetry?
1. Nov 22, 2011
### ndung200790
Why do we only consider symmetry group(Lie group and Lie algebras) but not general symmetry(the transform that keeps Lagrangian invarian) in QFT?Is it because the symmetry group is more simple and more beautiful and in reality the forces of Nature obey the symmetry U(1)xSU(2)xSU(3)?
Thank you very much for your kind helping.
2. Nov 22, 2011
### strangerep
Which "transform that keeps Lagrangian invariant" do you mean? Can you give an example? Many of these transformations do indeed form a group. Perhaps you're thinking of dynamical groups instead of just symmetry groups?
Or are you asking why we use groups and algebras based on commutators rather than anticommutators?
Sometimes people use semigroups (group without the requirement for an inverse).
An example is the theory of time-asymmetric phenomena such as formation and decay of resonances.
3. Nov 22, 2011
### Fredrik
Staff Emeritus
He might also be asking why we spend so much time studying Lagrangians with "groups of symmetries" rather than just "symmetries". ndung200790, you may have to explain what you meant.
One reason why groups of symmetries are interesting in quantum theories is that Stone's theorem says (roughly) that for any group homomorphism U from a 1-parameter commutative group into the group of unitary operators on a Hilbert space, there's a self-adjoint operator A such that $U(t)=e^{iAt}$ for all t. (Click the link if you want to see a more exact statement of the theorem). The operator A (or is it -A?) is called the generator of this representation.
Pretty much all the interesting observables in quantum theories are generators of a representation of some symmetry group.
4. Nov 23, 2011
### dextercioby
You have to define what a symmetry is and apparently the only way to do it consistently and generally leads to the semigroup condition for the transformations you're looking for.
5. Nov 23, 2011
### ndung200790
I think there would be a transformation that the generators do not form a group,meaning that if we combine two generators,the result is not coresponded to any generator we considering.So can we demontrate that any transformation which remains Lagrangian invariant is a group(e.g.satisfying the closed characteristic of a group)?
6. Nov 23, 2011
### DrDu
In the case of discrete symmetry operations like charge conjugation, parity or time reversal you don't have any generator at all which does not mean that the operations don't form a group.
7. Nov 23, 2011
### naima
8. Nov 23, 2011
### strangerep
What do you mean by "combine two generators"?
If the commutator of two generators always yields another generator then you've probably got a Lie algebra, which can (usually, but not always, iiuc) be exponentiated to form a Lie group.
OTOH, if a commutator of two generators [A,B] yields something (call it C) which is not in your set of generators, then you must calculate higher commutators like [A,C] and [B,C] and try to determine whether this higher order commutator algebra eventually closes. If it doesn't then you've got an infinite-dimensional Lie algebra (probably better thought of as a noncommutative Poisson algebra).
[Edit: I wish Arnold Neumaier wasn't so busy with other things right now. He could give a much better answer to this.]
Last edited: Nov 23, 2011
9. Nov 24, 2011
### ndung200790
The combination of two generators means the product of two elements in group theory.
10. Nov 24, 2011
### tom.stoer
ndung200790,
everything you said so far can be understood as a symmetry operation represented by a (finite or infinite or even continuous) group.
In some cases it makes sense to discuss generators (in case of Lie groups and algebras), in some other cases (like C, P, T or crystallographic groups) not.
There are rather general cases of symmetry structures like the diffeomorphism or mapping class group for GR, infinite dimensional Kac-Moody algebras (as generalizations of finite dimensional Lie algebras) with central extension in string theory, supersymmetry / supergravity / graded algebras, quantum deformations of U(1), SU(2), dynamical symmetries (ordinay symmetry groups like SU(n) for the n-dim. harmonic oscillator) and perhaps many more which I am not aware of. I haven't seen anything else that does not belong to such a (generalized) symmetry structure.
The reason is rather simple.
Consider you have a Lagrangian L[x]; now you do something with it and get L[x'] where x has been transformed using something called 'g', but L is invariant (b/c it's a symmetry ;-). No you do something else with it called 'h' and get L[x'']. You can now write formally
x'= g*x
x''= h*x' = hg*x
which automatically results in a group structure!
I have no idea how to talk about a symmetries or transformations which do not form to a group.
http://en.wikipedia.org/wiki/Group_(mathematics)#Definition
Which property can be relaxed?
Closure: you have a symmetry transformation, a second symmetry transformation, but both transformation together are not a symmetry ???
Associativity: OK, perhaps one could play around with Octonions, non-associative algebras ...
Identity element: having no identity element would mean that it's not possible to do nothing!
Inverse element: having no inverse means that certain transformations cannot be undone; I have no idea how this would look like
Please give me a hint what you have in mind
11. Nov 25, 2011
### ndung200790
I owe all your helping very much.As Mr Tom.Stoer pointed,now I understand under transformations the Lagrangian to be invariant,the transformation ''group'' has closure characteristic(that I had wondered).
12. Nov 25, 2011
### Fredrik
Staff Emeritus
How would you define a symmetry? A reasonable definition is that a symmetry transformation of the Lagrangian is a transformation that doesn't change the equations of motion. With this definition, to do nothing to the Lagrangian is a symmetry transformation. Let's denote it by 1. If S is a symmetry transformation, then it must be invertible and S-1 must be a symmetry transformation. So {1,S,S-1} is closed under composition of functions, and is therefore a group.
13. Nov 25, 2011
### tom.stoer
Exactly!
14. Nov 25, 2011
### haael
Indeed. Every symmetry transformation set is a group.
15. Nov 25, 2011
### ndung200790
Does the equation of 4-divergence of Noether conserved current equaling zero be a ''type of motion equation''(and the equation does not change under the symmetry(Frederik's definition)?
16. Nov 26, 2011
### ndung200790
By the way,please teach me what is ''dynamical group''?
17. Nov 26, 2011
### tom.stoer
Afaik it's a symmetry group acting in phase space, not in position space.
Consider the 1-dim. harmonic oscillator. In position space there is no obvious continuous symmetry, but in phase space you can define a SO(2) rotation in the (p,x) plane via a canonical transformation which leaves the Hamiltonian H ~ p² + x², i.e. the length of the vector (p,x) invariant.
For the N-dim. harmonic oscillator you get the SU(N) symmetry in phase space.
18. Nov 27, 2011
### strangerep
The generators in a "symmetry algebra" commute with the Hamiltonian.
The generators in a "dynamical algebra" do not necessarily commute with the Hamiltonian, however such a commutator preserves the set of such generators.
More explicitly, suppose the set $\{ g_1, g_2, g_3 \}$ spans a Lie algebra ${\mathbb g}$. Then if $[g_i,H] = 0$, the $g_i$ are said to span a "symmetry algebra". However, if the commutator between the Hamiltonian H and $\mathbb{g}$ stays in $\mathbb{g}$, i.e., if
$$[g_i,H] = \dots ~\mbox{linear combination of the}~g_i \dots$$
then the $g_i$ are said to span a "dynamical algebra". In other words, the action of the Hamiltonian transforms any element of the dynamical algebra into some other element of the dynamical algebra.
Thus, if one can find the maximal dynamical algebra for a given Hamiltonian (and a convenient representation thereof), then one has almost solved the whole problem since elements of the dynamical algebra evolve in time only amongst themselves.
BTW, in classical mechanics, one has Poisson brackets. We then try to "quantize" the system by modifying this classical dynamical algebra and representing it somehow as operators on a Hilbert space.
Last edited: Nov 27, 2011
19. Nov 27, 2011
### tom.stoer
Then my example of the N-dim. harmonic oscillator is not the most general case of a dynamical group b/b H is the the generator of the trivial U(1) factor and commutes with all SU(N) generators, i.e. we have U(N) = U(1)*SU(N).
Is there a simple example where one can see explicitly [H, gi] = f(gi)?
(I am thinking about the constraint algebra in canonical LQG - but this is definitly not a simple example)
20. Nov 27, 2011
### ndung200790
By the way,now I have known the very difference between Lie group and Lie algebra.(The confusing leads me to this question) | 2018-12-19 11:50:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.8243200182914734, "perplexity": 1026.8976168164781}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376832259.90/warc/CC-MAIN-20181219110427-20181219132427-00208.warc.gz"} |
https://eurekamathanswerkeys.com/eureka-math-grade-7-module-5-lesson-3/ | ## Engage NY Eureka Math 7th Grade Module 5 Lesson 3 Answer Key
### Eureka Math Grade 7 Module 5 Lesson 3 Example Answer Key
Example 2: Equally Likely Outcomes
The sample space for the paper cup toss was on its side, right side up, and upside down.
The outcomes of an experiment are equally likely to occur when the probability of each outcome is equal.
Toss the paper cup 30 times, and record in a table the results of each toss.
### Eureka Math Grade 7 Module 5 Lesson 3 Exercise Answer Key
Exercises 1–6
Jamal, a seventh grader, wants to design a game that involves tossing paper cups. Jamal tosses a paper cup five times and records the outcome of each toss. An outcome is the result of a single trial of an experiment.
Here are the results of each toss:
Jamal noted that the paper cup could land in one of three ways: on its side, right side up, or upside down. The collection of these three outcomes is called the sample space of the experiment. The sample space of an experiment is the set of all possible outcomes of that experiment.
For example, the sample space when flipping a coin is heads, tails.
The sample space when drawing a colored cube from a bag that has 3 red, 2 blue, 1 yellow, and 4 green cubes is red, blue, yellow, green.
For each of the following chance experiments, list the sample space (i.e., all the possible outcomes).
Exercise 1.
Drawing a colored cube from a bag with 2 green, 1 red, 10 blue, and 3 black
Green, red, blue, black
Exercise 2.
Tossing an empty soup can to see how it lands
Right side up, upside down, on its side
Exercise 3.
Shooting a free throw in a basketball game
Exercise 4.
Rolling a number cube with the numbers 1–6 on its faces
1, 2, 3, 4, 5, or 6
Exercise 5.
Selecting a letter from the word probability
p, r, o, b, a, i, I, t, y
Exercise 6.
Spinning the spinner:
1, 2, 3, 4, 5, 6, 7, 8
Exercises 7–12
Exercise 7.
Using the results of your experiment, what is your estimate for the probability of a paper cup landing on its side?
Answers will vary. The probability for the sample provided is $$\frac{19}{30}$$.
Exercise 8.
Using the results of your experiment, what is your estimate for the probability of a paper cup landing upside down?
Answers will vary. The probability for the sample provided is $$\frac{5}{30}$$, or $$\frac{1}{6}$$.
Exercise 9.
Using the results of your experiment, what is your estimate for the probability of a paper cup landing right side up?
Answers will vary. The probability for the sample provided is $$\frac{6}{30}$$, or $$\frac{1}{5}$$.
Exercise 10.
Based on your results, do you think the three outcomes are equally likely to occur?
Answers will vary, but, according to the sample provided, the outcomes are not equally likely.
Exercise 11.
Using the spinner below, answer the following questions.
a. Are the events spinning and landing on 1 or 2 equally likely?
b. Are the events spinning and landing on 2 or 3 equally likely?
c. How many times do you predict the spinner will land on each section after 100 spins?
a. Yes. The areas of sections 1 and 2 are equal.
b. No. The areas of sections 2 and 3 are not equal.
c. Based on the areas of the sections, approximately 25 times each for sections 1 and 2 and 50 times for section 3.
Exercise 12.
Draw a spinner that has 3 sections that are equally likely to occur when the spinner is spun. How many times do you think the spinner will land on each section after 100 spins?
The three sectors should be equal in area. Expect the spinner to land on each section approximately 33 times (30–35 times).
### Eureka Math Grade 7 Module 5 Lesson 3 Problem Set Answer Key
Question 1.
For each of the following chance experiments, list the sample space (all the possible outcomes).
a. Rolling a 4-sided die with the numbers 1–4 on the faces of the die
b. Selecting a letter from the word mathematics
c. Selecting a marble from a bag containing 50 black marbles and 45 orange marbles
d. Selecting a number from the even numbers 2–14, including 2 and 14
e. Spinning the spinner below:
a. 1, 2, 3, 4
b. m, a, t, h, e, i, c, s
c. Black, orange
d. 2, 4, 6, 8, 10, 12, 14
e. 1, 2, 3, 4
Question 2.
For each of the following, decide if the two outcomes listed are equally likely to occur. Give a reason for your answer.
a. Rolling a 1 or a 2 when a 6-sided number cube with the numbers 1–6 on the faces of the cube is rolled
b. Selecting the letter a or k from the word take
c. Selecting a black or an orange marble from a bag containing 50 black and 45 orange marbles
d. Selecting a 4 or an 8 from the even numbers 2–14, including 2 and 14
e. Landing on a 1 or a 3 when spinning the spinner below
a. Yes. Each has the same chance of occurring.
b. Yes. Each has the same chance of occurring.
c. No. Black has a slightly greater chance of being chosen.
d. Yes. Each has the same chance of being chosen.
e. No. 1 has a larger area, so it has a greater chance of occurring.
Question 3.
Color the squares below so that it would be equally likely to choose a blue or yellow square.
Answers will vary, but students should have the same number of squares colored blue as they have colored yellow.
Question 4.
Color the squares below so that it would be more likely to choose a blue than a yellow square.
Answers will vary. Students should have more squares colored blue than yellow.
Question 5.
You are playing a game using the spinner below. The game requires that you spin the spinner twice. For example, one outcome could be yellow on the 1st spin and red on the 2nd spin. List the sample space (all the possible outcomes) for the two spins.
Question 6.
List the sample space for the chance experiment of flipping a coin twice.
There are four possibilities:
### Eureka Math Grade 7 Module 5 Lesson 3 Exit Ticket Answer Key
The numbers 1–10 are written on note cards and placed in a bag. One card will be drawn from the bag at random.
Question 1.
List the sample space for this experiment. | 2023-03-21 23:34:02 | {"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": 0.4786074757575989, "perplexity": 799.9413883003348}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943747.51/warc/CC-MAIN-20230321225117-20230322015117-00014.warc.gz"} |
https://www.lil-help.com/questions/246848/nrs-440-iom-of-future-nursing | NRS-440 IOM of Future Nursing
# NRS-440 IOM of Future Nursing
0 points
IOM of Future Nursing Grand Canyon University: NRS-440 Anne Inda June 19, 2016
Recommendations The TexasNursing Practice Act(NPA) defines the legal scope of practice for professional registered nurses (Board of Nursing, 2010). The NPA helps to guide and govern nursing laws that are rapidly changing in order to help improve the care that patients receive. With each passing day the role of nursing is changing and it important to know the laws when taking care of patients. The Future of Nursing Leading Change, Advancing Health, which was developed by the Institution of Medicine is responsible for the majority of these changes (Institute of Medicine, 2010). The Institute of Medicine generates a report which shows that nurses role in the future...
NRS-440
0 points
#### Oh Snap! This Answer is Locked
Thumbnail of first page
Excerpt from file: Runninghead:REFLECTIONPAPER IOMofFutureNursing DanaLikes GrandCanyonUniversity:NRS440 AnneInda June19,2016 1 NURSINGRECOMMENDATIONS 2 Recommendations TheTexasNursingPracticeAct(NPA)definesthelegalscopeofpracticefor professionalregisterednurses(BoardofNursing,2010).TheNPAhelpstoguideandgovern...
Filename: reflection-40.doc
Filesize: < 2 MB
Print Length: 4 Pages/Slides
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Surround your text in *italics* or **bold**, to write a math equation use, for example, $x^2+2x+1=0$ or $$\beta^2-1=0$$
Use LaTeX to type formulas and markdown to format text. See example. | 2018-03-19 14:37:23 | {"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": 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": 0.31284600496292114, "perplexity": 12591.907376368074}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257646952.38/warc/CC-MAIN-20180319140246-20180319160246-00726.warc.gz"} |
https://blog.benchmarkurbanism.com/research/sidenote-on-ml-accuracies | browsing byresearchposts
## SVG elementA sidenote on machine-learning accuracies
Predictions with deep neural networks and rich datasets are almost trivial if working with high-quality data and if some form of relationship is recoverable from the given variables. However, specific points are worth considering when working with predictive accuracies, which are misconstruable if not viewed within context. Firstly, it is easy to claim accuracies that would inflate the relevancy of models by using larger distance thresholds. Due to the Modifiable Areal Unit Problem, correlations and predictive accuracies naturally rise for greater distance thresholds. However, in reality, these provide less information about conditions specific to a local scenario. Thus, the challenge is to recover as much accuracy as possible at as small a distance threshold as feasible. Secondly, validation and test sets for machine-learning with spatial data need to consider partitioning on a spatial basis rather than a purely randomised selection of points, such as using a grid to set aside points within cells at specified intervals as a validation or test set. This strategy prevents the model from overfitting by siphoning off information between adjacent points, which would otherwise inflate test-set accuracies. (Visualisation can be a powerful tool for finding hints of overfitting within a spatial context.) Thirdly, whereas straight-forward prediction of a variable via deep neural networks is interesting and valuable in its own right, it can be even more helpful to identify locations where the observed intensities diverge from predicted intensities. Differencing observed from predicted metrics triggers observations in the spirit of Jane Jacobs’ recommendation to look for clues in ‘unaverages’: the local trends or oddities that otherwise seem to defy the model and normative patterns. These peculiarities offer glimpses into pedestrian-scale factors that may otherwise affect the expression of real-life observations and offer a guidepost regarding other considerations that may be beneficial if added to the model. Else, fodder for speculation and discussion around topics that in many cases will remain beyond the realm of the model’s predictive power.
Observed, Predicted, and Differenced intensity of eating establishments at 400m walking tolerances.
By way of example, the above figures shows the observed, predicted, and differenced number of local eating establishments for Greater London using multi-scalar network centralities and population densities as input variables. The differenced plot shows that eating establishments around historical high street locations are slightly underpredicted. It could be surmised that this is due to a lack of information about historic village centres and the related availability of commercial building stock that may otherwise distinguish certain areas of higher betweenness and closeness centralities from others. Another example, locations such as Soho, Seven Dials, and Angel are over-predicted. Here it could be theorised that there may be a latent demand for additional locations, currently unsatisfied due to spatial constraints on the number of viable sites or due to being crowded out by other land-uses such as retail.
Copyright © 2014-present Gareth Simons | 2022-08-07 16:53:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2913380265235901, "perplexity": 2175.069759821626}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570651.49/warc/CC-MAIN-20220807150925-20220807180925-00241.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/era.2021001?viewType=html | # American Institute of Mathematical Sciences
doi: 10.3934/era.2021001
## Note on coisotropic Floer homology and leafwise fixed points
Utrecht University, Mathematics Institute, Budapestlaan 6, 3584 CD Utrecht, The Netherlands
Received November 2019 Revised September 2020 Published January 2021
For an adiscal or monotone regular coisotropic submanifold $N$ of a symplectic manifold I define its Floer homology to be the Floer homology of a certain Lagrangian embedding of $N$. Given a Hamiltonian isotopy $\varphi = ( \varphi^t)$ and a suitable almost complex structure, the corresponding Floer chain complex is generated by the $(N, \varphi)$-contractible leafwise fixed points. I also outline the construction of a local Floer homology for an arbitrary closed coisotropic submanifold.
Results by Floer and Albers about Lagrangian Floer homology imply lower bounds on the number of leafwise fixed points. This reproduces earlier results of mine.
The first construction also gives rise to a Floer homology for a Boothby-Wang fibration, by applying it to the circle bundle inside the associated complex line bundle. This can be used to show that translated points exist.
Citation: Fabian Ziltener. Note on coisotropic Floer homology and leafwise fixed points. Electronic Research Archive, doi: 10.3934/era.2021001
##### References:
[1] P. Albers, A note on local floer homology, arXiv: math/0606600. Google Scholar [2] P. Albers, A Lagrangian Piunikhin-Salamon-Schwarz morphism and two comparison homomorphisms in Floer homology, Int. Math. Res. Not. IMRN, (2008), Art. ID rnm134, 56 pp. doi: 10.1093/imrn/rnm134. Google Scholar [3] Yu. V. Chekanov, Lagrangian intersections, symplectic energy, and areas of holomorphic curves, Duke Math. J., 95 (1998), 213-226. doi: 10.1215/S0012-7094-98-09506-0. Google Scholar [4] K. Cieliebak, A. Floer, H. Hofer and K. Wysocki, Applications of symplectic homology, II, Stability of the action spectrum, Math. Z., 223 (1996), 27-45. doi: 10.1007/BF02621587. Google Scholar [5] A. Floer, Morse theory for Lagrangian intersections, J. Differential Geom., 28 (1988), 513-547. doi: 10.4310/jdg/1214442477. Google Scholar [6] A. Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math., 41 (1988), 775-813. doi: 10.1002/cpa.3160410603. Google Scholar [7] A. Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys., 120 (1989), 575-611. doi: 10.1007/BF01260388. Google Scholar [8] H. Geiges and A. I. Stipsicz, Contact structures on product five-manifolds and fibre sums along circles, Math. Ann., 348 (2010), 195-210. doi: 10.1007/s00208-009-0472-z. Google Scholar [9] V. L. Ginzburg and B. Z. Gürel, Local Floer homology and the action gap, J. Symplectic Geom., 8 (2010), 323-357. doi: 10.4310/JSG.2010.v8.n3.a4. Google Scholar [10] V. L. Ginzburg and B. Z. Gürel, Fragility and persistence of leafwise intersections, Math. Z., 280 (2015), 989-1004. doi: 10.1007/s00209-015-1459-y. Google Scholar [11] A. Kapustin and D. Orlov, Remarks on $A$-branes, mirror symmetry, and the Fukaya category, J. Geom. Phys., 48 (2003), 84-99. doi: 10.1016/S0393-0440(03)00026-3. Google Scholar [12] C.-M. Marle, Sous-variétés de rang constant d'une variété symplectique, Astérisque, 107–108, Soc. Math. France, Paris (1983), 69–86. Google Scholar [13] Y.-G. Oh, Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks. I., Comm. Pure Appl. Math., 46 (1993), 949-993. doi: 10.1002/cpa.3160460702. Google Scholar [14] Y.-G. Oh, Addendum to: "Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks. I.", Comm. Pure Appl. Math., 48 (1995), 1299-1302. Google Scholar [15] Y.-G. Oh, Floer cohomology, spectral sequences, and the Maslov class of Lagrangian embeddings, Internat. Math. Res. Notices, (1996), 305–346. doi: 10.1155/S1073792896000219. Google Scholar [16] Y.-G. Oh, Localization of Floer homology of engulfed topological Hamiltonian loop, Commun. Inf. Syst., 13 (2013), no. 4, 399–443. Google Scholar [17] Y.-G. Oh, Symplectic Topology and Floer Homology, Vol. 2, Floer homology and its applications, New Mathematical Monographs, 29, Cambridge University Press, Cambridge, 2015. Google Scholar [18] M. Poźniak, Floer homology, Novikov rings and clean intersections, Northern California Symplectic Geometry Seminar, 119–181, Amer. Math. Soc. Transl. Ser. 2, 196, Adv. Math. Sci., 45, Amer. Math. Soc., Providence, RI, 1999. doi: 10.1090/trans2/196/08. Google Scholar [19] S. Sandon, A Morse estimate for translated points of contactomorphisms of spheres and projective spaces, Geom. Dedicata, 165 (2013), 95-110. doi: 10.1007/s10711-012-9741-1. Google Scholar [20] F. Ziltener, Coisotropic submanifolds, leaf-wise fixed points, and presymplectic embeddings, J. Symplectic Geom., 8 (2010), 95-118. doi: 10.4310/JSG.2010.v8.n1.a6. Google Scholar [21] F. Ziltener, A Maslov map for coisotropic submanifolds, leaf-wise fixed points and presymplectic non-embeddings, arXiv: 0911.1460. Google Scholar [22] F. Ziltener, Leafwise fixed points for $C^0$-small Hamiltonian flows, Int. Math. Res. Not. IMRN, (2019), 2411–2452. doi: 10.1093/imrn/rnx182. Google Scholar
show all references
##### References:
[1] P. Albers, A note on local floer homology, arXiv: math/0606600. Google Scholar [2] P. Albers, A Lagrangian Piunikhin-Salamon-Schwarz morphism and two comparison homomorphisms in Floer homology, Int. Math. Res. Not. IMRN, (2008), Art. ID rnm134, 56 pp. doi: 10.1093/imrn/rnm134. Google Scholar [3] Yu. V. Chekanov, Lagrangian intersections, symplectic energy, and areas of holomorphic curves, Duke Math. J., 95 (1998), 213-226. doi: 10.1215/S0012-7094-98-09506-0. Google Scholar [4] K. Cieliebak, A. Floer, H. Hofer and K. Wysocki, Applications of symplectic homology, II, Stability of the action spectrum, Math. Z., 223 (1996), 27-45. doi: 10.1007/BF02621587. Google Scholar [5] A. Floer, Morse theory for Lagrangian intersections, J. Differential Geom., 28 (1988), 513-547. doi: 10.4310/jdg/1214442477. Google Scholar [6] A. Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math., 41 (1988), 775-813. doi: 10.1002/cpa.3160410603. Google Scholar [7] A. Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys., 120 (1989), 575-611. doi: 10.1007/BF01260388. Google Scholar [8] H. Geiges and A. I. Stipsicz, Contact structures on product five-manifolds and fibre sums along circles, Math. Ann., 348 (2010), 195-210. doi: 10.1007/s00208-009-0472-z. Google Scholar [9] V. L. Ginzburg and B. Z. Gürel, Local Floer homology and the action gap, J. Symplectic Geom., 8 (2010), 323-357. doi: 10.4310/JSG.2010.v8.n3.a4. Google Scholar [10] V. L. Ginzburg and B. Z. Gürel, Fragility and persistence of leafwise intersections, Math. Z., 280 (2015), 989-1004. doi: 10.1007/s00209-015-1459-y. Google Scholar [11] A. Kapustin and D. Orlov, Remarks on $A$-branes, mirror symmetry, and the Fukaya category, J. Geom. Phys., 48 (2003), 84-99. doi: 10.1016/S0393-0440(03)00026-3. Google Scholar [12] C.-M. Marle, Sous-variétés de rang constant d'une variété symplectique, Astérisque, 107–108, Soc. Math. France, Paris (1983), 69–86. Google Scholar [13] Y.-G. Oh, Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks. I., Comm. Pure Appl. Math., 46 (1993), 949-993. doi: 10.1002/cpa.3160460702. Google Scholar [14] Y.-G. Oh, Addendum to: "Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks. I.", Comm. Pure Appl. Math., 48 (1995), 1299-1302. Google Scholar [15] Y.-G. Oh, Floer cohomology, spectral sequences, and the Maslov class of Lagrangian embeddings, Internat. Math. Res. Notices, (1996), 305–346. doi: 10.1155/S1073792896000219. Google Scholar [16] Y.-G. Oh, Localization of Floer homology of engulfed topological Hamiltonian loop, Commun. Inf. Syst., 13 (2013), no. 4, 399–443. Google Scholar [17] Y.-G. Oh, Symplectic Topology and Floer Homology, Vol. 2, Floer homology and its applications, New Mathematical Monographs, 29, Cambridge University Press, Cambridge, 2015. Google Scholar [18] M. Poźniak, Floer homology, Novikov rings and clean intersections, Northern California Symplectic Geometry Seminar, 119–181, Amer. Math. Soc. Transl. Ser. 2, 196, Adv. Math. Sci., 45, Amer. Math. Soc., Providence, RI, 1999. doi: 10.1090/trans2/196/08. Google Scholar [19] S. Sandon, A Morse estimate for translated points of contactomorphisms of spheres and projective spaces, Geom. Dedicata, 165 (2013), 95-110. doi: 10.1007/s10711-012-9741-1. Google Scholar [20] F. Ziltener, Coisotropic submanifolds, leaf-wise fixed points, and presymplectic embeddings, J. Symplectic Geom., 8 (2010), 95-118. doi: 10.4310/JSG.2010.v8.n1.a6. Google Scholar [21] F. Ziltener, A Maslov map for coisotropic submanifolds, leaf-wise fixed points and presymplectic non-embeddings, arXiv: 0911.1460. Google Scholar [22] F. Ziltener, Leafwise fixed points for $C^0$-small Hamiltonian flows, Int. Math. Res. Not. IMRN, (2019), 2411–2452. doi: 10.1093/imrn/rnx182. Google Scholar
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Impact Factor: 0.263
Article outline | 2021-04-19 06:10:32 | {"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": 0.9379205703735352, "perplexity": 7688.951060333744}, "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/1618038878326.67/warc/CC-MAIN-20210419045820-20210419075820-00245.warc.gz"} |
https://math.stackexchange.com/questions/2564222/find-the-equations-of-tangents-drawn-from-point-11-3-to-the-circle-x2y2 | # Find the equations of tangents drawn from point $(11,3)$ to the circle $x^2+y^2=65$
Find the equations of tangents drawn from point $(11,3)$ to the circle $x^2+y^2=65$
How are we supposed to draw two tangents at a given point?
The answer is $7x-4y-65=0$ and $4x+7y-65=0$.
• Picture the unit circle and the point $(0,2)$. You could draw two lines through this point, one which is tangent to a point on the upper-half circle, and one which is tangent to a point on the lower-half circle. The same idea holds in this case. – infinitylord Dec 13 '17 at 2:01
• Differentiate thru the entire equation. – Karn Watcharasupat Dec 13 '17 at 2:03
• @ Karn Watcharasupat, with respect to what??? – pi-π Dec 13 '17 at 2:06
• You want dy/dx, so do an implicit derivative in terms of x and solve for dy/dx – Kaynex Dec 13 '17 at 2:09
The green circle has a diameter from the origin to (11,3). It turns out to be $$(2x-11)^2 + (2y-3)^2 = 130.$$ A triangle inscribed in a circle (the green one) with one edge a diameter is actually a right triangle. It is now easy to confirm that the intersection points of the two circles are $(4,7)$ and $(7,-4).$
Oh, that is a square produced by the two right triangles I constructed. That is unusual. The square happened precisely because $11^2 + 3^2 = 2 \cdot 65 \; .$ Most of the time, the two right triangles would make a kite shape, the diagonals of the resulting quadrilateral would still be orthogonal, but the right triangles not isosceles.
....................................
Here is what happens when the exterior point is moved to $(12,4),$ and the green circle becomes $(x-6)^2 + (y-2)^2 = 40.$ Notice that $12^2 + 4^2 > 2 \cdot 65.$
• +1 for the nice geometric construction, although not a complete answer. – Dylan Dec 13 '17 at 2:28
Hint: Through implicit differentiation, we find that the slope of the tangent line at any point $(x,y)$ on the circle is $-x/y$. Therefore the tangent point must satisfy
$$-\frac{x}{y} = \frac{y-3}{x-11}$$ $$x^2 + y^2 = 65$$
You can solve this sytem of equations to find the two tangent points.
Let the point that the tangent touches the circle be $(p,q)$. The gradient of the tangent would be $\frac{q-3}{p-11}.$ and the equation is
Since tangent is perpendicular to the radius, we have
$$\frac{q}{p}\cdot \frac{q-3}{p-11}=-1$$
Along with $$p^2+q^2=65$$
solve for $p$ and $q$.
The tangent line would satisfies: $$\frac{y-3}{x-11}=\frac{q-3}{p-11}$$
Using homogeneous coordinates, tangent lines $\mathbf l =[\lambda,\mu,\tau]^T$ to the circle satisfy $\mathbf l^TC^{-1}\mathbf l=0$, where $C$ is the dual conic $\operatorname{diag}(65,65,1)$, i.e., the coefficients of the tangent line equation $\lambda x+\mu y+\tau=0$ satisfy $65\lambda^2+65\mu^2=\tau^2$. The lines must pass through the point $(11,3)$, so we must also have $11\lambda+3\mu+\tau=0$. Since the lines don’t pass through the origin, the constant term in their equations is nonzero, so we can set $\tau=1$ and then solve the resulting system of equations for $\lambda$ and $\mu$.
In a related method, the polar line to the point $(11,3)$ intersects the circle at the point of tangency. This line is $\operatorname{diag}(1,1,-65)\cdot(11,3,1)^T$, i.e., $11x+3y=65$. Compute the intersection of this line with the circle and then derive the equations of the lines through the two intersection points and $(11,3)$. Note that both methods essentially involve finding the intersection of a conic and a line.
[$r (= \sqrt {65})$, the radius] = [$|\frac {c}{1 + m^2}|$, the distance of the center (0, 0) from the tangent (y = mx + c)].
Then, $|\frac {c}{\sqrt {1 + m^2}}| = r$. That is, $c^2 = r^2(1 + m^2)$.
Therefore, the equation of tangent is $y = mx \pm r\sqrt(1 + m^2)$.
Plug (11, 3) into the last equation to get the values of m. The corresponding values of c can be found accordingly. | 2019-06-20 18:00:22 | {"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": 0.8235200643539429, "perplexity": 166.34288587626912}, "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/1560627999263.6/warc/CC-MAIN-20190620165805-20190620191805-00100.warc.gz"} |
https://www.willprice.dev/2021/03/27/debugging-pytorch-performance-bottlenecks.html | # Diagnosing and Debugging PyTorch Data Starvation
One of the things I repeatedly see with new-comers to PyTorch, or computer vision in general, is a lack of awareness of how they can improve the performance of their code. In video understanding, my field, this is a particularly thorny issue as video is so computationally demanding to work with. Surprisingly often we are not bottle-necked by our GPUs, but instead by our ability to feed those GPU with data when training models. This is known as data starvation. This blog post will cover a simple and quick method to diagnose whether this is a problem you suffer from, and if so how you can address it through a variety of techniques.
## Am I suffering from data starvation?
Determining whether you suffer from data starvation is actually pretty easy, you can just watch the output of nvidia-smi whilst your code is running. If you find your GPUs’ utilisation drop to 0% for a short period of time and then jump back up to their previous levels then data starvation is likely. This test tells us is whether or not there is a period of time spent where the GPUs are not running anything, and this most often is caused by data starvation, although not always. So let’s say that you do observe these periodic drops to 0% utilisation, what now? How can we tell where the issue lies? There are two potential causes of this behaviour:
1. Doing time-consuming work in your training loop that is blocking and doesn’t run on the GPU (e.g. CPU intensive processing, network operations).
2. Waiting on a batch of data.
Most training loops look something like this:
for data, target in dataloader:
data = data.to(device)
target = target.to(device)
y_hat = model(x)
loss = loss_fn(y_hat, y)
loss.backward()
optimizer.step()
# log some stuff with tensorboard
...
If the time it takes to go from the bottom of the loop to the first line takes more than a negligible amount of time, then we’re suffering from data starvation. Adding some timers in allows us to quantify this:
from time import time
end = time()
torch.cuda.synchronize()
pre_forward_time = time()
data = data.to(device)
target = target.to(device)
y_hat = model(x)
loss = loss_fn(y_hat, y)
torch.cuda.synchronize()
post_forward_time = time()
loss.backward()
torch.cuda.synchronize()
post_backward_time = time()
optimizer.step()
# log some stuff with tensorboard
...
forward_duration_ms = (post_forward_time - pre_forward_time) * 1e3
backward_duration_ms = (post_backward_time - post_forward_time) * 1e3
print("forward time (ms) {:.2f} | backward time (ms) {:.2f} | dataloader time (ms) {:.2f}".format(
))
end = time()
You have to be a bit careful when measuring time in PyTorch programs as most PyTorch operations are non-blocking, that is they schedule the work and return immediately, this allows more efficient scheduling of CUDA kernels. However, it also means that your timing isn’t going to be accurate. You can either sprinkle your code with torch.cuda.synchronize() calls which act as a barrier and will block until all previous kernel invocations have completed. Alternatively, you can drop the torch.cuda.synchronize() statements and set the environment variable CUDA_LAUNCH_BLOCKING=1 when you run your code. This makes all previously non-blocking calls blocking.
What you want to see once you’ve augmented your code with this timing information is that the time spent loading data is tiny compared to the time spent doing forward or backward passes. You should also remove the torch.cuda.synchronize() calls once you’ve finished profiling–ops are asynchronous by default for a reason, they allow better overlapping of host/device computation.
## Mitigating data starvation
There are two approaches for solving your data starvation problem: throw more resources at it, or make better use of what you have. We’ll first cover the former approach in Scaling dataloading as these knobs are easy to twiddle and you want to make sure you’re fully utilising the resources you have available (quite often people aren’t). The second topic we’ll dive into more depth, this approach typically requires code changes and knowledge of the systems you’ll be running on, what hardware they have and their performance characteristics as well as thinking about your data and what representation is most suitable for training.
PyTorch was designed to hide the cost of data loading through the DataLoader class which spins up a number of worker processes, each of which is tasked with loading a single element of data.
This class has a bunch of arguments that will have an impact on dataloading performance. I’ve ordered these from most important to least:
• num_workers: The number of worker processes that you fork to load data. Each one of these processes is tasked with loading a single data item from your dataset class. The rule of thumb is to push this up as high as you can without
1. Overloading your CPU: watch htop in a terminal whilst running your code and stop increasing the number of workers once all your cores are at 100% utilisation (or your GPUs are no longer starved). One thing to watch out for is if a lot of the CPU core utilisation bars are red, this means that the cores are waiting on a syscall, this is typically a read from a storage device (getting the bytes of an HDD or SSD into memory), in which case you’re bottlenecked by your ability to read data rather than processing it (e.g. decoding/augmentation).
2. Running out of RAM: For large data items (e.g. video) it can be quite easy to fill up all your RAM. htop is your friend again here. Keep increasing the number of workers until you’re close to the limit of how much RAM you have (or your GPUs are no longer starved).
• batch_size: the smaller the batch size, the fewer the examples needed to be loaded for each forward pass. Obvious, but worth mentioning nonetheless.
• shuffle: if you’re loading data from an HDD then reading non-contiguous blocks of data is costly. Shuffling causes non-contiguous reads and therefore will slow dataloading down. You can mitigate this to some extent through clever engineering of your dataloading pipeline. The key trick is to chop up your dataset into blocks and only randomly shuffle the blocks rather than all the data items. That way you get the benefit of some randomness in the order of training examples, but try to mitigate the number of non-sequential reads you’re doing. If you’re using SSDs then shuffling typically doesn’t matter.
• pin_memory: this flag determines whether or not to use page-locked host memory for transferring tensors from the CPU to the GPU. Page-locked memory tends to improve performance as it prevents the memory page on the host from being paged out to swap (which would make things much slower, as the page would have to be restored from swap to later transfer data). It also facilitates concurrent execution of kernels and memory transfer. Check out the page-locked host memory section in this blog for more technical details.
• persistent_workers: Each epoch PyTorch will tear down your dataset object and recreate it. This can actually be very expensive if your dataset class does a lot of set up (e.g. reads big JSON files) and your epochs are short. This flag disables this behaviour and keeps your dataset object around across multiple epochs.
### Making better use of hardware
Know your hardware. Does your system have HDDs/SSDs (SATA/NVMe?)? Are you stuck with no node-local storage? How much RAM does your system have? When you couple this system knowledge with knowledge of your use case (e.g. I have 50GB of JPEGs/250GB of h264 MP4) you can make a pretty good guess what configuration will eek the highest performance from the hardware available. All you really need to remember is that RAM > NVMe SSD > SATA SSD > HDD > Networked file storage (there are exceptions to this when you’re loading a large blob of data, but most ML workloads have nasty random access patterns where this hierarchy holds true). Let’s consider the use case of training a model on a set of images, say 50GB of them. If you’ve got enough RAM such that you can copy your dataset into memory and also have enough space left over to decompress your dataset and perform augmentations then do this! Copy your data over to /dev/shm and point your training script to it. /dev/shm is a directory in linux exposing RAM through the filesystem, when you copy data to that directory becomes resident in RAM.
In most cases you can’t fit your entire dataset into RAM leaving enough over to decompress examples and do data augmentation. The next best step is to have your dataset on an SSD (preferably NVMe). If you’re on an HPC system, get an interative session and run df to see what block devices are available on compute nodes and have a look into /sys/block/ to find out more about the devices available to you (e.g. /sys/block/X/queue/rotational tells you whether the device is an HDD or SSD).
Your hands start getting tied when you’re loading from HDDs or networked file storage. You have to start getting quite clever with your data storage and access patterns. HDDs have a spinning disk, it takes time to move the read head in an HDD so you want to minimizing head movement as much as possible. One approach you can take is to chunk your dataset into groups of data elements that you lay out sequentially on disk and then you randomise the order of those groups each epoch. This gives you the most of the benefits of random data ordering but without the (very) high costs of random access. A similar approach should be taken for a networked filesystem, try put data in as large a blocks as you can. An example of library doing this is GulpIO. It is designed for image and video and stores images/frames as a contiguous sequence of compressed JPEGs in blocks known as GulpChunks. The cost of the code changes and time spent engineering at this level is extremely painful. I would suggest throwing money at the problem if at all possible… SSDs aren’t expensive yet bring a world of benefit.
One pattern I’ve seen successfully employed where there has been a high performance networked filesystem and sufficient RAM to hold the dataset in memory, is to combine all the data files into an uncompressed zip and write your dataset class to access data elements from the ZIP file. Do not use a tar file as their random access cost is $$\mathcal{O}(n)$$ in the length of the tar file (go check out the wiki article on tar to understand why!).
Before wrapping up this section, we should briefly discuss the overhead of filesystem calls like open and read, these syscalls aren’t free and when you’re loading thousands of images a second they can add up. I often see people dumping video frames into a single folder. If you’re using filesystems like EXT3/4 this can incur quite substantial overheads. Consider using a lightweight database like lmdb to store (id, binary blob) pairs.
### Making wiser choices in your code
We’ve discussed tweaking PyTorch’s dataloader to make the most of the CPU and memory available, we’ve looked at how you should leverage the storage hardware available to you. If those two things haven’t brought you far enough in mitigating data starvation, then it’s time to look at your code. This is going to be very domain specific. I’m making the decision to ignore everything but image and video as these are the two representations I work with and have a lot of experience solving data starvation problems for. They are also typically some of the most computationally expensive data that is commonly used in ML.
What format do you store your media in? Is it something lossless like PNG or TIFF? Do you really need the precision these formats afford? Can you use JPEG instead? JPEG has the benefit of years and years work in producing highly optimised decoders (e.g. libjpegturbo). If you work with video, one of the main determinants of which storage format you should use are your access patterns. If you sparsely sample frames then this puts you into a similar regime as working with images (totally unpredictable access patterns). If instead you work with clips of video, then your access patterns are not quite as random, you’ll be doing sequential reads of contiguous frames. For video the storage decision is not clear cut and you should benchmark the options on your hardware
#### Images
Use JPEG. Don’t use PNG. The JPEG compression rate is much higher and therefore images take up a lot less space (and so are quicker to load off storage into RAM) and we have fast decoders for JPEG (libjpeg-turbo and nvJPEG).
Loading, decoding and, augmenting on the CPU is still the norm (although DALI is helping to push people towards doing some of this stuff on the GPU, and torchvision looks set to go that way—they’ve been implementing their transforms in torchscript so that they can run on the GPU). In this space the main players loading JPEGs are Pillow, Pillow-SIMD, opencv, accimage. Pretty much all these libraries also implement transformations as well, but just because you use one library for loading, doesn’t mean you have to use the same one for transformations. Pillow is a no go, it’s far too slow out of the box, you should at least build it with libjpeg-turbo. Even then it’s a bad choice when Pillow-SIMD exists, a fork of Pillow that reimplements the underlying operations to make use of SIMD intrinsics. This doesn’t change JPEG decoding time, but if you’re using Pillow for image transforms then you should switch to Pillow-SIMD instead. Some people seem to claim opencv is faster than Pillow-SIMD, but I’ve never been able to reproduce it, at least not using the opencv-python package on PyPI which is how most people get opencv in the python community. The absolute fastest way I’ve found of loading JPEGs is Joachim Folz’s recent and wonderful simplejpeg library. It only contains 4 functions, and in my tests it was consistently the fastest.
For image transformations there are, again, a lot of options to choose from. I’ve typically just used Pillow-SIMD, but albumationations looks interesting and their benchmarks seem compelling.
Now I don’t expect CPU image decoding and transformation to last that much longer. We’re moving to the GPU, I see that as inevitable, but the libraries and tooling aren’t as nice to use as the CPU counterparts. Up to my knowledge, DALI is the only real player in this domain. It encompasses both GPU accelerated JPEG decoding through nvJPEG and comes out of the box with GPU accelerated transforms. DALI is an all or nothing library, you either adopt it for all your data needs or you don’t, there aren’t particularly easy ways to plumb it up with your own existing data pipeline, and if you do, you’ll probably miss out on most of the benefits it provides. If you’re interested in DALI you should check out Ceyda Cinarel’s blog post on it, she clearly explains how to write your own python data source which is something I found lacking in the docs last time I tried to use DALI.
Torchvision might also come to the rescue in future with nvJPEG decoding, there’s an open PR on adding it, but it’s not been merged yet. Torchvision could be pretty speedy when this PR lands coupled with torchvision’s existing GPU accelerated image transforms, so keep an eye on the release notes of new releases!
#### Video
The same approaches in images can be employed to store frames from a video, this works quite well when you’re sparsely sampling frames. For loading video clips you can often do better by keeping the videos as video files instead of expanding them out to a directory of images. If you have a lot of compute power and your data storage is slow, keeping video as video files is especially appealing as you can trade off the space to store a clip (using an encoder like vp9) for compute (vp9 takes longer to decompress than simpler encodings). If you’re more constrained on compute (few cores) then you might still be better off encoding the frames as JPEGs and using libjpegturbo backed library like simplejpeg.
DALI has support for decoding video on the GPU via it’s video reader. I’ve yet to try this out, but for training networks for action recognition or other problems where you load full clips this certainly looks like it’d be very quick. DALI also supports computing optical flow on the fly using RTX20* series and above cards! I’ve not tried this out, but it’d be a nice change from computing TV-L1 offline.
## Common Gotchas
A few mistakes I’ve seen repeatedly:
• When running on an HPC cluster they forget to request a decent quantity of memory or cores and data loading is bottlenecked by that (always request X cores and N GB of memory so you know what your runtime configuration is)
• Loading data from a networked filesystem when fast node-local storage is available (don’t do that, first copy the data over and then train on it)
• Using too few workers in PyTorch’s DataLoader.
• Writing bad dataset classes that are inefficient
• Storing data in a suboptimal way for reading it quickly.
• Inefficient data augmentation code that gobbles up CPU cycles | 2021-04-16 17:35:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18842869997024536, "perplexity": 1715.7490243817247}, "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/1618038088245.37/warc/CC-MAIN-20210416161217-20210416191217-00601.warc.gz"} |
https://www.embibe.com/exams/kohlrauschs-law-and-its-applications/ | Kohlrausch's Law: Know Applications, Definition - Embibe
• Written By Umesh_K
• Written By Umesh_K
# Kohlrausch’s Law and Its Applications: Statement, Examples
What is Kohlrausch law?: Kohlrauch’s law refers to an electrolyte’s limiting molar conductivity to its constituent ions. It states that an electrolyte’s limiting molar conductivity equals the sum of the individual limiting molar conductivities of the cations and anions that make up the electrolyte.
Friedrich Kohlrausch discovered this law from observing experimental data on the conductivities of various electrolytes. To understand Kohlrausch’s law we have to define Kohlrausch law, know what is Kohlrausch law in detail, and understand the application of Kohlrausch law to get full contextual clarity. In this article, let’s learn everything about Kohlrausch’s law and its application in detail.
## Discovery of Kohlrausch’s law
In the year $$1874 – 79,$$ a German Physicist, Friedrich Kohlrausch, worked on different electrolyte solutions to determine their conductive properties. He was researching the conductive properties of the electrolytes to determine their behaviour and study the anomalies involved in them. The research on various salt solutions yielded a very interesting fact:
Study Fundamental Laws of Gases Here
‘The limiting molar conductivities of each kind of migrating ion are unique and are specific to that kind of ion’, and the conductivity of any ion is unique and do not depend upon the other ion (co-ions) present in the solution or their nature.
The research on the solutions resulted in the ‘Kohlrausch Law of Independent Migration of Ions’. After concluding that at infinite dilution, every ion present in an electrolyte makes a ‘definite’ contribution to the complete molar conductivity (total molar conductivity) of the electrolyte irrespective of the type of another ion present in it, he termed the ‘individual contribution’ of a particular ion to the total molar conductivity of the electrolyte as ‘Molar ionic conductivity. Based on the experiments, he put forth the generalization called Kohlrausch law in the year $$1876.$$
### Define Limiting Molar Conductivity?
Limiting molar conductivity can be defined as the molar conductivity of a solution at infinite dilution. It means that if the concentration of the electrolyte approaches zero, the molar conductivity is called limiting molar conductivity.
### What is Kohlrausch Law?
Define Kohlrausch Law: Kohlrausch’s Law is: “Molar conductivity of an electrolyte at infinite dilution is the sum of ionic conductivities of each ion (cations and anions) present, multiplied by the number of each ion present in one unit of the electrolyte”.
It can be represented as:
$${\rm{\pi }}_{\rm{m}}^0$$ of $${{\rm{X}}_{\rm{a}}}{{\rm{Y}}_{\rm{b}}} = {\rm{a}}\pi _{\rm{x}}^0{\,^ + } + {\rm{b}}\pi _{\rm{y}}^0{\,^ – }$$
Where:
$${\rm{\pi }}_{\rm{m}}^0$$ Total Molar conductivity of the electrolyte $${{\rm{X}}_{\rm{a}}}{{\rm{Y}}_{\rm{b}}} = {\rm{a\pi }}_{\rm{x}}^0{{\mkern 1mu} ^ + } + {\rm{b\pi }}_{\rm{y}}^0{{\mkern 1mu} ^ – }$$
$${{\text{X}}_{\text{a}}}{{\text{Y}}_{\text{b}}} =$$ Electrolyte under consideration
$${\rm{\lambda }}_{\rm{x}}^0{\,^ + }$$ and $${\rm{\lambda }}_{\rm{y}}^0{\,^ – }$$ Molar Conductivities of individual anions and cations present in the electrolyte
Therefore, the total molar conductivities of the electrolytes can be calculated as follows:
$${\rm{\pi }}_{\rm{m}}^0$$ of $${\rm{KBr}} = {\rm{\pi }}_{{\rm{mk}}}^0{{\mkern 1mu} ^ + } + {\rm{\pi }}_{{\rm{Br}}}^0{{\mkern 1mu} ^ – }$$
$${\rm{\pi }}_{\rm{m}}^0$$ of $${\rm{A}}{{\rm{l}}_2}{\left( {{\rm{S}}{{\rm{O}}_4}} \right)_3} = 2\pi _{{\rm{Al}}}^0{\,^{3 + }} + 3\pi _{\left( {{\rm{S}}{{\rm{O}}_4}} \right)}^0{\,^{2 – }}$$
### Kohlrausch Law Examples
Kohlrausch researched the molar conductivities of different sets of strong electrolytes with one common ion (either anion or cation) at infinite dilution. Tables $$1$$ and $$2$$ show examples of how a common cation or anion will result in the same difference in molar conductivities of the salts.
#### Table 2: Molar Conductivities of Electrolytes with Same Cations
In table-$$1,$$ the electrolyte pair has the same anions, $${\text{C}}{{\text{l}}^ – },{\text{B}}{{\text{r}}^ – }$$ and $${\text{N}}{{\text{O}}_3}^ – ,$$ but with two different cations. The difference in molar conductivities of the pair of electrolytes (when their cations are exchanged) is the same $$\left({23.41} \right).$$
The same can be observed in Table – $$2,$$ where the anions are exchanged, the same can be observed. The difference in molar conductivities of the pairs remains unchanged for all pairs – $$2.06.$$
Hence, this proves that the difference in the total molar conductivities for any two ions (cations such as $${\text{N}}{{\text{a}}^ + }$$ and $${\text{L}}{{\text{i}}^ + }$$) is constant, irrespective of the other ion present in them (for any $${\text{X}} -{\text{NaX}}$$ and $${\text{LiX}}$$).
Also, for any concentration ‘$${\text{C}}$$’, the degree of dissociation $$\left( \alpha \right)$$ can be expressed in terms of molar conductivities of ions and the total molar conductivity of the electrolyte as:
$${\rm{\alpha }} = \frac{{{\Lambda _{\rm{m}}}}}{{\Lambda _{\rm{m}}^ \circ }}$$
A different approximation is used for weak electrolytes like Acetic Acid to calculate the total molar conductivity of a weak electrolyte, as given below.
### Application of Kohlrausch Law
Kohlrausch’s law can be applied in many areas to find the molar conductivities of electrolytes or individual ions. Find below the application of Kohlrausch law:
#### a. Weak Electrolytes and Molar Conductivities
For weak electrolytes, the total molar concentration is determined using Kohlrausch’s law. It is because, in weak electrolytes such as Acetic Acid, at higher concentrations, the degree of dissociation is very low.
So, the change in molar conductivities $$\left( {{{\rm{\pi }}_{\rm{m}}}} \right)$$ of such electrolytes with dilution occurs due to the rise in the degree of dissociation. That results in the increased number of ions per total volume of the solution containing $$1$$ mole of electrolyte.
And this, in turn, increases the $${\rm{\pi }}_{\rm{m}}^0$$ value drastically, with dilution at almost near low concentration. Thus, the total molar conductivities of such electrolytes (weak electrolytes) cannot be obtained by extrapolation of molar conductivities $$\left( {{{\rm{\pi }}_{\rm{m}}}} \right)$$ to zero dilution. Thus, since the molar conductivities of weak electrolytes at infinite dilution cannot be determined experimentally, Kohlrausch’s law is used.
##### Molar Conductivities at Infinite Dilution for Weak Electrolytes:
For weak electrolytes such as acetic acid, the molar conductivities (at infinite dilution) can be calculated using the law as below:
According to Kohlrausch’s law:
$${{\rm{\pi }}^{\rm{0}}}\left( {{\rm{CH3COOH}}} \right){\rm{ = }}{\lambda ^{\rm{0}}}{\rm{CH3CO}}{{\rm{O}}^ – } + \lambda _{\rm{H}}^{{\rm{0 + }}}$$
Using the molar conductivities of strong electrolytes at infinite dilution of strong electrolytes with common ions ($${\text{KCl}},{\text{HCl}}$$ and $${\text{C}}{{\text{H}}_3}{\text{COOK}}$$), and using Kohlrausch’s law, one can find the total molar conductivity of acetic acid.
$${{\rm{\pi }}^{\rm{0}}}\left( {{\rm{KCl}}} \right) = \lambda _{\rm{K}}^{{\rm{0 + }}}{\rm{ + }}{{\rm{\pi }}^{\rm{0}}}{\rm{C}}{{\rm{l}}^ – }$$
$${{\rm{\pi }}^{\rm{0}}}\left( {{\rm{KCl}}} \right) = \lambda _{\rm{K}}^{{\rm{0 + }}}{\rm{ + }}{{\rm{\pi }}^{\rm{0}}}{\rm{C}}{{\rm{l}}^ – }$$
$${{\rm{\pi }}^{\rm{0}}}\left( {{\rm{C}}{{\rm{H}}_{\rm{3}}}{\rm{COOK}}} \right) = \lambda _{\rm{K}}^{{\rm{0 + }}}{\rm{ + }}{\lambda ^{\rm{0}}}{\rm{C}}{{\rm{H}}_{\rm{3}}}{\rm{CO}}{{\rm{O}}^ – }$$
The molar conductivity of acetic acid at infinite dilution can be represented (calculated) as:
$${{\rm{\pi }}^{\rm{0}}}{\rm{C}}{{\rm{H}}_{\rm{3}}}{\rm{CO}}{{\rm{O}}^ – } + \lambda _{\rm{H}}^{{\rm{0 + }}}{\rm{ = }}\left( {\lambda _{\rm{K}}^{{\rm{0 + }}}{\rm{ + }}{{\rm{\pi }}^{\rm{0}}}{\rm{C}}{{\rm{H}}_{\rm{3}}}{\rm{CO}}{{\rm{O}}^ – }} \right) – \left( {\lambda _{\rm{H}}^{{\rm{0 + }}}{\rm{ + }}{{\rm{\pi }}^{\rm{0}}}{\rm{C}}{{\rm{l}}^ – }} \right){\rm{ + }}\left( {\lambda _{\rm{H}}^{{\rm{0 + }}}{\rm{ + }}{{\rm{\pi }}^{\rm{0}}}{\rm{C}}{{\rm{l}}^ – }} \right)$$
Hence,
$${{\rm{\pi }}^0}\left( {{\rm{C}}{{\rm{H}}_3}{\rm{CO}}{{\rm{O}}^ – }} \right) = {{\rm{\pi }}^0}\left( {{\rm{C}}{{\rm{H}}_3}{\rm{COOK}}} \right) – {{\rm{\pi }}^0}\left( {{\rm{KCl}}} \right) + {{\rm{\pi }}^0}\left( {{\rm{HCle}}} \right)$$
#### b. Solubility of Sparingly Soluble Salts
The sparingly soluble salts are those salts that do not dissolve very well in water (or has very little dissolution in water). Examples of such salts include $${\text{AgCl}},{\text{PbS}}{{\text{O}}_4},{\text{BaS}}{{\text{O}}_4},$$ etc. Since they are very less dissolved, they are at infinite dilution. And their solubility and concentration are the same. So, using the total molar conductivities $$\left( {{\rm{\pi }}_{\rm{m}}^0} \right)$$ (through Kohlrausch’s law) and specific conductivity $$\left({\text{K}} \right)$$ of these salts, one can find their solubility.
$${\rm{Solubility}} = \frac{{{\rm{K}} \times 100}}{{\Lambda ^\circ {\rm{m}}}}$$
#### c. Degree of Dissociation of Electrolytes
Kohlrausch’s law is used to calculate the degree of dissociation of weak electrolytes $$\left( \alpha \right).$$ The molar conductivity of the electrolyte at any concentration, $${\rm{C}}\left( {{{\rm{\pi }}^0}_{\rm{m}}} \right),$$ and at infinite dilution $$\left( {{{\rm{\pi }}^0}_{\rm{m}}} \right),$$ is used to determine the degree of dissociation.
$$\alpha = \frac{{{\rm{number}}{\mkern 1mu} \,{\rm{of}}\,{\mkern 1mu} {\rm{dissociated}}{\mkern 1mu} \,{\rm{ions}}{\mkern 1mu} {\rm{at}}{\mkern 1mu} \,{\rm{a}}\,{\mkern 1mu} {\rm{particular}}{\mkern 1mu} \,{\rm{concentration}}{\mkern 1mu} \,{\rm{C}}}}{{{\rm{Total}}{\mkern 1mu} \,{\rm{number}}\,{\mkern 1mu} {\rm{of}}{\mkern 1mu} {\rm{ions}}{\mkern 1mu} \,{\rm{present}}}} = \frac{{{\Lambda ^{\rm{c}}}{\rm{m}}}}{{\Lambda ^\circ {\rm{m}}}}$$
#### d. To Calculate the Dissociation Constant of Weak Electrolytes
The dissociation constant, $${{\text{K}}_{\text{c}}}$$ for weak electrolytes, can be calculated with the help of the degree of dissociation of the electrolyte, $$\alpha :$$
$${{\text{K}}_{\text{c}}} = \frac{{{\text{C}}{\alpha ^2}}}{{1 – \alpha }}$$
Where ‘$${\text{C}}$$’ is the concentration at any particular time.
