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http://cogsci.stackexchange.com/questions/6305/can-dreams-be-memorised | # Can dreams be memorised?
Would it be possible to activate the human memory and "access" it by means of encouraging certain hormones, to assist a sleeping body to memorize dreams and later (meaning minutes, days, months or even years) access it again with the same hormones - something like a trained body function.
This could perhaps help in solving certain criminal cases or assist in psychological healing (for schizophrenia and the likes). I'm just curious about the possibilities and have absolutely no knowledge of how the brain works. This was just a wild idea that came to mind and I was wondering about the possibilities.
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This is a bit too "science fiction" at this point. I'd recommend poking through some of the upvoted questions within the dreams tag to familiarize yourself with some of the actual physiology first. – Chuck Sherrington Apr 26 '14 at 13:07
There's quite a bit of good information on Biology.SE as well. – Chuck Sherrington Apr 26 '14 at 13:08
I think this can be easily answered. I will find my course notes one of these days to give the details, but it is known that some neurotransmitter necessary for translating short-term into long-term menory is inactive during sleep. – Ana Apr 26 '14 at 17:42
@Ana The question in the title can be easily addressed, depending on how one defines "memorized", but the remainder of the question is just idle speculation. – Chuck Sherrington Apr 26 '14 at 19:13
Yes, dreams can be memorized, (but there are persons that don't remember their dreams), although they continue to be just dreams, not reality. Therefore how would they help to solve criminal cases, which are from real world? – Di Ana Apr 28 '14 at 2:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3785135746002197, "perplexity": 1312.8886429782458}, "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-2016-07/segments/1454701160958.15/warc/CC-MAIN-20160205193920-00074-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/97163/boolean-valued-models-have-no-essentially-new-ordinals | # Boolean-valued models have no essentially new ordinals
Since I still have some trouble with transferring theorems of ZFC into the Boolean-valued framework, would someone more at ease with this check the following short calculation?
This is a proposition in Jech's book, stating that $$\|z\text{ is an ordinal}\|=\bigvee_{\alpha\in\mathbf{ON}}\|z=\check{\alpha}\|$$ I can follow the proof given, but want to confirm the following proof of the inequality $$\|z\text{ is an ordinal}\|\leq\|z\in\check{\alpha}\|\vee\|z=\check{\alpha}\|\vee\|\check{\alpha}\in z\|$$
Fix a $B$-name $z$ and an ordinal $\alpha$. Classically, if $z$ were an ordinal, it would be comparable with $\alpha$, i.e. either $z\in\alpha,z=\alpha$ or $\alpha\in z$. However, the universal closure of this statement with respect to $z$ is not $\Delta_0$, so we can't directly use absoluteness (some sort of closure is required to avoid producing a check on $z$). Instead, we find $z$'s place in the von Neumann hierarchy, $z\in V_\gamma$. We can then take the universal closure of the above statement, bounded to $V_\gamma$, which is $\Delta_0$, and get $$\|\forall y\in\check{V_\gamma}:y\text{ is an ordinal}\Rightarrow y\in\check{\alpha}\vee y=\check{\alpha}\vee\check{\alpha}\in y\|=1$$ We can then specify this to $z$ and get the desired result.
I suppose this "trick" of replacing an unbounded quantifier with a bounded one is pretty standard. I realize all of this might be moot since we know that all of the axioms of ZFC are valid in $V^B$, which means all of the theorems are also valid. But since Jech proves the result in question before proving that $V^B$ models ZFC, I thought there must be a simpler way.
EDITED: After further thought, what I wrote above is wrong. We can't specify to $z$, but only to $\check{z}$. I'm at a loss again.
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I recall a year ago when studying this I ran into the same difficulty... – Asaf Karagila Jan 7 '12 at 13:03
Let us run through the proof of the lemma (Jech's Set Theory, 3rd Millennium Edition, Lemma 14.23): $\renewcommand{\Ord}{\mathrm{Ord}} \renewcommand{\Dom}{\operatorname{Dom}}$
Lemma 14.23: For every $x\in V^B$, $$\|x\text{ is an ordinal}\|=\sum_{\alpha\in\Ord}\|x=\check\alpha\|$$
For shortness sake, I'll denote $\phi(x)=x\text{ is an ordinal}$.
Proof: By a previous lemma, $\phi(x)$ is a $\Delta_0$ formula and thus absolute between $V$ and $V^B$. This means that $\|\phi(\check\alpha)\|=1$ for every $\alpha\in\Ord$, and clearly $\|x=\check\alpha\rightarrow\phi(x)\|=1$, therefore $\|x=\check\alpha\|\le\|\phi(x)\|$, for every $\alpha$. Therefore, $\sum\|x=\check\alpha\|\le\|\phi(x)\|$.
On the other hand, let $\|\phi(x)\|=u$, then for every ordinal $\gamma$ we have: $$\|\phi(x)\land x\in\check\gamma\|\le\sum_{\alpha\in\gamma}\|x=\check\alpha\|\tag 1$$ This is because $\check\gamma(t)=1$ for every $t\in\Dom(\check\gamma)$ and $\|x\in\check\gamma\|=\sum_{t\in\Dom(\check\gamma)}\|x=t\|\cdot\check\gamma(t)$, inductively we can show that $t\in\Dom(\check\gamma)\iff t=\check\alpha$ for $\alpha\in\gamma$.
Since ordinals are comparable then for every $\alpha$ we have: $$u=\|\phi(x)\|\le\|x\in\check\alpha\|+\|x=\check\alpha\|+\|\check\alpha\in x\|$$
This statement is equivalent to saying that $\phi(x)$ implies that $x$ and $\alpha$ are comparable, which is what we wanted to say.
Now since there is only set many $\alpha$ such that $x(\check\alpha)\neq 0$, we have that there is some $\gamma$ such that $u\le\|x\subseteq\check\gamma\|$, thus $\|\phi(x)\|\le\|x\subseteq\check\gamma\|$, and it means that $\|\phi(x)\|\le\|\phi(x)\land x\in\check\gamma\|$. Using $(1)$ we yield:
$$u=\|\phi(x)\|\le\sum_{\alpha\in\gamma}\|x=\check\alpha\|\le\sum_{\alpha\in\Ord}\|x=\check\alpha\|\le u$$
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First of all, I think we can do away with (1). $\|x\in\check{\alpha}\|+\|x=\check{\alpha}\|$ is the same as $\sum_{\beta\leq\alpha}\|x=\check{\beta}\|$. So, if we raise $\alpha$ sufficiently, we'll have $u\leq\sum_{\beta\leq\alpha}\|x=\check{\beta}\|$, which is enough. Secondly, I think I'm still not clear on the trichotomy inequality. Are you saying that the statement that ordinals are comparable is provable in pure predicate calculus? – Miha Habič Jan 7 '12 at 23:54
@Miha: The order of the ordinals is by $\in$, so $\varphi(x,y)=x\in y$ is the same as $x<y$ for ordinals. – Asaf Karagila Jan 8 '12 at 0:00
I'm sorry. It might be because it's late here, but I don't see what you're saying. $\phi(x)$ does indeed imply that $x$ and $\alpha$ are comparable, however, when pushing this formula into the Boolean model, we get a check over the $x$. I'm sure I'm misunderstanding you somewhere. – Miha Habič Jan 8 '12 at 0:22
@Miha: In ZF every two ordinals are comparable, because we defined the ordinals as transitive $\in$-well ordered sets. It follows that either $\alpha=\beta$ or $\alpha\in\beta$ or $\beta\in\alpha$. In the Boolean valued model we don't say that $\|\phi(x)\|$ is always valid, of course not. We say that it is the supremum of how equal you are to a real ordinal. – Asaf Karagila Jan 8 '12 at 7:10
Actually, it seems everything is all right. If I haven't made a mistake, all you need to prove that ordinals are comparable is Extensionality, and Jech proves that Extensionality is valid in $V^B$ in Lemma 14.17. So the result does need some validity of set theory in the Boolean-valued model
- | {"extraction_info": {"found_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": 0.9862773418426514, "perplexity": 189.94568233515878}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435376073161.33/warc/CC-MAIN-20150627033433-00003-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://www.lessonplanet.com/teachers/pet-math-enrichment-32 | # Pet Math Enrichment 3.2
In this pet math instructional activity, students use the total number of pets plus one other number to solve the missing number of pets. Students solve three problems. | {"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": 0.8817484378814697, "perplexity": 6664.874572259541}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794863949.27/warc/CC-MAIN-20180521043741-20180521063741-00523.warc.gz"} |
http://www.physicsforums.com/showpost.php?p=2461646&postcount=6 | View Single Post
PF Gold P: 2,019 This reminds me of when I was a kid and somebody gave me a chemistry set.I got bored by following the experiments in the instruction booklet so I mixed everything together and tried to set it all alight. | {"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": 0.8200131058692932, "perplexity": 1367.2362790056966}, "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-2014-35/segments/1408500815861.64/warc/CC-MAIN-20140820021335-00069-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://support.bioconductor.org/p/104400/ | Question: Representative gene expression value in one condition with several replicates
0
22 months ago by
Jack0
Jack0 wrote:
Hi all,
I want to know how to get a gene expression value for a condition with different replicates.
For example, I have condition M and N, each condition with two replicates M1, M2, N1, N2
I want to get one value to represent the gene expression value (FPKM or TPM) of M, can I just use the mean of each replicate? M=(M1+M2)/2?
Is there any other way to calculate the gene expression value for a condition?
rnaseq edger gene expression • 695 views
modified 22 months ago by Gordon Smyth38k • written 22 months ago by Jack0
Answer: Representvie gene expression value in one condition with several replicates
5
22 months ago by
Aaron Lun25k
Cambridge, United Kingdom
Aaron Lun25k wrote:
As Mike says, this isn't an edgeR question. But I will pretend it is. If you have the counts, go through an edgeR analysis - or at least to calling glmFit - with the following design matrix:
group <- c("M", "M", "N", "N")
design <- model.matrix(~0 + group)
You didn't specify the nature of your replicates, but you may need to add a blocking factor if M1 is related to N1 (e.g., from the same individual) and M2 is related to N2.
Anyway, once you've done that, you can obtain the log-average expression of each level of group from the \$coefficients field of the output of glmFit. This provides a general approach to getting condition-specific expression values, taking advantage of NB GLMs to give a more precise estimate than averaging FPKMs.
Thank you very much!!
Answer: Representvie gene expression value in one condition with several replicates
4
22 months ago by
Gordon Smyth38k
Walter and Eliza Hall Institute of Medical Research, Melbourne, Australia
Gordon Smyth38k wrote:
If you want expression values on a log-scale, then you can use the process explained by Aaron, which is similar to but better than just averaging the individual log-expression values.
If you want expression values on the unlogged scale, then the edgeR package provides functions to do this. Type
library(edgeR)
?cpmByGroup
?rpkmByGroup
Thank you very much for you advice!
Answer: Representvie gene expression value in one condition with several replicates
0
22 months ago by
Michael Love25k
United States
Michael Love25k wrote:
This isn't a DESeq2 (or edgeR) question really, so I'm removing the DESeq2 tag. The arithmetic or geometric mean of the TPM seems to be a reasonable number for the average relative abundance. I don't have any strong opinions about this though. | {"extraction_info": {"found_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": 0.5560984015464783, "perplexity": 2711.7647800288746}, "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/1570986649232.14/warc/CC-MAIN-20191014052140-20191014075140-00486.warc.gz"} |
http://mathhelpforum.com/calculus/219923-integration-parts-quick-question.html | # Math Help - Integration by parts, quick question
1. ## Integration by parts, quick question
So i understand this question mostly, i dont understand where they got the (1+4) from? and shouldnt there be a negative in front of the last part on the 2nd line.
cheers
Attached Thumbnails
2. ## Re: Integration by parts, quick question
At the end of the second line what you have is:
$\int e^{2t} \cos t dt = -[2e^{2t})(- \cos t)] + \int 4 e^{2t}(- \cos t) dt$
Notice that the last term is common with the left hand side, so move it to the other side to get:
$(1+4) \int e^{2t} \cos t dt = -2e^{2t}( - \cos t)$
And no, the plus sign before the last term of the 2nd line is correct. Starting with
$- \int 2 e ^{2t} \sin t dt$
and using integration by parts, let $u = -2e ^{2t}$, $dv = \sin t dt$,
then:
$\int u dv = uv - \int v du = -2e^{2t}(-\cos t) - \int (-\cos t) (-4) e^{2t} dt$
$= -2e^{2t} (-\cos t) + \int 4 e^{2t} (-\cos t) dt$
3. ## Re: Integration by parts, quick question
I agree, that is hard to make sense of- they leave a lot out. The problem is to integrate $\int_{-\pi}^{\pi} e^{2t}cos(t)dt$. They note that "it doesn't matter which function is chosen to differentiate" and then choose to differentiate the $e^{2t}$.
That is we let $u= e^{2t}$ and $dv= cos(t)dt$. Then $du= 2e^{2t}dt$ and $v= sin(t)$.
$uv- \int v du$, then, is $e^{2t}sin(t)\left]_{-\pi}^\pi- 2\int_{-\pi}^\pi e^{2t}sin(t)dt$
Of course, $sin(\pi)= sin(-\pi)=$ so that first term is 0. That's the first "0" in the second line. What's left is $2\int_{-\pi}^\pi e^{2t}sin(t)dt$.
Now, do the integration by parts again, letting $u= e^{2t}$ and $dv= sin(t)dt$ so that $du= 2e^{2t}dt$ and $v= -cos(t)$.
$2\int_{-\pi}^\pi e^{2t}sin(t)dt= 2\left( -e^{2t}cos(t)\right]_{-\pi}^\pi- 2\int_{-\pi}^\pi e^{2t}cos(t)dt\right)$
$cos(\pi)= cos(-\pi)= -1$ so the first term is $2((-1)e^{2\pi}-(-1)e^{-2\pi})= 2(e^{-\pi}- e^{\pi})$
The integral, at this point is $\int e^{2t}cos(t)dt= 2(e^{-\pi}- e^{\pi})- 4\int_{-\pi}^\pi e^{2t}cos(t) dt$
Now, here's the point. Because the first integral takes us from "cos(t)" to "sin(t)" and the second integral takes back to "cos(t)", while the derivatives of $e^{2t}$ always gives " $e^{2t}$", we have come right back (that integral on the right) to what we started with (the integral on the left). So combine those by adding $4\int_{-\pi}^\pi e^{2t}cos(t)dt$, giving $5\int_{-\pi}^\pi e^{2t}cox(t)dt$ on the left. That is where the "4+ 1= 5" on the left came from.
4. ## Re: Integration by parts, quick question
x1________x2
same______integrate **************(line one)
-(diff______same)
same________integrate
-(diff________same) *******************(line 2)
This is a boss way for noobs like me to remember the order. brackets mean with an integral sign at the front. | {"extraction_info": {"found_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": 29, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9614162445068359, "perplexity": 481.6885230309652}, "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-2015-48/segments/1448398449145.52/warc/CC-MAIN-20151124205409-00172-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/403429/does-an-inward-vector-field-on-a-boundary-require-a-zero-point-or-singularity-in | # Does an inward vector field on a boundary require a zero point or singularity in the interior?
Consider a continuous 3D vector field $\vec{V}:\mathbb{R}^n\to\mathbb{R}^n$ except that $\vec{V}$ may have isolated singularities, and an open region $\Omega\subset\mathbb{R}^n$. Suppose $\vec{V}(\vec{r})$ is nonsingular for $\vec{r}\in\partial\Omega$, and let $\vec{n}(\vec{r})$ be the outward-pointing normal at a boundary point $\vec{r}\in\partial\Omega$. If the normal component of the vector field points inward at every point on the boundary,
$$\vec{V}(\vec{r})\cdot \vec{n}(\vec{r}) < 0\ \forall\ \vec{r}\in\partial\Omega.$$
Does this imply that $\vec{V}(\vec{r})$ is either zero or singular somewhere in $\Omega$? How would it be shown? I imagine this must be a reasonably well known result but I wasn't sure how to look for it.
I did find this question, which states for $\vec{V}$ defined on the unit $n$-ball $B^n$, if $\vec{V}(\vec{r})\neq 0\ \forall\ \vec{r}\in B^n$, there must be a point $\vec{r}\in\partial B^n$ at which $\vec{V}(\vec{r})$ points outward and one at which it points inward. Logically, then, if those points don't exist on $\partial B^n$ (such as if $\vec{V}$ points inward everywhere), then there must be some point in $B^n$ at which $\vec{V}(\vec{r}) = 0$, or $\vec{V}$ has a singularity in $B^n$. Intuitively I would think this should continue to hold for any region topologically equivalent to a ball, since a homotopy between $B^n$ and $\Omega$ wouldn't change whether a given zero or singularity of $V$ is inside or outside the region or on the boundary. (Is this right so far?) But what about spaces with holes? Does anything change about the argument when $\Omega$ is not homotopic to a ball?
For the curious: I was inspired to think about this by considering whether any continuous mass distribution necessarily has a point at which the gravitational forces from all different parts of the distribution cancel out. That question is easily answered in the affirmative, because the gravitational field is a gradient of a scalar function which must have some local minimum, but then I started wondering if the condition that the vector field is a gradient was really necessary.
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+1 for the physics inspiration/application – Sammy Black May 27 '13 at 2:09
I suspect that the Poincaré-Hopf index theorem is relevant. en.wikipedia.org/wiki/Poincar%C3%A9%E2%80%93Hopf_theorem – Sammy Black May 27 '13 at 2:15
Your instincts are right about a region equivalent to a ball. But the topology of the region definitely matters. Imagine a closed annulus (say $\{x\in \mathbb R^2: 1\le |x|\le 2\}$), with the flow spiralling in from the outside and out from the inside and a limit cycle at \$|x|=3/2 cycling around. In general, see Milnor's Topology from the Differentiable Viewpoint or http://arxiv.org/pdf/0903.0697.pdf for the Poincaré-Hopf Theorem, even on manifolds with boundary. They typically specify that the vector field be normal and outward-pointing on the boundary (so you can glue two copies of the manifold with boundary, together with the vector field, smoothly along the boundary). Inward-pointing is just as good, and your case can be smoothly deformed to that. | {"extraction_info": {"found_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": 0.9333638548851013, "perplexity": 136.41875694779336}, "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-2014-23/segments/1406510273663.2/warc/CC-MAIN-20140728011753-00222-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/how-fast-can-you-switch-between-superconducting-and-normal-modes.656408/ | # How fast can you 'switch' between superconducting and normal modes?
1. Dec 3, 2012
### VortexLattice
The title, basically. If we're at a temperature below the critical temperature (let's just say for a Type 1 superconductor) and an applied magnetic field less than the critical magnetic field, it will be in the superconducting state.
But if we increase the field beyond the critical point, it will go into the normal state. So if we set the temperature well below $T_c$ and made the applied field right below $H_c$, it seems like we could oscillate $H$ to make it go in and out of the superconducting state. Is this the case, first of all?
Second, if that's not somehow impossible, I imagine there must be some sort of upper limit to the frequency you could do this at. You can get pretty damn fast magnetic field oscillations. Will the superconductor switches states back and forth that fast?
2. Dec 3, 2012
### f95toli
Look up some papers (and there are many) on transition edge detectors.
These are often used for radio astronomy, and are based upon the principle you describe (but with temperature, not B-field).
3. Dec 3, 2012
### christopher.s
This paper1 describes an ideal integrating bolometer using a superconducting strip of aluminum as a heat switch. They apply a magnetic field by the application of current through niobium leads which effectively switches the aluminum leads between their superconducting and non-superconducting state. I don't know how fast the limit is, but they state their sampling rate is 2khz for the detector, so it is at least that fast! That is an awesome question, I imagine it is limited by the inductance of the coil or something. I don't understand what is happening well enough to know.
1 - http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20040074297_2004071214.pdf
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https://zhusuan.readthedocs.io/en/latest/api/zhusuan.distributions.html | # zhusuan.distributions¶
## Base class¶
class Distribution(dtype, param_dtype, is_continuous, is_reparameterized, use_path_derivative=False, group_ndims=0, **kwargs)
Bases: object
The Distribution class is the base class for various probabilistic distributions which support batch inputs, generating batches of samples and evaluate probabilities at batches of given values.
The typical input shape for a Distribution is like batch_shape + input_shape. where input_shape represents the shape of non-batch input parameter, batch_shape represents how many independent inputs are fed into the distribution.
Samples generated are of shape ([n_samples]+ )batch_shape + value_shape. The first additional axis is omitted only when passed n_samples is None (by default), in which case one sample is generated. value_shape is the non-batch value shape of the distribution. For a univariate distribution, its value_shape is [].
There are cases where a batch of random variables are grouped into a single event so that their probabilities should be computed together. This is achieved by setting group_ndims argument, which defaults to 0. The last group_ndims number of axes in batch_shape are grouped into a single event. For example, Normal(..., group_ndims=1) will set the last axis of its batch_shape to a single event, i.e., a multivariate Normal with identity covariance matrix.
When evaluating probabilities at given values, the given Tensor should be broadcastable to shape (... + )batch_shape + value_shape. The returned Tensor has shape (... + )batch_shape[:-group_ndims].
For more details and examples, please refer to Basic Concepts in ZhuSuan.
For both, the parameter dtype represents type of samples. For discrete, can be set by user. For continuous, automatically determined from parameter types.
The value type of prob and log_prob will be param_dtype which is deduced from the parameter(s) when initializating. And dtype must be among int16, int32, int64, float16, float32 and float64.
When two or more parameters are tensors and they have different type, TypeError will be raised.
Parameters: dtype – The value type of samples from the distribution. param_dtype – The parameter(s) type of the distribution. is_continuous – Whether the distribution is continuous. is_reparameterized – A bool. Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013). use_path_derivative – A bool. Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference” group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See above for more detailed explanation.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
## Univariate distributions¶
class Normal(mean=0.0, _sentinel=None, std=None, logstd=None, group_ndims=0, is_reparameterized=True, use_path_derivative=False, check_numerics=False, **kwargs)
The class of univariate Normal distribution. See Distribution for details.
Warning
The order of arguments logstd/std has changed to std/logstd since 0.3.1. Please use named arguments: Normal(mean, std=..., ...) or Normal(mean, logstd=..., ...).
Parameters: mean – A float Tensor. The mean of the Normal distribution. Should be broadcastable to match std or logstd. _sentinel – Used to prevent positional parameters. Internal, do not use. std – A float Tensor. The standard deviation of the Normal distribution. Should be positive and broadcastable to match mean. logstd – A float Tensor. The log standard deviation of the Normal distribution. Should be broadcastable to match mean. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation. is_reparameterized – A Bool. If True, gradients on samples from this distribution are allowed to propagate into inputs, using the reparametrization trick from (Kingma, 2013). use_path_derivative – A bool. Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference” check_numerics – Bool. Whether to check numeric issues.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
logstd
The log standard deviation of the Normal distribution.
mean
The mean of the Normal distribution.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
std
The standard deviation of the Normal distribution.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
class FoldNormal(mean=0.0, _sentinel=None, std=None, logstd=None, group_ndims=0, is_reparameterized=True, use_path_derivative=False, check_numerics=False, **kwargs)
The class of univariate FoldNormal distribution. See Distribution for details.
Warning
The order of arguments logstd/std has changed to std/logstd since 0.3.1. Please use named arguments: FoldNormal(mean, std=..., ...) or FoldNormal(mean, logstd=..., ...).
Parameters: mean – A float Tensor. The mean of the FoldNormal distribution. Should be broadcastable to match std or logstd. _sentinel – Used to prevent positional parameters. Internal, do not use. std – A float Tensor. The standard deviation of the FoldNormal distribution. Should be positive and broadcastable to match mean. logstd – A float Tensor. The log standard deviation of the FoldNormal distribution. Should be broadcastable to match mean. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation. is_reparameterized – A Bool. If True, gradients on samples from this distribution are allowed to propagate into inputs, using the reparametrization trick from (Kingma, 2013). use_path_derivative – A bool. Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference” check_numerics – Bool. Whether to check numeric issues.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
logstd
The log standard deviation of the FoldNormal distribution.
mean
The mean of the FoldNormal distribution.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
std
The standard deviation of the FoldNormal distribution.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
class Bernoulli(logits, dtype=tf.int32, group_ndims=0, **kwargs)
The class of univariate Bernoulli distribution. See Distribution for details.
Parameters: logits – A float Tensor. The log-odds of probabilities of being 1. $\mathrm{logits} = \log \frac{p}{1 - p}$ dtype – The value type of samples from the distribution. Can be int (tf.int16, tf.int32, tf.int64) or float (tf.float16, tf.float32, tf.float64). Default is int32. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
logits
The log-odds of probabilities of being 1.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
class Categorical(logits, dtype=tf.int32, group_ndims=0, **kwargs)
The class of univariate Categorical distribution. See Distribution for details.
Parameters: logits – A N-D (N >= 1) float32 or float64 Tensor of shape (…, n_categories). Each slice [i, j,…, k, :] represents the un-normalized log probabilities for all categories. $\mathrm{logits} \propto \log p$ dtype – The value type of samples from the distribution. Can be float32, float64, int32, or int64. Default is int32. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation.
A single sample is a (N-1)-D Tensor with tf.int32 values in range [0, n_categories).
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
logits
The un-normalized log probabilities.
n_categories
The number of categories in the distribution.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
Discrete
class Uniform(minval=0.0, maxval=1.0, group_ndims=0, is_reparameterized=True, check_numerics=False, **kwargs)
The class of univariate Uniform distribution. See Distribution for details.
Parameters: minval – A float Tensor. The lower bound on the range of the uniform distribution. Should be broadcastable to match maxval. maxval – A float Tensor. The upper bound on the range of the uniform distribution. Should be element-wise bigger than minval. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation. is_reparameterized – A Bool. If True, gradients on samples from this distribution are allowed to propagate into inputs, using the reparametrization trick from (Kingma, 2013). check_numerics – Bool. Whether to check numeric issues.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
maxval
The upper bound on the range of the uniform distribution.
minval
The lower bound on the range of the uniform distribution.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
class Gamma(alpha, beta, group_ndims=0, check_numerics=False, **kwargs)
The class of univariate Gamma distribution. See Distribution for details.
Parameters: alpha – A float Tensor. The shape parameter of the Gamma distribution. Should be positive and broadcastable to match beta. beta – A float Tensor. The inverse scale parameter of the Gamma distribution. Should be positive and broadcastable to match alpha. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation. check_numerics – Bool. Whether to check numeric issues.
alpha
The shape parameter of the Gamma distribution.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
beta
The inverse scale parameter of the Gamma distribution.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
class Beta(alpha, beta, group_ndims=0, check_numerics=False, **kwargs)
The class of univariate Beta distribution. See Distribution for details.
Parameters: alpha – A float Tensor. One of the two shape parameters of the Beta distribution. Should be positive and broadcastable to match beta. beta – A float Tensor. One of the two shape parameters of the Beta distribution. Should be positive and broadcastable to match alpha. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation. check_numerics – Bool. Whether to check numeric issues.
alpha
One of the two shape parameters of the Beta distribution.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
beta
One of the two shape parameters of the Beta distribution.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
class Poisson(rate, dtype=tf.int32, group_ndims=0, check_numerics=False, **kwargs)
The class of univariate Poisson distribution. See Distribution for details.
Parameters: rate – A float Tensor. The rate parameter of Poisson distribution. Must be positive. dtype – The value type of samples from the distribution. Can be int (tf.int16, tf.int32, tf.int64) or float (tf.float16, tf.float32, tf.float64). Default is int32. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation. check_numerics – Bool. Whether to check numeric issues.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
rate
The rate parameter of Poisson.
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
class Binomial(logits, n_experiments, dtype=tf.int32, group_ndims=0, check_numerics=False, **kwargs)
The class of univariate Binomial distribution. See Distribution for details.
Parameters: logits – A float Tensor. The log-odds of probabilities. $\mathrm{logits} = \log \frac{p}{1 - p}$ n_experiments – A 0-D int32 Tensor. The number of experiments for each sample. dtype – The value type of samples from the distribution. Can be int (tf.int16, tf.int32, tf.int64) or float (tf.float16, tf.float32, tf.float64). Default is int32. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation. check_numerics – Bool. Whether to check numeric issues.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
logits
The log-odds of probabilities.
n_experiments
The number of experiments.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
class InverseGamma(alpha, beta, group_ndims=0, check_numerics=False, **kwargs)
The class of univariate InverseGamma distribution. See Distribution for details.
Parameters: alpha – A float Tensor. The shape parameter of the InverseGamma distribution. Should be positive and broadcastable to match beta. beta – A float Tensor. The scale parameter of the InverseGamma distribution. Should be positive and broadcastable to match alpha. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation. check_numerics – Bool. Whether to check numeric issues.
alpha
The shape parameter of the InverseGamma distribution.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
beta
The scale parameter of the InverseGamma distribution.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
class Laplace(loc, scale, group_ndims=0, is_reparameterized=True, use_path_derivative=False, check_numerics=False, **kwargs)
The class of univariate Laplace distribution. See Distribution for details.
Parameters: loc – A float Tensor. The location parameter of the Laplace distribution. Should be broadcastable to match scale. scale – A float Tensor. The scale parameter of the Laplace distribution. Should be positive and broadcastable to match loc. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation. is_reparameterized – A Bool. If True, gradients on samples from this distribution are allowed to propagate into inputs, using the reparametrization trick from (Kingma, 2013). use_path_derivative – A bool. Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference” check_numerics – Bool. Whether to check numeric issues.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
loc
The location parameter of the Laplace distribution.
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
scale
The scale parameter of the Laplace distribution.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
class BinConcrete(temperature, logits, group_ndims=0, is_reparameterized=True, use_path_derivative=False, check_numerics=False, **kwargs)
The class of univariate BinConcrete distribution from (Maddison, 2016). It is the binary case of Concrete. See Distribution for details.
Parameters: temperature – A 0-D float Tensor. The temperature of the relaxed distribution. The temperature should be positive. logits – A float Tensor. The log-odds of probabilities of being 1. $\mathrm{logits} = \log \frac{p}{1 - p}$ group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation. is_reparameterized – A Bool. If True, gradients on samples from this distribution are allowed to propagate into inputs, using the reparametrization trick from (Kingma, 2013). use_path_derivative – A bool. Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference” check_numerics – Bool. Whether to check numeric issues.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
logits
The log-odds of probabilities.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
temperature
The temperature of BinConcrete.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
BinGumbelSoftmax
## Multivariate distributions¶
class MultivariateNormalCholesky(mean, cov_tril, group_ndims=0, is_reparameterized=True, use_path_derivative=False, check_numerics=False, **kwargs)
The class of multivariate normal distribution, where covariance is parameterized with the lower triangular matrix $$L$$ in Cholesky decomposition $$LL^T = \Sigma$$.
See Distribution for details.
Parameters: mean – An N-D float Tensor of shape […, n_dim]. Each slice [i, j, …, k, :] represents the mean of a single multivariate normal distribution. cov_tril – An (N+1)-D float Tensor of shape […, n_dim, n_dim]. Each slice [i, …, k, :, :] represents the lower triangular matrix in the Cholesky decomposition of the covariance of a single distribution. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation. is_reparameterized – A Bool. If True, gradients on samples from this distribution are allowed to propagate into inputs, using the reparametrization trick from (Kingma, 2013). use_path_derivative – A bool. Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference” check_numerics – Bool. Whether to check numeric issues.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
cov_tril
The lower triangular matrix in the cholosky decomposition of the covariance.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
mean
The mean of the normal distribution.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
class Multinomial(logits, n_experiments, normalize_logits=True, dtype=tf.int32, group_ndims=0, **kwargs)
The class of Multinomial distribution. See Distribution for details.
Parameters: logits – A N-D (N >= 1) float Tensor of shape […, n_categories]. Each slice [i, j, …, k, :] represents the log probabilities for all categories. By default (when normalize_logits=True), the probabilities could be un-normalized. $\mathrm{logits} \propto \log p$ n_experiments – A 0-D int32 Tensor or None. When it is a 0-D int32 integer, it represents the number of experiments for each sample, which should be invariant among samples. In this situation _sample function is supported. When it is None, _sample function is not supported, and when calculating probabilities the number of experiments will be inferred from given, so it could vary among samples. normalize_logits – A bool indicating whether logits should be normalized when computing probability. If you believe logits is already normalized, set it to False to speed up. Default is True. dtype – The value type of samples from the distribution. Can be int (tf.int16, tf.int32, tf.int64) or float (tf.float16, tf.float32, tf.float64). Default is int32. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation.
A single sample is a N-D Tensor with the same shape as logits. Each slice [i, j, …, k, :] is a vector of counts for all categories.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
logits
The un-normalized log probabilities.
n_categories
The number of categories in the distribution.
n_experiments
The number of experiments for each sample.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
class UnnormalizedMultinomial(logits, normalize_logits=True, dtype=tf.int32, group_ndims=0, **kwargs)
The class of UnnormalizedMultinomial distribution. UnnormalizedMultinomial distribution calculates probabilities differently from Multinomial: It considers the bag-of-words given as a statistics of an ordered result sequence, and calculates the probability of the (imagined) ordered sequence. Hence it does not multiply the term
$\binom{n}{k_1, k_2, \dots} = \frac{n!}{\prod_{i} k_i!}$
See Distribution for details.
Parameters: logits – A N-D (N >= 1) float Tensor of shape […, n_categories]. Each slice [i, j, …, k, :] represents the log probabilities for all categories. By default (when normalize_logits=True), the probabilities could be un-normalized. $\mathrm{logits} \propto \log p$ normalize_logits – A bool indicating whether logits should be normalized when computing probability. If you believe logits is already normalized, set it to False to speed up. Default is True. dtype – The value type of samples from the distribution. Can be int (tf.int16, tf.int32, tf.int64) or float (tf.float16, tf.float32, tf.float64). Default is int32. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation.
A single sample is a N-D Tensor with the same shape as logits. Each slice [i, j, …, k, :] is a vector of counts for all categories.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
logits
The un-normalized log probabilities.
n_categories
The number of categories in the distribution.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
BagofCategoricals
class OnehotCategorical(logits, dtype=tf.int32, group_ndims=0, **kwargs)
The class of one-hot Categorical distribution. See Distribution for details.
Parameters: logits – A N-D (N >= 1) float Tensor of shape (…, n_categories). Each slice [i, j, …, k, :] represents the un-normalized log probabilities for all categories. $\mathrm{logits} \propto \log p$ dtype – The value type of samples from the distribution. Can be int (tf.int16, tf.int32, tf.int64) or float (tf.float16, tf.float32, tf.float64). Default is int32. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation.
A single sample is a N-D Tensor with the same shape as logits. Each slice [i, j, …, k, :] is a one-hot vector of the selected category.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
logits
The un-normalized log probabilities.
n_categories
The number of categories in the distribution.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
OnehotDiscrete
class Dirichlet(alpha, group_ndims=0, check_numerics=False, **kwargs)
The class of Dirichlet distribution. See Distribution for details.
Parameters: alpha – A N-D (N >= 1) float Tensor of shape (…, n_categories). Each slice [i, j, …, k, :] represents the concentration parameter of a Dirichlet distribution. Should be positive. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation.
A single sample is a N-D Tensor with the same shape as alpha. Each slice [i, j, …, k, :] of the sample is a vector of probabilities of a Categorical distribution [x_1, x_2, … ], which lies on the simplex
$\sum_{i} x_i = 1, 0 < x_i < 1$
alpha
The concentration parameter of the Dirichlet distribution.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
n_categories
The number of categories in the distribution.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
class ExpConcrete(temperature, logits, group_ndims=0, is_reparameterized=True, use_path_derivative=False, check_numerics=False, **kwargs)
The class of ExpConcrete distribution from (Maddison, 2016), transformed from Concrete by taking logarithm. See Distribution for details.
Parameters: temperature – A 0-D float Tensor. The temperature of the relaxed distribution. The temperature should be positive. logits – A N-D (N >= 1) float Tensor of shape (…, n_categories). Each slice [i, j, …, k, :] represents the un-normalized log probabilities for all categories. $\mathrm{logits} \propto \log p$ group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation. is_reparameterized – A Bool. If True, gradients on samples from this distribution are allowed to propagate into inputs, using the reparametrization trick from (Kingma, 2013). use_path_derivative – A bool. Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference” check_numerics – Bool. Whether to check numeric issues.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
logits
The un-normalized log probabilities.
n_categories
The number of categories in the distribution.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
temperature
The temperature of ExpConcrete.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
ExpGumbelSoftmax
class Concrete(temperature, logits, group_ndims=0, is_reparameterized=True, use_path_derivative=False, check_numerics=False, **kwargs)
The class of Concrete (or Gumbel-Softmax) distribution from (Maddison, 2016; Jang, 2016), served as the continuous relaxation of the OnehotCategorical. See Distribution for details.
Parameters: temperature – A 0-D float Tensor. The temperature of the relaxed distribution. The temperature should be positive. logits – A N-D (N >= 1) float Tensor of shape (…, n_categories). Each slice [i, j, …, k, :] represents the un-normalized log probabilities for all categories. $\mathrm{logits} \propto \log p$ group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation. is_reparameterized – A Bool. If True, gradients on samples from this distribution are allowed to propagate into inputs, using the reparametrization trick from (Kingma, 2013). use_path_derivative – A bool. Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference” check_numerics – Bool. Whether to check numeric issues.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
logits
The un-normalized log probabilities.
n_categories
The number of categories in the distribution.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
temperature
The temperature of Concrete.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
GumbelSoftmax
class MatrixVariateNormalCholesky(mean, u_tril, v_tril, group_ndims=0, is_reparameterized=True, use_path_derivative=False, check_numerics=False, **kwargs)
The class of matrix variate normal distribution, where covariances $$U$$ and $$V$$ are parameterized with the lower triangular matrix in Cholesky decomposition,
$L_u \text{s.t.} L_u L_u^T = U,\; L_v \text{s.t.} L_v L_v^T = V$
See Distribution for details.
Parameters: mean – An N-D float Tensor of shape […, n_row, n_col]. Each slice [i, j, …, k, :, :] represents the mean of a single matrix variate normal distribution. u_tril – An N-D float Tensor of shape […, n_row, n_row]. Each slice [i, j, …, k, :, :] represents the lower triangular matrix in the Cholesky decomposition of the among-row covariance of a single matrix variate normal distribution. v_tril – An N-D float Tensor of shape […, n_col, n_col]. Each slice [i, j, …, k, :, :] represents the lower triangular matrix in the Cholesky decomposition of the among-column covariance of a single matrix variate normal distribution. group_ndims – A 0-D int32 Tensor representing the number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. Default is 0, which means a single value is an event. See Distribution for more detailed explanation. is_reparameterized – A Bool. If True, gradients on samples from this distribution are allowed to propagate into inputs, using the reparametrization trick from (Kingma, 2013). use_path_derivative – A bool. Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference” check_numerics – Bool. Whether to check numeric issues.
batch_shape
The shape showing how many independent inputs (which we call batches) are fed into the distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape. We borrow this concept from tf.contrib.distributions.
dtype
The sample type of the distribution.
get_batch_shape()
Static batch_shape.
Returns: A TensorShape instance.
get_value_shape()
Static value_shape.
Returns: A TensorShape instance.
group_ndims
The number of dimensions in batch_shape (counted from the end) that are grouped into a single event, so that their probabilities are calculated together. See Distribution for more detailed explanation.
is_continuous
Whether the distribution is continuous.
is_reparameterized
Whether the gradients of samples can and are allowed to propagate back into inputs, using the reparametrization trick from (Kingma, 2013).
log_prob(given)
Compute log probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate log probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
mean
The mean of the matrix variate normal distribution.
param_dtype
The parameter(s) type of the distribution.
path_param(param)
Automatically transforms a parameter based on use_path_derivative
prob(given)
Compute probability density (mass) function at given value.
Parameters: given – A Tensor. The value at which to evaluate probability density (mass) function. Must be able to broadcast to have a shape of (... + )batch_shape + value_shape. A Tensor of shape (... + )batch_shape[:-group_ndims].
sample(n_samples=None)
Return samples from the distribution. When n_samples is None (by default), one sample of shape batch_shape + value_shape is generated. For a scalar n_samples, the returned Tensor has a new sample dimension with size n_samples inserted at axis=0, i.e., the shape of samples is [n_samples] + batch_shape + value_shape.
Parameters: n_samples – A 0-D int32 Tensor or None. How many independent samples to draw from the distribution. A Tensor of samples.
u_tril
The lower triangular matrix in the Cholesky decomposition of the among-row covariance.
use_path_derivative
Whether when taking the gradients of the log-probability to propagate them through the parameters of the distribution (False meaning you do propagate them). This is based on the paper “Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inference”
v_tril
The lower triangular matrix in the Cholesky decomposition of the among-column covariance.
value_shape
The non-batch value shape of a distribution. For batch inputs, the shape of a generated sample is batch_shape + value_shape.
## Distribution utils¶
log_combination(n, ks)
Compute the log combination function.
$\log \binom{n}{k_1, k_2, \dots} = \log n! - \sum_{i}\log k_i!$
Parameters: n – A N-D float Tensor. Can broadcast to match tf.shape(ks)[:-1]. ks – A (N + 1)-D float Tensor. Each slice [i, j, …, k, :] is a vector of [k_1, k_2, …]. A N-D Tensor of type same as n.
explicit_broadcast(x, y, x_name, y_name)
Explicit broadcast two Tensors to have the same shape.
maybe_explicit_broadcast(x, y, x_name, y_name)
is_same_dynamic_shape(x, y) | {"extraction_info": {"found_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": 0.7360451221466064, "perplexity": 2971.663466814557}, "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-20190819011034-20190819033034-00434.warc.gz"} |
https://physics.stackexchange.com/questions/249899/why-positron-emission-is-unlikely-to-occur-for-nuclei-with-an-excess-of-neutrons | # Why positron emission is unlikely to occur for nuclei with an excess of neutrons?
Is it because a neutron decays into a proton and electron rather than a positron. Which type of nucleus emits positron and which emits electrons . Is it something to do with beta plus and beta minus decay .
• Possible duplicate? physics.stackexchange.com/questions/249036/… Apr 16, 2016 at 6:59
• @Farcher: "Possible duplicate? Why beta+- decay occurs?" -- Not really: at least the OP question title implies an inquiry to justify, roughly, "why there is a line/valley of stability in the isotope chart (rather than, say, a line/ridge of instability)". However, admittedly, this request is not (yet) spelled out in the OP question text. Apr 16, 2016 at 7:57
• Follow the logic. "Positron emission can only occur when a ___ is converted into a ___ inside the nucleus, but in a neutron rich nucleus adding a ___ takes more energy than you get from removing a ___ so the event results in a net energy gain to the nucleus." Apr 16, 2016 at 15:28
• @dmckee: "Follow the logic. [...]" -- Logic allows at least to fill in the blanks you left: "Positron emission can only occur when a _$p$_ is converted into a _$n$_ inside the nucleus" -- (That's by plain charge conservation; a gimmee.) "but in a neutron rich nucleus adding a _$n$_ takes more energy than you get from removing a _$p$_ so [...]" -- So the presumed logic holds. But why does converting $p$ to $n$ in an already $n$-rich nucleous take more energy than the reverse?? (Why "valley of stability" rather than "ridge of instability"??) And: Does the OP ask this question? Apr 17, 2016 at 6:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.865040123462677, "perplexity": 2201.3671943829654}, "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/1652662604794.68/warc/CC-MAIN-20220526100301-20220526130301-00402.warc.gz"} |
https://textbook.prob140.org/notebooks-md/18_03_The_Gamma_Family.html | The Gamma Family¶
You have seen in exercises that a non-negative random variable $X$ has the gamma $(r, \lambda)$ distribution for two positive parameters $r$ and $\lambda$ if the density of $X$ is given by
$$f_X(x) ~ = ~ \frac{\lambda^r}{\Gamma(r)} x^{r-1}e^{-\lambda x}, ~~~~~ x \ge 0$$
Here $$\Gamma(r) ~ = ~ \int_0^\infty x^{r-1}e^{-x} dx$$ is the Gamma function applied to $r$, and is part of the constant that makes the density integrate to 1.
As you have shown, the key fact about the Gamma function is the recursion
$$\Gamma(r+1) ~ = ~ r\Gamma (r), ~~~~ r > 0$$
which implies in particular that $$\Gamma(r) ~ = ~ (r-1)! ~~~~ \text{if } r \text{ is a positive integer}$$
You have put all this together to show that
$$E(X) ~ = ~ \frac{r}{\lambda} ~~~~~~~~~~~~~~ SD(X) ~ = ~ \frac{\sqrt{r}}{\lambda}$$
You have observed that the square of a standard normal variable has the gamma $(1/2, 1/2)$ distribution, and that the exponential $(\lambda)$ distribution is the same as the gamma $(1, \lambda)$ distribution.
The Rate $\lambda$¶
For fixed $r$, the larger $\lambda$ is, the smaller $X$ is expected to be. Also like the exponential, the parameter $\lambda$ essentially identifies the units of measurement – for a positive constant $c$, the random variable $Y = cX$ has the gamma $(r, \lambda/c)$ distribution. You can see this by applying the linear change of variable formula for densities. For positive $y$, the density of $Y$ is
$$f_Y(y) ~ = ~ f_X(\frac{y}{c}) \cdot \frac{1}{c} ~ = ~ \frac{(\lambda/c)^r}{\Gamma(r)} y^{r-1}e^{-(\lambda/c) y}$$
SciPy calls $1/\lambda$ the "scale" parameter of the gamma distribution. Because the parameter just determines the scale on the horizontal axis of the graph of the density, it is often taken to be 1. That's what we will do to study the other parameter $r$.
The Shape Parameter $r$¶
Here are the graphs of the gamma $(r, 1)$ densities for $r = 1$, $1.5$, and 2.
When $r = 1$ the density is exponential. As $r$ gets larger the density moves to the right and flattens out, consistent with the increasing mean $r$ and SD $\sqrt{r}$.
When $r = 10$, the gamma density looks almost normal. To see why, we will examine sums of independent gamma variables.
Sums of Independent Gamma Variables with the Same Rate¶
If $X$ has the gamma $(r, \lambda)$ distribution and $Y$ independent of $X$ has the gamma $(s, \lambda)$ distribution, then $X+Y$ has the gamma $(r+s, \lambda)$ distribution.
Note that for the result to apply, the rate parameter has to be the same for $X$ and $Y$. The rate parameter turns out to be the same for $X+Y$ as well, and the shape parameters add up.
We will prove this result in the next chapter along with the corresponding result for sums of independent normal variables. For now, let's test out the result by simulation just as we did with the sums of normals. The first three lines in the cell below set the values of $\lambda$, $r$, and $s$. The rest simulates 10000 values of $X+Y$ and plots the gamma $(r+s, \lambda)$ density over the simulated values.
# Change these three parameters as you wish.
lam = 1
r = 3
s = 7
# Leave the rest of the code alone.
x = stats.gamma.rvs(r, scale=1/lam, size=10000)
y = stats.gamma.rvs(s, scale=1/lam, size=10000)
w = x+y
Table().with_column('X+Y', w).hist(bins=20)
t = np.arange(min(w), max(w)+0.1, (max(w) - min(w))/100)
dens = stats.gamma.pdf(t, r+s, scale=1/lam)
plt.plot(t, dens, color='red', lw=2, label='gamma $(r+s, \lambda)$')
plt.legend()
plt.title('$X+Y$ where $X$: gamma$(r, \lambda)$ and $Y$: gamma$(s, \lambda)$');
You can now see why the gamma $(r, \lambda)$ distribution is approximately normal for large $r$. By the result above, for integer $r$ the sum of $r$ i.i.d. exponential $(\lambda)$ random variables has the gamma $(r, \lambda)$ distribution. For fixed $\lambda$ and increasing $r$, the Central Limit Theorem says the distribution of the sum tends to the normal.
The gamma family is used for modeling right-skewed distributions of non-negative variables. In data science, the gamma family also appears in the context of squaring "centered" normal random variables, that is, normal random variables with mean 0. The next section sets out the details. | {"extraction_info": {"found_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": 0.9903777837753296, "perplexity": 276.0681830827869}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989916.34/warc/CC-MAIN-20210513111525-20210513141525-00273.warc.gz"} |
http://math.stackexchange.com/questions/32981/solve-two-equations/33142 | # Solve two equations
I've tried unsuccessfully to solve these two problems. I'd grateful for any help here.
1. What is the biggest real number $z$ that obeys these two conditions: $$x + y + z=5 \quad\text{and}\quad xy +xz + yz=3\quad\text{?}$$
2. Find the lower positive number for $$xy + 2xz + 3yz$$ if $xyz =48$.
-
What level are we talking about? Calculus, algebra? Is there a specific method you are expected to use? (E.g., the first problem can be solved in several ways, Lagrange multipliers among them). – Arturo Magidin Apr 14 '11 at 13:44
@tom: It seems you have received useful answers to at least some of your questions. Please accept the ones you like by clicking the gray checkmark to the left. – Ross Millikan Apr 14 '11 at 13:46
If they are homework, they seem standard problems of Lagrange multipliers. – N. S. Apr 14 '11 at 13:52
I'm just a high school student, so I think the simplest method. I suppose that it could be solved by arithmetic but I'm not completely sure of that. – tom Apr 14 '11 at 15:07
@tom Please add and state what $x$, $y$ and $z$ are. Complex numbers? Real numbers? Positive real numbers? Please state!! – user38268 Apr 14 '11 at 23:58
For 1: Observe that $(x+y+z)^2=x^2+y^2+z^2+2(xy+xz+yz)$. From here you can get $x^2+y^2+z^2=19$.
-
So do I have to solve that system to find out the lower number? – tom Apr 14 '11 at 15:10
@tom: Now you just need the largest allowable $z$ that satisfies the last. What should $x$ and $y$ be for this? – Ross Millikan Apr 14 '11 at 15:28
@Ross Millikan hmmm, I don't know because the numbers are real. I know how to solve that kind of system though. But it's very boring. – tom Apr 15 '11 at 1:18
@tom: The greatest $z$ is $\sqrt{19}$ when $x=y=0$ – Ross Millikan Apr 15 '11 at 3:29
@Ross Millikan: I don't think so because it is true for just one of the equations. We should remember that the sum of values must be five, then what you think it is not the answer. IMHO. – tom Apr 15 '11 at 12:35
For 1, it is "obvious" (and can be proven using calculus) that to make $z$ big, you want $x, y$ small and from symmetry they should be equal. Then your equations become $2x+z=5, x^2+2xz=3$ which you can combine, eliminating $z$ to $x=\frac{10\pm \sqrt{100-36}}{6}=\frac{1}{3},3$, choose the smaller root, and $x=y=\frac{1}{3}, z=\frac{13}{3}$
The more rigorous approach would be to write $x=\frac{3-yz}{y+z}$ and substitute in to get $(y+z)^2+3-yz=5(y+z), z=\frac{5-y\pm \sqrt{13+10y-3y^2}}{2}$, take the derivative with respect to $y$, set to $0$...
-
Very interesting, thank you so much. It really taught me a great idea. – tom Apr 15 '11 at 20:28 | {"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": 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": 0.8154461979866028, "perplexity": 319.3692101530528}, "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-2015-48/segments/1448398450659.10/warc/CC-MAIN-20151124205410-00087-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition/chapter-4-inverse-exponential-and-logarithmic-functions-4-1-inverse-functions-4-1-exercises-page-406/4 | ## Precalculus (6th Edition)
Fill the blanks with ... $x$ ... $(g\circ f)(x)$ ..
Let $f$ be a one-to-one function. Then $g$ is the inverse function of $f$ if $(f\circ g)(x)=x$ for every $x$ in the domain of $g$, and $(g\circ f)(x)=x$ for every $x$ in the domain of $f$. --------------- Fill the blanks with ... $x$ ... $(g\circ f)(x)$ ... | {"extraction_info": {"found_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": 0.9128574728965759, "perplexity": 122.21737643857038}, "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-2018-17/segments/1524125945143.71/warc/CC-MAIN-20180421110245-20180421130245-00149.warc.gz"} |
https://wiki.openvz.org/index.php?title=Ploop/diskinodes&diff=15647&oldid=15633 | # Difference between revisions of "Ploop/diskinodes"
Everything you wanted to know about DISKINODES for ploop but were afraid to ask.
## Limitations
With simfs layout, vzquota is used to set limits for DISKSPACE and DISKINODES, so these limits can be changed any time.
Unlike simfs, ploop contains a real file system, so amount of disk space and disk inodes are properties of the file system, determined while creating a filesystem. It is possible to resize an ext4 file system in terms of disk space, but there's no way to change the number of available inodes.
Note: There is no way to change DISKINODES for existing ploop. This is a limitation of ext4.
In other words, vzctl set --diskinodes is ignored for ploop layout -- it can only be specified on create.
## Default value
By default, ext4 allocates 1 (one) inode per each 16 KB of data; this is practically the same as to assume that the average file size will be 16KB.
For example, when creating a ploop with 40GB of disk space, 2621440 inodes will be available:
${\displaystyle {\frac {40*1024*1024}{16}}=2621440}$
## Increasing
If the above default is too low for your usage (for example, a container has or will have too many small files), you can specify a larger value for DISKINODES during container creation or conversion only. The feature works since vzctl 4.7.
Note: You can only specify --diskinodes for vzctl create or vzctl convert.
The way it works is the following. First, a file system big enough to accommodate the requested number of DISKINODES is created, and then ploop resize is performed to downsize the file system to meet the requested amount of DISKSPACE.
Example:
vzctl create 123 --diskspace 40G --diskinodes 5242880
Here, a filesystem big enough to have 5242880 of diskinodes will be created (it's 5242880 * 16K = 80G), then downsized to 40G.
## Issues
### Too high DISKINODES value
Sometimes, when the amount of DISKINODES specified is too high, a very large filesystem is created, and it can not be downsized to a specified amount. In this case, the following error will be shown when converting a container from simfs to ploop:
vzctl set CTID --diskspace 40G --diskinodes 1000000000 --save
...
vzctl convert CTID
...
Error in ploop_resize_image (ploop.c:2477): Unable to change image size to 83877888 sectors, minimal size is 502423144
Unmounting file system at /vz/private/101.ploop/root.hdd/root.hdd.mnt
Unmounting device /dev/ploop37776
Failed to resize image: Error in ploop_resize_image (ploop.c:2477): Unable to change image size to 83877888 sectors, minimal size is 502423144 [38]
In this case, 1G inodes requirement leads to creation of 16TB filesystem (remember, 1 inode per 16K). Unfortunately, such huge FS can't be downsized to as low as 40G, the minimum seems to be around 240G (values printed in the error message are in sectors which are 512 bytes each).
Solution 1: please be reasonable when requesting diskinodes for ploop.
Solution 2: please set DISKINODES to 0 before conversion:
vzctl stop CTID
vzctl set CTID --diskspace xxxG--diskinodes 0 --save
vzctl convert CTID
This will lead to creating a filesystem with default number of inodes.
### Too low DISKINODES value
If DISKINODES specified during create or convert is lower than the default (1 inode per 16K of disk space), it is silently ignored. In other words, there is no way to limit DISKINODES to lower than DISKSPACE / 16384. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "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": 0.4320738613605499, "perplexity": 5491.317755809993}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304528.78/warc/CC-MAIN-20220124094120-20220124124120-00687.warc.gz"} |
http://docs.lbpclabs.com/en/latest/autoscript/tutorial.html | # Tutorial¶
This tutorial will teach you some very basic Python and AutoScript functions so you can get started writing scripts right away. For a full Python tutorial visit http://docs.python.org/3/tutorial/.
## AutoScript Scripting Environment¶
First, take a look at the user interface for writing scripts. In the center there is a text area with line numbering and syntax highliting. On the top there’s a main menu containing options to save/open scripts and execute them as well as to open the documentation. There are shortcuts for these actions on the bottom bar. Note that on this bar there’s also a toggle button to enable the “land on error” behavior, which will automatically make the AR.Drone land when an error in the script is occurrs. Also, apart from executing the scripts you can also simulate them. When simulating a script no commands will be sent to the drone. Instead, what would happen gets printed in the script output and the program needs the user to enter simulated sensor values. This feature is useful for testing your scripts and making sure everything works as expected.
Note
When editing a script you can always press F1 to open the documentation. If there’s an AutoScript command in the current line, the description of that command will be opened automatically. (Try it!)
## Take Off and Land¶
Let’s start with something very simple. Send a take off command to the drone, keep it in the air for some seconds, and land. To make the drone take off, the function
control.takeOff()
has to be called. It’s that simple. This function, however, does only send the take off command without waiting for the drone to actually take off, so we’ll have to wait a few seconds. Python has a function called sleep() which does exactly this. It can be found in the time module. To use functions in the time module, you have to import it. This is done at the beginning of the Python script, using the import command followed by the module you want to import, in this case
import time
Then you can use the sleep function with the time you want to sleep as parameter, in parentheses.
time.sleep(6)
The above function waits 6 seconds before letting the script contine. This will be enough time for the AR.Drone to take off. The rest of the time it will simply stay in the air. Now it’s time to land the drone. The function for doing that is
control.land()
Finally, we’ll show a message saying that the script worked. Python has a command that shows a message called print. Let’s print our message
print("I just made the drone automatically take off and land!")
The finished script would look like this:
import time
control.takeOff()
time.sleep(6)
control.land()
print("I just made the drone automatically take off and land!")
Now it’s time to run that script. Click run (The 4th button on the bottom bar, counting from the left). If there’s a typo and the drone doesn’t land because an error ocurred, you can just land the drone manually (switch to the main window and press T), check your code for typos and try to run it again.
If everything worked, congratulations! You ran your first AR.Drone-controlling-Python-script!
## More coming soon¶
You can take a look at the official Python tutorial and all the available functions to experiment a bit! | {"extraction_info": {"found_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": 0.31479522585868835, "perplexity": 1353.0789900345542}, "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/1558232254253.31/warc/CC-MAIN-20190519061520-20190519083520-00163.warc.gz"} |
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# m05 q15
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28 Jan 2009, 06:26
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If $$x$$ is a positive integer, is $$\sqrt{x} \lt 2.5x - 5$$ ?
1. $$x \lt 3$$
2. $$x$$ is a prime number
Source: GMAT Club Tests - hardest GMAT questions
SOLUTION: m05-q15-75172-20.html#p1091067
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24 Aug 2009, 22:34
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ddtiku wrote:
I think serene is right.. root can be either +ve or -ve
Thats not correct. In fact thats misleading statement.
If root is already given without -ve sign, then it is already +ve. For ex:
If sqrt (x) = sqrt2, then it is +ve.
If square is given and you are taking sqrt, then only one sqrt is +ve and another is -ve and vice versa. For ex:
If x^2 = 2, then x = either sqrt2 or (-sqrt2).
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24 Aug 2009, 21:06
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sher676 wrote:
But the equation does not hold for x=1,2
x=1
sq1< 2.5(1) -5
1 <-2.5, which is not correct
x=2
sq2<2.5(2) -5
sq2<0, again the equation does not hold
Am i missing somethin?
You calculation is correct. and it means 1) can prove that "No, √x < 2.5x -5 is not correct", therefore choose A
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27 May 2011, 11:07
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thuylinh wrote:
I go for E.
1.x<3 -> x= 1 or 2. But both the two values don't match the first inequation -> wrong.
2.Assume a and b is the root of an inequation. The inequation has two ranges of number satisfied: x<a or x>b, there for there are plenty of number can satisfied.
Therefore, both are insufficient
Please see subhashghosh's solution above. that is correct.
"A" is indeed correct. Data Sufficiency is all about proving whether a given statement is sufficient to answer the question asked.
This is a classic example of Yes/No type data sufficiency:
Question asked: Is $$\sqrt{x} < 2.5x -5$$
In words: Is root of x less than 2.5 times x minus 5?
St1 is sufficient to answer the question asked with a definitive No.
No, root of x IS NOT less than 2.5 times x minus 5.
Sufficient.
St2: answer may be Yes or No. Not definite.
Not Sufficient.
Ans: "A"
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18 Feb 2009, 14:33
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Isnt root of x either negative or positive?
for x=2, the -(root)of 2 < 0 which is true.
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26 May 2010, 05:09
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Quote:
It's not.
Square of any value is positive. A value is square of its root. So, the value you find from its square root is always positive.
So, x is 4 if sqrt(x) is 2 or -2. It can never be -4.
At the same time, if x = 4, x = 2^2 or x = -2^2. So, square root of x is 2 or -2.
This says, square root of some value can be either positive or negative.
Your logic is perfect, but this is a matter of convention.
In GMAT math, the roots of x are expressed as $$+\sqrt{x}$$ and $$-\sqrt{x}$$
$$\sqrt{x}$$ itself is ALWAYS positive. I completely understand your logic, but if you don't accept this as a convention, you are bound to either get DS sums wrong or frown on several PS sums.
For example, the solutions for $$x$$ in the equation $$x^2 = 25$$ are $$x=5$$ and $$x=-5$$.
HOWEVER, if $$x = 25$$, then $$\sqrt{x} = 5$$. PERIOD. Remember, convention not logic!
Good luck!
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30 May 2011, 04:23
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seku wrote:
Question: $$\sqrt{x} < (2.5x - 5)$$ and x is a positive integer
By squaring on both sides, it can be simplified as $$x < (2.5x-5)^2$$. This is not always correct.
statement 1. x < 3, which means the possible values are 1 or 2 only
substitute 1 in the simplified equation, $$1 < (2.5 (1) - 5)^2 => 1 < (-2.5)^2 => 1 < 6.25$$ True
substitute 2 in the simplified equation, $$2 < (2.5 (2) - 5)^2 => 2 < (0)^2 => 2 < 0$$ False
NOT SUFFICIENT
statement 2. x is prime #, which means the possible values are 2,3,5,7 etc
substitute 2 in the simplified equation, $$2 < (2.5 (2) - 5)^2 => 2 < (0)^2 => 2 < 0$$ False
substitute 3 in the simplified equation, $$3 < (2.5 (3) - 5)^2 => 3 < (2.5)^2 => 3 < 6.25$$ True
NOT SUFFICIENT
So, my pick was E. Any comments ?
$$-100<1$$
$$(-100)^2>1^2$$
$$-0.1<1$$
$$(-0.1)^2<1^2$$
$$1<2$$
$$1^2<2^2$$
Thus, squaring both sides in inequality may give undesired result, esp when we don't know the signs of the expression on both sides.
Something similar happened here:
$$\sqrt{x}<{2.5*x-5}$$ ------------1
For x=1
$$\sqrt{1}<{2.5*1-5}$$
No.
$$(\sqrt{1})^2<(2.5*1-5)^2$$ ------------2
$$1<6.25$$
Yes.
Does this make statement 1 insufficient? No.
It just proves the following:
if $$a<b$$
then, $$a^2<b^2$$ may not be true.
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28 Jan 2009, 12:40
ConkergMat wrote:
If x is a positive integer, is √x < (2.5x -5)?
1. x < 3
2. x is a prime number
1: x could be 1 or 2. suff.
A.
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19 Feb 2009, 09:22
I think serene is right.. root can be either +ve or -ve
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24 Aug 2009, 17:18
But the equation does not hold for x=1,2
x=1
sq1< 2.5(1) -5
1 <-2.5, which is not correct
x=2
sq2<2.5(2) -5
sq2<0, again the equation does not hold
Am i missing somethin?
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25 May 2010, 09:24
GMAT TIGER wrote:
ddtiku wrote:
I think serene is right.. root can be either +ve or -ve
Thats not correct. In fact thats misleading statement.
If root is already given without -ve sign, then it is already +ve. For ex:
If sqrt (x) = sqrt2, then it is +ve.
If square is given and you are taking sqrt, then only one sqrt is +ve and another is -ve and vice versa. For ex:
If x^2 = 2, then x = either sqrt2 or (-sqrt2).
Consider X^2=4 , roots are x=+-2
case2, if x= 4 & we have to find $$\sqrt{x}$$ , so according to above quote
if x is known to be +ve , value of $$\sqrt{x}$$ shall be +2 only....
Generalizing :- if X^even , then roots are =+-x
However if $$\sqrt{x}$$ is asked and x is +ve , then we have only one root =+$$\sqrt{x}$$
Is it right , i don't know .............
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25 May 2010, 09:53
Yes, by definition square root function only yields positive numbers.
However, as stated above, if you are solving for roots you have to consider all cases.
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25 May 2010, 19:04
gsothee wrote:
GMAT TIGER wrote:
ddtiku wrote:
I think serene is right.. root can be either +ve or -ve
Thats not correct. In fact thats misleading statement.
If root is already given without -ve sign, then it is already +ve. For ex:
If sqrt (x) = sqrt2, then it is +ve.
If square is given and you are taking sqrt, then only one sqrt is +ve and another is -ve and vice versa. For ex:
If x^2 = 2, then x = either sqrt2 or (-sqrt2).
Consider X^2=4 , roots are x=+-2
case2, if x= 4 & we have to find $$\sqrt{x}$$ , so according to above quote
if x is known to be +ve , value of $$\sqrt{x}$$ shall be +2 only....
Generalizing :- if X^even , then roots are =+-x
However if $$\sqrt{x}$$ is asked and x is +ve , then we have only one root =+$$\sqrt{x}$$
Is it right , i don't know .............
It's not.
Square of any value is positive. A value is square of its root. So, the value you find from its square root is always positive.
So, x is 4 if sqrt(x) is 2 or -2. It can never be -4.
At the same time, if x = 4, x = 2^2 or x = -2^2. So, square root of x is 2 or -2.
This says, square root of some value can be either positive or negative.
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26 May 2010, 10:41
I found (1) is sufficient by testing 0,1, and 2 and for each the answer is No. Therefore it is sufficient.
For statement (2) there are prime integers that can yield a yes or a no and is therefore insufficient.
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26 May 2010, 14:08
marcusaurelius wrote:
I found (1) is sufficient by testing 0,1, and 2 and for each the answer is No. Therefore it is sufficient.
For statement (2) there are prime integers that can yield a yes or a no and is therefore insufficient.