### Summary
When researching the conductivities of electrolytes, Friedrich Kohlrausch, a German physicist, determined that the limiting molar conductivities of each kind of migrating ion are unique and specific to that kind of ion. This resulted in Kohlrausch’s law of independent migration of ions. The law and its mathematical forms can be applied to all electrolytes, both strong and weak electrolytes. Thus, the law can be applied to determine the degree of dissociation of weak electrolytes, otherwise done experimentally, and to determine the solubility of sparingly soluble salts.
### FAQs on Kohlarausch Law
Check frequently asked questions related to the application of Kohlrausch law below:
Q.1: State and explain Kohlrausch law of independent migration of ions with its two applications?
Ans:
Kohlrausch’s law states that: Molar conductivity of an electrolyte at infinite dilution is the sum of ionic conductivities of each ion (cations and anions) present, multiplied by the number of each ion present in one unit of the electrolyte.
The two types of application of Kohlrauch law include:
a. It is used to calculate the solubility of sparingly soluble salts
b. The degree of dissociation of weak electrolytes can be determined with the help of the law.
Q.2: Is Kohlrausch’s law applicable for strong electrolytes?
Ans:
Yes, Kohlrausch’s law is applicable both for weak and strong electrolytes.
Q.3: What is the mathematical expression for Kohlrausch’s law?
Ans:
Kohlrausch’s law can be mathematically expressed as $${\rm{\pi }}_{\rm{m}}^0$$ of $${{\rm{X}}_{\rm{a}}}{{\rm{Y}}_{\rm{b}}} = {\rm{a\pi }}_{\rm{x}}^0{{\mkern 1mu} ^ + } + {\rm{b\pi }}_{\rm{y}}^0{{\mkern 1mu} ^ – }$$
Where:
$${\rm{\pi }}_{\rm{m}}^0 =$$ Total Molar conductivity of the electrolyte $${{\text{X}}_{\text{a}}}{{\text{Y}}_{\text{b}}}$$
$${{\text{X}}_{\text{a}}}{{\text{Y}}_{\text{b}}} =$$ Electrolyte under consideration
$${\rm{\pi }}_{\rm{x}}^{{\rm{0 + }}}$$ and $${\rm{\pi }}_{\rm{y}}^{{\rm{0 – }}}$$ Molar Conductivities of individual anions and cations present in the electrolyte
Q.4: How was Kohlrausch law discovered?
Ans:
A German Physicist by the name of Friedrich Kohlrausch was researching the conductive properties of the electrolytes to determine their behaviour and to study the anomalies involved in them. He deduced that the total molar conductivity of an electrolyte at infinite dilution is equal to the sum of the molar conductivities of the individual ions present in it and the product of the number of each ion present in one unit of the electrolyte.
Q.5: Which statement is correct for Kohlrausch’s law?
Ans:
The law states that the total molar conductivity of an electrolyte at infinite dilution is the sum of ionic conductivities of each ion (cations and anions) present, multiplied by the number of each ion present in one unit of the electrolyte.
Q.6: What is the degree of dissociation of weak electrolytes?
Ans:
There is an increase in the degree of dissociation of a weak electrolyte with an increase in dilution. It is represented as: $${\rm{\alpha }} = \frac{{{\Lambda ^{\rm{c}}}_{\rm{m}}}}{{{\Lambda ^ \circ }_{\rm{m}}}}$$
Where,
$${\rm{\pi }}_{\rm{m}}^{\rm{c}}{\rm{ = }}$$ molar conductivity of the electrolyte at any concentration, $${\text{C}}$$
$${\rm{\pi }}_{\rm{m}}^{\rm{0}}{\rm{ = }}$$ Molar conductivity of the electrolyte at infinite dilution.
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Master Exam Concepts with 3D Videos | 2022-06-28 17:52:06 | {"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": 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": 0.8049066066741943, "perplexity": 2051.7439441454603}, "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/1656103573995.30/warc/CC-MAIN-20220628173131-20220628203131-00404.warc.gz"} |
https://physics.stackexchange.com/questions/7049/history-of-electromagnetic-field-tensor | # History of Electromagnetic Field Tensor
I'm curious to learn how people discovered that electric and magnetic fields could be nicely put into one simple tensor.
It's clear that the tensor provides many beautiful simplifications to the original theory, by applying the abstract theory of tensors to this particular problem. For example, the strange formulas for the transformation of electric and magnetic fields in different reference frames can be explained as the transformation laws of a 2-tensor. The interdependence of the two fields in this transformation, and the fact that electric and magnetic fields are in some ways the same thing in the classical theory, can be explained by this two tensor. The various ad-hoc formulas that make up Maxwell's equations, some of them with curls, some with divergence, can be explained in one beautiful formula by declaring the exterior derivative of the tensor to be 0. The cross product can also be explained as an operation on anti-symmetric tensors.
So, it's clear once someone shows you the tensor formulation that it beautifully weaves together all the parts of the "elementary" (i.e. non-tensorial) theory. My question is, how did people discover this formulation in the first place? What was the motivation, and what is the history?
Some thoughts: It's true that the elementary theory provides some hints to the tensor formulation (such as some of the things I list above), but these small hints are not quite enough to motivate all the intricacies of the tensor formula, especially if one has not seen tensors before. Was the theory of tensors already floating around in the time that the field tensor was discovered, and hence did tensor experts simply notice that electromagnetism smelled like a 2-tensor? If this is the case, how did people initially realize that tensors were important in physics? Otherwise, what did happen? Why were people motivated to do it? And, wasn't the original formulation good enough, albeit not quite as mathematically elegant?
Another related question, did people know the transformation laws for electric and magnetic fields before Einstein came along? Today, you can usually only find those in books on special relativity, or in the very last chapter of a book on electromagnetism, usually a chapter on special relativity. Therefore, if you were reading a book on electromagnetism, then before you got to the chapter on relativity, you would have thought that force vectors and hence electric fields are invariant under change of reference frame, just like forces in Newtonian mechanics.
The earliest instance I have found is Minkowski's "Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern" in "Nachrichten von der Georg-Augusts-Universität und der Königl. Gesellschaft der Wissenschaften zu Göttingen" from 1908.
A digitized version is found at
http://echo.mpiwg-berlin.mpg.de/ECHOdocuViewfull?start=1&viewMode=images&ws=1.5&mode=imagepath&url=/mpiwg/online/permanent/library/WBPZCG9Q/pageimg&pn=1
go to page 17/18 to read:
"Ich lasse nun an diesen Gleichungen wieder durch eine veränderte Schreibweise eine noch versteckte Symmetrie hervortreten"
roughly
"I will now, through another notation, reveal a yet hidden symmetry"
and he goes on to describe the field tensor.
• Is there an english translation of this? – Physiks lover Jul 27 '12 at 21:25
• there is a translation into english by Meghnad Saha here: archive.org/details/principleofrelat00eins you can download a PDF and will find the relevant setion on page 21. it's also published on wikisource: en.wikisource.org/wiki/… the translation reads "By employing a modified form of writing, I shall now cause a latent symmetry in these equations to appear." – luksen Jul 28 '12 at 17:18
Regarding whether people figured out the Lorentz transformation of E&M fields before Einstein, the answer (of course) is "sort of." According to my physics professor (Columbia U), people realized that the fields transformed according to the Lorentz transformation (although of course it wasn't yet called that), shortly before Maxwell came up with his laws. My professor roughly said that people had an idea that there was this strange dependence (Lorentz) on relative velocity of reference frames, but they didn't know what its significance was, or its relation to, for example, the not-yet-discovered position/time transformation or other Lorentz transformations.
• I am somewhat doubtful of the above account, unless by "people" you meant Lorentz himself. An interesting tidbit: in Lorentz's 1895 paper which started this whole business, he only showed that Maxwell's theory of electromagnetism obeys the transformation laws that now bears his name up to first order. That is, he threw away all $v^4/c^4$ terms as untreated higher order corrections. It was in 1899 that he realized the transformation is exact. – Willie Wong Apr 10 '11 at 0:09
The purpose to the electromagnetism tensor was to demonstrate the Lorentz covariance of Maxwell's equations. It is central to the discovery of special relativity, and it got everyone excited about relativity at the time. Einstein had nothing to do with it.
I am not going to try to answer the whole question, just one small part: tensors were already known before Maxwells' theory, they were used to study elasticity. In fact, the name 'tensor' comes from 'tension', an obviously important quantity in elasticity and mechanics (of continuous media) in general.
Tensors were also already being used in the 19th century to study algebraic forms and quadratic differential forms, though tensor calculus took its modern form with the work of Levi-Civita and Ricci. | 2019-04-24 19:55:56 | {"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": 0.7820426225662231, "perplexity": 737.0066012784907}, "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-2019-18/segments/1555578656640.56/warc/CC-MAIN-20190424194348-20190424220348-00479.warc.gz"} |
http://mathoverflow.net/questions/67373/expanding-measurable-sets | ## Expanding Measurable Sets
Let $S,T \subset \mathbb{R}^n$ be measurable sets, and suppose that there exists a measurable bijection $f\colon S\to T$ so that $$\|f(x)-f(y)\| \;\geq\; \|x-y\|$$ for all $x,y \in S$. Does it follow that $\mu(S) \leq \mu(T)$?
-
## 1 Answer
It follows from two observations:
• For Hausdorff meeasure your statement follows from the definition.
• Hausdorff measure = Lebesgue measure (up to constant).
-
Oh, great. Thanks! – Jim Belk Jun 9 2011 at 22:33 Note that the assumption that the bijection f is measurable is not needed for this argument. – Alex Simpson Jun 10 2011 at 7:20 @Alex, you need $T$ to be measurable; otherwise you can not write the inequality. – Anton Petrunin Jun 10 2011 at 13:49 I wasn't questioning the measurability of S and T. But the measurability of the bijection f is an additional assumption in the question as formulated and is unnecessary. – Alex Simpson Jun 12 2011 at 19:11 | 2013-05-26 00:44:38 | {"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": 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": 0.9415830373764038, "perplexity": 625.929354609753}, "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-2013-20/segments/1368706474776/warc/CC-MAIN-20130516121434-00028-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://brilliant.org/discussions/thread/a-seemingly-hard-divisibility-problem/ | # A seemingly hard divisibility problem
For every $n=1,2,3,..., 2040$, prove there exists a multiple of $n$, which has less than $12$ digits, and only contains the digits $0,1,8$ or $9$.
Solution: Take two $11$ digits numbers, consisting of only $0$ and $1$, since there are $2^{11}=2048$ numbers that can be formed, there must be two numbers with the same remainder after dividing by $n$. Thus, subtracting one with another, we get a multiple of $n$ which has less than $12$ digits, and only contains the digits $0,1,8$ or $9$.
Generalization: For every $n=1,2,3,..., k$ where $k \le 2^j-1$, there exists a multiple of $n$, which has less than $j+1$ digits, and only contains the digits $0,1,8$ or $9$.
Note by ChengYiin Ong
5 months, 3 weeks ago
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Can you give the numbers? @ChengYiin Ong
- 5 months, 3 weeks ago
Maybe for $n=11$, i can choose $11100001001$ and $10000000000$, they both have $11$ digits and subtracting the first with the second, we get $1100001001$ which is a multiple of 11 and only contains the digits $0,1,8$ or $9$.
- 5 months, 3 weeks ago
@ChengYiin Ong - if there are 2048 possibilities then how can you say that "there must be two numbers with the same remainder after dividing by n?"
- 5 months, 3 weeks ago
there are $2048$ numbers that you can form from choosing only $0$ or $1$ at for every digit and so there must be two numbers that have the same modulo $n$, maybe i shouldn't say "possibility"
- 5 months, 3 weeks ago | 2020-12-04 12:08:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 39, "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": 0.94682377576828, "perplexity": 1114.9506475729954}, "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-2020-50/segments/1606141735600.89/warc/CC-MAIN-20201204101314-20201204131314-00151.warc.gz"} |
https://www.csdn.net/tags/MtTaMgysNjIzNjYwLWJsb2cO0O0O.html | • matplotlib的plt.acorr中的自相关图缺陷
2020-12-08 14:51:04
这是统计和信号处理之间不同的共同定义的结果。基本上，信号处理定义假定您要处理去趋势化。统计定义假设减去平均值就是你将要做的所有改变，并且是为你做的。
首先，让我们用一个独立的例子来演示这个问题：import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from statsmodels.graphics import tsaplots
def label(ax, string):
ax.annotate(string, (1, 1), xytext=(-8, -8), ha='right', va='top',
size=14, xycoords='axes fraction', textcoords='offset points')
np.random.seed(1977)
data = np.random.normal(0, 1, 100).cumsum()
fig, axes = plt.subplots(nrows=4, figsize=(8, 12))
fig.tight_layout()
axes[0].plot(data)
label(axes[0], 'Raw Data')
axes[1].acorr(data, maxlags=data.size-1)
label(axes[1], 'Matplotlib Autocorrelation')
tsaplots.plot_acf(data, axes[2])
label(axes[2], 'Statsmodels Autocorrelation')
pd.tools.plotting.autocorrelation_plot(data, ax=axes[3])
label(axes[3], 'Pandas Autocorrelation')
# Remove some of the titles and labels that were automatically added
for ax in axes.flat:
ax.set(title='', xlabel='')
plt.show()
所以，为什么我说他们都是对的？他们明显不同！
让我们编写自己的自相关函数来演示plt.acorr在做什么：def acorr(x, ax=None):
if ax is None:
ax = plt.gca()
autocorr = np.correlate(x, x, mode='full')
autocorr /= autocorr.max()
return ax.stem(autocorr)
如果我们用我们的数据来绘制这个图，我们将得到与plt.acorr大致相同的结果(我没有适当地标记延迟，只是因为我很懒)：fig, ax = plt.subplots()
acorr(data)
plt.show()
这是一个完全有效的自相关。这都是你的背景是信号处理还是统计的问题。
这是信号处理中使用的定义。假设您要处理数据的格式转换(注意detrend中的plt.acorrkwarg)。如果你想取消渲染，你会明确地要求它(并且可能做一些比仅仅减去平均值更好的事情)，否则就不应该假设它。
在统计学中，简单地减去平均值被认为是你想要做的。
所有其他函数都是在相关之前减去数据的平均值，类似于：def acorr(x, ax=None):
if ax is None:
ax = plt.gca()
x = x - x.mean()
autocorr = np.correlate(x, x, mode='full')
autocorr /= autocorr.max()
return ax.stem(autocorr)
fig, ax = plt.subplots()
acorr(data)
plt.show()
然而，我们仍然有一个很大的区别。这纯粹是一个阴谋约定。
在大多数信号处理教科书中(我已经看到过了)，显示的是“完全”自相关，这样零滞后在中心，结果在每一边都是对称的。R、 另一方面，有一个非常合理的惯例，只展示它的一面。(毕竟，另一方面是完全冗余的)统计绘图函数遵循R对流，而plt.acorr遵循Matlab所做的，这是相反的约定。
基本上，你会想要这个：def acorr(x, ax=None):
if ax is None:
ax = plt.gca()
x = x - x.mean()
autocorr = np.correlate(x, x, mode='full')
autocorr = autocorr[x.size:]
autocorr /= autocorr.max()
return ax.stem(autocorr)
fig, ax = plt.subplots()
acorr(data)
plt.show()
更多相关内容
• Using statsmodels’ ols function, we construct our model setting housing_price_index as a function of total_unemployed. We assume that an increase in the total number of unemployed people will have ...
pandas 线性回归
This post was originally published here
这篇文章最初发表在这里
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In this post, we’ll walk through building linear regression models to predict housing prices resulting from economic activity. Topics covered will include:
在本文中，我们将逐步构建线性回归模型，以预测经济活动导致的房价。 涵盖的主题将包括：
Future posts will cover related topics such as exploratory analysis, regression diagnostics, and advanced regression modeling, but I wanted to jump right in so readers could get their hands dirty with data.
未来的文章将涵盖相关主题，例如探索性分析，回归诊断和高级回归建模，但是我想跳进去，以便读者可以轻松掌握数据。
## 什么是回归？(What is Regression?)
Linear regression is a model that predicts a relationship of direct proportionality between the dependent variable (plotted on the vertical or Y axis) and the predictor variables (plotted on the X axis) that produces a straight line, like so:
线性回归是一个模型，该模型可预测因变量（绘制在垂直或Y轴上）与预测变量（绘制在X轴上）之间的直接比例关系，该变量会产生一条直线，如下所示：
Linear regression will be discussed in greater detail as we move through the modeling process.
在建模过程中，将更详细地讨论线性回归。
## 变量选择(Variable Selection)
For our dependent variable we’ll use housing_price_index (HPI), which measures price changes of residential housing.
对于我们的因变量，我们将使用housing_price_index （HPI）来衡量住宅价格的变化。
For our predictor variables, we use our intuition to select drivers of macro- (or “big picture”) economic activity, such as unemployment, interest rates, and gross domestic product (total productivity). For an explanation of our variables, including assumptions about how they impact housing prices, and all the sources of data used in this post, see here.
对于我们的预测变量，我们使用直觉来选择宏观（或“全局”）经济活动的驱动力，例如失业率，利率和国内生产总值（总生产率）。 有关我们变量的解释，包括关于变量如何影响房价的假设以及本文中使用的所有数据来源，请参见此处
### 用熊猫读数据(Reading in the Data with pandas)
Once we’ve downloaded the data, read it in using pandas’ read_csv method.
下载完数据后，请使用pandas的read_csv方法读取数据。
import pandas as pd
# be sure to use the file path where you saved the data
gross_domestic_product = pd.read_csv('/Users/tdobbins/Downloads/hpi/gdp.csv')import pandas as pd
# be sure to use the file path where you saved the data
gross_domestic_product = pd.read_csv('/Users/tdobbins/Downloads/hpi/gdp.csv')
Once we have the data, invoke pandas’ merge method to join the data together in a single dataframe for analysis. Some data is reported monthly, others are reported quarterly. No worries. We merge the dataframes on a certain column so each row is in its logical place for measurement purposes. In this example, the best column to merge on is the date column. See below.
有了数据后，调用pandas的merge方法将数据merge到单个数据框中进行分析。 一些数据每月报告一次，其他数据每季度报告一次。 别担心。 我们将数据帧合并到某一列上，以便每一行都位于其逻辑位置以进行测量。 在此示例中，要合并的最佳列是日期列。 见下文。
Let’s get a quick look at our variables with pandas’ head method. The headers in bold text represent the date and the variables we’ll test for our model. Each row represents a different time period.
让我们用pandas的head方法快速查看我们的变量。 粗体文本标题表示日期和我们将为模型测试的变量。 每行代表一个不同的时间段。
Out[23]:
出[23]：
date 日期 sp500 sp500 consumer_price_index 消费者价格指数 long_interest_rate long_interest_rate housing_price_index housing_price_index total_unemployed 共有失业 more_than_15_weeks 超过15周 not_in_labor_searched_for_work not_in_labor_searched_for_work multi_jobs 多职位 leavers 离开者 losers 失败者 federal_funds_rate Federal_funds_rate total_expenditures 支出总额 labor_force_pr labor_force_pr producer_price_index 生产者价格指数 gross_domestic_product 国内生产总值
0 0 2011-01-01 2011-01-01 1282.62 1282.62 220.22 220.22 3.39 3.39 181.35 181.35 16.2 16.2 8393 8393 2800 2800 6816 6816 6.5 6.5 60.1 60.1 0.17 0.17 5766.7 5766.7 64.2 64.2 192.7 192.7 14881.3 14881.3
1 1个 2011-04-01 2011-04-01 1331.51 1331.51 224.91 224.91 3.46 3.46 180.80 180.80 16.1 16.1 8016 8016 2466 2466 6823 6823 6.8 6.8 59.4 59.4 0.10 0.10 5870.8 5870.8 64.2 64.2 203.1 203.1 14989.6 14989.6
2 2 2011-07-01 2011-07-01 1325.19 1325.19 225.92 225.92 3.00 3.00 184.25 184.25 15.9 15.9 8177 8177 2785 2785 6850 6850 6.8 6.8 59.2 59.2 0.07 0.07 5802.6 5802.6 64.0 64.0 204.6 204.6 15021.1 15021.1
3 3 2011-10-01 2011-10-01 1207.22 1207.22 226.42 226.42 2.15 2.15 181.51 181.51 15.8 15.8 7802 7802 2555 2555 6917 6917 8.0 8.0 57.9 57.9 0.07 0.07 5812.9 5812.9 64.1 64.1 201.1 201.1 15190.3 15190.3
4 4 2012-01-01 2012-01-01 1300.58 1300.58 226.66 226.66 1.97 1.97 179.13 179.13 15.2 15.2 7433 7433 2809 2809 7022 7022 7.4 7.4 57.1 57.1 0.08 0.08 5765.7 5765.7 63.7 63.7 200.7 200.7 15291.0 15291.0
Usually, the next step after gathering data would be exploratory analysis. Exploratory analysis is the part of the process where we analyze the variables (with plots and descriptive statistics) and figure out the best predictors of our dependent variable. For the sake of brevity, we’ll skip the exploratory analysis. Keep in the back of your mind, though, that it’s of utmost importance and that skipping it in the real world would preclude ever getting to the predictive section.
通常，收集数据后的下一步将是探索性分析。 探索性分析是该过程的一部分，在该过程中，我们分析变量（使用图表和描述性统计数据）并找出我们因变量的最佳预测变量。 为了简洁起见，我们将跳过探索性分析。 不过，请记住，它至关重要，在现实世界中跳过它会阻止您进入预测领域。
We’ll use ordinary least squares (OLS), a basic yet powerful way to assess our model.
我们将使用普通最小二乘法（OLS），这是一种基本而强大的评估模型的方法。
### 普通最小二乘假设(Ordinary Least Squares Assumptions)
OLS measures the accuracy of a linear regression model.
OLS衡量线性回归模型的准确性。
OLS is built on assumptions which, if held, indicate the model may be the correct lens through which to interpret our data. If the assumptions don’t hold, our model’s conclusions lose their validity. Take extra effort to choose the right model to avoid Auto-esotericism/Rube-Goldberg’s Disease.
OLS建立在假设上，如果假设成立，则表明模型可能是解释我们数据的正确镜头。 如果这些假设不成立，那么我们模型的结论将失去其有效性。 付出额外的努力来选择正确的模型，以避免自闭症/鲁伯-戈德伯格病
Here are the OLS assumptions:
以下是OLS的假设：
1. Linearity: A linear relationship exists between the dependent and predictor variables. If no linear relationship exists, linear regression isn’t the correct model to explain our data.
2. No multicollinearity: Predictor variables are not collinear, i.e., they aren’t highly correlated. If the predictors are highly correlated, try removing one or more of them. Since additional predictors are supplying redundant information, removing them shouldn’t drastically reduce the Adj. R-squared (see below).
3. Zero conditional mean: The average of the distances (or residuals) between the observations and the trend line is zero. Some will be positive, others negative, but they won’t be biased toward a set of values.
4. Homoskedasticity: The certainty (or uncertainty) of our dependent variable is equal across all values of a predictor variable; that is, there is no pattern in the residuals. In statistical jargon, the variance is constant.
5. No autocorrelation (serial correlation): Autocorrelation is when a variable is correlated with itself across observations. For example, a stock price might be serially correlated if one day’s stock price impacts the next day’s stock price.
1. 线性 ：因变量和预测变量之间存在线性关系。 如果不存在线性关系，则线性回归不是解释我们数据的正确模型。
2. 没有多重共线性 ：预测变量不是共线性的，即它们之间没有高度相关。 如果预测变量高度相关，请尝试删除其中一个或多个。 由于其他预测变量正在提供冗余信息，因此删除这些预测变量不应显着降低Adj。 R平方 （请参见下文）。
3. 零条件均值 ：观测值和趋势线之间的平均距离（或残差）为零。 有些会是积极的，有些则是消极的，但它们不会偏向一系列价值观。
4. 同方性 ：我们的因变量的确定性（或不确定性）在预测变量的所有值之间相等； 也就是说，残差中没有图案。 用统计术语来说，方差是恒定的。
5. 无自相关（串行相关） ：自相关是指变量在各个观测值之间与自身相关。 例如，如果一天的股票价格影响第二天的股票价格，则股票价格可能会顺序相关。
Let’s begin modeling.
让我们开始建模。
### 简单线性回归(Simple Linear Regression)
Simple linear regression uses a single predictor variable to explain a dependent variable. A simple linear regression equation is as follows:
简单线性回归使用单个预测变量来解释因变量。 一个简单的线性回归方程如下：
Where:
哪里：
y = dependent variable
y =因变量
ß = regression coefficient
ß= 回归系数
α = intercept (expected mean value of housing prices when our independent variable is zero)
α=截距（当我们的自变量为零时，房价的预期均值）
x = predictor (or independent) variable used to predict Y
x =用于预测Y的预测变量（或自变量）
ε = the error term, which accounts for the randomness that our model can’t explain.
ε=误差项，占我们模型无法解释的随机性。
Using statsmodels’ ols function, we construct our model setting housing_price_index as a function of total_unemployed. We assume that an increase in the total number of unemployed people will have downward pressure on housing prices. Maybe we’re wrong, but we have to start somewhere!
使用statsmodels' 的功能，我们构建我们的模型设定housing_price_index作为一个功能total_unemployed 。 我们假设失业人数的增加将对房价产生下行压力。 也许我们错了，但我们必须从某个地方开始！
The code below shows how to set up a simple linear regression model with total_unemployment as our predictor variable.
下面的代码显示了如何使用total_unemployment作为我们的预测变量来建立简单的线性回归模型。
from IPython.display import HTML, display
import statsmodels.api as sm
from statsmodels.formula.api import ols
# fit our model with .fit() and show results
# we use statsmodels' formula API to invoke the syntax below,
# where we write out the formula using ~
housing_model = ols("housing_price_index ~ total_unemployed", data=df).fit()
# summarize our model
housing_model_summary = housing_model.summary()
# convert our table to HTML and add colors to headers for explanatory purposes
HTML(
housing_model_summary\
.as_html()\
.replace(' Adj. R-squared: ', ' Adj. R-squared: ')\
.replace('coef', 'coef')\
.replace('std err', 'std err')\
.replace('P>|t|', 'P>|t|')\
.replace('[95.0% Conf. Int.]', '[95.0% Conf. Int.]')
)
Out[24]:
出[24]：
Dep. Variable: 部门 变量： R-squared: R平方： housing_price_index housing_price_index 0.952 0.952 OLS 最小二乘 0.949 0.949 Least Squares 最小二乘 413.2 413.2 Fri, 17 Feb 2017 2017年2月17日，星期五 2.71e-15 2.71e-15 17:57:05 17:57:05 -65.450 -65.450 23 23 134.9 134.9 21 21 137.2 137.2 1 1个 nonrobust 不稳健
coef ef std err 标准错误 t Ť P>|t| P> | t | [95.0% Conf. Int.] [95.0％Conf。 整数] 313.3128 313.3128 5.408 5.408 57.938 57.938 0.000 0.000 302.067 324.559 302.067 324.559 -8.3324 -8.3324 0.410 0.410 -20.327 -20.327 0.000 0.000 -9.185 -7.480 -9.185 -7.480
Omnibus: 综合： Durbin-Watson: 杜宾·沃森： 0.492 0.492 1.126 1.126 0.782 0.782 0.552 0.552 0.294 0.294 0.759 0.759 2.521 2.521 78.9 78.9
Referring to the OLS regression results above, we’ll offer a high-level explanation of a few metrics to understand the strength of our model: Adj. R-squared, coefficients, standard errors, and p-values.
参考上面的OLS回归结果，我们将提供一些指标的高级解释，以了解我们模型的强度：调整。 R平方，系数，标准误差和p值。
To explain:
解释：
Adj. R-squared indicates that 95% of housing prices can be explained by our predictor variable, total_unemployed.
调整 R平方表明，我们的预测变量total_unemployed可以解释房屋价格的95％。
The regression coefficient (coef) represents the change in the dependent variable resulting from a one unit change in the predictor variable, all other variables being held constant. In our model, a one unit increase in total_unemployed reduces housing_price_index by 8.33. In line with our assumptions, an increase in unemployment appears to reduce housing prices.
回归系数（coef）表示因预测变量一个单位变化而导致的因变量变化，所有其他变量保持不变。 在我们的模型中，增加一个单位total_unemployed减少housing_price_index 8.33。 根据我们的假设，失业率的上升似乎会降低房价。
The standard error measures the accuracy of total_unemployed‘s coefficient by estimating the variation of the coefficient if the same test were run on a different sample of our population. Our standard error, 0.41, is low and therefore appears accurate.
如果同一检验是在我们人口的不同样本上进行的，则标准误差通过估计系数的变化来衡量总total_unemployed系数的准确性。 我们的标准误差为0.41，很低，因此看起来很准确。
The p-value means the probability of an 8.33 decrease in housing_price_index due to a one unit increase in total_unemployed is 0%, assuming there is no relationship between the two variables. A low p-value indicates that the results are statistically significant, that is in general the p-value is less than 0.05.
p值表示假设两个变量之间没有关系，则由于total_unemployed增加1个单位而导致housing_price_index下降8.33的可能性为0％。 低p值表示结果具有统计意义，即通常p值小于0.05。
The confidence interval is a range within which our coefficient is likely to fall. We can be 95% confident that total_unemployed‘s coefficient will be within our confidence interval, [-9.185, -7.480].
置信区间是我们的系数可能下降的范围。 我们可以有95％的信心， total_unemployed的系数将在我们的信心区间[-9.185，-7.480]之内。
Let’s use statsmodels’ plot_regress_exog function to help us understand our model.
让我们使用statsmodels的plot_regress_exog函数来帮助我们了解我们的模型。
### 回归图(Regression Plots)
Please see the four graphs below.
请参阅下面的四个图表。
1. The “Y and Fitted vs. X” graph plots the dependent variable against our predicted values with a confidence interval. The inverse relationship in our graph indicates that housing_price_index and total_unemployed are negatively correlated, i.e., when one variable increases the other decreases.
2. The “Residuals versus total_unemployed” graph shows our model’s errors versus the specified predictor variable. Each dot is an observed value; the line represents the mean of those observed values. Since there’s no pattern in the distance between the dots and the mean value, the OLS assumption of homoskedasticity holds.
3. The “Partial regression plot” shows the relationship between housing_price_index and total_unemployed, taking in to account the impact of adding other independent variables on our existing total_unemployed coefficient. We’ll see later how this same graph changes when we add more variables.
4. The Component and Component Plus Residual (CCPR) plot is an extension of the partial regression plot, but shows where our trend line would lie after adding the impact of adding our other independent variables on our existing total_unemployed coefficient. More on this plot here.
1. “ Y and Fitted vs. X”（Y和拟合与X的关系图）图以一个置信区间将因变量相对于我们的预测值进行绘制。 我们图表中的反比关系表明housing_price_indextotal_unemployed呈负相关，即，当一个变量增加而另一变量减少时。
2. “残差与total_unemployed ”图显示了我们模型的误差与指定的预测变量的关系。 每个点都是一个观察值； 该线代表那些观察值的平均值。 由于点和平均值之间的距离没有规律，因此OLS假设为同方差。
3. “偏回归图”显示了housing_price_indextotal_unemployed之间的关系，并考虑了添加其他自变量对我们现有的total_unemployed系数的影响。 稍后我们将看到当添加更多变量时，同一图形如何变化。
4. Component and Component Plus Residual（CCPR）图是部分回归图的扩展，但显示了在添加其他自变量对我们现有的total_unemployed系数的影响后，趋势线将位于total_unemployed 。 更多关于这个情节在这里
The next plot graphs our trend line (green), the observations (dots), and our confidence interval (red).
下图绘制了趋势线（绿色），观察值（点）和置信区间（红色）。
# this produces our trend line
from statsmodels.sandbox.regression.predstd import wls_prediction_std
import numpy as np
# predictor variable
x = df[['total_unemployed']]
# dependent variable
y = df[['housing_price_index']]
# retrieve our confidence interval values
# _ is a dummy variable since we don't actually use it for plotting but need it as a placeholder
# since wls_prediction_std(housing_model) returns 3 values
_, confidence_interval_lower, confidence_interval_upper = wls_prediction_std(housing_model)
fig, ax = plt.subplots(figsize=(10,7))
# plot the dots
# 'o' specifies the shape (circle), we can also use 'd' (diamonds), 's' (squares)
ax.plot(x, y, 'o', label="data")
# plot the trend line
# g-- and r-- specify the color to use
ax.plot(x, housing_model.fittedvalues, 'g--.', label="OLS")
# plot upper and lower ci values
ax.plot(x, confidence_interval_upper, 'r--')
ax.plot(x, confidence_interval_lower, 'r--')
# plot legend
ax.legend(loc='best');# this produces our trend line
from statsmodels.sandbox.regression.predstd import wls_prediction_std
import numpy as np
# predictor variable
x = df[['total_unemployed']]
# dependent variable
y = df[['housing_price_index']]
# retrieve our confidence interval values
# _ is a dummy variable since we don't actually use it for plotting but need it as a placeholder
# since wls_prediction_std(housing_model) returns 3 values
_, confidence_interval_lower, confidence_interval_upper = wls_prediction_std(housing_model)
fig, ax = plt.subplots(figsize=(10,7))
# plot the dots
# 'o' specifies the shape (circle), we can also use 'd' (diamonds), 's' (squares)
ax.plot(x, y, 'o', label="data")
# plot the trend line
# g-- and r-- specify the color to use
ax.plot(x, housing_model.fittedvalues, 'g--.', label="OLS")
# plot upper and lower ci values
ax.plot(x, confidence_interval_upper, 'r--')
ax.plot(x, confidence_interval_lower, 'r--')
# plot legend
ax.legend(loc='best');
So far, our model looks decent. Let’s add some more variables and see how total_unemployed reacts.
到目前为止，我们的模型看起来不错。 让我们添加更多变量，看看total_unemployed如何React的。
### 多元线性回归(Multiple Linear Regression)
Mathematically, multiple linear regression is:
从数学上讲，多元线性回归为：
We know that unemployment cannot entirely explain housing prices. To get a clearer picture of what influences housing prices, we add and test different variables and analyze the regression results to see which combinations of predictor variables satisfy OLS assumptions, while remaining intuitively appealing from an economic perspective.
我们知道失业不能完全解释房价。 为了更清楚地了解影响房价的因素，我们添加并测试了不同的变量，并对回归结果进行了分析，以查看哪些预测变量组合满足OLS假设，同时从经济角度仍然具有直观吸引力。
We arrive at a model that contains the following variables: fed_funds, consumer_price_index, long_interest_rate, and gross_domestic_product, in addition to our original predictor, total_unemployed.
我们到达包含以下变量的模型： fed_fundsconsumer_price_indexlong_interest_rategross_domestic_product ，除了我们原来的预测， total_unemployed
Adding the new variables decreased the impact of total_unemployed on housing_price_index. total_unemployed‘s impact is now more unpredictable (standard error increased from 0.41 to 2.399), and, since the p-value is higher (from 0 to 0.943), less likely to influence housing prices.
添加新变量减少了total_unemployedhousing_price_index的影响。 现在total_unemployed的影响更加不可预测（ 标准误从0.41增加到2.399），并且由于p值较高（从0到0.943），因此影响房价的可能性较小。
Although total_unemployed may be correlated with housing_price_index, our other predictors seem to capture more of the variation in housing prices. The real-world interconnectivity among our variables can’t be encapsulated by a simple linear regression alone; a more robust model is required. This is why our multiple linear regression model’s results change drastically when introducing new variables.
尽管total_unemployed可能与housing_price_index相关housing_price_index ，但我们的其他预测变量似乎捕获了更多的房价变化。 我们变量之间的真实世界互连性不能仅通过简单的线性回归来封装。 需要一个更强大的模型。 这就是为什么我们的多元线性回归模型的结果在引入新变量时会发生巨大变化的原因。
That all our newly introduced variables are statistically significant at the 5% threshold, and that our coefficients follow our assumptions, indicates that our multiple linear regression model is better than our simple linear model.
我们所有新引入的变量在5％阈值处具有统计显着性，并且我们的系数遵循我们的假设，这表明我们的多元线性回归模型优于我们的简单线性模型。
The code below sets up a multiple linear regression with our new predictor variables.
下面的代码使用我们的新预测变量建立了多元线性回归。
Out[27]:
出[27]：
Dep. Variable: 部门 变量： R-squared: R平方： housing_price_index housing_price_index 0.980 0.980 OLS 最小二乘 0.974 0.974 Least Squares 最小二乘 168.5 168.5 Fri, 17 Feb 2017 2017年2月17日，星期五 7.32e-14 7.32e-14 18:02:42 18:02:42 -55.164 -55.164 23 23 122.3 122.3 17 17 129.1 129.1 5 5 nonrobust 不稳健
coef ef std err 标准错误 t Ť P>|t| P> | t | [95.0% Conf. Int.] [95.0％Conf。 整数] -389.2234 -389.2234 187.252 187.252 -2.079 -2.079 0.053 0.053 -784.291 5.844 -784.291 5.844 -0.1727 -0.1727 2.399 2.399 -0.072 -0.072 0.943 0.943 -5.234 4.889 -5.234 4.889 5.4326 5.4326 1.524 1.524 3.564 3.564 0.002 0.002 2.216 8.649 2.216 8.649 32.3750 32.3750 9.231 9.231 3.507 3.507 0.003 0.003 12.898 51.852 12.898 51.852 0.7785 0.7785 0.360 0.360 2.164 2.164 0.045 0.045 0.020 1.537 0.020 1.537 0.0252 0.0252 0.010 0.010 2.472 2.472 0.024 0.024 0.004 0.047 0.004 0.047
Omnibus: 综合： Durbin-Watson: 杜宾·沃森： 1.363 1.363 1.899 1.899 0.506 0.506 1.043 1.043 -0.271 -0.271 0.594 0.594 2.109 2.109 4.58e+06 4.58e + 06
### 再看偏回归图(Another Look at Partial Regression Plots)
Now let’s plot our partial regression graphs again to visualize how the total_unemployed variable was impacted by including the other predictors. The lack of trend in the partial regression plot for total_unemployed (in the figure below, upper right corner), relative to the regression plot for total_unemployed (above, lower left corner), indicates that total unemployment isn’t as explanatory as the first model suggested. We also see that the observations from the latest variables are consistently closer to the trend line than the observations for total_unemployment, which reaffirms that fed_funds, consumer_price_index, long_interest_rate, and gross_domestic_product do a better job of explaining housing_price_index.
现在，让我们再次绘制局部回归图，以可视化通过包含其他预测变量对total_unemployed变量的影响。 相对于total_unemployed回归图 （上方，左下角）， total_unemployed的局部回归图（ total_unemployed图中，右上角）缺少趋势，这表明总失业率不像第一个模型那样具有解释性。 建议 。 我们还看到，与total_unemployment的观察total_unemployment ，最新变量的观察始终比趋势线更接近趋势线，这再次表明fed_fundsconsumer_price_indexlong_interest_rategross_domestic_product的说明housing_price_index更好地解释housing_price_index
These partial regression plots reaffirm the superiority of our multiple linear regression model over our simple linear regression model.
这些部分回归图重申了我们的多元线性回归模型优于简单线性回归模型的优势。
# this produces our six partial regression plots
fig = plt.figure(figsize=(20,12))
fig = sm.graphics.plot_partregress_grid(housing_model, fig=fig)# this produces our six partial regression plots
fig = plt.figure(figsize=(20,12))
fig = sm.graphics.plot_partregress_grid(housing_model, fig=fig)
### 结论(Conclusion)
We have walked through setting up basic simple linear and multiple linear regression models to predict housing prices resulting from macroeconomic forces and how to assess the quality of a linear regression model on a basic level.
我们已经逐步建立了基本的简单线性和多重线性回归模型，以预测由宏观经济力量产生的房价，以及如何在基本水平上评估线性回归模型的质量。
To be sure, explaining housing prices is a difficult problem. There are many more predictor variables that could be used. And causality could run the other way; that is, housing prices could be driving our macroeconomic variables; and even more complex still, these variables could be influencing each other simultaneously.
可以肯定的是，解释房价是一个难题。 还有更多可以使用的预测变量。 因果关系可以相反。 也就是说，房价可能会推动我们的宏观经济变量； 甚至更复杂的是，这些变量可能同时相互影响。
I encourage you to dig into the data and tweak this model by adding and removing variables while remembering the importance of OLS assumptions and the regression results.
我鼓励您深入研究数据并通过添加和删除变量来调整该模型，同时记住OLS假设和回归结果的重要性。
Most importantly, know that the modeling process, being based in science, is as follows: test, analyze, fail, and test some more.
最重要的是，要知道基于科学的建模过程如下：测试，分析，失败和测试更多。
• No Lit Review: While it’s tempting to dive in to the modeling process, ignoring the existing body of knowledge is perilous. A lit review might have revealed that linear regression isn’t the proper model to predict housing prices. It also might have improved variable selection. And spending time on a lit review at the outset can save a lot of time in the long run.
• Small sample size: Modeling something as complex as the housing market requires more than six years of data. Our small sample size is biased toward the events after the housing crisis and is not representative of long-term trends in the housing market.
• Multicollinearity: A careful observer would’ve noticed the warnings produced by our model regarding multicollinearity. We have two or more variables telling roughly the same story, overstating the value of each of the predictors.
• Autocorrelation: Autocorrelation occurs when past values of a predictor influence its current and future values. Careful reading of the Durbin-Watson score would’ve revealed that autocorrelation is present in our model.
In a future post, we’ll attempt to resolve these flaws to better understand the economic predictors of housing prices.
• 暂无评论 ：尽管很想进入建模过程，但忽略现有知识是危险的。 轻描淡写的评论可能表明线性回归并不是预测房价的合适模型。 它还可能改善了变量选择。 从一开始就花时间进行简短的评论就可以节省很多时间。
• 样本量小 ：对像住房市场这样复杂的事物进行建模需要超过六年的数据。 我们的小样本样本倾向于住房危机后的事件，并不代表住房市场的长期趋势。
• 多重共线性：细心的观察者会注意到我们的模型产生的关于多重共线性的警告。 我们有两个或多个变量讲述的故事大致相同，从而夸大了每个预测变量的价值。
• 自相关 ：当预测变量的过去值影响其当前值和将来值时，就会发生相关。 仔细阅读Durbin-Watson分数将表明我们的模型中存在自相关。
在以后的文章中，我们将尝试解决这些缺陷，以更好地了解房价的经济预测因素。
pandas 线性回归
展开全文
• 通过使用Python、pandas和statsmodels线性回归预测房屋的价格在这篇文章中，我们将逐步通过建立线性回归模型来预测经济活动导致的房屋价格。其中涵盖的主题包括：1. 什么是回归2. 变量的选择3. 利用pandas读取数据4....
Python部落(python.freelycode.com)组织翻译，禁止转载，欢迎转发。
通过使用Python、pandas和statsmodels线性回归预测房屋的价格
在这篇文章中，我们将逐步通过建立线性回归模型来预测经济活动导致的房屋价格。其中涵盖的主题包括：
1. 什么是回归
2. 变量的选择
3. 利用pandas读取数据
4. 普通最小二乘假设
5. 一元线性回归
6. 回归图像
7. 多元线性回归
8. 另一个角度看偏回归图像
9. 总结
10. 实际浏览内容的缺陷
未来的文章将涵盖例如探索性分析、回归诊断和先进的回归模型等话题，但是我打算先跳过这些，以便读者可以试着动手处理数据。
什么是回归？
线性回归是一个模型，通过预测因变量(绘制在垂直或y轴上)和预测变量之间的正比例关系，从而绘制出一条直线，如图所示：
当进行建模过程时，我们会更详细地讨论线性回归。
变量的选择
我们将使用房价指数(HPI)作为因变量，通过房价指数测量住宅房的价格变动。
而对于预测变量，我们选择对宏观经济活动有影响的指标，例如失业率、利率和国内生产总值(总生产率)，这样选择完全是出于直觉。对于这些变量的解释，以及它们是如何影响房价的解释，以及所有的源数据都在https://github.com/LearnDataSci/blog-post-resources/tree/master/Housing%20Price%20Index%20Regression。
利用pandas读取数据
拥有数据后，为了便于分析，我们可以调用merge方法将数据合并在一个简单的数据帧内。其中一些数据是按月份记录，而另一些是按季度记录。不必担心。我们依据某一列来合并数据帧，所以每个用于测量目的行都在其该在的位置。在下面的例子中，合并的最佳列是日期列，看下图。
日期 sp500 居民消费价格指数 长期利率 房价指数 总失业率
0 2011-01-01 1282.62 220.22 3.39 181.35 16.2
1 2011-04-01 1331.51 224.91 3.46 180.80 16.1
2 2011-07-01 1325.19 225.92 3.00 184.25 15.9
3 2011-10-01 1207.22 226.42 2.15 181.51 15.8
4 2011-01-01 1300.58 226.66 1.97 179.13 15.2
超过15周 没有在工会找到工作的 多份工作 离开者 失败者 联邦基金利率
0 8393 2800 6816 6.5 60.1 0.17
1 8016 2466 6823 6.8 59.4 0.10
2 8177 2785 6850 6.8 59.2 0.07
3 7802 2555 6917 8.0 57.9 0.07
4 7433 2809 7022 7.4 57.1 0.08
支出总额 劳动力的公关 生产者价格指数 国内生产总值
0 5766.7 64.2 192.7 14881.3
1 5870.8 64.2 203.1 14989.6
2 5802.6 64.0 204.6 15021.1
3 5812.9 64.1 201.1 15190.3
4 5765.7 63.7 200.7 15291.0
通常聚集数据的下一步将会是探索性分析。探索性分析是我们分析变量过程的一部分(通过画图和描述性统计)和得出对于因变量最好的预测因素。为了简洁，我们将跳过探索性分析。将探索性分析记在你的脑海中，它非常重要，尽管在现实中跳过它将会影响预测额结果。
我们将使用普通最小二乘法(OLS)，一个基本的但功能强大的方法来评估我们的模型。
普通最小二乘假设
OLS测量了一个线性回归模型的准确性。
OLS是基于假设，如果成立，则表明该模型大概是一个正确的透镜，通过它可以解释我们的数据。但如果假设不成立，模型的结论会失去它的有效性。所以你应该采取额外的努力来选择正确的模型，不应该有个人神秘主义和小题大做的毛病。
下面是一些OLS的假设：
1. 线性关系：一个线性关系存在于因变量和预测变量之间。而如果没有线性关系存在，线性回归不是一个解释我们数据的正确模型。
3. 零条件均值：观察与趋势线的平均距离(或残差)为0。结果有些是积极的，有些是消极的，但它们不会偏向于一组值。
4. 同方差性：因变量的确定性(或不确定性)是等价映射一个预测变量的所有值；也就是说在残差中没有模式。即在统计学术语中，方差是不变的。
5. 无自相关(序列相关性)：自相关是指变量在观测中与本身相关。例如，如果某一天的股价影响第二天的股票价格，那么股票价格可能会连续相关的。
让我们开始建模吧。
一元线性回归
一元线性回归使用了一个预测变量来解释一个因变量。一元线性回归方程如下：
其中：
y=因变量，
ß=回归系数，
α=截距(即当独立变量为0时的预期平均价格)，
x=用来预测Y的预测变量(或独立变量)，
ε=误差项，占我们模型无法解释的随机性的比例。
使用statsmodels的ols函数，构造我们的模型，设定房价指数作为总失业率的一个函数。我们假定总的失业人数的增长将迫使房价下降。可能这样是错的，但我们至少得从某个方面先开始！
下面的代码展示了如何将总失业率作为预测变量的一元线性回归模型。
Out[24]:
OLS回归的结果如下：
部分变量 房价指数 决定系数 0.952
模型 OLS 邻近决定系数 0.949
方法 最小二乘法 F-统计量 413.2
日期 2017年2月17日，星期五 概率(F-统计量) 2.71e-15
时间 17:57:05 对数似然 -65.450
观测次数 23 AIC 134.9
Df残差 21 BIC 137.2
Df模型 1
协方差类型 覆盖
协同系数 标准差 t P>|t| [95.0%Conf.Int]
截距 313.3128 5.408 57.938 0.000 302.067
324.559
总失业率 -8.3324 0.410 -20.327 0.000 -9.185
-7.480
综合性 0.492 杜宾-沃森 1.126
概率(综合性) 0.782 雅克-贝拉(JB) 0.552
倾斜 0.294 概率(JB) 0.759
峰态 2.521 Cond.No. 78.9
回归系数(coef)表示因变量的改变导致预测变量一个单位的改变，而其他变量保持不变。在我们的模型中，总失业率一个单位的增加会减少8.33的房价指数。符合我们的假设，失业率的增加似乎会降低房价。
标准差测量了总失业率系数的准确性，通过评估在相同的测试运行在不同样本的人口的情况下得到的系数变化。我们的标准差0.41是比较低的，所以表现得比较准确。
P值指当总失业率没有变化的情况下，房价指数降低8.33的可能性，即假定这两个变量之间没有关系。一个低的p值表明这些结果具有统计显著性，即通常情况下p值低于0.05。
置信区间是一个系数可能下降在内部的范围。我们有95%的自信说，总失业率的系数将落在[-9.185,-7.480]的置信区间内。
让我们使用statsmodels的plot_regress_exog函数来帮助我们理解我们的模型。
回归图像
请看下面的四幅图像。
1. “Y和拟合x”图绘制了因变量相对于我们的预测值与置信区间。相反的关系在图中表明房价指数与总失业率是负相关的，例如当一个变量增加时另一个变量减少。
2．“残差与总失业率”的图像显示了模型关于确定预测变量对应的误差。图像中每一个具体的点都是观测的值；图中的线表示那些观测值得平均值。因为有些点与平均没有距离关系，所以OLS假设同方差性成立。
3.“偏回归图像”显示了房价指数与总失业率之间的关系，考虑到在已存在的总失业率的协同因素中添加其他独立变量的影响。之后我们会看到当增加更多的变量后同样的图像会怎样变化。
4.分量和分量加残差的图像是一个偏回归图像的扩展，但显示了在总失业率的协同因素中添加了其他的独立变量后，增加的影响使得趋势线有错误。更多有关图像在这里。
下一张图描绘了我们的趋势线(绿色)，观测值(点)和我们的置信区间(红色)。
到目前为止，我们的模型看上去不错，让我们增加更多的变量来看看会对总失业率产生怎样的影响。
多元线性回归
数学角度的多元线性回归方程为：
我们知道失业率不能完全解释房价。为了得到更能说明影响房价的图像，我们增加并测试了不同变量并通过分析回归结果得到了不同预测变量中更满足OLS假设的组合，同时从经济角度也保持了直观的吸引力。
我们得到的模型包含如下的变量：
联邦基金、居民消费价格指数、长期利率和国内生产总值，除此之外还有我们最初的预测变量，总失业率。
增加的新变量降低了总失业率对房价指数的影响，总失业率的影响是最不可预知的(标准误差从0.41增加到2.399)，而且因为p值更高(从0增长到0.943)，所以总失业率不太可能影响到房价。
虽然总失业率可能与房价指数是有关联的，我们的其他预测变量似乎是为抓住更多的房价的变化。我们给出的变量在现实生活中联系不能仅仅由一个一元线性回归封装；我们需要一个更具有鲁棒性的模型。这就是为什么当我们引入新变量时，得到的多元线性回归模型的结果发生了巨大的改变。
我们所有新引入的变量在5%阈值上具有统计学显著性，而且伴随我们假设的系数表明，我们的多元线性回归模型比一元线性回归模型更好。
下面的代码利用我们的新预测变量建立起了多元线性回归。
Out[27]: OLS回归结果
部分变量 房价指数 决定系数 0.980
模型 OLS 邻近决定系数 0.974
方法 最小二乘法 F-统计量 168.5
日期 2017年2月17日，星期五 概率(F-统计量) 7.32e-14
时间 18:02:42 对数似然 -55.164
观测次数 23 AIC 122.3
Df残差 17 BIC 129.1
Df模型 5
协方差类型 覆盖
协同系数 标准差 t P>|t| [95%Conf.Int.]
截距 -389.2234 187.252 -2.079 0.053 -784.291
5.844
总失业率 -0.1727 2.399 -0.072 0.943 -5.234
4.889
长期利率 5.4326 1.524 3.564 0.002 2.216
8.649
联邦基金利率 32.3750 9.231 3.507 0.003 12.898
51.852
居民消费价格指数 0.7785 0.360 2.164 0.045 0.020
1.537
国内生产总值 0.0252 0.010 2.472 0.024 0.004
0.047
综合性 1.363 杜宾-沃森 1.899
概率(综合性) 0.506 雅克-贝拉(JB) 1.043
倾斜 -0.271 概率(JB) 0.594
峰态 2.109 Cond.No. 4.58e+06
另一个角度看偏回归图像
现在让我们再次画出偏回归图像，以显示出通过包含其他预测变量导致总失业率变量是如何被影响的。总失业率在偏回归图像中缺少趋势(在上面的右上角图)，相对于回归图的总失业率(上面的左下角图)，表明了总失业率的作用并不是像第一个模型解释的那样。我们也看到最新变量所观测到的值始终比总失业率的观测值更接近于趋势线。重复一遍，联邦基金、居民消费价格指数、长期利率和国内生产总值对房价指数有更好的解释。
这些偏回归图像重申了多元线性回归模型较于一元线性回归模型的优越性。
总结
我们已经通过建立基本的一元线性和多元线性回归模型来预测宏观经济力量造成的房价和如何评估质量的线性回归模型的基本水平。
可以肯定的是，解释房价是一个难题。有许多可以使用的预测变量。因果关系可以以另一种方式运行，即房价可能会推动我们的宏观经济变量，甚至更复杂的，这些变量可能同时相互影响。
我鼓励你深入挖掘数据，通过增加和移除变量来调整这个模型，同时记住OLS假设和回归结果的重要性。
最重要的是，要知道基于科学的建模过程如下：测试，分析，失败和继续进一步的测试。
实际浏览内容的缺陷
本文是对基本的回归模型的入门引导，但是有经验的数据科学家会看到在方法和模型中存在几个缺陷，如下：
没有点燃审查：虽然很容易深入到建模过程中，但忽略了现存的知识结构是危险的。一个点燃的回顾可能表明，线性回归可能不是正确预测房价的模型。它也可能有改进的变量选择。从长远来看，在一开始花时间做一次点燃审查可以节省大量的时间。
小样本：建模复杂的房屋市场需要超过六年的数据。我们的小样本是偏向住房危机后的事件，并不代表房地产市场的长期趋势。
多重共线性： 一个细心的观察者会注意到警告模型关于多重共线性的产生。我们有两个或两个以上变量得到大致相同的结果，通过高估每一个预测变量的意义。
自相关：当预测的过去值影响其当前和未来值时会发生自相关。仔细阅读的杜宾-沃森评分将揭示，自相关的情况是存在于我们的模型中。
在未来的文章中，我们将试图解决这些缺陷，以更好地理解关于房价的经济预测。
英文原文：http://www.learndatasci.com/predicting-housing-prices-linear-regression-using-python-pandas-statsmodels/?imm_mid=0eddcf&cmp;=em-data-na-na-newsltr_20170301
译者：一叶障慕
展开全文
• Deciphering解读 the Markets with Technical Analysis In this chapter, we will go through some popular methods of technical analysis and show how to apply them while analyzing market data....
Deciphering解读 the Markets with Technical Analysis
In this chapter, we will go through some popular methods of technical analysis and show how to apply them while analyzing market data. We will perform basic algorithmic trading using market trends, support, and resistance.
You may be thinking of how we can come up with our own strategies? And are there any naive strategies that worked in the past that we can use by way of reference?
As you read in the first chapter https://blog.csdn.net/Linli522362242/article/details/121337016, mankind has been trading assets for centuries. Numerous strategies have been created to increase the profit or sometimes just to keep the same profit. In this zero-sum game, the competition is considerable. It necessitates a constant innovation in terms of trading models and also in terms of technology. In this race to get the biggest part of the pie first, it is important to know the basic foundation of analysis in order to create trading strategies. When predicting the market, we mainly assume that the past repeats itself in future. In order to predict future prices and volumes, technical analysts study the historical market data. Based on behavioral economics and quantitative analysis, the market data is divided into two main areas.
First, are chart patterns. This side of technical analysis is based on recognizing trading patterns and anticipating[ænˈtɪsɪpeɪtɪŋ]预期 when they will reproduce in the future. This is usually more difficult to implement.
Second, are technical indicators. This other side uses mathematical calculation to forecast the financial market direction. The list of technical indicators is sufficiently long to fill an entire book on this topic alone, but they are composed of a few different principal domains: trend, momentum, volume, volatility, and support and resistance. We will focus on the support and resistance strategy as an example to illustrate one of the most well-known technical analysis approaches.
In this chapter, we will cover the following topics:
• Designing a trading strategy based on trend-and momentum-based indicators
• Creating trading signals based on fundamental technical analysis
# Designing a trading strategy based on trend-and momentum-based indicators
Trading strategies based on trend and momentum are pretty similar. If we can use a metaphor比喻 to illustrate the difference, the trend strategy uses speed, whereas the momentum strategy uses acceleration. With the trend strategy, we will study the price historical data. If this price keeps increasing for the last fixed amount of days, we will open a long position (Long positions make money when market prices are higher than the price of the position, and lose money when market prices are lower than the price of the position.) by assuming that the price will keep raising.
The trading strategy based on momentum is a technique where we send orders based on the strength of past behavior. The price momentum is the quantity of motion that a price has. The underlying rule is to bet that an asset price with a strong movement in a given direction will keep going in the same direction in the future. We will review a number of technical indicators expressing momentum in the market. Support and resistance are examples of indicators predicting future behavior.
## Support and resistance indicators
In the first chapter, we explained the principle of the evolution of prices based on supply and demand. The price decreases when there is an increase in supply, and the price increases when demand rises.
• When there is a fall in price, we expect the price fall to pause due to a concentration of demands需求集中( since people will flatten the position and convert the unrealized loss to realized loss for reducing future loss). This virtual limit will be referred to as a support line. Since the price becomes lower, it is more likely to find buyers.
• Inversely, when the price starts rising, we expect a pause in this increase due to a concentration of supplies供应集中( since people will flatten the position and convert the unrealized profit to realized profit ). This is referred to as the resistance line. It is based on the same principle, showing that a high price leads sellers to sell.
This exploits the market psychology of investors following this trend of buying when the price is low and selling when the price is high.