I chose D. Please can you give examples of prime numbers that give a "yes" and those
that give a "no" in statement (2)
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26 May 2010, 14:15
gmatbull wrote:
marcusaurelius wrote:
I found (1) is sufficient by testing 0,1, and 2 and for each the answer is No. Therefore it is sufficient.
For statement (2) there are prime integers that can yield a yes or a no and is therefore insufficient.
I chose D. Please can you give examples of prime numbers that give a "yes" and those
that give a "no" in statement (2)
If $$x = 2$$ then the inequality is not satisfied, since $$\sqrt{2}$$ is not less than $$2.5*2 - 5 = 0$$
If $$x = 3$$ then the inequality is satisfied, since $$\sqrt{3}$$ is less than $$2.5*3 - 5 = 2.5$$
So Statement 2 alone is INSUFFICIENT.
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28 May 2010, 08:39
I think its E
1. Statement 1: x<3
Hence x=1 or x=2
If x=1, 1<2.5(1)-5
1<-2.5, we have a unique answer
If x=2, √2=2.5(2)-5
A square root will have a +ve value & a -ve value
So √2= +1.4 or -1.4
Hence, we have two answers: 1.4>0 & -1.4<0
So A is out.
2. Statement 2 will have multiple answers due to +ve & -ve value of square roots
So B &D are out.
3. If we combine both statements, we again arrive at x=2 & 1.4>0 & -1.4<0,
So C is out.
Please correct me if I'm wrong. Thanks.
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13 Jun 2010, 04:22
I jumped to C, forgetting that there are only 3 positive integers < 3, which give same answer. Now I get i. Thanks.
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27 May 2011, 05:45
(1)
x can be 1 and 2 only, and the answer is definitive no for both.
Sufficient.
(2)
for x = 2, answer is No, for x = 5, answer is yes
Not sufficient.
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27 May 2011, 06:59
I go for E.
1.x<3 -> x= 1 or 2. But both the two values don't match the first inequation -> wrong.
2.Assume a and b is the root of an inequation. The inequation has two ranges of number satisfied: x<a or x>b, there for there are plenty of number can satisfied.
Therefore, both are insufficient
Re: m05 q15 [#permalink] 27 May 2011, 06:59
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# m05 q15
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Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | {"extraction_info": {"found_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": 0.6810245513916016, "perplexity": 5165.770783263229}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257824319.59/warc/CC-MAIN-20160723071024-00208-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/510071/what-are-some-examples-of-difficult-sums?answertab=active | # What are some examples of difficult sums?
I'm looking for sums such that evaluating $f(x)$ is easy and fast, but evaluating
$$\sum_a^{a+n}{f(x)}$$
is slow and hard.
To be more scientific, evaluating $f(x)$ takes time $O(n)$, but evaluating the definite sum of $f(x)$ takes time $\Omega(m) >> O(n)$.
NOTE
I'd prefer functions $f(x)$ that use only elementary functions, such as $\sin(x), e^x, \cosh(x),$ etc.
-
Unless $a$ and $b$ are allowed to grow with $n$, this is obviously impossible; perhaps you should phrase your limits as being from $1$ to $n$ for concreteness? (i.e., effectively an 'indefinite sum') – Steven Stadnicki Sep 30 '13 at 15:44
How can evaluating $f(x)$ take time $O(n)$ when $n$ is not a parameter of $f$? – marty cohen Sep 30 '13 at 16:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8584089279174805, "perplexity": 797.3885506676583}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414637899041.10/warc/CC-MAIN-20141030025819-00148-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://joshbloom.org/tags/astrophysics/page/2/ | # Astrophysics
## Type Ia Supernovae Are Good Standard Candles in the Near Infrared: Evidence from PAIRITEL
We have obtained 1087 NIR (JHK$_s$) measurements of 21 SNe Ia using PAIRITEL, nearly doubling the number of well-sampled NIR SN Ia light curves. These data strengthen the evidence that SNe Ia are excellent standard candles in the NIR, even without …
## A photometric redshift of z = 1.8$^+0.4$$_-0.3$ for the AGILE GRB 080514B
The AGILE gamma-ray burst GRB 080514B is the first detected to have emission above 30 MeV and an optical afterglow. However, no spectroscopic redshift for this burst is known. We report on our ground-based optical/NIR and millimeter follow-up …
## GRB 071003: Broadband Follow-up Observations of a Very Bright Gamma-Ray Burst in a Galactic Halo
The optical afterglow of long-duration GRB 071003 is among the brightest yet to be detected from any GRB, with R ≈ 12 mag in KAIT observations starting 42 s after the GRB trigger, including filtered detections during prompt emission. However, our …
## Late-Time Observations of SN 2006gy: Still Going Strong
Owing to its extremely high luminosity and long duration, supernova (SN) 2006gy radiated more energy in visual light than any other known SN. Two hypotheses to explain its high luminosity at early times—that it was powered by shock interaction with …
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We present observations of a new low-mass, double-lined eclipsing binary system discovered using repeat observations of the celestial equator from the Sloan Digital Sky Survey II. Using near- infrared photometry and optical spectroscopy we have …
## Near-Infrared Monitoring of Ultracool Dwarfs: Prospects for Searching for Transiting Companions
Stars of late-M and L spectral types, collectively known as ultracool dwarfs (UCDs), may be excellent targets for searches for extrasolar planets. Owing to their small radii, the signal from an Earth-size planet transiting a UCD is, in principle, …
## The complex light curve of the afterglow of GRB071010A
We present and discuss the results of an extensive observational campaign devoted to GRB071010A, a long-duration gamma-ray burst detected by the Swift satellite. This event was followed for almost a month in the optical/near-infrared (NIR) with …
## Gamma-ray Bursts, Classified Physically
From Galactic binary sources, to extragalactic magnetized neutron stars, to long-duration GRBs without associated supernovae, the types of sources we now believe capable of producing bursts of gamma- rays continues to grow apace. With this emergent …
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GRB 070610 is a typical high-energy event with a duration of 5 s. Yet within the burst localization we detect a highly unusual X-ray and optical transient, Swift J195509.6+261406. We see high- amplitude X-ray and optical variability on very short …
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We review current research related to spectroscopy of gamma-ray burst (GRB) after-glows with particular emphasis on the interstellar medium (ISM) of the galaxies hosting these high redshift events. These studies reveal the physical conditions of … | {"extraction_info": {"found_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": 0.7884029150009155, "perplexity": 7384.94984660704}, "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/1656104628307.87/warc/CC-MAIN-20220705205356-20220705235356-00684.warc.gz"} |
https://mospace.umsystem.edu/xmlui/handle/10355/8001/browse?value=Moore%2C+Aaron&type=author | Now showing items 1-1 of 1
• #### Determination of scour susceptibility through rapid assessment
(University of Missouri--Kansas City, 2012-06-21)
A need existed to efficiently predict the potential scour that could be expected at nearly 20,000 existing off-system bridges in the State of Kansas to assign a National Bridge Inspection Standards (NBIS) Item 113 coding. ... | {"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": 0.8006870150566101, "perplexity": 25284.4990915512}, "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-2016-07/segments/1454701152982.47/warc/CC-MAIN-20160205193912-00189-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://mathhelpforum.com/algebra/96696-bonus-calculation.html | 1. ## Bonus Calculation
I need to calculate bonuses for my employees based on participation on a particular project and embarrassingly enough, it won't come to me this morning.
Example:
Total bonus $400 employee 1 100% participation employee 2 95% participation employee 3 30% participation employee 4 70% participation employee 5 10% participation 2. Originally Posted by black6 I need to calculate bonuses for my employees based on participation on a particular project and embarrassingly enough, it won't come to me this morning. Example: Total bonus$400
employee 1 100% participation
employee 2 95% participation
employee 3 30% participation
employee 4 70% participation
employee 5 10% participation
1. $400$
2. $.95\cdot400$
3. $.30\cdot400$
4..........
That will give you how much you should give to each.
Assuming each employee starts out with a potential bonus of 400.
If you are to spred the 400 around, that's different
3. Right, I need to spread the 400 around between the 5 people
4. Originally Posted by black6
Right, I need to spread the 400 around between the 5 people
No problem
Let x be the amount that the person who participated the least is to get, then
$x+3x+7x+9.5x+10x=400$
$30.5x=400$
$x=\frac{400}{30.5}$
Can you proceed?
5. Thanks
6. Originally Posted by black6
Thanks
No problem. | {"extraction_info": {"found_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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7748592495918274, "perplexity": 4384.447200896581}, "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-2017-30/segments/1500549423785.29/warc/CC-MAIN-20170721142410-20170721162410-00177.warc.gz"} |
https://www.physicsforums.com/threads/combining-two-equations.170967/ | Combining two equations
1. May 19, 2007
music_lover12
How do I combine these two equations?
Fc=mv(squared)/r
Fg=qvb
2. May 19, 2007
cristo
Staff Emeritus
You need to make an effort yourself, and furthermore, defined your symbols. For example, on the LHS of each equation, you have Fc and Fg, respectively. Are these Fxc and Fxg, or are they different variables Fc and Fg?
3. May 19, 2007
music_lover12
It is with the smaller c and g.
4. May 19, 2007
cristo
Staff Emeritus
Well, in that case, can you rearrange the second equation to get it into the form v=... ?
5. May 19, 2007
music_lover12
Yeah, it would be v=f/qB....
6. May 19, 2007
music_lover12
...also I'm trying to combine the two equations to find m, which is mass.
7. May 19, 2007
cristo
Staff Emeritus
Ok, so you now have Fc=mv2/r and v=Fg/qB. Now, can you substitute the second equation into the first? [i.e. replace v^2 in the first with Fg/qb]
Right, well if you manage to do the substitution above, then you need to rearrange the equation you obtain to get it in the form m=...
8. May 19, 2007
music_lover12
Okay, so I substituted the second equation into the first and I got Fc=m*fg/qB/R. Is that right?
9. May 19, 2007
cristo
Staff Emeritus
No, v is squared in the first equation, and thus substituting the second into the first should yield $$F_c=\frac{m}{r}\left(\frac{F_g}{qB}\right)^2$$. Can you rearrange this?
10. May 19, 2007
music_lover12
m=Fcr*qB/Fg^2 :uhh:
11. May 19, 2007
cristo
Staff Emeritus
Well, you're missing a square on q and B; adding parentheses like this m=Fcr*(qB/Fg)^2 gives the correct solution.
12. May 19, 2007
music_lover12
Oh okay. I see. Thank you very much!
13. May 19, 2007
cristo
Staff Emeritus
You're welcome. | {"extraction_info": {"found_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": 0.9179491400718689, "perplexity": 1937.1499696270162}, "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-2017-09/segments/1487501170600.29/warc/CC-MAIN-20170219104610-00498-ip-10-171-10-108.ec2.internal.warc.gz"} |
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## Optimal algorithms concerning the solving of equations by interpolation
Abstract In this paper we approach two aspects concerning the optimality problems arising from the consideration of the iterative methods for… | {"extraction_info": {"found_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": 0.838615357875824, "perplexity": 2812.1133043311174}, "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/1610703527850.55/warc/CC-MAIN-20210121194330-20210121224330-00769.warc.gz"} |
https://infoscience.epfl.ch/record/190216 | Infoscience
Journal article
# Symmetric and asymmetric excitations of a strong-leg quantum spin ladder
The zero-field excitation spectrum of the strong-leg spin ladder (C7H10N)(2)CuBr4 is studied with a neutron time-of-flight technique. The spectrum is decomposed into its symmetric and asymmetric parts with respect to the rung momentum and compared with theoretical results obtained by the density matrix renormalization group method. Additionally, the calculated dynamical correlations are shown for a wide range of rung and leg coupling ratios in order to point out the evolution of arising excitations, as, e.g., of the two-magnon bound state from the strong to the weak coupling limit. | {"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": 0.8692634105682373, "perplexity": 1167.8112104811587}, "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-2017-30/segments/1500549425193.20/warc/CC-MAIN-20170725122451-20170725142451-00504.warc.gz"} |
http://math.stackexchange.com/users/10948/caleb-jares?tab=activity&sort=posts | Caleb Jares
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Computer Science Undergraduate at UNL. C#, .NET 4.5, Windows 8 lover.
18 Posts
Dec3 asked Is it possible to combine the formula for $f_0$ and $f_{n\ge1}$ to get $f_{n\ge0}$? Apr17 asked Showing a polynomial $f\in\mathbb Q[x]$ is irreducible if it has rational coefficients? Mar10 asked In polar/cylindrical coordinates, does $r dr d\theta=r d\theta dr$? Feb27 asked In a group $G$ with operation $\star$, can I apply $\star$ to both sides of an equation? Feb14 asked Proving $4^{47}\equiv 4\pmod{12}$ Jun22 asked When representing a base-n number in decimal ($\frac{x}{n^l}$), will there be a different set of terminating representable numbers than base-10? Dec12 asked How many unique pairs of integers between $1$ and $100$ (inclusive) have a sum that is even? Dec11 asked Prove $\sum \limits_{i=1}^n i^2 \in \Theta (n^3)$ Nov15 asked Evaluating $\sum\limits_{n=0}^{20} \frac{(-1)^{n}2^{n+1}}{3^{n}},$ Nov13 asked Find which values of p the integral is convergent Nov2 asked Sum of the series $\sum_{n=1}^\infty \frac{(-1)^n}{n2^{n+1}}$ Oct23 asked Solving $y = xc^x + x + 1$, where c is a constant Sep20 asked Evaluate $\int \sqrt{1+x^{\frac{3}{2}}} \operatorname d x$ Sep18 asked Differences in $\varnothing$, {$\varnothing$}, and $\subseteq$ Sep12 asked Truth Value of Theorems in Axiomatic Set Theory May29 answered Mathematical Career Advice to a young 16 year wannabe mathematician May16 asked Finding the limit when denominator = 0 May16 asked Finding a one sided limit algebraically (not plugging in numbers) | {"extraction_info": {"found_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": 0.3888355493545532, "perplexity": 2392.6801389575858}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507443901.32/warc/CC-MAIN-20141017005723-00281-ip-10-16-133-185.ec2.internal.warc.gz"} |
http://kleine.mat.uniroma3.it/mp_arc-bin/mpa?yn=96-135 | 96-135 Marco Lenci
Escape Orbits for Non-Compact Flat Billiards (18K, LaTeX) Apr 15, 96
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers
Abstract. It is proven that, under some conditions on $f$, the non-compact flat billiard $\Omega = \{ (x,y) \in \R_0^{+} \times \R_0^{+};\ 0\le y \le f(x) \}$ has no orbits going {\em directly} to $+\infty$. The relevance of such sufficient conditions is discussed.
Files: 96-135.src( desc , 96-135.tex ) | {"extraction_info": {"found_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": 0.983502209186554, "perplexity": 10154.865938102499}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125948738.65/warc/CC-MAIN-20180427002118-20180427022118-00066.warc.gz"} |
https://en.wikisource.org/wiki/Translation:The_Entrainment_of_Light_by_Moving_Bodies_in_Accordance_with_the_Principle_of_Relativity | # Translation:The Entrainment of Light by Moving Bodies in Accordance with the Principle of Relativity
The Entrainment of Light by Moving Bodies According to the Principle of Relativity (1907)
by Max von Laue, translated from German by Wikisource
In German: Die Mitführung des Lichtes durch bewegte Körper nach dem Relativitätsprinzip, Annalen der Physik 328 (10): 989–990, Online
(Published September 24, 1907.)
The Entrainment of Light by Moving Bodies According to the Principle of Relativity
by M. Laue.
Since Einstein's electrodynamics,[1] which is based on the principle of relativity, is equivalent with the older theory of Lorentz as long one restricts himself to the first power of the relations of all body velocities to the speed of light, it is obvious that it allows to calculate Fresnel's dragging coefficient as a first approximation. But no reference is made in the literature as to how much easier this problem is resolved by the relativity principle than by the other theory, even with the simplification recently given by Lorentz.[2]
Namely, this is only an example of Einstein's addition theorem of velocities. There are two coordinate systems with parallel axes, the "primed" and the "unprimed", moving against each other along the direction of X with velocity v. A velocity w with respect to the primed system, whose direction forms the angle θ with the X'-axis, corresponds to a velocity in the unprimed system
$w=\frac{\sqrt{v^{2}+w'^{2}+2vw'\cos\vartheta'-\frac{1}{c^{2}}v^{2}w'^{2}\sin^{2}\vartheta'}}{1+\frac{1}{c^{2}}vw'\cos\vartheta'}$.[3]
Now, if a body of refractive index n is at rest in the primed system, then the phase velocity of light in the primed system is:
$w'=\frac{c}{n}$.
[ 990 ] The corresponding velocity in the unprimed system is therefore
$w=\frac{\sqrt{v^{2}+\frac{c^{2}}{n^{2}}+2v\frac{c}{n}\cos\vartheta'-\frac{v^{2}}{n^{2}}\sin^{2}\vartheta'}}{1+\frac{v}{cn}\cos\vartheta'}$.
If the directions of the velocities v and c/n coincide, as in the experiment of Fresnel, then it is $\cos\vartheta'=\pm1$, and
$w=\frac{\frac{c}{n}\pm v}{1\pm\frac{v}{cn}}$ $=\frac{c}{n}+\left(1-\frac{1}{n^{2}}\right)\left\{ \pm v-\frac{v^{2}}{cn}\pm\frac{v^{3}}{(cn)^{2}}-\frac{v^{4}}{(cn)^{3}}\pm\dots\right\}$.
If, however, for example $\vartheta'=\pm\pi/2$, it is
$w=\sqrt{\frac{c^{2}}{n^{2}}+v^{2}\left(1-\frac{1}{n^{2}}\right)}=\frac{c}{n}+\frac{1}{2}\frac{v^{2}}{nc}\left(n^{2}-1\right)$ $-\frac{1}{2}\cdot\frac{1}{4}\frac{v^{4}}{nc^{3}}(n^{2}-1)^{2}+\frac{1}{2}\cdot\frac{1}{4}\cdot\frac{3}{6}\frac{v^{6}}{nc^{5}}(n^{2}-1)^{3}\dots$
In dispersive substances we have to fill in the value for n corresponding to the frequency in the primed system.
For the group velocity it is exactly the same, if we replace the refractive index n by the expression n + v(dn/dv) (v is frequency).
So, according to the relativity principle, light is completely carried by the body, however, just because of this its velocity relative to an observer (who does not participate in the motion of the body) is not the same as the vector sum of its velocity relative to the body and that of the body relative to an observer. In this way we are relieved of the need to introduce into optics an "aether", which penetrates the bodies without sharing their motion.
Berlin, July 1907. | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 9, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8855636715888977, "perplexity": 423.1258418247921}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928923.85/warc/CC-MAIN-20150521113208-00016-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://www.indianacademics.com/profit-loss/ | ## PROFIT AND LOSS
### Introduction
Cost Price = cost of item
Selling price = price at which item is sold.
Gain = Selling price – Cost price (SP > CP)
Loss = Cost price – Selling price (CP > SP)
SP={(100+GAIN%) /100}*CP SP={(100-LOSS%)/100}*CP CP=100/(100+GAIN%)}*SP CP=100/(100-LOSS%)}*SP
So when an article of Rs 100 is sold at 35% gain that means SP is Rs.135
So when an article of CP = 100 is sold for loss of 35% its SP is Rs. 65.
When a item is sold for x% gain and other for x% loss, the seller incurs a loss of
Loss = ( X / 10) ^ 2
• Direct Costs or Variable Costs : This is the cost associated with direct selling of product/service. In other words, this is the cost that varies with every unit of the product sold. Hence, if the variable cost in selling a pen for 20 is 5, then the variable cost for selling 10 units of the same pen is 10 × 5 = Rs. 50.
• Indirect Costs (Overhead Costs) or Fixed Costs : There are some types of costs that have to be incurred irrespective of the number of items sold and are called as fixed or indirect costs. For example, irrespective of the number of units of a product sold, the rent of the corporate office is fixed. Now, whether the company sells 10 units or 100 units, this rent is fixed and is hence a fixed cost.
• Apportionment of indirect (or fixed) costs : Fixed Costs are apportioned equally among each unit of the product sold. Thus, if n units of a product is sold, then the fixed cost to be apportioned to each unit sold is given by : Fixed costn
• The Concept of the Break-even Point : The break-even point is defined as the volume of sale at which there is no profit or no loss. In other words, the sales value in terms of the number of units sold at which the company breaks even is called the break-even point. This point is also called the break-even sales.
• Since for every unit of the product the contribution goes towards recovering the fixed costs, as soon as a company sells more than the break-even sales, the company starts earning a profit. Conversely, when the sales value in terms of the number of units is below the break-even sales, the company makes losses. The entire scenario is best described through the following example.
Q. Let us suppose that a paan shop has to pay a rent of 1000 per month and salaries of 4000 to the assistants. Also suppose that this paan shop sells only one variety of paan for 5 each
• The direct cost (variable cost) in making one paan is 2.50 per paan, then the margin is (5 – 2.50) = 2.50 per paan.
• Now, break-even sales will be given by: Break-even-sales = Fixed costs/Margin per unit = 5000/2.5 = 2000 paans
• Hence, the paan shop breaks-even on a monthly basis by selling 2000 paans
• Selling every additional paan after the 2000th paan goes towards increasing the profit of the shop. Also, in the case of the shop incurring a loss, the number of paans that are left to be sold to break-even will determine the quantum of the loss
• Profit = (Actual sales – Break-even sales) × Contribution per unit
• Loss = (Break-even sales – Actual sales) × Contribution per unit
• Profit Calculation on the Basis of Equating the Amount Spent and the Amount Earned
• A fruit vendor recovers the cost of 25 mangoes by selling 20 mangoes. Find his percentage profit.
• Since the money spent is equal to the money earned the percentage profit is given by
• % Profit = Goods leftGoods sold100 = 5* 100/20 = 25%
IF THE TRADER PROFESSES TO SELL HIS GOODS AT COST PRICE BUT USES FALSE WEIGHTS,THEN
• GAIN= ERROR(TRUE VALUE)-(ERROR)100%
Q. A dishonest dealer professes to sell his goods at cost price but uses a weight of 960 gms for a kg weight . Find his gain percent.
• GAIN= ERROR(TRUE VALUE)-(ERROR)100%
• 40960100%
• 4 1/6 %
Q. A person incurs loss of 5% by selling a watch for Rs 1140. At what price should the watch be sold to earn a 5% profit ?
A. CP is 100/95 * 1140 as a loss of 5% on CP is 1140 so CP is 100/95% of 1140 [SP] as per formula above.New selling price = (100 / 95) * ( 105 / 100) * 1140 = 1260
Q. By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent .
A.
Selling price of 33m – CP of 33 m = SP of 11m [Gain].
SP of 22 m = CP of 33m i.e. SP of 2 m = CP of 3 m
Assume CP of 1 m = Re. 1 so 3 m is Rs. 3.
SP of 2 m = Rs. 3 and SP of 1 m = Rs. 1.5 so gain is 50%.
Q. A man brought toffees at 3 for a rupee. How many for a rupee must he sell to gain 50%?
A. Cost of a toffee is 3 toffees is re. 1. So he needs to sell them at Rs. 1.5 to make a gain of 50% so at 50 paise each or 2 for a rupee.
Q. A grocer purchased 80 kg of sugar at Rs.13.50 per kg and mixed it with 120kg sugar at Rs.16per kg. At what rate should he sell the mixer to gain 16%?
A. The cost of the mixture
= (weight1 * price1) + (weight2*price2) / (weight1+weight2)
= (80*13.5) + (120*16) / (120+80)
=(1080+1920)/200 = 3000/200 = Rs. 15 / kg
SP = 116/100 * 15 = 1.16*15=17.4 Rs
Q. Pure ghee cost Rs.100 per kg. After adulterating it with vegetable oil costing Rs.50 per kg, A shopkeeper sells the mixture at the rate of Rs.96 per kg, thereby making a profit of 20%. In What ratio does he mix the two?
A. SP of mixture = 96 ; CP of mixture = 80 as SP is 20% more than CP;
Rule of alligation:
(Quantity of oil : Quantity of ghee)
= ( CP of ghee – Mean price) / (Mean price – CP of oil)
= (100-80) / (80-50)
=20/30 = 2:3
Q. Monika purchased a pressure cooker at 9/10th of its selling price and sold it at 8% more than its S.P .find her gain percent.
A. Assume it was with a SP of Rs. 100 it was bought for Rs. 90 and sold for Rs. 108 thus making profit of Rs. 18 which is 20% more than Rs. 90.
Q. A tradesman sold an article at a loss of 20%. if the selling price has been increased by Rs 100, there would have been a gain of 5%. what was the cost price of the article?
A. SP(old) = 80% of CP
SP(new) = 105% of CP; we know (105% of CP) – (80% of CP) = 100
i.e. 25% of CP = 100; Hence CP = Rs. 400
Q. A man sells an article at a profit of 25% if he had bought it 20% less and sold it for Rs 10.50 less, he would have gained 30% find the cost price of the article.
A. SP1 = 1.25CP1 as it is sold for 25% profit. CP2 = (4/5)*CP1;
SP2 = (130/100)*CP2
SP2 = SP1 – 10.5 = 1.25CP1 – 10.5
so we get
1.25CP1 – 10.5 = (130/100)*(4/5)*CP1
1.25CP1 – 1.04CP1 = 10.5
0.21CP1 = 10.5
CP1 = Rs.50
Q. A dealer sold three-fourth of his article at a gain of 20% and remaining at a cost price. Find the gain earned by him at the two transaction.
A. assume he had 4 articles of CP = 100 so he sold three at 120 and 1 at 100. so he earned profit of Rs. 60. CP of total inventory is 400 so profit is 15%.
Q. A man bought a horse and a bull for Rs 3000.he sold the horse at a gain of 20% and the bull at a loss of 10%,thereby gaining 2% on the whole. find the cost of the horse.
A. 1.2x + 0.9(3000-x) = 3600 is the equation as ‘x’ is price of horse. 1.2x is SP of horse at 20% profit and 0.9(3000-x) is SP of bull at 10% loss. rs 3600 is the SP of total transaction at 2% profit over Rs. 3000.
Q. find the single discount equivalent to a series discount of 20% ,10% and 5%
A. assume CP=100 so apply 20% discount to get CP=80 and then 10% to get 72 and then 5% to get 72-3.6 = 68.4 so total is 31.6%.
Q. A retailer marks all its goods at 50% above the cost price and thinking that he will still make 25% profit,offers a discount of 25% on the marked price.what is the actual profit on the sales?
A. Assume price is 100 so SP is 150 and 25% discount on SP gives new SP as Rs 112.5. So profit is 12.5%
Q. At what % above C.P must an article be marked so as to gain 33% after allowing a customer a discount of 5%?
A. We have to find the value of SP [assume as ‘x’] whose 95% is 33% above CP. Assume CP to be Rs 100 and SP(new) will be Rs. 133.
0.95x = 133
x = 133 * 100 / 95 = 133 * 20 / 19 = 140
Q. A merchant sold his goods for Rs.75 at a profit percent equal to C.P. The C.P was :
A. SP = (100+Gain%) * CP /100 we get below equation by substituting these values
75 = ( 100 + x) * x / 100
### Quiz
Score more than 80% marks and move ahead else stay back and read again!
Q1: Find selling price if gain of 20% is made on a good worth Rs. 300
360
330
300
350
ANS.360
Q2: Find selling price if loss of 20% is made on a good worth Rs. 300
240
250
260
270
ANS.240
Q3: Find cost price if gain of 20% is made on a good sold at Rs. 300
275
250
300
360
ANS.250
Q4: Find cost price if loss of 20% is made on a good sold at Rs. 300
360
250
375
320
ANS.3
Q5: When a item is sold for 10% gain and other for 10% loss, the seller incurs
loss of 1%
profit of 1%
loss of 2%
profit of 2%
ANS.LOSS of 1% | {"extraction_info": {"found_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": 0.47050145268440247, "perplexity": 3125.084215108982}, "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/1634323587593.0/warc/CC-MAIN-20211024173743-20211024203743-00033.warc.gz"} |
http://legisquebec.gouv.qc.ca/en/showversion/cs/S-3.3?code=sc-nb:1&pointInTime=20200213 | ### S-3.3 - Act to ensure safety in guided land transport
REPEAL SCHEDULES
In accordance with section 9 of the Act respecting the consolidation of the statutes and regulations (chapter R-3), chapter 57 of the statutes of 1988, in force on 1 March 1990, is repealed, except section 89, effective from the coming into force of chapter S-3.3 of the Revised Statutes.
In accordance with section 9 of the Act respecting the consolidation of the statutes and regulations (chapter R-3), sections 4 to 18, 23, 27, 29, 36, 44 to 47, 49 to 62, the first paragraph of section 63 and sections 64 to 68 of chapter 57 of the statutes of 1988, in force on 1 April 2001, are repealed effective from the coming into force of the updating to 1 April 2001 of chapter S-3.3 of the Revised Statutes.
REPEAL SCHEDULE
In accordance with section 9 of the Act respecting the consolidation of the statutes and regulations (chapter R-3), chapter 57 of the statutes of 1988, in force on 1 March 1990, is repealed, except section 89, effective from the coming into force of chapter S-3.3 of the Revised Statutes. | {"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": 0.8066821694374084, "perplexity": 2082.9127509696964}, "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-2020-16/segments/1585370500331.13/warc/CC-MAIN-20200331053639-20200331083639-00497.warc.gz"} |
https://link.springer.com/article/10.1186/s13662-017-1218-y | Advances in Difference Equations
, 2017:161
# Effect of increased global temperatures on biological control of green lacewings on the spread of mealybugs in a cassava field: a simulation study
Open Access
Research
Part of the following topical collections:
1. Proceedings of the International Conference in Mathematics and Application 2016
## Abstract
Even though the effect of release frequency of green lacewings in controlling the spread of mealybugs in a cassava field was investigated by Promrak and Rattanakul in 2015, the effect of increased global temperature was not taken into account. In this work, cellular automata and Monte Carlo simulation are employed in order to study the effect of an increased global temperature on the life cycles of mealybugs and green lacewings which in turn effects the efficacy of the biological control of the spread of mealybugs. Computer simulations are carried out at different temperatures so that an efficient biological control of the spread of mealybugs in a cassava field is obtained.
### Keywords
biological control cassava cellular automata green lacewings mealybugs Monte Carlo simulation
## 1 Introduction
The term ‘global warming’ refers to an increase in the average temperature of Earth’s atmosphere and oceans. According to the report from Goddard Institute for Space Studies (GISS) and Climatic Research Unit (CRU), the temperature has been increasing almost every year since 1880 and has climbed up fast in the last few decades. The Intergovernmental Panel on Climate Change (IPCC) forecasts that, for the next two decades, a further warming trend will occur at the rate 0.1-0.2C per decade. Global warming may cause several severe problems such as the increase in the spread of insect-borne diseases, heavier rainfall and flooding, food and water deficiency, season changing and migration [1]. On crops and insect pests, the increase in the global temperature may lead to the change in the life cycle of insect pests at any stage and the rate of pest development might be higher while the host plants are more attractive to insect pests in drought areas [2, 3]. As a result, the loss of crop yields will then increases.
Under the global increased temperature condition, crops which can thrive in hot and dry climates such as cassava is considered as a key for food security. Cassava (Manihot esculenta Crantz) is also known as yuca, manioc, tapioca, mandioc, etc. Its root and tuber are the main source of food for Africans and are popular in the tropics [4]. Since it requires little skill to cultivate with moderate soil nutrient and water, this crop is very attractive to agriculturists worldwide [5]. In 2005, the top importers of cassava are East Asia (US$460,070,000), EU25 (US$59,534,000), and NAFTA (US$48,725,000) while the primary exporters are South East Asia (US$533,926,000), Central America (US$66,173,000), and EU25 (US$ 7,853,000) [6]. For Thailand, the cassava export of the year 2015 has been reported as 79.56% of the global market share [7]. Therefore, cassava is considered as an economic plant of Thailand.
The major crop loss of cassava is due to its insect pests, especially cassava mealybug (Phenacoccus manihoti Matile-Ferrero) which was first detected in Zaire and Congo in the early 1970s and quickly became the most severe pest on cassava [8]. To control the spread of mealybugs, biological control using their natural enemies has proved experimentally to be successful [9, 10, 11, 12, 13, 14]. One of the natural enemies of mealybugs that has been used popularly is green lacewings. It has been used in a mealybug controlling project in Thailand [15, 16] as well. However, various instructions are recommended to farmers in Thailand when the spread of mealybugs is detected. Moreover, the effect of an increased global temperature on the life cycles of both mealybugs and green lacewings has not been taken into account yet.
In our previous work [17], a cellular automata (CA) model together with the Monte Carlo simulation technique has been employed to study the effect of the release frequency of green lacewings in controlling the spread of mealybugs in a cassava field [17]. Since the effect of an increased global temperature on the life cycles of mealybugs and green lacewings should be investigated so that we can appropriately modify the usual practices in the control of the spread of mealybugs in response to those changes, we investigate the effect of an increased temperature on the controlling of the spread of mealybugs in a cassava field using green lacewings in this paper.