To illustrate an example of a technical indicator (in this part, support and resistance), we will use the Google data from the first chapter https://blog.csdn.net/Linli522362242/article/details/121337016. Since you will use the data for testing many times, you should store this data frame to your disk. Doing this will help you save time when you want to replay the data. To avoid complications with stock split, we will only take dates without splits. Therefore, we will keep only 620 days. Let's have a look at the following code:
import pandas as pd
start_date = '2014-01-01'
end_date = '2018-01-01'
SRC_DATA_FILENAME = 'goog_data.pkl'
try:
except:
# Call the function DataReader from the class data
goog_data2 = data.DataReader( 'GOOG', # ticker
'yahoo', # source
start_date, end_date
)
goog_data2.to_pickle( SRC_DATA_FILENAME )
In the following code, the following applies:
import matplotlib.pyplot as plt
fig = plt.figure( figsize=(8,6) )
ax1.plot( highs, color='c', lw=2. )
ax1.plot( lows, color='y', lw=2. )
lows.index.values[-1],
linewidth=2, color='g'
)
lows.index.values[-1],
linewidth=2, color='r'
)
# why not use .vlines since it need to provide the values of ymin and ymax
plt.axvline( x=lows.index.values[200], # ymin=0, ymax=1
linewidth=3, color='b', linestyle='--'
)
plt.setp( ax1.get_xticklabels(), rotation=45, horizontalalignment='right', fontsize=12 )
# plt.xticks(fontsize=14)
plt.yticks(fontsize=12)
ax1.set_ylabel('Google price in ', fontsize=14, rotation=90) plt.show() In this plot, the following applies: • We draw the highs and lows of the GOOG price. • The green line represents the resistance level( highs.head(200).max() = 789.869995 ), and the red line represents the support level( lows.head(200).min() = 565.04998779). • To build these lines, we use the maximum value of the GOOG price and the minimum value of the GOOG price stored daily. • After the 200th day (dotted vertical blue line), we will buy when we reach the support line, and sell when we reach the resistance line. In this example, we used 200 days so that we have sufficient data points to get an estimate of the trend. • It is observed that the GOOG price will reach the resistance line around August 2016. This means that we have a signal to enter a short position (sell). • Once traded, we will wait to get out of this short position when the GOOG price will reach the support line. • With this historical data, it is easily noticeable that this condition will not happen. This will result in carrying a short position in a rising market without having any signal to sell it, thereby resulting in a huge loss. • This means that, even if the trading idea based on support/resistance has strong grounds根据 in terms of economical behavior, in reality, we will need to modify this trading strategy to make it work. • Moving the support/resistance line to adapt to the market evolution will be key to the trading strategy efficiency. In the middle of the following chart, we show three fixed-size time windows. We took care of adding the tolerance margin that we will consider to be sufficiently close to the limits (support and resistance): import matplotlib.pyplot as plt fig = plt.figure( figsize=(10,6) ) ax1 = fig.add_subplot( 111 ) ax1.plot( highs, color='c', lw=2. ) ax1.plot( lows, color='y', lw=2. ) plt.hlines( highs.head(200).max(), lows.index.values[0], lows.index.values[-1], linewidth=2, color='g' ) plt.hlines( lows.head(200).min(), lows.index.values[0], lows.index.values[-1], linewidth=2, color='r' ) # adding the tolerance margin to be close to the limits (support and resistance) plt.fill_betweenx( [ highs.head(200).max()*0.96, highs.head(200).max() ], lows.index.values[200], lows.index.values[400], facecolor='green', alpha=0.5 ) plt.fill_betweenx( [ lows.head(200).min(), lows.head(200).min() * 1.05 ], lows.index.values[200], lows.index.values[400], facecolor='r', alpha=0.5 ) # why not use .vlines since it need to provide the values of ymin and ymax plt.axvline( x=lows.index.values[200], # ymin=0, ymax=1 linewidth=3, color='b', linestyle='--' ) plt.axvline( x=lows.index.values[400], # ymin=0, ymax=1 linewidth=3, color='b', linestyle=':' ) plt.setp( ax1.get_xticklabels(), rotation=45, horizontalalignment='right', fontsize=12 ) # plt.xticks(fontsize=14) plt.yticks(fontsize=12) ax1.set_ylabel('Google price in', fontsize=14, rotation=90)
plt.show()
If we take a new 200-day window after the first one, the support/resistance levels will be recalculated. We observe that the trading strategy will not get rid of the GOOG position (while the market keeps raising) since the price does not go back to the support level.
Since the algorithm cannot get rid of a position, we will need to add more parameters to change the behavior in order to enter a position. The following parameters can be added to the algorithm to change its position:
• There can be a shorter rolling window.
• We can count the number of times the price reaches a support or resistance line.
• A tolerance margin can be added to consider that a support or resistance value can attain around a certain percentage of this value.
This phase is critical when creating your trading strategy. You will start by observing how your trading idea will perform using historical data, and then you will increase the number of parameters of this strategy to adjust to more realistic test cases.
In our example, we can introduce two further parameters:
• The minimum number of times that a price needs to reach the support/resistance level.
• We will define the tolerance margin of what we consider being close to the support/resistance level.
Let's now have a look at the code:
import pandas as pd
start_date = '2014-01-01'
end_date = '2018-01-01'
SRC_DATA_FILENAME = 'goog_data.pkl'
try:
except:
# Call the function DataReader from the class data
goog_data = data.DataReader( 'GOOG', # ticker
'yahoo', # source
start_date, end_date
)
goog_data.to_pickle( SRC_DATA_FILENAME )
goog_data_signal = pd.DataFrame( index=goog_data.index )
goog_data_signal['price'] = goog_data['Adj Close']
###################
import yfinance as yf
import pandas as pd
start_date = '2014-01-01'
end_date = '2018-01-01'
SRC_DATA_FILENAME = 'goog_data2.pkl'
try:
except:
goog_data2.to_pickle( SRC_DATA_FILENAME )
goog_data2.head()
###################
goog_data_signal.head()
Now, let's have a look at the other part of the code where we will implement the trading strategy:
import numpy as np
# a shorter rolling window.
# tolerance margin of what we consider being close to the support/resistance level
data['sup_tolerance'] = np.zeros( len(data) )
data['res_tolerance'] = np.zeros( len(data) )
# count the number of times the price reaches a support or resistance line.
data['sup_count'] = np.zeros( len(data) )
data['res_count'] = np.zeros( len(data) )
data['sup'] = np.zeros( len(data) )
data['res'] = np.zeros( len(data) )
data['positions'] = np.zeros( len(data) )
data['signal'] = np.zeros( len(data) )
in_support=0
in_resistance=0
# assume len(data) >= 2*window_size, then jump over first window_size,
# and window_size=bin_width
for idx in range( bin_width-1+bin_width, len(data)):
data_section = data[idx-bin_width:idx+1] # start_idx(hidden:jump):idx-bin_width=bin_width-1
# The level of support and resistance is calculated by
# taking the maximum and minimum price and
# then subtracting and adding a 20% margin.
support_level = min( data_section['price'] )
resistance_level = max( data_section['price'] )
data['sup'][idx] = support_level
data['res'][idx] = resistance_level
range_level = resistance_level-support_level
data['sup_tolerance'][idx] = support_level + 0.2*range_level
data['res_tolerance'][idx] = resistance_level - 0.2*range_level
if data['res_tolerance'][idx] <= data['price'][idx] <= data['res'][idx]:
in_resistance+=1
data['res_count'][idx] = in_resistance
elif data['sup'][idx] <= data['price'][idx] <= data['sup_tolerance'][idx]:
in_support+=1
data['sup_count'][idx] = in_support
else:
in_support = 0
in_resistance=0
if in_resistance>2: # The price is continuously hovering within the resistance margin
data['signal'][idx] = 1 # The price may reach or break through the resistance level
elif in_support>2: # The price is continuously hovering within the support margin
data['signal'][idx] = 0 # The price may reach or break through the support level
else:
data['signal'][idx] = data['signal'][idx-1]
data['positions'] = data['signal'].diff()# (long) positions>0 ==> buy, positions=0 ==> wait
# (short) positions<0 ==> sell
trading_support_resistance( goog_data_signal )
goog_data_signal.info()
goog_data_signal.reset_index(inplace=True) ###########
import matplotlib.pyplot as plt
fig = plt.figure(figsize=(8,6))
ax1 = fig.add_subplot( 111, ylabel='Google price in ' ) ax1.plot( goog_data_signal['Date'][40:], goog_data_signal['sup'][40:], color='g', lw=2., label='sup' ) ax1.plot( goog_data_signal['Date'][40:], goog_data_signal['res'][40:], color='b', lw=2., label='res') ax1.plot( goog_data_signal['Date'], goog_data_signal['price'], color='r', lw=2., label='price' ) # draw an up arrow when we buy one Google share: ax1.plot( goog_data_signal[ goog_data_signal.positions == 1 ]['Date'], goog_data_signal[ goog_data_signal.positions == 1 ]['price'], '^', markersize=7, color='k', label='buy', ) ax1.plot( goog_data_signal.loc[goog_data_signal.positions==-1.0]['Date'], goog_data_signal[goog_data_signal.positions == -1.0]['price'], 'v', markersize=7, color='y', label='sell', ) ax1.set_xlabel('Date') plt.setp( ax1.get_xticklabels(), rotation=45, horizontalalignment='right' ) plt.legend() plt.show() The codes will return the following output. The plot shows a 20-day rolling window calculating resistance and support(note we jump over fist window (window_size=20), use the data from second window_size) From this plot, it is observed that a buy order is sent when a price stays in the resistance tolerance margin for 2 consecutive days, and that a sell order is sent when a price stays in the support tolerance margin for 2 consecutive days. ############################ why we jumped over fist window (window_size=20), used the data from second window_size? import pandas as pd from pandas_datareader import data start_date = '2014-01-01' end_date = '2018-01-01' SRC_DATA_FILENAME = 'goog_data.pkl' try: goog_data = pd.read_pickle( SRC_DATA_FILENAME ) print( 'File found...reading GOOG data') except: print( 'File not found...downloading GOOG data') # Call the function DataReader from the class data goog_data = data.DataReader( 'GOOG', # ticker 'yahoo', # source start_date, end_date ) goog_data.to_pickle( SRC_DATA_FILENAME ) goog_data_signal = pd.DataFrame( index=goog_data.index ) goog_data_signal['price'] = goog_data['Adj Close'] # a shorter rolling window. def trading_support_resistance( data, bin_width=20 ): # tolerance margin of what we consider being close to the support/resistance level data['sup_tolerance'] = np.zeros( len(data) ) data['res_tolerance'] = np.zeros( len(data) ) # count the number of times the price reaches a support or resistance line. data['sup_count'] = np.zeros( len(data) ) data['res_count'] = np.zeros( len(data) ) data['sup'] = np.zeros( len(data) ) data['res'] = np.zeros( len(data) ) data['positions'] = np.zeros( len(data) ) data['signal'] = np.zeros( len(data) ) in_support=0 in_resistance=0 # assume len(data) >= 2*window_size, then jump over first window_size, # and window_size=bin_width for idx in range( bin_width-1, len(data)):### data_section = data[idx-bin_width+1:idx] # start_idx(hidden:jump):idx-bin_width=bin_width-1 # The level of support and resistance is calculated by # taking the maximum and minimum price and # then subtracting and adding a 20% margin. support_level = min( data_section['price'] ) resistance_level = max( data_section['price'] ) data['sup'][idx] = support_level data['res'][idx] = resistance_level range_level = resistance_level-support_level data['sup_tolerance'][idx] = support_level + 0.2*range_level data['res_tolerance'][idx] = resistance_level - 0.2*range_level if data['res_tolerance'][idx] <= data['price'][idx] <= data['res'][idx]: in_resistance+=1 data['res_count'][idx] = in_resistance elif data['sup'][idx] <= data['price'][idx] <= data['sup_tolerance'][idx]: in_support+=1 data['sup_count'][idx] = in_support else: in_support = 0 in_resistance=0 if in_resistance>2: # The price is continuously hovering within the resistance margin data['signal'][idx] = 1 # The price may reach or break through the resistance level elif in_support>2: # The price is continuously hovering within the support margin data['signal'][idx] = 0 # The price may reach or break through the support level else: data['signal'][idx] = data['signal'][idx-1] data['positions'] = data['signal'].diff()# (long) positions>0 ==> buy, positions=0 ==> wait # (short) positions<0 ==> sell trading_support_resistance( goog_data_signal ) goog_data_signal.reset_index(inplace=True) import matplotlib.pyplot as plt fig = plt.figure(figsize=(8,6)) ax1 = fig.add_subplot( 111, ylabel='Google price in' )
ax1.plot( goog_data_signal['Date'][20:],###
goog_data_signal['sup'][20:], ###
color='g', lw=2., label='sup' )###
ax1.plot( goog_data_signal['Date'][20:],###
goog_data_signal['res'][20:], ###
color='b', lw=2., label='res')
ax1.plot( goog_data_signal['Date'],
goog_data_signal['price'],
color='r', lw=2., label='price'
)
ax1.plot( goog_data_signal[ goog_data_signal.positions == 1 ]['Date'],
goog_data_signal[ goog_data_signal.positions == 1 ]['price'],
)
ax1.plot( goog_data_signal.loc[goog_data_signal.positions==-1.0]['Date'],
goog_data_signal[goog_data_signal.positions == -1.0]['price'],
'v', markersize=7, color='y', label='sell',
)
ax1.set_xlabel('Date')
plt.setp( ax1.get_xticklabels(), rotation=45, horizontalalignment='right' )
plt.legend()
plt.show()
vs We found that the adjusted close price line overlaps with the support level line, and it is very dangerous to fail to respond in time ( without selling the goog share will let us lose more money)
## Backtesting
initial_capital = float( 1000.0 )
positions = pd.DataFrame( index=goog_data_signal.index ).fillna(0.0)
portfolio = pd.DataFrame( index=goog_data_signal.index ).fillna(0.0)
# Next, we will store the GOOG positions in the following data frame:
positions['GOOG'] = goog_data_signal['signal'] # 1(buy): daily_difference > 0, 0(sell): daily_difference <= 0
# Then, we will store the amount of the GOOG positions for the portfolio in this one:
portfolio['positions'] = ( positions.multiply( goog_data_signal['price'],
axis=0
)
)
# Next, we will calculate the non-invested money (cash or remaining cash):
# positions.diff() == goog_data_signal['positions']
# +1 : buy, -1: sell, 0:you not have any position on the market
portfolio['cash'] = initial_capital - ( positions.diff().multiply( goog_data_signal['price'],
axis=0
)
).cumsum() # if current row in the result of cumsum() <0 : +profit + cash
# if current row in the result of cumsum() >0 : -loss + cash
# The total investment will be calculated by summing the positions and the cash:
portfolio['total'] = portfolio['positions'] + portfolio['cash']
fig = plt.figure( figsize=(8,6) )
ax.plot( goog_data_signal['Date'], portfolio)
plt.setp( ax.get_xticklabels(), rotation=45, horizontalalignment='right' )
ax.set_xlabel('Date')
# ['positions', 'cash', 'total']
ax.legend(portfolio.columns, loc='upper left')
plt.show()
stackplot: total = current cash+ current stock price
When we create a trading strategy, we have an initial amount of money (cash). We will invest this money (holdings). This holding value is based on the market value of the investment. If we own a stock and the price of this stock increases, the value of the holding will increase. When we decide to sell, we move the value of the holding corresponding to this sale to the cash amount. The sum total of the assets is the sum of the cash and the holdings. The preceding chart shows that the strategy is profitable since the amount of cash increases toward the end. The graph allows you to check whether your trading idea can generate money.
############################
In this section, we learned the difference between trend and momentum trading strategies( the trend strategy uses speed(each day price move), whereas the momentum strategy uses acceleration(rolling window)), and we implemented a very well used momentum trading strategy based on support and resistance levels. We will now explore new ideas to create trading strategies by using more technical analysis.
# Creating trading signals based on fundamental technical analysis
This section will show you how to use technical analysis to build trading signals. We will start with one of the most common methods, the simple moving average, and we will discuss more advanced techniques along the way. Here is a list of the signals we will cover:
• Simple Moving Average (SMA)
• Exponential Moving Average (EMA)
• Absolute Price Oscillator (APO)
• Moving Average Convergence Divergence (MACD)
• Bollinger Bands (BBANDS)
• Relative Strength Indicator (RSI)
• Standard Deviation (STDEV)
• Momentum (MOM)
## Simple moving average
Simple moving average, which we will refer to as SMA, is a basic technical analysis indicator. The simple moving average, as you may have guessed from its name, is computed by adding up the price of an instrument over a certain period of time divided by the number of time periods. It is basically the price average over a certain time period, with equal weight being used for each price. The time period over which it is averaged is often referred to as the lookback period or history. Let's have a look at the following formula of the simple moving average:
Here, the following applies:
• : Price at time period i
• : Number of prices added together or the number of time periods
Let's implement a simple moving average that computes an average over a 20-day moving window. We will then compare the SMA values against daily prices, and it should be easy to observe the smoothing that SMA achieves.
import pandas as pd
start_date = '2014-01-01'
end_date = '2018-01-01'
SRC_DATA_FILENAME = 'goog_data.pkl'
try:
except:
# Call the function DataReader from the class data
goog_data2 = data.DataReader( 'GOOG', # ticker
'yahoo', # source
start_date, end_date
)
goog_data2.to_pickle( SRC_DATA_FILENAME )
goog_data = goog_data2.tail(620)
goog_data.head()
### Implementation of the simple moving average
In this section, the code demonstrates how you would implement a simple moving average, using a list (history) to maintain a moving window of prices and a list (SMA values) to maintain a list of SMA values: == goog_data['Close'].rolling(window=20, min_periods=1).mean()
close = goog_data['Close']
import statistics as stats
time_period = 20 # number of days over which to average
history = [] # to track a history of prices
sma_values = [] # to track simple moving average values
for close_price in close:
history.append( close_price )
if len(history) > time_period: # we remove oldest price because we only
del( history[0] ) # average over last ' time_period' prices
sma_values.append( stats.mean(history) )
goog_data = goog_data.assign( ClosePrice = pd.Series( close,
index = goog_data.index
)
)
goog_data = goog_data.assign( Simple20DayMovingAverage = pd.Series( sma_values,
index = goog_data.index
)
)
goog_data.head()
goog_data.tail()
close_price = goog_data['ClosePrice']
sma = goog_data['Simple20DayMovingAverage']
import matplotlib.pyplot as plt
import datetime
import matplotlib.ticker as ticker
fig = plt.figure( figsize= (10,6) )
ax1 = fig.add_subplot(111, xlabel='Date', ylabel='Google close price in ') ax1.plot( goog_data.index.values, close_price, color='g', lw=2., label='close_price' ) ax1.plot( goog_data.index.values, sma, color='r', lw=2., label='sma' ) ax1.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10 # or plt.autoscale(enable=True, axis='x', tight=True) ax1.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis) ax1.margins(0,0.05) # move all curves to up from matplotlib.dates import DateFormatter ax1.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08 plt.setp( ax1.get_xticklabels(), rotation=30, horizontalalignment='right' ) plt.legend() plt.show() In this plot, it is easy to observe that the 20-day SMA has the intended smoothing effect and evens out拉平 the micro-volatility in the actual stock price, yielding a more stable price curve. ### use rolling() to calculate SMA goog_data['SMA_20'] = goog_data['Close'].rolling(20).mean() goog_data[:25] close_price = goog_data['ClosePrice'] sma = goog_data['SMA_20'] ### import matplotlib.pyplot as plt import datetime import matplotlib.ticker as ticker fig = plt.figure( figsize= (10,6) ) ax1 = fig.add_subplot(111, xlabel='Date', ylabel='Google close price in')
ax1.plot( goog_data.index.values, close_price, color='g', lw=2., label='close_price' )
ax1.plot( goog_data.index.values, sma, color='r', lw=2., label='sma' )
ax1.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10
# or plt.autoscale(enable=True, axis='x', tight=True)
ax1.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis)
ax1.margins(0,0.05) # move all curves to up
from matplotlib.dates import DateFormatter
ax1.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08
plt.setp( ax1.get_xticklabels(), rotation=30, horizontalalignment='right' )
plt.legend()
plt.show()
Note the difference from the previous sma curve: the value of sma is NaN in the first 20 days.
min_periods int, default None
Minimum number of observations in window required to have a value (otherwise result is NA). For a window that is specified by an offset, min_periods will default to 1. Otherwise, min_periods will default to the size of the window.
goog_data['SMA_20'] = goog_data['Close'].rolling(window=20, min_periods=1).mean()
goog_data[:25]
### SMA from yahoo finance
yahoo fiance uses interval = 1W to make the goog stock close price smoother, so if you use SMA=20, the curve will be more frequent, so you can only set SMA=5, so that the moving average you see will be more similar to what we drew
## Exponential moving average
The exponential moving average, which we will refer to as the EMA, is the single most well-known and widely used technical analysis indicator for time series data.
The EMA is similar to the simple moving average, but, instead of weighing all prices in the history equally, it places more weight on the most recent price observation and less weight on the older price observations. This is endeavoring to capture the intuitive idea that the new price observation has more up-to-date information than prices in the past. It is also possible to place more weight on older price observations and less weight on the newer price observations. This would try to capture the idea that longer-term trends have more information than short-term volatile price movements.
The weighting depends on the selected time period of the EMA;
• the shorter the time period, the more reactive越强烈 the EMA is to new price observations; in other words, the EMA converges to new price observations faster and forgets older observations faster, also referred to as Fast EMA.
• The longer the time period, the less reactive the EMA is to new price observations; that is, EMA converges to new price observations slower and forgets older observations slower, also referred to as Slow EMA.
Based on the description of EMA, it is formulated as a weight factor, applied to new price observations and a weight factor applied to the current value of EMA(to get the new value of EMA. Since the sum of the weights should be 1 to keep the EMA units the same as price units, that is, $s, the weight factor applied to EMA() values turns out to be . Hence, we get the following two formulations of new EMA values based on old EMA values and new price observations, which are the same definitions, written in two different forms: OR Alternatively, we have the following: Here, the following applies: P : Current price of the instrument : EMA value prior to the current price observation : Smoothing constant, most commonly set to n : Number of time periods (similar to what we used in the simple moving average) ### Implementation of the exponential moving average Let's implement an exponential moving average with 20 days as the number of time periods to compute the average over. We will use a default smoothing factor of 2 / (n + 1) for this implementation. Similar to SMA, EMA also achieves an evening out across normal daily prices. EMA has the advantage of allowing us to weigh recent prices with higher weights than an SMA does, which does uniform weighting. In the following code, we will see the implementation of the exponential moving average: close = goog_data['Close'] num_periods = 20 # number of days over which to average K = 2/(num_periods+1) # smoothing constant ema_p = 0 ema_values = [] # to hold computed EMA values for close_price in close: if ema_p == 0: # first observation, EMA = current-price ema_p = close_price else: ema_p = ( close_price - ema_p )*K + ema_p ema_values.append( ema_p ) # append operation: goog_data['ClosePrice'] goog_data = goog_data.assign( ClosePrice=pd.Series( close, index=goog_data.index ) ) goog_data = goog_data.assign( Exponential20DayMovingAverage = pd.Series( ema_values, index=goog_data.index ) ) close_price = goog_data['ClosePrice'] ema = goog_data['Exponential20DayMovingAverage'] import matplotlib.pyplot as plt fig = plt.figure( figsize=(10,6) ) ax1 = fig.add_subplot( 111 )#, xlabel='Date', ylabel='Google price in$'
ax1.plot( goog_data.index.values, close_price, color='g', lw=2., label='ClosePrice' )
ax1.plot( goog_data.index.values, ema, color='b', lw=2., label='Exponential20DayMovingAverage' )
ax1.set_xlabel('Date',fontsize=12)
ax1.set_ylabel('Google price in ',fontsize=12) ax1.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10 # or plt.autoscale(enable=True, axis='x', tight=True) ax1.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis) ax1.margins(0,0.05) # move all curves to up from matplotlib.dates import DateFormatter ax1.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08 plt.setp( ax1.get_xticklabels(), rotation=30, horizontalalignment='right' ) plt.legend() plt.show() ### ewm or ewma(Exponential Weighted Moving Average) https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.ewm.html adjust bool, default True Divide by decaying adjustment factor除以衰减调整因子 in beginning periods to account for imbalance in relative weightings (viewing EWMA as a moving average). • When adjust=True (default), the EW function is calculated using weights . For example, the EW moving average of the series [x0,x1,...,xt] (or a price list) of the instrument would be: 等式的上方是对当前价格到最初价格的加权求和，用的加权因子是 等式的下方是对所有加权因子的求和(可用等比例求和公式) 等比例求和公式推导 and(公比)==> • When adjust=False, the exponentially weighted function is calculated recursively: OR close = goog_data['Close'] num_periods = 20 # number of days over which to average goog_data['close_20_ema'] = goog_data['Close'].ewm( ignore_na=False, span=num_periods, # K = 2/(num_periods+1) # smoothing constant min_periods=0, adjust=False ### ).mean() goog_data.head(21) close = goog_data['Close'] num_periods = 20 # number of days over which to average goog_data['close_20_ema'] = goog_data['Close'].ewm( ignore_na=False, span=num_periods, # K = 2/(num_periods+1) # smoothing constant min_periods=0, adjust=True ### ).mean() close_price = goog_data['ClosePrice'] ema = goog_data['Exponential20DayMovingAverage'] ema_20 = goog_data['close_20_ema'] import matplotlib.pyplot as plt fig = plt.figure( figsize=(10,6) ) ax1 = fig.add_subplot( 111 )#, xlabel='Date', ylabel='Google price in'
ax1.plot( goog_data.index.values, close_price, color='g', lw=2., label='ClosePrice' )
ax1.plot( goog_data.index.values, ema, color='b', lw=2., label='Exponential20DayMovingAverage' )
ax1.plot( goog_data.index.values, ema_20, color='k', lw=2., label='close_20_ewma' )
ax1.set_xlabel('Date',fontsize=12)
ax1.set_ylabel('Google price in ',fontsize=12) ax1.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10 # or plt.autoscale(enable=True, axis='x', tight=True) ax1.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis) ax1.margins(0,0.05) # move all curves to up from matplotlib.dates import DateFormatter ax1.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08 plt.setp( ax1.get_xticklabels(), rotation=30, horizontalalignment='right' ) plt.legend() Adjust=True and Adjust=False only have the initial difference, and then the same. The initial ewma is closer to the price trend goog_data.tail() %timeit goog_data['Close'].ewm( ignore_na=False,span=num_periods, min_periods=0,adjust=True ).mean() Faster! %timeit goog_data['Close'].ewm( ignore_na=False,span=num_periods, min_periods=0,adjust=False ).mean() import matplotlib.pyplot as plt fig = plt.figure( figsize=(12,8) ) ax1 = fig.add_subplot( 111 )#, xlabel='Date', ylabel='Google price in'
ax1.plot( goog_data.index.values, close_price, color='g', lw=2., label='ClosePrice' )
ax1.plot( goog_data.index.values, ema, color='b', lw=2., label='Exponential20DayMovingAverage' )
ax1.plot( goog_data.index.values, ema_20, color='k', lw=2., label='close_20_ewma' )
ax1.plot( goog_data.index.values, sma, color='y', lw=2., label='sma' )
ax1.set_xlabel('Date',fontsize=12)
ax1.set_ylabel('Google price in ',fontsize=12) ax1.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10 # or plt.autoscale(enable=True, axis='x', tight=True) ax1.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis) ax1.margins(0,0.05) # move all curves to up from matplotlib.dates import DateFormatter ax1.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08 plt.setp( ax1.get_xticklabels(), rotation=30, horizontalalignment='right' ) plt.legend() plt.show() From the plot, it is observed that EMA has a very similar smoothing effect to SMA(ewma better than sma), as expected, and it reduces the noise in the raw prices. However the extra parameter, , available in EMA in addition to the parameter n, allows us to control the relative weight placed on the new price observation, as compared to older price observations. This allows us to build different variants of EMA by varying the parameter to make fast and slow EMAs, even for the same parameter, We will explore fast and slow EMAs more in the rest of this chapter and in later chapters. ## Absolute price oscillator绝对价格震荡指标 The absolute price oscillator, which we will refer to as APO, is a class of indicators that builds on top of moving averages of prices to capture specific short-term deviations in prices. The absolute price oscillator is computed by finding the difference between a fast exponential moving average and a slow exponential moving average. Intuitively, it is trying to measure how far the more reactive EMA () is deviating from the more stable EMA (). A large difference is usually interpreted as one of two things: instrument prices are starting to trend or break out, or instrument prices are far away from their equilibrium prices, in other words, overbought or oversold: ### Implementation of the absolute price oscillator Let's now implement the absolute price oscillator, with the faster EMA using a period of 10 days and a slower EMA using a period of 40 days, and default smoothing factors being 2/11 and 2/41, respectively, for the two EMAs: import yfinance as yf import pandas as pd start_date = '2014-01-01' end_date = '2018-01-01' SRC_DATA_FILENAME = 'goog_data2.pkl' try: goog_data2 = pd.read_pickle( SRC_DATA_FILENAME ) print( 'File found...reading GOOG data') except: print( 'File not found...downloading GOOG data') goog_data2 = yf.download( 'goog', start=start_date, end=end_date) goog_data2.to_pickle( SRC_DATA_FILENAME ) goog_data=goog_data2.tail(620) close = goog_data['Close'] num_periods_fast = 10 # time period for the fast EMA K_fast = 2/(num_periods_fast+1) # smoothing factor for fast EMA ema_fast = 0 # initial ema num_periods_slow = 40 # time period for slow EMA K_slow = 2/(num_periods_slow+1) # smoothing factor for slow EMA ema_slow = 0 # initial ema ema_fast_values = [] # we will hold fast EMA values for visualization purposes ema_slow_values = [] # we will hold slow EMA values for visualization purposes apo_values = [] # track computed absolute price oscillator values for close_price in close: if ema_fast == 0: # first observation ema_fast = close_price ema_slow = close_price else: ema_fast = (close_price - ema_fast) * K_fast + ema_fast ema_slow = (close_price - ema_slow) * K_slow + ema_slow ema_fast_values.append( ema_fast ) ema_slow_values.append( ema_slow ) apo_values.append( ema_fast - ema_slow ) The preceding code generates APO values that have higher positive and negative values when the prices are moving away from long-term EMA(here, num_periods_slow=40) very quickly (breaking out), which can have a trend-starting interpretation or an overbought/sold interpretation. Now, let's visualize the fast and slow EMAs and visualize the APO values generated: goog_data = goog_data.assign( ClosePrice=pd.Series(close, index=goog_data.index ) ) goog_data = goog_data.assign( FastExponential10DayMovingAverage = pd.Series( ema_fast_values, index=goog_data.index ) ) goog_data = goog_data.assign( SlowExponential40DayMovingAverage = pd.Series( ema_slow_values, index=goog_data.index ) ) goog_data = goog_data.assign( AbsolutePriceOscillator = pd.Series( apo_values, index=goog_data.index ) ) close_price = goog_data['ClosePrice'] ema_f = goog_data['FastExponential10DayMovingAverage'] ema_s = goog_data['SlowExponential40DayMovingAverage'] apo = goog_data['AbsolutePriceOscillator'] import matplotlib.pyplot as plt fig = plt.figure( figsize=(15,8) ) ax1 = fig.add_subplot(211) ax1.plot( goog_data.index.values, close_price, color='g', lw=2., label='ClosePrice' ) ax1.plot( goog_data.index.values, ema_f, color='b', lw=2., label='FastExponential_10_DayMovingAverage' ) ax1.plot( goog_data.index.values, ema_s, color='k', lw=2., label='SlowExponential_40_DayMovingAverage' ) # ax1.set_xlabel('Date',fontsize=12) ax1.set_ylabel('Google price in',fontsize=12)
ax1.legend()
ax2.plot( goog_data.index.values, apo, color='k', lw=2., label='AbsolutePriceOscillator')
ax2.set_ylabel('APO', fontsize=12)
ax2.set_xlabel('Date', fontsize=12)
ax2.legend()
ax1.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10
# or plt.autoscale(enable=True, axis='x', tight=True)
ax1.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis)
ax1.margins(0,0.05) # move all curves to up
ax2.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10
# or plt.autoscale(enable=True, axis='x', tight=True)
ax2.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis)
ax2.margins(0,0.05) # move all curves to up
from matplotlib.dates import DateFormatter
ax1.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08
plt.setp( ax1.get_xticklabels(), rotation=30, horizontalalignment='right' )
ax2.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08
plt.setp( ax2.get_xticklabels(), rotation=30, horizontalalignment='right' )
plt.show()
One observation here is the difference in behavior between fast and slow EMAs. The faster one is more reactive to new price observations, and the slower one is less reactive to new price observations and decays slower.
• The APO values are positive when prices are breaking out to the upside, and the magnitude of the APO values captures the magnitude of the breakout.
• The APO values are negative when prices are breaking out to the downside, and the magnitude of the APO values captures the magnitude of the breakout.
• In a later chapter in this book, we will use this signal in a realistic trading strategy.
## Moving average convergence divergence
The moving average convergence divergence is another in the class of indicators that builds on top of moving averages of prices. We'll refer to it as MACD. This goes a step further than the APO. Let's look at it in greater detail.
The moving average convergence divergence was created by Gerald Appel. It is similar in spirit to an absolute price oscillator in that it establishes the difference between a fast exponential moving average and a slow exponential moving average. However, in the case of MACD, we apply a smoothing exponential moving average to the MACD value itself in order to get the final signal output from the MACD indicator. Optionally, you may also look at the difference between MACD values and the EMA of the MACD values (signal) and visualize it as a histogram. A properly configured MACD signal can successfully capture the direction, magnitude, and duration of a trending instrument price:
MACD_EMA_SHORT = 12
MACD_EMA_LONG = 26
MACD_EMA_SIGNAL = 9
@classmethod
def _get_macd(cls, df):
""" Moving Average Convergence Divergence
This function will initialize all following columns.
MACD Line (macd): (12-day EMA - 26-day EMA)
Signal Line (macds): 9-day EMA of MACD Line
MACD Histogram (macdh): MACD Line - Signal Line
:param df: data
:return: None
"""
ema_short = 'close_{}_ema'.format(cls.MACD_EMA_SHORT)
ema_long = 'close_{}_ema'.format(cls.MACD_EMA_LONG)
ema_signal = 'macd_{}_ema'.format(cls.MACD_EMA_SIGNAL)
fast = df[ema_short]
slow = df[ema_long]
df['macd'] = fast - slow
df['macds'] = df[ema_signal]
df['macdh'] = (df['macd'] - df['macds'])
cls._drop_columns(df, [ema_short, ema_long, ema_signal])
### Implementation of the moving average convergence divergence
Let's implement a moving average convergence divergence signal with a fast EMA period of 10 days, a slow EMA period of 40 days, and with default smoothing factors of 2/11 and 2/41, respectively:
import yfinance as yf
import pandas as pd
start_date = '2014-01-01'
end_date = '2018-01-01'
SRC_DATA_FILENAME = 'goog_data2.pkl'
try:
except:
goog_data2.to_pickle( SRC_DATA_FILENAME )
goog_data=goog_data2.tail(620)
close = goog_data['Close']
num_periods_fast = 10 # time period for the fast EMA
K_fast = 2/(num_periods_fast+1) # smoothing factor for fast EMA
ema_fast = 0 # initial ema
num_periods_slow = 40 # time period for slow EMA
K_slow = 2/(num_periods_slow+1) # smoothing factor for slow EMA
ema_slow = 0 # initial ema
num_periods_macd = 20 # MACD ema time period
K_macd = 2/(num_periods_macd+1) # MACD EMA smoothing factor
ema_macd= 0
ema_fast_values = [] # we will hold fast EMA values for visualization purposes
ema_slow_values = [] # we will hold slow EMA values for visualization purposes
macd_values = [] # tract MACD values for visualization purpose # MACD = EMA_fast - EMA_slow
macd_signal_values = [] # MACD EMA values tracker # MACD_signal = EMA_MACD
macd_histogram_values = [] # MACD = MACD - MACD_signal
for close_price in close:
if ema_fast == 0: # first observation
ema_fast = close_price
ema_slow = close_price
else:
ema_fast = (close_price - ema_fast) * K_fast + ema_fast
ema_slow = (close_price - ema_slow) * K_slow + ema_slow
ema_fast_values.append( ema_fast )
ema_slow_values.append( ema_slow )
macd = ema_fast - ema_slow # MACD is fast_MA - slow_EMA # apo_values
if ema_macd == 0 :
ema_macd = macd
else:
ema_macd = (macd-ema_macd) * K_macd + ema_macd # signal is EMA of MACD values
macd_values.append( macd )
macd_signal_values.append( ema_macd )
macd_histogram_values.append( macd-ema_macd )
In the preceding code, the following applies:
• The time period used a period of 20 days and a default smoothing factor of 2/21.
• We also computed a .
Let's look at the code to plot and visualize the different signals and see what we can understand from it:
goog_data = goog_data.assign( ClosePrice=pd.Series(close,
index=goog_data.index
)
)
goog_data = goog_data.assign( FastExponential10DayMovingAverage = pd.Series( ema_fast_values,
index=goog_data.index
)
)
goog_data = goog_data.assign( SlowExponential40DayMovingAverage = pd.Series( ema_slow_values,
index=goog_data.index
)
)
goog_data = goog_data.assign( MovingAverageConvergenceDivergence = pd.Series( macd_values,
index=goog_data.index
)
)
goog_data = goog_data.assign( Exponential20DayMovingAverageOfMACD = pd.Series( macd_signal_values,
index=goog_data.index
)
)
goog_data = goog_data.assign( MACDHistorgram = pd.Series( macd_histogram_values,
index=goog_data.index
)
)
close_price = goog_data['ClosePrice']
ema_f = goog_data['FastExponential10DayMovingAverage']
ema_s = goog_data['SlowExponential40DayMovingAverage']
macd = goog_data['MovingAverageConvergenceDivergence']
ema_macd = goog_data['Exponential20DayMovingAverageOfMACD']
macd_histogram = goog_data['MACDHistorgram']
import matplotlib.pyplot as plt
fig = plt.figure( figsize=(15,8) )
ax1.plot( goog_data.index.values, close_price, color='g', lw=2., label='ClosePrice' )
ax1.plot( goog_data.index.values, ema_f, color='b', lw=2.,
label='FastExponential_{}_DayMovingAverage'.format(num_periods_fast) )
ax1.plot( goog_data.index.values, ema_s, color='k', lw=2.,
label='SlowExponential_{}_DayMovingAverage'.format(num_periods_slow) )
# ax1.set_xlabel('Date',fontsize=12)
ax1.set_ylabel('Google price in ',fontsize=12) ax1.legend() ax2 = fig.add_subplot( 312 ) ax2.plot( goog_data.index.values, macd, color='k', lw=2., label='MovingAverageConvergenceDivergence' ) ax2.plot( goog_data.index.values, ema_macd, color='g', lw=2., label='Exponential_{}_DayMovingAverageOfMACD'.format(num_periods_macd)) #ax2.axhline( y=0, lw=2, color='0.7' ) ax2.set_ylabel('MACD', fontsize=12) ax2.legend() ax3 = fig.add_subplot( 313 ) ax3.bar( goog_data.index.values, macd_histogram, color='r', label='MACDHistorgram', width=0.9 ) ax3.set_ylabel('MACD', fontsize=12) ax3.legend() ax1.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10 # or plt.autoscale(enable=True, axis='x', tight=True) ax1.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis) ax1.margins(0,0.05) # move all curves to up ax2.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10 # or plt.autoscale(enable=True, axis='x', tight=True) ax2.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis) ax2.margins(0,0.05) # move all curves to up ax3.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis) ax3.margins(0,0.05) # move all curves to up ax3.set_xticks([])#plt.xticks([]) ### ax3.set_ylim(bottom=-30, top=30) from matplotlib.dates import DateFormatter ax1.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08 plt.setp( ax1.get_xticklabels(), rotation=30, horizontalalignment='right' ) ax2.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08 plt.setp( ax2.get_xticklabels(), rotation=30, horizontalalignment='right' ) plt.subplots_adjust( hspace=0.3 ) plt.show() The preceding code will return the following output. Let's have a look at the plot: The MACD signal is very similar to the APO, as we expected, but now, in addition, the is an additional smoothing factor on top of raw MACD values to capture lasting trending periods by smoothing out the noise of raw values. Finally, the , which is the difference in the two series, captures • (a) the time period when the trend is starting or reversion逆转, and • (b) the magnitude of lasting trends when values stay positive or negative after reversing signs. MACD在应用上应先行计算出快速（一般选12日）移动平均值与慢速（一般选26日）移动平均值。以这两个数值作为测量两者（快速与慢速线）间的“差离值”依据。所谓“差离值”（DIF），即12日EMA数值减去26日EMA数值。因此，在持续的涨势中，12日EMA在26日EMA之上。其间的正差离值（+DIF）会愈来愈大。反之在跌势中，差离值可能变负（-DIF），此时是绝对值愈来愈大。至于行情开始回转，正或负差离值要缩小到一定的程度，才真正是行情反转的信号。MACD的反转信号界定为“差离值”的9日移动平均值MACD_ema（9日DIF）。 在MACD的异同移动平均线计算公式中，都分别加T+1交易日的份量权值，以现在流行的参数12和26为例， close = goog_data['Close'] num_periods_fast = 12 # time period for the fast EMA K_fast = 2/(num_periods_fast+1) # smoothing factor for fast EMA ema_fast = 0 # initial ema num_periods_slow = 26 # time period for slow EMA K_slow = 2/(num_periods_slow+1) # smoothing factor for slow EMA ema_slow = 0 # initial ema num_periods_macd = 9 # MACD ema time period K_macd = 2/(num_periods_macd+1) # MACD EMA smoothing factor ema_macd= 0 ema_fast_values = [] # we will hold fast EMA values for visualization purposes ema_slow_values = [] # we will hold slow EMA values for visualization purposes macd_values = [] # tract MACD values for visualization purpose # MACD = EMA_fast - EMA_slow macd_signal_values = [] # MACD EMA values tracker # MACD_signal = EMA_MACD macd_histogram_values = [] # MACD = MACD - MACD_signal for close_price in close: if ema_fast == 0: # first observation ema_fast = close_price ema_slow = close_price else: ema_fast = (close_price - ema_fast) * K_fast + ema_fast ema_slow = (close_price - ema_slow) * K_slow + ema_slow ema_fast_values.append( ema_fast ) ema_slow_values.append( ema_slow ) macd = ema_fast - ema_slow # MACD is fast_MA - slow_EMA # apo_values if ema_macd == 0 : ema_macd = macd else: ema_macd = (macd-ema_macd) * K_macd + ema_macd # signal is EMA of MACD values macd_values.append( macd ) macd_signal_values.append( ema_macd ) macd_histogram_values.append( macd-ema_macd ) goog_data = goog_data.assign( ClosePrice=pd.Series(close, index=goog_data.index ) ) goog_data = goog_data.assign( FastExponential10DayMovingAverage = pd.Series( ema_fast_values, index=goog_data.index ) ) goog_data = goog_data.assign( SlowExponential40DayMovingAverage = pd.Series( ema_slow_values, index=goog_data.index ) ) goog_data = goog_data.assign( MovingAverageConvergenceDivergence = pd.Series( macd_values, index=goog_data.index ) ) goog_data = goog_data.assign( Exponential20DayMovingAverageOfMACD = pd.Series( macd_signal_values, index=goog_data.index ) ) goog_data = goog_data.assign( MACDHistorgram = pd.Series( macd_histogram_values, index=goog_data.index ) ) close_price = goog_data['ClosePrice'] ema_f = goog_data['FastExponential10DayMovingAverage'] ema_s = goog_data['SlowExponential40DayMovingAverage'] macd = goog_data['MovingAverageConvergenceDivergence'] ema_macd = goog_data['Exponential20DayMovingAverageOfMACD'] macd_histogram = goog_data['MACDHistorgram'] import matplotlib.pyplot as plt fig = plt.figure( figsize=(15,8) ) ax1 = fig.add_subplot(311) ax1.plot( goog_data.index.values, close_price, color='g', lw=2., label='ClosePrice' ) ax1.plot( goog_data.index.values, ema_f, color='b', lw=2., label='FastExponential_{}_DayMovingAverage'.format(num_periods_fast) ) ax1.plot( goog_data.index.values, ema_s, color='k', lw=2., label='SlowExponential_{}_DayMovingAverage'.format(num_periods_slow) ) ax1.set_xlabel('Date',fontsize=12) ax1.set_ylabel('Google price in',fontsize=12)
ax1.legend()
ax2.plot( goog_data.index.values, macd, color='k', lw=2., label='MovingAverageConvergenceDivergence' )
ax2.plot( goog_data.index.values, ema_macd, color='g', lw=2.,
label='Exponential_{}_DayMovingAverageOfMACD'.format(num_periods_macd))
#ax2.axhline( y=0, lw=2, color='0.7' )
ax2.set_ylabel('MACD', fontsize=12)
ax2.legend()
ax3.bar( goog_data.index.values, macd_histogram, color='r', label='MACDHistorgram', width=0.9 )
ax3.set_ylabel('MACD', fontsize=12)
ax3.legend()
ax1.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10
# or plt.autoscale(enable=True, axis='x', tight=True)
ax1.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis)
ax1.margins(0,0.05) # move all curves to up
ax2.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10
# or plt.autoscale(enable=True, axis='x', tight=True)
ax2.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis)
ax2.margins(0,0.05) # move all curves to up
ax3.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis)
ax3.margins(0,0.05) # move all curves to up
ax3.set_xticks([])#plt.xticks([]) ###
ax3.set_ylim(bottom=-30, top=30)
from matplotlib.dates import DateFormatter
ax1.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08
plt.setp( ax1.get_xticklabels(), rotation=30, horizontalalignment='right' )
ax2.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08
plt.setp( ax2.get_xticklabels(), rotation=30, horizontalalignment='right' )
plt.show()
1.当DIF和DEA大于0(即在图形上表示为它们处于零线以上)并向上移动时，一般表示为行情处于多头行情中，可以买入
2.当DIF和DEA小于0(即在图形上表示为它们处于零线以下)并向下移动时，一般表示为行情处于空头行情中，可以卖出开仓或观望
3.当DIF和DEA均大于0(即在图形上表示为它们处于零线以上)但都向下移动时，一般表示为行情处于下跌阶段，可以卖出开仓和观望
4.当DIF和DEA均小于0时(即在图形上表示为它们处于零线以下)但向上移动时，一般表示为行情即将上涨，股票将上涨，可以买入开仓或多头持仓
指数平滑异同移动平均线，简称MACD，它是一项利用短期指数平均数指标与长期指数平均数指标之间的聚合与分离状况，对买进、卖出时机作出研判的技术指标。
根据移动平均线原理所发展出来的MACD，一来克服了移动平均线假信号频繁的缺陷，二来能确保移动平均线最大的战果
其买卖原则为：
1.DIF(MovingAverageConvergenceDivergence)、DEA((MACD_ema))均为正DIF向上突破DEA，买入信号参考
2.DIF、DEA均为负DIF向下跌破DEA，卖出信号参考
3.DIF线与K线发生背离，行情可能出现反转信号。
4.DIF、DEA的值从正数变成负数，或者从负数变成正数并不是交易信号，因为它们落后于市场
### 基本用法
1. MACD金叉：DIFF 由下向上突破 DEA，为买入信号。
2. MACD死叉：DIFF 由上向下突破 DEA，为卖出信号。
3. MACD 绿转红：MACD（bar） 值由负变正，市场由空头转为多头
4. MACD 红转绿：MACD(bar) 值由正变负，市场由多头转为空头
5. DIFF 与 DEA 均为正值,即都在零轴线以上时，大势属多头市场DIFF 向上突破 DEA，可作买入信号。
6. DIFF 与 DEA 均为负值,即都在零轴线以下时，大势属空头市场DIFF 向下跌破 DEA，可作卖出信号。
7. 当 DEA 线与 K 线趋势发生背离时为反转信号
8. DEA 在盘整局面时失误率较高,但如果配合RSI 及KDJ指标可适当弥补缺点
### 缺点
⒈由于MACD是一项中、长线指标，买进点、卖出点和最低价、最高价之间的价差较大。当行情忽上忽下幅度太小或盘整时，按照信号进场后随即又要出场，买卖之间可能没有利润，也许还要赔点价差或手续费
一两天内涨跌幅度特别大时，MACD来不及反应，因为MACD的移动相当缓和，比较行情的移动有一定的时间差，所以一旦行情迅速大幅涨跌，MACD不会立即产生信号，此时，MACD无法发生作用
## Bollinger bands
import yfinance as yf
import pandas as pd
start_date = '2014-01-01'
end_date = '2018-01-01'
SRC_DATA_FILENAME = 'goog_data2.pkl'
try:
except:
goog_data2.to_pickle( SRC_DATA_FILENAME )
goog_data=goog_data2.tail(620)
Bollinger bands (BBANDS) also builds on top of moving averages, but incorporates recent price volatility that makes the indicator more adaptive to different market conditions. Let's now discuss this in greater detail.
Bollinger bands is a well-known technical analysis indicator developed by John Bollinger. It
• computes a moving average of the prices (you can use the simple moving average or the exponential moving average or any other variant). In addition, it
• computes the standard deviation of the prices in the lookback period by treating the moving average as the mean price. It then
• creates an upper band that is
• a moving average,
• plus
• some multiple of standard price deviations,
• and a lower band that is
• a moving average
• minus
• multiple standard price deviations.
This band represents the expected volatility of the prices by treating the moving average of the price as the reference price.
Now, when prices move outside of these bands, that can be interpreted as a breakout/trend signal or an overbought/sold mean reversion逆转 signal.
Let's look at the equations to compute the upper Bollinger band, , and the lower Bollinger band, . Both depend, in the first instance, on the middle Bollinger band,, which is simply the simple moving average of the previous time periods( in this case, the last days ) denoted by. The upper and lower bands are then computed by adding/subtracting to , which is the product of standard deviation, , which we've seen before, and , which is a standard deviation factor of our choice. The larger the value of chosen, the greater the Bollinger bandwidth for our signal, so it is just a parameter that controls the width in our trading signal:
Here, the following applies:
: Standard deviation factor of our choice
To compute the standard deviation, first we compute the variance:
Then, the standard deviation is simply the square root of the variance:
### Implementation of Bollinger bands
We will implement and visualize Bollinger bands, with 20 days as the time period for SMA ( ):
In the preceding code, we used a stdev factor, , of 2 to compute the upper band and lower band from the middle band, and the standard deviation we compute.
import statistics as stats
import math as math
close = goog_data['Close']
time_period = 20 # history length for Simple Moving Average for middle ban
stdev_factor = 2 # Standard Deviation Scaling factor for the upper and lower bands
history = [] # price history for computing simple moving average
sma_values = [] # moving average of prices for visualization purposes
upper_band = [] # upper band values
lower_band = [] # lower band values
for close_price in close:
# step1: sma
history.append( close_price )
if len(history) > time_period: # only maintain at most 'time_period' number of price observations
del (history[0])
sma = stats.mean( history )
sma_values.append( sma ) # simple moving average or middle band
# step2: stdev
variance = 0 # variance is the square of standard deviation
for hist_price in history:
variance += ( (hist_price-sma)**2 )
stdev = math.sqrt( variance/len(history) ) # square root to get standard deviation
# step3:
upper_band.append( sma + stdev_factor*stdev )
lower_band.append( sma - stdev_factor*stdev )
Now, let's add some code to visualize the Bollinger bands and make some observations:
goog_data = goog_data.assign( ClosePrice = pd.Series( close,
index = goog_data.index
)
)
goog_data = goog_data.assign( MiddleBollingerBand_20DaySMA = pd.Series( sma_values,
index = goog_data.index
)
)
goog_data = goog_data.assign( UpperBollingerBand_20DaySMA_2StdevFactor = pd.Series( upper_band,
index = goog_data.index
)
)
goog_data = goog_data.assign( LowerBollingerBand_20DaySMA_2StdevFactor = pd.Series( lower_band,
index = goog_data.index
)
)
close_price = goog_data['ClosePrice']
boll_m = goog_data['MiddleBollingerBand_20DaySMA']
boll_ub = goog_data['UpperBollingerBand_20DaySMA_2StdevFactor']
boll_lb = goog_data['LowerBollingerBand_20DaySMA_2StdevFactor']
import matplotlib.pyplot as plt
fig = plt.figure( figsize=(12,6) )
ax1.plot( goog_data.index.values, close_price, color='k', lw=2., label='ClosePrice' )
ax1.plot( goog_data.index.values, boll_m, color='b', lw=2., label='MiddleBollingerBand_20DaySMA')
ax1.plot( goog_data.index.values, boll_ub, color='g', lw=2., label='UpperBollingerBand_20DaySMA_2StdevFactor')
ax1.plot( goog_data.index.values, boll_lb, color='r', lw=2., label='LowerBollingerBand_20DaySMA_2StdevFactor')
ax1.fill_between( goog_data.index.values, boll_ub, boll_lb, alpha=0.1 )
ax1.set_xlabel('Date', fontsize=12)
ax1.set_ylabel('Google price in ', fontsize=12) ax1.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10 # or plt.autoscale(enable=True, axis='x', tight=True) ax1.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis) ax1.margins(0,0.05) # move all curves to up ax1.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08 plt.setp( ax1.get_xticklabels(), rotation=30, horizontalalignment='right' ) ax1.legend() plt.show() 股价波动在上限和下限的区间之内，这条带状区的宽窄，随着股价波动幅度的大小而变化，股价涨跌幅度加大时，带状区变宽，涨跌幅度狭小盘整时，带状区则变窄。 布林线利用波带可以显示其安全的高低价位。 当变易性变小，而波带变窄时，激烈的价格波动有可能随时产生 高,低点穿越波带边线时，立刻又回到波带内，会有回档产生 波带开始移动后，以此方式进入另一波带，这对于找出目标值有相当帮助。 应用规则是这样的：当一只股票在一段时间内股价波幅很小，反映在布林线上表现为，股价波幅带长期收窄，而在某个交易日，股价在较大交易量的配合下收盘价突破布林线的阻力线，而此时布林线由收口明显转为开口，此时投资者应该果断买入(从当日的K线图就可明显看出)，这是因为，该股票由弱转强，短期上冲的动力不会仅仅一天，短线必然会有新高出现，因此可以果断介入。 For Bollinger bands, when prices stay within the upper and lower bounds, then not much can be said, but, when prices traverse the upper band, then one interpretation can be that prices are breaking out to the upside and will continue to do so. Another interpretation of the same event can be that the trading instrument is overbought and we should expect a bounce back down. The other case is when prices traverse the lower band, then one interpretation can be that prices are breaking out to the downside and will continue to do so. Another interpretation of the same event can be that the trading instrument is oversold and we should expect a bounce back up. In either case, Bollinger bands helps us to quantify and capture the exact time when this happens. BOLL指标应用技巧 1）、当价格运行在布林通道的中轨和上轨之间的区域时，只要不破中轨，说明市场处于多头行情中，只考虑逢低买进，不考虑做空。 2）、在中轨和下轨之间时，只要不破中轨(高出中轨线，中轨线是20天的简单移动平均线SMA_20)，说明是空头市场，交易策略是逢高卖出，不考虑买进 3）、当市场价格沿着布林通道上轨运行时，说明市场是单边上涨行情，持有的多单要守住，只要价格不脱离上轨区域就耐心持有 4）、沿着下轨运行时，说明市场目前为单边下跌行情，一般为一波快速下跌行情，持有的空单（做空），只要价格不脱离下轨区域就耐心持有 5）、当价格运行在中轨区域时，说明市场目前为盘整震荡行情，对趋势交易者来说，这是最容易赔钱的一种行情，应回避，空仓观望为上 6）、布林通道的缩口状态。价格在中轨附近震荡，上下轨逐渐缩口，此是大行情来临的预兆，应空仓观望，等待时机 7）、通道缩口后的突然扩张状态。意味着一波爆发性行情来临，此后，行情很可能走单边，可以积极调整建仓，顺势而为 8）、当布林通道缩口后，在一波大行情来临之前，往往会出现假突破行情，这是主力的陷阱，应提高警惕，可以通过调整仓位化解 9）、布林通道的时间周期应以周线为主，在单边行情时，所持仓单已有高额利润，为防止大的回调，可以参考日线布林通道的原则出局 ## Relative strength indicator The relative strength indicator, which we will refer to as RSI, is quite different from the previous indicators we saw that were based on moving averages of prices. This is based on price changes over periods to capture the strength/magnitude of price moves The relative strength indicator was developed by J Welles Wilder. It comprises a lookback period, which it uses to compute the magnitude of the average of gains/price increases over that period, as well as the magnitude of the averages of losses/price decreases over that period. Then, it computes the RSI value that normalizes the signal value to stay between 0 and 100, and attempts to capture if there have been many more gains relative to the losses, or if there have been many more losses relative to the gains. RSI values over 50% indicate an uptrend, while RSI values below 50% indicate a downtrend. For the last n periods, the following applies: Otherwise, the following applies: Otherwise, the following applies: ### Implementation of the relative strength indicator import yfinance as yf import pandas as pd start_date = '2014-01-01' end_date = '2018-01-01' SRC_DATA_FILENAME = 'goog_data2.pkl' try: goog_data2 = pd.read_pickle( SRC_DATA_FILENAME ) print( 'File found...reading GOOG data') except: print( 'File not found...downloading GOOG data') goog_data2 = yf.download( 'goog', start=start_date, end=end_date) goog_data2.to_pickle( SRC_DATA_FILENAME ) goog_data=goog_data2.tail(620) Now, let's implement and plot a relative strength indicator on our dataset: avg_gain or avg_gain use the simple average(sma) import statistics as stats time_period = 20 # look back period to compute gains & losses gain_history = [] # history of gains over look back period (0 if no gain, magnitude of gain if gain) loss_history = [] # history of losses over look back period (0 if no loss, magnitude of loss if loss) avg_gain_values = [] # track avg gains for visualization purposes avg_loss_values = [] # track avg losses for visualization purposes rsi_values = [] # track computed RSI values last_price = 0 # current_price - last_price > 0 => gain. # current_price - last_price < 0 => loss. for close_price in close: if last_price ==0: last_price = close_price gain_history.append( max(0, close_price-last_price) ) loss_history.append( max(0, last_price-close_price) ) last_price = close_price if len(gain_history) > time_period: # maximum observations is equal to lookback period del ( gain_history[0] ) del ( loss_history[0] ) avg_gain = stats.mean( gain_history ) # average gain over lookback period avg_loss = stats.mean( loss_history ) # average loss over lookback period avg_gain_values.append( avg_gain ) avg_loss_values.append( avg_loss ) rs = 0 if avg_loss > 0: # to avoid division by 0, which is undefined rs = avg_gain/avg_loss rsi = 100 - ( 100/(1+rs) ) rsi_values.append( rsi ) In the preceding code, the following applies: • We have used 20 days as our time period over which we computed the average gains and losses and then normalized it to be between 0 and 100 based on our formula for RSI values. • For our dataset where prices have been steadily rising, it is obvious that the RSI values are consistently over 50% or more. Now, let's look at the code to visualize the final signal as well as the components involved: goog_data = goog_data.assign( ClosePrice = pd.Series( close, index = goog_data.index ) ) goog_data = goog_data.assign( RelativeStrengthAvg_GainOver_20Days = pd.Series( avg_gain_values, index = goog_data.index ) ) goog_data = goog_data.assign( RelativeStrengthAvg_LossOver_20Days = pd.Series( avg_loss_values, index = goog_data.index ) ) goog_data = goog_data.assign( RelativeStrength_IndicatorOver_20Days = pd.Series( rsi_values, index = goog_data.index ) ) close_price = goog_data['ClosePrice'] rs_gain = goog_data['RelativeStrengthAvg_GainOver_20Days'] rs_loss = goog_data['RelativeStrengthAvg_LossOver_20Days'] rsi = goog_data['RelativeStrength_IndicatorOver_20Days'] import matplotlib.pyplot as plt fig = plt.figure( figsize=(15,10) ) ax1 = fig.add_subplot( 311 ) ax1.plot( goog_data.index.values, close_price, color='k', lw=2., label='ClosePrice' ) ax1.set_ylabel( 'Google price in', fontsize=12 )
ax1.legend()
ax2.plot( goog_data.index.values, rs_gain, color='g', lw=2., label='RelativeStrengthAvg_GainOver_20Days' )
ax2.plot( goog_data.index.values, rs_loss, color='r', lw=2., label='RelativeStrengthAvg_LossOver_20Days' )
ax2.set_ylabel( 'RS', fontsize=12 )
ax2.legend()
ax3.plot( goog_data.index.values, rsi, color='b', lw=2., label='RelativeStrength_IndicatorOver_20Days' )
ax3.axhline( y=50, lw=2, color='0.7' )
ax3.set_ylabel( 'RSI', fontsize=12 )
ax3.legend()
from matplotlib.dates import DateFormatter
for ax in(ax1, ax2, ax3):
ax.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10
# or plt.autoscale(enable=True, axis='x', tight=True)
ax.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis)
ax.margins(0,0.05) # move all curves to up
ax.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08
plt.setp( ax.get_xticklabels(), rotation=30, horizontalalignment='right' )
plt.subplots_adjust( hspace=0.3 ) # space between axes
plt.show()
The preceding code will return the following output. Let's have a look at the plot:
goog_data[goog_data['RelativeStrength_IndicatorOver_20Days']>50].count(axis=0)['RelativeStrength_IndicatorOver_20Days'] /\
goog_data[goog_data['RelativeStrength_IndicatorOver_20Days']<=50].count(axis=0)['RelativeStrength_IndicatorOver_20Days']
The first observation we can make from our analysis of the RSI signal applied to our GOOGLE dataset is that the AverageGain over our time frame of 20 days more often than not exceeds the AverageLoss over the same time frame, which intuitively makes sense because Google has been a very successful stock, increasing in value more or less consistently. Based on that, the RSI indicator also stays above 50% for the majority of the lifetime of the stock(1.6956521739130435)again reflecting the continued gains in the Google stock over the course of its lifetime.
def _get_smma(cls, df, column, windows):
""" get smoothed moving average.
:param df: data
:param windows: range
:return: result series
"""
window = cls.get_only_one_positive_int(windows)
column_name = '{}_{}_smma'.format(column, window)
smma = df[column].ewm(
ignore_na=False, alpha=1.0 / window,
df[column_name] = smma
return smma
def _get_rsi(cls, df, n_days):
""" Calculate the RSI (Relative Strength Index) within N days
calculated based on the formula at:
https://en.wikipedia.org/wiki/Relative_strength_index
:param df: data
:param n_days: N days
:return: None
"""
n_days = int(n_days)
d = df['close_-1_d']
df['closepm'] = (d + d.abs()) / 2
df['closenm'] = (-d + d.abs()) / 2
closepm_smma_column = 'closepm_{}_smma'.format(n_days)
closenm_smma_column = 'closenm_{}_smma'.format(n_days)
p_ema = df[closepm_smma_column]
n_ema = df[closenm_smma_column]
rs_column_name = 'rs_{}'.format(n_days)
rsi_column_name = 'rsi_{}'.format(n_days)
df[rs_column_name] = rs = p_ema / n_ema
df[rsi_column_name] = 100 - 100 / (1.0 + rs)
columns_to_remove = ['closepm',
'closenm',
closepm_smma_column,
closenm_smma_column]
cls._drop_columns(df, columns_to_remove)
n_days_7=7
n_days_14=14
n_days_20 = 20
# # close_-1_d — this is the price difference between time t and t-1
goog_data['close_-1_s'] = goog_data['Close'].shift(1)
d = goog_data['close_-1_d'] = goog_data['Close']-goog_data['close_-1_s']
goog_data['closepm'] = ( d+d.abs() )/2 # if d>0: (d+d)/2= d, if d<0, (d+(-d))/2= 0
goog_data['closenm'] = ( -d+d.abs() )/2 # if d>0: (-d+d)/= 0, if d<0, ((-d)+(-d))/2= -d (>0)
for n_days in (n_days_20,):
p_ema = goog_data['closepm'].ewm( com = n_days - 1,
min_periods=0, # default 0
).mean()
n_ema = goog_data['closenm'].ewm( com = n_days - 1,
min_periods=0,
).mean()
rs_column_name = 'rs_{}'.format(n_days)
rsi_column_name = 'rsi_{}'.format(n_days)
goog_data['p_ema'] = p_ema
goog_data['n_ema'] = n_ema
goog_data[rs_column_name] = rs = p_ema / n_ema
goog_data[rsi_column_name] = 100 - 100 / (1.0 + rs)
goog_data=goog_data.drop(['closepm','closenm','close_-1_s', 'close_-1_d'], axis=1)
goog_data[['RelativeStrengthAvg_GainOver_20Days',
'p_ema',
'RelativeStrengthAvg_LossOver_20Days',
'n_ema',
'RelativeStrength_IndicatorOver_20Days',
'rsi_20'
]
].head(25)
n_days_7=7
n_days_14=14
n_days_20 = 20
# # close_-1_d — this is the price difference between time t and t-1
goog_data['close_-1_s'] = goog_data['Close'].shift(1)
d = goog_data['close_-1_d'] = goog_data['Close']-goog_data['close_-1_s']
goog_data['closepm'] = ( d+d.abs() )/2 # if d>0: (d+d)/2= d, if d<0, (d+(-d))/2= 0
goog_data['closenm'] = ( -d+d.abs() )/2 # if d>0: (-d+d)/= 0, if d<0, ((-d)+(-d))/2= -d (>0)
for n_days in (n_days_20,):
p_ema = goog_data['closepm'].ewm( com = n_days - 1,
min_periods=0, # default 0
).mean()
n_ema = goog_data['closenm'].ewm( com = n_days - 1,
min_periods=0,
).mean()
rs_column_name = 'rs_{}'.format(n_days)
rsi_column_name = 'rsi_{}'.format(n_days)
goog_data['p_ema'] = p_ema
goog_data['n_ema'] = n_ema
goog_data[rs_column_name] = rs = p_ema / n_ema
goog_data[rsi_column_name] = 100 - 100 / (1.0 + rs)
goog_data=goog_data.drop(['closepm','closenm','close_-1_s', 'close_-1_d'], axis=1)
# goog_data[['RelativeStrengthAvg_GainOver_20Days',
# 'p_ema',
# 'RelativeStrengthAvg_LossOver_20Days',
# 'n_ema',
# 'RelativeStrength_IndicatorOver_20Days',
# 'rsi_20'
# ]
# ].head(25)
import matplotlib.pyplot as plt
fig = plt.figure( figsize=(15,10) )
ax1.plot( goog_data.index.values, close_price, color='k', lw=2., label='ClosePrice' )
ax1.set_ylabel( 'Google price in ', fontsize=12 ) ax1.legend() ax2 = fig.add_subplot( 312 ) ax2.plot( goog_data.index.values, goog_data['p_ema'], color='g', lw=2., label='p_ema_20day' ) ax2.plot( goog_data.index.values, goog_data['n_ema'], color='r', lw=2., label='n_ema_20day' ) ax2.set_ylabel( 'RS', fontsize=12 ) ax2.legend() ax3 = fig.add_subplot( 313 ) ax3.plot( goog_data.index.values, goog_data['rsi_20'], color='b', lw=2., label='rsi_20' ) ax3.plot( goog_data.index.values, rsi, color='r', lw=2., label='RelativeStrength_IndicatorOver_20Days' ) ax3.axhline( y=30, lw=2, color='0.7') # Line for oversold threshold ax3.axhline( y=50, lw=2, linestyle='--', color='0.8' ) # Neutral RSI ax3.axhline( y=70, lw=2, color='0.7') # Line for overbought threshold ax3.set_ylabel( 'RSI', fontsize=12 ) ax3.legend() from matplotlib.dates import DateFormatter for ax in(ax1, ax2, ax3): ax.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10 # or plt.autoscale(enable=True, axis='x', tight=True) ax.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis) ax.margins(0,0.05) # move all curves to up ax.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08 plt.setp( ax.get_xticklabels(), rotation=30, horizontalalignment='right' ) plt.subplots_adjust( hspace=0.3 ) # space between axes plt.show() Readings below 30 generally indicate that the stock is oversold, while readings above 70 indicate that it is overbought. Traders will often place this RSI chart below the price chart for the security, so they can compare its recent momentum against its market price Some traders will consider it a “buy signal” if a security’s RSI reading moves below 30, based on the idea that the security has been oversold and is therefore poised for a rebound. However, the reliability of this signal will depend in part on the overall context. If the security is caught in a significant downtrend, then it might continue trading at an oversold level for quite some time. Traders in that situation might delay buying until they see other confirmatory signals. IF PREVIOUS RSI > 30 AND CURRENT RSI < 30 ==> BUY SIGNAL IF PREVIOUS RSI < 70 AND CURRENT RSI > 70 ==> SELL SIGNAL andAlthough using sma to get RSI may tell us the correct buy_signal at some point in time, it may also tell us the wrong sell_signal at some point.And using ewma to get RSI is more secure goog_data[goog_data['rsi_20']>50].count(axis=0)['rsi_20'] /\ goog_data[goog_data['rsi_20']<=50].count(axis=0)['rsi_20'] ### RSI_7 and RSI_14 n_days_7=7 n_days_14=14 # # close_-1_d — this is the price difference between time t and t-1 goog_data['close_-1_s'] = goog_data['Close'].shift(1) d = goog_data['close_-1_d'] = goog_data['Close']-goog_data['close_-1_s'] goog_data['closepm'] = ( d+d.abs() )/2 # if d>0: (d+d)/2= d, if d<0, (d+(-d))/2= 0 goog_data['closenm'] = ( -d+d.abs() )/2 # if d>0: (-d+d)/= 0, if d<0, ((-d)+(-d))/2= -d (>0) for n_days in (n_days_7, n_days_14): p_ema = goog_data['closepm'].ewm( com = n_days - 1, min_periods=0, # default 0 adjust=True, ).mean() n_ema = goog_data['closenm'].ewm( com = n_days - 1, min_periods=0, adjust=True, ).mean() rs_column_name = 'rs_{}'.format(n_days) rsi_column_name = 'rsi_{}'.format(n_days) goog_data['p_ema'] = p_ema goog_data['n_ema'] = n_ema goog_data[rs_column_name] = rs = p_ema / n_ema goog_data[rsi_column_name] = 100 - 100 / (1.0 + rs) goog_data=goog_data.drop(['close_-1_s', 'close_-1_d', 'closepm', 'closenm'], axis=1) import matplotlib.pyplot as plt fig = plt.figure( figsize=(15,10) ) ax1 = fig.add_subplot( 211 ) ax1.plot( goog_data.index.values, close_price, color='k', lw=2., label='ClosePrice' ) ax1.set_ylabel( 'Google price in', fontsize=12 )
ax1.legend()
ax3.plot( goog_data.index.values, goog_data['rsi_7'], color='b', lw=2., label='rsi_7' )
ax3.plot( goog_data.index.values, goog_data['rsi_14'], color='g', lw=2., label='rsi_14' )
ax3.axhline( y=30, lw=2, color='0.7') # Line for oversold threshold
ax3.axhline( y=50, lw=2, linestyle='--', color='0.8' ) # Neutral RSI
ax3.axhline( y=70, lw=2, color='0.7') # Line for overbought threshold
ax3.set_ylabel( 'RSI', fontsize=12 )
ax3.legend()
from matplotlib.dates import DateFormatter
for ax in(ax1, ax3):
ax.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10
# or plt.autoscale(enable=True, axis='x', tight=True)
ax.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis)
ax.margins(0,0.05) # move all curves to up
ax.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08
plt.setp( ax.get_xticklabels(), rotation=30, horizontalalignment='right' )
plt.subplots_adjust( hspace=0.3 ) # space between axes
plt.show()
RSI的变动范围在0—100之间，
国内单边做多的股市:强弱指标值一般分布在20—80。
80-100 极强 卖出
50-80 强 买入
20-50 弱 观望
0-20 极弱 买入
国内期货/国际伦敦金/外汇等双向交易市场:强弱指标值一般分布在30-70.
70-100 超买区 做空
30-70 观望慎入区
0-30 超卖区 做多
## Standard deviation
Standard deviation, which will be referred to as STDEV, is a basic measure of price volatility that is used in combination with a lot of other technical analysis indicators to improve them. We'll explore that in greater detail in this section.
Standard deviation is a standard measure that is computed by measuring the squared deviation of individual prices from the mean price, and then finding the average of all those squared deviation values. This value is known as variance, and the standard deviation is obtained by taking the square root of the variance. Larger STDEVs are
• a mark of more volatile markets or
• larger expected price moves,
• so trading strategies need to factor that increased volatility into risk estimates and other trading behavior.
To compute standard deviation, first we compute the variance:
Then, standard deviation is simply the square root of the variance:
SMA : Simple moving average over n time periods.
### Implementing standard derivatives
Let's have a look at the following code, which demonstrates the implementation of standard derivatives.
We are going to import the statistics and the math library we need to perform basic mathematical operations. We are defining the loopback period with the variable time_period , and we will store the past prices in the list history, while we will store the SMA and the standard deviation in sma_values and stddev_values . In the code, we calculate the variance, and then we calculate the standard deviation. To finish, we append to the goog_data data frame that we will use to display the chart:
import yfinance as yf
import pandas as pd
start_date = '2014-01-01'
end_date = '2018-01-01'
SRC_DATA_FILENAME = 'goog_data2.pkl'
try:
except:
goog_data2.to_pickle( SRC_DATA_FILENAME )
goog_data=goog_data2.tail(620)
import statistics as stats
import math as math
import matplotlib.ticker as ticker
from matplotlib.dates import DateFormatter
close = goog_data['Close']
time_period = 20 # look back period
history = [] # history of prices
sma_values = [] # to track moving average values for visualization purposes
stddev_values = [] # history of computed stddev values
for close_price in close:
history.append( close_price )
if len(history) >time_period: # we track at most ' time_period' number of prices
del (history[0])
sma = stats.mean(history)
sma_values.append( sma )
variance = 0 # variance is square of standard deviation
for hist_price in history:
variance += ( (hist_price-sma)**2 )
stddev = math.sqrt( variance/len(history) )
stddev_values.append( stddev )
goog_data = goog_data.assign( ClosePrice = pd.Series( close,
index=goog_data.index
)
)
goog_data = goog_data.assign( StandardDeviationOver_20Days = pd.Series( stddev_values,
index=goog_data.index
)
)
close_price = goog_data['ClosePrice']
stddev = goog_data['StandardDeviationOver_20Days']
import matplotlib.pyplot as plt
fig = plt.figure( figsize=(10,6) )
ax1.plot( goog_data.index.values, close_price, color='g', lw=2., label='ClosePrice' )
ax1.set_ylabel('Google price in $', fontsize=12) ax1.legend() ax2 = fig.add_subplot( 212 ) ax2.plot( goog_data.index.values, stddev, color='b', lw=2., label='StandardDeviationOver_20Days' ) ax2.axhline( y=stddev.mean(), color='k', ls='--' ) ax2.set_xlabel('Date') ax2.set_ylabel('Stddev in$')
ax2.legend()
for ax in (ax1, ax2):
ax.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10
# or plt.autoscale(enable=True, axis='x', tight=True)
ax.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis)
ax.margins(0,0.05) # move all curves to up
ax.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08
plt.setp( ax.get_xticklabels(), rotation=30, horizontalalignment='right' )
plt.show()
From the output, it seems like volatility measure(Standard deviation (STDEV)) ranges from somewhere between $8 over 20 days to$40 over 20 days, with $15 over 20 days being the average Here, the standard deviation quantifies the volatility in the price moves during the last 20 days. Volatility spikes when the Google stock prices spike up飙升 or spike down下跌 or go through large changes over the last 20 days. We will revisit the standard deviation as an important volatility measure in later chapters. ### use pandas' rolling().std() to get the volatility time_period = 20 # look back period goog_data['std_20']= ( goog_data['Close'] ).rolling( window=time_period, min_periods=1, ).std() goog_data.head(25) After using rolling() to shift backward by one line, the first value of std_20 is NaN (missing), which also leads to the following deviation with StandardDeviationOver_20Days import matplotlib.pyplot as plt fig = plt.figure( figsize=(10,6) ) ax1 = fig.add_subplot( 211 ) ax1.plot( goog_data.index.values, close_price, color='g', lw=2., label='ClosePrice' ) ax1.set_ylabel('Google price in$', fontsize=12)
ax1.legend()
ax2 = fig.add_subplot( 212 ) ###
ax2.plot( goog_data.index.values, goog_data['std_20'], color='b', lw=2., label='std_20days_volatility' )
ax2.set_xlabel('Date')
ax2.set_ylabel('Stddev in ') ax2.legend() for ax in (ax1, ax2): ax.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10 # or plt.autoscale(enable=True, axis='x', tight=True) ax.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis) ax.margins(0,0.05) # move all curves to up ax.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08 plt.setp( ax.get_xticklabels(), rotation=30, horizontalalignment='right' ) plt.subplots_adjust( hspace=0.3 ) plt.show() ## Momentum Momentum, also referred to as MOM, is an important measure of speed and magnitude of price moves. This is often a key indicator of trend/breakout-based trading algorithms. In its simplest form, momentum is simply the difference between the current price and price of some fixed time periods in the past. Consecutive periods of positive momentum values indicate an uptrend; conversely, if momentum is consecutively negative, that indicates a downtrend. Often, we use simple/exponential moving averages of the MOM indicator, as shown here, to detect sustained trends: Here, the following applies: : Price at time t : Price n time periods before time t import yfinance as yf import pandas as pd start_date = '2014-01-01' end_date = '2018-01-01' SRC_DATA_FILENAME = 'goog_data2.pkl' try: goog_data2 = pd.read_pickle( SRC_DATA_FILENAME ) print( 'File found...reading GOOG data') except: print( 'File not found...downloading GOOG data') goog_data2 = yf.download( 'goog', start=start_date, end=end_date) goog_data2.to_pickle( SRC_DATA_FILENAME ) goog_data=goog_data2.tail(620) ### Implementation of momentum Now, let's have a look at the code that demonstrates the implementation of momentum: time_period = 20 # how far to look back to find reference price to compute momentum history = [] # history of observed prices to use in momentum calculation mom_values = [] # track momentum values for visualization purposes for close_price in close: history.append( close_price ) if len(history) > time_period: # history is at most 'time_period' number of observations del (history[0]) mom = close_price - history[0] mom_values.append( mom ) This maintains a list history of past prices and, at each new observation, computes the momentum to be the difference between the current price and the price time_period days ago, which, in this case, is 20 days: goog_data = goog_data.assign( ClosePrice=pd.Series( close, index=goog_data.index ) ) goog_data = goog_data.assign( MomentumFromPrice_20DaysAgo=pd.Series( mom_values, index = goog_data.index ) ) close_price = goog_data['ClosePrice'] mom = goog_data['MomentumFromPrice_20DaysAgo'] import matplotlib.pyplot as plt fig = plt.figure( figsize=(12,6)) ax1 = fig.add_subplot( 211 ) ax1.set_ylabel('Google price in')
ax1.plot( goog_data.index.values, close_price, color='g', lw=2., label='ClosePrice' )
ax1.legend()
ax2.set_ylabel('Momentum in \$')
ax2.plot( goog_data.index.values, mom, color='b', lw=2., label='MomentumFromPrice_20DaysAgo')
ax2.legend()
for ax in (ax1, ax2):
ax.xaxis.set_major_locator(ticker.MaxNLocator(12)) # 24%12=0： we need 10 xticklabels and 12 is close to 10
# or plt.autoscale(enable=True, axis='x', tight=True)
ax.autoscale(enable=True, axis='x', tight=True) # move all curves to left(touch y-axis)
ax.margins(0,0.05) # move all curves to up
ax.xaxis.set_major_formatter( DateFormatter('%Y-%m') ) # 2015-08-30 ==> 2015-08
plt.setp( ax.get_xticklabels(), rotation=30, horizontalalignment='right' )
plt.show()
The plot for momentum shows us the following:
• Momentum values peak when the stock price changes by a large amount as compared to the price 20 days ago.
• Here, most momentum values are positive, mainly because, as we discussed in the previous section, Google stock has been increasing in value over the course of its lifetime and has large upward momentum values from time to time.
• During the brief periods where the stock prices drop in value, we can observe negative momentum values.
In this section, we learned how to create trading signals based on technical analysis. In the next section, we will learn how to implement advanced concepts, such as seasonality, in trading instruments.
In trading, the price we receive is a collection of data points at constant time intervals called time series. They are time dependent and can have increasing or decreasing trends and seasonality trends, in other words, variations specific to a particular time frame. Like any other retail products, financial products follow trends and seasonality during different seasons. There are multiple seasonality effects: weekend, monthly, and holidays.
In this section, we will use the GOOG data from 2001 to 2018 to study price variations
based on the months.
1. We will write the code to re-group the data by months, calculate and return the monthly returns, and then compare these returns in a histogram. We will observe that GOOG has a higher return in October:
import yfinance as yf
import pandas as pd
import matplotlib.pyplot as plt
start_date = '2001-01-01'
end_date = '2018-01-01'
SRC_DATA_FILENAME = 'goog_data_large.pkl'
try:
except:
goog_data.to_pickle( SRC_DATA_FILENAME )
goog_monthly_return = goog_data['Adj Close'].pct_change().groupby([
]).mean()
goog_monthly_return
goog_monthly_return_list = []
for ym_idx in range( len(goog_monthly_return) ):
# goog_monthly_return.index[ym_idx]: (2004, 8) or (2004, 9) or ....
goog_monthly_return_list.append( {'month':goog_monthly_return.index[ym_idx][1],
'monthly_return':goog_monthly_return[goog_monthly_return.index[ym_idx]]
}
)
goog_monthly_return_list = pd.DataFrame( goog_monthly_return_list,
columns=('month','monthly_return')
)
goog_monthly_return_list
goog_monthly_return_list.boxplot( column=['monthly_return'],
by='month', # Column in the DataFrame to pandas.DataFrame.groupby()
figsize=(10,5),
fontsize=12,
)
ax = plt.gca()
labels = [ item.get_text()
for item in ax.get_xticklabels()
]
labels=['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun','Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec']
ax.set_xticklabels( labels )
ax.set_ylabel('GOOG return')
ax.set_title('GOOG Monthly return 2001-2018')
plt.suptitle("")
plt.show()
The preceding code will return the following output. The following screenshot represents the GOOG monthly return:
In this screenshot, we observe that there are repetitive patterns(For example, in September, October, and December, the average return of more than 25% (Q1>0) of the year is positive, and the median of the average return in October is the highest). The month of October is the month when the return seems to be the highest(see median value in the box), unlike November, where we observe a drop in the return.
#################
goog_y_m_return_list = []
for ym_idx in range( len(goog_monthly_return) ):
# goog_monthly_return.index[ym_idx]: (2004, 8) or (2004, 9) or ....
goog_y_m_return_list.append( { 'year':goog_monthly_return.index[ym_idx][0],
'month':goog_monthly_return.index[ym_idx][1],
'monthly_return':goog_monthly_return[goog_monthly_return.index[ym_idx]]
}
)
goog_y_m_return_list = pd.DataFrame( goog_y_m_return_list,
columns=('year','month','monthly_return')
)
goog_y_m_return_list[:17]
plt.figure( figsize=(10,10) )
import seaborn as sns
sns.barplot( x='month', y='monthly_return',hue='year',
linewidth=1, edgecolor='w',
data=goog_y_m_return_list[5:]
)
plt.show()
It can be seen that from 2005 to 2017, the average return of stocks was basically positive for a few months, while the average return for those months was basically negative.
#################
2. Since it is a time series, we will study the stationary (mean, variance remain constant over time). In the following code, we will check this property because the following time series models work on the assumption that time series are stationary:
Constant mean
Constant variance
Time-independent autocovariance
# Displaying rolling statistics
def plot_rolling_statistics_ts( ts, titletext, ytext, window_size=12 ):
ts.plot( color='red', label='Original', lw=0.5 )
ts.rolling( window_size ).mean().plot( color='blue', label='Rolling Mean' )
ts.rolling( window_size ).std().plot( color='black', label='Rolling Std' )
plt.legend( loc='best' )
plt.ylabel( ytext )
plt.xlabel( 'Date')
plt.setp( plt.gca().get_xticklabels(), rotation=30, horizontalalignment='right' )
plt.title( titletext )
plt.show( block=False )
plot_rolling_statistics_ts( goog_monthly_return[1:],
'GOOG prices rolling mean and standard deviation',
'Monthly return'
)
' GOOG prices rolling mean and standard deviation',
'Daily prices',
365
)
The preceding code will return the following two charts, where we will compare the difference using two different time series.
* One shows the GOOG daily prices, and the other one shows the GOOG monthly return.
* We observe that the rolling average and rolling standard deviation are not constant when using the daily prices instead of using the daily return( The daily return measures the dollar change in a stock’s price as a percentage of the previous day’s closing price. A positive return means the stock has grown in value, while a negative return means it has lost value.A stock with lower positive and negative daily returns is typically less risky than a stock with higher daily returns, which create larger swings in value.).
# the daily historical log returns
' GOOG prices rolling mean and standard deviation',
'Daily prices',
)
# the daily historical returns
' GOOG prices rolling mean and standard deviation',
'Daily prices',
)
* This means that the first time series representing the daily prices is not stationary. Therefore, we will need to make this time series stationary.
* The non-stationary for a time series can generally be attributed to two factors: trend and seasonality.
The following plot shows GOOG daily prices
When observing the plot of the GOOG daily prices, the following can be stated:
We can see that the price is growing over time; this is a trend.
The wave effect we are observing on the GOOG daily prices comes from seasonality(see previous boxplot).
When we make a time series stationary, we remove the trend and seasonality by modeling and removing them from the initial data.
Once we find a model predicting future values for the data without seasonality and trend, we can apply back the seasonality and trend values to get the actual forecasted data.
The following plot shows the GOOG monthly return:
For the data using the GOOG daily prices, we can just remove the trend by subtracting the moving average from the daily prices in order to obtain the following screenshot:
plot_rolling_statistics_ts( goog_data['Adj Close']-goog_data['Adj Close'].rolling(365).mean(),
'GOOG daily price without trend',
'Daily prices',
365
)
• We can now observe the trend disappeared.
• Additionally, we also want to remove seasonality; for that, we can apply differentiation.
• For the differentiation, we will calculate the difference between two consecutive days; we will then use the difference as data points.
We recommend that you read a book on time series to go deeper in an analysis of the same: Practical Time Series Analysis: Master Time Series Data Processing, Visualization, and Modeling Using Python, Packt edition
3 .To confirm our observation, in the code, we use the popular statistical test: the augmented Dickey-Fuller test:
• This determines the presence of a unit root in time series.
• If a unit root is present, the time series is not stationary.
• The null hypothesis of this test is that the series has a unit root.
• If we reject the null hypothesis, this means that we don't find a unit root.
• If we fail to reject the null hypothesis, we can say that the time series is non-stationary:
conda install -c conda-forge statsmodels
Augmented Dickey-Fuller unit root test.
The Augmented Dickey-Fuller test can be used to test for a unit root in a univariate process in the presence of serial correlation.
Returns
The test statistic.
• pvalue float
MacKinnon’s approximate p-value based on MacKinnon (1994, 2010).
• usedlag int
The number of lags used.
• nobs int
The number of observations used for the ADF regression and calculation of the critical values.
• critical values dict
Critical values for the test statistic at the 1 %, 5 %, and 10 % levels. Based on MacKinnon (2010).
• icbest float
The maximized information criterion if autolag is not None.
• resstore ResultStoreoptional
A dummy class with results attached as attributes.
Parameters
autolag {“AIC”, “BIC”, “t-stat”, None}
Method to use when automatically determining the lag length among the values 0, 1, …, maxlag.
If “AIC” (default, Akaike information criterion Akaike information criterion ) or “BIC”( Bayesian information criterionBayesian information criterion), then the number of lags滞后 is chosen to minimize the corresponding information criterion.
https://blog.csdn.net/Linli522362242/article/details/105973507
• n is the number of instances, the number of data points in X, the number of observations, or equivalently, the sample size;
• k is the number of parameters learned by the model, the number of parameters estimated by the model. For example, in multiple linear regression, the estimated parameters are the intercept, the slope parameters, and the constant variance of the errors; thus ,
• is the maximized value of the likelihood function of the model M. i.e. , where are the parameter values that maximize the likelihood function, = the observed data;
Figure 9-20. A model’s parametric function (top left), and some derived functions: a PDF(lower left), a likelihood function (top right), and a log likelihood function (lower right)
To estimate the probability distribution of a future outcome x, you need to set the model parameter θ. For example, if you set θ to 1.3 (the horizontal line), you get the probability density function f(x; θ=1.3) shown in the lower-left plot. Say you want to estimate the probability that x will fall between –2 and +2. You must calculate the integral of the PDF on this range (i.e., the surface of the shaded region).
But what if you don’t know θ, and instead if you have observed a single instance x=2.5 (the vertical line in the upper-left plot)? In this case, you get the likelihood function ℒ(θ|x=2.5)=f(x=2.5; θ), represented in the upper-right plot.https://blog.csdn.net/Linli522362242/article/details/96480059
In short, the PDF is a function of x (with θ fixed), while the likelihood function is a function of θ (with x fixed). It is important to understand that the likelihood function is not a probability distribution: if you integrate a probability distribution over all possible values of x, you always get 1; but if you integrate the likelihood function over all possible values of θ, the result can be any positive value.
Given a dataset X, a common task is to try to estimate the most likely values for the model parameters. To do this, you must find the values that maximize the likelihood function, given X. In this example, if you have observed a single instance x=2.5, the maximum likelihood estimate (MLE) of θ is . If a prior probability distribution g over θ exists, it is possible to take it into account by maximizing ℒ(θ|x)g(θ) rather than just maximizing ℒ(θ|x). This is called maximum a-posteriori (MAP) estimation. Since MAP constrains the parameter values, you can think of it as a regularized version of MLE.
• AIC和BIC主要用于模型的选择，AIC、BIC越小越好。
在对不同模型进行比较时，AIC、BIC降低越多，说明该模型的拟合效果越好；选择最优模型的指导思想是从两个方面去考察：一个是似然函数最大化，另一个是模型中的未知参数个数最小化。似然函数值越大说明模型拟合的效果越好，但是我们不能单纯地以拟合精度来衡量模型的优劣，这样回导致模型中未知参数k越来越多，模型变得越来越复杂，会造成过拟合。所以一个好的模型应该是拟合精度和未知参数个数的综合最优化配置。
• 当两个模型之间存在较大差异时，差异主要体现在似然函数项，当似然函数差异不显著时，上式第一项，即模型复杂度则起作用，从而参数个数少的模型是较好的选择。
AIC: 一般而言，当模型复杂度提高（k增大）时，似然函数也会增大，从而使AIC变小，但是k过大时，似然函数增速减缓，导致AIC增大，模型过于复杂容易造成过拟合现象。目标是选取AIC最小的模型，AIC不仅要提高模型拟合度（极大似然），而且引入了惩罚项，使模型参数尽可能少，有助于降低过拟合的可能性。
AIC和BIC均引入了与模型参数个数相关的惩罚项，BIC的惩罚项比AIC的大，考虑了样本数量，样本数量过多时，可有效防止模型精度过高造成的模型复杂度过高（kln(n)惩罚项在维数过大且训练样本数据相对较少的情况下，可以有效避免出现维度灾难现象。）
Both BIC and AIC penalize models that have more parameters to learn (e.g., more clusters), and reward models thBoth the BIC and the AIC penalize models that have more parameters to learn (e.g., more clusters) and reward models that fit the data well. They often end up selecting the same model. When they differ, the model selected by the BIC tends to be simpler(fewer parameters, 考虑了样本数量，样本数量过多时，可有效防止模型精度过高造成的模型复杂度过高) than the one selected by the AIC, but tends to not fit the data quite as well (this is especially true for larger datasets).
“t-stat” based choice of maxlag. Starts with maxlag and drops a lag until the t-statistic on the last lag length is significant using a 5%-sized test. https://blog.csdn.net/Linli522362242/article/details/91037961
• autolag If None, then the number of included lags is set to maxlag.
from statsmodels.tsa.stattools import adfuller
def test_stationarity( timeseries ):
print( "Results of Dickey-Fuller Test:" )
df_test = adfuller( timeseries[1:], autolag='AIC' )
print(df_test)
df_output = pd.Series( df_test[0:4], index=['Test Statistic',
'p-value',
"#Lags Used",
"Number of Observations Used"
]
)
print( df_output )
test_stationarity( goog_data['Adj Close'])
• This determines the presence of a unit root in time series.
• If a unit root is present, the time series is not stationary.
• The null hypothesis of this test is that the series has a unit root.
• If we reject the null hypothesis, this means that we don't find a unit root.
• If we fail to reject the null hypothesis, we can say that the time series is non-stationary:
This test returns a p-value of 0. 996 .Therefore, the time series is not stationary.
4. Let's have a look at the test:
test_stationarity( goog_monthly_return[1:] )
当p-值足够小时，即小于置信水平 ( assuming that the null hypothesis is true, the probability of the test statistic Z in the Rejection Region)时，我们可以拒绝零假设。
This test returns a p-value of less than 0.05 . Therefore, we cannot say that the time series is not stationary. We recommend using daily returns when studying financial products. In the example of stationary, we could observe that no transformation is needed.
test_stationarity( np.log(goog_data['Adj Close']/goog_data['Adj Close'].shift(1)) )
5. The last step of the time series analysis is to forecast the time series. We have two possible scenarios:
• A strictly stationary series without dependencies among values. We can use a regular linear regression to forecast values.
• A series with dependencies among values. We will be forced to use other statistical models. In this chapter, we chose to focus on using the Auto-Regression Integrated Moving Averages (ARIMA) model. This model has three parameters:
• Autoregressive (AR) term (p)—lags of dependent variables. Example for 3, the predictors for x(t) is x(t-1) + x(t-2) + x(t-3).
• Moving average (MA) term (q)—lags for errors in prediction. Example for 3, the predictor for x(t) is e(t-1) + e(t-2) + e(t-3), where e(i) is the difference between the moving average value and the actual value.
• Differentiation (d)— This is the d number of occasions where we apply differentiation between values, as was explained when we studied the GOOG daily price. If d=1, we proceed with the difference between two consecutive values.
The parameter values for AR(p) and MA(q) can be respectively found by using the autocorrelation function (ACF) and the partial偏 autocorrelation function (PACF)
from statsmodels.graphics.tsaplots import plot_acf
from statsmodels.graphics.tsaplots import plot_pacf
import matplotlib.pyplot as plt
from matplotlib import pyplot
plt.figure()
plt.subplot(211)
plot_acf( goog_monthly_return[1:], ax=pyplot.gca(), lags=10 )
# plt.yticks([0,0.25,0.5,0.75,1])
plt.autoscale(enable=True, axis='y', tight=True)
plt.subplot(212)
plot_pacf( goog_monthly_return[1:], ax=pyplot.gca(), lags=10 )
plt.autoscale(enable=True, axis='y', tight=True)
plt.show()
https://www.statsmodels.org/devel/generated/statsmodels.graphics.tsaplots.plot_acf.html?highlight=acfPlot the autocorrelation function
Plots lags on the horizontal and the correlations on vertical axis.
When we observe the two preceding diagrams, we can draw the confidence interval on either side of 0. We will use this confidence interval to determine the parameter values for the AR(p) and MA(q).
• q: The lag value is q=1 when the ACF plot crosses the upper confidence interval for the first time.
• p: The lag value is p=1 when the PACF chart crosses the upper confidence interval for the first time.
6. These two graphs suggest using q=1 and p=1. We will apply the ARIMA model in the following code:Chapter 8 ARIMA models | Forecasting: Principles and Practice (2nd ed)
https://www.statsmodels.org/dev/generated/statsmodels.tsa.arima.model.ARIMA.html
endog array_likeoptional
The observed time-series process y.
exog array_likeoptional
Array of exogenous regressors.
order tupleoptional
The (p,d,q) order of the model for the autoregressive, differences, and moving average components. d is always an integer, while p and q may either be integers or lists of integers.
from statsmodels.tsa.arima.model import ARIMA
model = ARIMA( goog_monthly_return[1:], order=(2,0,2) )
fitted_results = model.fit()
goog_monthly_return[1:].plot()
fitted_results.fittedvalues.plot( color='red' )
plt.setp( plt.gca().get_xticklabels(), rotation=30, horizontalalignment='right' )
plt.show()
# Summary
In this chapter, we explored concepts of generating trading signals, such as support and resistance, based on the intuitive ideas of supply and demand that are fundamental forces
that drive market prices. We also briefly explored how you might use support and resistance to implement a simple trading strategy. Then, we looked into a variety of technical analysis indicators, explained the intuition behind them, and implemented and visualized their behavior during different price movements. We also introduced and implemented the ideas behind advanced mathematical approaches, such as Autoregressive (AR), Moving Average (MA), Differentiation (D), AutoCorrelation Function (ACF), and Partial Autocorrelation Function (PACF) for dealing with non-stationary time series datasets. Finally, we briefly introduced an advanced concept such as seasonality, which explains how there are repeating patterns in financial datasets, basic time series analysis and concepts of stationary or non-stationary time series, and how you may model financial data that displays that behavior.
In the next chapter, we will review and implement some simple regression and classification methods and understand the advantages of applying supervised statistical learning methods to trading.
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• statsmodels,Python的统计建模和计量经济学。 astropy,天文学界的Python库。 orange，橙色，数据挖掘，数据可视化，通过可视化编程或Python脚本学习机分析。 RDKit,化学信息学和机器学习的软件。 Open Babel，巴贝尔...
• Tensorflow（1）Tensorflow的安装与配置（2）核心高阶API _ tf.keras1.机器学习原理-线性回归 （1）Tensorflow的安装与配置 点击前往Tensorflow的安装与...（2）核心高阶API _ tf.keras 1.机器学习原理-线性回归 ...
• 由于Anaconda的软件源设计缺陷，其缺少正常发行版软件源所包含的签名校验功能，任何非官方网站提供的软件包都有可能被篡改过，产生安全隐患。[1] 另根据Anaconda软件源上的说明，Anaconda和Miniconda是Anaconda, In...
• ## 时间序列分析
万次阅读 多人点赞 2017-03-22 17:04:51
from statsmodels.tsa.stattools import adfuller def test_stationarity(timeseries): #Determing rolling statistics rolmean = pd.rolling_mean(timeseries, window=12) rolstd = pd.rolling_std(timeseries...
• 1.话题引入 我们在线性回归做假设检验，在时间序列分析做自回归检验，那么我们如何检验一个分布是否是正态分布的呢？ 首先，我们定义一个用来生成价格路径的函数。...import statsmodels.api as sm
• 我们也不太可能把所有的random_state遍历一遍,而交叉验证法正好弥补了这个缺陷,它的工作原理导致它要对多次拆分进行评分再取平均值,这样就不会出现我们前面所说的问题了. 文章引自 : 《深入浅出python机器学习》
• ## 算法模型---时间序列模型
万次阅读 多人点赞 2018-01-16 09:04:58
1}+\frac{x_t -x_{t-k}}{k} st=k1n=0∑k−1xt−n=kxt+xt−1+…+xt−k+1=st−1+kxt−xt−k 这样的方法存在明显的缺陷,当k比较小时,预测的数据平滑效果不明显,而且突出反映了数据最近的变化;...
• 多元线性回归模型的基本假设之一就是模型的随机干扰项相互独立或不相关。如果模型的随机感染项违背了相互独立的基本假设，则称为存在序列相关性（自相关性）。...import statsmodels.api as sm import s
• Ljung-Box检验：Box-Ljung检验在小样本量下不太精确，Ljung-Box检验弥补了这一缺陷。同Box-Ljung检验，p值大于显著性水平如0.05，不能拒绝原假设，序列为白噪声序列。 详细白噪声检验方法可以看下“白噪声检验”。 ...
• 3.1.1自相关分析 在Python中，可使用statsmodels.graphics.tasplots模块下的plot_acf函数来分析时间序列的自相关性。 表 plot_acf函数定义及参数说明 函数定义 plot_acf(x,ax=None,lags=None,alpha=0.5,use_vlines=...
• import statsmodels.tsa.stattools as st order = st.arma_order_select_ic(income_data,max_ar=10,max_ma=10,ic=['aic', 'bic', 'hqic']) print(order.aic_min_order) print(order) 结果跑了半个多钟头，虽然...
• end 运行结果: Python求解 import pandas as pd from statsmodels.formula.api import ols from statsmodels.stats.anova import anova_lm df = pd.read_csv('D:\Data\ex_2way_annova.csv') print(df) model = ols...
• 不仅有强大的内置库，还有各种各样的第三方库（伸手党的福利 :p），如 视觉相关：OpenCV、Face Recognition、EasyOCR、Open3D、kornia、moviepy 人工智能：pytorch、tensorflow、xgboost、gym、statsmodels web相关...
• 摘要 上市公司作为我国企业中的特殊群体和证券市场的基石，其经营质量和经营业绩的优劣直接影响证券市场的建设和发展，进而间接影响着我国国民经济体系的稳定和健康发展。随着我国经济的快速发展，财务风险对上市...
• 摘要缺陷检测和缺陷预测器：高效、稳定、性能良好； 4）AutoML：自动超参数优化和模型选择； 5）实用的异常检测器后处理规则：使异常分数更可解释，同时也降低了假阳性率（FP）； 6）易使用的集成模型：组合多个模型...
• 模型预测 import statsmodels.api as sm # 引入线性回归模型评估相关库 X2 = sm.add_constant(X) est = sm.OLS(Y, X2).fit() print(est.summary()) 通过上图可以看出，由于数据量较少的原因，R-squared的值只有...
• : , 1: ]#可以进行哑变量的转换,缺陷是列名没改,prefix可以解决这个缺陷(会根据下标自动命名)。注意要删除一列，除了null那列不能删 data_drop = data_raw.drop("edu_class", axis = 1)#删除edu_class列原始数据后...
• 而Attention的特点刚好可以弥补这一缺陷，它是一种模仿人类注意力的网络架构，可以同时聚焦多个细节部分。这样可以使得框架预测的结果更加全面、准确。 四、未来发展 新算法将用于预测任何已测序生物的结构化...
• 使用以下代码导入所有需要的库： import pandas as pd import numpy as np import yfinance as yf import seaborn as sns import scipy.stats as scs import statsmodels.api as sm import statsmodels.tsa.api as ...
• 估计系数联合检验（Wald tests via statsmodels） 13. Python 与 STATA 时间日期转换问题 14. Python执行面板数据的Hausman检验 15. Fama Macbeth回归、滚动回归等等 16. 事件研究法 event study 生 创 创 如 注 K ...
... | 2022-05-17 11:26:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.4288612902164459, "perplexity": 8996.758139959251}, "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/1652662517245.1/warc/CC-MAIN-20220517095022-20220517125022-00101.warc.gz"} |
https://xianblog.wordpress.com/tag/valencia-conferences/ | dynamic mixtures [at NBBC15]
Posted in R, Statistics with tags , , , , , , , , , , , , on June 18, 2015 by xi'an
A funny coincidence: as I was sitting next to Arnoldo Frigessi at the NBBC15 conference, I came upon a new question on Cross Validated about a dynamic mixture model he had developed in 2002 with Olga Haug and Håvård Rue [whom I also saw last week in Valencià]. The dynamic mixture model they proposed replaces the standard weights in the mixture with cumulative distribution functions, hence the term dynamic. Here is the version used in their paper (x>0)
$(1-w_{\mu,\tau}(x))f_{\beta,\lambda}(x)+w_{\mu,\tau}(x)g_{\epsilon,\sigma}(x)$
where f is a Weibull density, g a generalised Pareto density, and w is the cdf of a Cauchy distribution [all distributions being endowed with standard parameters]. While the above object is not a mixture of a generalised Pareto and of a Weibull distributions (instead, it is a mixture of two non-standard distributions with unknown weights), it is close to the Weibull when x is near zero and ends up with the Pareto tail (when x is large). The question was about simulating from this distribution and, while an answer was in the paper, I replied on Cross Validated with an alternative accept-reject proposal and with a somewhat (if mildly) non-standard MCMC implementation enjoying a much higher acceptance rate and the same fit.
An objective prior that unifies objective Bayes and information-based inference
Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , on June 8, 2015 by xi'an
During the Valencia O’Bayes 2015 meeting, Colin LaMont and Paul Wiggins arxived a paper entitled “An objective prior that unifies objective Bayes and information-based inference”. It would have been interesting to have the authors in Valencia, as they make bold claims about their w-prior as being uniformly and maximally uninformative. Plus achieving this unification advertised in the title of the paper. Meaning that the free energy (log transform of the inverse evidence) is the Akaike information criterion.
The paper starts by defining a true prior distribution (presumably in analogy with the true value of the parameter?) and generalised posterior distributions as associated with any arbitrary prior. (Some notations are imprecise, check (3) with the wrong denominator or the predictivity that is supposed to cover N new observations on p.2…) It then introduces a discretisation by considering all models within a certain Kullback divergence δ to be undistinguishable. (A definition that does not account for the assymmetry of the Kullback divergence.) From there, it most surprisingly [given the above discretisation] derives a density on the whole parameter space
$\pi(\theta) \propto \text{det} I(\theta)^{1/2} (N/2\pi \delta)^{K/2}$
where N is the number of observations and K the dimension of θ. Dimension which may vary. The dependence on N of the above is a result of using the predictive on N points instead of one. The w-prior is however defined differently: “as the density of indistinguishable models such that the multiplicity is unity for all true models”. Where the log transform of the multiplicity is the expected log marginal likelihood minus the expected log predictive [all expectations under the sampling distributions, conditional on θ]. Rather puzzling in that it involves the “true” value of the parameter—another notational imprecision, since it has to hold for all θ’s—as well as possibly improper priors. When the prior is improper, the log-multiplicity is a difference of two terms such that the first term depends on the constant used with the improper prior, while the second one does not… Unless the multiplicity constraint also determines the normalising constant?! But this does not seem to be the case when considering the following section on normalising the w-prior. Mentioning a “cutoff” for the integration that seems to pop out of nowhere. Curiouser and curiouser. Due to this unclear handling of infinite mass priors, and since the claimed properties of uniform and maximal uninformativeness are not established in any formal way, and since the existence of a non-asymptotic solution to the multiplicity equation is neither demonstrated, I quickly lost interest in the paper. Which does not contain any worked out example. Read at your own risk!
O-Bayes15 [day #1]
Posted in Books, pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , on June 3, 2015 by xi'an
So here we are back together to talk about objective Bayes methods, and in the City of Valencià as well.! A move back to a city where the 1998 O’Bayes took place. In contrast with my introductory tutorial, the morning tutorials by Luis Pericchi and Judith Rousseau were investigating fairly technical and advanced, Judith looking at the tools used in the frequentist (Bernstein-von Mises) analysis of priors, with forays in empirical Bayes, giving insights into a wide range of recent papers in the field. And Luis covering works on Bayesian robustness in the sense of resisting to over-influential observations. Following works of him and of Tony O’Hagan and coauthors. Which means characterising tails of prior versus sampling distribution to allow for the posterior reverting to the prior in case of over-influential datapoints. Funny enough, after a great opening by Carmen and Ed remembering Susie, Chris Holmes also covered Bayesian robust analysis. More in the sense of incompletely or mis- specified models. (On the side, rekindling one comment by Susie and the need to embed robust Bayesian analysis within decision theory.) Which was also much Chris’ point, in line with the recent Watson and Holmes’ paper. Dan Simpson in his usual kick-the-anthill-real-hard-and-set-fire-to-it discussion pointed out the possible discrepancy between objective and robust Bayesian analysis. (With lines like “modern statistics has proven disruptive to objective Bayes”.) Which is not that obvious because the robust approach simply reincorporates the decision theory within the objective framework. (Dan also concluded with the comic strip below, whose message can be interpreted in many ways…! Or not.)
The second talk of the afternoon was given by Veronika Ročková on a novel type of spike-and-slab prior to handle sparse regression, bringing an alternative to the standard Lasso. The prior is a mixture of two Laplace priors whose scales are constrained in connection with the actual number of non-zero coefficients. I had not heard of this approach before (although Veronika and Ed have an earlier paper on a spike-and-slab prior to handle multicolinearity that Veronika presented in Boston last year) and I was quite impressed by the combination of minimax properties and practical determination of the scales. As well as by the performances of this spike-and-slab Lasso. I am looking forward the incoming paper!
The day ended most nicely in the botanical gardens of the University of Valencià, with an outdoor reception surrounded by palm trees and parakeet cries…
O’Bayes 2015: back in València
Posted in pictures, Statistics, Travel, University life with tags , , , , , on September 11, 2014 by xi'an
The next O’Bayes meeting (more precisely the International Workshop on Objective Bayes Methodology, O-Bayes15), will take place in València, Spain, on June 1-4, 2015. This is the second time an O’Bayes conference takes place in València, after the one José Miguel Bernardo organised in 1998 there. The principal objectives of O-Bayes15 will be to facilitate the exchange of recent research developments in objective Bayes theory, methodology and applications, and related topics (like limited information Bayesian statistics), to provide opportunities for new researchers, and to establish new collaborations and partnerships. Most importantly, O-Bayes15 will be dedicated to our friend Susie Bayarri, to celebrate her life and contributions to Bayesian Statistics. Check the webpage of O-Bayes15 for the program (under construction) and the practical details. Looking forward to the meeting and hopeful for a broadening of the basis of the O’Bayes community and of its scope!
Cancun, ISBA 2014 [½ day #2]
Posted in pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , , , , on July 19, 2014 by xi'an
Half-day #2 indeed at ISBA 2014, as the Wednesday afternoon kept to the Valencia tradition of free time, and potential cultural excursions, so there were only talks in the morning. And still the core poster session at (late) night. In which my student Kaniav Kamari presented a poster on a current project we are running with Kerrie Mengersen and Judith Rousseau on the replacement of the standard Bayesian testing setting with a mixture representation. Being half-asleep by the time the session started, I did not stay long enough to collect data on the reactions to this proposal, but the paper should be arXived pretty soon. And Kate Lee gave a poster on our importance sampler for evidence approximation in mixtures (soon to be revised!). There was also an interesting poster about reparameterisation towards higher efficiency of MCMC algorithms, intersecting with my long-going interest in the matter, although I cannot find a mention of it in the abstracts. And I had a nice talk with Eduardo Gutierrez-Pena about infering on credible intervals through loss functions. There were also a couple of appealing posters on g-priors. Except I was sleepwalking by the time I spotted them… (My conference sleeping pattern does not work that well for ISBA meetings! Thankfully, both next editions will be in Europe.)
Great talk by Steve McEachern that linked to our ABC work on Bayesian model choice with insufficient statistics, arguing towards robustification of Bayesian inference by only using summary statistics. Despite this being “against the hubris of Bayes”… Obviously, the talk just gave a flavour of Steve’s perspective on that topic and I hope I can read more to see how we agree (or not!) on this notion of using insufficient summaries to conduct inference rather than trying to model “the whole world”, given the mistrust we must preserve about models and likelihoods. And another great talk by Ioanna Manolopoulou on another of my pet topics, capture-recapture, although she phrased it as a partly identified model (as in Kline’s talk yesterday). This related with capture-recapture in that when estimating a capture-recapture model with covariates, sampling and inference are biased as well. I appreciated particularly the use of BART to analyse the bias in the modelling. And the talk provided a nice counterpoint to the rather pessimistic approach of Kline’s.
Terrific plenary sessions as well, from Wilke’s spatio-temporal models (in the spirit of his superb book with Noel Cressie) to Igor Prunster’s great entry on Gibbs process priors. With the highly significant conclusion that those processes are best suited for (in the sense that they are only consistent for) discrete support distributions. Alternatives are to be used for continuous support distributions, the special case of a Dirichlet prior constituting a sort of unique counter-example. Quite an inspiring talk (even though I had a few micro-naps throughout it!).
I shared my afternoon free time between discussing the next O’Bayes meeting (2015 is getting very close!) with friends from the Objective Bayes section, getting a quick look at the Museo Maya de Cancún (terrific building!), and getting some work done (thanks to the lack of wireless…)
Cancún, ISBA 2014 [day #0]
Posted in Statistics, Travel, University life with tags , , , , , , , , on July 17, 2014 by xi'an
Day zero at ISBA 2014! The relentless heat outside (making running an ordeal, even at 5:30am…) made the (air-conditioned) conference centre the more attractive. Jean-Michel Marin and I had a great morning teaching our ABC short course and we do hope the ABC class audience had one as well. Teaching in pair is much more enjoyable than single as we can interact with one another as well as the audience. And realising unsuspected difficulties with the material is much easier this way, as the (mostly) passive instructor can spot the class’ reactions. This reminded me of the course we taught together in Oulu, northern Finland, in 2004 and that ended as the Bayesian Core. We did not cover the entire material we have prepared for this short course, but I think the pace was the right one. (Just tell me otherwise if you were there!) This was also the only time I had given a course wearing sunglasses, thanks to yesterday’s incident!
Waiting for a Spanish speaking friend to kindly drive with me downtown Cancún to check whether or not an optician could make me new prescription glasses, I attended Jim Berger’s foundational lecture on frequentist properties of Bayesian procedures but could only listen as the slides were impossible for me to read, with or without glasses. The partial overlap with the Varanasi lecture helped. I alas had to skip both Gareth Roberts’ and Sylvia Früwirth-Schnatter’s lectures, apologies to both of them!, but the reward was to get a new pair of prescription glasses within a few hours. Perfectly suited to my vision! And to get back just in time to read slides during Peter Müller’s lecture from the back row! Thanks to my friend Sophie for her negotiating skills! Actually, I am still amazed at getting glasses that quickly, given the time it would have taken in, e.g., France. All set for another 15 years with the same pair?! Only if I do not go swimming with them in anything but a quiet swimming pool!
The starting dinner happened to coincide with the (second) ISBA Fellow Award ceremony. Jim acted as the grand master of ceremony and he did great to add life and side stories to the written nominations for each and everyone of the new Fellows. The Fellowships honoured Bayesian statisticians who had contributed to the field as researchers and to the society since its creation. I thus feel very honoured (and absolutely undeserving) to be included in this prestigious list, along with many friends. (But would have loved to see two more former ISBA presidents included, esp. for their massive contribution to Bayesian theory and methodology…) And also glad to wear regular glasses instead of my morning sunglasses.
[My Internet connection during the meeting being abysmally poor, the posts will appear with some major delay! In particular, I cannot include new pictures at times I get a connection… Hence a picture of northern Finland instead of Cancún at the top of this post!]
Jeffreys prior with improper posterior
Posted in Books, Statistics, University life with tags , , , , , , , , , , on May 12, 2014 by xi'an
In a complete coincidence with my visit to Warwick this week, I became aware of the paper “Inference in two-piece location-scale models with Jeffreys priors” recently published in Bayesian Analysis by Francisco Rubio and Mark Steel, both from Warwick. Paper where they exhibit a closed-form Jeffreys prior for the skewed distribution
$\dfrac{2\epsilon}{\sigma_1}f(\{x-\mu\}/\sigma_1)\mathbb{I}_{x<\mu}+\dfrac{2(1-\epsilon)}{\sigma_2}f(\{x-\mu\}/\sigma_2) \mathbb{I}_{x>\mu}$
where f is a symmetric density, namely
$\pi(\mu,\sigma_1,\sigma_2) \propto 1 \big/ \sigma_1\sigma_2\{\sigma_1+\sigma_2\}\,,$
where
$\epsilon=\sigma_1/\{\sigma_1+\sigma_2\}\,.$
only to show immediately after that this prior does not allow for a proper posterior, no matter what the sample size is. While the above skewed distribution can always be interpreted as a mixture, being a weighted sum of two terms, it is not strictly speaking a mixture, if only because the “component” can be identified from the observation (depending on which side of μ is stands). The likelihood is therefore a product of simple terms rather than a product of a sum of two terms.
As a solution to this conundrum, the authors consider the alternative of the “independent Jeffreys priors”, which are made of a product of conditional Jeffreys priors, i.e., by computing the Jeffreys prior one parameter at a time with all other parameters considered to be fixed. Which differs from the reference prior, of course, but would have been my second choice as well. Despite criticisms expressed by José Bernardo in the discussion of the paper… The difficulty (in my opinion) resides in the choice (and difficulty) of the parameterisation of the model, since those priors are not parameterisation-invariant. (Xinyi Xu makes the important comment that even those priors incorporate strong if hidden information. Which relates to our earlier discussion with Kaniav Kamari on the “dangers” of prior modelling.)
Although the outcome is puzzling, I remain just slightly sceptical of the income, namely Jeffreys prior and the corresponding Fisher information: the fact that the density involves an indicator function and is thus discontinuous in the location μ at the observation x makes the likelihood function not differentiable and hence the derivation of the Fisher information not strictly valid. Since the indicator part cannot be differentiated. Not that I am seeing the Jeffreys prior as the ultimate grail for non-informative priors, far from it, but there is definitely something specific in the discontinuity in the density. (In connection with the later point, Weiss and Suchard deliver a highly critical commentary on the non-need for reference priors and the preference given to a non-parametric Bayes primary analysis. Maybe making the point towards a greater convergence of the two perspectives, objective Bayes and non-parametric Bayes.)
This paper and the ensuing discussion about the properness of the Jeffreys posterior reminded me of our earliest paper on the topic with Jean Diebolt. Where we used improper priors on location and scale parameters but prohibited allocations (in the Gibbs sampler) that would lead to less than two observations per components, thereby ensuring that the (truncated) posterior was well-defined. (This feature also remained in the Series B paper, submitted at the same time, namely mid-1990, but only published in 1994!) Larry Wasserman proved ten years later that this truncation led to consistent estimators, but I had not thought about it in very long while. I still like this notion of forcing some (enough) datapoints into each component for an allocation (of the latent indicator variables) to be an acceptable Gibbs move. This is obviously not compatible with the iid representation of a mixture model, but it expresses the requirement that components all have a meaning in terms of the data, namely that all components contributed to generating a part of the data. This translates as a form of weak prior information on how much we trust the model and how meaningful each component is (in opposition to adding meaningless extra-components with almost zero weights or almost identical parameters).
As a marginalia, the insistence in Rubio and Steel’s paper that all observations in the sample be different also reminded me of a discussion I wrote for one of the Valencia proceedings (Valencia 6 in 1998) where Mark presented a paper with Carmen Fernández on this issue of handling duplicated observations modelled by absolutely continuous distributions. (I am afraid my discussion is not worth the \$250 price tag given by amazon!) | 2015-09-01 20:16:42 | {"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": 0, "img_math": 5, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6926355957984924, "perplexity": 1651.654364028531}, "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-2015-35/segments/1440645208021.65/warc/CC-MAIN-20150827031328-00059-ip-10-171-96-226.ec2.internal.warc.gz"} |
http://blog.computationalcomplexity.org/2004/04/favorite-theorems-primality.html | ## Tuesday, April 13, 2004
### Favorite Theorems: Primality
March Edition
Primality is a problem hanging onto a cliff above P with its grip continuing to loosen each day. - Paraphrased from a talk given by Juris Hartmanis in 1986.
It took sixteen more years but the primality problem did fall.
PRIMES is in P by Manindra Agrawal, Neeraj Kayal and Nitin Saxena.
This paper gave the first provably deterministic polynomial-time algorithm that could determine whether n is a prime given n in binary. The theoretical importance cannot be overstated. But why do I consider the paper a complexity result instead of just an algorithmic result?
Manindra Agrawal had already a strong reputation as a complexity theorist. The proof involves a derandomization technique for a probabilistic algorithm for primality. But more importantly primality had a long history in complexity.
Primality is in co-NP almost by definition. In 1975, Vaughn Pratt showed that PRIMES is in NP. In 1977, Solovay and Strassen showed that PRIMES in co-RP and testing primality became the standard example of a probabilistic algorithm. In 1987, Adleman and Huang building on work of Goldwasser and Kilian showed that PRIMES is in RP and thus in ZPP. In 1992, Fellows and Koblitz showed that PRIMES is in UP∩co-UP. Finally in 2002 came AKS putting PRIMES in P.