## 2 Cellular automata model
We assume that cassava is planted in the field based on the recommended instructions of the Department of Agricultural Extension, Ministry of Agriculture and Cooperatives, Thailand. Cassava is then planted at the beginning of the rainy season and the stem cuttings are soaked by the recommended chemical reactants before they are planted in the cassava field. Hence, the major factor of the spread of mealybugs in the field that we will take into account is the wind. Note that only mealybugs of the instar stage can be blown by the wind. Moreover, the recommended planting distance between two cassava plants is 1 m and the planting period of cassava is 1 year. We also assume further that the survey for the spread of mealybugs will be conducted every 2 weeks after a month of planting in the recommended manner by many agricultural technical officers from the Thai Tapioca Development Institute and the Department of Agriculture, Ministry of Agriculture and Cooperatives, Thailand [18].
A cellular automaton with Moore’s neighborhood of a square lattice with the size $$80\times80$$ is used to represent a cassava field of the area 4 rai (or 0.64 ha) as shown in Figure 1. The possible states of each cell in the lattice are susceptible cassava (S), infested cassava (I) and removed cassava (E) representing a cassava plant that is free from mealybugs, a cassava plant that is infested with mealybugs and a cassava plant that is removed from the field, respectively.
At each time step (1 time step $$\Delta t=1$$ day), a number r, $$0\leq r\leq1$$ is randomized and each cell will be updated at random according to the following rules:
1. (a)
If the randomized cell is a removed cassava (E), then it remains the removed cassava.
2. (b)
If the randomized cell is a susceptible cassava (S), then there are possibilities that the randomized cell may become an infested cassava (I) due to the following reasons:
1. (i)
Mealybugs of the instar stage from outside of the cassava field might be blown through the wind to the randomized cell. If the randomized cell belongs to the first two rows next to each of the four borders of the lattice then the cell may become an infested cell with the probability $$w_{1}$$, $$0\leq w_{1}\leq1$$ or else the randomized cell may become an infested cell with the probability $$w_{2}$$, $$0\leq w_{2} < w_{1}\leq1$$.
2. (ii)
Mealybugs of the instar stage from the neighborhood of the randomized might be blown through the wind to the randomized cells. Here, we consider only three levels of neighborhood of the randomized cell which are the immediate neighborhood, the distant neighborhood and the far distant neighborhood as shown in Figure 2. The probabilities that mealybugs of the instar stage from the immediate neighborhood, distant neighborhood and far distant neighborhood might be blown through the wind to the randomized cells are $$n_{1}$$, $$n_{2}$$ and $$n_{3}$$, respectively, where $$0\leq n_{3} < n_{2} < n_{1}\leq1$$.
3. (c)
If the randomized cell is an infested cassava (I), then the following rules will be used.
1. (i)
It may become a removed cassava (E) if it is subjected to a survey during the first 4 months or the last 5 months of planting or the number of mealybugs on the randomized cell is greater than $$m_{1}$$.
2. (ii)
It may become a susceptible cassava (S) if green lacewings feed on mealybugs on the cassava plant in the randomized cell successfully and there is no mealybug on the cassava plant in the randomized cell.
When a month has passed after cassava planting, if there is an infested cassava plant among the surveyed cassava plants, green lacewings are to be released every 2 months if there still are mealybugs on the surveyed cassava plants in the field. If the number of surveyed infested cassava plants is less than a half of the total number of surveyed cassava plants in the field, the number of green lacewings to be released in the field is $$R_{1}$$ per rai (or $$R_{1}/0.16$$ per ha) or else the number of green lacewings to be released in the field is $$R_{2}$$ per rai (or $$R_{2}/0.16$$ per ha).
In what follows, we let $$P^{i}_{t}$$, $$P^{m}_{t}$$, $$P^{e}_{t}$$ be the number of instar mealybugs, adult mealybugs and mealybug’s eggs, respectively, at time t. Let $$M^{i}_{t}$$, $$M^{d}_{t}$$, $$M^{m}_{t}$$ and $$M^{e}_{t}$$ be the number of larva green lacewings, pupa green lacewings, adult green lacewings and green lacewings’ egg, respectively, at time t. The numbers of mealybugs and green lacewings at each stage on the cassava plant in each cell of the lattice are also updated according to the life cycles of mealybugs and green lacewings using a system of difference equations as follows.
Instar mealybug:
\begin{aligned} P^{i}_{t+\Delta t} =&P^{i}_{t}+r_{1} \alpha_{1} P^{e}_{t}-\alpha_{2} P^{i}_{t}-\beta _{1}\bigl(P^{i}_{t},M^{i}_{t} \bigr)M^{i}_{t} . \end{aligned}
(1)
Equation (1) represents the number of instar mealybugs at the time step $$t+\Delta t$$. The first term on the right hand side represents the number of instar mealybugs at the time step t. The second term on the right hand side represents the number of instar mealybugs developed from mealybug’s egg of the time step t. The third term on the right hand side represents the number of instar mealybugs of the time step t that develop into adult mealybugs in the time step $$t+\Delta t$$. The last term on the right hand side represents the number of instar mealybugs eaten by green lacewings of the larva stage in the time step t.
\begin{aligned} P^{m}_{t+\Delta t} =&P^{m}_{t}+r_{2} \alpha_{2} P^{i}_{t}-\alpha_{3} P^{m}_{t}-\beta _{2}\bigl(P^{m}_{t},M^{i}_{t} \bigr)M^{i}_{t}. \end{aligned}
(2)
Equation (2) represents the number of adult mealybugs at the time step $$t+\Delta t$$. The first term on right hand side represents the number of adult mealybugs at the time step t. The second term on the right hand side represents the number of adult mealybugs developed from instar mealybug of the time step t. The third term on the right hand side represents the number of adult mealybugs of the time step t that die in the time step $$t+1$$ due to mealybug’s life cycle. The last term on the right hand side represents the number of adult mealybugs eaten by green lacewings of the larva stage in the time step t.
Mealybug’s egg:
\begin{aligned} P^{e}_{t+\Delta t} =&P^{e}_{t}+r_{3} \alpha_{4} v_{1} P^{m}_{t}- \alpha_{1} P^{e}_{t}-\beta _{3} \bigl(P^{e}_{t},M^{i}_{t} \bigr)M^{i}_{t}. \end{aligned}
(3)
Equation (3) represents the number of mealybug’s eggs at the time step $$t+\Delta t$$. The first term on the right hand side represents the number of mealybug’s eggs at the time step t. The second term on the right hand side represents the number of mealybug’s eggs laid by adult mealybugs of the time step t. The third term on the right hand side represents the number of mealybug’s eggs in the time step t that develop into instar mealybugs in the time step $$t+\Delta t$$. The last term on the right hand side represents the number of mealybug’s eggs eaten by green lacewings of the larva stage in the time step t.
Larva green lacewing:
\begin{aligned} M^{i}_{t+\Delta t} =&M^{i}_{t}+s_{1} \gamma_{1} M^{e}_{t}-\gamma_{2} M^{i}_{t} . \end{aligned}
(4)
Equation (4) represents the number of larva green lacewings at the time step $$t+\Delta t$$. The first term on the right hand side represents the number of larva green lacewings at the time step t. The second term on the right hand side represents the number of larva green lacewings developed from green lacewing’s eggs of the time step t. The last term on the right hand side represents the number of larva green lacewings in the time step t that develop into pupa green lacewings in the time step $$t+\Delta t$$.
Pupa green lacewing:
\begin{aligned} M^{d}_{t+\Delta t} =&M^{d}_{t}+s_{2} \gamma_{2} \delta_{1}\bigl(P^{i}_{t},P^{m}_{t},P^{e}_{t},M^{i}_{t} \bigr) M^{i}_{t}-\gamma_{3} M^{d}_{t} . \end{aligned}
(5)
Equation (5) represents the number of pupa green lacewings at the time step $$t+\Delta t$$. The first term on the right hand side represents the number of pupa green lacewings at the time step t. The second term on the right hand side represents the number of pupa green lacewings developed from larva green lacewings of the time step t depending on the number of consumed mealybugs. The last term on the right hand side represents the number of pupa green lacewings in the time step t that develop into adult green lacewings in the time step $$t+\Delta t$$.
\begin{aligned} M^{m}_{t+\Delta t} =&M^{m}_{t}+s_{3} \gamma_{3} M^{d}_{t}-\delta_{2} M^{m}_{t} . \end{aligned}
(6)
Equation (6) represents the number of adult green lacewings at the time step $$t+\Delta t$$. The first term on the right hand side represents the number of adult green lacewings at the time step t. The second term on the right hand side represents the number of adult green lacewings developed from pupa green lacewings of the time step t. The last term on the right hand side represents the number of adult green lacewings of the time step t that die in the time step $$t+\Delta t$$ due to green lacewing’s life cycle.
Green lacewing’s eggs:
\begin{aligned} M^{e}_{t+\Delta t} =&M^{e}_{t}+s_{4} v_{2} M^{m}_{t}-\gamma_{1} M^{e}_{t}. \end{aligned}
(7)
Equation (7) represents the number of green lacewing’s eggs at the time step $$t+\Delta t$$. The first term on the right hand side represents the number of green lacewing’s eggs at the time step t. The second term on the right hand side represents the number of green lacewing’s eggs laid by adult green lacewings of the time step t. The last term on the right hand side represents the number of green lacewing’s eggs in the time step t that develop into larva green lacewings in the time step $$t+\Delta t$$.
$$\beta_{1} (P^{i}_{t}, M^{i}_{t} )$$, $$\beta_{2} (P^{m}_{t}, M^{i}_{t} )$$ and $$\beta_{3} (P^{e}_{t}, M^{i}_{t} )$$ are the numbers of instar mealybugs, adult mealybugs and mealybug’s eggs eaten by green lacewings of the larva stage, respectively, in one time step and $$\delta_{1} (P^{i}_{t},P^{m}_{t},P^{e}_{t},M^{i}_{t} )$$ is the efficiency of converting larva green lacewing to pupa green lacewing. The definitions of other parameters in the model are given in Table 1 together with their approximated values calculated from the literature [19, 20, 21] at three different temperatures.
Table 1
Parameters in the system of difference equations ( 1 )-( 7 )
Parameter
Definition
$$\boldsymbol{t=25^{\circ}}\mathbf{C}$$
$$\boldsymbol{t=27^{\circ}}\mathbf{C}$$
$$\boldsymbol{t=30^{\circ}}\mathbf{C}$$
• Mealybugs
$$\alpha_{1}$$
The fraction of mealybug’s eggs that develop into instar mealybugs in one time step
0.1075
0.1163
0.1493
$$\alpha_{2}$$
The fraction of instar mealybugs that develop into adult mealybugs in one time step
0.0435
0.0482
0.0388
$$\alpha_{3}$$
The natural death rate of adult mealybugs
0.0612
0.0665
0.0596
$$\alpha_{4}$$
The fraction of female adult mealybugs in the reproductive period
0.4591
0.4991
0.4468
$$r_{1}$$
The survival rate of mealybug’s eggs that develop into instar mealybugs
0.8900
0.8700
0.9120
$$r_{2}$$
The survival rate of instar mealybugs that develop into adult mealybugs
0.7737
0.6079
0.6589
$$r_{3}$$
The fraction of female adult mealybugs
0.7400
0.7200
0.8500
$$v_{1}$$
The average number of eggs laid by a female adult mealybug in one time step
40.0000
36.5300
2.9126
• Green lacewings
$$\gamma_{1}$$
The fraction of green lacewing’s eggs that develop into larva green lacewing in one time step
0.1639
0.2222
0.2703
$$\gamma_{2}$$
The fraction of larva green lacewings that develop into pupa green lacewing in one time step
0.0521
0.0585
0.00625
$$\gamma_{3}$$
The fraction of pupa green lacewings that develop into adult green lacewings in one time step
0.0714
0.0885
0.1053
$$\delta_{2}$$
The natural death rate of adult green lacewings
0.0227
0.0175
0.0206
$$s_{1}$$
The survival rate of green lacewing’s eggs that develop into larva green lacewing
0.8040
0.8210
0.8170
$$s_{2}$$
The survival rate of larva green lacewing that develop into pupa green lacewing
0.9191
0.9629
0.7938
$$s_{3}$$
The survival rate of pupa green lacewing that develop into adult green lacewings
0.9586
0.9614
0.7402
$$s_{4}$$
The fraction of female adult green lacewings
0.5400
0.5500
0.4850
$$v_{2}$$
The average number of eggs laid by a female adult green lacewings in one time step
7.2789
5.8237
2.3876
Furthermore, the approximated total crop yield is also monitored. We also assume that the estimated crop yield is a kilograms per cassava plant if there is no mealybug in the cassava field. The estimated crop yield will be reduced by 100%, 30% and 10%, approximately, if mealybugs spread on the cassava plants during the first 4 months, during the 5th and the 7th month, and during the 8th and the 12th month, respectively, according to the surveys of the Thai Tapioca Development Institute in 2007-2010. Hence, the estimated crop yield at each time step, $$Y(t)$$, is then assumed to be represented by the following equation:
$$Y(t) = a\cdot C_{1}+(0.9\times a)\cdot C_{2}+(0.7\times a) \cdot C_{3},$$
(8)
where $$C_{1}$$ is the total number of susceptible cassava at the time step t, $$C_{2}$$ is the total number of cassava infested by mealybugs during the 8th and the 12th month at the time step t and $$C_{3}$$ is the total number of cassava infested by mealybugs during the 5th and the 7th month at the time step t.
## 3 Simulation results
In this section, numerical simulations at the three different temperatures 25C, 27C and 30C are carried out in order to investigate the effect of increased temperatures on the control of mealybugs.
When biological control is applied, we assume that the survey for the spread of mealybugs will be done every two weeks beginning one month after planting as recommended by many agricultural technical officers from the Thai Tapioca Development Institute and the Department of Agriculture, Ministry of Agriculture and Cooperatives, Thailand. According to the recommendation of the Department of Agricultural Extension, Ministry of Agriculture and Cooperatives, Thailand, the cassava field will be surveyed by collecting the numbers of mealybugs at all stages on the cassava plants that are not planted on the two rows next to the four borders of the cassava field. The survey will be conducted on every two rows of plants, and every 11 plants. On the cassava field of the size 80 m × 80 m with 1 m between two cassava plants, a cassava plant might be surveyed with the probability
\begin{aligned} f =&\text{the number of surveyed cassava plants in the field} \\ &{}\div\text{the total number of cassava plants that have not been removed} \\ &\text{from the cassava field.} \end{aligned}
Flow charts of the simulations are given in Figures 3-9. The results shown in Figures 10-15 are the averaged values of the 100 runs using MATLAB software. In the simulations, the parameters in the system of difference equations (1)-(7) are as in Table 1 where $$n_{1}=0.05$$, $$n_{2}=0.005$$, $$n_{3}=0.0005$$, $$w_{1}=0.001$$, $$w_{2}=0.0001$$, $$a=2.25$$, $$R_{1}=800$$, $$R_{2}=1{,}000$$ and
\begin{aligned}& \beta_{1} \bigl(P^{i}_{t}, M^{i}_{t} \bigr) = \min \biggl\{ 20, \frac {P^{i}_{t}(i,j)}{M^{i}_{t}(i,j)} \biggr\} , \\& \beta_{2} \bigl(P^{m}_{t}, M^{i}_{t} \bigr) = \min \biggl\{ 20, \frac {P^{m}_{t}(i,j)}{M^{i}_{t}(i,j)} \biggr\} , \\& \beta_{3} \bigl(P^{e}_{t}, M^{i}_{t} \bigr)= \min \biggl\{ 20, \frac {P^{e}_{t}(i,j)}{M^{i}_{t}(i,j)} \biggr\} , \\& \delta_{1} \bigl(P^{i}_{t},P^{m}_{t},P^{e}_{t},M^{i}_{t} \bigr)= 0.0521\times \min \biggl\{ 1, \frac {P^{i}_{t}(i,j)+P^{m}_{t}(i,j)+P^{e}_{t}(i,j)}{M^{i}_{t}(i,j)}\div60 \biggr\} . \end{aligned}
First, we investigate the spread of mealybugs when there is no biological control, when larva green lacewings are released to control the spread of mealybugs and when adult green lacewings are released to control the spread of mealybugs. The number of susceptible cassava plants, the number of infested cassava plants, the number of removed cassava plants and the estimated crop yield at 25C, 27C and 30C are as shown in Figures 10, 11, 12 and 13.
Next, the total numbers of larva and adult green lacewings that are released to control the spread of mealybugs in a cassava field at 25C, 27C and 30C are presented in comparison as shown in Figure 14. Moreover, the number of instar mealybugs when there is no biological control, when larva green lacewings are released to control the spread of mealybugs and when adult green lacewings are released to control the spread of mealybugs at 25C, 27C and 30C are also shown in Figure 15.
We can see from the simulation results that even though the average numbers of instar mealybugs is very high when a biological control is applied, the number of the infested cassava plants is not that high. This means that the spread of mealybugs can be controlled to be located on only a small number of cassava plants although the number of mealybugs might be high on those cassava plants. Here, snapshots showing the distribution of susceptible cassava, infested cassava and removed cassava in the cassava field of a simulation at 30C are also given in Figures 16 and 17 for a better understanding.
## 4 Discussion and conclusion
The increase in global temperatures affects the sex ratio, survival rate, reproduction rate and life cycle of both mealybugs and green lacewings. Simulations of the spread of mealybugs in a cassava field at 25C, 27C and 30C have been carried out.
Without biological control, the estimated crop yield decreases dramatically and tends to zero at 25C, and at 27C approximately 4 months after planting. At 30C, the estimated crop yield decreases and tends to a constant level which is lower than 30% of the maximum estimated crop yield.
With biological control, green lacewings at the larva stage or adult stage may be released in the cassava field to control the spread of mealybugs. Hence, we study both manners of biological control. We can see that the number of infested cassava plants decreases whereas the number of susceptible cassava plants increases when the temperature increases which might be the results of shorter life cycle, lower survival rate, lower fecundity and shorter adult longevity of mealybugs. We can also see that the release of green lacewing larva gives a better result when there is a spread of mealybugs even though the lower amount of larva green lacewing is released compared to adult green lacewings. The reasons for this might be the shorter life span, lower survival rate, lower fecundity or shorter adult longevity of green lacewings because only green lacewings at the larva stage behave like a predator of mealybugs and if we release adult green lacewings it will take a period of time before they will lay eggs which develop into green lacewing larva, finally behaving like a predator of mealybugs. With the increase of temperature, the survival rate and the fecundity rate are even lower and hence the greater amount of adult green lacewings should be released in the cassava field to control the spread of mealybugs. On the other hand, the estimated crop yield also increases when the temperature increases with the same level of released green lacewings. This implies that if farmers are satisfied with the estimated crop yield at the end of planting period when the temperature is 25C, they might reduce the number of green lacewings released in the cassava field so that the cost for biological control will be decreased and the farmers then earn more profit. On the other hand, if the farmers would like to gain more estimated crop yield at the end of planting period, they might keep the released amount of green lacewings at the same level as they use when the temperature is 25C. However, the cost for a green lacewings is approximately 0.50 baht (US$0.015) while the selling price for cassava is quite low, approximately 2.50 baht (US$0.072) per kilogram. Hence, the cost of biological control and the increase in crop yield should be calculated in order to obtain the most efficient biological control that maximizes profit.
## Notes
### Acknowledgements
This work was supported by the Development and Promotion of Science and Technology Talents Project (DPST), the Centre of Excellence in Mathematics, Thailand, The Thailand Research Fund and Mahidol University, Thailand (contract number RSA5880004).
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http://tex.stackexchange.com/tags/biblatex/new | # Tag Info
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You may create a customized command: \documentclass{article} \usepackage[style=authoryear,maxnames=3, backend=biber]{biblatex} \addbibresource{biblatex-examples.bib} % creation of \citeallnames command \newcommand\citeallnames{\AtNextCite{\defcounter{maxnames}{99}}\citename} \begin{document} This should print Aks\i{}n et al. (2006): \textcite{aksin} \...
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Using the BibLaTeX command \notecite{KEY} does what you want, i.e., it will create a back-reference, add the citation to your references, but it will not attempt to format a citation in the document itself. \notecite's intended use is for cases where you've included all the necessary details in text but you still want to leverage biblatex's other features, ...
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There is no general method to change a style. But in many simple cases it it possible to do it by looking at the code. In your case the title is handled by a simple boolean that you can switch locally: \documentclass{article} \usepackage[utf8]{inputenc} \usepackage[english]{babel} \usepackage{filecontents} \begin{filecontents*}{main.bib} @article{refA, ...
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Add the following redefinitions of macros from authoryear.bbx to your preamble The part for a) is a slightly modernised version of lockstep's answer to biblatex: How to remove the comma before ed./eds.? \makeatletter \DeclareFieldFormat{editortype}{\mkbibparens{#1}} \DeclareFieldFormat{parensbold}{\mkbibparens{\mkbibbold{#1}}} \newbibmacro*{bbx:editor}[1]{%...
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With the following compilable MWE I can see no problems. Please copy the MWE, run it on your system and compare the resulting PDF. If you have error messages or warnings please report them in your question. If you are using a different document class or bibliography style, please copy my MWE, change it to reflect your situation and add it to your ...
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I use BibTeX, here's my suggestion: A quick Google Scholar search comes up with this entry: @article{mclaughlin2009development, title={Development of an FCW algorithm evaluation methodology with evaluation of three alert algorithms}, author={McLaughlin, Shane B and Hankey, Jonathan M and Dingus, Thomas A and Klauer, Sheila G}, journal={National ...
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Beamer has its own mechanism to control colours, so the following motto applies \setbeamercolor{bibliography entry author}{fg=black} Same works for bibliography entry title, bibliography entry location, bibliography entry note and bibliography item.
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Biblatex 3.4 introduces new commands to define "delimiters" and these are context dependent. The format of a delimiter is defined by the command \DeclareDelimFormat[context]{delimiter}{code} The context can be used to indicate where the delimiter is used (bibliography, citation, in text citation and so on, and it is possible to defined new contexts). ...
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This was really a bug. It is fixed in biblatex 3.5 (requires biber 2.6) (both currently in DEV on Sourceforge). It is now possible to specify resetnumbers=false as normal to suppress the implicit reset. I contemplated revoking this implicit reset but I can see why it was implemented - people would often expect that a change of prefix (or perhaps the mere ...
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With biblatex 3.5+biber 2.6 (both currently in DEV on Sourceforge), this behaviour is finally fixed. It is now possible to override the implicit resetnumbers in the normal way (example updated for changes to prefixnumbers which moved into the refcontext mechanism with a name change to labelprefix in biblatex 3.3): \section{Part A1} \newrefcontext[...
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Based on Paul's answer, this is a drop-in replacement for the \IEEEtriggeratref macro that works with biblatex: \usepackage{ifthen} \makeatletter \newcounter{IEEE@bibentries} \renewcommand\IEEEtriggeratref[1]{% \renewbibmacro{finentry}{% \stepcounter{IEEE@bibentries}% \ifthenelse{\equal{\value{IEEE@bibentries}}{#1}} {\finentry\@IEEEtriggercmd}...
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If you don't want to see the parent entry conf1, you might want to have a look at the mincrossrefs option (pp. 51, 24 of the biblatex docs). By default it is set to 2. That means that if you have two entries in your bibliography that crossref the same entry, that entry is automatically added to the bibliography even if it wasn't cited. You can effectively ...
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I suggest you use the solution from Highlight an author in bibliography using biblatex allowing bibliography style to format it which in turn is based on Audrey's solution to Make specific author bold using biblatex, but with hashes instead of string comparison. Since in biblatex 3.3 some internal macros were renamed (see Biblatex 3.3 name formatting) you ...
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A possible workaround is to use \DeclareSourcemap to copy the value of the keywords list in a different field (let us say usera) and use this field to sort the entries. Here is the definition of the source map \DeclareSourcemap{ \maps[datatype=bibtex]{ \map[overwrite]{ \step[fieldsource=keywords] \step[fieldset=usera, origfieldval, final]...
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To make \sidecite consistent with \footcite we can add \bibfootnotewrapper to the wrapper command (originally we removed \mkbibfootnote, but with \bibfootnotewrapper we retain consistency) \DeclareCiteCommand{\sidecitehelper}[\bibfootnotewrapper] {\usebibmacro{prenote}} {\usebibmacro{citeindex}% \usebibmacro{cite}} {\multicitedelim} {\usebibmacro{...
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It seems like the option you need to set is Tex_BIBINPUTS. If you have modelines enabled, you can probably add a modeline in the specific files of your thesis to setup this variable, or you can set it in your .vimrc : let g:Tex_BIBINPUTS="path/to/bibfolder/"
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This is due to the default \DeclareNosort setting which strips two letters followed by a dash from strings before sorting. You can fix this by putting this in your preamble: \DeclareNosort{ \nosort{type_name}{\regexp{}} }
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The culprit is the line \DeclareFieldFormat[article,book,thesis,incollection,unpublished,inproceedings]{titlecase}{\MakeSentenceCase*{#1}}% \MakeSentenceCase* checks for the document language as saved in \bbl@main@language, since you load neither babel nor polyglossia, no such command is available and biblatex complains. The problem has been addressed in ...
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At the end I've found the solution by myself. I've deleted the code for the "unified hyperlinks" which was referred to authoryear, not to authoryear-icomp, and I've created my own \citet and \citep commands. Here is the code: \documentclass[11pt,openright]{book} \usepackage[T1]{fontenc} \usepackage[latin9]{inputenc} \usepackage{verbatim} \usepackage[...
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Recent version of biblatex removed the sorting option from \printbibliography and move it to \refcontext. Thus you have to add the \refcontexts for the bibliography you want to display. Accordingly, the MWE should look like \documentclass{article} \usepackage{filecontents} @book{test1, Author = {{Karl Marx}}, Title = {Capital}, Year = {1867}} ...
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You can use \DeclareFieldFormat for this, which allows formatting on a per-entry type. (I've changed your documentclass to article, since I don't have your class). Note: This is a temporary answer, which although it works has some problems as noted in the comments. I will update with a better solution. \documentclass[]{article} \begin{filecontents}{\...
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Try the options [alldates=terse, datezeros=false]
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journaltitle is a field in biblatex not bibtex, but \bibitems are used by bibliography created by bibtex and not for biblatex. The corresponding fielder bibtex is journal (which is also recognised by biblatex)
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Because you mentioned that you are willing to change to biblatex please see the MWE later. For biblatex are own styles defined, the one simular to your used rsc.bst is chem-rsc and best is to use biber instead of your used bibtex. The following code does what you need (package filecontents is only used to have bib file and tex code together in one ...
0
This is a rough solution... I hope someone else will improve it! \documentclass[nobib]{tufte-handout} \usepackage{xparse} \usepackage{xpatch} \usepackage[ style=verbose, autocite=footnote, backend=biber ]{biblatex} \addbibresource{biblatex-examples.bib} \makeatletter \xpatchcmd{\@footnotetext}% {\color@begingroup} {\color@begingroup\...
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Use in the bibliographische entry the url field: @article{ ... Url={https://en.wikipedia.org/wiki/Bidirectional_scattering_distribution_function}, }
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your bibliography style is trying to print https://en.wikipedia.org/wiki/Bidirectional_scattering_distribution_function as text but _ is the math subscript command so generates an error if used in text, you need to make sure that your URL are either in bibliography fields that are just used for URL in which case the bibliography style can quote them ...
1
The keyword field is a comma separated list. If you just append doe to a list like keya,keyb you get keya,keybdoe, but of course you want keya,keyb,doe, so you need to append ,doe (that may leave you with an empty entry if the keyword field was empty, you might even get a warning, but you can ignore it). You would then use \DeclareSourcemap{ \maps[...
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When two variants exists for a term, then you get the longer term with the option abbreviate=false -- this affects naturally all other terms too.
2
Here is a way of selectively removing n.d.: .bib file: @misc1{draftnotice, Author = {{COMMUNICATION FROM THE COMMISSION}}, Howpublished = {Draft Commission Notice of 2014 on the notion of State aid pursuant to Article 107 (1) TFEU}} @BOOK{Dodgson, AUTHOR = {Lewis Carroll}, TITLE = {The Hunting of the Snark}, PUBLISHER = {...
1
Regarding Question 1: Correct as per APA style? I believe that the examples and rules described under 6.16 in the APA Manual (6th ed.) indeed suggest that moewe’s solution gives us what the APA wants in such cases. The manual says that we must sort multiple citations within the same parentheses, “including citations that would otherwise shorten to et al.” (...
0
The bib-file with biblatex is incorporated with the command \addbibresource{Bibtest.bib} The command \bibliography is no longer valid. I would also recommend to remove the .aux file since it may contain information which is no longer valid.
5
This answer assumes biblatex version >= 3.4. We will have to change the code so it complies to the new name format (cf. Biblatex 3.3 name formatting). Furthermore I have changed the code to use name hashes instead of relying to recognise the names by string comparison. This feature only works properly if the uniquename feature is turned on (as if the case ...
2
The following example (with example.bib being your provided bib example) should do the trick: \documentclass{article} \usepackage[backend=biber, style=apa, sorting=nyt, sortcites=true]{biblatex} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage{lmodern} \addbibresource{example.bib} \begin{document} \cite{sarndal_estimation_2005} \end{...
0
If you just want your multi-citations to appear in the order that you cite them, while keeping your bibliography sorted, you need to specify sortcites=false when you load biblatex. For example: \usepackage[style=authoryear,sorting=nyt,sortcites=false]{biblatex} I owe this to @UlrikeFischer's comment, but because I missed it on first read, I thought I ...
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Adding square brackets around the raised citations can be done from the natbib package with one simple command: \usepackage[super,square]{natbib}
0
It is kind of sad, but it seems like some weird condition, buried within the arcane maze of texlive internals, caused this problem. The following hack provides a quick workaround: \newlength{\bibhang} \setlength{\bibhang}{5mm} But ultimately, I don't see a solution other than installing texlive 2016 after all. Thanks for all the helpful comments! As ...
0
If you modify the editor macros anyway you can switch from \bibstring which gives context sensitive capitalisation to \bibcpstring which capitalises all the time. For example \makeatletter \renewbibmacro*{editor+othersstrg}{% \iffieldundef{editortype} {\ifboolexpr{ test {\ifnumgreater{\value{editor}}{1}} or test {\ifandothers{...
1
The answer is given here http://tex.stackexchange.com/a/207676/8917 Replacing citefield with citename for entry author. For the entry journal one has to use journaltitle even though the entry is called journal in the bibfile. \item \citename{example}{author} \item \citefield{example}{journaltitle}
1
Use the label field: @online{texse, url={http://tex.stackexchange.com}, title={Awesome website}, label={TexSE}, }
2
You can set a prenote - arbitrary text - to be used just after the heading has been set: \defbibnote{legaldoc}{\markboth{Legal Documents}{Legal Documents}} \printbibliography[title=Legal Documents,prenote=legaldoc] The above legaldoc note overrides whatever other marks have been set.
2
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The prefixnumbers is no longer supported on the most recent version of biblatex. \begin{filecontents}{\jobname.bib} @InProceedings{Baader1989, Title = {Direct self control of inverter-fed induction machine, a basis for speed control without speed-measurement}, Author = {Baader, U. and Depenbrock, M. and Gierse, Georg}...
1
You can go down the route from biblatex-biber: How to customize the order in the bibliography?. Call citestyle=numeric (or the member of the numeric family you currently use) and bibstyle=authoryear, then import numeric.bbx to get the proper bibliography environment again. (The sorting will by default be sorting=nyt, if you want sorting=none you will need ...
0
You can combine them: \documentclass{article} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage[citestyle=numeric,bibstyle=authoryear]{biblatex} \addbibresource{biblatex-examples.bib} \AtEveryBibitem{[\printfield{labelnumber}]\addspace}%Numbers in the bib \begin{document} \cite{herrmann}, \cite{doody}, \printbibliography \end{...
5
Author names in the bib file must be separated by 'and' not commas. So the correct bib file entry should look like this: @article{Übeyli, title={An alternative model for mixtures of experts}, author={Xu, L. and Jordan, M.I. and Hinton, G.E.}, journal={Advances in neural information processing systems}, pages={633--640}, year={1995}, publisher={...
1
What you did is correct. For me there's just a small problem with your code: the apa style requires a \DeclareLanguageMapping declaration. Also, you should load csquotes. So add these lines to your preamble: \usepackage[english]{babel} \DeclareLanguageMapping{english}{english-apa} \usepackage{csquotes}
0
It looks like the problem is solved. It is hard to detect what and when went wrong, but apparently after the conflict between Biber and biblatex occurred (although it is still a mystery why it did occur in the first place) updating the Biber version from 2.4 to 2.5 didn't help because my Avast antivirus was blocking the biber.exe file.
2
Unfortunately, -comp styles are often a bit ugly to modify (one ends up with many lines of codes even for relatively trifling changes). The modification needed for the cite bibmacro, however, is straightforward. Replace the test \iffieldundef{shorthand} by \ifboolexpr{test {\iffieldundef{shorthand}} or not test {\ifciteseen}} and add \usebibmacro{...