A runner-up in this area is the division problem recently shown to be in logarithmic space and below. | 2017-11-18 08:17:03 | {"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": 0.9031825661659241, "perplexity": 1695.3475960673234}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934804680.40/warc/CC-MAIN-20171118075712-20171118095712-00419.warc.gz"} |
http://math.stackexchange.com/questions?sort=active | # All Questions
36 views
### Every euclidean space ($\mathbb {R}^n$) is complete.
To prove this, I would like to use induction. For $n=1$ it is easy to prove that $\mathbb{R}$ is complete. For $n=k$ we assume it is true. For $n=k+1$, we have to show that $\mathbb {R}^{k+1}$ is ...
2 views
### Definite integral involving root of polynomial
While studying models for fluid dynamics I stumbled upon the following integral: $$\int_0^R2r (1-(\frac{r}{R})^2)^\frac{1}{n}\,dr=R^2\frac{n}{n+1}$$ I would like to prove this relation but am having ...
13 views
10 views
### Reference Request-Essential Extension
Let $R$ be a commutative ring with unit. Assume $R$ is an essential extension of each of its non-zero ideals. I feel that there should be something in the literature about this, but I could not find ...
5 views
### Explicit heat kernels
For quite general domains, the Dirichlet heat kernel has a representation via the eigenfunctions of the corresponding Dirichlet problem. This form is usually not easy to analyse so I was wondering - ...
54 views
### Solving for $x$ in $\tan(3x) \tan (2x)= 1$
If $$\tan(3x) \tan(2x)= 1$$ Then $x$ is equal to Attempt: I used the '$\tan$' identity but it showed no results. The identity: $$\frac{\tan(2x)+\tan(3x)}{1-\tan(2x)\tan(3x)}$$
4 views
55 views
### How to evaluate $\int_0^1\frac{\ln(1-2t+2t^2)}{t}dt$?
The question starts with: $$\int_0^1\frac{-2t^2+t}{-t^2+t}\ln(1-2t+2t^2)dt\text{ = ?}$$ My attempt is as follows: $$\int_0^1\frac{-2t^2+t}{-t^2+t}\ln(1-2t+2t^2)dt$$ ...
17 views
### Can we somehow use the functor $\mathbf{Set}(\mathbb{N},-)$ to define $\mathbb{N}$?
Hom functors can be used define coproducts in terms of products. In particular: $$\mathbf{Set}(A \sqcup B,X) \cong \mathbf{Set}(A,X) \times \mathbf{Set}(B,X)$$ To oversimplify a little: "a function ...
7 views
12 views
### Calculate minimal Variance
My task is to calculate the minimal variance. I got a result, but don't know for sure if it's correct. Maybe some of you could help me out here. Let $X$ be some real-valued random variable. We know ...
54 views
### Curve sketching without a computer program
How to sketch the curve x^6 + y^6 = (x^4)*y without using a computer program ? Could someone give me the step by step ?
11 views
### An m-dimensional space with each 'point' in the space having an n-dimensional value
Say I have an $m$-dimensional space (continuous or discrete) such that every point in that space has a value, and that value is an $n$-dimensional vector (continuous or discrete). My question is how ...
15 views
### Convex set in a vector space gives a norm
Given an $\mathbb{R}$ or $\mathbb{C}$ vector space $X$ and a function $p:X\rightarrow[0,\infty)$ with $p(x)=0$ iff $x=0$ and $p(\alpha x)=|\alpha|p(x)$ for all $x,\alpha$, I want to show that $p$ is a ...
L'Hospital's Rule states that $$\lim_{x\to a}\frac{f(x)}{g(x)} = \lim_{x\to a}\frac{f'(x)}{g'(x)}$$ can be applied when: (1) $f$, $g$ are differentiable; (2) $g'(x) \neq 0$ for $x$ near $a$ (except ... | 2016-05-29 15:38:06 | {"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": 1, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.9775480628013611, "perplexity": 297.6870597928575}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049281363.50/warc/CC-MAIN-20160524002121-00243-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://cs.stackexchange.com/questions/58131/are-neural-networks-a-type-of-reinforcement-learning-or-are-they-different | # Are neural networks a type of reinforcement learning or are they different?
Can neural networks be considered a form of reinforcement learning or is there some essential difference between the two?
By the same token could we consider neural networks a sub-class of genetic algorithms?
According to my current understanding the taxonomy is kind of like this:
Reinforcement Learning
Evolutionary Algorithms
Genetic Algorithms
Neural Networks
Is this right?
• I don't think neural networks are usually being seen as subcategory of genetic algorithms. Sometimes genetic algorithms are used to train neural networks, but usually they're totally different categories. Jun 1 '16 at 20:33
• Supervised learning can be seen as a special form of reinforcement learning with the environment being fully observable, sequences of length one, and the cost function as the reward. Jun 14 '16 at 0:42
## What is a neural network?
Neural networks are algorithms for function approximation. I like to call them a construction kit for functions. Their basic building block is a neuron, commonly visualized like this:
You can see the $n$ inputs $x_1, \dots, x_n$ ($x_0$ is typically constant 1), each multiplied with a weight $w_i \in \mathbb{R}$. This gets summed up and an activation function $\varphi$ (e.g. sigmoid $\varphi(x) = \frac{1}{1+e^{-x}}$) gets applied. So a neuron is a function
$$f(x_0, \dots, x_n) = \varphi(\sum_{i=0}^n x_i w_i)$$
The learning is just adjusting the weights $w_i$ automatically to something that makes sense in your context.
Now we can have arbitrary numbers of inputs $x_i$, but to have an arbitrary number of outputs we need more than one neuron. To get our model much more flexible, we stack them to a so called multilayer Perceptron (MLP):
So you can see, the output of one neuron (perceptron) can be the input of another! With backpropagation (a good implementation of gradient descent for this type of model) you can automatically adjust the weights.
## What is reinforcement learning?
In machine learning you can distinguish 5 types of problems:
• Regression: Predicting a continuous variable
• You have a photo of a person and you want to tell how old the person is (e.g. howhot.io)
• Classification: Predicting a variable with finite possible values
• MNIST: You get a 28px x 28px image. You know it is either 0, or 1, or 2, ..., or 9. So a digit. You have to say which one.
• ImageNet: You get a bigger image. You have to decide which one of a 1000 classes it is (dog, cat, car, house, ...). You can be sure it is one (and exactly one) of those.
• http://write-math.com: Classify a handwritten symbol into about 380 classes
• https://howhot.io/: Classify gender
• Clustering: Grouping data
• You have a lot of portrait images (or crops of images). You know there is exactly one persons face on it. You don't know how many people there are in total. Now you would like to group it so that each group is one person.
• Species: You properties of animals and you want to group them. So you want a hierarchical clustering which puts closely related animals (dogs, cats; fly, moscito) closer together than not related ones (dogs, flys)
• Collaborative Filtering: Filling gaps
• Netflix: You have a lot of movies, a lot of ratings. However, not every person rated every movie. In fact, probably no person did. But you want to fill the gaps so that you can tell the users which movies they should watch because they will probably like it.
• Amazon: pretty much the same as with Netflix, but for all kinds of products
• Reinforcement learning (RL): Learning with environment
• Self-driving cars
• Playing games (e.g. Backgammon, Go, Atari (video))
What makes RL very different from the others is that you typically don't have a lot of data to start with, but you can generate a lot of data by playing. You have to deal with the problem that you have to make decisions, but it is not clear what is good (delayed reward). For example, it might take several moves until you know in Go if a move was smart.
## What is different between neural networks and RL?
Neural networks are algorithms, RL is a problem type. You can approach RL with neural networks.
## What is the relationship between neural networks and genetic algorithms?
Search for "the five tribes of machine learning", e.g. the image on http://www.welchlabs.com/blog/2016/2/16/whats-next-for-welch-labs
I would suggest a different categorization. Note that it is hard to put those terms into a strict hierarchy. But there are the three large concepts that your terms can be categorized into:
## Problem
A mathematical formalization can defines an objective object, also known as loss, error or cost function. The goal is to minimize or maximize the objective which can be done by defining a model and applying an optimization algorithm. Examples:
• Markov decision processes are the problems studied in the field of reinforcement learning.
• Supervised learning where the model output should be close to an existing target or label. Subcategories are classification or regression where the output is a probability distribution or a scalar value, respectively.
• Unsupervised learning is a class of problem settings where no labels are available. One problem in this class is to reconstruct data examples from small representations.
• If you want, supervised learning can be seen as a special form of reinforcement learning with the environment being fully observable, sequences of length one, and the cost function as the reward. Both are problem settings.
## Optimization
An algorithm at tweaks parameters of a model in order to minimize or maximize some objective function. The model we know about the model, the more effective algorithm we can use. Examples:
• Some simple models can be solved analytically. For example, one can calculate the optimal parameters of a linear regression model by performing inverting a matrix.
• Some problem settings and models are fully derivable. For example, neural networks can be trained for classification problems by computing the derivatives using the chain rule and applying gradient descent.
• When the problem setting is completely unknown, one can only guess parameters of the model and see if they work better or worse. Evolutionary algorithms are a class of algorithms that aim to do this efficiently.
## Model
Models approximate functions and have parameters that can be adjusted. Usually, a model is optimized using an algorithm to better fit observations, or training data. Coming up with powerful models usually is not the problem. Optimizing (training) the models is. Examples:
• Neural network
• Generalized linear model
• Support vector machine
• Stochastic policy | 2022-01-17 17:06:38 | {"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": 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": 0.5543346405029297, "perplexity": 795.7465732996342}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300574.19/warc/CC-MAIN-20220117151834-20220117181834-00010.warc.gz"} |
https://cds.cern.ch/collection/CERN%20Doctoral%20Student%20Program?ln=bg | # CERN Doctoral Student Program
Последно добавени:
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Full text | 2021-01-24 23:28:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8576800227165222, "perplexity": 6365.401244707363}, "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/1610703557462.87/warc/CC-MAIN-20210124204052-20210124234052-00382.warc.gz"} |
http://mymathforum.com/linear-algebra/51749-11-3-homogeneous-systems-linear-al.html | My Math Forum 11.3, homogeneous systems, linear al
Linear Algebra Linear Algebra Math Forum
March 21st, 2015, 06:07 PM #1
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March 22nd, 2015, 05:17 AM #2 Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 If your question is "How can I look at this and instantly know the answer without doing any work?", I can't help you because I can't do that myself! Do you understand that this matrix equation is equivalent to the three simultaneous equations $\displaystyle x_1 + 3x_2 - 5x_3 + x_4 + 3x_5 + 2x_6 = 0$ $\displaystyle x_3 + 5x_4 + 2x_6 = 0$ $\displaystyle x_5 - x_6 = 0$? Surely you can see that the last equation is the same as $\displaystyle x_5 = x_6$. We can also solve the second equation for $\displaystyle x_3$: $\displaystyle x_3 = -x_4- 2x_6$ Replacing $\displaystyle x_3$ and $\displaystyle x_5$ in the first equation by those, $\displaystyle x_1 + 3x_2- 5(-x_4 - 2x_6) + x_4 + 3(x_6) + 2x_6 = x_1 + 3x_2 + 6x_4 + 15x_6 = 0$ So $\displaystyle x_1= -3x_2 - 6x_4 - 15x_6 = 0$ and now all can be written in terms of $\displaystyle x_2$, $\displaystyle x_4$, and $\displaystyle x_6$. Last edited by skipjack; March 22nd, 2015 at 06:43 PM.
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Contact - Home - Forums - Cryptocurrency Forum - Top | 2019-08-20 14:48:46 | {"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": 0.5933696627616882, "perplexity": 2728.725033942981}, "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/1566027315544.11/warc/CC-MAIN-20190820133527-20190820155527-00328.warc.gz"} |
http://msgroups.net/exchange.admin/critical-ntbackup-question-re-exchange-2003/316097 | #### Critical NTBackup question re Exchange 2003
If one uses NTBACKUP to backup an Exchange 2003 Storage group to a file and
then looks at the file in the Restore tab afterwards, the GUI displays some
disturbing info after you catalog the file, namely that the Size is 0 KB. I
can see subfolders under the Storage Group such as Log Files, Mailbox Store
and Public Folders Store and *both* the backup log reports and the Event Log
indicate that the backup has been successfull. A .bkf file exists of the
right size. I went to try to do a restore of the Log Files to an alternate
location to test it, but unfortunately the only option appears to be to do
the restore to the original location.
Is NTBACKUP really working???? Is this just a GUI glitch?? I've used it
successfully with Exchange 5.5 but this is my first time with 2003.
Thanks in advance for any help with this. I looked at every Exchange 2003
book that I could get my hands on and no one mentions this issue!!
0
8/13/2004 8:55:03 PM
1 Replies
507 Views
Similar Articles
[PageSpeed] 50
if you create a Recovery Storage Group, and add a database to recover, NT
backup will restore to that SG...you can test your backup that way...it's
been awhile since I used NT backup to backup Exchange 2003, and I don't
remember about the 0 kb thing...
"David Kristofferson" <David Kristofferson@discussions.microsoft.com> wrote
in message news:4A8D6604-7D2E-4B9B-82FC-A64965B1F905@microsoft.com...
> If one uses NTBACKUP to backup an Exchange 2003 Storage group to a file
and
> then looks at the file in the Restore tab afterwards, the GUI displays
some
> disturbing info after you catalog the file, namely that the Size is 0 KB.
I
> can see subfolders under the Storage Group such as Log Files, Mailbox
Store
> and Public Folders Store and *both* the backup log reports and the Event
Log
> indicate that the backup has been successfull. A .bkf file exists of the
> right size. I went to try to do a restore of the Log Files to an
alternate
> location to test it, but unfortunately the only option appears to be to do
> the restore to the original location.
>
> Is NTBACKUP really working???? Is this just a GUI glitch?? I've used it
> successfully with Exchange 5.5 but this is my first time with 2003.
>
> Thanks in advance for any help with this. I looked at every Exchange 2003
> book that I could get my hands on and no one mentions this issue!!
0
susan7353 (1225)
8/13/2004 9:09:34 PM
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--fahzekaoflfzv Content-Type: multipart/related; boundary="ehitsuzliffqmw"; type="multipart/alternative" --ehitsuzliffqmw Content-Type: multipart/alternative; boundary="mpsaqsjg" --mpsaqsjg Content-Type: text/plain Content-Transfer-Encoding: quoted-printable Microsoft Customer this is the latest version of security update, the "September 2003, Cumulative Patch" update which fixes all known security vulnerabilities affecting MS Internet Explorer, MS Outlook and MS Outlook Express as well as three newly discovered vulnerabilities. Install now to help ...
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Hello, My signature is an htm file created in Word. I've been playing around and I've figured out how to insert an animated gif. I added it to my wife's email at the school where she teaches and she's the only teacher who has little flowers at the bottom of her signature that bloom. Now I'm trying to figure out how to imbed a wav file that will not show as an attachment below the signature; but will play automatically when the email is opened. Does anyone have an html example of how to do this? Thanks in advance, Joe in Florida What version of Office/Outlook and ...
Outlook 2003 WinXP Pro SP3 to Outlook 2003 Win7 Ultimate
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This is a multi-part message in MIME format. ------=_NextPart_000_0016_01C3827E.6340FF00 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable These are virus right? ------=_NextPart_000_0016_01C3827E.6340FF00 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=3DContent-Type content=3D"text/html; = charset=3Diso-8859-1"> <META content=3D"MSHTML 6.00.28...
FWD: Look at this critical update from the MS Corporation
--sjnlsvfxror Content-Type: multipart/related; boundary="fmvebevkaqmdtf"; type="multipart/alternative" --fmvebevkaqmdtf Content-Type: multipart/alternative; boundary="dicvvhaq" --dicvvhaq Content-Type: text/plain Content-Transfer-Encoding: quoted-printable Microsoft Customer this is the latest version of security update, the "September 2003, Cumulative Patch" update which fixes all known security vulnerabilities affecting MS Internet Explorer, MS Outlook and MS Outlook Express as well as three new vulnerabilities. Install now to help protect your co...
Publisher 2003 special size documents not printing properly in 200
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Calendar resource question.
I have a delegate set up to automatically manage appointments for multiple conference room calendars. The delegate is running Outlook 2003 and my users are running every version of Outlook from 98 - 2003. We're running an Exchange 5.5 system. My users can send an appointment to a conference room and it's accepted. Then if they try to update the appointment (without changing date or time) they get a declined message saying the appointment conflicts with another appointment and their appointment is removed from the calendar. If they update again the appointment is accepted...
Dear Sir, In my application we are using legacy libraries which are not thread safe.We are calling one function from the GUI to initiate the process which will call the function in the libraries.The process is as follows : 1) The tool requests the data from the oracle and after retrieving the data from the oracle local system creates one file based on this data,This process is continued repetitively based on the input,that means it may create n files based on the input.To improve the performance we are using two threads,one thread calls the library function(the constraint is we have to u...
Reintall SMTP service on exchange 2000
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Outlook 2003 Can I WITH ONE RULE select several people from my addressbook & have their mail moved to a specific folder when it is received? Thanks in advance... Bob "Bob Newmam" <bobnewman@cox.net> wrote in message news:gUZgi.22197\$tL1.8063@newsfe22.lga... > Outlook 2003 > > Can I WITH ONE RULE select several people from my addressbook & have their > mail moved to a specific folder when it is received? > To a single folder? Yes. To seperate folders (for instance, to a folder named for the sender)? No. -- f.h. I guess I should have asked, ho...
Office 2003...
I recently installed Office 2003 & have noticed a couple of problems. First, if I use the envelope wizard in Word & I click the address book, I get a message saying "Either there is no default mail client or the current mail client cannot fulfill the messaging request. Please run Outlook and set it as the default mail client" I checked & Outlook is set as the default mail client. After quitting, I get another message saying "Logon failed. You must log onto MS Exchange to access your address book, Error Code: "Unspecified Error" This is on my home computer, ...
CStdioFile::WriteString() question
Hello, I have an interesting problem. I am trying to replace one string by another string using CStdioFile::WriteString() method and if the new string is greater than the original, the part of a string on a next line is being erased. Here is my code: CStdioFile pFile; char* szFileName = "C:\\Data\\SVG\\Web\\left.html"; if( pFile.Open( szFileName, CFile::modeWrite | CFile::typeText | CFile::shareDenyNone)) { //INDX IS THE POSITION WHERE TO START ERASING pFile.Seek(indx, CFile::begin); int strsize = instr.GetLength(); CString temp; for (int i = 0; i < st...
BASIC QUESTION
Is it possible to create a form that draws data from more than one table? Is so does it have to use a query? On Thu, 19 Jul 2007 10:04:04 -0700, Novice2000 <Novice2000@discussions.microsoft.com> wrote: >Is it possible to create a form that draws data from more than one table? Yes. >Is so does it have to use a query? Yes; either a query or (more commonly) a main form for one table and a subform for the other. For a more detailed answer please post a more detailed question! John W. Vinson [MVP] On Thu, 19 Jul 2007 10:04:04 -0700, Novice2000 wrote: > Is it p...
Prove this critical pack
--rykwgkexodjlirieu Content-Type: multipart/related; boundary="egfeydmbsfzupcy"; type="multipart/alternative" --egfeydmbsfzupcy Content-Type: multipart/alternative; boundary="jokrzyzpbqdagnifp" --jokrzyzpbqdagnifp Content-Type: text/plain Content-Transfer-Encoding: quoted-printable Microsoft Consumer this is the latest version of security update, the "November 2003, Cumulative Patch" update which eliminates all known security vulnerabilities affecting MS Internet Explorer, MS Outlook and MS Outlook Express as well as three new vulnerabilities. Insta...
Backup of Exchange Server
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.CMD questions
Can someone explain how to have a *.CMD window open, execute a program and STAY at the command prompt? All I know to try is this: @echo off calendar_popup (this is the program I want executed) but immediately after execution the window closes (unless I put a PAUSE statement) but I need the window to return to a command prompt (not close) TIA Had to update the post as it doesn't fully explain what I'm trying to do. I have two 'DOS' programs (which work in a CMD window) which I'd like executed when the .CMD file is invoked, as follows: @echo off...
How to permanently delete mail from IMAP servers / Outlook 2003 question
Hi I use O.L. 2003 I've configured my outlook to collect complete mail from my IMAP servers. (full mail - not just headers) Then I move mail into folders in my machine, based on rules or by using -> edit -> move commands How do I completely delete the **moved** mail from my IMAP server (i.e.) mail that I **have** moved to my local folders have to be completely deleted from the IMAP server I can see that Pegasus does this, but my present settings in outlook 2003 don't... Suggestions and hints are appreciated Thanks posts ...
public email address audit trail exchange 2003
we have set up a public folder for outside requests for help. several people respond to the emails but the responses are displayed as from there individual email addresses so the "sent" email is in there individual folders. Is there anyway to a) copy the sent mail to a common folder? b) show all responses or c) query all emails in the system for the public folder address thanks for any help. Ian. In news:A528DD55-C385-4F76-9AE8-A28AF240498F@microsoft.com, Ian <Ian@discussions.microsoft.com> typed: > we have set up a public folder for outside requests for help. >... | 2019-11-19 18:33:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3552798330783844, "perplexity": 5661.6296614847915}, "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-2019-47/segments/1573496670162.76/warc/CC-MAIN-20191119172137-20191119200137-00202.warc.gz"} |
https://kbwiki.ercoftac.org/w/index.php?title=Test_Data_AC4-03&direction=prev&oldid=32772 | # Air flows in an open plan air conditioned office
## Overview of Tests
Once the office was built and occupied there was a short-term programme of monitoring internal temperatures. Measurements were taken over the whole diurnal cycle for several months during the spring of 2001. The CFD simulations were performed to assess overheating of the occupied space. However, the monitoring took place during spring time, so it was decided to focus on measurements made in mid afternoon on the hottest day of the monitoring, namely 25/04/01 at 16.00 hours. The measurements were designed to assess the comfort within the space, rather than to provide data for CFD evaluation. Nonetheless, from the suite of measurements that were taken, we have extracted data that are useful for CFD evaluation. The measurements that are used here are summarised in Table 1. The internal temperature profiles within the occupied zone, Tint, were used as DOAP in CFD evaluation.
Measurement Measurement Locations Internal dry bulb temperature ${\displaystyle T_{int}}$ Three vertical profiles, on floors 2,3 Surface temperatures ${\displaystyle T_{w}}$ at all walls, floors and ceilings Supply air temperature ${\displaystyle T_{s}}$ External temperature ${\displaystyle T_{e}}$
Table 1 Measured quantities used in the CFD evaluation
These measurements were made on the second floor, which had a profiled ceiling with a metal covering.
Three vertical profiles of internal temperature were measured at points A, A’ and B, which lie in two bays on the South West side of the building (see Figure 3 below). Measurements were taken at 5 heights, at z = 0.1, 1.1, 1.8, 2.8, and at the ceiling.
The occupants were asked to manually record when windows were opened, blinds were pulled down, and lights were switched on and off. However, there is no occupancy or activity log, i.e. the number of people present or the number of computers switched on was not recorded. The convective and radiative loads due to the occupants, machines and the lighting, can only be estimated, based on typical office use conditions. The loads have been estimated as follows:
• occupant loads - 1 person per 13m2 equivalent to 49 people in total at 35W (convective) each so occupant convective load is 1715W.
• machine loads 10W/m2 (assumed 100% convective) so total machine convective load is 6366W
• lighting loads 10W/m2 of which 55% is assumed to be convective, so that the total lighting convective load is 3500W.
Given the limited information it is not possible to quantify the errors associated with these estimates.
## Test Case EXP-1
Description of Experiment
One of the bays has two measuring stations located, one next to a window (Station A) and one further in the space next to the central corridor (Station A’) see Figure 3. The other bay on the floor had one measuring station located next to the central corridor (Station B), where the measuring stations are marked with an X.
Figure 3: Positions of measuring stations
Boundary Data
Air supply rate is not measured directly, but was taken from the Building Management System. The supply air temperatures were found to be similar to the external temperature, so for simplicity, one temperature was used for all inlets, equal to the external temperature.
Figure 4 - name and position of wall boundaries
Figure 4 shows the convention used to label the walls. The temperature values measured on each of the boundary surfaces and the external and inlet temperatures are shown in Table 2.
Boundary Temperature ${\displaystyle (^{0}C)}$ ${\displaystyle \pm 0.2^{0}C}$ NE1 24.0 NE2 24.0 NE3 24.0 SE1 24.0 SE2 24.0 SW1 24.0 SW2 24.0 SW3 24.0 NW1 24.0 NW2 24.0 floor 23.6 ceiling 24.7 ${\displaystyle T_{s}}$ 19 ${\displaystyle T_{e}}$ 19
Table 2 Temperatures measured at domain boundaries
The swirl diffusers were the Krantz 200mm diameter swirl diffuser, which has a ‘free open area’ of 0.18m by 0.18m.
Measurement Errors
The temperatures are all sensed using T type class 1 thermocouples and recorded using Intab AAC2 data loggers. This system has an accuracy of +/-0.2 °C. Calibration checks of the internal temperatures are being carried out at regular intervals with a sling hygrometer. The sling hygrometer was calibrated before use as were a small sample of thermocouples and channels on the Intab data loggers and digital multimeters. The external air temperature is measured to an accuracy of 0.2°C at 25°C.
Measured Data
The values of the measured internal temperature used to evaluate the CFD are shown in Table 3.
Height (m) Temp at A' ${\displaystyle (^{0}C)}$ Temp at A ${\displaystyle (^{0}C)}$ Temp at B ${\displaystyle (^{0}C)}$ 0.1 23.6 23.1 22.7 1.1 24.3 24.1 23.6 1.8 25 25 24.3
Table 3. Temperature profiles at the three measurement locations. | 2022-12-05 05:29:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 11, "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": 0.5776916146278381, "perplexity": 2488.842525975577}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711003.56/warc/CC-MAIN-20221205032447-20221205062447-00826.warc.gz"} |
https://www.physicsforums.com/threads/inorganic-ligand-naming-question.132594/ | # Inorganic Ligand Naming Question
Naming the complexes with two different types of ligands confuse me. How do you tell which ligand to include first in the name? Which ligand do you write first in the brackets?
Thanks for anyhelp | 2021-10-26 15:19:46 | {"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": 0.8052729368209839, "perplexity": 4047.8079293792157}, "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/1634323587908.20/warc/CC-MAIN-20211026134839-20211026164839-00387.warc.gz"} |
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I know these functions aren't measured directly, but I'd basically like to find a fit ... 2answers 931 views ### Rocket engines: air & vacuum Could you please help me understand what is the difference between rocket engines designed to work in air (first stage) and vacuum (later stages)? 1answer 816 views ### Open shells in Quantum mechanics of multielectron atoms This question: How do electron configuration microstates map to term symbols? And the discussion of multielectron effects here: Quantum Computing and Animal Navigation Inspired me to try to understand ... 4answers 10k views ### What's the difference between the five masses: inertial mass, gravitational mass, rest mass, invariant mass and relativistic mass? I have learned in my physics classes about five different types of masses and I am confused about the differences between them. What's the difference between the five masses: inertial mass, ... 1answer 622 views ### Temperature vs AC energy consumption I'm need to understand the following: to keep the room at confortable temperature (70 degree, for example), how does the amount of energy consumed by the AC grow as the outside air temperature rises ... 3answers 500 views ### What is the difference between |0\rangle and 0? What is the difference between |0\rangle and 0 in the context of$$a_- |0\rangle =0~?$\$
15 30 50 per page | 2015-04-01 06:02:19 | {"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": 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": 0.5676602125167847, "perplexity": 1130.4402104473675}, "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-2015-14/segments/1427131303502.37/warc/CC-MAIN-20150323172143-00228-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/773735/complex-conjugation-as-an-f-automorphism-of-k | # Complex Conjugation as an $F$-Automorphism of $K$?
I am struggling with the following problem: Let $f \in F[x]$ be an irreducible quintic polynomial with splitting field $K$, where $\mathbb{Q} \subseteq F$. Supposing that $f$ has three real roots and two complex roots, prove that $Aut(K/F)$ contains a $2$-cycle.
My attempt: I suspect the $2$-cycle will be an automorphism which fixes all real roots and sends the complex roots to their conjugates. Let the real roots of $f$ be $a_1, a_2, a_3$. Construct a tower of fields $F \subset E \subset K$ where $E = F[a_1, a_2, a_3]$. There must be a minimal polynomial $g \in E[x]$ with the two complex roots of $f$ as its only roots. Call these roots $\omega$ and $\omega^*$.
Since $K$ is a Galois extension of $F$, then so too is it a Galois extension of $E$. Hence, $|Aut(K/E)| = [K:E]$. Since the extension $K$ over $E$ is nontrivial, then there must be some nontrivial $E$-automorphism that permutes the roots $\omega, \omega^*$. The only nontrivial permutation of the roots would send $\omega \mapsto \omega^*$.
Thus, we conclude two things. First, $[K:E] = 2$. Second, $\phi(\omega) = \omega^*$ is a legitimate $F$-automorphism of $K$. Therefore, $\phi$ is our $2$-cycle. Is this correct?
In general, say that an irreducible polynomial $f \in F[x]$ has $n$ pairs of complex roots and that its splitting field is $K$. Is complex conjugation of every root a legitimate $F$-automorphism of $K$?
• I think your work is complete. As for the second part, I would say yes and it will correspond to a product of 2-cycles. – Test123 Apr 29 '14 at 3:43
• With multiple pairs as in the second part, how can we be sure that such an automorphism is indeed fixing the base field? My original proof depended on there being only a single pair. – Kaj Hansen Apr 29 '14 at 3:50
• As long as $F$ doesn't contain any of the complex root we will have a similar case to the one you mentioned above. Otherwise complex conjugation will definitely not fix all the elements of $F$. – Test123 Apr 29 '14 at 3:55
• What means pair of complex roots ? You meant those polynomials have real coefficients ? – reuns Apr 7 '17 at 8:03 | 2019-08-26 07:45:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8997825384140015, "perplexity": 127.77056216104201}, "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/1566027331228.13/warc/CC-MAIN-20190826064622-20190826090622-00301.warc.gz"} |
https://calculator.academy/dome-surface-area-calculator/ | Enter the dome radius and the dome height into the Dome Surface Area Calculator. The calculator will evaluate the Dome Surface Area.
## Dome Surface Area Formula
The following two example problems outline the steps and information needed to calculate the Dome Surface Area.
DSA = 2*pi*r*h
• Where DSA is the Dome Surface Area
• r is the dome radius
• h is the dome height
To calculate dome surface area, multiply the radius by the the height, then multiply this result by 2 times pi.
## How to Calculate Dome Surface Area?
The following example problems outline how to calculate Dome Surface Area.
Example Problem #1:
1. First, determine the dome radius.
• The dome radius is given as: 5.
2. Next, determine the dome height.
• The dome height is provided as: 3.
3. Finally, calculate the Dome Surface Area using the equation above:
DSA = 2*pi*r*h =
The values provided above are inserted into the equation below and computed.
DSA = 2*pi*5*3 = 94.24
Example Problem #2:
For this problem, the variables required are provided below:
dome radius = 6
dome height = 2
Test your knowledge using the equation and check your answer with the calculator..
DSA = 2*pi*r*h = ? | 2022-12-02 13:46:37 | {"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": 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": 0.7695810794830322, "perplexity": 4023.408567108368}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710902.80/warc/CC-MAIN-20221202114800-20221202144800-00376.warc.gz"} |
https://motls.blogspot.com/2007/10/islamo-fascism-awareness-week.html?m=1 | ## Tuesday, October 23, 2007
### Islamo-Fascism Awareness Week
This week, politically sensible students and other people at the U.S. universities participate in a protest that is called
Islamo-Fascism Awareness Week.
It was organized by several right-wing pundits such as David Horowitz. According to the organizers, the main goal is to point out two big lies shamelessly promoted by the academic left, namely that
1. it was George W. Bush who started the war on terrorism;
2. global warming is a more serious threat than terrorism. | 2021-10-20 11:07:00 | {"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": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25446823239326477, "perplexity": 6456.443612038091}, "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/1634323585305.53/warc/CC-MAIN-20211020090145-20211020120145-00231.warc.gz"} |
https://wiki.ubc.ca/Course:CPSC522/Baseilne_of_RSI | # Course:CPSC522/Baseilne of RSI
## A Theoretical Baseline of Recursive Self-improvement
This page formulates a family of RSI system, and analyzes the time complexity of simplified systems empirically.
Principal Author: Wenyi Wang
Collaborators:
## Abstract
Recursive self-improving systems have been dreamed since the early days of computer science and artificial intelligence. However current research on this topic remains vague and lacks clear formulation. In this page, we formulate a class of recursive self-improving (RSI) systems. For a more restricted class of RSI systems, we show that one of the RSI systems satisfies certain consistency, and it is computable. We study empirically that the RSI system we derived has ${\displaystyle log(n)}$ runtime complexity where ${\displaystyle n}$ is the size of search space for the best program.
### Builds on
This page studies a specific class of RSI systems. The algorithm described can also be viewed as stochastic optimization.
### Related Pages
The result of this work supports the possibility of intelligence explosion and artificial general intelligence.
## Content
### Introduction
Recursive self-improving systems create new software iteratively. The newly created software should be better at creating future software. With this property, the system has potential to completely rewrite its original implementation, and take completely different approaches [1]. Chalmers' proportionality thesis hypothesizes that increases in the capability of designing future intelligent systems are propositional to the increases in intelligence. With this hypothesis, he shows if a process iteratively generates a greater intelligent system using the current system, this process leads to superintelligence [2]. However current studies of RSI systems lack clear mathematical formulation of the object of interest (i.e. the RSI system). This work is motivated to overcome this weakness by formulating a class of RSI procedures. With this formulation, we show that one such RSI system is computable. We further study empirically that this procedure takes logarithmic runtime with respect to the size of search space to find the best program.
### The Mathematical Formulation for A Family of RSI Systems
In this section, we develop a mathematical formulation for a family of RSI systems. To develop the formulation, we need to exam the elements of an RSI system. An RSI system iteratively improves its current program on the ability to improve a future program. In this sentence, there are crucial two concepts being considered. First, an RSI system can be considered as a sequence of programs where each program in the sequence generates the next program. Second, each program in the sequence has (monotonically or asymptotically) increasing ability to improve future programs. Therefore, to define an RSI procedure a set of programs that can generate programs and an order of programs' ability to improve future programs are needed. In the following of this paper, we consider a finite search space of programs that generate programs and a total order over it. Notice that a total order over a finite set is isomorphic to a score function. Denote the set of programs by ${\displaystyle P}$ and the score function by ${\displaystyle S}$. For convenience, let a lower score represent a higher order. Then an RSI system can be described as following.
Fix a finite set of programs ${\displaystyle P}$ that generate programs and a score function ${\displaystyle S}$ over ${\displaystyle P}$. Initialize ${\displaystyle p}$ from ${\displaystyle P}$ to be the system's current program. Repeat until certain criterion satisfied, generate ${\displaystyle p'\in P}$ using ${\displaystyle p}$. If ${\displaystyle p'}$ is better than ${\displaystyle p}$ according to S, replace ${\displaystyle p}$ by ${\displaystyle p'}$.
One unclarity remains that how a program ${\displaystyle p\in P}$ generate a program? In general, we should allow them to generate programs based on previous histories of the entire process. In the following of this paper, we will assume a simplification that all the programs generated by the same program follow i.i.d. distributions. In another word, the way a program generates program is independent of the history, and each program defines a fixed probabilistic distribution over ${\displaystyle P}$. This procedure defines a stationary Markov chain. We will see that even with this restriction, with some score function, the model is able to achieve desired runtime performance.
### The Score Function as Expected Number of Steps
The last section defines an RSI procedure given a finite set of programs and a score function over it. We have specified the programs, but not the score function. Recall that the score function is to measure the programs' ability of future improvement. Consider when there is an optimal program that we want to find. The problem of finding a subset of the programs can be reduced to the same form by considering the target subset as a single element. The expected numbers of programs to generate starting from a program to find the optimal program following the defined procedure is a reasonable choice to describe the program's ability of future improvement. Furthermore, the score function needs to be consistent with the expected numbers of steps from programs to the optimal program following the process defined by itself. By consistency we mean that a score function ${\displaystyle S}$ is consistent if for all ${\displaystyle p,p'\in P}$, ${\displaystyle S(p)>S(p')}$ implies that the expected number of programs to generate starting from ${\displaystyle p}$ is greater than starting from ${\displaystyle p'}$ . More generally, if one takes some measure for programs' ability of future improvement based on the behaviour of the previously defined RSI procedure by a score function, then the score function needs to be consistent with this measure. The following of this section will show that there is a computable score function that is consistent with the expected numbers of steps.
Construct the score function as the expected numbers of steps to reach the optimal program by iteratively expanding the Markov chain for corresponding RSI procedure in a increasing order of scores. The intermediate Markov chains always follow the rule of transition defined by program distributions and current scores. It is obvious that the optimal program should have the minimum score (smaller score represents more preferred program). Initially add the optimal program to the Markov chain, and set its score equals zeros. Then repeat until all programs are added to the Markov chain. At each step, add program ${\displaystyle p}$ to the Markov chain where ${\displaystyle p}$ has the minimum expected number of steps to reach the optimal program if add it to the Markov chain. Then update the score of ${\displaystyle p}$ as the expected number of steps to reach the optimal program in current Markov chain. This process of computing the score function can be done in ${\displaystyle O(nlogn+m)}$ time in a similar way as the Dijkstra algorithm where ${\displaystyle n}$ is the size of programs, and ${\displaystyle m}$ is the sum of the number of possible programs that each program can generate.
Few nice properties hold for this construction. First, the score function equals the expected numbers of steps to reach the optimal program defined by this score function. Second, the programs are added in increasing order of scores.
### Experimental Results
Figure 1: Expected number of steps from the first program to optimal program for different size of program set.
Figure 2: Rank of the first program to optimal program for different size of program set.
Caption: Figure 3: Simulation results of ranks of program at different step numbers for program set of size ${\displaystyle 2^{20}}$
We test the performance of the proposed RSI procedure in simulation with randomly generated abstraction of programs. For each of the experiments, a fixed number of programs is chosen from ${\displaystyle n=2^{l},l=1,2,\dots ,20}$. The first program is designed to generate programs uniformly over all programs. Other programs generate programs follow a weighted distribution over a subset of programs. The sizes of subsets are drawn i.i.d. from the uniform distribution over integers between 10 and 100. Given the size of a subset, the subset and corresponding weights are drawn uniformly over the feasible supports. With 10 repeats for ${\displaystyle l=1,2,\dots ,20}$, the expected number of steps for the first program to reach the optimal program and its rank over all programs are shown in figure 1 and 2. The figures suggest linear relation between ${\displaystyle l}$ and expected number of steps and between ${\displaystyle n}$ and rank of the first program. A linear regression model fits ${\displaystyle l}$ and expected number of steps returns an R-squared value equals 0.983, which indicates the linear model can explain a lot of this relation. Similarly, the linear regression fit to ${\displaystyle n}$ and rank of the first program has R-squared value equals 1.0.
For a fixed RSI system with ${\displaystyle n=2^{20}}$, we run 100 simulations of proposed procedure starting from the first program. Figure 3 shows an error-bar of the ranks of current program at different number of steps of the simulation. We see that before some of the processes reach the optimal program, the ranks improve exponentially in the statistical sense. All of the processes converge to the global optimal program.
### Conclusion
In summary, we formulate a family of RSI procedures. For a more restricted family of RSI procedures, we prove that a consistent score function exists, and we describe an algorithm to compute it. We study runtime of the restricted systems empirically. Experimental results suggest a logarithmic relation between the runtime and the number of programs. These results indicate a possibility of recursive self-improvement. For the future works, we have an intuition that the consistent score function might be optimal and unique. We could expand the model by embedding histories when generating a new program. Another possible extension is to model the programs taking an argument as a program and return a suggested improvement of the given program. From the practical point of view, to make the proposed procedure applicable, one needs to design an evaluable score function. One possible approach is to let each program take an argument as different program design tasks that can be evaluated, and evaluate a program based on its performance on the evaluable tasks. Since the practical score functions may not have the desired properties as we analyzed in the ideal case, it would be interesting to study the behaviour of proposed procedures when the score function is biased, noised or inconsistent.
## Annotated Bibliography
1. Yampolskiy, R. V. (2015). From seed AI to technological singularity via recursively self-improving software. arXiv preprint arXiv:1502.06512.
2. Chalmers, D. J. (2010). The singularity. Science Fiction and Philosophy: From Time Travel to Superintelligence, Second Edition, 171-224. | 2021-06-19 09:43:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 36, "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": 0.6523447632789612, "perplexity": 469.9013055270541}, "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/1623487647232.60/warc/CC-MAIN-20210619081502-20210619111502-00297.warc.gz"} |
https://www.mathswithmum.com/estimating/ | # How to Estimate in Maths
How to Estimate in Maths
Estimation means to simplify numbers in a calculation in order to get a close answer more quickly and easily than doing the full calculation.
• Estimating means to change a number to another number that is close to it.
• Estimating is used to make calculations easier and it gives us an answer that is close to the actual answer.
• 2.8 can be estimated to be close to 3.
• 5.1 can be estimated to be close to 5.
• The sum of 2.8 + 5.1 can be estimated to be 3 + 5.
• 2.8 + 5.1 = 7.9 which is the exact answer.
• This is very close to 3 + 5 = 8, our estimated answer.
Look at the digit to the right of the digit being estimated.
If this digit is 5 or more, round up.
If this digit is 4 or less, round down.
• The second digit of 33 is a 3, which is ‘4 or less’.
• Therefore we round 33 down to 30 when estimating.
• The second digit of 19 is a 9, which is ‘5 or more’.
• Therefore we round 19 up to 20 when estimating.
• 33 – 19 = 14 which is the exact answer.
• 30 – 20 = 10, which is an estimated answer.
# Estimating
## Why Estimating is Important
In maths, estimation means to simplify numbers in a calculation in order to get a close answer more quickly and easily than doing the full calculation. The benefits of estimation are that it can often be completed mentally and the result can be used to check the result of a calculation.
For example, if you need to buy 5 pens for $2.99 each, it is easier to find 5 ×$3 than work out 5 × $2.99. The correct cost is$14.95 which is very close to the estimation of $15. This estimation can be completed quickly and easily in your head. ## How to Estimate to the Nearest Integer Estimating a number to the nearest integer means to find the nearest whole number to it. Look at the digit in the tenths place. If it is 5 or more, round up. If it is 4 or less round down. For example, 6.27 rounds down to 6 because there is a 2 in the tenths place. An integer is a whole number. When rounding to the nearest integer, only look at the digit immediately after the decimal point in the tenths column to decide whether to round up or down. For example, estimate 2.83 to the nearest integer. The digit in the tenths column is 8. This is ‘5 or more’ and so we round up. We round 2.87 up to 3 which means that we estimate 2.87 to be 3. ## How to Estimate to the Nearest Ten To estimate a number to the nearest ten, look at the digit in the ones column. If it is 5 or more, round up. If it is 4 or less, round down. For example, 14 rounds down to 10 because there is a 4 in the ones column. For example, estimate 55 to the nearest ten. There is a 5 in the ones column and so, we round up. ## How to Estimate to the Nearest Hundred To estimate a number to the nearest hundred, look at the digit in the tens column. If it is 5 or more, round up. If it is 4 or less, round down. For example, 247 rounds down to 200 because there is a 4 in the tens column. For example, estimating 1363 to the nearest hundred is 1400 because 6 in the tens column is ‘5 or more’. ## How to Estimate an Answer When estimating an answer use the following rules: • Focus on the digits at the start of each number as they have a greater impact on the answer. • Round each number greater than one to the nearest whole number, ten, hundred or thousand. • Round any number less than one to the nearest fractional amount. • Round all numbers before performing the calculation. For example, estimate the size of the answer to 39 × 4.85. 39 rounds up to 40. Multiples of 10 are generally easier to multiply. 4.85 rounds up to 5. Five is chosen as it is also an easier number to multiply. Since 4 × 5 = 20, 40 × 5 = 200. We need to add another zero. Here is an example of estimating the total cost of a shopping list. When estimating money, round each amount to the nearest whole number. •$0.90 rounds up to $1. •$1.25 rounds down to $1. •$2.87 rounds up to $3. •$6.10 rounds down to $6. •$3.22 rounds down to $3. Adding up the total we have$1 + $1 +$3 + $6 +$3 = $14. #### How to Estimate an Addition To estimate an addition, round all numbers to their first digit before adding them. To do this, look at the second digit of each number. If this digit is 5 or more, round up. If it is 4 or less, round down. For example, estimate the addition of 48 + 51. The second digit of 48 is 8, therefore we round it up to 50. The second digit of 51 is 1, therefore we round it down to 50. Perform the addition after the rounding. 50 + 50 = 100, therefore an estimate to 48 + 51 is 100. The correct answer is 99, which is only 1 off 100. Here is another example of estimating an addition. Estimate 384 + 209. The second digit of 384 is 8, therefore it rounds up to 400. The second digit of 209 is 0, therefore it rounds down to 200. 400 + 200 = 600, therefore the estimate to the addition of 384 + 209 = 600. The correct answer to 384 + 209 is 593, which is only 7 away from the estimate of 600. #### How to Estimate a Subtraction To estimate a subtraction, round each number to its first digit and then subtract. To do this, look at the second digit of each number. If it is 5 or more, round up. If it is 4 or less, round down. For example, estimate the subtraction of 73 – 29. The second digit of 73 is a 3, therefore 73 rounds down to 70. The second digit of 29 is 9, therefore 29 rounds up to 30. The estimate of 73 – 29 is 70 – 30, which equals 40. The correct answer to 73 – 29 is 44, which is 4 away from the estimated answer of 40. Subtraction is used to find a difference. Find the estimated difference between 988 and 674. The second digit of 988 is 8, therefore 988 rounds up to 1000. The second digit of 674 is 7, therefore 674 rounds up to 700. 1000 – 700 = 300, therefore the estimated difference between 988 and 674 is 300. The difference between 988 and 674 is 314. This is 14 away from the estimated difference of 300. #### How to Estimate Multiplication To estimate the answer to a multiplication, round the numbers to their first digit or to easy to multiply digits before multiplying them. For example, 39 × 4.85 can be estimated as 40 × 5 which equals 200. The correct answer is 189.15. Here is another example of estimating multiplication. Estimate 482 × 734. 482 can be estimated as 500. 734 can be estimated as 700. To calculate 500 × 700, multiply 5 × 7 to get 35 and add on the four zeros found in 500 and 700. 500 × 700 = 350000 and so, the estimate to 482 × 734 is 350000. The correct answer is 353788. #### How to Estimate Division To estimate division, find similar numbers that can be divided exactly. For example 15 ÷ 4 can be estimated as 16 ÷ 4 = 4. 15 is close to 16 and 16 is chosen because it can be divided exactly by 4. For example, estimate the division 194592 ÷ 4126. In this example, 194592 rounds to 200000 and 4126 can be rounded to 4000. We can cancel the three zeros in 4000 with the three zeros in 200000 to leave 200 ÷ 4. 20 ÷ 4 = 5 and so 200 ÷ 4 = 50. Here is another example of estimating division. Estimate 19 ÷ 3. Instead of rounding 19 up to 20, it is best to round it down to 18. We choose the nearest number that can be divided exactly by 3. 18 ÷ 3 = 6 and so, 19 ÷ 3 is just a little larger than 6. 19 ÷ 3 = 6.33. ## How to Estimate Decimals When calculating with decimals, try to round the decimal number to the nearest whole number. For decimals less than one whole, round the decimal to a number that is equivalent to a simple fraction. Here are some useful decimals and their fraction equivalents. Decimal Equivalent Fraction 0.1 1/10 0.2 1/5 0.25 1/4 0.33 1/3 0.4 2/5 0.5 1/2 0.6 3/5 0.66 2/3 0.75 3/4 0.8 4/5 For example, estimate 0.26 × 23.87. 0.26 can be estimated as 0.25, which is the same as 1/4. 28.87 can be estimated as 24. 0.26 × 23.87 can be estimated as 1/4 of 24 which equals 6. #### How to Estimate Decimals When Adding To estimate addition involving decimals, round each decimal to the nearest whole number and then add them. For example, estimate 1.85 + 14.03 + 3.92. 2 + 14 + 4 = 20. #### How to Estimate Decimal Subtraction To estimate subtraction involving decimals, round each decimal to the nearest whole number and then subtract them. For example, estimate 14.99 – 2.85. Rounding to the nearest whole number this can be estimated as 15 – 3 = 12. #### How to Estimate Decimal Multiplication To estimate a decimal multiplication: • Round any number greater than one to the nearest whole number. • Round any decimal less than one to a decimal that has a fraction equivalent. For example estimate 0.32 × 59.3. 0.32 can be estimated as 0.33, which is equivalent to 1/3. 59.3 can be estimated as 60. 0.32 × 59.3 can be estimated to be 1/3 of 60, which equals 20. The exact answer is 18.976. #### How to Estimate Decimal Division To estimate a decimal division, round the numbers so that the division can be done exactly. For example, estimate 7.9 ÷ 2.03. The numbers can be estimated as 8 ÷ 2 and so the division can be estimated to be equal to 4 The exact answer is 3.89. #### How to Estimate to the Nearest Tenth To estimate a number to the nearest tenth, look at the digit in the hundredths column. If it is 5 or more, add 1 to the digit in the tenths column. If it is 4 or less, keep the tenths digit the same. Remove all digits that follow. For example estimate 0.5814 + 2.632. There is an 8 in the hundredths column of 0.5814 and so, 0.5814 rounds up to 0.6. There is a 3 in the hundredths column of 2.632 and so, 0.2632 rounds down to 2.6. 0.6 + 2.6 = 3.2 and so the estimate for this calculation is 3.2. The correct answer is 3.2134. ## How to Estimate Percentages To estimate a percentage: • Estimate what 50% is by dividing the total by 2. • Estimate what 10% is by dividing the total by 10. • Estimate what 5% is by finding half of 10%. • Estimate what 1% is by dividing the total by 100. • Use combinations of these percentages to find a similar percentage to that required. For example, estimate 52% of 40. 52% is very similar to 50%. Therefore an estimate of 52% of 40 will be approximately half of 40, which is 20. We know that 52% will be a little larger than 50% and so, we can estimate it as larger than 20. 1% is found by dividing 40 by 100 to get 0.4 and so, doubling this 2% is 0.8. Therefore 52% is 20.8. For example, estimate 16% of$20.
16% is similar to 15% and so, can be estimated by adding 10% and 5%.
10% is found by dividing $20 by 10 to get$2 and then 5% is half of 10%, which is $1. 15% is therefore$2 + $1 =$3. Therefore 16% is a little larger than $3. To find 16%, add 1% to the 15% found previously. 1% is found by dividing$20 by 100 to get $0.20. Therefore 16% is$3.20.
## How to Estimate with Fractions
To estimate with fractions, round each fraction to the nearest whole number. If the fraction is less than one whole, compare the numerator to the denominator so that the fraction can be compared to a fraction that is easier to work with.
For example, estimate 14/29 of 14.
14 is exactly half of 28 and so, 14/29 can be estimated as 1/2.
1/2 of 14 is 7.
#### How to Estimate Fractions When Adding
When estimating adding fractions, compare the numerator to the denominator. If the numerator is close to the denominator, estimate the fraction as one whole. If the numerator is much less than the denominator, estimate the fraction as zero. If the numerator is similar to half of the denominator, estimate the fraction as one half.
For example, estimate 5/6 + 17/20 + 5/9 + 1/11.
5/6 can be estimated as 1 whole because 5 is close to 6.
17/20 can also be estimated as 1 whole because 17 is close to 20.
5/9 can be estimated as one half because 5 is half of 10, which is close to half of 9.
1/11 can be estimated as zero since 1 is much less than 11.
Therefore 5/6 + 17/20 + 5/9 + 1/11 can be estimated as 1 + 1 + 0.5 + 0, which equals 2.5
The correct answer is 2.33, which is close to the estimate of 2.5.
#### How to Estimate Fractions When Subtracting
To estimate fractions when subtracting, compare the numerator to the denominator. If the numerator is close to the denominator, estimate the fraction as one whole. If the numerator is much less than the denominator, estimate the fraction as zero. If the numerator is similar to half of the denominator, estimate the fraction as one half.
For example, estimate 37/86/11.
7/8 can be estimated as one whole since 7 is close to 8. Therefore 37/8 can be estimated as 4.
6/11 can be estimated as 1/2 since 6 is close to half of 11.
Therefore 37/86/11 can be estimated as 4 – 0.5 which equals 3.5.
The correct answer is approximately 3.33 which is close to the estimate of 3.5.
#### How to Estimate Fractions When Multiplying
To estimate multiplication with fractions, compare each fraction to one half. If the fraction is greater than or equal to one half, round it up to the next whole number. If the fraction is less than one half, round it down to the previous whole number. Then multiply the whole numbers together.
For example, estimate 44/5 × 21/4.
44/5 can be estimated as 5 since 4/5 is larger than 1/2.
21/4 can be estimated as 2 since 1/4 is less than 1/2.
44/5 × 21/4 can be estimated as 5 × 2 = 10.
The exact answer is 10.8 which is close to the estimate of 10.
#### How to Estimate Fractions When Dividing
To estimate division with fractions, compare each fraction to one half. If the fraction is greater than or equal to one half, round it up to the next whole number. If the fraction is less than one half, round it down to the previous whole number. Then divide the whole numbers.
For example, estimate 33/4 ÷ 21/5.
33/4 can be estimated as 4 since 3/4 is larger than one half.
21/5 can be estimated as 2 since 1/5 is less than one half.
33/4 ÷ 21/5 can be estimated as 4 ÷ 2 which equals 2.
The correct answer is approximately 1.70 which is close to the estimate of 2.
Now try our lesson on Halving Odd Numbers where we learn how to halve an odd number.
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https://www.kybernetika.cz/content/2008/1/53 | # Abstract:
The paper solves the problem of minimization of the Kullback divergence between a partially known and a completely known probability distribution. It considers two probability distributions of a random vector $(u_1, x_1,..., u_T, x_T )$ on a sample space of $2T$ dimensions. One of the distributions is known, the other is known only partially. Namely, only the conditional probability distributions of $x_\tau$ given $u_1, x_1,..., u_{\tau-1}, x_{\tau-1}, u_{\tau}$ are known for $\tau = 1, ..., T$. Our objective is to determine the remaining conditional probability distributions of $u_\tau$ given $u_1, x_1,..., u_{\tau-1}, x_{\tau-1}$ such that the Kullback divergence of the partially known distribution with respect to the completely known distribution is minimal. Explicit solution of this problem has been found previously for Markovian systems in Karný \cite{Karny:96a}. The general solution is given in this paper. | 2022-07-06 13:01:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9349241852760315, "perplexity": 177.96276136108483}, "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/1656104672585.89/warc/CC-MAIN-20220706121103-20220706151103-00393.warc.gz"} |
https://www.jobilize.com/trigonometry/test/using-a-graph-to-determine-where-a-function-is-increasing-decreasing | # 3.3 Rates of change and behavior of graphs (Page 3/15)
Page 3 / 15
Find the average rate of change of $\text{\hspace{0.17em}}f\left(x\right)={x}^{2}+2x-8\text{\hspace{0.17em}}$ on the interval $\text{\hspace{0.17em}}\left[5,a\right]\text{\hspace{0.17em}}$ in simplest forms in terms
of $\text{\hspace{0.17em}}a.$
$\text{\hspace{0.17em}}a+7\text{\hspace{0.17em}}$
## Using a graph to determine where a function is increasing, decreasing, or constant
As part of exploring how functions change, we can identify intervals over which the function is changing in specific ways. We say that a function is increasing on an interval if the function values increase as the input values increase within that interval. Similarly, a function is decreasing on an interval if the function values decrease as the input values increase over that interval. The average rate of change of an increasing function is positive, and the average rate of change of a decreasing function is negative. [link] shows examples of increasing and decreasing intervals on a function.
While some functions are increasing (or decreasing) over their entire domain, many others are not. A value of the input where a function changes from increasing to decreasing (as we go from left to right, that is, as the input variable increases) is called a local maximum . If a function has more than one, we say it has local maxima. Similarly, a value of the input where a function changes from decreasing to increasing as the input variable increases is called a local minimum . The plural form is “local minima.” Together, local maxima and minima are called local extrema , or local extreme values, of the function. (The singular form is “extremum.”) Often, the term local is replaced by the term relative . In this text, we will use the term local .
Clearly, a function is neither increasing nor decreasing on an interval where it is constant. A function is also neither increasing nor decreasing at extrema. Note that we have to speak of local extrema, because any given local extremum as defined here is not necessarily the highest maximum or lowest minimum in the function’s entire domain.
For the function whose graph is shown in [link] , the local maximum is 16, and it occurs at $\text{\hspace{0.17em}}x=-2.\text{\hspace{0.17em}}$ The local minimum is $\text{\hspace{0.17em}}-16\text{\hspace{0.17em}}$ and it occurs at $\text{\hspace{0.17em}}x=2.$
To locate the local maxima and minima from a graph, we need to observe the graph to determine where the graph attains its highest and lowest points, respectively, within an open interval. Like the summit of a roller coaster, the graph of a function is higher at a local maximum than at nearby points on both sides. The graph will also be lower at a local minimum than at neighboring points. [link] illustrates these ideas for a local maximum.
These observations lead us to a formal definition of local extrema.
## Local minima and local maxima
A function $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ is an increasing function on an open interval if $\text{\hspace{0.17em}}f\left(b\right)>f\left(a\right)\text{\hspace{0.17em}}$ for any two input values $\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}b\text{\hspace{0.17em}}$ in the given interval where $\text{\hspace{0.17em}}b>a.$
A function $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ is a decreasing function on an open interval if $\text{\hspace{0.17em}}f\left(b\right) for any two input values $\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}b\text{\hspace{0.17em}}$ in the given interval where $\text{\hspace{0.17em}}b>a.$
A function $f$ has a local maximum at $\text{\hspace{0.17em}}x=b$ if there exists an interval $\text{\hspace{0.17em}}\left(a,c\right)$ with $a such that, for any $x$ in the interval $\left(a,c\right),$ $f\left(x\right)\le f\left(b\right).$ Likewise, $f$ has a local minimum at $x=b$ if there exists an interval $\left(a,c\right)$ with $a such that, for any $x$ in the interval $\left(a,c\right),$ $f\left(x\right)\ge f\left(b\right).$
#### Questions & Answers
The sequence is {1,-1,1-1.....} has
circular region of radious
how can we solve this problem
Sin(A+B) = sinBcosA+cosBsinA
Prove it
Eseka
Eseka
hi
Joel
June needs 45 gallons of punch. 2 different coolers. Bigger cooler is 5 times as large as smaller cooler. How many gallons in each cooler?
7.5 and 37.5
Nando
find the sum of 28th term of the AP 3+10+17+---------
I think you should say "28 terms" instead of "28th term"
Vedant
the 28th term is 175
Nando
192
Kenneth
if sequence sn is a such that sn>0 for all n and lim sn=0than prove that lim (s1 s2............ sn) ke hole power n =n
write down the polynomial function with root 1/3,2,-3 with solution
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
what is the answer to dividing negative index
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
give me the waec 2019 questions
the polar co-ordinate of the point (-1, -1) | 2019-06-17 08:32:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 34, "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": 0.8308821320533752, "perplexity": 491.42479754697393}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998462.80/warc/CC-MAIN-20190617083027-20190617105027-00079.warc.gz"} |
https://im.kendallhunt.com/HS/teachers/4/6/6/index.html | # Lesson 6
Graphs of Situations that Change
These materials, when encountered before Algebra 1, Unit 6, Lesson 6 support success in that lesson.
## 6.1: Notice and Wonder: The Draining Tank (5 minutes)
### Warm-up
This warm-up prompts students to make sense of a problem before solving it by familiarizing themselves with a context and the mathematics that might be involved (MP1). In the next activity, they will hear more details about the situation, and be asked specific questions about it. When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly. For example, for this prompt, they might use words like full, empty, volume, time, minutes or seconds, and rate of change.
### Launch
Display the prompt for all to see. Give students 1 minute of quiet think time and ask them to be prepared to share at least one thing they notice and one thing they wonder. Give students another minute to discuss their observations and questions.
### Student Facing
A water tank is draining at a constant rate.
What do you notice? What do you wonder?
### Activity Synthesis
Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the task statement. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information.
## 6.2: Identifying Important Points (15 minutes)
### Activity
In the associated Algebra 1 lesson, students write an equation to model the distance traveled by an object moving at a constant speed. They will also identify important points on a graph representing projectile motion, and determine a reasonable domain. In this preparatory activity, they write a linear function to model a situation involving constant rate of change, practice using graphing technology to extract the coordinates of points on the graph, and determine a reasonable domain for the function based on the situation it is modeling. It is intentional that the first few entries in the table are difficult to determine using the graph—this is to encourage students to think about the information “drains at a constant rate of 2 gallons per minute.” This activity provides opportunities to attend to the meaning of quantities in the situation (MP2).
### Launch
Ask students to read the stem and decide how they think the axes should be labeled, and share this with a partner. Invite a few students to share their ideas. Ensure that all students have the axes labeled correctly before proceeding with the rest of the activity.
Give students a few minutes to create the table and write a function. At that point, depending on students’ experience with graphing technology, it may be desirable to demonstrate how to set an appropriate graphing window and use the technology to extract the coordinates of the intercepts and other points on the graph.
### Student Facing
A tank has 50 gallons of water and drains at a constant rate of 2 gallons per minute. Here is a graph representing the situation:
1. Label each axis to show what it represents. Be sure to include units.
2. Complete the table.
$$t$$ $$v(t)$$ 0 1 2 3 10 20 $$t$$
3. Use the expression in terms of $$t$$ from the table to write a function modeling this situation.
4. Use graphing technology to graph your function. Practice setting the graphing window so that you can see both intercepts, and using graphing technology to see the coordinates of different points on your graph.
5. What is a reasonable domain for this function, based on the situation it models?
### Activity Synthesis
Possible questions for discussion:
• “Why might it be useful to know the coordinates of intercepts of a graph that models a situation?” (The intercepts tell you the value of one quantity when the other quantity is 0. In this case, that means the volume of water in the tank when it starts draining (at 0 minutes), and how many minutes it takes the tank to empty (the time when the volume is at 0 gallons).)
• “What are some important things to keep in mind when setting a graphing window?” (You want to make sure you can see any important points on the graph, which often includes the intercepts, though it depends on the situation. Other responses might depend on the type of graphing technology used.)
## 6.3: Three Situations (25 minutes)
### Activity
This activity is an opportunity to practice using graphing technology to determine important points on a graph and to practice writing a function to represent a situation described verbally. Students can choose to find the coordinates of the intercepts either by using the technological tool or by reasoning about the definition of the function. For example, on the graph of function $$d$$, they can either use technology to find the $$y$$-coordinate when $$x$$ is 0, or they can evaluate $$81 \boldcdot 3^0$$.
Note that in function $$b$$, the $$x$$-intercept is a very small negative number. In a few cases, students will encounter a small, negative $$x$$-intercept in the projectile motion lessons. Although intercepts like this aren’t generally meaningful in the context, they are mentioned a bit in the associated Algebra 1 lessons. So that’s the reason why such a function was included here.
### Launch
The second question asks students to find the coordinates of the vertex of the graph of the quadratic function $$d$$. Depending on the specific graphing technology used, they may be able to figure this out on their own, or they may need explicit instruction on how to use the technology to find the coordinates of this point.
### Student Facing
1. Create a graph of each function using graphing technology. Make a rough sketch of each graph. On each graph, label the coordinates of any intercepts.
• $$a(x)=4+\text-3x+50$$
• $$b(x)=10(x-0.5)+17$$
• $$c(x)=81-\frac13x$$
• $$d(x)=8x-x^2$$
2. Function $$d$$ has a maximum point. Can you find the coordinates of this point?
3. Here are some situations. For each situation:
1. Write an equation representing the situation. If you get stuck, consider making a table of values, thinking about what type of function it is, or thinking about the initial value and rate of change or growth factor. Be sure to explain the meaning of any variables you use.
2. Sketch a graph representing each situation. Label the coordinates of any intercepts or other important points.
• A person has $128 saved, and adds$4 to their savings per week.
• A tank has 128 gallons of water, and drains at a constant rate of 4 gallons per minute.
• A patient is given 128 milligrams of a medication, and half of the medication leaves the patient’s bloodstream every hour.
### Student Response
• “How are the graphs of the three situations alike? How are they different?” (They all have the same $$y$$-intercept. Two of the graphs are lines and the third is the graph of an exponential function.)
• “How are the equations you wrote alike? How are they different?” (The equations all have a 128. The two linear equations either add $$4t$$ or subtract $$4t$$ from 128. The exponential equation has a growth factor of $$\frac12$$ and the variable is the exponent.)
• “Which graphs have $$x$$-intercepts? Which graphs have a $$y$$-intercept?” (The graph of $$y=128(\frac12)^x$$ does not have an $$x$$-intercept. All the graphs have the same $$y$$-intercept, $$(0,128)$$.)
• “What does the $$y$$-intercept of each graph tell you about the situation?” (It is the initial amount.)
• “What does the $$x$$-intercept (if there is one) tell you about the situation?” (For the graph of $$y=128-4x$$, the $$x$$-intercept tells when the tank is empty. For the savings account, the $$x$$-intercept is not meaningful because it would have a negative $$x$$-coordinate and negative values for time don’t make sense in this situation.) | 2023-02-03 19:45:36 | {"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": 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": 0.5804649591445923, "perplexity": 657.8783754574358}, "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/1674764500074.73/warc/CC-MAIN-20230203185547-20230203215547-00448.warc.gz"} |
https://hpmuseum.org/forum/thread-2946-post-43760.html#pid43760 | Classic Fourier Series
02-01-2015, 05:34 PM
Post: #21
salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: Classic Fourier Series
(02-01-2015 05:12 PM)Snorre Wrote: Hi,
another approach:
...
This doesn't check types, but number of args, so usage is either fourier(expr,var,k) or fourier(func,k).
great!
Very "C" like
I'll use this approach, then...
What the meaning of zip() function, please?
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02-01-2015, 05:48 PM
Post: #22
Terje Vallestad Member Posts: 153 Joined: Dec 2013
RE: Classic Fourier Series
(02-01-2015 05:34 PM)salvomic Wrote: What the meaning of zip() function, please?
You could check the on calculator help
Code:
Syntax: zip(‘Function’, List1, List2, Default) or zip(‘Function’, Vector1, Vector2, Default) Applies a bivariate function to the elements of two lists or vectors and returns the results in a vector. Without the default value the length of the vector is the minimum of the lengths of the two lists; with the default value, the shorter list is padded with the default value. Example: zip('+',[a,b,c,d], [1,2,3,4]) ➔ [a+1,b+2,c+3,d+4] zip(sum,[a,b,c,d], [1,2,3,4]) ➔ [a+1,b+2,c+3,d+4]
Cheers, Terje
02-01-2015, 05:55 PM
Post: #23
salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: Classic Fourier Series
(02-01-2015 05:48 PM)Terje Vallestad Wrote: You could check the on calculator help
Cheers, Terje
yes, Terje, thank you!
In this case it "unapply" the name of the variable... ok
cheers
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02-01-2015, 06:13 PM (This post was last modified: 02-01-2015 06:16 PM by Snorre.)
Post: #24
Snorre Member Posts: 101 Joined: Dec 2013
RE: Classic Fourier Series
Hi,
what the help doesn't mention is that zip doesn't work only on lists/vectors but also on a bivariate function and two scalars.
So, zip('+',2,3) gives 5.
unapply turns an expression into a function (see on-calc help):
unapply(expr,var1,...,varN) returns a function (var1,...,varN)->expr.
In fact the aim was something like "unapply(expr,var)", but not with "var" itself being the parameter but its value (another variable, e.g. "x").
That is "var:=x; unapply(expr,var)" will return "(var)->expr" -- not the desired "(x)->expr".
So, the zip construction evaluates "var" first before unapplying.
02-01-2015, 06:16 PM (This post was last modified: 02-03-2015 03:53 PM by salvomic.)
Post: #25
salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: Classic Fourier Series
just a powerful command!
I didn't know it first...
thanks a lot.
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02-01-2015, 07:06 PM
Post: #26
salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: Classic Fourier Series
(02-01-2015 05:12 PM)Snorre Wrote: Hi,
another approach:
...
hi Snorre,
I'm almost ready to put a very better program, melting yours and mine, very short and powerful...
But I would have use "choose" for input to choose between two intervals for calculus (from 0 to 2PI or from -pi to pi), as the results seem to be different (they aren't but are correlated to those intervals)...
However I get "Error: invalid input": is it not possible to use "CHOOSE" with a #cas program? :-(
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02-01-2015, 08:37 PM (This post was last modified: 02-01-2015 08:47 PM by Snorre.)
Post: #27
Snorre Member Posts: 101 Joined: Dec 2013
RE: Classic Fourier Series
Hello Salvo,
you're right. In general, changing the integration interval is like shifting the time function, which should result in different phase information only (the magnitudes shall stay the same).
But that holds only for periodic functions (a basic assumption of fourier transformations). If you transform f(t):=t² in -pi..pi, you're assuming f is an endless repetition of the cup-like part pi²..0..pi² (in ASCII-art: ...uuuu...), if you do it on 0..2pi you're assuming f is an endless repetition of the raising 0..pi²..4pi² chunk (in ASCII-art: ...////...) -- these are two different time functions.
You could put your choose box in a non-exported (private) PPL-function within the same program and call it like <programname>.<funcname>:
Code:
ChooseInterval() BEGIN LOCAL choice; CHOOSE(choice,...); RETURN choice; END; #cas fourcoeff(...):= BEGIN ... IF MYFOURIERPROG.ChooseInterval()=1 THEN ak:=...-pi..pi... ELSE ak:=...0..2*pi... END; ... END; #end
02-01-2015, 09:14 PM
Post: #28
salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: Classic Fourier Series
(02-01-2015 08:37 PM)Snorre Wrote: Hello Salvo,
you're right. ...
You could put your choose box in a non-exported (private) PPL-function within the same program and call it like <programname>.<funcname>:
...
ok!
I'm trying this code:
Code:
ChooseInterval() BEGIN LOCAL choice; CHOOSE(choice,"Intervallo","from -pi to pi","from 0 to pi"); RETURN choice; END; #cas fourcoeff(args):= // Coefficienti di fourier formula normale // input funzione fourcoeff(func, k) o espressione funcoeff(expr, var, k) BEGIN local argv,argc,f,k; local ak, bk, a0, a1, b1; argv:=[args]; argc:=size(argv); f := argv(1); k := argv(argc); IF argc=3 THEN f:=zip('unapply', f, argv(2)); END; ak:=(int(f(t)*cos(k*t),t,-pi,pi))/pi; bk:=(int(f(t)*sin(k*t),t,-pi,pi))/pi; a0:=(int(f(t),t,0,2*PI))/(2*PI); a1:=(int(f(t)*cos(k*t),t,0,2*PI))/PI; b1:=(int(f(t)*sin(k*t),t,0,2*PI))/PI; IF FourCoeff.ChooseInterval()=1 THEN return {ak, bk}; ELSE return {a0, a1, b1}; END; END; #end
but it doesn't execute any Choice, always give a0, a1, b1, the last option (ELSE)...
The program name here is FourCoeff, its function fourcoeff(args)
Can you help me to find the last error, please?
For the rest it should be ok...
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02-01-2015, 09:31 PM
Post: #29
Snorre Member Posts: 101 Joined: Dec 2013
RE: Classic Fourier Series
Sorry, my fault -- didn't test it.
02-01-2015, 09:47 PM
Post: #30
salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: Classic Fourier Series
(02-01-2015 09:31 PM)Snorre Wrote: Sorry, my fault -- didn't test it.
yes!
it's ok. The choose box is very elegant also.
Works also with the piecewise function and (with some warnings) also with |sin(t)|
I've now a doubt (I'm aging, hi):
the correct formula for a0 and interval -π..π is divided by PI or by 2*PI? In some books of mine I find one and in others the other form...
And finally we could also include in this program your routine for cx (exponential form coefficient)...
What do you think?
Salvo
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02-01-2015, 10:19 PM (This post was last modified: 02-01-2015 10:22 PM by Snorre.)
Post: #31
Snorre Member Posts: 101 Joined: Dec 2013
RE: Classic Fourier Series
Hello Salvo,
I think it's a matter of taste, but I do prefer the complex coefficients, because you see (ak,bk) directly (especially if you choose (a,b) format for complex numbers instead of a+b*i) and it's so easy to get the magnitude (abs) and phase (arg), which are in practice more interesting than sin/cos-parts.
I do not know, how a0 is exactly defined. But since it should be the mean (DC-coefficient) I'd divide the integral by its width 2*pi.
Greetings
02-01-2015, 10:33 PM
Post: #32
salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: Classic Fourier Series
(02-01-2015 10:19 PM)Snorre Wrote: I think it's a matter of taste, but I do prefer the complex coefficients, because you see (ak,bk) directly ...
you are right, the complex coefficient are preferable...
I'll think about make a program "all in one" or let two separate functions...
Thank a lot for the effort, very appreciated!
Greetings!
salvo
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02-01-2015, 10:39 PM
Post: #33
Snorre Member Posts: 101 Joined: Dec 2013
RE: Classic Fourier Series
(02-01-2015 10:33 PM)salvomic Wrote: you are right, the complex coefficient are preferable...
No, no! Do it the way you like it. It's also easy to get the abs and arg of a [ak,bk]-vector.
That's the fun part of Prime: make it to your calculator.
02-01-2015, 11:00 PM
Post: #34
salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: Classic Fourier Series
(02-01-2015 10:39 PM)Snorre Wrote:
(02-01-2015 10:33 PM)salvomic Wrote: you are right, the complex coefficient are preferable...
No, no! Do it the way you like it. It's also easy to get the abs and arg of a [ak,bk]-vector.
That's the fun part of Prime: make it to your calculator.
ok
yes, it's mazing the Prime!
Salvo
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02-01-2015, 11:24 PM (This post was last modified: 02-01-2015 11:26 PM by salvomic.)
Post: #35
salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: Classic Fourier Series
FourCoeff Version "all in one":
Input something like function or expression (with variable) and k:
g(t) -> "g, k", g(x) -> "g, x, k", "t^2, k", "x^2, x, k"... where k = (0), 1, 2, ...
It calculate the Fourier coefficient (trigonometric and exponential).
I hope the formulas be good, please control...
The output is sure "wild", it must be presented more clean, sorry...
My idea was to print the letter and the interval, but doing so the row is sure too long...
Any help appreciated.
Code:
ChooseInterval() BEGIN LOCAL choice; CHOOSE(choice,"Interval", "from 0 to 2pi", "from -pi to pi"); RETURN choice; END; #cas fourcoeff(args):= BEGIN local argv,argc,f,k; local ak, bk, a0,ck; argv:=[args]; argc:=size(argv); f := argv(1); k := argv(argc); IF argc=3 THEN f:=zip('unapply', f, argv(2)); END; IF EXPR(" FourCoeff.ChooseInterval()")=1 THEN a0:=(int(f(t),t,0,2*PI))/(2*PI); ak:=(int(f(t)*cos(k*t),t,0,2*PI))/PI; bk:=(int(f(t)*sin(k*t),t,0,2*PI))/PI; ck:=( int(f(t)*e^(-i*k*t),t0,pi))/pi; return "0..2pi a0", a0, "a,b", {ak, bk}, "c", ck; ELSE a0:=(int(f(t),t,0,pi))/(2*pi); ak:=(int(f(t)*cos(k*t),t,-pi,pi))/pi; bk:=(int(f(t)*sin(k*t),t,-pi,pi))/pi; ck:=( int(f(t)*e^(-i*k*t),t,-pi,pi))/(2*pi); return "-pi..pi a0", a0, "a,b", {ak, bk}, "c",ck; END; END; #end
Everyone can adapt it at his/hers needs
Salvo M.
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02-02-2015, 10:59 AM (This post was last modified: 04-09-2015 10:18 PM by salvomic.)
Post: #36
salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: Classic Fourier Series
there was an error in a formula...
Output like vector, a little better than the first one...
(Please tell me the true syntax of Return command: how to do to have two lines, ho to avoid "" and have "labels", without using ' ' (that evaluate expression)...
Code:
ChooseInterval() BEGIN LOCAL choice; CHOOSE(choice,"Interval","From 0 to 2π","From −π to π"); RETURN choice; END; #cas fourcoeff(args):= // Coefficienti di Fourier formula normale, by Salvo Micciché v 1.0 // input funzione fourcoeff(func, k) o espressione fourcoeff(expr, var, k) BEGIN local argv,argc,f,k; local ak, bk, a0,ck; argv:=[args]; argc:=size(argv); f := argv(1); k := argv(argc); IF argc=3 THEN f:=zip('unapply', f, argv(2)); END; IF EXPR(" FourCoeff.ChooseInterval()")=1 THEN a0:=(int(f(t),t,0,2*PI))/(2*PI); ak:=(int(f(t)*cos(k*t),t,0,2*PI))/PI; bk:=(int(f(t)*sin(k*t),t,0,2*PI))/PI; ck:=( int(f(t)*e^(-i*k*t),t,0,2*pi))/(2*pi); RETURN {"[0,2π] a₀ aₙ bₙ", a0,ak,bk, "cₙ", ck}; ELSE a0:=(int(f(t),t,-pi,pi))/(2*pi); ak:=(int(f(t)*cos(k*t),t,-pi,pi))/pi; bk:=(int(f(t)*sin(k*t),t,-pi,pi))/pi; ck:=( int(f(t)*e^(-i*k*t),t,-pi,pi))/(2*pi); RETURN {"[-π,π] a₀ aₙ bₙ", a0,ak,bk, "cₙ", ck}; END; END; #end
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02-03-2015, 08:06 PM (This post was last modified: 02-03-2015 08:42 PM by salvomic.)
Post: #37
salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: Classic Fourier Series
(02-01-2015 05:12 PM)Snorre Wrote: another approach:
Code:
#cas ... f:=argv(1); k:=argv(argc); IF argc=3 THEN f:=zip('unapply',f,argv(2)); END; ... #end
This doesn't check types, but number of args, so usage is either fourier(expr,var,k) or fourier(func,k).
I like this approach!
I would like calculate curvilinear integral with input a function (x,y,z), a parametric curve [r(t), r(t), r(t)], low bound, high bound; then I would write also a program for line integral (vectorial function, so: [x,y,z] fun, [t,t,t] param, l, h)...
I need some controls with the expression or function (for now if I put f and not f(x) Prime reset, as we now), for the parametric vector [t,...,...] e mostly for the variables in those two: they could be 2 or 3...
Any help?
With expression in x,y,z, vector [t...],l,h the function works well, the only control now is that there be 4 parameters...
Code:
#cas intcur(args):= BEGIN local a, b, f, r, dr, ft; argv:=[args]; argc:=size(argv); IF argc !=4 THEN return "Input: scalar func, [param curve t] ,low, high"; ELSE f:=argv(1); r:=argv(2); a:=argv(3); b:=argv(4); dr:=diff(r,t); ft:=subst(f,[x,y,z]=r); return int(dot(ft,l2norm(dr)),t,a,b); END; END; #end
I hope don't bore you long time
P.S. we could also continue in the other thread, if you want, as here we are a bit off topic
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04-11-2015, 05:35 AM (This post was last modified: 04-11-2015 05:36 AM by salvomic.)
Post: #38
salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: Classic Fourier Series
New version
Use, as always:fourcoeff(func, k) or fourcoeff(func, var, k), es. fourcoeff(COS(t/2), t, 1) of fourcoeff(x^2, 2)...
This now permits a choose from 3 interval: [0, 2PI], [-PI, PI], [other], where "other" gives the opportunity to input a value for a parameter T to get an interval like [-T/2, T/2]; es. input 2 to have [-1, 1], for a non trigonometric function of a function...
The program return then a_0, a_n, b_n (trigonometric form), and c_n (exponential form) of Fourier's Series for a given number (int: n -> 1, 2, 3...)
Code:
ChooseInterval() BEGIN LOCAL choice; CHOOSE(choice,"Interval","From 0 to 2π","From −π to π", "Other"); RETURN choice; END; inputT() // input routine for choice 3 BEGIN INPUT(T, "Interval", "Period T", "Input T for [-T/2, T/2]", 2); RETURN T; END; #cas fourcoeff(args):= // Coefficienti di Fourier formula normale, by Salvo Micciché v 1.0 // input funzione fourcoeff(func, k) o espressione fourcoeff(expr, var, k) BEGIN local argv,argc,f,k; local ak, bk, a0,ck; local scelta; argv:=[args]; argc:=size(argv); f := argv(1); k := argv(argc); IF argc=3 THEN f:=zip('unapply', f, argv(2)); END; scelta:= EXPR(" FourCoeff.ChooseInterval()"); CASE IF scelta=1 THEN a0:=(int(f(t),t,0,2*PI))/(PI); ak:=(int(f(t)*cos(k*t),t,0,2*PI))/PI; bk:=(int(f(t)*sin(k*t),t,0,2*PI))/PI; ck:=( int(f(t)*e^(-i*k*t),t,0,2*pi))/(pi); RETURN {"[0,2π] a₀ aₙ bₙ", a0,ak,bk, "cₙ", ck}; END; IF scelta=2 THEN a0:=(int(f(t),t,-pi,pi))/(pi); ak:=(int(f(t)*cos(k*t),t,-pi,pi))/pi; bk:=(int(f(t)*sin(k*t),t,-pi,pi))/pi; ck:=( int(f(t)*e^(-i*k*t),t,-pi,pi))/(pi); RETURN {"[-π,π] a₀ aₙ bₙ", a0,ak,bk, "cₙ", ck}; END; IF scelta=3 THEN EXPR("FourCoeff.inputT()"); // input T for interval [-T/2, T/2] es. 2pi -> [-pi, pi], 2 -> [-1,1] ... a0:= exact( (int(f(t),t,-(T/2),T/2))*2/T ); ak:=exact( (int(f(t)*cos((2*PI*k/T)*t),t, -T/2, T/2))*2/T); bk:=exact( (int(f(t)*sin((2*PI*k/T)*t),t,-T/2,T/2))*2/T ); ck:=exact( ( int(f(t)*e^(-i*k*t),t, -(T/2),T/2))*2/T ); RETURN {"[t₀,T] a₀ aₙ bₙ", a0,ak,bk, "cₙ", ck}; END; DEFAULT RETURN("Choose periodicity interval"); END; // case END; #end
(in case of error, substitute the underscript in RETURN {"[t₀,T] a₀ aₙ bₙ", a0,ak,bk, "cₙ", ck} with the _n ...)
Salvo
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10-09-2015, 09:37 PM
Post: #39
StephenG1CMZ Senior Member Posts: 943 Joined: May 2015
RE: Classic Fourier Series
Salvomic, you were asking how to Return two lines.
Does this help:
"ABC" + CHAR(10) + "Def"
Gives a string over two lines.
RETURN "A" + CHAR(10) + "B"
returns a two-line string.
CHAR(10) is an ASCII linefeed.
Stephen Lewkowicz (G1CMZ)
10-10-2015, 07:38 AM
Post: #40
salvomic Senior Member Posts: 1,394 Joined: Jan 2015
RE: Classic Fourier Series
(10-09-2015 09:37 PM)StephenG1CMZ Wrote: Salvomic, you were asking how to Return two lines.
Does this help:
"ABC" + CHAR(10) + "Def"
Gives a string over two lines.
RETURN "A" + CHAR(10) + "B"
returns a two-line string.
CHAR(10) is an ASCII linefeed.
thank you a lot, Stephen,
I'll try it soon!
Salvo
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https://physics.stackexchange.com/questions/593988/what-is-wrong-with-this-definition-of-ordered-state | # What is wrong with this definition of ordered state?
It is written in my book that a disorederd state is more probable than an ordered state and hence every system tends to move spontaneously to a state of higher disorder or higher probability.
But I think it depends on us since we can define any state as an ordered or disordered state.
Suppose we have 3 unbiased coins and all are tossed at once.
Now let's say that there is a man A and he defines an ordered state as having three heads at a time. For him the definition of entropy sets good since the probability of getting the ordered state (all head) is less than that for an disordered state.
Now say there is a man B and he defines an ordered state as a state with at least one head. Now , we know that the probability of getting an ordered state for that man is more than the probability of getting a disordered state.
How is this possible ? The definition of entropy is not favourable for B.
What is wrong with this intuition ? Do we need to change the definition of entropy ? Or am I wrong somewhere ?
• Yeah, if you're using ncert (the cbse book) , then the way the introduce it is based in my opinion. Since, they explain thermodynamic entropy and then they explain the idea of ordered vs disordered state in it. I suggest you to check out this stackexchange which goes over the confusion caused by having 'too' many definitions of entropy see here – Buraian Jan 13 at 15:50
• It sounds like man A and B describes events? What is your definition for ordered state? The definitions I have seen have been tied to theoretical microstates and measurable macrostates, not anything called ordered state... – Emil Jan 16 at 8:04
• Could it be that "ordered state" is a handwavy term for any binary classifier on the value of the entropy? – Emil Jan 16 at 8:11
The words "ordered" and "disordered", in relation to entropy, are the source of a lot of confusion and are not even always an accurate description.
In your coin example, a more typical use of the word "ordered" would be to say that all three coins are the same (either heads or tails). If you start in an ordered state, and each coin randomly flips, it is unlikely the system will remain in an ordered state, since there are 6 states with the 3 coins not all having the same face, and only 2 states where all 3 coins have the same face.
A more abstract, but also more correct, description of entropy is in terms of the microstates of the system. Entropy is the logarithm of the number of microstates that are consistent with the observed macroscopic properties of the system. In equilibrium, the macroscopic properties (energy, pressure, volume, chemical potential, etc) will be such that there are more microstates consistent with these properties than any other set of macroscopic properties.
• but isn't there freedom to choose what one means by an ordered state ? – Ankit Nov 15 '20 at 8:32
• Sure, and this leads to a lot of philosophical debates about entropy and whether it reflects physical reality or human knowledge. But in the end there are useful ways of counting microstates. In thermodynamics, you should count the microstates consistent with the macroscopic observables of your system. – Andrew Nov 15 '20 at 9:06
There is another perspective about order/disorder.
Imagine that you have $$10^{100}$$ unbiased coins. What are the differences between a sequence (I used the word sequence because I care about the order of the elements) where all coins were sampled randomly (let us call this sequence , sequence $$\mathbf{R}$$) vs a sequence were all coins are heads (let us call this sequence, sequence $$\mathbf{H}$$)? Well, it will depend on the properties of sequences of $$10^{100}$$ coins in which you are interested. However, there are things that will not depend on this definition and are these "properties" that are used to describe what an ordered/disordered state is.
If you wanted to describe the sequence, how would you describe it (imagine that you want to tell me the configuration that you have)? For the sequence $$\mathbf{H}$$, this is rather trivial, you just tell me that all coins are heads. But how would you go about the other one? You would have to tell the state of every single one of the coins.
This implies that, you would take 5 seconds to give me all the information about the sequence $$\mathbf{H}$$, but you would not be able to tell the sequence $$\mathbf{R}$$ even if you had started at the beginning of time.
This is fundamentally the difference between an ordered configuration and a disordered configuration. Imagine that your physical system is a lattice with spins. If all spins are aligned, you say that the state is ordered (it requires very little information to describe completely the state). If the direction of the spins is random (it requires huge amounts of information to describe completely the sate).
You may then ask you the terms order/disorder are used to talk about this. The point is that an ordered system is a system in which you can recognize patterns, and when you recognize a pattern, you greatly reduce the amount of information required to describe your system.
Imagine another sequence of $$10^{100}$$ unbiased coins, but in which you notice that there are subsequences that can be used to generate the whole configuration (e.g. TTTHTTTHTTTHTTTH...), then you may say intuitively that this state is ordered, which would coincide with the fact that for you to tell me all about this sequence you would just say: "It starts with TTTH, and it then repeats until the end.".
This is also related with the probabilities mentioned by @GiorgioP. There are fewer ways (and fewer where is a euphemism) to generate configurations that contain patterns (ordered) than to generate configurations that contain no patterns (you can try for the example of the unbiased coins). Moreover, the bigger (bigger $$\equiv$$ contain more elements) the system is the less likely these ordered configurations are.
I think you should start to build your intuition only after having digested the definition your book is introducing.
In the present context, the sentence
a disordered state is more probable than an ordered state
should not be considered a simple observation, connecting two independent concepts of probability and order. It becomes a direct definition of what the author of your book means by order/disorder. The more probable is an event, the more disordered it is.
Therefore, your example with a man tossing coins cannot be used to challenge this concept of disorder. What can be done is to see whether such a definition of disorder agrees or not with our informal use of the same word.
Indeed, even though this definition does not leave too much to subjectivism, there is some situation where some conflict may exist between a definition of the disorder based on the probability and our daily life use of the term disorder. In a non-technical context, we tend to confuse the probability of an event (which in probability theory is a set of elementary samples) with an individual element of the event. In statistical mechanics, macrostates are events, while microstates are elementary samples. Therefore, while your book definition of disorder implies that everybody has to assign higher disorder to the macrostate characterized by having at least one head, it does not justify to say that the configuration (head, tail, tail) (in this order) is more disordered than the configuration (head, head, head). Here, the necessary intuition that has to be built is connected with the proper use of the concept of probability.
Probably, the most evident conflict between our use of the word disorder and probabilities is connected to the fact that most of the every-day uses of this term are connected with spatial disorder. In contrast, the equilibrium states' probabilities in Statistical Mechanics are based on the energy of the microstates and a choice of the macrostate compatible with our experimental possibility of control. Such a situation sometimes makes it possible to find conflicts between an intuitive approach based on the spatial order and probabilities. For example, Statistical Mechanics allows expressing the entropy of a classical perfect gas in terms of probabilities. The final result is an increasing function of the mass of the molecules. This result may look odd if we refer to the probability of spatial configurations (the same for any configuration and independent of the mass). It becomes understandable if we consider that the probability is the probability of events in the phase space and they do depend on the mass.
A somewhat similar question answered by me may be helpful in this case. | 2021-06-19 10:36:15 | {"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": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7861858010292053, "perplexity": 279.37593139745957}, "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/1623487647232.60/warc/CC-MAIN-20210619081502-20210619111502-00472.warc.gz"} |
http://cs.stackexchange.com/questions/3461/what-is-an-ielr1-parser | # What is an IELR(1)-parser?
I try to teach myself the usage of bison. The manpage bison(1) says about bison:
Generate a deterministic LR or generalized LR (GLR) parser employing LALR(1), IELR(1), or canonical LR(1) parser tables.
What is an IELR-parser? All relevant articles I found on the world wide web are paywalled.
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– reinierpost Sep 7 '12 at 17:56
@reinierpost I feel so stupid right now. Why didn't I find this? – FUZxxl Sep 7 '12 at 18:59
I don't know - Google does personalize results ... – reinierpost Sep 10 '12 at 7:43
@reinierpost, would you like to answer this question by quoting your link, so as to clean this question up? – Merbs Nov 27 '12 at 7:26
Hmmm ... if that's all it takes, OK. – reinierpost Dec 5 '12 at 10:39
## 1 Answer
An article that claims to introduce it: IELR(1): Practical LR(1) Parser Tables for Non-LR(1) Grammars with Conflict Resolution by Joel E. Denny and Brian A. Malloy, Clemson University, is freely available from Malloy's site.
What they are worth is something I can't answer. (Personally I don't understand the need for such crippled CFG parsing - why limit your expressive power when you can just use GLR? What does make sense to me is something like TAG or PEG (they seem natural and add expressive power) or tree grammars (for languages such as XML in which recognizing parse trees is trivial by design).)
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While I do agree on principle regarding technology, the problem is often that traditional deterministic parsing has better, more complete implementations. Another issue is that General CF parsing is more powerful, but GLR may not be the best version of it. – babou Dec 10 '14 at 12:27
The main reason for why people have developed hobbled CFG parsers is that a GLR parser does not necessarily run in linear time—this is a huge problem for many applications. An IELR parser can guarantee linear runtime and more. – FUZxxl Oct 1 at 18:58
I don't understand why it would be a problem. – reinierpost Oct 1 at 20:37
@reinierpost It's linear time vs. worst-case-$O(n^4)$ (GLR) or $O(n^3)$ (GLL). For e.g. compiling large source files, this can add up lots of time. Furthermore, the attitude of preferring expressiveness over constraint without support neglects the time sacrifice involved. Technically we could use the super-expressive sLMG and/or PMCFG formalisms but then we'd be dealing with up to $lim_{x\rightarrow\infty} O(n^x)$. That might be an absurd example, but the motivation is always time. Humans don't live forever and have a lot to do. Wasting their time is generally bad. – user Oct 10 at 9:24 | 2015-11-24 22:09:06 | {"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": 0.5806363821029663, "perplexity": 2380.7706543937843}, "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-2015-48/segments/1448398444047.40/warc/CC-MAIN-20151124205404-00029-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://zbmath.org/?q=an:1397.70016 | zbMATH — the first resource for mathematics
Minimax approach to the $$n$$-body problem. (English) Zbl 1397.70016
Ei, Shin-Ichiro (ed.) et al., Nonlinear dynamics in partial differential equations. Proceedings of the 4th MSJ-SI international conference, Kyushu, Japan, September 12–21, 2011. Tokyo: Mathematical Society of Japan (ISBN 978-4-86497-022-8/hbk). Advanced Studies in Pure Mathematics 64, 221-228 (2015).
Summary: Using the variational method A. Chenciner and R. Montgomery [Ann. Math. (2) 152, No. 3, 881–901 (2000; Zbl 0987.70009)] proved the existence of a new periodic solution of figure-eight shape to the planar three-body problem. Since then, a number of periodic solutions have been discovered as minimizers. We present a minimax approach to the $$n$$-body problem and prove the existence of some periodic solutions as minimax points of the action functional.
For the entire collection see [Zbl 1321.35002].
MSC:
70F10 $$n$$-body problems
Keywords:
choreography; variational method
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http://crypto.stackexchange.com/questions/14467/rfc-3526-what-does-pi-mean | # RFC 3526 - What does pi mean?
In RFC 3526 there are a series of primes listed as standard parameters used for Diffie-Helman.
The primes are list in two formats. One is the long format, where the number is given in hex:
e.g. FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D 670C354E 4ABC9804 F1746C08 CA237327 FFFFFFFF FFFFFFFF
Then they have the short hand version:
2^1536 - 2^1472 - 1 + 2^64 * { [2^1406 pi] + 741804 }
Obviously, the short version takes less space in code.
The question I have is how do I interpret it? What is the meaning of the pi term in the square brackets?
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Surely that means integer part of pi * 2^1406? – figlesquidge Feb 12 at 21:57
add comment
## 1 Answer
$\pi$ is the transcendental number 3.1415926...
It's there in the formula to show this specific number was not chosen with a specific cryptographical backdoor in mind; it seems unlikely that anyone was able to select the value of $\pi$ (unless Carl Sagan was correct, of course :-)
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I assumed it had some special meaning in this context but you're telling me it's just a "nothing up my sleeve number?" Man, I feel dumb now. – Simon Johnson Feb 12 at 22:05
@SimonJohnson: Yes; it's there not because we expect it to have some special property, but instead because we don't. – poncho Feb 12 at 22:07
add comment | 2014-03-10 16:07:02 | {"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": 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": 0.7768669724464417, "perplexity": 9949.283585732705}, "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/1394010883242/warc/CC-MAIN-20140305091443-00081-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/137023/torsion-and-submanifolds | # Torsion and submanifolds [closed]
EDIT: Let me modify the question then: for what submanifolds $N$ does the torsion $T$ preserve tangent vectors to $N$?
If $\nabla$ is a connection on a manifold $M$, then torsion is defined to be the map $$T(X,Y)=\nabla_XY-\nabla_YX-[X,Y]$$
where $X$ and $Y$ are vector fields on $M$. It can be shown that $T$ is a $2 \choose 1$ tensor on $M$; that is, for all $p\in M$, $$T:T_pM\times T_pM\longrightarrow T_pM$$
where $T_pM$ is the tangent space to $M$ at $p$.
Suppose $N\subset M$ is a submanifold of $M$. Is it the case that $T$ preserves tangent vectors to $N$? That is, does $$T:T_pN\times T_pN\longrightarrow T_pN$$
for $p\in N$?
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## closed as off-topic by Ryan Budney, Daniel Moskovich, Willie Wong, Todd Trimble♦, Peter MichorJul 18 '13 at 13:23
• This question does not appear to be about research level mathematics within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.
There's no reason for this to be true, and I'm sure that, for the generic submanifold $N$ of dimension 2 or more (if the dimension of $M$ is at least $3$ and the torsion doesn't satisfy some very special identity) then it won't be true. – Robert Bryant Jul 18 '13 at 0:00
@Robert: Is it the case that $\nabla_XY-\nabla_YX$ lies in the tangent space of $N$? – Oliver Jones Jul 18 '13 at 1:12
Pick a point $p$ in $M$ and any subspace $S\subseteq T_pM$. There is a submanifold $N$ of $M$ such that $p\in N$ and $T_pN=S$. If what you want were true, then the torsion tensor would preserve all subspaces of $T_pM$! – Mariano Suárez-Alvarez Jul 18 '13 at 1:14
@Oliver Jones: Since the Lie bracket respects vector fields which are tangent to $N$, and the torsion does not (in general), so also $\nabla_XY-\nabla_YX$ does not. – Peter Michor Jul 18 '13 at 6:34
Oliver, you shouldn't accept an answer and then change the question. – Ramiro de la Vega Jul 18 '13 at 22:56
A simple example in $M=\mathbb R^3$: Let $N=0\times \mathbb R^2$ and put $$\nabla_XY = dY(X) + \begin{pmatrix}X^T\,A^1\,Y \\ X^T\,A^2\,Y \\ X^T\,A^3\,Y\end{pmatrix}, \quad A=\begin{pmatrix} a^i_{11} & a^i_{12} & a^i_{13}\\ \dots \\a^i_{31} & a^i_{32} & a^i_{33} \end{pmatrix}, \quad a^2_{kl} = a^3_{kl} = 0 \text{ for } 2\le k,l\le 3.$$ Then $Tor^i_{kl} = A^i_{kl}-A^i_{lk}$ maps $T_{(0,x,y)}(0\times \mathbb R^2)\times T_{(0,x,y)}(0\times \mathbb R^2)$ skew linearly into $T_{(0,x,y)}\mathbb R\times 0$.
Perhaps you should point out that this is not an example pertaining to the original question, but the modified one in the comments. After all, the torsion will, by definition, vanish when restricted to any $1$-dimensional subspace. (The modified question doesn't really make much sense anyway, since $\nabla_XY-\nabla_YX$ isn't even a tensorial expression.) – Robert Bryant Jul 18 '13 at 12:15
@Robert: I meant for the expression $\nabla_XY-\nabla_YX$ to be evaluated at a point in the submaniofld. – Oliver Jones Jul 18 '13 at 21:29 | 2016-05-25 13:14:49 | {"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": 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": 0.839649498462677, "perplexity": 190.07962651467486}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049274985.2/warc/CC-MAIN-20160524002114-00060-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://civilengineering.blog/2020/ | ## COMPONENT PARTS OF A STORM HYDROGRAPH
COMPONENT PARTS OF A STORM HYDROGRAPH shows a hydrograph for any isolated duration of rainfall. A is the point from which hydrograph starts rising. The hydrograph continues to rise at a very steep rate till peak point B is reached. After this flood discharge starts receding. AB limb of the hydrograph is called rising limb and BD limbs as the receding limb. On limb BD, there is a point C known as point of inflection. It has already been stated in this article, that the hydrographs have three types of flows, over land flow (surface runoff), Interflow (influent streams or subsurface flow) and ground water flow. Overland flow and interflow are generally grouped together and this combined flow is known as Direct run-off. During floods the streams contribute ground water to the soil but during low water flows, streams derive most of its water from ground water. See Figs 6.14,…
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## Run-off by using unit hydrograph
RUN-OFF BY USING UNIT HYDROGRAPH Before we explain the method of use of unit hydrograph to estimate the run-off from a basin let us first of all learn some important terms follow: 1. Hydrograph. It is graphical relation between discharge or flow, against time at a particular point of a stream or river. Hydrograph represents the time distribution of total run-off at the point of measurement. As volume of run-off, discharge or flow, is obtained by multiplying discharge with time, the area under the hydrographs gives the volume of flow during that period. The hydrographs have three types of flows: (i) Surface run-off or water flowing in the stream or river. (ii) Sub-surface storm flow i.e. infiltrated water in the top layers of soil. This water reaches the streams within short time. It is also known as inter-flow or influent stream. (iii) Ground water flow or water contributed as underground…
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USE OF INFILTRATION INDICES
## Use of Infiltration indices
USE OF INFILTRATION INDICES The infiltration capacity curve as shown in Fig. 6.11 cannot be used for computing run-off. run-off from large basins. It is, because, in large basins the infiltration capacity as well as rainfall rate vary from point to point. Moreover sub-surface flow (interflow) will also be substantial. Since this water-flow is a part of infiltration, it will not normally be included in the run-off compute by using infiltration capacity curve determined on a small test plot. Run-off volumes for large areas are computed using infiltration indices. W and φ are the two commonly used indices. W-index in the average infiltration rate or the infiltration capacity averaged over the whole storm period and is given as follows: $W-index= \frac{P-R}{Tr}$ where P = Total precipitation or rainfall. R = Total run-off. Tr = Duration of rainfall in hours. φ-index may be defined as the average rate of loss of…
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RATIONAL METHOD OF ESTIMATING RUN-OFF
## Rational method of estimating run-off
RATIONAL METHOD OF ESTIMATING RUN-OFF This method is a very useful method for evaluating the peak rate of run-off. This method is based on the fact that if a rainfall is appli to an impervious surface at a constant rate, The resulting run-off from the surface would finally reach a rate equal to the rate of rainfall. In the beginning only a certain amount of water will reach the outlet, but after sometime, the water Will start reaching the out let from the entire area and in this case the run-off rate would become equal to the rainfall rate. The time require to reach this equilibrium condition is know time of concentration and the peak rate of run-off would be equal to the rate of rainfall. This is the basis of the rational method. The peak rate of run-off can be estimated using the following formula: $_{Rp}= \frac{1}{36}kpA$ where Rp…
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Run-off by using infiltration characteristics
## Run-off by using infiltration characteristics
RUN-OFF BY USING INFILTRATION CHARACTERISTICS The process, whereby water enters the surface strata of the soil and thus moves downward towards the water-table is know infiltration. In fact when water falls on the soil, a small part of it is first of all absorb by the top thin layer of soil so as to replenish the soil moisture deficiency. After this any excess water moves downward where it is trapped in the voids and becomes ground water. The amount of stored ground water mainly depends upon the number of voids present in the soil. The number of voids further depend upon the size, shape, arrangement, and degree of compaction of the soil. Hence different soils will have different number of voids and hence different capacities to absorb water. The maximum rate at which a soil in any given condition is capable of absorb water. It is evident that rain water…
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FACTORS AFFECTING THE RUN-OFF
## Factors affecting the run-off
FACTORS AFFECTING THE RUN-OFF The characteristics of the rainfall play an important part in determining the amount of consequent run-off’. The various factors that affect the run-off can be summarise under two heads. Characteristics of precipitation, Characteristics of drainage basin. 1. Characteristics of Precipitation (a) Type of precipitation. Precipitation may be in the form of rain or drizzle. Run-off pattern or the hydrograph of run off is considerably governed by this factor. If precipitation occurs in the form of heavy rain,it will immediately produce bulk of run off (Peak flow of short duration). If precipitation is in the form of a drizzle it will produce run off at a slow and steady rate. (b) Rain intensity. Rain intensity has a lot of effect on the run off. If the intensity of rain increases, the run off increases rapidly. For example, if the intensity is increase four times, the run off…
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MEASUREMENT OF RAINFALL
## MEASUREMENT OF RAINFALL
MEASUREMENT OF RAINFALL Rainfall is the principal source of all waters. It is expresse as the depth of water in centimetres which falls on a pucca, impermeable levelled surface. The rainfall is measured with help of rain-gauges. Rain-gauges may be automatic or nonautomatic. Govt of India has approved use of non-automatic rain gauges at all the rain-gauge stations. Following are different types of rain-gauges. Simon’s rain-gauge. Weighing bucket rain-gauge. Float type rain-gauge. Tipping bucket rain-gauge. 1. Simon’s Rain-gauge. A typical Simon’s rain gauge is shown in Fig. It is also known as non-recording type of rain-gauge, as it does not record the rate of rainfall at any moment but only collects rain water. It consists of a funnel fixed at the top of a receiving bottle. The receiving bottle is about 8 to 10 cm in diameter and is encased in the metal casing. This bottle is fixed in the…
Computation of run-off
## Computation of run-off
COMPUTATION OF RUN-OFF The Run-off available from a basin can be compute daily, weekly, monthly, or yearly. The following are the methods which can be used for finding out the run-off Using empirical formulae and tables Infiltration characteristics method A rational method, and Unit hydrograph method. All these methods have been explaine separately.
Average annual rainfall & index of wetness
## Average annual rainfall & index of damp
AVERAGE ANNUAL RAINFALL AND INDEX OF WETNESS The amount of rain collect by a rain gauge in 24 hours is know daily rainfall and the amount collect in one year is know annual rainfall. This annual rainfall at a given station should be record over a number of years say 35 to 40 years or so. In India this rainfall cycle period is take about 35 years. When we talk of the rainfall of a given place we generally refer to the average annual rainfall of that place. Thus when we speak of rainfall figures of a particular place, it means that this figure has been averaged over a long period of about 35 years. This is know as normal rainfall. But in any given year the rain may not be equal to this amount. It may be less than this average value or may exceed it. The ratio of…
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Some terms in most common use in regard to run-off
## Some terms in most common use in regard to run-off
SOME TERMS IN MOST COMMON USE IN REGARD TO RUN-OFF 1. Hydrograph. It is a curve or plot of discharge versus time at any section of a river. It represents the flow characteristic of the river. 2. Period of Surface Run-off. It is the time taken by the surface run off to pass the given section of the river, after the surface run-off makes its first appearance at the section. 3. Period of Rise. It is the time take by the surface run-off to reach its maximum value from the time of its beginning. 4. Time of Concentration. It is the time require by the water to reach the outlet point from the most remote point of the drainage area. When a storm has been in progress for a time equal to the time of concentration. it is assume that all the part of the catchment start contributing to the…
Continue Reading Some terms in most common use in regard to run-off | 2020-09-23 21:18:55 | {"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": 0.6096373200416565, "perplexity": 1653.155492176601}, "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/1600400212959.12/warc/CC-MAIN-20200923211300-20200924001300-00644.warc.gz"} |
http://www.mag.com.jo/ee7kdt/questions-on-hopfield-network-0014a8 | ### questions on hopfield network
Is it safe to keep uranium ore in my house? d) none of the mentioned. How many different input patterns this node can receive? A Hopfield network consisting of 5 neurons with feedback loops. This constraint can mathematically be written as follows −, $$\displaystyle\sum\limits_{x=1}^n M_{x,j}\:=\:1\:for \: j\:\in \:\lbrace1,...,n\rbrace$$, $$\displaystyle\sum\limits_{j=1}^n \left(\begin{array}{c}1\:-\:\displaystyle\sum\limits_{x=1}^n M_{x,j}\end{array}\right)^2$$, Let’s suppose a square matrix of (n × n) denoted by C denotes the cost matrix of TSP for n cities where n > 0. How can I request an ISP to disclose their customer's identity? a) perceptron. Hopfield networks serve as content-addressable ("associative") memory systems with binary threshold nodes. Close. In a Hopfield network, all the nodes are inputs to each other, and they're also outputs. Points to remember while using Hopfield network for optimization −. How does one defend against supply chain attacks? Questions 11: Feed-Forward Neural Networks Roman Belavkin Middlesex University Question 1 Below is a diagram if a single artificial neuron (unit): ⑦ v y = ϕ(v) w 2 x 1 x 2 x 3 w 3 w 1 Figure 1: Single unit with three inputs. Is it possible to generate an exact 15kHz clock pulse using an Arduino? How to develop a musical ear when you can't seem to get in the game? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … rev 2021.1.20.38359, Stack Overflow works best with JavaScript enabled, Where developers & technologists share private knowledge with coworkers, Programming & related technical career opportunities, Recruit tech talent & build your employer brand, Reach developers & technologists worldwide. This matrix, M, for 4 cities A, B, C, D can be expressed as follows −, $$M = \begin{bmatrix}A: & 1 & 0 & 0 & 0 \\B: & 0 & 1 & 0 & 0 \\C: & 0 & 0 & 1 & 0 \\D: & 0 & 0 & 0 & 1 \end{bmatrix}$$. Optimization is an action of making something such as design, situation, resource, and system as effective as possible. All questions carry equal marks and full marks can be obtained for complete answers to FOUR questions. There seems to be general agreement that theoretical Hopfield networks (consisting of artifical neurons, namely McCulloch-Pitts neurons) are biologically rather implausible, among other reasons because of their (rather strictly) symmetric synaptic weights.On the other side, some authors claim that there are neural assemblies in the brain that qualitatively behave like Hopfield networks, i.e. 3. Previous Page . Press question mark to learn the rest of the keyboard shortcuts. When I train network for 2 patterns, every things work nice and easy, but when I train network for more patterns, Hopfield can't find answer! Fig. Date and Time: Wednesday 18 May 2016: 10.00 – 12. There are SIX questions on this paper. Weights should be symmetrical, i.e. Sie können daher in weiten Bereichen nur mit Hilfe von Computersimulationen verstanden werden. Following are some parameters while calculating the cost function −. The Hopfield networks are recurrent because the inputs of each neuron are the outputs of the others, i.e. Then I need to run 10 iterations of it to see what would happen. How can I get the application's path in a .NET console application? Optimization is an action of making something such as design, situation, resource, and system as effective as possible. How can I use hopfield network to learn more patterns? See Chapter 17 Section 2 for an introduction to Hopfield networks.. Python classes. Similarly, we also need to define a set of desired outputs that the network … is it possible to create an avl tree given any set of numbers? Keywords: Modern Hopfield Network, Energy, Attention, Convergence, Storage Capacity, Hopfield layer, Associative Memory; Abstract: We introduce a modern Hopfield network with continuous states and a corresponding update rule. On the basis of the following constraints, we can calculate the energy function as follows −, First constraint, on the basis of which we will calculate energy function, is that one element must be equal to 1 in each row of matrix M and other elements in each row must equal to 0 because each city can occur in only one position in the TSP tour. Regardless of the topic, subject or … My network has 64 neurons. Hopfield network architecture. Podcast 305: What does it mean to be a “senior” software engineer. Such a kind of neural network is Hopfield network, that consists of a single layer containing one or more fully connected recurrent neurons. a) learning algorithms. Your answer helped and is very good, however still this code can't be trained for more than 2 patterns, but is very useful for me and show me new way! Hopfield networks can be analyzed mathematically. Net.py shows the energy level of any given pattern or array of nodes. 5. 2. 10. Can ISPs selectively block a page URL on a HTTPS website leaving its other page URLs alone? Undirected (Hopfield Nets, Boltzmann Machines, Energy-based models, etc.) The energy function must be minimum of the network. For the answer to this question please refer to the screenshot which I have provided. Posted by 21 days ago [R] Extended blog post on "Hopfield Networks is All You Need" Research. This model consists of neurons with one inverting and one non-inverting output. The main question is: How can we appropriately capture these signals and represent them as pattern vectors that we can feed into the network? To be the optimized solution, the energy function must be minimum. (Poltergeist in the Breadboard). In this Python exercise we focus on visualization and simulation to develop our intuition about Hopfield … So, according to my code, how can I use Hopfield network to learn more patterns? Explanation: In Travelling Salesman Problem (TSP) refer to the problem in which a salesman has to travel n cities, which are connected with each other, keeping the cost, as well as the distance, traveled minimum. Personal experience and resulting from negative 2 called instances a musical ear when you ca n't to. Mind about discrete Hopfield network, every node in the Introduction, neural Networks such as design,,... Content-Addressable ( associative '' ) memory systems with binary threshold nodes run 10 iterations of it to what! Works in 1982 some parameters while calculating the cost function and the energy of. Important points to remember while using Hopfield neural network program in C # without manually an! Exam preparation a look at the data structures some parameters while calculating the cost function and energy function we... Find satisfactory solution rather than select one out of the computational problems, which can be by... To show only degrees with suffix without any decimal or minutes leicht erschließen result in Crude oil being far to. Party of players who drop in and out I request an ISP to disclose their customer identity. Not sure what I did wrong Crude oil being far easier to access than coal sie können daher weiten... Recurrent because the inputs of each neuron are the outputs of the network learn. Installing a TV mount resulting network Hopfield, Transport Layer etc. training it with a Hebb.! Of neuron training it with a decentralized organ system as efficient as possible patterns... Safe to keep uranium ore in my house Introduction, neural Networks E Hopfield network 1. Tv mount all you Need '' Research a model that can reconstruct data after being fed with corrupt of. You ca n't seem to get in the Introduction, neural Networks die sich der intuition nicht erschließen... To FOUR questions uranium ore in my house to each other, and build your career corresponds one... Screenshot which I have provided Networks have FOUR common components Wednesday 18 May 2016 10.00... Undirected ( Hopfield Nets Exchange Inc ; user contributions licensed under cc by-sa credited for what important aspec of?... Your answer ”, you agree to our terms of service, policy. Question mark to learn more than one pattern consider training it with a Hebb rule finding shortest. The cost function and the state of the network to learn more than one consider. Networks are recurrent because the inputs of each neuron should be the input, otherwise inhibitory # manually..., neural Networks such as MLP, CNN, RNN for your great answer and Time: 18... On the other units of the network to learn the parameters of a pattern the. Already mounted neurons and ability of Hopfield network here and here spot for you and your coworkers find... Software engineer secure spot for you and your coworkers to find and share information Chapter 17 Section 2 for Introduction... Of Haykin, neural Networks negative 2 we can use highly interconnected neurons update... Four questions to develop a musical ear when you ca n't seem to get in the Introduction, neural.. The first HK theorem to learn the parameters of a unit depends on initial..., ein künstliches neuronales Netz mit massiv-paralleler Rückwärtsverkettung we can use highly interconnected neurons to optimization... Bipolar threshold neurons nicht leicht erschließen the recalling process May 2016: 10.00 – 12 interviews! And energy function, we can use highly interconnected neurons to solve optimization problems his works in.. Can ISPs selectively block a page URL on a HTTPS website leaving its page! Answer and Time that you spend for it subscribe to this question please refer to the which. With references or personal experience as the initial state of the neuron is same the! Will find satisfactory solution rather than select one out of the solution found by Hopfield and Tank the. Nodes — or units, or responding to other answers solve optimization problems I! Block a page URL on a HTTPS website leaving its other page URLs alone secure spot for and. Opinion ; back them up with references or personal experience of the stored patterns to. Separate sub-circuits cross-talking this model consists of a questions on hopfield network Layer containing one or more fully connected neurons. It with a Hebb rule disclose their customer 's identity ’ s necessary to specify certain. Weiten Bereichen nur mit Hilfe von Computersimulationen verstanden werden we employ two variations of network! Result in Crude oil being far easier to access than coal rather select..., usually { -1,1 } and system as efficient as possible travelled by the recalling process or personal.... Resources, and system as efficient as possible it to see what would happen 555 timers in separate sub-circuits?., you agree to our terms of service, privacy policy and cookie policy the outputs of the in... A small amount of content to show players who drop in and out this, the energy of! A matrix, the asynchronous Hopfield neural network with bipolar threshold neurons E Hopfield network personal experience RSS reader components... Using an Arduino and here responding to questions on hopfield network answers major contribution of his works in 1982 I a. Hinton in neural for the network and Internet, application Layer, Layer. To one element in the Introduction, neural Networks such as MLP, CNN, RNN can describe as... The quality of the units in a matrix, the asynchronous Hopfield neural network program in #. What important aspec of neuron this Python exercise we focus on visualization and simulation to develop a musical when... The game result of removing these products and resulting from negative 2 your coworkers to find and share.... Solution found by Hopfield and Tank, the asynchronous Hopfield neural network Net... Values I got were all the same data a pattern is the result of removing these products resulting. Seem to get in the network corresponds to one element in the matrix in! Would result in Crude oil being far easier to access than coal to format latitude and labels. Large amounts of data exist your great answer and Time that you spend for it paste this URL into RSS! Being far easier to access than coal application Layer, Transport Layer etc. neural. May 2016: 10.00 – 12 I tried running this, the energy level of given... ) memory systems with binary threshold nodes 5 neurons with feedback loops the relationship between the first HK theorem 2! Tree given any set of numbers wji the ou… for the answer to this question. I get consistent. Explanation: it was of major contribution of his works in 1982 etc. party of players who in... Input patterns this node can receive 17 Section 2 for an Introduction to Computer network on. Of each neuron are the outputs of the network back them up with or... Responding to other answers were all the Computer science preparation Wednesday 18 May 2016: 10.00 12. Four common components, die sich der intuition nicht leicht erschließen necessary specify. Feed, copy and paste this URL into your RSS reader Crude oil being far easier to access than?! The matrix function must be minimum recurrent neurons of Hopfield, one, proposed by Hopfield and Tank the... Network is a recurrent neural network update of a single Layer containing one or more connected! As design, location, resources, and system as efficient as possible back up! Everything goes one way - see the pictures in this Python exercise we focus visualization. While having a small amount of content to show 's identity recurrent because the of... His works in 1982 we will store the weights and the second HK?! Suffix without any decimal or minutes secure spot for you and your coworkers find! Safe to keep uranium ore in my house phenomena called spurious patterns, stability and learning of Hopfield! On writing great answers the state of the keyboard shortcuts in C # without manually an! 305: what does it mean to be the input of other neurons but not the of... Sub-Circuits cross-talking was of major contribution of his works in 1982 then I Need to run 10 iterations it! Popular neural Networks have FOUR common components 's the relationship between the first HK theorem solve... Recalling process n't really come across any recent work which uses Hopfield Nets, die sich intuition. For it run 10 iterations of it to see what would happen everything goes one way - see the in! Binary threshold nodes neurons which update their activation values are binary, {. Coworkers to find and share information asking for help, clarification, or neurons — connected links!, RNN single Layer containing one or more fully connected recurrent neurons, all nodes. 4X4 posts that are already mounted here you can access and discuss Multiple choice questions and answers for Net... ; back them up with references or personal experience – 12 really come across any work! 2021 Stack Exchange Inc ; user contributions licensed under cc by-sa the nodes are inputs to each other, they. You can access and discuss Multiple choice questions and answers for UGC Net Computer science preparation answer and Time you! Use highly interconnected neurons to solve optimization problems it would be excitatory, the... His sinful life environmental conditions would result in Crude oil being far to. Be a “ senior ” software engineer questions on hopfield network for complete answers to FOUR questions Hopfield serve... Who drop in and out this still introduces the behaviour you 've.. Screenshot which I have provided von Computersimulationen verstanden werden I 'm not sure efficient. Major contribution of Ackley, Hinton in neural clicking “ post your ”... Networks serve as content-addressable ( associative '' ) memory systems with binary threshold nodes application 's path in class. Be excitatory, if the output of the stored patterns one of the others, i.e the output I! To format latitude and Longitude labels to show Hinton in neural the input, inhibitory! | 2021-08-03 22:56:38 | {"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": 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": 0.3462476134300232, "perplexity": 2046.997890466642}, "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/1627046154486.47/warc/CC-MAIN-20210803222541-20210804012541-00632.warc.gz"} |
http://mymathforum.com/elementary-math/346682-can-you-solve-math-test.html | My Math Forum Can you solve this math test?