3
You will find that @techreports get mapped to @report with type = {techreport}, while @phdthesis and @mastersthesis both get mapped to @thesis with type = {phdthesis} and type = {mastersthesis} respectively. So there is a way to differentiate the types, just not via the entry type, but the type field. I would have thought that the output for the types is ...
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http://ocve.koehler-paderborn.de/isometric-grid-angles.html | See Figure 3B-5. Vector image "Isometric Vector Seamless Grid Background - Thirty Degree Angle" can be used for personal and commercial purposes according to the conditions of the purchased Royalty-free license. Isometric - Grid points aligned along lines at 30° from design plane x-axis and y-axis. Use isometric grid paper (30, 90, 150 lines) or underlay paper to provide the axes and sketch the object. 5, 1) which simulates dimetric projection angles. I am planning on doing it from more angles though. The dimension OA is the Isometric dimension of Natural 35 mm. Isometric Worksheet 1. Or you can set textures directly in code. I created a set of 6 actions for Illustrator to help me create isometric illustrations, now I'm sharing them. Learn vocabulary, terms, and more with flashcards, games, and other study tools. A 1420 or 1425 wall angle is pop riveted to the lower corner to hold and cover the lay-in panel edges. Calculate the shape of ellipses using the Ordinates method. Choose the dot spacing, dot color, and dot size for each sheet. Just make sure you don't resize the grid using the sketch scale tool. Paper seamless pattern. As WeslomPo has mentioned, it's easier to get a grasp of if you consider that the actual game world remains top-down and conversions only happen when drawing things. To open the Preferences dialog box: Go to Settings > Preferences or press CTRL+K. Coordinates are used to describe locations. Getting started. Use a 90 corner to set the straight edge squarely on the paper. This graph paper is preferred by those people who need all three dimensions as their prime requirements. The QCad is released under the GNU General Public License. Grid with dots. (An Isometric grid is actually a special case of an Offset grid. Isometric Icons Bundle Desc A beautiful collection of Isometric icons built in 3D from the Flat icons you already know; all of them share the same palette, angles and construction, so they can be articulated together in a web or application. The isometric grid is made up of equilateral triangles. Tablet of 50 sheets of Isometric Grid Paper. I've actually recently started doing an isometric view of Cassalanter Villa, since that is my player's main villain. Mar 17, 2017- Explore kinzk70's board "Isometric grid", followed by 458 people on Pinterest. however, for a particular drawing i'd like to lie this assembly down flat and use that view. Specifically, you should know that the program provides you with isometric snap, grid and ortho. Flat icons is a good rule of thumb, but people tend to miss out on an exciting, new innovation: the isometric icon. Create an isometric drawing with a Block Diagram With Perspective template. /img/imp_fig11. Affinity Designer has a versatile grid system with some really good tools for things like icon design, and it also has isometric grids for doing graphics for games. A rigid transformation preserves angles as well as distances. Cisco Network Topology Icons. As for your isometric scene; if your viewing angle is 45 degrees, moving your mouse up 1 unit will give 1 unit on rhe map times a constant. An isometric image has no perspective and all parallel straight lines are at the same angle. Isometric strength or contraction refers to the muscle's ability to sustain tension while remaining static. Being a geometry of equal vectors and equal 60° angles, it is possible to extend this equilibrium array infinitely outward from the center point of the VE, producing what is called the Isotropic Vector Matrix (IVM). W hen it comes to a set of icons that everyone agrees is "well designed," your options may seem limited: flat or round icons. When you set the Snap Style setting to Isometric Snap and then set the Snap Isometric Pair setting to Left, Top or Right, the snap intervals, grid, and crosshairs align with the selected plane. This is used to draw a line in isometric view if that line’s angle was the same as in orthogonal view. Isometric graph paper or 3D graph paper is a triangular graph paper which uses a series of three guidelines forming a 60° grid of small triangles. com where we believe that there is nothing wrong with being square! This page includes Geometry Worksheets on angles, coordinate geometry, triangles, quadrilaterals, transformations and three-dimensional geometry worksheets. When I was a child I used to draw houses on plain paper until I discovered isometric graph paper, I would spend hours and hours drawing buildings. Find other pairs of non-congruent isosceles triangles which have equal areas. The triangles are arranged in groups of six to make hexagons. Solar on Grid & Grid Tie Systems - On Grid Solar PV Systems are also referred to as 'grid-direct systems', 'solar grid tie systems' or 'grid connect systems'. Using the back side of grid paper, your engineering notebook, or graph paper (as indicated by your instructor) recreate the two isometric views for practice. This grid is designed to create illustrations using isometric projection. Bluecurve icons are all drawn in isometric perspective in accordance with a particular grid. Isometric Space. with an isometric grid the basic shape of an equilateral triangle can be used to determine other angles see potentially earlier work on 7 pins later work can then focus on deciding upon and establishing (i. We recently released our ‘Complete Guide to Email Marketing’ and in this tutorial we will look at how to create your own isometric grid using Adobe Illustrator so that you can create a similar art style to that used in the guide, which you can use in your own email marketing material. The best thing about Isometric drawing is that each plane is in the same angle relative to the 'picture plane'. Draftsight is a 2D CAD program, but that doesn't mean you can't create an isometric view. Buying graph paper is not a problem. Isometric places the markers at 30 ° to horizontal for guiding isometric drawings. For over a year I was using isometric drawings on a daily basis. Select Grid & Snap from the Preferences dialog box to view or modify these preferences. It projects the length, width, and height of the diagram. That's the trick. Armed with the grid, some settings under Tools > Snap & Glue, and the Line tool, you can do a good job of drawing consistent “isometric” shapes, as long as they are fairly simple. This means that the planes of an object are projected onto three sloping planes. ISOMETRIC DRAWINGS Views use 30 degrees for lines showing ‘horizontals’ of the object: This is the most widely used drawing convention and you should be very confident that you know what the term ‘ Isometric ’ means. Escher's art and drawing three-dimensional forms using an isometric grid. Being an isometric game, there are many sprites in the player rotation animation, and I want the sprites to match up with a certain rotation. Reading Time: 4 minutes Using an Isometric Grid. In first four cases, you are prompted for size of coupling through a dialogue box. 344 degrees. I've got a question regarding SolidWorks 2010 Premium. Over 20 years experience as a Special Class pipe Welder, in a range of industries including: Oil &Gas, Pipelines, LNG, Petrochemical, Chemical, Power Generation, Mining, and live plant maintenance, shutdowns and construction, across a variety of challenging environments and conditions from workshops to construction sites Offshore and overseas. Your 30/60/90 triangle. Creating Isometric Sketches. edu/mjohnson/autocad/ChA. You can select different variables to customize the type of graph paper that will be produced. The purpose of this warm-up is to familiarize students with an isometric grid. the uniform grid setting is just a special case that the leaning angle of line “m” equals to zero. The QCad is released under the GNU General Public License. Two are smaller and one is larger than 60°. Isometric graph paper or 3D graph paper is a triangular graph paper which uses a series of three guidelines forming a 60° grid of small triangles. Grid & Snap Preferences. Using the back side of the printed grid paper will allow more contrast between your object lines and the grid lines. Isometric Graph Paper in. The I-225 line would take up way too much space with stations spaced too far apart if the isometric grid was adhered to, and the proliferation of commuter rail routes out of Union Station is almost impossible to convey with only a couple of viable angle options to work with. The pseudo-isometric view can let the player move diagonal as well, which would also result in 8 angles. I created a set of 6 actions for Illustrator to help me create isometric illustrations, now I'm sharing them. 768x800 Collection Of Flash Drive Isometric Drawing High Quality - Isometric Sketch Of A. Dot Size: points That is a 53. This angle is a combination of the magnetic declination (the True-to-Magnetic angle) and the Grid Variance (the Grid-to-True angle), rounded to the nearest degree. The triangles can be arranged in groups of six to make hexagons. Hexagonal ones use regular hexagons instead of squares. All of these types of engineering paper are great for sketching ideas and making hand drawings whenever you need to, and they work great for getting ideas down while you’re meeting with a new client. One of three different rhombuses can be selected and dragged to different positions on the grid. This is NOT an isometric grid. What is an Isometric graph paper? An Isometric graph paper is also named as the 3D graph paper. It's ideal for 3D-sketching. To produce an isometric projection, it is necessary to place the object so that its principal edges make equal angles with the plane of projection and are therefore foreshortened equally. A 60-degree grid of small triangles is formed on the paper. Orthogonal place the grid at right angles to the X and Y axis. It is similar to graph paper, except the horizontal lines are drawn at 30 degree angles to the vertical lines. Isometric Worksheet 2. In the Hexagonal graph paper, the grids are not in the shape of the square but in the shape of a hexagon which is known as hex grids. Here I’m creating the first part of our 3D illo: the square, or plane through which the arrow will pass. Vertical and diagonal lines are equally spaced to create this template. LINE From Point: {Click on the screen. tiling, or onto an integer grid of fixed or variable dimension [7]. Over 20 years experience as a Special Class pipe Welder, in a range of industries including: Oil &Gas, Pipelines, LNG, Petrochemical, Chemical, Power Generation, Mining, and live plant maintenance, shutdowns and construction, across a variety of challenging environments and conditions from workshops to construction sites Offshore and overseas. Ensure that your lower back is flat against the ground and you aren't tensing your neck or shoulders. in physics: see wave wave, in physics, the transfer of energy by the regular vibration, or oscillatory motion, either of some material medium or by the. See Figure 3B-5. Intro to Isometric Drawing Posted on July 27, 2012 by AutoCAD Tips AutoCAD has an isometric drawing mode that lets you drawing 3D-looking objects in 2D just like when you draw 3D objects on a flat sheet of paper. To create a grid you would first draw a line using the pen tool and constrain it vertically by holding the Shift key. The basic floor isometric grid is simply 2 lines in a 30 and 150 degree (120 degree separation) to the main grid of illustrator. Isometric grid paper is a convenient aid in sketching isometric drawings with both straight edges and circular features. What is Isometric (disambiguation)? Meaning of Isometric (disambiguation) medical term. If you set the snap style to isometric, the cursor will automatically change so that the horizontal line switches to a 30 degree angle. Make sure Ortho is activated and the crosshairs are set at 100% for easier visualization of planes. The triangles have a length along the y axis (the side of the column). Rather, it'd be used to calculate where the ball lands, rolls, etc. You have to then select, through dialog box, the angle of side branch. Age 11 to 14. Intra-articular length was calculated for each point on the femur to the tibia at all flexion angles and grouped to represent areas for bone tunnels. The primary difference is that the angle on Axonometric is 45 degrees whereas it’s 30 degrees for Isometric. Start studying Drafting 1: sketching. Offsets the grid's starting position from the top-left corner of the document, in pixels. The isometric grid is made up of equilateral triangles. Showing results for "isometric drawing" as the word app is considered too common Isometric Line Tool Free Adobe Illustrator plugin to draw straight lines constrained to isometric angles. Isometric Cubes Drawing Tool. We'll start by showing the grid. The player's movement is based on the direction they are pointing. Spike is large-scale, contemporary and crisp. Effects of pennation angle, electrodes orientation and knee angle on surface electromyography of vastus lateralis during isometric contractions. Is it really just a simple square grid? I know I can manually set up a grid using guides, but often from image to image I need to make minor adjustment to the angles of the axes. In this guide I will show you how to draw out a simple isometric house. To achieve this: a rotation about the horizontal axis of 45 degrees; followed by a rotation about the vertical axis by the arcsine of cosine 30 degrees. Free Isometric Graph Paper - "3D Paper" Download and print as many isometric graphing sheets as you need If you are making perspective illustrations of buildings, products, or other objects, a piece of paper with guide lines makes it much easier to maintain a consistent perspective throughout your illustration. Showing results for "isometric drawing" as the word app is considered too common Isometric Line Tool Free Adobe Illustrator plugin to draw straight lines constrained to isometric angles. The angles in the triangles all measure 60 degrees, making the isometric grid convenient for showing rotations of 60 degrees. 5'' at Blick. In manual drawing and sketching days, an isometric grid was used to lay out all lines before the lines were transferred to paper or Mylar for pen and ink drawings. Note that there is an axis that runs vertically and two other axes that make a 30° angle to the horizontal. /img/imp_fig11. Aligns snap and grid along 90- and 150-degree axes. Building Isometric Grid From Scratch. Main Style. Variations include the number of dots per inch, and the size of the paper (legal, letter, ledger, and A4). This grid is designed to create illustrations using isometric projection. As a treat, I added 2. These bends are reinforced with flat metal angles or corner caps. A regular polygon has all sides of equal length and all angles of equal measure. The vertical. Note that an isometric view created from a product can be re-used for generating an exploded view. Slide the 30 angle along the straight edge to make the part lines and construction lines at 30, 90, and 150. It provides the minimal amount of page support to line your drawings and equations up neatly and you can use as much or as little space as you need to create a coordinate plane, graph or other structure exactly where you want it on the page. An isometric image has no perspective and all parallel straight lines are at the same angle. Ground Projection. Coordinates in Source are (X, Y, Z), where X is forward/East, Y is left/North, and Z is up. the uniform grid setting is just a special case that the leaning angle of line “m” equals to zero. In manual drawing and sketching days, an isometric grid was used to lay out all lines before the lines were transferred to paper or Mylar for pen and ink drawings. Synonyms for isometric contraction phase in Free Thesaurus. Isometric Line Tool 12. I created a set of 6 actions for Illustrator to help me create isometric illustrations, now I'm sharing them. Sketch the objects in the same orientation that they are pictured in. The isometric paper is created from a grid of small triangles to simulate an isometric view or perhaps to aid in the triangle embroidery plan. 46 synonyms for phase: stage, time, state, point, position, step. You can create isometric graphics in Illustrator by using an isometric grid (as seen in the image below). It can sometimes be seen described as a ‘pictorial’ view. For 3D scenes you'll have to use gluUnproject. Find everything you need for your next creative project online. But when I import the assets in unity, they seem to have wrong angles: Never had a problem with this method. I create a variety of G-Rated content, appropriate for everyone. W hen it comes to a set of icons that everyone agrees is "well designed," your options may seem limited: flat or round icons. If you don't see a paper design or category that you want, please take a moment to let us know what you are looking for. PROGRAM for PIPING ISOMETRIC DRAWINGS draws coupling and you can continue drawing pipe line. Transfer the letters from the isometric drawing onto the same plane surfaces of the orthogonal drawing. Isometric Projection. The proper term is “piping isometric”. in default isometric view it is narrow, deep, and tall. These grid papers are not only used in the field of mathematics you can also make many other creative and artistic purposes. Now, for the Viewport to be the Isometric, be sure that it is set to parallel, set the target at the base (object side) of the camera view line, and. Dot Size: points That is a 53. Isometric grid paper is a convenient aid in sketching isometric drawings with both straight edges and circular features. Your crosshairs are now angled to show you which isoplane you are currently on and the Grid is laid out differently from what you may be used to. The triangles are arranged in groups of six to make hexagons. These Graph Paper PDF files range from speciality graph paper for standard grid, single quadrant graph paper, four quadrant graph paper, and polar coordinate graph paper. It is an axonometric projection in which the three coordinate axes appear equally foreshortened and the angle between any two of them is 120 degrees. When you switch from orthographic to isometric drawing, the grid and grid snap will change from a rectangular pattern to a diamond pattern corresponding to the isometric angles. In spite of its multiple grids and curves, I would label it an isometric, since the main grid of columns is close to the requisite 30-degree angle. A hexagonal grid paper is a three-dimensional on which you can make 3D shapes. 3 Profile Plane of Projection. Perspective drawing distorts the angles and shapes of objects to suggest form. NEN 2536 describes an isometric projection that is symmetric with regards to the vertical axis; the angle between the x- and y-axes, and between the z- and y-axes, is 60 degrees. Extension lines indicate the points between which the dimension figures apply. In this guide I will show you how to draw out a simple isometric house. If the Snap Angle is 0, the three isometric axes are 30 degrees, 90 degrees, and 150 degrees. Name each view. Press OK and you'll see that the grid is set up for isometric drawing for the left isoplane in 1/2 unit increments. 5D prototypes as well as your 2D maps. By using the ISODRAFT command, several system variables and settings are automatically changed to values that facilitate isometric angles. pdf Free Download Here Isometric Drawings - San Jose State University http://www. Rotate isometric view in 90 degree increments : With thanks to some fellow called Richard for sharing this on the discussion groups. I enjoy playing with isometric grids but I haven't built anything with one it quite a while. This uses vector mode and is designed for isometric art. Previously, I wrote about isometric drawing in AutoCAD. This is a graph paper generator for creating a custom grid to your specifications. I can't find any meaningful controls for Illustrator's grid. This 3D graph paper is formed using a string of three guidelines forming a grid of small equilateral triangles. Isometric Graph Paper Download this printable isometric graph paper and start learning to draw 3D objects. NET] Detect click on Isometric Grid Mini Spy. A second type of grid is called an isometric grid. Camera angle (54. In this article, I will tell you about making isometric dimension and text in an isometric drawing. * Figure 11. 291 icons spanning the full set of Cisco products plus miscellaneous icons useful in network diagramming. See Figure 3B-5. Using the back side of the printed grid paper will allow more contrast between your object lines and the grid lines. The default way these are made gives you parallel horizontal lines. Isometric Projection. Practice Your Math Skills With This Printable 2-Centimeter Graph Paper Charts And Graphs Math Charts Isometric Paper Geometry Dots Printables Drawings Graph Paper Math Skills Math Charts, Grids, Isometric Paper, Graph Paper. ISOMETRIC Photograph Isolated on grid and Green BG of a red Stapler Vector Seamless Colorful Geometric Blocks Isometric White Outline Grid Tiling Pattern isometric grid lines for isometric drawings. How to position the camera for isometric assets. Short animated lesson showing isometric grid angles. Questions? Call us at 1-800-234-3729. An isometric drawing is a type of 3D drawing that is set out using 30-degree angles. W hen it comes to a set of icons that everyone agrees is "well designed," your options may seem limited: flat or round icons. Notebook (Journal) Completed activity 3. In an isometric em-bedding, the unweighted distance between any two vertices in the graph equals theL 1 distance of their placements in the grid. It is most commonly used by artists to suggest depth and distance. This idea helps when sketching isometric pictorials on writing surfaces that do not have isometric grids. How can you create your assets so that they match the unity grid lines?. If it's an angle between points, quite often you can simply convert both points to isometric coordinates, and find an angle between those (now in isometric space). In this guide I will show you how to draw out a simple isometric house. How to design isometric buildings Published on January 29, Isometric grid setting. Previously, I wrote about isometric drawing in AutoCAD. In the 3D Extrude & Bevel options, use the Isometric Top preset to automatically set the angles to generate an accurate layout. “Iso” means „equal‟ and “metric projection” means „a projection to a reduced measure‟. If the Snap Angle is 0, the three isometric axes are 30 degrees, 90 degrees, and 150 degrees. Grids are a useful feature in any design software. Isometric Icons Bundle Desc A beautiful collection of Isometric icons built in 3D from the Flat icons you already know; all of them share the same palette, angles and construction, so they can be articulated together in a web or application. Use a 90 corner to set the straight edge squarely on the paper. , angles 45 deg. While students may notice and wonder many things, characteristics such as the measures of the angles in the grid and the diagonal parallel lines will be important properties for students to notice in their future work performing transformations on the isometric grid. This difference in angle gives 3 dimensional drawings a bit of a distorted look. To achieve this: a rotation about the horizontal axis of 45 degrees; followed by a rotation about the vertical axis by the arcsine of cosine 30 degrees. Isometry is often used in engineering drafting and design, for example in computer games. Is there a way to exclude this layer from the unlock all command? As a default, Illustrator seems to constrain angles in 45°: increments: 45°, 90°, 135°, 180° ect. 5 inches in size, with the perfect Isometric Dot Grid in light grey from edge to edge of each page. Angles project true size only when the plane containing the angle and plane of projection are this: The angle between each axis for an isometric drawing is. Isometry Grid 2. Lines, Rays, and Angles. with an isometric grid the basic shape of an equilateral triangle can be used to determine other angles see potentially earlier work on 7 pins later work can then focus on deciding upon and establishing (i. Choose Edit > Preferences > Performance. Calculate the shape of ellipses using the Ordinates method. See more ideas about Isometric drawing, Drawings and Isometric grid. isometric drawings on Visio 30,60,150 degree angles. Printable dot paper is a lighter weight approach to standard graph paper. You can nudge the most recent addition by using the up down left right keys. Learn about grids and coordinates with this interactive grid game for kids. Practice Your Math Skills With This Printable 2-Centimeter Graph Paper Charts And Graphs Math Charts Isometric Paper Geometry Dots Printables Drawings Graph Paper Math Skills Math Charts, Grids, Isometric Paper, Graph Paper. Coordinates in Source are (X, Y, Z), where X is forward/East, Y is left/North, and Z is up. Click OK to exit drafting settings window. Isometric Graph Paper in. Tell them that this work of art was created in 1969 by an artist named Victor Vasarely. The drawing in the render above wouldn't be seen by the player. Study the isometric views that follow. Principles of Dimensioning RULES for the use of the dimension form. Isometric drawing is a way of 3D representation of an object on 2D surface. It is commonly used in engineering, architecture and related fields. Scale 1:2 This means that a centimetre in your drawing shows two centimetres in real life. Hexagon is a polygon but with six sides. This grid is designed to create illustrations using isometric projection. You can e-mail me if you want to further refresh your memory in either case. You can load an isometric map file (which is a JSON file describing which terrain textures go where, and, if there are any game objects on the map, where they are and what they do). Drafting settings window will pop up from this window select snap and grid tab and make sure Isometric snap radio button is checked. The camera angle used by most "isometric" games is actually 30 degrees (a true isometric view where the x, y, and z axis have the same length is 35. Author: harley Created Date: 4/10/1999 11:15:25 AM. A true time saving tool for graphic artists and icon builder. But have you tried to annotate your isometric drawings? How about dimensions and text, is it appear properly? No it’s. Since an isometric projection of an object will show that object in a three dimensional view, the isometric graph paper must have three axes. Isometric Sketches Answer Key Purpose How do reading the face of a clock and sketching isometric pictorials relate to each other? Picture a cube in your mind. How can I prove the sum of the highlighted angles in the following 3 times 3 square grid is equal to $\pi$? 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. 5'' at Blick. Toggle the grid on and off from the Status bar. Isometric graph paper or 3D graph paper is a triangular graph paper which uses a series of three guidelines forming a 60? grid of small triangles. The default way these are made gives you parallel horizontal lines. Building Isometric Grid From Scratch. These are the proportions of an isometric grid, as in Gravit. For example anything using the cartesian system can make use of graph paper since the cartesian system which is essentially a grid. The above online tool is great for drawing Isometric cubes. Circles on the isometric planes appear as ellipses in isometric sketches. Ø It's popular within the process piping industry because it can be laid out and drawn with ease and portrays the object in a realistic view. The proportions along each axis are in the ratio 1:1:1. Here is a collection of free isometric graph paper to print. The links below are to worksheets we found on the Internet for Isometric Drawing. It is used for isometric views or pseudo-three dimensional views. From the two angles needed for an isometric projection, the value of the second may seem counter intuitive and deserves some further explanation. Controls the look. Therefore, you will receive polar paper at various angles or radii, depending on your requirement. One of three different rhombuses can be selected and dragged to different positions on the grid. Go to Object > Expand Appearance to permanently apply the 3D effect and convert the text into a series of individual face shapes. These are ready to install kits that will be connected to the grid or energy power supply in order to continue with the supply even when the solar system fails to produce adequate energy for your home. doc Author: Administrator Created Date: 9/12/2003 12:50:21 PM. however , i find 26. Free Isometric Graph Paper - "3D Paper" Download and print as many isometric graphing sheets as you need If you are making perspective illustrations of buildings, products, or other objects, a piece of paper with guide lines makes it much easier to maintain a consistent perspective throughout your illustration. If you set the snap style to isometric, the cursor will automatically change so that the horizontal line switches to a 30 degree angle. Age 11 to 14. Sketch the objects in the same orientation that they are pictured in. Two-point perspective drawing via Keo. The symbols that represent fittings, Valves and flanges are modified to adapt to the isometric grid. three dimensional joints in joinery). an isometric drawing is a one view drawing that shows both elevation and location of building materials and also manufactured parts. The proper term is “piping isometric”. For people who have no background in engineering or architectural, a multi-view drawing can be difficult to understand. The cube opposite, has been drawn in isometric projection. The best thing about Isometric drawing is that each plane is in the same angle relative to the 'picture plane'. Download 130+ Royalty Free Isometric Graph Paper Grid Vector Images. You can also undo and erase segments with ease. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Creating an isometric drawing. We’re going to show you step-by-step how to start from the beginning. Template page News : 23-Apr-2019 - Added A4 size Template page with ISO Grid for creating 3D Isometric Topology diagrams. This is used to draw a line in isometric view if that line’s angle was the same as in orthogonal view. The triangles are arranged in groups of six to make hexagons. 344 degrees. I want to know what is the better angle for drawing isometric stuff , Searching came up with 30 or 26. Isometric drawings can be used by product/industrial designers to help sell new product concepts. You will apply your sketching skills in later that are not given in isometric orientation and to represent your ideas and designs. Draftsight Highlights – Easily draw “Isometric Views” within Draftsight. You can chose from 3x3 or 4x4 grid sizes and select from several pictures, you unlock more as you go. Using Orthagonal, Isometric and oblique drawing in 2D Design. In classes such as algebra and algebra II, graph paper is essential to accurately draw x and y coordinates, functions, and quadratic equations. Direct students to view this image of an optical illusion. Transfer the letters from the isometric drawing onto the same plane surfaces of the orthogonal drawing. Paper seamless pattern. With snap activated, the pointer selects only points positioned directly on the snap grid. Previously, I wrote about isometric drawing in AutoCAD. Drawing Paper Engineering Supply has a broad selection of drawing paper for engineers and architects, including isometric paper (which can be used to draw three-dimensional figures). The name suggests the use for isometric views or pseudo-three-dimensional views. Grid Background One two three - vector puzzle pieces with numbers Isometric graph paper Binary data zero one assembler coding flat isometric vector 3d Isometric road elements. This time, we'll cover two ways on how to make an isometric grid. doc Author: Administrator Created Date: 9/12/2003 12:50:21 PM. | {"extraction_info": {"found_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": 0.21790505945682526, "perplexity": 1488.0064775491871}, "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-2019-47/segments/1573496668699.77/warc/CC-MAIN-20191115171915-20191115195915-00078.warc.gz"} |
https://docs.galpy.org/en/v1.8.1/reference/aaecczmaxrperirap.html | # galpy.actionAngle.actionAngle.EccZmaxRperiRap¶
actionAngle.EccZmaxRperiRap(*args, **kwargs)[source]
NAME:
EccZmaxRperiRap
PURPOSE:
evaluate the eccentricity, maximum height above the plane, peri- and apocenter
INPUT:
Either:
1. R,vR,vT,z,vz[,phi]:
1. floats: phase-space value for single object (phi is optional) (each can be a Quantity)
2. numpy.ndarray: [N] phase-space values for N objects (each can be a Quantity)
2. Orbit instance: initial condition used if that’s it, orbit(t) if there is a time given as well as the second argument
OUTPUT:
(e,zmax,rperi,rap)
HISTORY:
2017-12-12 - Written - Bovy (UofT) | {"extraction_info": {"found_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": 0.6990008354187012, "perplexity": 10267.887053580118}, "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/1669446711126.30/warc/CC-MAIN-20221207021130-20221207051130-00269.warc.gz"} |
http://blog.nguyenvq.com/blog/2011/03/14/alt-key-and-copy-paste/ | # Xterm – Alt key and copy + paste
I recently went back to using xterm as my default terminal since in Gnome-Terminal, Alt-V gets sent to the menu, and not to emacs when it is running. In Xterm, the Alt key did not work immediately; it gave me wierd characters. This post shows me how to fix the problem (put in ~/.Xresources instead). Also, copy and paste does not work intuitively by default. This post shows a fix. Both involves tweaking the options in ~/.Xresources. | {"extraction_info": {"found_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": 0.5157638788223267, "perplexity": 3927.1397712871235}, "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/1521257645405.20/warc/CC-MAIN-20180317233618-20180318013618-00744.warc.gz"} |
http://www.polar.ox.ac.uk/publication/a-lagged-response-to-the-11-year-solar-cycle-in-observed-winter-atlanticeuropean-weather-patterns/ | # A lagged response to the 11 year solar cycle in observed winter Atlantic/European weather patterns
Peer Reviewed
Gray LJ, Scaife AA, Mitchell DM, Osprey S, Ineson S, Hardiman S, Butchart N, Knight J, Sutton R, & Kodera K
Journal of Geophysical Research: Atmospheres 118, Issue 24, pages 13,405–13,420, 2013, 10.1002/2013JD020062.
The surface response to 11 year solar cycle variations is investigated by analyzing the long-term mean sea level pressure and sea surface temperature observations for the period 1870–2010. The analysis reveals a statistically significant 11 year solar signal over Europe, and the North Atlantic provided that the data are lagged by a few years. The delayed signal resembles the positive phase of the North Atlantic Oscillation (NAO) following a solar maximum. The corresponding sea surface temperature response is consistent with this. A similar analysis is performed on long-term climate simulations from a coupled ocean-atmosphere version of the Hadley Centre model that has an extended upper lid so that influences of solar variability via the stratosphere are well resolved. The model reproduces the positive NAO signal over the Atlantic/European sector, but the lag of the surface response is not well reproduced. Possible mechanisms for the lagged nature of the observed response are discussed.
Keywords: Solar cycle, Climate
Categories: Arctic, Natural Science | {"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": 0.8834395408630371, "perplexity": 3710.840595211744}, "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/1634323588246.79/warc/CC-MAIN-20211028003812-20211028033812-00064.warc.gz"} |
https://robotics.stackexchange.com/questions/5095/following-a-trajectory-with-lqr-controller/5100 | # following a trajectory with LQR controller
We want our wheeled robot to follow a (rather short) trajectory. We wrote an LQR controller, which works well in simulation. However, our robot offers two problems:
1.) The reported state information does not seem to be very accurate.
2.) Its motion seems to underly some random deviations. We did not succeed in establishing a good model to predict the robots motion with a given control input.
Is it possible to manage these problems with the LQR controller? If yes, how?
It is possible under limited conditions. The Linear-quadratic regulator (LQR) controller assumes that the system under control has linear dynamics and that the transition and observation models are deterministic. While in practice it works if these conditions are violated, the more extreme the violation the more likely it is to fail.
An alternative is the Linear-quadratic-gaussian controller because it allows for noise in the motions and percepts. A challenge with using LQG is that you must have model of the noise.
More specifically, assume you have the following dynamical model:
$\dot{\mathbf{x}}(t) = A\mathbf{x}(t) + B\mathbf{u}(t) + \mathbf{v}(t), \mathbf{v}(t) \sim \mathcal{N}(0, M) \\ \mathbf{y}(t) = C\mathbf{x}(t) + \mathbf{w}(t), \mathbf{w}(t) \sim \mathcal{N}(0, N)$
where $\mathbf{x}(t)$, and $\mathbf{u}(t)$ represent the state of the system and the control applied to at it at time $t$ respectively, $A$, $B$, and $C$ represent the natural dynamics, the control dynamics, and the observation dynamics respectively, and finally $\mathbf{v}(t)$ and $\mathbf{w}(t)$ represent noise of the motion and observation models respectively and are zero mean gaussian distributions with covariances $M$ and $N$.
In order to use LQG you need to know $A$, $B$, $C$, $M$, and $N$ as well as the initial state of the system, i.e. $\mathbf{x}(0)$.
It depends on the actual source of problems. If you just have a lot of noise in your state estimate you can improve things a bit by adjusting weights to be less aggressive.
If the problem is that your state estimate is consistently far off you can't do anything until you fix your estimator. Quite often in vehicle control this is actually the biggest challenge. | {"extraction_info": {"found_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": 0.884979784488678, "perplexity": 365.80511911697704}, "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/1566027313715.51/warc/CC-MAIN-20190818062817-20190818084817-00112.warc.gz"} |
https://ntguardian.wordpress.com/2016/09/19/introduction-stock-market-data-python-1/?utm_campaign=Revue%20newsletter&utm_medium=Newsletter&utm_source=revue | # An Introduction to Stock Market Data Analysis with Python (Part 1)
This post is the first in a two-part series on stock data analysis using Python, based on a lecture I gave on the subject for MATH 3900 (Data Science) at the University of Utah. In these posts, I will discuss basics such as obtaining the data from Yahoo! Finance using pandas, visualizing stock data, moving averages, developing a moving-average crossover strategy, backtesting, and benchmarking. The final post will include practice problems. This first post discusses topics up to introducing moving averages.
NOTE: The information in this post is of a general nature containing information and opinions from the author’s perspective. None of the content of this post should be considered financial advice. Furthermore, any code written here is provided without any form of guarantee. Individuals who choose to use it do so at their own risk.
## Introduction
Advanced mathematics and statistics has been present in finance for some time. Prior to the 1980s, banking and finance were well known for being “boring”; investment banking was distinct from commercial banking and the primary role of the industry was handling “simple” (at least in comparison to today) financial instruments, such as loans. Deregulation under the Reagan administration, coupled with an influx of mathematical talent, transformed the industry from the “boring” business of banking to what it is today, and since then, finance has joined the other sciences as a motivation for mathematical research and advancement. For example one of the biggest recent achievements of mathematics was the derivation of the Black-Scholes formula, which facilitated the pricing of stock options (a contract giving the holder the right to purchase or sell a stock at a particular price to the issuer of the option). That said, bad statistical models, including the Black-Scholes formula, hold part of the blame for the 2008 financial crisis.
In recent years, computer science has joined advanced mathematics in revolutionizing finance and trading, the practice of buying and selling of financial assets for the purpose of making a profit. In recent years, trading has become dominated by computers; algorithms are responsible for making rapid split-second trading decisions faster than humans could make (so rapidly, the speed at which light travels is a limitation when designing systems). Additionally, machine learning and data mining techniques are growing in popularity in the financial sector, and likely will continue to do so. In fact, a large part of algorithmic trading is high-frequency trading (HFT). While algorithms may outperform humans, the technology is still new and playing in a famously turbulent, high-stakes arena. HFT was responsible for phenomena such as the 2010 flash crash and a 2013 flash crash prompted by a hacked Associated Press tweet about an attack on the White House.
This lecture, however, will not be about how to crash the stock market with bad mathematical models or trading algorithms. Instead, I intend to provide you with basic tools for handling and analyzing stock market data with Python. I will also discuss moving averages, how to construct trading strategies using moving averages, how to formulate exit strategies upon entering a position, and how to evaluate a strategy with backtesting.
DISCLAIMER: THIS IS NOT FINANCIAL ADVICE!!! Furthermore, I have ZERO experience as a trader (a lot of this knowledge comes from a one-semester course on stock trading I took at Salt Lake Community College)! This is purely introductory knowledge, not enough to make a living trading stocks. People can and do lose money trading stocks, and you do so at your own risk!
## Getting and Visualizing Stock Data
### Getting Data from Yahoo! Finance with pandas
Before we play with stock data, we need to get it in some workable format. Stock data can be obtained from Yahoo! Finance, Google Finance, or a number of other sources, and the pandas package provides easy access to Yahoo! Finance and Google Finance data, along with other sources. In this lecture, we will get our data from Yahoo! Finance.
The following code demonstrates how to create directly a DataFrame object containing stock information. (You can read more about remote data access here.)
import pandas as pd
import pandas.io.data as web # Package and modules for importing data; this code may change depending on pandas version
import datetime
# We will look at stock prices over the past year, starting at January 1, 2016
start = datetime.datetime(2016,1,1)
end = datetime.date.today()
# Let's get Apple stock data; Apple's ticker symbol is AAPL
# First argument is the series we want, second is the source ("yahoo" for Yahoo! Finance), third is the start date, fourth is the end date
apple = web.DataReader("AAPL", "yahoo", start, end)
type(apple)
C:\Anaconda3\lib\site-packages\pandas\io\data.py:35: FutureWarning:
The pandas.io.data module is moved to a separate package (pandas-datareader) and will be removed from pandas in a future version.
After installing the pandas-datareader package (https://github.com/pydata/pandas-datareader), you can change the import from pandas.io import data, wb to from pandas_datareader import data, wb.
FutureWarning)
pandas.core.frame.DataFrame
apple.head()
Open High Low Close Volume Adj Close
Date
2016-01-04 102.610001 105.370003 102.000000 105.349998 67649400 103.586180
2016-01-05 105.750000 105.849998 102.410004 102.709999 55791000 100.990380
2016-01-06 100.559998 102.370003 99.870003 100.699997 68457400 99.014030
2016-01-07 98.680000 100.129997 96.430000 96.449997 81094400 94.835186
2016-01-08 98.550003 99.110001 96.760002 96.959999 70798000 95.336649
Let’s briefly discuss this. Open is the price of the stock at the beginning of the trading day (it need not be the closing price of the previous trading day), high is the highest price of the stock on that trading day, low the lowest price of the stock on that trading day, and close the price of the stock at closing time. Volume indicates how many stocks were traded. Adjusted close is the closing price of the stock that adjusts the price of the stock for corporate actions. While stock prices are considered to be set mostly by traders, stock splits (when the company makes each extant stock worth two and halves the price) and dividends (payout of company profits per share) also affect the price of a stock and should be accounted for.
### Visualizing Stock Data
Now that we have stock data we would like to visualize it. I first demonstrate how to do so using the matplotlib package. Notice that the apple DataFrame object has a convenience method, plot(), which makes creating plots easier.
import matplotlib.pyplot as plt # Import matplotlib
# This line is necessary for the plot to appear in a Jupyter notebook
%matplotlib inline
# Control the default size of figures in this Jupyter notebook
%pylab inline
pylab.rcParams['figure.figsize'] = (15, 9) # Change the size of plots
apple["Adj Close"].plot(grid = True) # Plot the adjusted closing price of AAPL
Populating the interactive namespace from numpy and matplotlib
A linechart is fine, but there are at least four variables involved for each date (open, high, low, and close), and we would like to have some visual way to see all four variables that does not require plotting four separate lines. Financial data is often plotted with a Japanese candlestick plot, so named because it was first created by 18th century Japanese rice traders. Such a chart can be created with matplotlib, though it requires considerable effort.
I have made a function you are welcome to use to more easily create candlestick charts from pandas data frames, and use it to plot our stock data. (Code is based off this example, and you can read the documentation for the functions involved here.)
from matplotlib.dates import DateFormatter, WeekdayLocator,\
DayLocator, MONDAY
from matplotlib.finance import candlestick_ohlc
def pandas_candlestick_ohlc(dat, stick = "day", otherseries = None):
"""
:param dat: pandas DataFrame object with datetime64 index, and float columns "Open", "High", "Low", and "Close", likely created via DataReader from "yahoo"
:param stick: A string or number indicating the period of time covered by a single candlestick. Valid string inputs include "day", "week", "month", and "year", ("day" default), and any numeric input indicates the number of trading days included in a period
:param otherseries: An iterable that will be coerced into a list, containing the columns of dat that hold other series to be plotted as lines
This will show a Japanese candlestick plot for stock data stored in dat, also plotting other series if passed.
"""
mondays = WeekdayLocator(MONDAY) # major ticks on the mondays
alldays = DayLocator() # minor ticks on the days
dayFormatter = DateFormatter('%d') # e.g., 12
# Create a new DataFrame which includes OHLC data for each period specified by stick input
transdat = dat.loc[:,["Open", "High", "Low", "Close"]]
if (type(stick) == str):
if stick == "day":
plotdat = transdat
stick = 1 # Used for plotting
elif stick in ["week", "month", "year"]:
if stick == "week":
transdat["week"] = pd.to_datetime(transdat.index).map(lambda x: x.isocalendar()[1]) # Identify weeks
elif stick == "month":
transdat["month"] = pd.to_datetime(transdat.index).map(lambda x: x.month) # Identify months
transdat["year"] = pd.to_datetime(transdat.index).map(lambda x: x.isocalendar()[0]) # Identify years
grouped = transdat.groupby(list(set(["year",stick]))) # Group by year and other appropriate variable
plotdat = pd.DataFrame({"Open": [], "High": [], "Low": [], "Close": []}) # Create empty data frame containing what will be plotted
for name, group in grouped:
plotdat = plotdat.append(pd.DataFrame({"Open": group.iloc[0,0],
"High": max(group.High),
"Low": min(group.Low),
"Close": group.iloc[-1,3]},
index = [group.index[0]]))
if stick == "week": stick = 5
elif stick == "month": stick = 30
elif stick == "year": stick = 365
elif (type(stick) == int and stick >= 1):
transdat["stick"] = [np.floor(i / stick) for i in range(len(transdat.index))]
grouped = transdat.groupby("stick")
plotdat = pd.DataFrame({"Open": [], "High": [], "Low": [], "Close": []}) # Create empty data frame containing what will be plotted
for name, group in grouped:
plotdat = plotdat.append(pd.DataFrame({"Open": group.iloc[0,0],
"High": max(group.High),
"Low": min(group.Low),
"Close": group.iloc[-1,3]},
index = [group.index[0]]))
else:
raise ValueError('Valid inputs to argument "stick" include the strings "day", "week", "month", "year", or a positive integer')
# Set plot parameters, including the axis object ax used for plotting
fig, ax = plt.subplots()
if plotdat.index[-1] - plotdat.index[0] < pd.Timedelta('730 days'):
weekFormatter = DateFormatter('%b %d') # e.g., Jan 12
ax.xaxis.set_major_locator(mondays)
ax.xaxis.set_minor_locator(alldays)
else:
weekFormatter = DateFormatter('%b %d, %Y')
ax.xaxis.set_major_formatter(weekFormatter)
ax.grid(True)
# Create the candelstick chart
candlestick_ohlc(ax, list(zip(list(date2num(plotdat.index.tolist())), plotdat["Open"].tolist(), plotdat["High"].tolist(),
plotdat["Low"].tolist(), plotdat["Close"].tolist())),
colorup = "black", colordown = "red", width = stick * .4)
# Plot other series (such as moving averages) as lines
if otherseries != None:
if type(otherseries) != list:
otherseries = [otherseries]
dat.loc[:,otherseries].plot(ax = ax, lw = 1.3, grid = True)
ax.xaxis_date()
ax.autoscale_view()
plt.setp(plt.gca().get_xticklabels(), rotation=45, horizontalalignment='right')
plt.show()
pandas_candlestick_ohlc(apple)
With a candlestick chart, a black candlestick indicates a day where the closing price was higher than the open (a gain), while a red candlestick indicates a day where the open was higher than the close (a loss). The wicks indicate the high and the low, and the body the open and close (hue is used to determine which end of the body is the open and which the close). Candlestick charts are popular in finance and some strategies in technical analysis use them to make trading decisions, depending on the shape, color, and position of the candles. I will not cover such strategies today.
We may wish to plot multiple financial instruments together; we may want to compare stocks, compare them to the market, or look at other securities such as exchange-traded funds (ETFs). Later, we will also want to see how to plot a financial instrument against some indicator, like a moving average. For this you would rather use a line chart than a candlestick chart. (How would you plot multiple candlestick charts on top of one another without cluttering the chart?)
Below, I get stock data for some other tech companies and plot their adjusted close together.
microsoft = web.DataReader("MSFT", "yahoo", start, end)
# Below I create a DataFrame consisting of the adjusted closing price of these stocks, first by making a list of these objects and using the join method
AAPL GOOG MSFT
Date
2016-01-04 103.586180 741.840027 53.696756
2016-01-05 100.990380 742.580017 53.941723
2016-01-06 99.014030 743.619995 52.961855
2016-01-07 94.835186 726.390015 51.119702
2016-01-08 95.336649 714.469971 51.276485
stocks.plot(grid = True)
What’s wrong with this chart? While absolute price is important (pricy stocks are difficult to purchase, which affects not only their volatility but your ability to trade that stock), when trading, we are more concerned about the relative change of an asset rather than its absolute price. Google’s stocks are much more expensive than Apple’s or Microsoft’s, and this difference makes Apple’s and Microsoft’s stocks appear much less volatile than they truly are.
One solution would be to use two different scales when plotting the data; one scale will be used by Apple and Microsoft stocks, and the other by Google.
stocks.plot(secondary_y = ["AAPL", "MSFT"], grid = True)
A “better” solution, though, would be to plot the information we actually want: the stock’s returns. This involves transforming the data into something more useful for our purposes. There are multiple transformations we could apply.
One transformation would be to consider the stock’s return since the beginning of the period of interest. In other words, we plot:
$\text{return}_{t,0} = \frac{\text{price}_t}{\text{price}_0}$
This will require transforming the data in the stocks object, which I do next.
# df.apply(arg) will apply the function arg to each column in df, and return a DataFrame with the result
# Recall that lambda x is an anonymous function accepting parameter x; in this case, x will be a pandas Series object
stock_return = stocks.apply(lambda x: x / x[0])
AAPL GOOG MSFT
Date
2016-01-04 1.000000 1.000000 1.000000
2016-01-05 0.974941 1.000998 1.004562
2016-01-06 0.955861 1.002399 0.986314
2016-01-07 0.915520 0.979173 0.952007
2016-01-08 0.920361 0.963105 0.954927
stock_return.plot(grid = True).axhline(y = 1, color = "black", lw = 2)
This is a much more useful plot. We can now see how profitable each stock was since the beginning of the period. Furthermore, we see that these stocks are highly correlated; they generally move in the same direction, a fact that was difficult to see in the other charts.
Alternatively, we could plot the change of each stock per day. One way to do so would be to plot the percentage increase of a stock when comparing day $t$ to day $t + 1$, with the formula:
$\text{growth}_t = \frac{\text{price}_{t + 1} - \text{price}_t}{\text{price}_t}$
But change could be thought of differently as:
$\text{increase}_t = \frac{\text{price}_{t} - \text{price}_{t-1}}{\text{price}_t}$
These formulas are not the same and can lead to differing conclusions, but there is another way to model the growth of a stock: with log differences.
$\text{change}_t = \log(\text{price}_{t}) - \log(\text{price}_{t - 1})$
(Here, $\log$ is the natural log, and our definition does not depend as strongly on whether we use $\log(\text{price}_{t}) - \log(\text{price}_{t - 1})$ or $\log(\text{price}_{t+1}) - \log(\text{price}_{t})$.) The advantage of using log differences is that this difference can be interpreted as the percentage change in a stock but does not depend on the denominator of a fraction.
We can obtain and plot the log differences of the data in stocks as follows:
# Let's use NumPy's log function, though math's log function would work just as well
import numpy as np
stock_change = stocks.apply(lambda x: np.log(x) - np.log(x.shift(1))) # shift moves dates back by 1.
AAPL GOOG MSFT
Date
2016-01-04 NaN NaN NaN
2016-01-05 -0.025379 0.000997 0.004552
2016-01-06 -0.019764 0.001400 -0.018332
2016-01-07 -0.043121 -0.023443 -0.035402
2016-01-08 0.005274 -0.016546 0.003062
stock_change.plot(grid = True).axhline(y = 0, color = "black", lw = 2)
Which transformation do you prefer? Looking at returns since the beginning of the period make the overall trend of the securities in question much more apparent. Changes between days, though, are what more advanced methods actually consider when modelling the behavior of a stock. so they should not be ignored.
## Moving Averages
Charts are very useful. In fact, some traders base their strategies almost entirely off charts (these are the “technicians”, since trading strategies based off finding patterns in charts is a part of the trading doctrine known as technical analysis). Let’s now consider how we can find trends in stocks.
A $q$-day moving average is, for a series $x_t$ and a point in time $t$, the average of the past $q$ days: that is, if $MA^q_t$ denotes a moving average process, then:
$MA^q_t = \frac{1}{q} \sum_{i = 0}^{q-1} x_{t - i}$latex
Moving averages smooth a series and helps identify trends. The larger $q$ is, the less responsive a moving average process is to short-term fluctuations in the series $x_t$. The idea is that moving average processes help identify trends from “noise”. Fast moving averages have smaller $q$ and more closely follow the stock, while slow moving averages have larger $q$, resulting in them responding less to the fluctuations of the stock and being more stable.
pandas provides functionality for easily computing moving averages. I demonstrate its use by creating a 20-day (one month) moving average for the Apple data, and plotting it alongside the stock.
apple["20d"] = np.round(apple["Close"].rolling(window = 20, center = False).mean(), 2)
pandas_candlestick_ohlc(apple.loc['2016-01-04':'2016-08-07',:], otherseries = "20d")
Notice how late the rolling average begins. It cannot be computed until 20 days have passed. This limitation becomes more severe for longer moving averages. Because I would like to be able to compute 200-day moving averages, I’m going to extend out how much AAPL data we have. That said, we will still largely focus on 2016.
start = datetime.datetime(2010,1,1)
apple = web.DataReader("AAPL", "yahoo", start, end)
apple["20d"] = np.round(apple["Close"].rolling(window = 20, center = False).mean(), 2)
pandas_candlestick_ohlc(apple.loc['2016-01-04':'2016-08-07',:], otherseries = "20d")
You will notice that a moving average is much smoother than the actua stock data. Additionally, it’s a stubborn indicator; a stock needs to be above or below the moving average line in order for the line to change direction. Thus, crossing a moving average signals a possible change in trend, and should draw attention.
Traders are usually interested in multiple moving averages, such as the 20-day, 50-day, and 200-day moving averages. It’s easy to examine multiple moving averages at once.
apple["50d"] = np.round(apple["Close"].rolling(window = 50, center = False).mean(), 2)
apple["200d"] = np.round(apple["Close"].rolling(window = 200, center = False).mean(), 2)
pandas_candlestick_ohlc(apple.loc['2016-01-04':'2016-08-07',:], otherseries = ["20d", "50d", "200d"])
The 20-day moving average is the most sensitive to local changes, and the 200-day moving average the least. Here, the 200-day moving average indicates an overall bearish trend: the stock is trending downward over time. The 20-day moving average is at times bearish and at other times bullish, where a positive swing is expected. You can also see that the crossing of moving average lines indicate changes in trend. These crossings are what we can use as trading signals, or indications that a financial security is changing direction and a profitable trade might be made.
Visit next week to read about how to design and test a trading strategy using moving averages.
Update: An earlier version of this article suggested that algorithmic trading was synonymous as high-frequency trading. As pointed out in the comments by dissolved, this need not be the case; algorithms can be used to identify trades without necessarily being high frequency. While HFT is a large subset of algorithmic trading, it is not equal to it.
## 80 thoughts on “An Introduction to Stock Market Data Analysis with Python (Part 1)”
1. Thanks for this! Did you get to fix the weekend gaps in your candlestick charts? I’ve been trying to look for a more elegant solution to this. I want to remove the gaps — weekends and public holidays (when the market is closed). Thanks!
Like
• In this post only candlestick pattern chart is shown ; it is very hard to find a website or a forum where python code for renko , Three Line break ,point and figure patterns are summarized. Do any one of you have logic and python code for this pattern pls post and feedback to my e ma i l mbmarx gmail com
Like
2. Great article, thanks for writing! One nitpick though, “High Frequency Trading” is a subset (albeit very large subset) of “Algorithmic Trading”, not another name for it. There is absolutely no reason a trading algorithm has to have high turnover.
Liked by 1 person
3. candlestick_ohlc does no longer exist in matplotlib.finance.
I find another one called candlestick there. However, the generated chart is only black in color.
Like
4. OK, it’s easy to get the data having the ticker symbols. But how do we get the ticker symbols in the first place? If we check the market today we are introducing survivor bias in our analysis. This is the very first step and I’ve been having trouble with it so far. Thank you.
Like
5. I did some searching and it’s possible what you are asking for cannot be done with the APIs and packages used here. You may need to go to the exchange of interest (I.e. NASDAQ, NYSE etc.) and find the list, perhaps in a CSV file.
Like
6. For those of who don’t want a simpler version of the candlestick code, might I suggest you look into plotly, I got the same result with only about 6 lines of code. It did take a few hours of experimenting to get those six lines working, however.
Like
7. This is exactly the knowledge I’ve been trying to find. I’ve taken about 8 MOOC’s trying to find information that was concise and straight to the point, like your posts. Thank you very much for making my quest for writing financial strategies SO much easier. Please post more on this subject whenever you have time, or if you already have more information posted, could you leave me a link pointing me towards the site(s)???
Liked by 1 person
• I don’t have any more posts on finance data analysis. I REALLY want to write more for my blog (and I probably would write more on financial topics, if I could think up some; requests are welcome), but I tend to be very busy these days. But thank you for your kind words. 🙂
Like
8. Hi Curtis,
I am following the tutorial you put up for R here: https://www.r-bloggers.com/an-introduction-to-stock-market-data-analysis-with-r-part-1/. I got to this part :
if (!require(“magrittr”)) {
install.packages(“magrittr”)
library(magrittr)
}
stock_return % t % > % as.xts
But, I keep getting this error –
Error: unexpected ‘>’ in “stock_return % t % >”
Please how do I resolve this?
Like
9. Thanks for the post !
In this post and the second part, the moving average is computed by using the ‘Close’ price, why not use the ‘Adj Close’ directly ? such that in the second part, when we compute the profit, we don’t need to adjust there ?
Like
10. Line
apple[“20d”] = np.round(apple[“Close”].rolling(window = 20, center = False).mean(), 2)
[b]TypeError: round() takes at most 2 arguments (3 given)[/b]
i am using 2.7
Thanks.
—————————————————————————
TypeError Traceback (most recent call last)
in ()
—-> 1 apple[“20d”] = np.round(apple[“Close”].rolling(window = 20, center = False).mean(), 2)
2 #pandas_candlestick_ohlc(apple.loc[‘2016-01-04′:’2016-08-07′,:], otherseries = “20d”)
F:\Program Files\Anaconda2\lib\site-packages\numpy\core\fromnumeric.pyc in round_(a, decimals, out)
2784 except AttributeError:
2785 return _wrapit(a, ’round’, decimals, out)
-> 2786 return round(decimals, out)
2787
2788
TypeError: round() takes at most 2 arguments (3 given)
Like
11. This is a great tutorial, thank you for sharing. For anyone getting the following error:
“NameError: name ‘date2num’ is not defined”
I got around it by changing ‘date2num’ to ‘mdates.date2num’ and it worked.
Liked by 2 people
12. Wow, awesome code there, just had to copy it to python and try to run it. As soon as I ran the code I got this error message:
File “main.py”, line 16
%matplotlib inline
^
SyntaxError: invalid syntax
exited with non-zero status
It came from this section of the code:
import matplotlib.pyplot as plt # Import matplotlib
# This line is necessary for the plot to appear in a Jupyter notebook
%matplotlib inline
# Control the default size of figures in this Jupyter notebook
%pylab inline
pylab.rcParams[‘figure.figsize’] = (15, 9) # Change the size of plots
Can someone please help me out here, would definitely like to use this as example for other prediction models for stocks and commodities.
Cheers!
Like
• The line is an IPython magic function, which does not work in vanilla Python. Run in an IPython environment, like a Jupyter Notebook, or erase the calls to magic functions (but I make no promises about how the program will function if you do).
Like
• Python shell requires a specific plot.show(). So after commenting out the magic IPython IDE specific commands (%…) try this –
apple.plot(grid – True)
plt.show()
Like
• Yahoo! Finance no longer works. Replace source with “google” you’ll be good to go, but there will be a lot of stuff from these tutorials that won’t apply since Google only adjusts for stock splits.
Like
13. Hi Curtis,
I am happy to find this post. Thanks for your effort. I am a market technician (old school, price action / pattern trader) and profitable , but I miss too many opportunities in the market to make more money cause I dont know how to code.
So, after learning the basics of MatLab language, and doing my due diligence, I decided to change and learn Python.
My question is, If I want to use time series (10 years of daily data, high, open, close and low price, plus volume) to scan 4,000 stocks in a weekly basis. How exactly should I learn Python? I read about Panda (AQR capital management recommends it) in this post and other ones, and I also found that you use matplotlib, and other things, which I dont have a clue. And I struggled when I tried to download Python a week ago from their website. I also tried https://jupyter.org/ to learn the very basics, but it seems that it would not work for what i want.
My goal is to develop my proprietary trading software for swing trading using my trading style. If you can put some links or shed some light to understand this world. I would appreciate it !
Thanks a lot! keep the good work
BisTec
Like
14. Hello, I am a year 10 student, doing an extension project about coding a stock exchange monitor. I wanted to know if I could use your code as a base for my program, and if you had any other resources for stock exchange coding in python.
Thanks.
Like
• So long as you cite me in at least the comments and your report, go for it. Best of luck, and feel free to share what you do in the comments.
I’ve written other blog posts about using Python for finance. Some books on my reading list include Python for Finance by Yves Hilpisch and Mastering Python for Finance by James Ma Weiming. I would also recommend Wes McKinney’s Python for Data Analysis since he writes a lot about pandas (which he initially created) and pandas is very useful for finance (that’s the package’s original use case). I learn a lot by reading the tutorials developers of interesting packages write. If you’re interested in algo trading, consider the tutorials for the zipline package or backtrader. I have written a getting started post on backtrader and that is my preferred algo trading and backtesting package.
Like
15. Hi,
This very nice example . But when i tried to get the symbol historical data by pandas_datareader for NSE (Indian Stock exchange) i got error . even i have used NSE as exchange name it is not working
INFY = web.DataReader(“NSE;INFY”, “yahoo”, start, end).
Kindly help me understand how i can download NSE exchange historical data.
Regards
Purushottam
Like
16. Hi,
I am getting lots of error in “def pandas_candlestick_ohlc” in candlestick chart creation. Can you please fix.
Thanks & regards
Like | {"extraction_info": {"found_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": 16, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19308289885520935, "perplexity": 2348.750927683596}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867277.64/warc/CC-MAIN-20180526014543-20180526034531-00034.warc.gz"} |
http://cds.cern.ch/collection/All%20CERN%20Accelerators%20documents?ln=en | # All CERN Accelerators documents
Announcement
This new collection aggregates CERN accelerator-related documents on CDS. It will continuously be enriched and improved in the near future.
2014-08-22
23:03
Higher Order Mode Couplers Optimization for the 800 MHz Harmonic System for HL-LHC / Papadopoulos, Sotirios (CERN) This report summarizes the work that has been done during the authors stay at CERN as a summer school student. [...] CERN-STUDENTS-Note-2014-114. - 2014. Access to fulltext
2014-08-22
11:08
Mathias Luidor Heltberg Summer Student Report / Heltberg, Mathias Luidor (CERN) This report describes my work at the Summer Student Programme, where I have worked on the ATLAS detector, in the luminosity group, under the supervision of Eric Torrence. [...] CERN-STUDENTS-Note-2014-065. - 2014. Access to fulltext
2014-08-22
08:24
Study on o-momentum tail scraping in the LHC / Mirarchi, D ; Redaelli, S ; Bruce, R A study on o-momentum tail population in the LHC was performed through collimator scraping at high dispersion region. [...] CERN-ACC-NOTE-2014-0061. - 2014. - 13 p.
2014-08-21
18:48
Damage limits of accelerator equipment / Rosell, Gemma (CERN) Beam losses occur in particle accelerators for various reasons. [...] CERN-STUDENTS-Note-2014-059. - 2014. Access to fulltext
2014-08-21
17:18
Investigation of Coupling during the Non-Local Fast Extraction in the SPS / Alekou, A ; Bartosik, H ; Papaphilippou, Y The CENF (CERN Neutrino Facility) requires a high-intensity and high-energy beam (100 GeV) to be extracted in only one machine revolution from the Long Straight Section 2 (LSS2) of the SPS. [...] CERN-ACC-NOTE-2014-0060. - 2014. - 11 p. Full text
2014-08-18
08:06
Simulations Of The Acceleration In Two-Beam Test Stand In Ctf3 And Comparison With The Measurements / Kononenko, Oleksiy (CERN) The simulations of the beam acceleration in the presence of the structure's detuning are performed and a good agreement with the experimental results is demonstrated [...] CERN-OPEN-2014-040. - 2011. - 8 p. Preprint
2014-08-15
13:10
Electron Cloud studies with transverse beam islands / Pradhan, Neetish (CERN) Using 5 island and 3 island scrubbing beams to simulate electron cloud generation, with PyECloud.. CERN-STUDENTS-Note-2014-039. - 2014. Access to fulltext
2014-08-14
16:08
Future Circular Collider (FCC) Design Study / Herbie, Smith My project was part of the Future Circular Collider (FCC) design study . [...] CERN-STUDENTS-Note-2014-031. - 2014. Access to fulltext
2014-08-12
15:37
Recent Developments at the High-Charge PHIN Photoinjector and the CERN Photoemission Laboratory / Hessler, C ; Chevallay, E ; Doebert, S ; Fedosseev, V ; Martini, I ; Martyanov, M ; Perillo Marcone, A ; Sroka, S The high-charge PHIN photoinjector has originally been developed to study the feasibility of a photoinjector option for the drive beam of the CLIC Test Facility 3 (CTF3) at CERN and is now being used to inevestigate the feasibility of a drive beam photoinjector for CLIC. In this paper recent R&D; efforts to improve the parameters of the existing system towards CLIC requirements will be discussed. [...] CERN-ACC-2014-0193.- Geneva : CERN, 2014 - 4 p. Fulltext: PDF; In : 5th International Particle Accelerator Conference , Dresden, Germany, 15 - 20 Jun 2014, pp.4
2014-08-12
15:21
FEM Analysis of Beam-Coupling Impedance and RF Contacts Criticality of the LHC UA9 Piezo Goniometer / Danisi, A ; Zannini, C ; Passarelli, A ; Masi, A ; Losito, R ; Salvant, B The UA9 piezo-goniometer has been designed to guarantee micro-radians-accuracy angular positioning of a silicon crystal for a crystal collimation experiment in the LHC, and to minimize the impact on the LHC beam coupling impedance. This paper presents a Finite Element Method (FEM) study of the device, in both parking and operational positions, to evaluate its impact on the LHC impedance budget. [...] CERN-ACC-2014-0192.- Geneva : CERN, 2014 - 4 p. Fulltext: PDF; In : 5th International Particle Accelerator Conference , Dresden, Germany, 15 - 20 Jun 2014, pp.4 | {"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": 0.8261112570762634, "perplexity": 9608.346021582895}, "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-2014-35/segments/1408500825567.38/warc/CC-MAIN-20140820021345-00005-ip-10-180-136-8.ec2.internal.warc.gz"} |
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## GMATPrep RC - Economics
tagged by: mevicks
This topic has 2 member replies
mevicks Master | Next Rank: 500 Posts
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#### GMATPrep RC - Economics
Thu Oct 17, 2013 7:07 pm
Is it possible to decrease inflation without causing a recession and its concomitant increase in unemployment? The orthodox answer is "no." Whether they support the "inertia" theory of inflation (that today's inflation rate is caused by yesterday's inflation, the state of the economic cycle, and external influences such as import prices) or the "rational expectations" theory (that inflation is caused by workers' and employers' expectations, coupled with a lack of credible monetary and fiscal policies), most economists agree that tight monetary and fiscal policies, which cause recessions, are necessary to decelerate inflation. They point out that in the 1980's, many European countries and the United States conquered high (by these countries' standards) inflation, but only by applying tight monetary and fiscal policies that sharply increased unemployment. Nevertheless, some governments' policymakers insist that direct controls on wages and prices, without tight monetary and fiscal policies, can succeed in decreasing inflation. Unfortunately, because this approach fails to deal with the underlying causes of inflation, wage and price controls eventually collapse, the hitherto-repressed inflation resurfaces, and in the meantime, though the policy-makers succeed in avoiding a recession, a frozen structure of relative prices imposes distortions that do damage to the economy's prospects for long-term growth.
Which of the following, if true, would most strengthen the author’s conclusion about the use of wage and price controls?
A) Countries that repeatedly use wage and price controls tend to have lower long-term economic growth rates than do other countries.
B) Countries that have extremely high inflation frequently place very stringent controls on wages and prices in an attempt to decrease the inflation.
C) Some countries have found that the use of wage and price controls succeeds in decreasing inflation but also causes a recession.
D) Policymakers who advocate the use of wage and price controls believe that these controls will deal with the underlying causes of inflation.
E) Policymakers who advocate the use of wage and price controls are usually more concerned about long-term economic goals than about short-term economic goals.
The passage suggests that the high inflation in the United States and many European countries in the 1980’s differed from inflation elsewhere in which of the following ways?
A) It fit the rational expectations theory of inflation but not the inertia theory of inflation.
B) It was possible to control without causing a recession.
C) It was easier to control in those countries by applying tight monetary and fiscal policies than it would have been elsewhere.
D) It was not caused by workers’ and employers’ expectations.
E) It would not necessarily be considered high elsewhere.
The primary purpose of the passage is to
A) apply two conventional theories.
B) examine a generally accepted position
C) support a controversial policy
D) explain the underlying causes of a phenomenon
E) propose an innovative solution
OA: A E B
Last edited by mevicks on Sun Oct 20, 2013 7:29 pm; edited 1 time in total
sahilchaudhary Master | Next Rank: 500 Posts
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Test Date:
27 Dec 2013
Target GMAT Score:
700
GMAT Score:
540
Sun Oct 20, 2013 10:39 am
1. Conclusion - The author thinks that wage and price controls damage economy's prospects for long-term growth.
A - Correct (Seems best of all)
B - Irrelevant to the conclusion
C - Weakens, as the author says it helps to avoid recession
D - Weaken, as the author says they do not deal with underlying causes of inflation
E - Weaken, because if the policy makers thought about long term economic goals, they would have not used wage and price controls.
2. "They point out that in the 1980's, many European countries and the United States conquered high (by these countries' standards)"
A - Incorrect
B - Incorrect
C - Incorrect
D - Incorrect
E - Correct
3. The passage states 2 theories, then gives an example and then provides his own views.
A - Incorrect, as the author is not applying both the theories.
B - Incorrect, as the author is not examining a generally accepted position
C - Incorrect, as the author doesn't support it, but says that it fails to deal with the underlying causes of inflation.
D - Correct
E - Incorrect, as the author is not proposing a solution.
Please share the OA for the above questions.
If my answer/explanations are incorrect, please correct me.