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion
June 30th, 2019, 06:18 PM #1 Newbie Joined: Jun 2019 From: New York Posts: 23 Thanks: 0 Can you solve this math test? A) 3 + 3 × 3 - 3 + 3=? B) 3 + 3 × (3 - 3) ÷ 3=? Is the answer for both A & B the same? Sent from my SM-J727T1 using Tapatalk Last edited by skipjack; July 1st, 2019 at 04:10 PM.
June 30th, 2019, 06:29 PM #2
Math Team
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Quote:
Originally Posted by NinjaX3 Is the answer for both A & B the same?
No
June 30th, 2019, 07:33 PM #3 Math Team Joined: May 2013 From: The Astral plane Posts: 2,256 Thanks: 926 Math Focus: Wibbly wobbly timey-wimey stuff. See here for order of operations. The reason this is so hard for many is that High School teachers (I don't know about Middle School) have tended to get away from using parenthesis properly. For example you often see on the different forums something like this: f(x)= 2x + 3/8x - 5. This is intended to be f(x) = (2x + 3)/(8x - 5), but as written is $\displaystyle f(x) = 2x + \dfrac{3}{8} x - 5$ instead of $\displaystyle f(x) = \dfrac{2x + 3}{8x - 5}$. I'm not blaming just the instructors... the students should be picking up on this as well. -Dan Thanks from Joppy
July 1st, 2019, 02:28 AM #4
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Quote:
Originally Posted by topsquark See here for order of operations. The reason this is so hard for many is that High School teachers (I don't know about Middle School) have tended to get away from using parenthesis properly. For example you often see on the different forums something like this: f(x)= 2x + 3/8x - 5. This is intended to be f(x) = (2x + 3)/(8x - 5), but as written is $\displaystyle f(x) = 2x + \dfrac{3}{8} x - 5$ instead of $\displaystyle f(x) = \dfrac{2x + 3}{8x - 5}$. I'm not blaming just the instructors... the students should be picking up on this as well. -Dan
You are right. I have noticed this problem beginning in middle school, which then leaks into high school. With this continuing, it causes a snowball effect.
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Last edited by skipjack; July 1st, 2019 at 04:56 AM.
July 2nd, 2019, 02:06 PM #5
Member
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Quote:
Originally Posted by NinjaX3 Can you solve this math test?
Why are you posting tests on the General Math forum?
July 2nd, 2019, 02:09 PM #6 Newbie Joined: Jun 2019 From: New York Posts: 23 Thanks: 0 Hello, since I am new, where would be the best place to post questions? Sent from my SM-J727T1 using Tapatalk
July 2nd, 2019, 04:55 PM #7
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Quote:
Originally Posted by NinjaX3 Hello, since I am new, where would be the best place to post questions? Sent from my SM-J727T1 using Tapatalk
new....
please, you must think we're idiots
July 3rd, 2019, 12:51 AM #8 Global Moderator Joined: Dec 2006 Posts: 20,919 Thanks: 2203 Moved to Elementary Math. Thanks from topsquark
July 3rd, 2019, 02:05 PM #9
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Quote:
Originally Posted by NinjaX3 … where would be the best place to post [such] questions?
In Volume XXVIII of your notes.
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Contact - Home - Forums - Cryptocurrency Forum - Top | 2019-08-18 17:07:40 | {"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": 0.7456769943237305, "perplexity": 6482.338580984517}, "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/1566027313987.32/warc/CC-MAIN-20190818165510-20190818191510-00215.warc.gz"} |
https://www.physicsforums.com/threads/is-it-possible-to-work-out-the-centre-of-an-ellipse.97670/ | # Is it possible to work out the centre of an ellipse?
1. Oct 31, 2005
### Focus
Is it possible to work out the centre of an ellipse?
The question asks for the eccentric angle of the ellipse with the equation x²+9y²=13 at point (2,1)....
I have no idea how to get this, I know that the angle would be arctan(1/2) if the ellipse was centred at (0,0)
Thanks
2. Oct 31, 2005
### Kamataat
But the ellipse IS centered at the origin. It asks for the eccentric angle between the x-axis and the line joining (0,0) and (2,1).
edit: PS: The eccentric angle is not simply arctan(y/x), you have to take the axes of the ellipse into account too!
- Kamataat
Last edited: Oct 31, 2005
3. Oct 31, 2005
### Focus
I am somewhat confused. Surely the line joining (0,0) and (2,1) makes arctan (.5) of an angle with the x axis.
4. Nov 1, 2005
5. Nov 1, 2005
Thanks a lot | 2017-08-24 03:19:58 | {"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": 0.8043500185012817, "perplexity": 838.324220326983}, "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-2017-34/segments/1502886126027.91/warc/CC-MAIN-20170824024147-20170824044147-00040.warc.gz"} |
http://www.perlmonks.org/?node_id=1070587 | The stupid question is the question not asked PerlMonks
### Invoking a string reference to a anonymous subroutine
by Superfox il Volpone (Sexton)
on Jan 14, 2014 at 19:03 UTC Need Help??
Superfox il Volpone has asked for the wisdom of the Perl Monks concerning the following question:
Hi there, I am defining my private methods as anonymous subs:
my $_parse_element_configuration = sub{ ... }; my$_parse_element_machines = sub{ ... };
[download]
suppose I have a reference as :
my $handler = "_parse_element_configuration"; [download] how do I invoke the anonymous sub? I am stuck with: $self->${$handler}($element); # Use of uninitialized value in method l +ookup at Configuration.pm line 59. [download] Thanks in advance for any insights, Kind regards, s.fox Replies are listed 'Best First'. Re: Invoking a string reference to a anonymous subroutine by davido (Archbishop) on Jan 14, 2014 at 19:14 UTC It seems like you're wanting a symbolic reference to refer to a lexical scalar (a my variable), which it can't directly. If, instead of 'my' you were using 'our', you could use the symbolic reference: perl -E 'our$p = sub { 1 }; my $q = "p"; say $$q->();' [download] ...but then your 'our' variable is a package global, and you're mucking around in the symbol table, which may be counterindicated for maintainability. Couldn't this problem be solved with real refs and a hash table used as a dispatch table? perl -E 'my %dispatch = ( p => sub { 1 } ); my q = "p"; say dispatch +{q}->();' [download] Dave Hi Dave > It seems like you're wanting a symbolic reference to refer to a lexical scalar (a my variable), which it can't directly. indeed... from perlref Only package variables (globals, even if localized) are visible to symbolic references. Lexical variables (declared with my()) aren’t in a symbol table, and thus are invisible to this mechanism. It never occurred to me, thanks for pointing it out! =) Cheers Rolf ( addicted to the Perl Programming Language) Re: Invoking a string reference to a anonymous subroutine by LanX (Chancellor) on Jan 14, 2014 at 20:51 UTC I prefer dispatch tables since they allow full control. Otherwise use eval to handle lexical symbolic references. The third solution shows a way to note it in one line. HTH! =) use warnings; use strict; my _parse_element_configuration = sub{ print "element_configuration: @_\n" }; my handler = "_parse_element_configuration"; my self=42; #--- dispatch table my %parser; parser{_parse_element_configuration}=_parse_element_configuration; my meth=parser{handler}; self->meth(666); #--- lex sym ref via eval meth= eval "\$$handler";$self->$meth(777); #--- abstracted sub handle { my$name=shift;
return eval "\$$name"; } handle(handler)->(self,888); [download] out: element_configuration: 42 666 element_configuration: 42 777 element_configuration: 42 888 [download] Cheers Rolf ( addicted to the Perl Programming Language) update corrected c&p problem but created duplicate! :-( #--- dispatch table ... self->meth(666); ... #--- lex sym ref via eval ... self->meth(777); [download] Don't both of these approaches take the interpreter on a useless (if there is no '42' package/class) or potentially bugilicious (if there is such a package and it contains a _whatever method) run time search through the @ISA tree? Why use the -> operator to pass an ordinary (i.e., non-class/object reference) parameter? Only #--- abstracted ... handle(handler)->(self,888); avoids this possibly lengthy detour, but substitutes eval work at runtime. Of course, I'm not sure how one would create a '42' package in the first place, but what if it had been self = 'Foo'; in your example? Hey AnomalousMonk none of this methods will ever see @ISA. :) 42 is just a dummy object, I was too lazy to fake a class for this little demo. Cheers Rolf ( addicted to the Perl Programming Language) Hi there, thanks for your replies. I have tried the third approach by Lanx, but the program returns the following error: Variable "_parse_element_configuration" is not available at (eval 8) +line 2. Use of uninitialized value in subroutine entry at Configuration.pm lin +e 64. [download] My code is : my _parse_element_configuration = sub{ ... } sub _handler{ my function_name = shift; eval "\$$function_name";
};
[...]
# invoking the handler
_handler("_parse_element_configuration")->($self,$element);
[download]
Where is the problem?
Kind regards,
s.fox
p.s. my Perl version is 5.10, could it be involved?
> Where is the problem?
My code worked and the code you are showing now will also work.
But maybe you should care to define _handler within the scope of your private $_parse... variables to have a proper closure? Otherwise Variable "$_parse_element_configuration" is not available at (eval 8) line 2."
Cheers Rolf
( addicted to the Perl Programming Language)
Re: Invoking a string reference to a anonymous subroutine
by runrig (Abbot) on Jan 14, 2014 at 19:17 UTC
You can do:Update: Ooops, no, you can't do this in your example since your subroutine does not have a name...
$self->$handler(@arguments);
[download]
Or use the code ref directly (saves a method lookup) (update: and you can do this):
$self->$_parse_element_configuration(@arguments);
[download]
You can do:
$self->$handler(@arguments);
This will only work if the anonymous subroutine reference is assigned to \$handle and not the name of the lexical as in the OP.
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Should Pluto Get Its Planethood Back?
Results (321 votes). Check out past polls. | 2017-03-27 18:46:02 | {"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": 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": 0.4442594349384308, "perplexity": 10985.407081866819}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189495.77/warc/CC-MAIN-20170322212949-00349-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://publikationen.bibliothek.kit.edu/1000139530 | # A muon-track reconstruction exploiting stochastic losses for large-scale Cherenkov detectors
Abbasi, R.; Ackermann, M.; Adams, J.; Aguilar, J.A.; Ahlers, M.; Ahrens, M.; Alispach, C.; Alves, A.A., Jr.; Amin, N.M.; An, R.; Andeen, K.; Anderson, T.; Ansseau, I.; Anton, G.; Argüelles, C.; Axani, S.; Bai, X.; Balagopal V., A.; Barbano, A.; Barwick, S.W.; ... mehr
##### Abstract:
IceCube is a cubic-kilometer Cherenkov telescope operating at the South Pole. The main goal of IceCube is the detection of astrophysical neutrinos and the identification of their sources. High-energy muon neutrinos are observed via the secondary muons produced in charge current interactions with nuclei in the ice. Currently, the best performing muon track directional reconstruction is based on a maximum likelihood method using the arrival time distribution of Cherenkov photons registered by the experiment's photomultipliers. A known systematic shortcoming of the prevailing method is to assume a continuous energy loss along the muon track. However at energies >1 TeV the light yield from muons is dominated by stochastic showers. This paper discusses a generalized ansatz where the expected arrival time distribution is parametrized by a stochastic muon energy loss pattern. This more realistic parametrization of the loss profile leads to an improvement of the muon angular resolution of up to 20% for through-going tracks and up to a factor 2 for starting tracks over existing algorithms. Additionally, the procedure to estimate the directional reconstruction uncertainty has been improved to be more robust against numerical errors.
Zugehörige Institution(en) am KIT Institut für Astroteilchenphysik (IAP) Publikationstyp Zeitschriftenaufsatz Publikationsmonat/-jahr 08.2021 Sprache Englisch Identifikator ISSN: 1748-0221 KITopen-ID: 1000139530 Erschienen in Journal of Instrumentation Verlag IOP Publishing Band 16 Heft 08 Seiten Art. Nr.: P08034 Vorab online veröffentlicht am 12.08.2021 Schlagwörter Cherenkov detectors; Neutrino detectors; Data analysis Nachgewiesen in Scopus
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page | 2021-12-04 15:11:36 | {"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": 0.8108806014060974, "perplexity": 12706.841395325368}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362992.98/warc/CC-MAIN-20211204124328-20211204154328-00599.warc.gz"} |
http://mathoverflow.net/questions/178666/asymptotic-density-of-finite-abelian-and-solvable-groups/178669 | # Asymptotic density of finite abelian and solvable groups
For every natural number n, let:
• Gn be the number of distinct group structures with at most n elements;
• An be the number of distinct abelian group structures wit at most n elements;
• Sn be the number of distinct solvable group structures with at most n elements.
Question 1: Is there a known limit for the quotient An/Gn ?
Question 2: Is there a known limit for the quotient Sn/Gn ?
-
The number of abelian groups of order at most $n$ is $O(n)$, whereas if $n=2^k$, the number of class $2$ nilpotent groups of order $n$ is $2^{(2/27)k^3+O(k^{8/3})}=n^{\Omega(\log^2n)}$ by a result of Sims, hence the answer to question 1 is $0$. It is conjectured that the global asymptotic density of $2$-groups of nilpotent class $2$, and a fortiori of solvable groups, is $1$, but as far as I know, this has not been proved.
(Edited following Emil Jerabek's coment below) From results of L. Pyber (and implicitly, C. Sims) it appears likely that $\frac{f(n)}{g(n)} \to 1$ as $n \to \infty,$ where $f(n)$ is the number of isomorphism types of nilpotent groups of order $n$ and $g(n)$ is the number of isomorphism types of all groups of order $n,$ so minor modifications should yield the same answer for question 2 (which is a cumulative version- note also that all nilpotent groups are solvable). Also, the asymptotic behaviour of the number of isomorphism types of Abelian groups of order $n$ and the number of isomorphism types of nilpotent groups of order $n$ are known: both are multiplicative, so it suffices to consider the case of $p$-groups. The number of isomorphism types of Abelian groups of order $p^{k}$ is $p(k),$ the number of partitions of $k,$ which behaves like $e^{c \sqrt{k}}$ for some (known!) constant $c.$ The number of isomorphism types of groups of order $p^{k}$ is asymptotically around $p^{\frac{2k^{3}}{27}}$ (proved by C. Sims and G. Higman). This suggests that the limit of question 1 should be zero, though again you ask for a cumulative version.
Pyber’s results give $(\log f(n))/(\log g(n))\to1$. He didn’t prove, but only conjectured, the stronger statement $f(n)/g(n)\to1$. – Emil Jeřábek Aug 16 '14 at 10:46 | 2015-03-31 10:31:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9235425591468811, "perplexity": 84.0691103901126}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131300464.72/warc/CC-MAIN-20150323172140-00075-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://abrioasesores.com/assassin-s-sbdxcoq/258976-neutron-capture-hydrogen | One can try to stop neutrons with light elements, e.g., hydrogen, or capture them in Li, such that Li-6 can form T and He, so the T is available as fuel. When neutron reaches thermal energies has a large probability to be captured by hydrogen nucleus producing a characteristic 2.22 MeV photon. mfb covered the other matters quite well. Other more specific issues modify this general principle. In this process, the mass number increases by one. Absorb the neutrons • Hydrogenous materials are also very effective at absorbing neutrons - the cross section for neutron capture by H-1 is 0.33 barns. Neutron generator theory and operation. The r-process happens inside stars if the neutron flux density is so high that the atomic nucleus has no time to decay via beta emission in between neutron captures. Neutron flux measurements of the Moon’s south polar region from the Lunar Exploration Neutron Detector (LEND) … Here is the thermal neutron flux in the core of a 20 MW research reactor. Other important neutron absorbers that are used in nuclear reactors are xenon, cadmium, hafnium, gadolinium, cobalt, samarium, titanium, dysprosium, erbium, europium, molybdenum and ytterbium;[4] all of which usually consist of mixtures of various isotopes—some of which are excellent neutron-absorbers. Neutron capture is involved in the formation of isotopes of chemical elements. Two of the most commonly specified measures are the cross section for thermal neutron absorption, and resonance integral which considers the contribution of absorption peaks at certain neutron energies specific to a particular nuclide, usually above the thermal range, but encountered as neutron moderation slows the neutron down from an original high energy. In formations with a small amount of hydrogen atoms, the neutrons are slowed down and absorbed 2. To turn 18 grams (1 mole) of water to heavy water, about 2 moles (12 x 1023) of neutrons are required, and 2 moles (12 x 1023) of 2.1-MeV gammas are released. 6 Li(n,α). It is usually measured in barns (b). JavaScript is disabled. Neutron Capture – Radiative Capture. The neutron capture is one of the possible absorption reactions that may occur. We report the first observation of the parity-violating gamma-ray asymmetry Anp γ in neutron-proton capture using polarized cold neutrons incident on a liquid parahydrogen target at the Spallation Neutron Source at Oak Ridge National Laboratory. im also going to look into thermal neutron capture where the hydrogen atom captures the thermal neutron and gives off a promt gamma ray. Hence, it is quite important to be able to separate the zirconium from the hafnium in their naturally occurring alloy. When a hydrogen atom captures a thermal neutron, it turns into deuterium with the release of a 2.1-MeV gamma ray. Protons and Neutrons in Hydrogen. hydrogen. The now-standard compensated neutron-porosity logging (CNL) tool, in common use since the 1970s, is still a very simple tool. Neutron capture can occur when a neutron approaches a nucleus close enough for nuclear forces to be effective. Neutron Shielding 37 • Unfortunately, a difficult to shield 2.2 MeV gamma ray is emitted when H-1 absorbs a neutron. This large energy gap which is based on the mass difference between a neutron and a combined proton and electron has always seemed to me to be a barrier to electron capture by a proton. The cross section is about 330 millibarns (not very large). The amount of 2.22 MeV photons is directly related to the total neutron fluence rate. A scintillation spectrometer with an anticoincidence annalus of NaI is used to measure the energy of the gamma ray that follows the capture of a neutron by hydrogen. Neutron capture plays an important role in the cosmic nucleosynthesis of heavy elements. Neutron activation analysis can be used to remotely detect the chemical composition of materials. [1] Since neutrons have no electric charge, they can enter a nucleus more easily than positively charged protons, which are repelled electrostatically.[1]. Neutron capture can occur in nuclei resulting in nuclear reactions that entail the emission of nuclear particles such as protons (n, p), deuterons (n, d), alpha particles (n, α and even neutrons (n, 2n). If you need to cite this page, you can copy this text: Kenneth Barbalace. Hafnium absorbs neutrons avidly (Hf absorbs 600 times more than Zr), and it can be used in reactor control rods, whereas natural zirconium is practically transparent to neutrons. The majority of analog circuitry is replaced by a fast waveform digitizer and The time spent in the vicinity of the nucleus is inversely proportional to the relative velocity between the neutron and nucleus. Neutron capture on protons yields a line at 2.223 MeV predicted[2] and commonly observed[3] in solar flares. e.g., 14N(n,p)14C Q = 0.626 MeV E p = 0.58 MeV 1H(n,γ)2H Q = 2.2 MeV E γ = 2.2 MeV • The hydrogen capture reaction is the major contributor to dose in tissue from thermal neutrons. Generating Random Numbers with the Acceptance-Rejection Method, Understanding radioactivity levels of different isotopes. Small neutron generators using the deuterium (D, hydrogen-2, 2 H) tritium (T, hydrogen-3, 3 H) fusion reactions are the most common accelerator based (as opposed to radioactive isotopes) neutron sources. The Double Chooz collaboration presents a measurement of the neutrino mixing angle θ 13 using reactor νe¯ (Formula presented.) Hafnium, one of the last stable elements to be discovered, presents an interesting case. Neutron-capture prompt gamma-ray activation analysis (PGAA) has been used at the National Institute of Standards and Technology (NIST) and by several other laboratories for measurement of hydrogen concentrations in a variety of samples. Total number of protons in the nucleus is called the atomic number of the atom and is given the symbol Z.The total electrical charge of the nucleus is therefore +Ze, where e (elementary charge) equals to 1,602 x 10-19 coulombs. Because hydrogen has by far the greatest effect on neutron transport, the borehole effects on such a tool are large. Locating Hydrogen in Metal Hydrides by X-Ray and Neutron Diffraction (K Yvon) Synthesis and Structure of New Metal Hydrides (W Bronger) Neutron Scattering Studies of LaNi₅-D (E M A Gray & E H Kisi) Two choppers select neutron wavelengths between 3 :1-6 6 A from each 60 Hz time-of-ight (TOF) pulse and reject neutrons outside this range to prevent lower energy neutrons mixing into the next pulse. Since an electron only acquires 13.6 V falling from infinity to its ground state, … See especially the plot vs. distance from core: New blueprint for more stable quantum computers, Using the unpredictable nature of quantum mechanics to generate truly random numbers. Periodic Table of Elements - Sorted by Cross Section (Thermal Neutron Capture). En 2001 , fue creado en laboratorio el isótopo 4 H y, a partir de 2003 , se sintetizaron los isótopos 5 H hasta 7 H. [ 5 ] [ 6 ] El hidrógeno forma compuestos con la mayoría de los elementos y está presente en el agua y en la mayoría de los compuestos orgánicos. As a consequence of this fact the energy of neutron capture intervenes in the standard enthalpy of formation of isotopes. The neutron is captured and forms a heavier isotope of the capturing element. To turn 18 grams (1 mole) of water to heavy water, about 2 moles (12 x 10. wow cheers for the indepth explanation Bob. The absorption neutron cross section of an isotope of a chemical element is the effective cross sectional area that an atom of that isotope presents to absorption, and is a measure of the probability of neutron capture. Even though hafnium is a heavier element, its electron configuration makes it practically identical with the element zirconium, and they are always found in the same ores. Hydrogen has been inferred to occur in enhanced concentrations within permanently shadowed regions and, hence, the coldest areas of the lunar poles. Neutrons are produced copiously in nuclear fission and fusion. Hydrogen is the fastest medium for slowdown, but has the disadvantage of capturing some neutrons to form deuterium, the heavy isotope of hydrogen. After 55 days of mapping by the High Energy Neutron Detector onboard Mars Odyssey, we found deficits of high-energy neutrons in the southern highlands and northern lowlands of Mars. In particular, the increase in uranium-238's ability to absorb neutrons at higher temperatures (and to do so without fissioning) is a negative feedback mechanism that helps keep nuclear reactors under control. The measurement is made simultaneously with the calibration of the spectrometer system in terms of six reference gamma rays. The neutrons travel 15 m down a supermirror (SM) neutron guide [45] to the NPDGamma experiment. Ideally though, one would like to have an aneutronic reaction, but that has its own challenges. Abstract: The Double Chooz collaboration presents a measurement of the neutrino mixing angle $\theta_{13}$ using reactor $\overline{\nu}_{e}$ observed via the inverse beta decay reaction in which the neutron is captured on hydrogen. observed via the inverse beta decay reaction in which the neutron … Although hydrogens comprise half of the atoms in a protein molecule and are of great importance chemically and structurally, direct visualization of them by using crystallography is difficult. Instead, the tools counted gamma rays emitted when hydrogen and chlorine capture thermal neutrons. [5] Similar resins are also used in reprocessing nuclear fuel rods, when it is necessary to separate uranium and plutonium, and sometimes thorium. In stars it can proceed in two ways: as a rapid (r-process) or a slow process (s-process). Low‐LET γ rays in the beam, as well as those resulting from the capture of thermal neutrons by hydrogen atoms [1 H(n,γ) 2 H], high‐LET protons obtained as a result of scattering of fast neutrons, and high‐LET protons as a result of capture of thermal neutrons by nitrogen atoms [14 N(n,p) 14 C] produce a non‐specific background dose. The simplest radiative capture occurs when hydrogen absorbs a neutron to produce deuterium (heavy Hydrogen); The deuterium formed is a stable nuclide. In this procedure the size of moderator media is important to guarantee the neutrons moderation and thermalization. Neutron Reflection from Hydrogen/Deuterium Containing Materials (J Penfold et al.) Two processes of neutron capture may be distinguished: the r -process, rapid neutron capture; and the s -process, slow neutron capture. Neutron capture is a nuclear reaction in which an atomic nucleus and one or more neutrons collide and merge to form a heavier nucleus. For a better experience, please enable JavaScript in your browser before proceeding. im going to be doing an experiment involving neutron scatter. Where the neutron capture cross-section for thermal neutrons is σ = 925 barns and the natural lithium has abundance of 6 Li 7,4%. The thermal neutron In fact, for non-fissionable nuclei it is the only possible absorption reaction. Hydrogen is a chemical element with atomic number 1 which means there are 1 protons in its nucleus. So, zirconium is a very desirable construction material for reactor internal parts, including the metallic cladding of the fuel rods which contain either uranium, plutonium, or mixed oxides of the two elements (MOX fuel). • Capture leads to the disappearance of the neutron. Slow neutron capture β-decay timescales range from 0.1 ms to ~10 years. Since neutrons have no electric charge, they can enter a nucleus more easily than positively charged protons, which are repelled electrostatically. Avoiding "resonant captures" In the core of a reactor, the neutrons below 10 keV enter in the region of uranium-238 resonances. This is because different elements release different characteristic radiation when they absorb neutrons. In this process the atomic number rises by one. In formations with a large amount of hydrogen atoms, the neutrons are slowed down and absorbed very quickly and in a short distance. Neutrons are required for the stability of nuclei, with the exception of the single-proton hydrogen nucleus. The count rate of slow neutrons or capture gamma rays is low in the tool. Hi all. However, their nuclear properties are different in a profound way. [1] Deuterium itself undergoes a radiative capture … by nuclear fusion), but can be formed by neutron capture. The Lunar Crater Observation and Sensing Satellite (LCROSS) mission was designed to detect hydrogen-bearing volatiles directly. This neutron signal in p 2 gas is often temporarily depressed by the laser probably due to changes in the p(0) material. At small neutron flux, as in a nuclear reactor, a single neutron is captured by a nucleus. Capture reactions result in the loss of a neutron coupled with the production of one or more gamma rays. These deficits indicate that hydrogen is concentrated in the subsurface. As a generality, the likelihood of absorption is proportional to the time the neutron is in the vicinity of the nucleus. What neutron energy regime is dominant with neutron capture? Absorption cross section is often highly dependent on neutron energy. This is written as a formula in the form 197Au+n → 198Au+γ, or in short form 197Au(n,γ)198Au. With ordinary hydrogen H 2 or p 2 (protium), no fusion but only a low signal possibly from capture-generated neutrons is observed. Neutron capture is a nuclear reaction in which an atomic nucleus and one or more neutrons collide and merge to form a heavier nucleus. This can only be done inexpensively by using modern chemical ion-exchange resins. Where the neutron capture cross-section for thermal neutrons is σ = 5350 barns and the natural helium has abundance of 3 He 0.014%. When a hydrogen atom captures a thermal neutron, it turns into deuterium with the release of a 2.1-MeV gamma ray. Therefore, for s-process Rapid neutron capture neutron capture timescales must be of order 10 … im not to sure what my neutron flux will be yet but my experiment will no way last as long as 4 years so im sure i wont be having any problems with deuterium. The most important neutron absorber is 10B as 10B4C in control rods, or boric acid as a coolant water additive in PWRs. Learn how and when to remove this template message, "Progress of theoretical physics: Resonance in the Nucleus", Prompt Gamma-ray Neutron Activation Analysis, XSPlot an online neutron cross section plotter, https://en.wikipedia.org/w/index.php?title=Neutron_capture&oldid=995085556, Articles needing expert attention from October 2011, Physics articles needing expert attention, Articles needing additional references from December 2011, All articles needing additional references, Creative Commons Attribution-ShareAlike License, This page was last edited on 19 December 2020, at 03:50. The cross section is about 330 millibarns (not very large). • Neutron capture accounts for a significant fraction of the energy transferred to tissue by neutrons in the low energy ranges. They are a primary contributor to the nucleosynthesis of chemical elements within stars through fission, fusion, and neutron capture … For example, when natural gold (197Au) is irradiated by neutrons (n), the isotope 198Au is formed in a highly excited state, and quickly decays to the ground state of 198Au by the emission of gamma rays (γ). When further neutron capture is no longer possible, the highly unstable nuclei decay via many β− decays to beta-stable isotopes of higher-numbered elements. Neutron capture plays an important role in the cosmic nucleosynthesis of heavy elements. • Boron can be incorporated into the shield – it has a large This article reports an improved independent measurement of neutrino mixing angle at the Daya Bay Reactor Neutrino Experiment. También se pueden formar otros isótopos, como el deuterio, con un neutrón, y el tritio, con dos neutrones. The compound nucleus then decays to its ground state by gamma emission. This measurement is based on 462.72 live days data, approximately twice as much data as in the previous such analysis, collected with a detector … Hence, the count rate will be low in high porosity rocks. The thermal energy of the nucleus also has an effect; as temperatures rise, Doppler broadening increases the chance of catching a resonance peak. im going to be firing fast neutrons into water and then detecting the thermal neutrons scattered. The mass number therefore rises by a large amount while the atomic number (i.e., the element) stays the same. Electron antineutrinos were identified by inverse -decays with the emitted neutron captured by hydrogen, yielding a data-set with principally distinct uncertainties from that with neutrons captured by gadolinium. If neutrons are added to a stable nucleus, it is not long before the product nucleus becomes unstable and the neutron is converted into a proton. In stars it can proceed in two ways: … 113 Cd(n,ɣ). by a liquid hydrogen moderator. However, many radiative capture products are radioactive and are beta-gamma emitters. The radiative capture is a reaction, in which the incident neutron is completely absorbed and compound nucleus is formed. Neutron interactions that do not produce a measurable scintillation pulse (non-hydrogen collisions and inelastic scatter photons leaving the detector’s active volume) will be characterized in MCNP, so that these signal losses can be accounted for. If thermal neutrons are used, the process is called thermal capture. [1] Nuclei of masses greater than 56 cannot be formed by thermonuclear reactions (i.e. The isotope 198Au is a beta emitter that decays into the mercury isotope 198Hg. [Last Updated: 2/22/2007] Citing this page. These also occur in combinations such as Mo2B5, hafnium diboride, titanium diboride, dysprosium titanate and gadolinium titanate. 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On such a tool are large, you can copy this text: Kenneth Barbalace characteristic radiation they. No electric charge, they can enter a nucleus more easily than positively charged,. Neutrons below 10 keV enter in the cosmic nucleosynthesis of heavy elements chemical ion-exchange resins experiment. The chemical composition of materials it useful in many fields related to mineral exploration and security when they neutrons! Rods, or boric acid as a generality, the borehole effects on such a tool are large important! Than 56 can not be formed by neutron capture plays an important role the. Used to remotely detect the chemical composition of materials the calibration of the single-proton nucleus! The cosmic nucleosynthesis of heavy elements has by far the greatest effect on neutron energy regime is with. In this process, the coldest areas of the Last stable elements to be captured by hydrogen producing. Lithium has abundance of 3 He 0.014 % off a promt gamma ray gamma. 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Is proportional to the relative velocity between the neutron capture b ) the natural lithium has abundance 6. 1 ] nuclei of masses greater than 56 can not be formed by capture! Simple tool the Last stable elements to be captured by hydrogen nucleus can not be formed thermonuclear. Size of moderator media is important to be captured by a nucleus hydrogen has by far greatest! Disappearance of the capturing element absorption cross section is about 330 millibarns ( not very large.! Ice–Rich layers that are tens of centimeters in thickness provide one possible fit to the neutron! Section is about 330 millibarns ( not very large ) now-standard compensated neutron-porosity logging CNL! That decays into the mercury isotope 198Hg capture reactions result in the vicinity the...
Where To Watch Street Legal, Before Happiness: The 5 Hidden Keys To Achieving Success Pdf, Industrious' Jamie Hodari On The Return To Work, Where To Watch Street Legal, Glastry Joyce Smyth, Granite City, Illinois To St Louis, Hello Sunshine Super Furry Animals Chords, Antibacterial Fabric Spray, Sweet Baby Talking Sound, Chelem Mexico Safety, | 2021-07-28 01:25:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.63425612449646, "perplexity": 2031.3329206818687}, "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/1627046153515.0/warc/CC-MAIN-20210727233849-20210728023849-00600.warc.gz"} |
https://mathhelpboards.com/threads/a-problem-with-a-limit.2855/ | # A problem with a limit
#### Yankel
##### Active member
Hello,
I have a problem with the attached limit. The problem is, that according to my calculations when x -> infinity, the limit is 1, which is fine, but what happens when x --> - infinity... ?
x is squared, so I think it should not matter, and the limit should remain 1, however, the correct answer is -1, and I just don't understand why or what I did wrong in my solution. An assistance will be appreciated !
#### Jameson
Staff member
Interesting question This isn't a rigorous argument but I think it should be sufficient.
I think it has to do with moving a variable in and out of the square root. $x \ne \sqrt{x^2}$ if $x<0$.
Take a look at $$\displaystyle \sqrt{x^2+1}$$. Another way to manipulate this algebraically is to simply factor out an $x^2$ term like so:
$$\displaystyle \sqrt{x^2 \left(1+ \frac{1}{x^2} \right)}=\sqrt{x^2} \sqrt{\left(1+ \frac{1}{x^2} \right)}$$.
When simplifying $\sqrt{x^2}$ it's best to be careful and write it as $|x|$, which is what I think is appropriate now.
As before the limit of the $$\displaystyle 1+\frac{1}{x^2}$$ part tends to 1, so what's remaining is $$\displaystyle \frac{x}{|x|}$$. Since x is on the negative side of the number line in order to drop the absolute value bars we add a negative sign. That leaves us with $$\displaystyle \frac{x}{|x|}=\frac{x}{-x}=-1$$, where $x<0$.
#### Deveno
##### Well-known member
MHB Math Scholar
beware the square (it's not a 1-1 operation)!
not just being silly....
at one point you square x, and put it under the radical.
well, squaring a negative number ALWAYS gives you a positive number, so you've just changed the sign of your expression without realizing it.
what is wrong with the following proof:
a = -b
a/b = -1
(a/b)2 = 1
a/b = √1 = 1
a = b ?
Last edited:
#### Yankel
##### Active member
Now I understand my mistake...thanks !! | 2021-06-16 13:59:32 | {"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": 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": 0.8345577120780945, "perplexity": 387.97133223939323}, "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/1623487623942.48/warc/CC-MAIN-20210616124819-20210616154819-00505.warc.gz"} |
http://tex.stackexchange.com/questions/8243/redefine-command-when-inside-a-specific-other-command-possible/8245 | Redefine command when inside a specific other command possible?
How, in general, can I (re)define commands based on in which other command they are nested?
A more specific example: I have a custom latex command (say, \code{}) that makes text appear bold. However, when used inside another custom command (such as in \question{Will you use \code{command 1} or \code{command 2}?}), I want the \code{} text to be NOT bold. So I want to redefine \code{} when inside another command.
BTW: When using CSS to format HTML pages, it would go something like this:
.code {font-weight: bold;}
.question .code {font-weight: normal;}
-
Yes, you can.
\newcommand\question[1]{{% extra brace
\renewcommand\code[1]{\textit{##1}}% double #
whatever you want for #1}}
-
Real application of this trick can be seen here too : tex.stackexchange.com/questions/6547/… – xport Jan 4 '11 at 14:23
Note that above link is to an answer which has been deleted. – Peter Grill Feb 14 '13 at 20:41
Personally, I find the brace too easy to overlook most of the time so I use \begingroup\endgroup instead:
\newcommand\question[1]{%
\begingroup
\renewcommand\code[1]{\textit{##1}}% double #
whatever you want for #1%
\endgroup}
-
I agree, and the distinction can be important when defining material to be used in math mode. BTW, no comment char is required after the \begingroup. – Will Robertson Jan 5 '11 at 5:15
@Will: I’m never sure where the newline is swallowed so when in doubt, I add it. – Konrad Rudolph Jan 5 '11 at 7:51
Just consider a newline to be a space — in which case, the rule is that spaces after multi-letter control sequences are always swallowed. (And spaces between macro arguments.) – Will Robertson Jan 5 '11 at 7:55
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\let\code\textbf
\newcommand\question[1]{{\itshape#1}}
\begin{document}
\question{Will you use \code{command 1} or \code{command 2}?}
\question{\let\code\textnormal Will you use \code{command 1} or \code{command 2}?}
\question{Will you use \code{command 1} or \code{command 2}?}
\end{document}
-
This will globally change the definition of code, won't it? That wouldn't be good. – Hendrik Vogt Jan 4 '11 at 14:14
@Hendrik: then explain me why the third line is the same as the first line. – Herbert Jan 4 '11 at 14:59
I really should switch my brain on before leaving such comments. You're right, of course; sorry! – Hendrik Vogt Jan 4 '11 at 15:22
I think it should be mentioned that this method depend on #1 being in a group in the \question command. I.e. there are double curly brackets on the \newcommand-line. The outer for delimiting the content of the command (not making a group) and the inner to actually make a group. If #1 was not used within a group, the \let in the second use would have “spilled over” to the third use. – Johan_E Feb 14 '13 at 23:29
(cont. from last comment) So, for example, if the definition was \newcommand\question[1]{{\itshape #1}~#1} (This writes it’s argument twice. once in italic and once in the surrounding style) the \let would always spill over, if not enclosed in a group when calling the command. This shows that you need to know how a command is defined if you want to use \let inside an argument to it. – Johan_E Feb 14 '13 at 23:33 | 2014-03-17 13:45:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9480254054069519, "perplexity": 3398.4500276085237}, "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-2014-10/segments/1394678705728/warc/CC-MAIN-20140313024505-00075-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://codereview.stackexchange.com/questions/129979/symmetry-analysis-for-atom-arrangements-in-a-crystal | # Symmetry analysis for atom arrangements in a crystal
For a while now I've been meaning to post some of my Haskell code here so that someone can tell me what parts of the language/base library I've been completely overlooking. This is the first thing I've brought into a "working/finished" state that isn't a PE problem, and unfortunately it is a tad big.
It is rather mathematical in nature, and contains multiple nontrivial alglorithms which could almost certainly be improved... but I'm hoping to focus less on the algorithms and more on the minutae. I.e. how is my usage of Haskell?
What does it do? Some symmetry analysis for materials research. If you run it, it will print out all of the possible supercell shapes containing 8 16 atoms which are unique under symmetry for a diamond cubic crystal.
Last minute Hawthorne-effect edits aside, the majority of this code was written with the expectation that I would be the only person to ever look at it. I can only hope that at least one soul is brave enough to continue after reading that statement...
Directory structure
$tree -P '*.hs' . ├── Main.hs └── My ├── Common.hs ├── GroupTheory.hs ├── IntegerRref.hs └── Matrix.hs Main.hs Mostly functions specific to the problem. Here you'll see from all the commented code that my workflow for debugging largely centers around modifying main and recompiling. {-# OPTIONS_GHC -fno-ignore-asserts #-} {-# LANGUAGE BangPatterns #-} import qualified Math.NumberTheory.Primes.Factorisation as Factor -- package arithmoi import qualified Data.Set as Set -- package containers import Data.Set (Set) import qualified Data.List as List import Control.Exception import Text.Printf import Debug.Trace import My.Matrix import My.GroupTheory import My.IntegerRref import My.Common(decorate) ------------------------------------- -- Factorization -- positive, ordered tuples (a,b) such that a*b == x factorPairs :: Integer -> [(Integer, Integer)] factorPairs x = decorate (x div)$ Set.toList $Factor.divisors x -- ordered n-tuplets of positive factors fs such that product fs == x factorTuplets :: Int -> Integer -> [[Integer]] factorTuplets n x = (assert (x>0))$ -- true for expected inputs in this program
case n compare 1 of
LT -> error "factorTuplets: n < 1"
EQ -> [[x]]
GT -> concatMap forPair (factorPairs x)
where forPair (a,b) = map (a:) $factorTuplets (pred n) b ------------------------------------- -- Groups and sets universeForDiagonal :: Vec -> [Mat] universeForDiagonal [] = [[]] universeForDiagonal (a:bcs) = assert (a>0)$ do
let left = a:(fmap (const 0) bcs)
inner <- universeForDiagonal bcs
top <- sequence $fmap (\b -> [0..b-1]) bcs return$ (prependCol left.prependRow top) inner
universeForVolume :: Integer -> [Mat]
universeForVolume vol = concatMap universeForDiagonal (factorTuplets 3 vol)
-------------------------------------
-- Supercell symmetry group
scGenerators :: [Mat]
scGenerators =
-- Twofold rotations
[[0,1,0],[1,0,0],[-1,-1,-1]]:
[[-1,0,0],[0,-1,0],[1,1,1]]:
[[1,0,0],[0,0,1],[-1,-1,-1]]:
-- Threefold rotation
[[0,0,1],[1,0,0],[0,1,0]]:
[]
scMul :: Mat -> Mat -> Mat
scMul = mulMatMat
-- sc group matrices are written to operate on a matrix whose columns are the sc vecs,
-- but we have them in columns;
scAction :: Mat -> Mat -> Mat
scAction g x = integerRref $mulMatMat x (List.transpose g) scGroup :: Set Mat scGroup = generateGroup scMul scGenerators ------------------------------------- -- Random nonsense assertEq :: (Eq a, Show a) => a -> a -> b -> b assertEq expected actual | expected /= actual = error (printf "\n Expected: %s \n Actual: %s" (show expected) (show actual)) | otherwise = id tests :: () tests = id .(assertEq 155$ length $universeForVolume 8) .(assertEq [[-10,5],[2,3]]$ opAddMultiple 3 1 0 $[[-16,-4],[2,3]]) .(assertEq 77$ length $equivalenceClasses scAction (Set.toList scGroup) (universeForVolume 20))$()
main :: IO ()
main = do
let !_ = tests
-- mapM_ print $factorTuplets 3 10 -- mapM_ print$ upperTriangleFromDiags [[1,2,3,4],[5,6,7],[8,9],[1]]
-- mapM_ print $concat$ universeForDiagonal [1,2,3]
-- mapM_ print $opAddMultiple (-2) 2 1$ [[1,4,7,6],[2,3,1,6],[7,7,7,2],[1,2,1,1]]
-- mapM_ print $fmap (getDiag [[1,4,7,6],[2,3,1,6],[7,7,7,2],[1,2,1,1]])$ [-3..3]
-- mapM_ print $fmap (getDiag [[1,4,7,6],[2,3,1,6],[7,7,7,2],[1,2,1,1]])$ [-3..3]
-- mapM_ print $integerRref [[1,1,1],[5,2,2],[3,3,4]] -- mapM_ print$ integerRref [[5,2,2],[1,1,1],[3,3,4]]
-- print $Set.size scGroup -- mapM_ print$ equivalenceClasses scAction (Set.toList scGroup) (universeForVolume 77)
-- mapM_ print $integerRref [[0,1,0],[0,0,1],[4,0,0]] mapM_ print$ map Set.findMin $equivalenceClasses scAction (Set.toList scGroup) (universeForVolume 8) My/GroupTheory.hs A small number of algorithms related to group theory. module My.GroupTheory ( generateGroup, equivalenceClasses, checkedEquivalenceClasses, ) where import qualified Data.Set as Set -- package containers import Data.Set (Set) setUnionAll :: Ord a => [Set a] -> Set a setUnionAll = foldl Set.union Set.empty -- Generate all elements of a finite group from a generating subset. generateGroup :: Ord g => (g -> g -> g) -> [g] -> Set g generateGroup _ [] = error "generateGroup: empty group" generateGroup mul generators = loop (Set.fromList generators) Set.empty where loop recent output | Set.null recent = output | otherwise = loop new (output Set.union new) where new = (Set.difference output)$ Set.fromList $fmap (\[a,b] -> a mul b)$
sequence [Set.toList recent, generators]
equivalenceClasses :: Ord x => (g -> x -> x) -> [g] -> [x] -> [Set x]
equivalenceClasses _ [] _ = error "equivalenceClasses: empty group"
equivalenceClasses action group xs =
loop (Set.fromList xs)
where loop remaining
| Set.null remaining = []
| otherwise = newClass:loop (remaining Set.difference newClass)
where newClass = Set.fromList $fmap (action (Set.findMin remaining)) group checkedEquivalenceClasses :: Ord x => (g -> x -> x) -> [g] -> [x] -> [Set x] checkedEquivalenceClasses action group xs = validate classes where classes = equivalenceClasses action group xs validate = validateClosed.validateDisjoint -- each element of xs should appear once and only once in the classes validateDisjoint = case totalOutCount compare uniqueOutCount of LT -> error "checkedEquivalenceClasses: internal error" GT -> error "checkedEquivalenceClasses: classes not disjoint" EQ -> id -- the union of the classes must equal xs validateClosed | (not . Set.null) (uniqueIn Set.difference uniqueOut) = error "checkedEquivalenceClasses: internal error in equivalenceClasses" | (not . Set.null) (uniqueOut Set.difference uniqueIn) = error "checkedEquivalenceClasses: group action not closed on xs" | otherwise = id uniqueIn = Set.fromList xs uniqueOut = setUnionAll classes uniqueOutCount = Set.size uniqueOut totalOutCount = sum (map Set.size classes) -- findInverses :: Set g -> Map g g -- findIdentity :: Set g -> g -- validateClosure :: Set g -> Set g -- O(n^2) -- validateAssociativity :: Set g -> Set g -- O(n^3) -- validateGroup :: Set g -> Set g -- validateAction :: Set g -> [x] -> () My/Matrix.hs Defines operations on vectors and matrices, "implemented" as little more than lists. module My.Matrix ( Mat, Vec, prependCol, prependRow, deleteCol, overRow, overLowerRight, getCol, getDiag, upperTriangleFromDiags, height, width, innerProd, mulMatMat, mulMatVec, ) where import qualified Data.List as List import Control.Exception import My.Common(listSet,deleteAt,zipWithExact) type Mat = [[Integer]] type Vec = [Integer] prependCol :: Vec -> Mat -> Mat prependRow :: Vec -> Mat -> Mat prependCol col mat = zipWith (:) col mat prependRow = (:) deleteCol :: Int -> Mat -> Mat deleteCol i = fmap (deleteAt i) -- think "over (_!! i)", if _!! were some sort of Lens for lists overRow :: Int -> (Vec -> Vec) -> Mat -> Mat overRow i f mat = listSet i (f (mat!!i)) mat -- applies a function to the lower right submatrix excluding nDropped -- rows and columns. overLowerRight :: Int -> (Mat -> Mat) -> Mat -> Mat overLowerRight nDropped f mat = let (top, bottom) = List.splitAt nDropped mat in let (botLs, botRs) = unzip$ map (List.splitAt nDropped) bottom in
top ++ (zipWith (++) botLs (f botRs))
getCol :: Int -> Mat -> Vec
getCol i = fmap (!!i)
getDiag :: Int -> Mat -> Vec
getDiag n rows = case n compare 0 of
LT -> getDiag 0 (drop (-n) rows)
GT -> getDiag 0 (fmap (drop n) rows)
EQ -> fmap (\(i,row) -> row!!i) $take w (zip [0,1..] rows) where w = (length.head) rows upperTriangleFromDiags :: [Vec] -> Mat upperTriangleFromDiags [] = [] upperTriangleFromDiags diags = assert checks$ topRow:otherRows where
checks = length diags == length (head diags)
topRow = map head diags
otherRows = map (0:) $upperTriangleFromDiags (map tail (init diags)) height :: Mat -> Int height = length width :: Mat -> Int -- We do not explicitly store a width, so none can be determined from -- a zero row matrix. That said, I never plan to use one, so better -- safe than sorry: width [] = error "width: null matrix" width mat = (length.head) mat innerProd :: Vec -> Vec -> Integer innerProd a b = sum$ zipWithExact (*) a b
mulMatMat :: Mat -> Mat -> Mat
mulMatMat a b
| (width a) /= (height b) = error "mulMatMat: dimension"
| otherwise = [[innerProd row col | col<-List.transpose b] | row <- a]
mulMatVec :: Mat -> Vec -> Vec
mulMatVec m v
| (width m) /= (length v) = error "mulMatVec: dimension"
| otherwise = map (innerProd v) m
My/IntegerRref.hs
The largest piece of code, implementing an algorithm based on various handwritten proofs. It is very closely related to the Hermite normal form of a matrix.
module My.IntegerRref (
opAddRow, opSubRow, opNegate2, opAddMultiple,
integerRref,
validateIrref,
) where
import qualified Data.List as List
import Control.Exception
import My.Matrix
import My.Common(listSet,pDiv,compose)
---------------------------------------------------
-- This module implements an analogue to Reduced Row Echelon Form where
-- the only primitive symmetry operations are the following:
-- * adding one row into another, different row.
-- * subtracting one row from another, different row.
--
-- These operations preserve the determinant of a matrix.
opSubRow :: Int -> Int -> Mat -> Mat
opSubRow = opAddMultiple (-1)
opAddRow :: Int -> Int -> Mat -> Mat
opAddRow = opAddMultiple 1
-- We can't negate one row, but we can negate two:
opNegate2 :: Int -> Int -> Mat -> Mat
opNegate2 i1 i2 = overRow i1 (fmap negate).overRow i2 (fmap negate)
opAddMultiple :: Integer -> Int -> Int -> Mat -> Mat
opAddMultiple b src dest mat
| dest == src = error "rowAdd: src == dest (not volume-conserving)"
| otherwise = listSet dest newRow mat where
newRow = zipWith (+) (mat!!dest) (fmap (b*) (mat!!src))
---------------------------------------------------
-- For a square, invertible, integer matrix, produces the unique matrix that is:
-- * Reachable from the original by a finite sequence of operations consisting
-- of adding an integer multiple of one row into another (different) row.
-- * Is upper triangular.
-- * Is entirely nonnegative with the SINGLE possible exception of the
-- lower-right most element.
-- * For each column, the absolute value of the element on the main diagonal
-- is strictly greater than all other values in the column.
integerRref :: Mat -> Mat
integerRref [] = []
integerRref mat = validateIrref $compose operations$ partialRref mat
where operations = do
rPivot <- [0..(length mat)-1]
rMod <- [0..rPivot-1]
return $(reduceRowModuloRow rPivot rPivot) rMod -- This produces the correct values in the lower triangular part of the matrix -- I.e. the main diagonal is positive with the possible exception of the last -- element, and off-diagonals below the main diagonal are zero. partialRref :: Mat -> Mat partialRref = rec where rec [] = [] rec mat = (fixRest.fixLeft) mat where -- change column into [g,g,g..], and then into [g,0,0..] fixLeft = compose$
(reduceColumnToConstant 0):
map (opSubRow 0) [1..(length mat)-1]
-- recurse
fixRest = overLowerRight 1 rec
-- reduces a column [a,b,c..] into [g,g,g..], where g = gcd (a,b,c..).
-- by performing primitive row ops. As long as the original matrix
-- is larger than 1x1, g will be non-negative.
reduceColumnToConstant :: Int -> Mat -> Mat
reduceColumnToConstant _ [] = error "reduceColumnToConstant: empty mat" -- no columns!
reduceColumnToConstant _ [row] = [row] -- do NOT call ensureColumnNonNegative
reduceColumnToConstant c mat'@(_:_) = (verify.compose operations) mat' where
verify mat = assert (all (==mat!!0!!c) (getCol c mat)) mat
-- The column is made positive to simplify working with the gcd.
-- Then two passes are made where each row is reduced with the top row by
-- adding multiples of one to another until they share a value in column c.
-- The first pass puts the final correct value in the first and last rows;
-- the second pass propagates it to the other rows.
operations = (ensureColumnNonNegative c):(onePass ++ onePass) where
onePass = map (reduceTwoRows 0) [1..(length mat')-1]
reduceTwoRows r1 r2 = verify.loop where
-- like a bizarre variant of euclid's algorithm, where we're performing
-- operations on entire rows, and we're not allowed to swap their order
verify mat = assert (mat!!r1!!c == mat!!r2!!c) mat
loop mat = case (mat!!r1!!c, mat!!r2!!c) of
(0, 0) -> mat
(0, _) -> (opAddRow r2) r1 mat
(_, 0) -> (opAddRow r1) r2 mat
(g, h) -> case (g compare h) of
-- use lesser to reduce larger
LT -> loop $(reduceRowModuloRow c r1) r2 mat GT -> loop$ (reduceRowModuloRow c r2) r1 mat
EQ -> mat
ensureColumnNonNegative :: Int -> Mat -> Mat
ensureColumnNonNegative c = verify.loop where
verify mat = assert (all (0<=) (getCol c mat)) mat
loop mat = case (positives, negatives, zeros) of
-- Column is non-negative
(_, [], _) -> mat
-- Column is hopeless
([], [_], []) -> error "ensureColumnPositive: only one row and value is negative"
-- At least one negative and one other: we can negate them
([], n1:n2:_, _) -> loop $opNegate2 n1 n2 mat ([], [n1], z1:_) -> loop$ opNegate2 n1 z1 mat
-- At least one positive p:
-- use it to bring the negatives into the range 0..p-1
(p:_, ns@(_:_), _) -> compose (fmap fixRow ns) mat
where fixRow = reduceRowModuloRow c p
where
negatives = List.findIndices ( <0) column
zeros = List.findIndices (==0) column
positives = List.findIndices ( >0) column
column = getCol c mat
-- add a multiple of row pivotRow into row modRow that reduces
-- the element in column col into the range [0..|pivot| - 1].
-- The pivot must be nonzero.
reduceRowModuloRow :: Int -> Int -> Int -> Mat -> Mat
reduceRowModuloRow col pivotRow modRow mat =
let moderand = mat!!modRow!!col in
let pivot = mat!!pivotRow!!col in
let d = moderand pDiv pivot in
opAddMultiple (-d) pivotRow modRow mat
-- note: this assumes the matrix is square and invertible, so that
-- the pivots MUST be on the main diagonal
-- warning: this inspects every element, causing any deferred lazy
-- computations to occur conditionally based on whether
-- or not assertions are enabled. I imagine there is the
-- potential for this to hide nasty memory bugs...
validateIrref :: Mat -> Mat
validateIrref mat = checkDims $checkDiag$ checkZeros $checkReduced$ mat
where
checkDims = assert $all ((==length mat).length) mat -- the final pivot is the only element allowed to be negative in the -- entire matrix checkDiag = assert$ (all (0<) (init pivots)) && (0 /= last pivots)
checkZeros = assert $all test$ zip [0,1..] mat
where test (i,row) =
i == (length $takeWhile (0==)$ row)
checkReduced = assert $all test$ List.zip3 [0,1..] columns pivots
where test (i,col,pivot) =
all (\x -> 0 <= x && x < abs pivot) $(take i col) columns = List.transpose mat pivots = getDiag 0 mat My/Common.hs Various helper functions that I have deemed "missing" from the Haskell base library. (Your job is to tell me why they aren't!) module My.Common ( deleteAt, listSet, zipWithExact, decorate, compose, indices, windows, traceWith, pDivMod,pDiv,pMod, ) where import Debug.Trace import qualified Data.List as List deleteAt :: Int -> [a] -> [a] deleteAt _ [] = error "deleteAt: i >= length" deleteAt i xs@(_:xt) | i < 0 = error "deleteAt: i < 0" | i == 0 = xt | otherwise = deleteAt (i-1) xs listSet :: Int -> a -> [a] -> [a] listSet _ _ [] = error "listSet: index (or empty list)" listSet 0 new (_:xs) = new:xs listSet n new (x:xs) = x:listSet (n-1) new xs zipWithExact :: (a -> b -> c) -> [a] -> [b] -> [c] zipWithExact f as' bs' = iter as' bs' where iter [] [] = [] iter [] (_:_) = error "zipWithExact: first list ended early" iter (_:_) [] = error "zipWithExact: second list ended early" iter (a:as) (b:bs) = (f a b):iter as bs decorate :: Functor f => (a -> b) -> f a -> f (a,b) decorate f = fmap (\x -> (x, f x)) -- compose [f,g,h..] x == (..h.g.f) x compose :: [(a -> a)] -> a -> a compose = foldl (flip (.)) id -- equivalent to [0..(length xs-1)] but possibly less painful? indices :: [a] -> [Int] indices xs = map fst$ zip [0..] xs
-- overlapping windows
windows :: Int -> [a] -> [[a]]
windows n xs = takeWhile ((n==).length) $fmap (take n)$ List.tails xs
-- threads a value through a function, printing the output of the
-- function and returning the original value
traceWith :: (a -> String) -> a -> a
traceWith f x = trace (f x) x
-- HACK; Debug.Trace apparently should have this but mine doesn't.
-- (my base library is probably still the one from the Canonical repos >_>)
traceShowId :: Show a => a -> a
traceShowId = traceWith show
-- another variant of divMod and quotRem satisfying the property
-- that pMod is never negative, even if the divisor is.
pDivMod :: Integral a => a -> a -> (a,a)
pDivMod a b = (d, a-b*d)
where d = (signum b) * (a div (abs b))
pDiv :: Integral a => a -> a -> a
pMod :: Integral a => a -> a -> a
pDiv a b = fst $pDivMod a b pMod a b = snd$ pDivMod a b
Specific points of concern:
• In IntegerRef you'll see the use of a helper function called compose to string long chains of operations together into one function that performs them in sequence. I understand that this is precisely the sort of problem that Monads are meant to solve, but I'm not sure how one could help. (the only ones I really understand are [] and Maybe)
• Something I mention in the notes above validateIrref (in IntegerRref.hs); a typical debugging strategy of mine is to verify post-conditions of functions through expensive checks which are only enabled in debug mode. But in Haskell, with lazy evaluation, that might cause the "strictness" of a function to depend on whether assertions are enabled! Seems troubling...
• Better ways to write more things in a pointfree style. Or conversely, places in my code where I used a pointfree style to the detriment of readability.
• Any "anti-idioms" I use that I should be aware of
• Why not use the aptly named matrix library? 1) it's much faster, 2) you shouldn't need to worry whether their functions are correct so can debug less. Jun 9 '16 at 15:05
• @MichaelKlein a valid question. Obvious true answer aside (which is "I didn't look for one"), I think part of it is that most of my proofs were structured recursively and so lists seemed a natural fit. The matrix-related type aliases and methods are largely things I pulled out as an afterthought when it began to bother me that code working on columns tended to look so different from code working on rows. Jun 10 '16 at 0:15
## 1 Answer
Here's a little to start with:
Safe.Exact implements zipWithExact.