_________________
Sahil Chaudhary
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mevicks Master | Next Rank: 500 Posts
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Sun Oct 20, 2013 7:27 pm
Nice explanations Sahil. The first two are correct, however the third one (which requires understanding the Big Picture of this convoluted passage) is indeed tricky when solving within strict time constraints.
Here are my 2 cents on the passage...
Main Idea (1st two lines):
It is actually not possible to decrease inflation without causing a recession and a corresponding increase in unemployment
Some keywords which point this out: Orthodox, most economists
Mapping:
Majority agree that tight monetary and fiscal policies reqd --> to reduce Inflation
(they might be supporting I-Theory or R-Theory BUT in the end agree on the above point)
US/Europe example provided to strengthen the above.
Some say that controls on wages and prices can decrease inflation without causing a recession (and dont support tight monetary and fiscal policies) --> This approach fails due to the reasons provided in the last line.
The primary purpose of the passage is to
A) apply two conventional theories.
Although 2 theories are mentioned (Inertia, Rational), they are not main point of the entire passage. The author only uses these theory to say something about the economists (economist support either of the two viewpoints)
B) examine a generally accepted position
This is not directly stated but if you consider the Big Picture this is indeed the answer. The word orthodox (conventional, generally accepted beliefs) signals this.
C) support a controversial policy
The author mentions a policy to which most economist agree (1st half), so there is no controversy as such
D) explain the underlying causes of a phenomenon
The author is not giving his viewpoints and justifying/detailing them. He is just presenting some facts and viewpoints of the economists.
E) propose an innovative solution
There is no innovation as such.
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See More Top Beat The GMAT Experts | {"extraction_info": {"found_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": 0.3332243859767914, "perplexity": 7164.212499544089}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125947328.78/warc/CC-MAIN-20180424202213-20180424222213-00235.warc.gz"} |
https://read.somethingorotherwhatever.com/entry/StatisticsDoneWrong | Statistics Done Wrong
• Published in 2015
If you’re a practicing scientist, you probably use statistics to analyze your data. From basic t tests and standard error calculations to Cox proportional hazards models and propensity score matching, we rely on statistics to give answers to scientific problems. This is unfortunate, because statistical errors are rife. Statistics Done Wrong is a guide to the most popular statistical errors and slip-ups committed by scientists every day, in the lab and in peer-reviewed journals. Many of the errors are prevalent in vast swaths of the published literature, casting doubt on the findings of thousands of papers. Statistics Done Wrong assumes no prior knowledge of statistics, so you can read it before your first statistics course or after thirty years of scientific practice.
BibTeX entry
@article{StatisticsDoneWrong,
title = {Statistics Done Wrong},
abstract = {If you’re a practicing scientist, you probably use statistics to analyze your data. From basic t tests and standard error calculations to Cox proportional hazards models and propensity score matching, we rely on statistics to give answers to scientific problems.
This is unfortunate, because statistical errors are rife.
Statistics Done Wrong is a guide to the most popular statistical errors and slip-ups committed by scientists every day, in the lab and in peer-reviewed journals. Many of the errors are prevalent in vast swaths of the published literature, casting doubt on the findings of thousands of papers. Statistics Done Wrong assumes no prior knowledge of statistics, so you can read it before your first statistics course or after thirty years of scientific practice.},
url = {https://www.statisticsdonewrong.com/},
author = {Alex Reinhart},
comment = {},
urldate = {2017-03-01},
collections = {Attention-grabbing titles,Lists and catalogues,Probability and statistics,Education},
year = 2015
} | {"extraction_info": {"found_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": 0.471425324678421, "perplexity": 1888.0719658851074}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347422803.50/warc/CC-MAIN-20200602033630-20200602063630-00420.warc.gz"} |
https://brilliant.org/problems/we-are-in-the-right-year-for-this-3/ | # We are in the right year for this! - (3)
Calculus Level 5
$\large \lim_{n\to\infty} \left( \frac{u_{n+1}}{u_1 u_2 u_3\cdots u_n}\right)^2$
Given a recurrence relation $$u_{n+1} = u_n ^2 - 2$$ with $$u_1 = \sqrt{2015}$$, find the value of the limit above.
× | {"extraction_info": {"found_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": 0.9431604146957397, "perplexity": 978.7872962438637}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607806.46/warc/CC-MAIN-20170524074252-20170524094252-00257.warc.gz"} |
http://libros.duhnnae.com/2017/aug/150164358342-Metrizable-TAP-HTAP-and-STAP-groups-Mathematics-General-Topology.php | # Metrizable TAP, HTAP and STAP groups - Mathematics > General Topology
Metrizable TAP, HTAP and STAP groups - Mathematics > General Topology - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.
Abstract: In a recent paper by D. Shakhmatov and J. Sp\v{e}v\-ak Group-valuedcontinuous functions with the topology of pointwise convergence, Topology andits Applications 2009, doi:10.1016-j.topol.2009.06.022 the concept of a\${ m TAP}\$ group is introduced and it is shown in particular that \${ m NSS}\$groups are \${ m TAP}\$. We prove that conversely, Weil complete metrizable\${ m TAP}\$ groups are \${ m NSS}\$. We define also the narrower class of \${ mSTAP}\$ groups, show that the \${ m NSS}\$ groups are in fact \${ m STAP}\$ andthat the converse statement is true in metrizable case. A remarkablecharacterization of pseudocompact spaces obtained in the paper by D. Shakhmatovand J. Sp\v{e}v\-ak asserts: a Tychonoff space \$X\$ is pseudocompact if and onlyif \$C pX,\mathbb R\$ has the \${ m TAP}\$ property. We show that for noinfinite Tychonoff space \$X\$, the group \$C pX,\mathbb R\$ has the \${ m STAP}\$property. We also show that a metrizable locally balanced topological vectorgroup is \${ m STAP}\$ iff it does not contain a subgroup topologicallyisomorphic to \$\mathbb Z^{\mathbb N}\$.
Autor: Xabier Domínguez Vaja Tarieladze
Fuente: https://arxiv.org/ | {"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": 0.9041504859924316, "perplexity": 18395.397894482612}, "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-2018-47/segments/1542039745015.71/warc/CC-MAIN-20181119023120-20181119045120-00360.warc.gz"} |
http://drake.mit.edu/doxygen_cxx/mobil__planner_8h_source.html | Drake
mobil_planner.h
Go to the documentation of this file.
1 #pragma once
2
3 #include <map>
4 #include <memory>
5 #include <utility>
6 #include <vector>
7
8 #include <Eigen/Geometry>
9
10
11 #include "drake/automotive/gen/idm_planner_parameters.h"
12 #include "drake/automotive/gen/mobil_planner_parameters.h"
23
24 namespace drake {
25 namespace automotive {
26
27 /// MOBIL (Minimizing Overall Braking Induced by Lane Changes) [1] is a planner
28 /// that minimizes braking requirement for the ego car while also minimizing
29 /// (per a weighting factor) the braking requirements of any trailing cars
30 /// within the ego car's immediate neighborhood. The weighting factor
31 /// encapsulates the politeness of the ego car to the surrounding traffic.
32 /// Neighboring cars are defined as those cars immediately ahead and behind the
33 /// ego, in the current lane and any adjacent lanes; these are determined from
34 /// the PoseSelector logic applied to a multi-lane Maliput road.
35 ///
36 /// The induced braking by the ego car and the car following immediately behind
37 /// it is compared with the induced braking by the ego and its new follower if
38 /// the ego were to move to any of the neighboring lanes. The choice that
39 /// minimizes the induced braking - alternatively maximizes the ego car's
40 /// "incentive" (the weighted sum of accelerations that the ego car and its
41 /// neighbors gain by changing lanes) - is chosen as the new lane request. The
42 /// request is expressed as a LaneDirection, that references a valid lane in the
43 /// provided RoadGeometry and the direction of travel.
44 ///
45 /// Assumptions:
46 /// 1) The planner supports only symmetric lane change rules, without giving
47 /// preference to lanes to the left or right.
48 /// 2) The planner assumes all traffic behaves according to the Intelligent
49 /// Driver Model (IDM).
50 /// 3) All neighboring lanes are confluent (i.e. with_s points in the same
51 /// direction).
52 ///
53 /// Instantiated templates for the following kinds of T's are provided:
54 /// - double
55 ///
56 /// They are already available to link against in the containing library.
57 ///
58 /// Input Port 0: A PoseVector for the ego car.
59 /// (InputPort getter: ego_pose_input())
60 ///
61 /// Input Port 1: A FrameVelocity for the ego car.
62 /// (InputPort getter: ego_velocity_input())
63 ///
64 /// Input Port 2: A BasicVector containing the ego car's commanded acceleration
65 /// value intercepted from the vehicle's controller (e.g. IdmController).
66 /// (InputPort getter: ego_acceleration_input())
67 ///
68 /// Input Port 3: A PoseBundle for the traffic cars, possibly including the ego
69 /// car's pose.
70 /// (InputPort getter: traffic_input())
71 ///
72 /// Output Port 0: A LaneDirection containing a lane that the ego vehicle must
73 /// move into and the direction of travel with respect to the lane's canonical
74 /// direction of travel. LaneDirection must be consistent with the provided
76 /// (OutputPort getter: lane_output())
77 ///
78 /// @ingroup automotive_controllers
79 ///
80 /// [1] Arne Kesting, Martin Treiber and Dirk Helbing, MOBIL: General
81 /// Lane-Changing Model for Car-Following Models, Journal of the
82 /// Transportation Research Board, v1999, 2007, pp 86-94.
83 /// http://trrjournalonline.trb.org/doi/abs/10.3141/1999-10.
84 template <typename T>
85 class MobilPlanner : public systems::LeafSystem<T> {
86 public:
87 typedef typename std::map<AheadOrBehind, const ClosestPose<T>> ClosestPoses;
88
90
91 /// A constructor that initializes the MOBIL planner.
92 /// @param road The pre-defined RoadGeometry.
93 /// @param initial_with_s The initial direction of travel in the lane
94 /// corresponding to the ego vehicle's initial state.
95 /// @param road_position_strategy Determines whether or not to memorize
96 /// RoadPosition. See calc_ongoing_road_position.h.
97 /// @param period_sec The update period to use if road_position_strategy ==
101 double period_sec);
102
103 /// See the class description for details on the following input ports.
104 /// @{
105 const systems::InputPort<T>& ego_pose_input() const;
106 const systems::InputPort<T>& ego_velocity_input() const;
107 const systems::InputPort<T>& ego_acceleration_input() const;
108 const systems::InputPort<T>& traffic_input() const;
109 const systems::OutputPort<T>& lane_output() const;
110 /// @}
111
112 /// Getters to mutable named-vector references associated with MobilPlanner's
113 /// Parameters groups.
114 /// @{
115 inline IdmPlannerParameters<T>& get_mutable_idm_params(
116 systems::Context<T>* context) const {
117 return this->template GetMutableNumericParameter<IdmPlannerParameters>(
118 context, kIdmParamsIndex);
119 }
120 inline MobilPlannerParameters<T>& get_mutable_mobil_params(
121 systems::Context<T>* context) const {
122 return this->template GetMutableNumericParameter<MobilPlannerParameters>(
123 context, kMobilParamsIndex);
124 }
125 /// @}
126
127 protected:
129 const systems::Context<T>& context,
131 systems::State<T>* state) const override;
132
133 private:
134 void CalcLaneDirection(const systems::Context<T>& context,
135 LaneDirection* lane_direction) const;
136
137 // Performs the calculations for the lane_output() port.
138 void ImplCalcLaneDirection(
139 const systems::rendering::PoseVector<T>& ego_pose,
140 const systems::rendering::FrameVelocity<T>& ego_velocity,
141 const systems::rendering::PoseBundle<T>& traffic_poses,
142 const systems::BasicVector<T>& ego_accel_command,
143 const IdmPlannerParameters<T>& idm_params,
144 const MobilPlannerParameters<T>& mobil_params,
145 const maliput::api::RoadPosition& ego_rp,
146 LaneDirection* lane_direction) const;
147
148 // Computes a pair of incentive measures for the provided neighboring lanes.
149 // The first and second elements in lanes correspond to, respectively, a
150 // pair of lanes included in the incentive query. The respective incentives
151 // for these lanes are returned as the first and second elements in the return
152 // value.
153 const std::pair<T, T> ComputeIncentives(
154 const std::pair<const maliput::api::Lane*, const maliput::api::Lane*>
155 lanes,
156 const IdmPlannerParameters<T>& idm_params,
157 const MobilPlannerParameters<T>& mobil_params,
158 const ClosestPose<T>& ego_closest_pose,
159 const systems::rendering::PoseVector<T>& ego_pose,
160 const systems::rendering::PoseBundle<T>& traffic_poses,
161 const T& ego_acceleration) const;
162
163 // Computes a pair of incentive measures that consider the leading and
164 // trailing vehicles that are closest to the pre-computed result in the
165 // current lane. closest_poses contains the odometries and relative
166 // distances to the leading and trailing cars.
167 void ComputeIncentiveOutOfLane(const IdmPlannerParameters<T>& idm_params,
168 const MobilPlannerParameters<T>& mobil_params,
169 const ClosestPoses& closest_poses,
170 const ClosestPose<T>& ego_closest_pose,
171 const T& ego_old_accel,
172 const T& trailing_delta_accel_this,
173 T* incentive) const;
174
175 // Computes an acceleration based on the IDM equation (via a call to
176 // IdmPlanner::Eval()).
177 const T EvaluateIdm(const IdmPlannerParameters<T>& idm_params,
178 const ClosestPose<T>& trailing_closest_pose,
179 const ClosestPose<T>& leading_closest_pose) const;
180
181 static constexpr int kIdmParamsIndex{0};
182 static constexpr int kMobilParamsIndex{1};
183 static constexpr double kDefaultLargeAccel{1e6}; // m/s^2
184
186 const bool with_s_{true};
188
189 // Indices for the input / output ports.
190 const int ego_pose_index_{};
191 const int ego_velocity_index_{};
192 const int ego_acceleration_index_{};
193 const int traffic_index_{};
194 const int lane_index_{};
195 };
196
197 } // namespace automotive
198 } // namespace drake
MobilPlannerParameters< T > & get_mutable_mobil_params(systems::Context< T > *context) const
Definition: mobil_planner.h:120
Definition: automotive_demo.cc:90
Context is an abstract class template that represents all the typed values that are used in a System'...
Definition: context.h:41
PoseBundle is a container for a set of poses, represented by an Isometry3, and corresponding velociti...
Definition: pose_bundle.h:40
This class represents an unrestricted update event.
Definition: event.h:482
Abstract API for the geometry of a road network, including both the network topology and the geometry...
void DoCalcUnrestrictedUpdate(const systems::Context< T > &context, const std::vector< const systems::UnrestrictedUpdateEvent< T > * > &, systems::State< T > *state) const override
Definition: mobil_planner.cc:303
std::vector< double > vector
Definition: translator_test.cc:20
If kCache, configures a planning system (e.g.
Definition: pose_selector.h:52
State is a container for all the data comprising the complete state of a particular System at a parti...
Definition: state.h:27
A superclass template that extends System with some convenience utilities that are not applicable to ...
Definition: leaf_system.h:84
LaneDirection holds the lane that a MaliputRailcar is traversing and the direction in which it is mov...
Definition: lane_direction.h:13
std::map< AheadOrBehind, const ClosestPose< T > > ClosestPoses
Definition: mobil_planner.h:87
const systems::InputPort< T > & ego_pose_input() const
See the class description for details on the following input ports.
Definition: mobil_planner.cc:64
A 7-vector representing the transform of frame A in the world frame, X_WA, in the form {p_WA...
Definition: pose_vector.h:19
BasicVector is a semantics-free wrapper around an Eigen vector that satisfies VectorBase.
Definition: basic_vector.h:25
const systems::InputPort< T > & ego_acceleration_input() const
Definition: mobil_planner.cc:75
const systems::InputPort< T > & ego_velocity_input() const
Definition: mobil_planner.cc:69
const systems::InputPort< T > & traffic_input() const
Definition: mobil_planner.cc:81
MOBIL (Minimizing Overall Braking Induced by Lane Changes) [1] is a planner that minimizes braking re...
Definition: mobil_planner.h:85
ClosestPose bundles together the RoadOdometry of a particular target along with its distance measure ...
Definition: pose_selector.h:25
const systems::OutputPort< T > & lane_output() const
Definition: mobil_planner.cc:86
A 6-vector representing the derivatives of the position transform of frame A in the world frame...
Definition: frame_velocity.h:22
#define DRAKE_NO_COPY_NO_MOVE_NO_ASSIGN(Classname)
DRAKE_NO_COPY_NO_MOVE_NO_ASSIGN deletes the special member functions for copy-construction, copy-assignment, move-construction, and move-assignment.
Definition: drake_copyable.h:33
A position in the road network, consisting of a pointer to a specific Lane and a Lane-frame position ...
Definition: lane_data.h:299
IdmPlannerParameters< T > & get_mutable_idm_params(systems::Context< T > *context) const
Getters to mutable named-vector references associated with MobilPlanner's Parameters groups...
Definition: mobil_planner.h:115
Provides careful macros to selectively enable or disable the special member functions for copy-constr... | {"extraction_info": {"found_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": 0.2385425716638565, "perplexity": 20424.248337740373}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590169.5/warc/CC-MAIN-20180718115544-20180718135544-00119.warc.gz"} |
http://physics.stackexchange.com/questions/27161/relationship-between-weak-cosmic-censorship-and-topological-censorship/27162 | # Relationship between Weak Cosmic Censorship and Topological Censorship
The weak cosmic censorship states that any singularity cannot be in the causual past of null infinity (reference).
The topological censorship hypothesis states that in a globally hyperbolic, asymptotically flat spacetime, every causal curve from $J^-$ to $J^+$ is homotopic to a topological trivial curve between the two points. (reference)
I am curious as to the relationship between these two; will a found violation of weak cosmic censorship necessarily mean a violation of topological censorship? [edit: or the converse]
-
BTW, isn't it a bit ironic to cite a paper with the words "Strong cosmic censorship" in the title as your reference to weak cosmic censorship? – Willie Wong Oct 3 '11 at 15:00
I was originally going to try to make a case relating Strong cosmic censorship to Topological censorship, but I decided I was more interested in weak censorship anyway :P That paper has a concise definition though. – Benjamin Horowitz Oct 3 '11 at 21:30
No.
Firstly, weak cosmic censorship can only hold in the generic sense, as there are known examples of nakedly singular space-times. (See, e.g. Christodoulou 1993, and Christodoulou 1999.)
Observe in particular that the nakedly singular space-time constructed in the 1993 paper is spherically symmetric with a central axis, and the initial data is prescribed on a set homeomorphic to $\mathbb{R}^3$. So the maximal globally hyperbolic development of this data, which leads to a naked singularity (hence violating cosmic censorship), is simply connected (homeomorphic to $\mathbb{R}^4$ actually). And hence must satisfy topological censorship.
BTW, if the implication you want were actually true, then given that nakedly singular solutions are known in the literature, it would be rather difficult to have topological censorship be a proven theorem in the generality that it is usually stated.
However, it is interesting to note that the converse (or something quite close to it) of the statement you are interested in actually holds. By a result of Galloway and Woolgar you have that, roughly speaking: weak cosmic censorship + null energy condition implies topological censorship. The contrapositive of which would say that failure of topological censorship + null energy condition holding will imply weak cosmic censorship is false.
- | {"extraction_info": {"found_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": 0.8216511011123657, "perplexity": 651.2455100426002}, "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-2014-35/segments/1408500811391.43/warc/CC-MAIN-20140820021331-00223-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://lambda-the-ultimate.org/archive/2018/03/18 | ## Non-transitivity of type unification
We know type unification is not transitive in general
a ~ b /\ b ~ c does not imply a ~ c
And it's easy to find examples that don't unify
a |-> Int; b |-> b; c |-> Bool
a |-> (Int, a'); b |-> (Int, Bool); c |-> (c', Bool)
In all the examples I can make up, there's two outer types that don't unify, and a piggy in the middle that is either strictly more general than the outers (bare b) or strictly subsumed (Int, Bool).
For some (malicious) testing, I want an example where each three pairings of types unify, but the three types together do not. That is
a ~ b /\ b ~ c /\ a ~ c but not mgu(a, b) ~ c
Can anybody concoct such an example?
Or point me to something showing it's impossible. | {"extraction_info": {"found_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": 0.5745956301689148, "perplexity": 5369.522670773726}, "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/1521257649627.3/warc/CC-MAIN-20180324015136-20180324035136-00717.warc.gz"} |
https://crad.ict.ac.cn/CN/Y2021/V58/I1/224 | ISSN 1000-1239 CN 11-1777/TP
• 软件技术 •
### 基于交互特征表示的评价对象抽取模型
1. 1（华南师范大学软件学院 广东佛山 528225）；2（华南师范大学计算机学院 广州 510631) (zengbiqing0528@163.com)
• 出版日期: 2021-01-01
• 基金资助:
国家自然科学基金项目(61772211，61503143)
### Aspect Extraction Model Based on Interactive Feature Representation
Zeng Biqing1, Zeng Feng2, Han Xuli2, Shang Qi2
1. 1（School of Software, South China Normal University, Foshan, Guangdong 528225）；2（School of Computer Science, South China Normal University, Guangzhou 510631)
• Online: 2021-01-01
• Supported by:
This work was supported by the National Natural Science Foundation of China (61772211, 61503143).
Abstract: Aspect extraction is one of the key tasks in aspect level sentiment analysis, whose result will directly affect the accuracy of aspect level sentiment classification. In aspect extraction task, it is both time and labor consuming to enhance the performance of the model by handcraft features. Aiming at resolving the problems of insufficient data scale, insufficient feature information, etc., aspect extraction model based on interactive feature representation (AEMIFR) is proposed. Compared with other models, AEMIFR combines character level embedding and word embedding to capture the semantic features of words, the morphological features of characters and the internal relationship between characters and words. Furthermore, AEMIFR obtains the local feature representation and context-dependent feature representation of text, learns the interaction between the two feature representations, enhances the importance of similar features between the two feature representations, reduces the negative impact of useless features on the model, and learns higher quality feature representations. Finally experiments are conducted on the data sets L-14, R-14, R-15 and R-16 in SimEval 2014, SemEval 2015 and SemEval 2016, and the competitive effect is achieved. | {"extraction_info": {"found_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": 0.17638275027275085, "perplexity": 6511.554538034839}, "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/1674764500641.25/warc/CC-MAIN-20230207201702-20230207231702-00744.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/140028-correlation.html | # Math Help - Correlation
1. ## Correlation
$X$ and $Y$ are random variables with expectation equal to zero and variances $\sigma^2$ and $\omega^2\sigma^2$ respectively.
a) If $X$ and $Y$ are independent show that the correlation of $X+Y$ and $X-Y$ is
$\frac{1-\omega^2}{1+\omega^2}$.
b) Find the corresponding correlation if $X$ and $Y$ are not independent but have correlation $\rho$.
2. how about starting with the defintion of correlation in terms of covariance? | {"extraction_info": {"found_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": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6724522113800049, "perplexity": 283.10864097442237}, "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-2014-10/segments/1393999664205/warc/CC-MAIN-20140305060744-00049-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://ei.is.tuebingen.mpg.de/publications?publication_type%5B%5D=Unpublished&publication_type%5B%5D=Technical+Report&year%5B%5D=2002&year%5B%5D=2015&year%5B%5D=1996&year%5B%5D=2018&year%5B%5D=2011&year%5B%5D=2019&year%5B%5D=2014&year%5B%5D=1993&year%5B%5D=2009&year%5B%5D=1999&year%5B%5D=2013 | 2015
Cosmology from Cosmic Shear with DES Science Verification Data
Abbott, T., Abdalla, F. B., Allam, S., Amara, A., Annis, J., Armstrong, R., Bacon, D., Banerji, M., Bauer, A. H., Baxter, E., others,
arXiv preprint arXiv:1507.05552, 2015 (techreport)
2015
The DES Science Verification Weak Lensing Shear Catalogs
Jarvis, M., Sheldon, E., Zuntz, J., Kacprzak, T., Bridle, S. L., Amara, A., Armstrong, R., Becker, M. R., Bernstein, G. M., Bonnett, C., others,
arXiv preprint arXiv:1507.05603, 2015 (techreport)
2013
Animating Samples from Gaussian Distributions
(8), Max Planck Institute for Intelligent Systems, Tübingen, Germany, 2013 (techreport)
2013
Maximizing Kepler science return per telemetered pixel: Detailed models of the focal plane in the two-wheel era
Hogg, D. W., Angus, R., Barclay, T., Dawson, R., Fergus, R., Foreman-Mackey, D., Harmeling, S., Hirsch, M., Lang, D., Montet, B. T., Schiminovich, D., Schölkopf, B.
arXiv:1309.0653, 2013 (techreport)
Maximizing Kepler science return per telemetered pixel: Searching the habitable zones of the brightest stars
Montet, B. T., Angus, R., Barclay, T., Dawson, R., Fergus, R., Foreman-Mackey, D., Harmeling, S., Hirsch, M., Hogg, D. W., Lang, D., Schiminovich, D., Schölkopf, B.
arXiv:1309.0654, 2013 (techreport)
2011
PAC-Bayesian Analysis of Martingales and Multiarmed Bandits
Seldin, Y., Laviolette, F., Shawe-Taylor, J., Peters, J., Auer, P.
Max Planck Institute for Biological Cybernetics, Tübingen, Germany, May 2011 (techreport)
Abstract
We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent random variables. The first is based on a new lemma that enables to bound expectations of convex functions of certain dependent random variables by expectations of the same functions of independent Bernoulli random variables. This lemma provides an alternative tool to Hoeffding-Azuma inequality to bound concentration of martingale values. Our second approach is based on integration of Hoeffding-Azuma inequality with PAC-Bayesian analysis. We also introduce a way to apply PAC-Bayesian analysis in situation of limited feedback. We combine the new tools to derive PAC-Bayesian generalization and regret bounds for the multiarmed bandit problem. Although our regret bound is not yet as tight as state-of-the-art regret bounds based on other well-established techniques, our results significantly expand the range of potential applications of PAC-Bayesian analysis and introduce a new analysis tool to reinforcement learning and many other fields, where martingales and limited feedback are encountered.
2011
Non-stationary Correction of Optical Aberrations
Schuler, C., Hirsch, M., Harmeling, S., Schölkopf, B.
(1), Max Planck Institute for Intelligent Systems, Tübingen, Germany, May 2011 (techreport)
Abstract
Taking a sharp photo at several megapixel resolution traditionally relies on high grade lenses. In this paper, we present an approach to alleviate image degradations caused by imperfect optics. We rely on a calibration step to encode the optical aberrations in a space-variant point spread function and obtain a corrected image by non-stationary deconvolution. By including the Bayer array in our image formation model, we can perform demosaicing as part of the deconvolution.
Multiple Kernel Learning: A Unifying Probabilistic Viewpoint
Max Planck Institute for Biological Cybernetics, March 2011 (techreport)
Abstract
We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable for regression, robust regression and classification that is lower bound of the marginal likelihood and contains many regularised risk approaches as special cases. Furthermore, we derive an efficient and provably convergent optimisation algorithm.
Multiple testing, uncertainty and realistic pictures
Langovoy, M., Wittich, O.
(2011-004), EURANDOM, Technische Universiteit Eindhoven, January 2011 (techreport)
Abstract
We study statistical detection of grayscale objects in noisy images. The object of interest is of unknown shape and has an unknown intensity, that can be varying over the object and can be negative. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. We propose an algorithm that can be used to detect grayscale objects of unknown shapes in the presence of nonparametric noise of unknown level. Our algorithm is based on a nonparametric multiple testing procedure. We establish the limit of applicability of our method via an explicit, closed-form, non-asymptotic and nonparametric consistency bound. This bound is valid for a wide class of nonparametric noise distributions. We achieve this by proving an uncertainty principle for percolation on nite lattices.
Nonconvex proximal splitting: batch and incremental algorithms
(2), Max Planck Institute for Intelligent Systems, Tübingen, Germany, 2011 (techreport)
Abstract
Within the unmanageably large class of nonconvex optimization, we consider the rich subclass of nonsmooth problems having composite objectives (this includes the extensively studied convex, composite objective problems as a special case). For this subclass, we introduce a powerful, new framework that permits asymptotically non-vanishing perturbations. In particular, we develop perturbation-based batch and incremental (online like) nonconvex proximal splitting algorithms. To our knowledge, this is the rst time that such perturbation-based nonconvex splitting algorithms are being proposed and analyzed. While the main contribution of the paper is the theoretical framework, we complement our results by presenting some empirical results on matrix factorization.
2009
Learning an Interactive Segmentation System
Nickisch, H., Kohli, P., Rother, C.
Max Planck Institute for Biological Cybernetics, December 2009 (techreport)
Abstract
Many successful applications of computer vision to image or video manipulation are interactive by nature. However, parameters of such systems are often trained neglecting the user. Traditionally, interactive systems have been treated in the same manner as their fully automatic counterparts. Their performance is evaluated by computing the accuracy of their solutions under some fixed set of user interactions. This paper proposes a new evaluation and learning method which brings the user in the loop. It is based on the use of an active robot user - a simulated model of a human user. We show how this approach can be used to evaluate and learn parameters of state-of-the-art interactive segmentation systems. We also show how simulated user models can be integrated into the popular max-margin method for parameter learning and propose an algorithm to solve the resulting optimisation problem.
2009
An Incremental GEM Framework for Multiframe Blind Deconvolution, Super-Resolution, and Saturation Correction
(187), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2009 (techreport)
Abstract
We develop an incremental generalized expectation maximization (GEM) framework to model the multiframe blind deconvolution problem. A simplistic version of this problem was recently studied by Harmeling etal~cite{harmeling09}. We solve a more realistic version of this problem which includes the following major features: (i) super-resolution ability emph{despite} noise and unknown blurring; (ii) saturation-correction, i.e., handling of overexposed pixels that can otherwise confound the image processing; and (iii) simultaneous handling of color channels. These features are seamlessly integrated into our incremental GEM framework to yield simple but efficient multiframe blind deconvolution algorithms. We present technical details concerning critical steps of our algorithms, especially to highlight how all operations can be written using matrix-vector multiplications. We apply our algorithm to real-world images from astronomy and super resolution tasks. Our experimental results show that our methods yield improve d resolution and deconvolution at the same time.
Detection of objects in noisy images and site percolation on square lattices
Langovoy, M., Wittich, O.
(2009-035), EURANDOM, Technische Universiteit Eindhoven, November 2009 (techreport)
Abstract
We propose a novel probabilistic method for detection of objects in noisy images. The method uses results from percolation and random graph theories. We present an algorithm that allows to detect objects of unknown shapes in the presence of random noise. Our procedure substantially differs from wavelets-based algorithms. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. We prove results on consistency and algorithmic complexity of our procedure.
Efficient Filter Flow for Space-Variant Multiframe Blind Deconvolution
(188), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, November 2009 (techreport)
Abstract
Ultimately being motivated by facilitating space-variant blind deconvolution, we present a class of linear transformations, that are expressive enough for space-variant filters, but at the same time especially designed for efficient matrix-vector-multiplications. Successful results on astronomical imaging through atmospheric turbulences and on noisy magnetic resonance images of constantly moving objects demonstrate the practical significance of our approach.
Algebraic polynomials and moments of stochastic integrals
(2009-031), EURANDOM, Technische Universiteit Eindhoven, October 2009 (techreport)
Expectation Propagation on the Maximum of Correlated Normal Variables
Cavendish Laboratory: University of Cambridge, July 2009 (techreport)
Abstract
Many inference problems involving questions of optimality ask for the maximum or the minimum of a finite set of unknown quantities. This technical report derives the first two posterior moments of the maximum of two correlated Gaussian variables and the first two posterior moments of the two generating variables (corresponding to Gaussian approximations minimizing relative entropy). It is shown how this can be used to build a heuristic approximation to the maximum relationship over a finite set of Gaussian variables, allowing approximate inference by Expectation Propagation on such quantities.
Consistent Nonparametric Tests of Independence
Gretton, A., Györfi, L.
(172), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, July 2009 (techreport)
Abstract
Three simple and explicit procedures for testing the independence of two multi-dimensional random variables are described. Two of the associated test statistics (L1, log-likelihood) are defined when the empirical distribution of the variables is restricted to finite partitions. A third test statistic is defined as a kernel-based independence measure. Two kinds of tests are provided. Distribution-free strong consistent tests are derived on the basis of large deviation bounds on the test statistcs: these tests make almost surely no Type I or Type II error after a random sample size. Asymptotically alpha-level tests are obtained from the limiting distribution of the test statistics. For the latter tests, the Type I error converges to a fixed non-zero value alpha, and the Type II error drops to zero, for increasing sample size. All tests reject the null hypothesis of independence if the test statistics become large. The performance of the tests is evaluated experimentally on benchmark data.
Semi-supervised subspace analysis of human functional magnetic resonance imaging data
Shelton, J., Blaschko, M., Bartels, A.