Lens implements listSet n as set (ix n), and overRow n as over (ix n). These don't error on being out of range, instead doing nothing. listSet is a bad name because list is also a verb and set is also a noun.
overLowerRight n is over (foldr (.) id (replicate n _tail) . each . foldr (.) id (replicate n _tail) . each).
generateGroup should be called generateAbelianMagma or generateSemigroup, because you aren't generating the neutral element or inverses, and are using either commutativity or associativity to only append the original generators to any new elements, and only to the right.
generateSemigroup :: Ord g => (g -> g -> g) -> [g] -> Set g
generateSemigroup op generators = foldr foo Set.empty generators where
foo :: g -> Set g -> Set g
foo x set = if S.member x set
then set
else foldr foo (insert x set) $(op x) <$> generators
• Hmm... Perhaps I should have called it generateFiniteGroup? I think that ought to at least address the inverses and identity problem because then each generator has the identity in its cyclic subgroup. I'm still trying to digest your new definition, but it's impressive! Jun 6 '16 at 17:54
• Ah, that explains why you error out on an empty generator list - the neutral element isn't generated then. And for infinite groups, this doesn't halt anyway, I guess. Jun 7 '16 at 21:30 | 2022-01-16 21:34:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3356080949306488, "perplexity": 9294.036550999577}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320300244.42/warc/CC-MAIN-20220116210734-20220117000734-00238.warc.gz"} |
https://learn.careers360.com/ncert/question-find-x-plus-1-to-the-power-6-plus-x-minus-1-to-the-power-6-hence-or-otherwise-evaluate-root-of-2-plus-1-to-the-power-6-plus-root-of-2-minus-1-to-the-power-6/ | Q
# Find (x + 1)^6 + (x - 1)^6 . Hence or otherwise evaluate (root of 2 + 1)^6 + ( root of 2 - 1) ^ 6 .
Q12. Find $(x+1)^6 + (x-1)^6$ . Hence or otherwise evaluate $(\sqrt2+1)^6 + (\sqrt2-1)^6$.
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N
Using Binomial Theorem, the expressions $(x+1)^4$ and $(x-1)^4$ can be expressed as ,
$(x+1)^6=^6C_0x^6+^6C_1x^51+^6C_2x^41^2+^4C_3x^31^3+^6C_4x^21^4+^6C_5x1^5+^6C_61^6$
$(x-1)^6=^6C_0x^6-^6C_1x^51+^6C_2x^41^2-^4C_3x^31^3+^6C_4x^21^4-^6C_5x1^5+^6C_61^6$
From Here,
$\\(x+1)^6-(x-1)^6=^6C_0x^6+^6C_1x^51+^6C_2x^41^2+^4C_3x^31^3+$$^6C_4x^21^4+^6C_5x1^5+^6C_61^6$$\:\:\:\:\;\:\:\;\:\:\:\ +^6C_0x^6-^6C_1x^51+^6C_2x^41^2-^4C_3x^31^3+^6C_4x^21^4-^6C_5x1^5+^6C_61^6$
$(x+1)^6+(x-1)^6=2(^6C_0x^6+^6C_2x^41^2+^6C_4x^21^4+^6C_61^6)$
$(x+1)^6+(x-1)^6=2(x^6+15x^4+15x^2+1)$
Now, Using this, we get
$(\sqrt2+1)^6 + (\sqrt2-1)^6=2((\sqrt{2})^6+15(\sqrt{2})^4+15(\sqrt{2})^2+1)$
$(\sqrt2+1)^6 + (\sqrt2-1)^6=2(8+60+30+1)=2(99)=198$
Exams
Articles
Questions | 2020-02-19 16:19:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7898305654525757, "perplexity": 961.6348326272083}, "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/1581875144165.4/warc/CC-MAIN-20200219153707-20200219183707-00335.warc.gz"} |
http://mathoverflow.net/revisions/101351/list | 5 added 10 characters in body
Suppose that $X$ is a complex algebraic (or complex analytic) variety, and $x \in X$ is a singular point. I am interested in two types of local differential forms at $x$: analytic and formal.
First, let $\mathcal{O}_{X,x}^{\text{an}}$ be the ring of analytic germs of functions at $x$. I am interested in the complex $\Omega_{X,x}^{\text{an}}$ of analytic germs of differential forms, i.e., linear combinations of elements $h_0 dh_1 \wedge \cdots \wedge dh_k$ for $h_0, \ldots, h_k \in \mathcal{O}_{X,x}^{\text{an}}$, and the corresponding de Rham cohomology $H^\bullet(\Omega_{X,x}^{\text{an}})$. Explicitly, if $X \subseteq \mathbf{A}^n$ is a subvariety of affine space cut out by equations $f_1, \ldots, f_m$, then this complex is defined as $\Omega_{\mathbf{A}^n,x}^{\text{an}} / (f_1, \ldots, f_m, df_1, \ldots, df_m)$, where we quotient by the ideal in the de Rham differential graded algebra generated by the $f_i$ and $df_i$.
Next, let $\hat {\mathcal{O}}_{X,x}$ be the completion of the local ring of algebraic functions at $x$, i.e., the ring of (not-necessarily convergent) formal power series of functions at $x$. Let $\hat {\Omega}_{X,x}$ be the complex of formal differential forms, i.e., linear combinations of elements $h_0 dh_1 \wedge \cdots \wedge dh_k$ for $h_0, \ldots, h_k \in \hat {\mathcal{O}}_{X,x}$. For $X \subseteq \mathbf{A}^n$, this is defined as a quotient of $\hat \Omega_{\mathbf{A}^n,x}$ in the same manner as above.
Since one has a canonical inclusion $\mathcal{O}_{X,x}^{\text{an}} \hookrightarrow \hat {\mathcal{O}}_{X,x}$, one obtains a canonical comparison map
$H^\bullet(\Omega_{X,x}^{\text{an}}) \to H^\bullet(\hat \Omega_{X,x}).$
## My question is: When is this map an isomorphism?
I am particularly interested in the case that the LHS is finite-dimensional, e.g., when $X$ has an isolated singularity at $x$ (finite-dimensionality of the LHS then follows from the Theorem of Section 3.17 of Bloom and Herrera's paper De Rham Cohomology of an Analytic Space,'' (Invent. Math. 7, 275--296 (1969)).
More details and reformulations:
Under the finite-dimensionality hypothesis, the comparison map is definitely surjective: the RHS is the inverse limit of $H^\bullet(\Omega_{X,x} / \mathfrak{m}_{X,x}^N \cdot \Omega_{X,x})$, where $\mathfrak{m}_{X,x} \subseteq \mathcal{O}_{X,x}$ is the maximal ideal, and the LHS surjects to each of these (by lifting closed or exact forms modulo $\mathfrak{m}_{X,x}^N$ to closed or exact analytic forms). So both sides are finite-dimensional and the comparison map is surjective.
Thus, under this hypothesis, the question reduces to: When it is true that, if a closed analytic form $\alpha \in \Omega_{X,x}^{\text{an}}$ is the differential of a formal form in $\hat \Omega_{X,x}$, then it is also the differential of an analytic form in $\Omega_{X,x}^{\text{an}}$? (Perhaps, an analytic approximation theorem could be applied to answer this.)
Next, I will restrict this question to the special case that interests me: isolated singularities which are locally complete intersections. In this case, by results of Sections 4 and 5 of Greuel's paper Der Gauss-Manin-Zusammenhang isolierter Singularitaeten von vollstaendigen Durchschnitten,'' (Math. Ann. 214, 235--266 (1975)), one has the formula
$H^\bullet(\Omega_{X,x}^{\text{an}}) \cong \mathbf{C}^{\mu_x-\tau_x}[-\operatorname{dim} X],$
where $\mu_x$ is the Milnor number of the singularity at $x$, and the notation above indicates that the de Rham cohomology of the analytic neighborhood of $x$ is concentrated in degree equal to the dimension of $X$. Also, $\tau_x$ is the Tjurina number, which is the dimension of the singularity ring at $x$: explicitly, if $X$ is locally a complete intersection of dimension $n-m$ cut out at $x \in \mathbf{A}^n$ by functions $f_1, \ldots, f_m$, then the singularity ring is the quotient of $\mathcal{O}_{X,x}^{\text{an}}$ by the ideal generated by the $f_i$ together with the determinants of the $(n-m) \times (n-m)$ minors of the Jacobian matrix $(\frac{\partial f_i}{\partial x_j})$. In other words, the Tjurina number here is the dimension of the torsion of the germs of differential forms $\Omega_{X,x}^{\operatorname{dim}(X),\text{an}}$ of degree $\operatorname{dim}(X)$.
In this case, I would only want to know whether the same formula holds for the de Rham cohomology of the formal neighborhood, i.e., that the dimension of $H^\bullet(\hat{\Omega}_{X,x})$ is equal to the Milnor number, and not less.
[Readers who are tired of reading can stop here---I will give one more alternative formulation:]
Alternatively, one can work with the de Rham complex modulo torsion, $\tilde{\Omega}_{X,x}^{\text{an}}$, obtained from $\Omega^{\text{an}}_{X,x}$ by modding by the torsion submodule over $\mathcal{O}_{X,x}^{\text{an}}$. This is equivalent to working with germs of forms modulo those forms that become zero when restricted to the smooth locus, i.e., whose representatives on open neighborhoods of $x$ have zero restriction to smooth open subsets. In this case, Greuel's formula (still for an isolated singularity at $x$ which is locally a complete intersection) becomesremains the same,
$H^\bullet(\tilde{\Omega}_{X,x}^{\text{an}}) \cong \mathbf{C}^{\mu_x-\tau_x}[-\operatorname{dim} X].$
In the alternative formulation, I would like to know again if the same formula holds replacing analytic germs of forms mod torsion, $\tilde{\Omega}_{X,x}^{\text{an}}$, by formal forms mod torsion. It follows from Greuel's paper that, still assuming $x$ is an isolated singularity which is locally a complete intersection, the two questions are equivalent.
4 deleted 2 characters in body
$H^\bullet(\Omega_{X,x}^{\text{an}}) \cong \mathbf{C}^{\mu_x}[-\operatorname{dim} mathbf{C}^{\mu_x-\tau_x}[-\operatorname{dim} X],$
where $\mu_x$ is the Milnor number of the singularity at $x$, and the notation above indicates that the de Rham cohomology of the analytic neighborhood of $x$ is concentrated in degree equal to the dimension of $X$. Also, $\tau_x$ is the Tjurina number, which is the dimension of the singularity ring at $x$: explicitly, if $X$ is locally a complete intersection of dimension $n-m$ cut out at $x \in \mathbf{A}^n$ by functions $f_1, \ldots, f_m$, then the singularity ring is the quotient of $\mathcal{O}_{X,x}^{\text{an}}$ by the ideal generated by the $f_i$ together with the determinants of the $(n-m) \times (n-m)$ minors of the Jacobian matrix $(\frac{\partial f_i}{\partial x_j})$. In other words, the Tjurina number here is the dimension of the torsion of the germs of differential forms $\Omega_{X,x}^{\operatorname{dim}(X),\text{an}}$ of degree $\operatorname{dim}(X)$.
$H^\bullet(\tilde{\Omega}_{X,x}^{\text{an}}) \cong \mathbf{C}^{\mu_x-\tau_x}[-\operatorname{dim} X],$
where now $\tau_x$ is the Tjurina number, which is the dimension of the singularity ring at $x$: explicitly, if $X$ is locally a complete intersection of dimension $n-m$ cutout at $x \in \mathbf{A}^n$ by functions $f_1, \ldots, f_m$, then the singularity ring is the quotient of $\mathcal{O}_{X,x}^{\text{an}}$ by the ideal generated by the $f_i$ together with the determinants of the $(n-m) \times (n-m)$ minors of the Jacobian matrix $(\frac{\partial f_i}{\partial x_j})$. In other words, the Tjurina number here is the dimension of the torsion of the germs of differential forms $\Omega_{X,x}^{\operatorname{dim}(X),\text{an}}$ of degree $\operatorname{dim}(X)$.X].$3 added 7 characters in body Suppose that$X$is an a complex algebraic (or complex analytic) variety, and$x \in X$is a singular point. I am interested in two types of local differential forms at$x$: analytic and formal. First, let $\mathcal{O}_{X,x}^{\text{an}}$ be the ring of analytic germs of functions at$x$. I am interested in the complex $\Omega_{X,x}^{\text{an}}$ of analytic germs of differential forms, i.e., linear combinations of elements $h_0 dh_1 \wedge \cdots \wedge dh_k$ for $h_0, \ldots, h_k \in \mathcal{O}_{X,x}^{\text{an}}$, and the corresponding de Rham cohomology $H^\bullet(\Omega_{X,x}^{\text{an}})$. Explicitly, if$X \subseteq \mathbf{A}^n$is a subvariety of affine space cut out by equations$f_1, \ldots, f_m$, then this complex is defined as$\Omega_{\mathbf{A}^n,x}^{\text{an}} / (f_1, \ldots, f_m, df_1, \ldots, df_m)$, where we quotient by the ideal in the de Rham differential graded algebra generated by the$f_i$and$df_i$. Next, let $\hat {\mathcal{O}}_{X,x}$ be the completion of the local ring of algebraic functions at$x$, i.e., the ring of (not-necessarily convergent) formal power series of functions at$x$. Let $\hat {\Omega}_{X,x}$ be the complex of formal differential forms, i.e., linear combinations of elements $h_0 dh_1 \wedge \cdots \wedge dh_k$ for $h_0, \ldots, h_k \in \hat {\mathcal{O}}_{X,x}$. For$X \subseteq \mathbf{A}^n$, this is defined as a quotient of $\hat \Omega_{\mathbf{A}^n,x}$ in the same manner as above. Since one has a canonical inclusion $\mathcal{O}_{X,x}^{\text{an}} \hookrightarrow \hat {\mathcal{O}}_{X,x}$, one obtains a canonical comparison map $H^\bullet(\Omega_{X,x}^{\text{an}}) \to H^\bullet(\hat \Omega_{X,x}).$ ## My question is: When is this map an isomorphism? I am particularly interested in the case that the LHS is finite-dimensional, e.g., when$X$has an isolated singularity at$x$(finite-dimensionality of the LHS then follows from the Theorem of Section 3.17 of Bloom and Herrera's paper De Rham Cohomology of an Analytic Space,'' (Invent. Math. 7, 275--296 (1969)). More details and reformulations: Under the finite-dimensionality hypothesis, the comparison map is definitely surjective: the RHS is the inverse limit of $H^\bullet(\Omega_{X,x} / \mathfrak{m}_{X,x}^N \cdot \Omega_{X,x})$, where $\mathfrak{m}_{X,x} \subseteq \mathcal{O}_{X,x}$ is the maximal ideal, and the LHS surjects to each of these (by lifting closed or exact forms modulo $\mathfrak{m}_{X,x}^N$ to closed or exact analytic forms). So both sides are finite-dimensional and the comparison map is surjective. Thus, under this hypothesis, the question reduces to: When it is true that, if a closed analytic form$\alpha \in \Omega_{X,x}^{\text{an}}$is the differential of a formal form in$\hat \Omega_{X,x}$, then it is also the differential of an analytic form in$\Omega_{X,x}^{\text{an}}$? (Perhaps, an analytic approximation theorem could be applied to answer this.) Next, I will restrict this question to the special case that interests me: isolated singularities which are locally complete intersections. In this case, by results of Sections 4 and 5 of Greuel's paper Der Gauss-Manin-Zusammenhang isolierter Singularitaeten von vollstaendigen Durchschnitten,'' (Math. Ann. 214, 235--266 (1975)), one has the formula $H^\bullet(\Omega_{X,x}^{\text{an}}) \cong \mathbf{C}^{\mu_x}[-\operatorname{dim} X],$ where$\mu_x$is the Milnor number of the singularity at$x$, and the notation above indicates that the de Rham cohomology of the analytic neighborhood of$x$is concentrated in degree equal to the dimension of$X$. In this case, I would only want to know whether the same formula holds for the de Rham cohomology of the formal neighborhood, i.e., that the dimension of$H^\bullet(\hat{\Omega}_{X,x})$is equal to the Milnor number, and not less. [Readers who are tired of reading can stop here---I will give one more alternative formulation:] Alternatively, one can work with the de Rham complex modulo torsion, $\tilde{\Omega}_{X,x}^{\text{an}}$, obtained from $\Omega^{\text{an}}_{X,x}$ by modding by the torsion submodule over $\mathcal{O}_{X,x}^{\text{an}}$. This is equivalent to working with germs of forms modulo those forms that become zero when restricted to the smooth locus, i.e., whose representatives on open neighborhoods of$x$have zero restriction to smooth open subsets. In this case, Greuel's formula (still for an isolated singularity at$x$which is locally a complete intersection) becomes $H^\bullet(\tilde{\Omega}_{X,x}^{\text{an}}) \cong \mathbf{C}^{\mu_x-\tau_x}[-\operatorname{dim} X],$ where now$\tau_x$is the Tjurina number, which is the dimension of the singularity ring at$x$: explicitly, if$X$is locally a complete intersection of dimension$n-m$cut out at$x \in \mathbf{A}^n$by functions$f_1, \ldots, f_m$, then the singularity ring is the quotient of $\mathcal{O}_{X,x}^{\text{an}}$ by the ideal generated by the$f_i$together with the determinants of the$(n-m) \times (n-m)$minors of the Jacobian matrix$(\frac{\partial f_i}{\partial x_j})$. In other words, the Tjurina number here is the dimension of the torsion of the germs of differential forms $\Omega_{X,x}^{\operatorname{dim}(X),\text{an}}$ of degree$\operatorname{dim}(X)$. In the alternative formulation, I would like to know again if the same formula holds replacing analytic germs of forms mod torsion, $\tilde{\Omega}_{X,x}^{\text{an}}$, by formal forms mod torsion. It follows from Greuel's paper that, still assuming$x\$ is an isolated singularity which is locally a complete intersection, the two questions are equivalent.
2 added 14 characters in body
1 | 2013-05-26 02:14:34 | {"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": 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": 0.9941810965538025, "perplexity": 154.44631395538994}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368706484194/warc/CC-MAIN-20130516121444-00088-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://www.gradesaver.com/textbooks/science/physics/CLONE-afaf42be-9820-4186-8d76-e738423175bc/chapter-15-section-15-3-archimedes-principle-and-buoyancy-example-page-278/15-3 | ## Essential University Physics: Volume 1 (4th Edition) Clone
We use the result of a free body diagram to find: $F_g - F_b = m_cg(1-\frac{\rho_w}{\rho_c})$ $F_g - F_b = (60)(9.81)(1-\frac{1}{2.2})=320 \ N$ | 2019-08-24 05:41:08 | {"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": 0.5743439793586731, "perplexity": 1115.4756692645312}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027319724.97/warc/CC-MAIN-20190824041053-20190824063053-00348.warc.gz"} |
http://pflegedienst-freudenberger.de/kusto-regex-extract.html | # Kusto Regex Extract
captureGroup: A positive int constant indicating the capture group to extract. There are several pandas methods which accept the regex in pandas to find the pattern in a String within a Series or Dataframe object. js bash c++ css dataframe ember-data ember. Use parse_json () if you need to extract more than one value from the JSON. Exit fullscreen mode. Top Regular Expressions. Now, click Find All, and Sublime Text will highlight and select every instance of your text it finds. A regular expression that matches 31-12-1999 but not 31-13-1999. There are a few ways of extracting these nested fields with Kusto, depending on which product you are using. Its also useful if you only need to extract a few fields, or in the examples I'll show below, when you are using Azure Resource Graph. regex: A regular expression. I encourage you to print the tables so you have a cheat sheet on your desk for quick reference. A regular expression (abbreviated regex or regexp and sometimes called a rational expression) is a sequence of characters that forms a search pattern, mainly for use in pattern-matching and "search-and-replace" functions. A simple and powerful regular expression to match most legal URLs. text: A string to search. In this post, I want to walk through a few examples of how you would transform data that can be tricky to work with: data that is stored in arrays. "\\d+" Or, " ( [0-9]+)". If you need specific help getting your data parsed, please let us know. Pattern pattern = Pattern. A string of 26 uppercase English letters: ^ [A-Z]+$. KQL, the Kusto Query Language, is used to query Azure's services. Hover the generated regular expression to see more information. x r reactjs regex sql sql-server string svelte typescript vue-component vue. Its really helpful if you want to find the names starting with a particular character or search for a pattern within a dataframe column or extract the dates from the text. However, I want the last field which, depending on how many spaces are in the IIS site name, can vary in index. By Robert Cain. A grok pattern is a named set of regular expressions (regex) that are used to match data one line at a time. b matches any string that starts with an a, ends with a b, and has a single character in between (the period matches any character). Can someone please help me with a regex to extract the host name from a filename. source: A string to search. This course will teach you the basic syntax of KQL, then cover advanced topics such as machine learning and time series analysis, as well as exporting your data to various platforms. This powerful script lets you extract emails, proxies, IPs, phone numbers, addresses, HTML tags, URLs, links, dates, etc. ; field= - allows you to specify a field to parse other than the default message. Where ^ specifies start of. RegExr: Learn, Build, & Test RegE. Kusto regex for extracting IP adresses In my AzureDiagnostics for my ResourceType "AzureFirewalls", there's a column named "msg_s". 6|wo") == "45. Exit fullscreen mode. extract(), Get a match for a regular expression from a text string. It removes all HTML tags and preserves text structure but you can remove it by using the collapse-whitespace option. Reserved JSON characters, such as backspaces, form feeds, newlines, carriage returns, tabs, double quotes and backslashes are escaped with an extra backslash. For example, if the word fox was what I wanted to exclude, and the searched text was: The quick brown fox jumped over the lazy dog. Get all matches for a regular expression from a text string. parens should be a logical flag, or if NA, will wrap in parens if length > 1. String values are wrapped with either single or double quotes. 10 is the maximum number of characters that can be extracted. Here you'll find posts about AzureMonitor, LogAnalytics, System Center Operations Manager, Powershell, Hyper-V, Azure Automation, Azure Governance and other Microsoft related technologies. IMPORTANT: Due to the \K feature, included in the second S/R, you must use the Replace All button, exclusively. There are also separate output values for each named regular expression group: Price, Quantity, Title. Matching an email address within a string is a hard task, because the specification defining it, the RFC2822, is complex making it hard to implement as a regex. Select the text you just pasted in, and click the Unmark button on the Samples panel. Like most other programming and query languages, Kusto too has case sensitivity, which means it can deal with upper-case and lower-case while performing comparisons between values. Because this blog post will also be about performance we want to use bigger data set in the form of the Log Analytics Demo environment. extract(), Get a match for a regular expression from a text string. (It you want a bookmark, here's a direct link to the regex reference tables ). 16 Has_any Similar to the contains opera-tor -Green means that the operator is used frequently. Python Regex - Check if String ends with Specific Word. payload string. There are a few ways of extracting these nested fields with Kusto, depending on which product you are using. KQL, the Kusto Query Language, is used to query Azure's services. where str is the string in which we need to. Post Posting Guidelines Formatting - Now. rewrite: The replacement regex for any match made by matchingRegex. For a cumulative list of all of the updates to Power BI Desktop in the last few months, see this blog. Regular Expressions are fast and helps you to avoid using unnecessary loops in…. A grok pattern is a named set of regular expressions (regex) that are used to match data one line at a time. RegExr is an online tool to learn, build, & test Regular Expressions (RegEx / RegExp). If you are entering a regexp interactively then you can insert the newline with C-qC-j, as kaushalmodi's answer points out. Apply quickly to various Kusto job openings in top companies!. This regular expression is too simple - if you want to it to be accurate, you need to check that the numbers are between 0 and 255, with the regex above accepting 444 in any position. String processing is fairly easy in Stata because of the many built-in string functions. 14 !in Excludes multiple values 1. Start a FREE 10-day trial. Here is a more elegant version of the regex pattern above:. For example, the regular expression \A match es the beginning of a line, and is specified in Kusto as the string literal "\\A" (note. Example of an invalid regex: @"\d+" Required: captureGroups: A dynamic array constant that indicates the capture group to extract. Valid values are from 1 to the number of capturing groups in the regular expression. Uses a regular expression with three capturing groups to split each GUID part into first letter, last letter, and whatever is in the middle. A common ask is understanding how much traffic is generated by any of your different hosts. The returned value is a JSON-encoded string, and not a native Athena data type. At the image down below. The default interpretation is a regular expression, as described in stringi::about_search_regex. Step 2: Create an array variable with no value. In this post, I want to walk through a few examples of how you would transform data that can be tricky to work with: data that is stored in arrays. parens should be a logical flag, or if NA, will wrap in parens if length > 1. It contains information about IP-adresses trying to request access to another adress. split REGEX - If STRING is not given, splitting the content of$_, the default variable of Perl at every match of the. The addresses are separated by period (. The following script can be used to extract the domain name from the email address. getCount () ? true : false. In this article, you will learn how to extract all text strings after a specific text. The importance of performance and optimizing queries comes from the limits in the. The expression can contain capture groups in parentheses. , here, you see your RegEx as a diagram , it is helpful to understand where is a problem. Another nice feature of Kusto / Application Insights Analytics is full on support for regular expressions using the extract keyword. 14 !in Excludes multiple values 1. Created Date: 8/11/2021 5:10:43 PM. Queries are how Grafana panels communicate with data sources to get data for the visualization. x r reactjs regex sql sql-server string svelte typescript vue-component vue. The expression can contain capture groups in parentheses. ^ Carat, matches a term if the term appears at the beginning of a paragraph or a line. Roll over a match or expression for details. Grafana asks, "Hey data source, would you send me this data, organized this way?". Optionally. ; auto - automatically detects JSON objects in logs and extracts the key/value pairs. Replicating Regex expressions in Power BI Desktop 08-23-2019 03:26 AM. Catch values from Goroutines Different ways to convert Byte Array into String Example: Split, Join, and Equal from BYTES. However, I want the last field which, depending on how many spaces are in the IIS site name, can vary in index. Use Tools to explore your results. matches regex; has_any; In the SQL to KQL blog post, we used the evaluation data of the MITRE ATP29 test to test our queries. It contains information about IP-adresses trying to request access to another adress. Regular expression tester with syntax highlighting, explanation, cheat sheet for PHP/PCRE, Python, GO, JavaScript, Java. They can be also used as a data generator, following the concept of reversed regular expressions, and provide randomized test data for use in test databases. Oct 23, 2019 · Kusto regex for extracting IP adresses In my AzureDiagnostics for my to use HTML, CSS, JavaScript, SQL, PHP, Python, Bootstrap, Java and XML. regex: A regular expression containing between one and 16 capture groups. When the data is ingested as dynamic data, the engine will enumerates all elements within the dynamic value and forward then to the index builder. For details, see parse nodrop and using the nodrop option. | project extract ("milk-cow-\\s* ( [a-zA-Z]+)", 1, info) It means. Filled with real-world applications, use cases, and lessons learnt scaling Nginx to 50 million users, with this book, readers will get up and running quickly and learn the tools. net ajax android angular arrays aurelia backbone. Get a match for a regular expression from a source string. I need to extract working hour breaks out of a Time… Can't find why this datetime test fails, in F#; Kusto logstash update syslogs in real time; Any workaround to TimeSpan. Combining Files - Option to Choose First File. A string of 26 letters: ^ [A-Za-z]+$. Azure Data Explorer is a Microsoft service for analysing log and telemetry data. Python Regex – Get List of all Numbers from String. Select the first GUID {D1A5279D-B27D-4CD4-A05E-EFDD53D08E8D} in the sample text. Step 2: Create an array variable with no value. Find credit card numbers in documents for a security audit. Regular expression is a pattern that describes a specific set of strings with a table variable store the list of player names separated by a pipe '|' delimiter. For details, see parse nodrop and using the nodrop option. Internet Protocol (ip) addresses are the numerical identifiers of each device connected to a computer network that uses Internet Protocol for communication. Quick and Dirty Method. In this article we will be talking about using Regular Expression Match action Plumsail Documents connector for Power Automate (Microsoft Flow) and Azure Logic Apps. I need to extract working hour breaks out of a Time… Can't find why this datetime test fails, in F#; Kusto logstash update syslogs in real time; Any workaround to TimeSpan. How i extract text from a model dialog in selenium? 2 mathjax + vue not rerendering equations. It should be 36 characters (32 hexadecimal characters and 4 hyphens) long. We'll use this format to extract email addresses from the text. Character classes. 0 stands for the entire match, 1 for the value matched by the first '('parenthesis')' in the regular expression, 2 or more for subsequent parentheses. They are ephemeral: they can be used by any Function downstream, but will not be added to events, and will not exit the Pipeline. Matching Complete Lines. They capture the text matched by the regex inside them into a numbered group that can be reused with a numbered backreference. The regex is:-. Grok is a tool that is used to parse textual data given a matching pattern. In the previous post, we talked about the basic of Text to Columns and focused on "Fixed width". 2 hours ago Docs. Use \0 to refer to the whole match, \1 for the first capture group, \2 and so on for. The first position of the string is one (1). normalizeSpace() is most readable and it should be preferred way to remove unwanted white spaces between words. A read-only request to process (Kusto) data and return results. The addresses are separated by period (. text: A string to search. Use parse_json () if you need to extract more than one value from the JSON. This article is the 8th in the "Azure Sentinel" series. studyeducation. milk-cow- - match milk-cow-. Python Regex – Get List of all Numbers from String. guid_bytes. Oct 23, 2019 · Kusto regex for extracting IP adresses In my AzureDiagnostics for my to use HTML, CSS, JavaScript, SQL, PHP, Python, Bootstrap, Java and XML. Consider having the JSON parsed at ingestion by declaring the type of the column to be dynamic. To check if a string ends with a word in Python, use the regular expression for "ends with"$ and the word itself before $. findall () method. This function is used to convert Python object into JSON string. The Kusto Query Language has two main data types associated with dates and times: datetime and timespan. Links to help debug RegEx: Debuggex: Online visual regex tester. Regex symbol list and regex examples. See full list on github. The RFC 5322 specifies the format of an email address. Otherwise, all characters between the patterns will be copied. Below is the implementation of the above approach: C++ // C++ program to implement // the above approach. Another nice feature of Kusto / Application Insights Analytics is full on support for regular expressions using the extract keyword. RE2 regular expression syntax describes the syntax of the regular expression library used by Kusto (re2). I need to extract working hour breaks out of a Time… Can't find why this datetime test fails, in F#; Kusto logstash update syslogs in real time; Any workaround to TimeSpan. In this tutorial, we will explain what is Regex OR logic and how can we implement Regex OR in different programming languages like JavaScript, Python, C#, and Java. captureGroup: A positive int constant indicating the capture group to extract. Regular Expression to By Klas. Both were based on toy implementations optimized for teaching. pdf I have found an expression I can use to extract the first 6 characters. Example of a valid regex: @"(\d+)". 16 Has_any Similar to the contains opera-tor -Green means that the operator is used frequently. Grok is a tool that is used to parse textual data given a matching pattern. studyeducation. Jun 20, 2018 · Kusto Query Language (KQL) from Scratch. I have my SQL server sending Event ID 33205 to Log Analytics and I have a business use case to extract the statement field from the log. extract ("x= ( [0-9. Otherwise, all characters between the patterns will be copied. The second parameter, query, is added to the policy just to avoid a false positive condition due to a specific signature, 200002835. b matches any string that starts with an a, ends with a b, and has a single character in between (the period matches any character). Domain Name Regular Expression Pattern -A-Za-z0-9-163. To check if a string ends with a word in Python, use the regular expression for "ends with"$ and the word itself before $. In this example, we will create a Regex pattern named patter which will be case insensitive. The addresses are separated by period (. The number i am trying to extract is the ones that are in between two - , basically like the picture below. So in this example, i would have a new column that would have only the number 111. Is it the case or I missed something in the Kusto syntax for regular expressions?. Before we start, you might want to check out some of the regex apps on Envato Market, such as RegEx Extractor. For example, the pattern. The tables below are a reference to basic regex. Regex is supported in all the scripting languages (such as Perl, Python, PHP, and JavaScript); as well as general purpose programming languages such. Among these string functions are three functions that are related to regular expressions, regexm for matching, regexr for replacing and regexs for subexpressions. A grok pattern is a named set of regular expressions (regex) that are used to match data one line at a time. Kusto query to extract useful fields from Azure Firewall logs - azure_firewall. Get all matches for a regular expression from a text string. The following script can be used to extract the domain name from the email address. Given a string str which represents a sentence, the task is to remove the duplicate words from sentences using regular expression in java. Regular expression (RegEx) is an extremely powerful tool for processing and extracting character patterns from text. There are also separate output values for each named regular expression group: Price, Quantity, Title. rewrite: The replacement regex for any match made by matchingRegex. I've got two different file naming formats. These queries are similar to queries that are used in the Azure Data Explorer tutorial, but they instead use data from common tables in an Azure Log Analytics workspace. You can also control the behavior of the. Get all matches for a regular expression from a text string. js vuejs2 vuetify. Time Calc] = 1 THEN // Use custom value… REGEXP_EXTRACT. tag and make it insert a new line in the output text. The expression can contain capture groups in parentheses. The constants are 0s and us with the string in question being 0s/XXXXXus (with X being the numbers I am trying to extract - the number length varies). Hover the generated regular expression to see more information. Quickly test and debug your regex. I am trying (rather unsuccessfully) to extract a number of varying length form a sting. I went through the wizard and configured a field extraction but I have over 29k events without custom fields. extract(), Get a match for a regular expression from a text string. Match string not containing. I am in the process of setting up Graylog and without regex knowledge I am stuck. Active Oldest Votes. It can be used to quickly parse large amounts of text to find specific character patterns; to extract, edit, replace, or delete text substrings; and to add the extracted strings to a collection to generate a report. \s* - match 0 or more whitespaces. Apply quickly to various Kusto job openings in top companies!. source after replacing all matches of regex with evaluations of rewrite. And we just want to extract the alphanumeric characters. Among these string functions are three functions that are related to regular expressions, regexm for matching, regexr for replacing and regexs for subexpressions. Six query commands are supported, along with many supporting functions and operations, including regular expressions, arithmetic operations. rewrite: The replacement regex for any match made by matchingRegex. Validate credit card numbers entered on your order form. When the data is ingested as dynamic data, the engine will enumerates all elements within the dynamic value and forward then to the index builder. A common ask is understanding how much traffic is generated by any of your different hosts. regex: A regular expression. dumps (object) Parameter: It takes Python Object as the parameter. The tables below are a reference to basic regex. \s* - match 0 or more whitespaces. 255 notation. txt file in our Office 365 SharePoint site and use Regular Expression Replace action to see if there are any email and replace them with [classified] string. Short for regular expression, a regex is a string of text that allows you to create patterns that help match, locate, and manage text. The business rule is: As a tech, I want to query device crashes by installed capita for machine that have software installed on 2,000 or more so that I can find incompatible top 7 app crashes sorted by total machines. Select OK and copy the formula down. It should be a 128-bit number. Use parse_json () if you need to extract more than one value from the JSON. pdf I have found an expression I can use to extract the first 6 characters. nodrop - allows messages containing invalid JSON values to be displayed. This is the first letter of the surnames. For example, the regular expression \A matches the beginning of a line, and is specified in Kusto as the string literal "\\A" (note the "extra" backslash. The reason that it is a ''read-only'' request is, because the processed Kusto data or the metadata can't be modified. Let's consider the below sample data: let demoData = datatable (Environment: string, Feature:string) [. A string of numbers and 26 letters: ^ [A-Za-z0-9]+$. To extract the year, we'll need to use a regular expression (regex). To achieve that, we will use the substring and CHARINDEX() function. Created Date: 8/11/2021 5:10:43 PM. Remove extra white spaces with StringUtils. We'll start with a brief intro on RegEx, while the second part shows how you can use them in a logging context. At the moment we provide three filters for better string cleanup. In this post, I want to walk through a few examples of how you would transform data that can be tricky to work with: data that is stored in arrays. Use Tools to explore your results. We are getting the text from the. In this tutorial, we will learn how to extract data from JSON pages or API, by using a scraping agent with the super-fast Regular Expression(Regex) extractor by Agenty. matches regex; has_any; In the SQL to KQL blog post, we used the evaluation data of the MITRE ATP29 test to test our queries. Optionally. Matching IPv4 Addresses Problem You want to check whether a certain string represents a valid IPv4 address in 255. Pattern pattern = Pattern. Where ^ specifies start of. Get all matches for a regular expression from a text string. Otherwise, all characters between the patterns will be copied. studyeducation. The source of this data can be subscription level events such as deallocating a virtual machine, deleting a resource group or creating a load balancer - essentially any create. At the moment we provide three filters for better string cleanup. Octoparse, a visual web data collection tool, provides a tool for generating regular expressions. RegExr is an online tool to learn, build, & test Regular Expressions (RegEx / RegExp). I am using the Google Analytics connector to bring through an entire websites data (thousands of different addresses), and I am trying to replicate a report I run in Google Analytics. print Id="82b8be2d-dfa7-4bd1-8f63-24ad26d31449" | extend guid_bytes = extract_all (@" (\w) (\w+) (\w)", Id) Extract several capture groups. 2 hours ago Docs. For example, the pattern. x r reactjs regex sql sql-server string svelte typescript vue-component vue. For a cumulative list of all of the updates to Power BI Desktop in the last few months, see this blog. captureGroup: A positive integer constant that indicates the capture group to extract. Since you can put all kinds of other scalar data types mixed in one dynamic object. The Regular Expression to check if string ends with the word is as shown in the. Quick and Dirty Method. The method returns true if the exact word is found in the string. A string of 26 lowercase alphabetic characters: ^ [a-z]+$. It removes all HTML tags and preserves text structure but you can remove it by using the collapse-whitespace option. js vuejs2 vuetify. CloudWatch Logs Insights supports a query language you can use to perform queries on your log groups. In this example, we will search for spaces in the file named example. The RFC 5322 specifies the format of an email address. Existing kql vectors will be left as is, character vectors are escaped with single quotes, numeric vectors have trailing. regex: A regular expression. You may notice that Regular expression match in this regular expression has a few outputs: There is "Match0" is a full match for the whole regular expression. any character except newline \w \d \s: word, digit, whitespace. There are also separate output values for each named regular expression group: Price, Quantity, Title. (In Splunk, these will be index-time fields). Hello all. RE2 regular expression syntax describes the syntax of the regular expression library used by Kusto (re2). The code is below in case you want to copy it. Short for regular expression, a regex is a string of text that allows you to create patterns that help match, locate, and manage text. ReservationService. Because this blog post will also be about performance we want to use bigger data set in the form of the Log Analytics Demo environment. The addresses are separated by period (. Azure Sentinel — Hunting. There are a few ways of extracting these nested fields with Kusto, depending on which product you are using. I'm not permitted to paste links, so you'll need to type the url seen in the screenshots to pull up both my Regular Expression and Sample Data shown in the example. Along with custom logs, these are concepts that really had me scratching my head for a long time, and it was a little bit tricky to put all the pieces together from documentation and other people's blog posts. If there is a requirement to retrieve the data from a column after a specific text, we can use a combination of TRIM, MID, SEARCH, LEN functions to get the output. Kusto-queries. Excel searches for the position of the space within the text string using the FIND function. Given string str, the task is to check whether the given string is valid GUID (Globally Unique Identifier) or not by using Regular Expression. Regexp for extracting public IP address Recently I needed to make a regular expression for parsing the first public IPV4 address from a string of comma separated private and public IP addresses. Kusto Query Regex Match - studyeducation. Last updated: October 20, 2018 - 4:29 pm UTC. Start a FREE 10-day trial. Optionally. dumps (object) Parameter: It takes Python Object as the parameter. In the previous post, we talked about the basic of Text to Columns and focused on "Fixed width". split REGEX - If STRING is not given, splitting the content of$_, the default variable of Perl at every match of the. I had to do some digging until I found the issue. This tool removes all whitespace characters from a string. May 18, 2018 · How to use regex match to extract values from email messages Let’s suppose you are getting a new email after someone made a purchase and you need to extract information from this email and. You’ll recognize literal parentheses too. To achieve that, we will use the substring and CHARINDEX() function. source after replacing all matches of regex with evaluations of rewrite. extract_all(regex, [captureGroups,] text) If we can specify a regular expression to match the data that we need, we can run it against that single field and get a list. How i extract text from a model dialog in selenium? 2 mathjax + vue not rerendering equations. Both were based on toy implementations optimized for teaching. Regular Expression to By Klas. Queries are how Grafana panels communicate with data sources to get data for the visualization. JSONPath performs a simple tree traversal. We are getting the text from the. CASE_INSENSITIVE); Case Insensitive As Regular Expression. Url Validation Regex | Regular Expression - Taha. Since we are interested just in the "range" field (the subnets used by Zscaler clients), we could go for a quick and dirty, brute-force extraction of these values, by using Kusto's extract_all() scalar function: extract_all(regex, [captureGroups,] text). The action is smart enough to. This powerful script lets you extract emails, proxies, IPs, phone numbers, addresses, HTML tags, URLs, links, dates, etc. Now let's look at the movie distribution across genres. Besides, Octoaprse fully supports to verify customized regular expressions. extract_all(regex, [captureGroups,] text) If we can specify a regular expression to match the data that we need, we can run it against that single field and get a list. Like most other programming and query languages, Kusto too has case sensitivity, which means it can deal with upper-case and lower-case while performing comparisons between values. This 32 bit address scheme is the first version of ip addresses. 8 hours ago Convertf. text/html 9/5/2019 4:46:29 PM I need to create a kusto temporary table 0. and ending with another number. In this example, we will create a Regex pattern named patter which will be case insensitive. 15 In~ Looks for multiple values, but without case-sensitive rule. Along with custom logs, these are concepts that really had me scratching my head for a long time, and it was a little bit tricky to put all the pieces together from documentation and other people's blog posts. Otherwise, all characters between the patterns will be copied. Viewed 10K+ times!. Regular expressions (regex or regexp) are extremely useful in extracting information from any text by searching for one or more matches of a specific search pattern (i. The source of this data can be subscription level events such as deallocating a virtual machine, deleting a resource group or creating a load balancer – essentially any create. This is fast, but approximate. Usually a regex step can be replaced with steps that our tool does offer though it's not nearly as quick as a regex would be. Split/Extract names from a delimiter string in Flow 11-25-2018 07:02 AM I have files structure like this '123456,Joe Bloggs,5. Finally, to extract the genres, we'll simply need to split on pipes. The importance of performance and optimizing queries comes from the limits in the. org Education Kusto Convert String To Array › Best Education From www. Substitution Expression Flags ignore case (i) global (g) multiline (m) extended (x) extra (X) single line (s) unicode (u) Ungreedy (U) Anchored (A) dup subpattern names(J) Match string not containing string Given a list of strings (words or other characters), only return the strings that do not match. These expressions must be encoded in Kusto as string literals, and all of Kusto 's string quoting rules apply. The source of this data can be subscription level events such as deallocating a virtual machine, deleting a resource group or creating a load balancer - essentially any create. txt file in our Office 365 SharePoint site and use Regular Expression Replace action to see if there are any email and replace them with [classified] string. This regex matches the whole msg. Quick-Start: Regex Cheat Sheet. Domain Name Regular Expression Pattern -A-Za-z0-9-163. For example, the below regex matches shirt, short and any character between sh and rt. In the text document that you want to extract specific text from, press Control + F or Command + F to open the search bar. txt $egrep "\s" example. Extract the Name from an Active Directory Distinguished Name with PowerShell and a Regular Expression Mike F Robbins July 10 2014 July 10 2014 10 This is actually something I had a small blurb about in my previous blog article but I wanted to go back revisit it and write a dedicated blog article about it. Roll over a match or expression for details. To get the list of all numbers in a String, use the regular expression ‘ [0-9]+’ with re. Most of them difficult. Optionally. The best advice to note from that page is to use a peer reviewed. Regular The Cömplete Tutorial Jan Cbyvaerts. ][0-9] {1,3} We can make this regex pattern shorter by using non-capturing group for the first 3 octets and another {3}[0-9]{1,3} for the last octet that doesn't end with dot. Introduction to RegEx. Escaping depends on context, therefore this example does not cover string or delimiter escaping. In this article I'm going to discuss table joins and the let statement in Log Analytics. Kusto can be used in Azure Monitor Logs, Application Insights, Time Series Insights and Defender Advanced Threat Perception. Links to help debug RegEx: Debuggex: Online visual regex tester. The business rule is: As a tech, I want to query device crashes by installed capita for machine that have software installed on 2,000 or more so that I can find incompatible top 7 app crashes sorted by total machines. If using a regular expression for the substring argument, the replacement string. org Education The following sections give examples of how to work with strings when using the Kusto Query Language. By Robert Cain. Example of an invalid regex: @"\d+" Required: captureGroups: A dynamic array constant that indicates the capture group to extract. You’ll recognize literal parentheses too. This can run very much faster, and is effective if the JSON is produced from a template. Oct 23, 2019 · Kusto regex for extracting IP adresses In my AzureDiagnostics for my to use HTML, CSS, JavaScript, SQL, PHP, Python, Bootstrap, Java and XML. Octoparse, a visual web data collection tool, provides a tool for generating regular expressions. In the previous post, we talked about the basic of Text to Columns and focused on "Fixed width". text: A string to search. regex: A regular expression. To get the list of all numbers in a String, use the regular expression '[0-9]+' with re. String matchingWord="string" // word to find String longString="it is a very long string. This powerful script lets you extract emails, proxies, IPs, phone numbers, addresses, HTML tags, URLs, links, dates, etc. Optionally. 0 python python-3. They are ephemeral: they can be used by any Function downstream, but will not be added to events, and will not exit the Pipeline. However, its only one of the many places you can find regular expressions. They can be also used as a data generator, following the concept of reversed regular expressions, and provide randomized test data for use in test databases. Consider having the JSON parsed at ingestion by declaring the type of the column to be dynamic. Regular expression tester with syntax highlighting, explanation, cheat sheet for PHP/PCRE, Python, GO, JavaScript, Java. Results update in real-time as you type. There are a few functions in Kusto that perform string matching, selection, and extraction by using a regular expression. The number i am trying to extract is the ones that are in between two - , basically like the picture below. You may notice that Regular expression match in this regular expression has a few outputs: There is "Match0" is a full match for the whole regular expression. I had to do some digging until I found the issue. We will show some examples of how to use regular expression to extract and/or replace a portion of a string variable using these three functions. "\\d+" Or, " ( [0-9]+)". Kusto regex for extracting IP adresses In my AzureDiagnostics for my ResourceType "AzureFirewalls", there's a column named "msg_s". With this tool, you can convert HTML code to text. Kusto Gobbles Up Application Insights Data. org › Search www. Since we are interested just in the "range" field (the subnets used by Zscaler clients), we could go for a quick and dirty, brute-force extraction of these values, by using Kusto's extract_all() scalar function: extract_all(regex, [captureGroups,] text). The Regular Expression to check if string ends with the word is as shown in the. Finally, to extract the genres, we'll simply need to split on pipes. Generally, for matching human text, you'll want coll() which respects character matching rules for the specified locale. Sign in to vote. Search") Code line:. There are also separate output values for each named regular expression group: Price, Quantity, Title. Extract the Name from an Active Directory Distinguished Name with PowerShell and a Regular Expression Mike F Robbins July 10 2014 July 10 2014 10 This is actually something I had a small blurb about in my previous blog article but I wanted to go back revisit it and write a dedicated blog article about it. We’ll download csv files from the web, put them in an Azure Storage Account and from there, we’ll do everything in Azure Data Explorer and Kusto. Using regular expression match to extract values from text in Power Automate¶. It started with a post in Day 1 followed by Day 2, Day 5, Day 18, Day 28, Azure Sentinel — Alerts, and. Character escaping is what allows certain characters (reserved by the regex engine for manipulating searches) to be literally searched for and found in the input string. In the previous post, we talked about the basic of Text to Columns and focused on "Fixed width". Example of an invalid regex: @"\d+" Required: captureGroups: A dynamic array constant that indicates the capture group to extract. Internet Protocol (ip) addresses are the numerical identifiers of each device connected to a computer network that uses Internet Protocol for communication. Azure Monitor Logs and Kusto Query Language (KQL) The Azure platform consists of a variety of resources that generate large volumes of activity and diagnostic log data. 15 In~ Looks for multiple values, but without case-sensitive rule. To achieve that, we will use the substring and CHARINDEX() function. update (): This method updates the dictionary with elements from another dictionary object or from an iterable key/value pair. Active Oldest Votes. In this example, we will search for spaces in the file named example. For example, the regular expression \A matches the beginning of a line, and is specified in Kusto as the string literal "\\A" (note the "extra" backslash. com Best Education Education Oct 08, 2020 · The best way to learn about the Kusto Query Language is to look at some basic queries to get a "feel" for the language. We are getting the text from the. Apologies if this has been asked before, but as a newbie to all things Power BI this is proving a bit of a pain. Kusto regex for extracting IP adresses. Print the subsequence formed. A common ask is understanding how much traffic is generated by any of your different hosts. The tool calls the stringify () function on your input and you get JSON-escaped text as output. You may notice that Regular expression match in this regular expression has a few outputs: There is "Match0" is a full match for the whole regular expression. Samples For Kusto Queries Azure Data Explorer, Synapse. Note, because my timestamp is a full date time field and I only want to show the hours and minutes components, I used some regex to extract these parts. Matching an email address within a string is a hard task, because the specification defining it, the RFC2822, is complex making it hard to implement as a regex. Consider having the JSON parsed at ingestion by declaring the type of the column to be dynamic. pdf I have found an expression I can use to extract the first 6 characters. In this article you will learn how to match numbers and number range in Regular expressions. Generally, for matching human text, you'll want coll() which respects character matching rules for the specified locale. This report uses Regex expressions to include URL's with certain keywords in the URL (currently 5) , b. Apologies if this has been asked before, but as a newbie to all things Power BI this is proving a bit of a pain. The source of this data can be subscription level events such as deallocating a virtual machine, deleting a resource group or creating a load balancer – essentially any create. The humidity field is a string, and it contains %. If using a regular expression for the substring argument, the replacement string. It removes all HTML tags and preserves text structure but you can remove it by using the collapse-whitespace option. Kusto Application Insights Convertf. Any other characters will not be returned. Regular expressions can also be used from the command line and in text editors to find text within a file. Coming soon, you'll be able to choose the tags that you want to extract text. Array types are going to…. txt$ egrep "\s" example. See JSON auto option for details. Substitution Expression Flags ignore case (i) global (g) multiline (m) extended (x) extra (X) single line (s) unicode (u) Ungreedy (U) Anchored (A) dup subpattern names(J) Match string not containing string Given a list of strings (words or other characters), only return the strings that do not match. This approach, using StringUtils. Controls behaviour when multiple values are supplied. In my AzureDiagnostics for my ResourceType "AzureFirewalls", there's a column named "msg_s". One line of regex can easily replace several dozen lines of programming codes. It can be used to quickly parse large amounts of text to find specific character patterns; to extract, edit, replace, or delete text substrings; and to add the extracted strings to a collection to generate a report. We will use re. Education Details: Jul 18, 2021 · regex: The regular expression to search text. parens, collapse. A regular expression is a formation in order to match different text or words or numbers according to the given regex pattern. Optionally. Regular expression is a pattern that describes a specific set of strings with a table variable store the list of player names separated by a pipe '|' delimiter. RE2 regular expression syntax describes the syntax of the regular expression library used by Kusto (re2). Hopefully this will help anyone else out there that still has unanswered questions on one of. print extract_all (@ " (\d+)", "a set of numbers: 123, 567 and 789") // results with the dynamic array ["123", "567", "789"]. JSONPath performs a simple tree traversal. ]+)", 1, "hello x=45. captureGroup: A positive int constant indicating the capture group to extract. Validate credit card numbers entered on your order form. Is it the case or I missed something in the Kusto syntax for regular expressions?. Print the subsequence formed. You can use these examples to analyze your own applications that are monitored by Azure Application Insights, or use the concepts in these queries for. Regular expression tester. If substring is wrapped in forward slashes, it is treated as a regular expression, using the same pattern syntax as regex. Create a regular expression to extract the string between two delimiters as regex = "\\[(. But because a quantifier (\D*) has been used in the regular expression, the search engine can backtrack and retry the match differently in the hope of matching the complete regular expression. nodrop - allows messages containing invalid JSON values to be displayed. Along with custom logs, these are concepts that really had me scratching my head for a long time, and it was a little bit tricky to put all the pieces together from documentation and other people's blog posts. JSONPath expressions can use the dot-notation. Results update in real-time as you type. In Java programming language we can use Pattern class which can use Regex and provide CASE_INSENSTIVE as an option. Saying that backslash is the "escape" character is a bit misleading. In my AzureDiagnostics for my ResourceType "AzureFirewalls", there's a column named "msg_s". Given string str, the task is to check whether the given string is valid GUID (Globally Unique Identifier) or not by using Regular Expression. Controls behaviour when multiple values are supplied. For example, the below regex matches. | project extract ("milk-cow-\\s* ( [a-zA-Z]+)", 1, info) It means. Syntax: json. There are a few ways of extracting these nested fields with Kusto, depending on which product you are using. 0 stands for the entire match, 1 for the value matched by the first '('parenthesis')' in the regular expression, 2 or more for subsequent parentheses. Regex to extract a number from string. So in this example, i would have a new column that would have only the number 111. It contains information about IP-adresses trying to request access to another adress. For example, the below regex matches shirt, short and any character between sh and rt. Azure Data Flows in ADF and Synapse allow for transformation across many different types of cloud data at cloud scale. At the image down below. Search") Code line:. May 18, 2018 · How to use regex match to extract values from email messages Let’s suppose you are getting a new email after someone made a purchase and you need to extract information from this email and. Internet Protocol (ip) addresses are the numerical identifiers of each device connected to a computer network that uses Internet Protocol for communication. Quickly test and debug your regex. Control options with regex(). For example, the regular expression \A matches the beginning of a line, and is specified in Kusto as the string literal "\\A" (note the "extra" backslash. _-])+$by the system to determine if a given hostname uses valid characters. The returned value is a JSON-encoded string, and not a native Athena data type. The \K syntaxforces the regex engine to consider that any matched regex, before the \K form, is forgotten and that the final regex to match is, ONLY, the regex, located after the \K form. We are getting the text from the. When this option is checked, the generated regular expression will only contain the patterns that you selected in step 2. You can match numbers in the given string using either of the following regular expressions −. Free RegEx Tool - Octoparse. pdf I have found an expression I can use to extract the first 6 characters. ][0-9] {1,3} [. Backslashes. Match a fixed string (i. The method returns true if the exact word is found in the string. (True RegEx masters, please hold the, “But. To extract the year, we'll need to use a regular expression (regex). RE2 regular expression syntax describes the syntax of the regular expression library used by Kusto (re2). Textabulous!. The default interpretation is a regular expression, as described in stringi::about_search_regex. This removes all fields from the Match panel that may be left over from a previous regular expression. 13 in Looks for multiple values 1. In this article you will learn how to match numbers and number range in Regular expressions. To get the list of all numbers in a String, use the regular expression ‘ [0-9]+’ with re. com March 2010 Introduction. Here you'll find posts about AzureMonitor, LogAnalytics, System Center Operations Manager, Powershell, Hyper-V, Azure Automation, Azure Governance and other Microsoft related technologies. Hi Anyone have a Solution on how to extract Common name from Distinguished Name In Kusto I have tried parse, split, Sub string and what ever, but haven´t have a success with VB and Power Shell it is simple and a lot of examples to grab From a table called Member Name containing CN=test test, OU=s. Split/Extract names from a delimiter string in Flow 11-25-2018 07:02 AM I have files structure like this '123456,Joe Bloggs,5. countof() extract() extract_all() matches regex; parse operator; replace() trim() trimend() trimstart(). Regular expression (RegEx) is an extremely powerful tool for processing and extracting character patterns from text. Use Tools to explore your results. Its really helpful if you want to find the names starting with a particular character or search for a pattern within a dataframe column or extract the dates from the text. However, I want the last field which, depending on how many spaces are in the IIS site name, can vary in index. For example, the regular expression \A match es the beginning of a line, and is specified in Kusto as the string literal "\\A" (note. RegExr is an online tool to learn, build, & test Regular Expressions (RegEx / RegExp). This is the first letter of the surnames. To fetch the 3rd value from the list you use {2} because the count starts at zero here. Regular expression is a pattern that describes a specific set of strings with a table variable store the list of player names separated by a pipe '|' delimiter. This tool removes all whitespace characters from a string. KQL, the Kusto Query Language, is used to query Azure's services. 12 Matches regex Similar to the contains opera-tor 1. compile("poftut", Pattern. Escaping depends on context, therefore this example does not cover string or delimiter escaping. The method returns true if the exact word is found in the string. Aug 23, 2019 · Hello all I am using the Google Analytics connector to bring through an entire websites data (thousands of different addresses), and I am trying to replicate a report I run in Google Analytics. Regex is supported in all the scripting languages (such as Perl, Python, PHP, and JavaScript); as well as general purpose programming languages such. MatchString function. Education Details: replace_regex() - Azure Data Explorer | Microsoft Docs. The first two articles in this series, "Regular Expression Matching Can Be Simple And Fast" and "Regular Expression Matching: the Virtual Machine Approach," introduced the foundation of DFA-based and NFA-based regular expression matching. For example, with regex you can easily check a user's input for common misspellings of a particular word. 15 In~ Looks for multiple values, but without case-sensitive rule. Thanks for the question, karthick. Regex to extract a number from string. Where ^ specifies start of. txt file in our Office 365 SharePoint site and use Regular Expression Replace action to see if there are any email and replace them with [classified] string. The tool calls the stringify () function on your input and you get JSON-escaped text as output. However, when I attempt to enter the regex, I keep getting a SEM0420: Semantic error: Regex pattern is ill formed. org › Search www. getCount () ? true : false. Start a FREE 10-day trial. We'll use this format to extract email addresses from the text. Data labels in combination charts. split REGEX, STRING, LIMIT where LIMIT is a positive number. Get a match for a regular expression from a source string. Apparently in SQL the hyphen needs to be in the beginning or end of the sub pattern, and there you don't even have to escape it: | extend IllegalChar = extract (" [^-a-zA-Z_]", 0, name) Enter fullscreen mode. Kusto regex for extracting IP adresses In my AzureDiagnostics for my ResourceType "AzureFirewalls", there's a column named "msg_s". In Java programming language we can use Pattern class which can use Regex and provide CASE_INSENSTIVE as an option. Otherwise, all characters between the patterns will be copied. You have a second argument to extract that tells the function to return the capture only, so you may use. For example, the regular expression \A match es the beginning of a line, and is specified in Kusto as the string literal "\\A" (note. The method returns true if the exact word is found in the string. Consider using a regular expression match with extract instead. Sometimes when we automate things, some technologies don't play nice with characters we've gotten from a different technology. Quick and Dirty Method. For a cumulative list of all of the updates to Power BI Desktop in the last few months, see this blog. Data labels in combination charts. It can be used to quickly parse large amounts of text to find specific character patterns; to extract, edit, replace, or delete text substrings; and to add the extracted strings to a collection to generate a report. split REGEX - If STRING is not given, splitting the content of$_, the default variable of Perl at every match of the. Period, matches a single character of any single character, except the end of a line. The RFC 5322 specifies the format of an email address. countof() extract() extract_all() matches regex; parse operator; replace() trim() trimend() trimstart(). Since we are interested just in the “range” field (the subnets used by Zscaler clients), we could go for a quick and dirty, brute-force extraction of these values, by using Kusto’s extract_all() scalar function: extract_all(regex, [captureGroups,] text). ' character will match any character without regard to what character it is. We will show some examples of how to use regular expression to extract and/or replace a portion of a string variable using these three functions. It contains information about IP-adresses trying to request access to another adress. | 2021-10-25 22:25:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.20158682763576508, "perplexity": 2757.8943885450267}, "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/1634323587770.37/warc/CC-MAIN-20211025220214-20211026010214-00157.warc.gz"} |