(185), Max Planck Institute for Biological Cybernetics, Tübingen, Germany, May 2009 (techreport)
Abstract
Kernel Canonical Correlation Analysis is a very general technique for subspace learning that incorporates PCA and LDA as special cases. Functional magnetic resonance imaging (fMRI) acquired data is naturally amenable to these techniques as data are well aligned. fMRI data of the human brain is a particularly interesting candidate. In this study we implemented various supervised and semi-supervised versions of KCCA on human fMRI data, with regression to single- and multi-variate labels (corresponding to video content subjects viewed during the image acquisition). In each variate condition, the semi-supervised variants of KCCA performed better than the supervised variants, including a supervised variant with Laplacian regularization. We additionally analyze the weights learned by the regression in order to infer brain regions that are important to different types of visual processing.
Model selection, large deviations and consistency of data-driven tests
(2009-007), EURANDOM, Technische Universiteit Eindhoven, March 2009 (techreport)
Abstract
We consider three general classes of data-driven statistical tests. Neyman's smooth tests, data-driven score tests and data-driven score tests for statistical inverse problems serve as important special examples for the classes of tests under consideration. Our tests are additionally incorporated with model selection rules. The rules are based on the penalization idea. Most of the optimal penalties, derived in statistical literature, can be used in our tests. We prove general consistency theorems for the tests from those classes. Our proofs make use of large deviations inequalities for deterministic and random quadratic forms. The paper shows that the tests can be applied for simple and composite parametric, semi- and nonparametric hypotheses. Applications to testing in statistical inverse problems and statistics for stochastic processes are also presented..
2002
Kernel Dependency Estimation
Weston, J., Chapelle, O., Elisseeff, A., Schölkopf, B., Vapnik, V.
(98), Max Planck Institute for Biological Cybernetics, August 2002 (techreport)
Abstract
We consider the learning problem of finding a dependency between a general class of objects and another, possibly different, general class of objects. The objects can be for example: vectors, images, strings, trees or graphs. Such a task is made possible by employing similarity measures in both input and output spaces using kernel functions, thus embedding the objects into vector spaces. Output kernels also make it possible to encode prior information and/or invariances in the loss function in an elegant way. We experimentally validate our approach on several tasks: mapping strings to strings, pattern recognition, and reconstruction from partial images.
2002
Global Geometry of SVM Classifiers
Zhou, D., Xiao, B., Zhou, H., Dai, R.
Max Planck Institute for Biological Cybernetics, Tübingen, Germany, June 2002 (techreport)
Abstract
We construct an geometry framework for any norm Support Vector Machine (SVM) classifiers. Within this framework, separating hyperplanes, dual descriptions and solutions of SVM classifiers are constructed by a purely geometric fashion. In contrast with the optimization theory used in SVM classifiers, we have no complicated computations any more. Each step in our theory is guided by elegant geometric intuitions.
Computationally Efficient Face Detection
Romdhani, S., Torr, P., Schölkopf, B., Blake, A.
(MSR-TR-2002-69), Microsoft Research, June 2002 (techreport)
Kernel-based nonlinear blind source separation
Harmeling, S., Ziehe, A., Kawanabe, M., Müller, K.
EU-Project BLISS, January 2002 (techreport)
A compression approach to support vector model selection
(101), Max Planck Institute for Biological Cybernetics, 2002, see more detailed JMLR version (techreport)
Abstract
In this paper we investigate connections between statistical learning theory and data compression on the basis of support vector machine (SVM) model selection. Inspired by several generalization bounds we construct compression coefficients'' for SVMs, which measure the amount by which the training labels can be compressed by some classification hypothesis. The main idea is to relate the coding precision of this hypothesis to the width of the margin of the SVM. The compression coefficients connect well known quantities such as the radius-margin ratio R^2/rho^2, the eigenvalues of the kernel matrix and the number of support vectors. To test whether they are useful in practice we ran model selection experiments on several real world datasets. As a result we found that compression coefficients can fairly accurately predict the parameters for which the test error is minimized.
Feature Selection and Transduction for Prediction of Molecular Bioactivity for Drug Design
Weston, J., Perez-Cruz, F., Bousquet, O., Chapelle, O., Elisseeff, A., Schölkopf, B.
Max Planck Institute for Biological Cybernetics / Biowulf Technologies, 2002 (techreport)
Observations on the Nyström Method for Gaussian Process Prediction
Williams, C., Rasmussen, C., Schwaighofer, A., Tresp, V.
Max Planck Institute for Biological Cybernetics, Tübingen, Germany, 2002 (techreport)
Abstract
A number of methods for speeding up Gaussian Process (GP) prediction have been proposed, including the Nystr{\"o}m method of Williams and Seeger (2001). In this paper we focus on two issues (1) the relationship of the Nystr{\"o}m method to the Subset of Regressors method (Poggio and Girosi 1990; Luo and Wahba, 1997) and (2) understanding in what circumstances the Nystr{\"o}m approximation would be expected to provide a good approximation to exact GP regression.
1999
Estimating the support of a high-dimensional distribution
Schölkopf, B., Platt, J., Shawe-Taylor, J., Smola, A., Williamson, R.
(MSR-TR-99-87), Microsoft Research, 1999 (techreport)
1999
Generalization Bounds via Eigenvalues of the Gram matrix
Schölkopf, B., Shawe-Taylor, J., Smola, A., Williamson, R.
(99-035), NeuroCOLT, 1999 (techreport)
Sparse kernel feature analysis
Smola, A., Mangasarian, O., Schölkopf, B.
(99-04), Data Mining Institute, 1999, 24th Annual Conference of Gesellschaft f{\"u}r Klassifikation, University of Passau (techreport)
1996
The DELVE user manual
Rasmussen, CE., Neal, RM., Hinton, GE., van Camp, D., Revow, M., Ghahramani, Z., Kustra, R., Tibshirani, R.
Department of Computer Science, University of Toronto, December 1996 (techreport)
Abstract
This manual describes the preliminary release of the DELVE environment. Some features described here have not yet implemented, as noted. Support for regression tasks is presently somewhat more developed than that for classification tasks. We recommend that you exercise caution when using this version of DELVE for real work, as it is possible that bugs remain in the software. We hope that you will send us reports of any problems you encounter, as well as any other comments you may have on the software or manual, at the e-mail address below. Please mention the version number of the manual and/or the software with any comments you send.
1996
Nonlinear Component Analysis as a Kernel Eigenvalue Problem
Schölkopf, B., Smola, A., Müller, K.
(44), Max Planck Institute for Biological Cybernetics Tübingen, December 1996, This technical report has also been published elsewhere (techreport)
Abstract
We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in high-dimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible 5-pixel products in 16 x 16 images. We give the derivation of the method, along with a discussion of other techniques which can be made nonlinear with the kernel approach; and present first experimental results on nonlinear feature extraction for pattern recognition.
Learning View Graphs for Robot Navigation
Franz, M., Schölkopf, B., Georg, P., Mallot, H., Bülthoff, H.
(33), Max Planck Institute for Biological Cybernetics, Tübingen,, July 1996 (techreport)
Abstract
We present a purely vision-based scheme for learning a parsimonious representation of an open environment. Using simple exploration behaviours, our system constructs a graph of appropriately chosen views. To navigate between views connected in the graph, we employ a homing strategy inspired by findings of insect ethology. Simulations and robot experiments demonstrate the feasibility of the proposed approach. | {"extraction_info": {"found_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": 0.3602187931537628, "perplexity": 2250.2485329562}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141184123.9/warc/CC-MAIN-20201125183823-20201125213823-00363.warc.gz"} |
http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=KHGGB3_2014_v23n12_2045 | Pressure Drop Predictions Using Multiple Regression Model in Pulse Jet Type Bag Filter Without Venturi
Title & Authors
Pressure Drop Predictions Using Multiple Regression Model in Pulse Jet Type Bag Filter Without Venturi
Suh, Jeong-Min; Park, Jeong-Ho; Cho, Jae-Hwan; Jin, Kyung-Ho; Jung, Moon-Sub; Yi, Pyong-In; Hong, Sung-Chul; Sivakumar, S.; Choi, Kum-Chan;
Abstract
In this study, pressure drop was measured in the pulse jet bag filter without venturi on which 16 numbers of filter bags (Ø$\small{140{\times}850{\ell}}$) are installed according to operation condition(filtration velocity, inlet dust concentration, pulse pressure, and pulse interval) using coke dust from steel mill. The obtained 180 pressure drop test data were used to predict pressure drop with multiple regression model so that pressure drop data can be used for effective operation condition and as basic data for economical design. The prediction results showed that when filtration velocity was increased by 1%, pressure drop was increased by 2.2% which indicated that filtration velocity among operation condition was attributed on the pressure drop the most. Pressure was dropped by 1.53% when pulse pressure was increased by 1% which also confirmed that pulse pressure was the major factor affecting on the pressure drop next to filtration velocity. Meanwhile, pressure drops were found increased by 0.3% and 0.37%, respectively when inlet dust concentration and pulse interval were increased by 1% implying that the effects of inlet dust concentration and pulse interval were less as compared with those changes of filtration velocity and pulse pressure. Therefore, the larger effect on the pressure drop the pulse jet bag filter was found in the order of filtration velocity($\small{V_f}$), pulse pressure($\small{P_p}$), inlet dust concentration($\small{C_i}$), pulse interval($\small{P_i}$). Also, the prediction result of filtration velocity, inlet dust concentration, pulse pressure, and pulse interval which showed the largest effect on the pressure drop indicated that stable operation can be executed with filtration velocity less than 1.5 m/min and inlet dust concentration less than $\small{4g/m^3}$. However, it was regarded that pulse pressure and pulse interval need to be adjusted when inlet dust concentration is higher than $\small{4g/m^3}$. When filtration velocity and pulse pressure were examined, operation was possible regardless of changes in pulse pressure if filtration velocity was at 1.5 m/min. If filtration velocity was increased to 2 m/min. operation would be possible only when pulse pressure was set at higher than $\small{5.8kgf/cm^2}$. Also, the prediction result of pressure drop with filtration velocity and pulse interval showed that operation with pulse interval less than 50 sec. should be carried out under filtration velocity at 1.5 m/min. While, pulse interval should be set at lower than 11 sec. if filtration velocity was set at 2 m/min. Under the conditions of filtration velocity lower than 1 m/min and high pulse pressure higher than $\small{7kgf/cm^2}$, though pressure drop would be less, in this case, economic feasibility would be low due to increased in installation and operation cost since scale of dust collection equipment becomes larger and life of filtration bag becomes shortened due to high pulse pressure.
Keywords
Pressure drop;Pulse jet type;Bag filter;Without venturi;Filtration velocity;
Language
Korean
Cited by
References
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Park, S. J., Choi, H. K., Park, Y. O., Son, J. E., 2003, Effects of a shroud tube on flow field and particle behavior inside a bag-filter vessel, Aerosol Sci. Technol., 37(9), 685-693.
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https://tw.dictionary.search.yahoo.com/search?p=at+the+time&ei=UTF-8 | # Yahoo奇摩字典 網頁搜尋
• 在那時
• 釋義
• 相關詞
### 片語
• 1. 在那時 He was very poor at the time. 他那時候很窮。
### at the same time
• 同時, 一起 Don't all speak at the same time. 大家別同時說。 She was laughing and crying at the same time. 她一面笑一面哭。
### at the same time
• 然而 He may be very rude sometimes but at the same time he is very kind. 有時候他可能很粗魯，然而他還是很善良。
### at the same time
• 然而 He may be very rude sometimes but at the same time he is very kind. 有時候他可能很粗魯，然而他還是很善良。
### even at the best of times
• 即使在最好的情況下 He's difficult at the best of times -- usually he's impossible. 他即使在情緒最好的時候, 都很難相處－－平常就更令人受不了了。
• 更多解釋
### at the time
美式
• 在那時 He was very poor at the time. 他那時候很窮。
### at the time
美式
• 在那時 He was very poor at the time. 他那時候很窮。
2. ### 知識+
• #### 下列兩個片語有何不同
at the same time 和 in the meantime 都是同時的意思，有時幾乎可通用，稍微不同的是在同一剎那...同一段時間內陸續發生的就用 in the meantime Adv. 1. at the same time - at the same instant 在同一剎那; "they spoke simultaneously" 他們在同一時刻...
• #### at the plan time和on schedule
"at the plan time" and "on schedule" generally don't mean the same, even... delivered on schedule. However, "at the plan time" can mean differently in different sentence, for examples...
• #### I forgot that how ...這句的文法有錯嗎？
...how I said the word in English at the time. 你這樣整個句子就不一樣了喔 因為word是單字沒有... that with the words in English at the time] 2008-09-19 22:50:53 補充： 但是要特別注意句點... | {"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": 0.8108272552490234, "perplexity": 7612.50300918999}, "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-2020-45/segments/1603107890028.58/warc/CC-MAIN-20201025212948-20201026002948-00447.warc.gz"} |
https://publications.hse.ru/en/articles/146143069 | • A
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• A
• ABC
• ABC
• ABC
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• А
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• Фазовое рассслоение в растворах гибких полиэлектролитов, обусловленное электростатическими взаимодействиями
## Фазовое рассслоение в растворах гибких полиэлектролитов, обусловленное электростатическими взаимодействиями
Будков Ю.А., Колесников А., Ноговицын Е., Киселев М.
A model of a polyelectrolyte solution has been formulated on the basis of the formalism of the thermodynamic perturbation theory. Macromolecules have been described in terms of the model of a flexible chain with an excluded volume and a variable electrical charge. During construction of the thermodynamic perturbation theory, a set of three independent subsystems—polyelectrolyte macromolecules placed in a structureless charge background of counterions, counterions placed in a structureless charge background of macromolecules, and Coulomb gas ions of a lowmolecularmass salt—has been taken as the reference sys tem. In the framework of this model, liquid–liquid phase separation due to strong correlationinduced attraction has been predicted. The behavior of the degree of ionization over a wide monomer concentration range, including the region of phase separation either in a saltfree solution or in the presence of univalent ions of a lowmolecularmass salt in the solution, has been studied. It has been shown that macromolecules in the coexisting phases should have different degrees of ionization. The occurrence of phase separation under normal conditions in the case when dimethylformamide is taken as a solvent and the nonoccurrence of this phase separation in the case of aqueous solutions of flexiblechain polyelectrolytes are predicted. | {"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": 0.8376386761665344, "perplexity": 5407.607410425589}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439735867.23/warc/CC-MAIN-20200804073038-20200804103038-00497.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/elementary-and-intermediate-algebra-concepts-and-applications-6th-edition/chapter-1-9-cumulative-review-page-625/9 | ## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
$-2\le x \le \dfrac{10}{3}$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $|3x-2|\le8 ,$ use the definition of less than (less than or equal to) absolute value inequality. Then use the properties of inequality to isolate the variable. $\bf{\text{Solution Details:}}$ Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), the inequality above is equivalent to \begin{array}{l}\require{cancel} -8\le 3x-2 \le8 .\end{array} Using the properties of inequality, the inequality above is equivalent to \begin{array}{l}\require{cancel} -8\le 3x-2 \le8 \\\\ -8+2\le 3x-2+2 \le8+2 \\\\ -6\le 3x \le10 \\\\ -\dfrac{6}{3}\le \dfrac{3x}{3} \le \dfrac{10}{3} \\\\ -2\le x \le \dfrac{10}{3} .\end{array} Hence, the solution set $-2\le x \le \dfrac{10}{3} .$ | {"extraction_info": {"found_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": 0.9995440244674683, "perplexity": 2748.6221255265446}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592523.89/warc/CC-MAIN-20180721110117-20180721130117-00349.warc.gz"} |
https://johncarlosbaez.wordpress.com/2013/07/02/relative-entropy-part-2/ | ## Relative Entropy (Part 2)
In the first part of this mini-series, I describe how various ideas important in probability theory arise naturally when you start doing linear algebra using only the nonnegative real numbers.
But after writing it, I got an email from a rather famous physicist saying he got “lost at line two”. So, you’ll be happy to hear that the first part is not a prerequisite for the remaining parts! I wrote it just to intimidate that guy.
Tobias Fritz and I have proved a theorem characterizing the concept of relative entropy, which is also known as ‘relative information’, ‘information gain’ or—most terrifying and least helpful of all—‘Kullback-Leibler divergence’. In this second part I’ll introduce two key players in this theorem. The first, $\mathrm{FinStat},$ is a category where:
• an object consists of a system with finitely many states, and a probability distribution on those states
and
• a morphism consists of a deterministic ‘measurement process’ mapping states of one system to states of another, together with a ‘hypothesis’ that lets the observer guess a probability distribution of states of the system being measured, based on what they observe.
The second, $\mathrm{FP},$ is a subcategory of $\mathrm{FinStat}.$ It has all the same objects, but only morphisms where the hypothesis is ‘optimal’. This means that if the observer measures the system many times, and uses the probability distribution of their observations together with their hypothesis to guess the probability distribution of states of the system, they get the correct answer (in the limit of many measurements).
In this part all I will really do is explain precisely what $\mathrm{FinStat}$ and $\mathrm{FP}$ are. But to whet your appetite, let me explain how we can use them to give a new characterization of relative entropy!
Suppose we have any morphism in $\mathrm{FinStat}.$ In other words: suppose we have a deterministic measurement process, together with a hypothesis that lets the observer guess a probability distribution of states of the system being measured, based on what they observe.
Then we have two probability distributions on the states of the system being measured! First, the ‘true’ probability distribution. Second, the probability that the observer will guess based on their observations.
Whenever we have two probability distributions on the same set, we can compute the entropy of the first relative to to the second. This describes how surprised you’ll be if you discover the probability distribution is really the first, when you thought it was the second.
So: any morphism in $\mathrm{FinStat}$ will have a relative entropy. It will describe how surprised the observer will be when they discover the true probability distribution, given what they had guessed.
But this amount of surprise will be zero if their hypothesis was ‘optimal’ in the sense I described. So, the relative entropy will vanish on morphisms in $\mathrm{FP}.$
Our theorem says this fact almost characterizes the concept of relative entropy! More precisely, it says that any convex-linear lower semicontinuous functor
$F : \mathrm{FinStat} \to [0,\infty]$
that vanishes on the subcategory $\mathrm{FP}$ must equal some constant times the relative entropy.
Don’t be scared! This should not make sense to you yet, since I haven’t said how I’m thinking of $[0,+\infty]$ as a category, nor what a ‘convex-linear lower semicontinuous functor’ is, nor how relative entropy gives one. I will explain all that later. I just want you to get a vague idea of where I’m going.
Now let me explain the categories $\mathrm{FinStat}$ and $\mathrm{FP}.$ We need to warm up a bit first.
### FinStoch
A stochastic map $f : X \leadsto Y$ is different from an ordinary function, because instead of assigning a unique element of $Y$ to each element of $X,$ it assigns a probability distribution on $Y$ to each element of $X.$ So you should imagine it as being like a function ‘with random noise added’, so that $f(x)$ is not a specific element of $Y,$ but instead has a probability of taking on different values. This is why I’m using a weird wiggly arrow to denote a stochastic map.
More formally:
Definition. Given finite sets $X$ and $Y,$ a stochastic map $f : X \leadsto Y$ assigns a real number $f_{yx}$ to each pair $x \in X, y \in Y,$ such that fixing any element $x,$ the numbers $f_{yx}$ form a probability distribution on $Y.$ We call $f_{yx}$ the probability of $y$ given $x.$
In more detail:
$f_{yx} \ge 0$ for all $x \in X,$ $y \in Y.$
and
$\displaystyle{ \sum_{y \in Y} f_{yx} = 1}$ for all $x \in X.$
Note that we can think of $f : X \leadsto Y$ as a $Y \times X$-shaped matrix of numbers. A matrix obeying the two properties above is called stochastic. This viewpoint is nice because it reduces the problem of composing stochastic maps to matrix multiplication. It’s easy to check that multiplying two stochastic matrices gives a stochastic matrix. So, composing stochastic maps gives a stochastic map.
We thus get a category:
Definition. Let $\mathrm{FinStoch}$ be the category of finite sets and stochastic maps between them.
In case you’re wondering why I’m restricting attention to finite sets, it’s merely because I want to keep things simple. I don’t want to worry about whether sums or integrals converge.
### FinProb
Now take your favorite 1-element set and call it $1.$ A function $p : 1 \to X$ is just a point of $X.$ But a stochastic map $p : 1 \leadsto X$ is something more interesting: it’s a probability distribution on $X.$
Why? Because it gives a probability distribution on $X$ for each element of $1,$ but that set has just one element.
Last time I introduced the rather long-winded phrase finite probability measure space to mean a finite set with a probability distribution on it. But now we’ve seen a very quick way to describe such a thing within $\mathrm{FinStoch}:$
And this gives a quick way to think about a measure-preserving function between finite probability measure spaces! It’s just a commutative triangle like this:
Note that the horizontal arrow $f: X \to Y$ is not wiggly. The straight arrow means it’s an honest function, not a stochastic map. But a function is a special case of a stochastic map! So it makes sense to compose a straight arrow with a wiggly arrow—and the result is, in general, a wiggly arrow. So, it makes sense to demand that this triangle commutes, and this says that the function $f: X \to Y$ is measure-preserving.
Let me work through the details, in case they’re not clear.
First: how is a function a special case of a stochastic map? Here’s how. If we start with a function $f: X \to Y,$ we get a matrix of numbers
$f_{yx} = \delta_{y,f(x)}$
where $\delta$ is the Kronecker delta. So, each element $x \in X$ gives a probability distribution that’s zero except at $f(x).$
Given this, we can work out what this commuting triangle really says:
If use $p_x$ to stand for the probability distribution that $p: 1 \leadsto X$ puts on $X,$ and similarly for $q_y,$ the commuting triangle says
$\displaystyle{ q_y = \sum_{x \in X} \delta_{y,f(x)} p_x}$
or in other words:
$\displaystyle{ q_y = \sum_{x \in X : f(x) = y} p_x }$
or if you like:
$\displaystyle{ q_y = \sum_{x \in f^{-1}(y)} p_x }$
In this situation people say $q$ is $p$ pushed forward along $f$, and they say $f$ is a measure-preserving function.
So, we’ve used $\mathrm{FinStoch}$ to describe another important category:
Definition. Let $\mathrm{FinProb}$ be the category of finite probability measure spaces and measure-preserving functions between them.
I can’t resist mentioning another variation:
A commuting triangle like this is a measure-preserving stochastic map. In other words, $p$ gives a probability measure on $X,$ $q$ gives a probability measure on $Y,$ and $f: X \leadsto Y$ is a stochastic map with
$\displaystyle{ q_y = \sum_{x \in X} f_{yx} p_x }$
### FinStat
The category we really need for relative entropy is a bit more subtle. An object is a finite probability measure space:
but a morphism looks like this:
The whole diagram doesn’t commute, but the two equations I wrote down hold. The first equation says that $f: X \to Y$ is a measure-preserving function. In other words, this triangle, which we’ve seen before, commutes:
The second equation says that $f \circ s$ is the identity, or in math jargon, $s$ is a section for $f.$
But what does that really mean?
The idea is that $X$ is the set of ‘states’ of some system, while $Y$ is a set of possible ‘observations’ you might make. The function $f$ is a ‘measurement process’. You ‘measure’ the system using $f,$ and if the system is in the the state $x$ you get the observation $f(x).$ The probability distribution $p$ says the probability that the system is any given state, while $q$ says the probability that you get any given observation when you do your measurement.
Note: are assuming for now that that there’s no random noise in the observation process! That’s why $f$ is a function instead of a stochastic map.
But what about $s?$ That’s the fun part: $s$ describes your ‘hypothesis’ about the system’s state given a particular measurement! If you measure the system and get a result $y \in Y,$ you guess it’s in the state $x$ with probability $s_{xy}.$
And we don’t want this hypothesis to be really dumb: that’s what
$f \circ s = 1_Y$
says. You see, this equation says that
$\sum_{x \in X} \delta_{y', f(x)} s_{xy} = \delta_{y' y}$
or in other words:
$\sum_{x \in f^{-1}(y')} s_{xy} = \delta_{y' y}$
If you think about it, this implies $s_{xy} = 0$ unless $f(x) = y.$
So, if you make an observation $y,$ you will guess the system is in state $x$ with probability zero unless $f(x) = y.$ In short, you won’t make a really dumb guess about the system’s state.
Here’s how we compose morphisms:
We get a measure-preserving function $g \circ f : X \to Z$ and a stochastic map going back, $s \circ t : Z \to Z.$ You can check that these obey the required equations:
$g \circ f \circ p = r$
$g \circ f \circ s \circ t = 1_Z$
So, we get a category:
Definition. Let $\mathrm{FinStat}$ be the category where an object is a finite probability measure space:
a morphism is a diagram obeying these equations:
and composition is defined as above.
### FP
As we’ve just seen, a morphism in $\mathrm{FinStat}$ consists of a ‘measurement process’ $f$ and a ‘hypothesis’ $s:$
But sometimes we’re lucky and our hypothesis is optimal, in the sense that
$s \circ q = p$
Conceptually, this says that if you take the probability distribution $q$ on our observations and use it to guess a probability distribution for the system’s state using our hypothesis $s,$ you get the correct answer: $p.$
Mathematically, it says that this diagram commutes:
In other words, $s$ is a measure-preserving stochastic map.
There’s a subcategory of $\mathrm{FinStat}$ with all the same objects, but only these ‘optimal’ morphisms. It’s important, but the name we have for it is not very exciting:
Definition. Let $\mathrm{FP}$ be the subcategory of $\mathrm{FinStat}$ where an object is a finite probability measure space
and a morphism is a diagram obeying these equations:
Why do we call this category $\mathrm{FP}$? Because it’s a close relative of $\mathrm{FinProb},$ where a morphism, you’ll remember, looks like this:
The point is that for a morphism in $\mathrm{FP},$ the conditions on $s$ are so strong that they completely determine it unless there are observations that happen with probability zero—that is, unless there are $y \in Y$ with $q_y = 0.$ To see this, note that
$s \circ q = p$
actually says
$\sum_{y \in Y} s_{xy} q_y = p_x$
for any choice of $x \in X.$ But we’ve already seen $s_{xy} = 0$ unless $f(x) = y,$ so the sum has just one term, and the equation says
$s_{x,f(x)} q_{f(x)} = p_x$
We can solve this for $s_{x,f(x)},$ so $s$ is completely determined… unless $q_{f(x)} = 0.$
This covers the case when $y = f(x).$ We also can’t figure out $s_{x,y}$ if $y$ isn’t in the image of $f.$
So, to be utterly precise, $s$ is determined by $p, q$ and $f$ unless there’s an element $y \in Y$ that has $q_y = 0.$ Except for this special case, a morphism in $\mathrm{FP}$ is just a morphism in $\mathrm{FinProb}.$ But in this special case, a morphism in $\mathrm{FP}$ has a little extra information: an arbitrary probability distribution on the inverse image of each point $y$ with this property.
In short, $\mathrm{FP}$ is the same as $\mathrm{FinProb}$ except that our observer’s ‘optimal hypothesis’ must provide a guess about the state of the system given an observation, even in cases of observations that occur with probability zero.
I’m going into these nitpicky details for two reasons. First, we’ll need $\mathrm{FP}$ for our characterization of relative entropy. But second, Tom Leinster already ran into this category in his work on entropy and category theory! He discussed it here:
• Tom Leinster, An operadic introduction to entropy.
Despite the common theme of entropy, he arrived at it from a very different starting-point.
### Conclusion
So, I hope that next time I can show you something like this:
and you’ll say “Oh, that’s a probability distribution on the states of some system!” Intuitively, you should think of the wiggly arrow $p$ as picking out a ‘random element’ of the set $X.$
I hope I can show you this:
and you’ll say “Oh, that’s a deterministic measurement process, sending a probability distribution on the states of the measured system to a probability distribution on observations!”
I hope I can show you this:
and you’ll say “Oh, that’s a deterministic measurement process, together with a hypothesis about the system’s state, given what is observed!”
And I hope I can show you this:
and you’ll say “Oh, that’s a deterministic measurement process, together with an optimal hypothesis about the system’s state, given what is observed!”
I don’t count on it… but I can hope.
### Postscript
And speaking of unrealistic hopes, if I were really optimistic I would hope you noticed that $\mathrm{FinStoch}$ and $\mathrm{FinProb},$ which underlie the more fancy categories I’ve discussed today, were themselves constructed starting from linear algebra over the nonnegative numbers $[0,\infty)$ in Part 1. That ‘foundational’ work is not really needed for what we’re doing now. However, I like the fact that we’re ultimately getting the concept of relative entropy starting from very little: just linear algebra, using only nonnegative numbers!
For more details, here’s the actual paper:
• John Baez and Tobias Fritz, A Bayesian characterization of relative entropy, Theory and Applications of Categories 29 (2014), 421–456.
And here’s my whole series of blog articles about it:
Relative Entropy (Part 1): how various structures important in probability theory arise naturally when you do linear algebra using only the nonnegative real numbers.
Relative Entropy (Part 2): a category related to statistical inference, $\mathrm{FinStat},$ and how relative entropy defines a functor on this category.
Relative Entropy (Part 3): how to characterize relative entropy as a functor from $\mathrm{FinStat}$ to $[0,\infty]).$
Relative Entropy (Part 4): wrap-up, and an invitation to read more about the underlying math at the n-Category Café.
### 11 Responses to Relative Entropy (Part 2)
1. arch1 says:
Thanks John, this was admirably clear & self contained; I think I got most of it using only an elementary understanding of sets, mappings, probability distributions, and summation and composition notation (though I might be deluding myself, as I’m still fuzzy on what a category is and on exactly what a morphism is; and I still don’t think I know what it means for a diagram to ‘commute’:-).
“unless there are observations that happen with probability zero—that is, unless there are $y \in X$“: Do you mean Y instead of X?
• John Baez says:
arch1 wrote:
“unless there are observations that happen with probability zero—that is, unless there are $y \in X$”: Do you mean $Y$ instead of $X$?
Yes, thanks—I’ll fix that. Deliberately calling an element of $X$$y$” would be heinous mathematical crime… here in Singapore I’d probably get caned for it.
I’m really glad you found the exposition clear! I’m warming up to write a paper about this, so I need to know what works and what doesn’t.
I’ll tell you what it means for a diagram to commute. Here’s a simple example:
A diagram commutes whenever, given two ways to get from one object to another by following a chain of arrows, those two ways are equal. In this case we have two ways to get from $1$ to $Y.$ There's a direct way using just $q$ and indirect way using first $p$ and then $f.$ But they are equal—that's what the equation below the diagram says. If I were talking to category theorists, I could skip the equation and just say "the diagram commutes".
This pays off in situations where we have big complicated diagrams like this:
(from the proof of the ‘zig-zag lemma’ on Wikipedia) or this:
(a typical sort of thing you see on an algebraic topologist’s whiteboard, drawn by Patrick Orson.) Instead of writing down dozens of equations, you get a nice visual depiction of what’s going on, and you can learn to reason very quickly with these diagrams.
Unfortunately my post is not a great introduction to commutative diagrams, for two reasons.
First, I’m heavily using two kinds of arrows, straight ones and wiggly ones. This is a bit nonstandard; it means my diagrams involve not just one category but two: the category of finite sets and stochastic maps (wiggly arrows), and a subcategory of that, the category of finite sets and functions (straight arrows). If you’re just getting started at this game, you’d want to start with one kind of arrow.
Second, lots of my diagrams don’t commute! They don’t completely commute, so I have to say which equations do hold, by writing them below the diagram, like here:
As an exercise you can try to guess an equation not listed here that would hold if the diagram did commute.
• Steve says:
Thanks for the broader overview of those diagrams! As long as we’re correcting small typos, I’m thinking that by “It’s each to check that multiplying two stochastic matrices gives a stochastic matrix,” you meant “It’s easy to check that multiplying two stochastic matrices gives a stochastic matrix.”
• John Baez says:
Yes indeed—I’ll fix that. Thanks!
2. arch1 says:
Thanks John. (The two arrow types don’t cause me problems if I remind myself that, as you said, functions are special cases of stochastic maps.)
I think that the equation ‘q then s yields the same distribution on X as p does’ answers your exercise (in other words, as you imply above, if its diagram commutes a hypothesis is optimal).
• John Baez says:
Yes, that’s one of the equations that would hold if the whole diagram above commuted. There’s also another:
$s \circ f = 1_X$
And this is something we really don’t want, usually. Taken together with
$f \circ s = 1_Y$
that would imply a very strong condition on our function $f.$
Can anyone see what this condition amounts to?
3. John Baez says:
This covers the case when $y = f(x).$ We also can’t figure out $s_{x,y}$ if $y$ isn’t in the image of $f.$
But now I see that second case never comes up! In this situation
we can show that the function $f$ is onto. The paper I’m writing with Tobias will explain this…
4. In the last couple days I’ve returned to working on a paper with Tobias Fritz where we give a Bayesian characterization of the concept of ‘relative entropy’. This summer I wrote two blog articles about this paper:
Relative Entropy (Part 1): how various structures important in probability theory arise naturally when you do linear algebra using only the nonnegative real numbers.
Relative Entropy (Part 2): a category related to statistical inference, $\mathrm{FinStat},$ and how relative entropy defines a functor on this category.
But then Tobias Fritz noticed a big problem.
5. […] but I don’t have the knowledge and training to develop this idea — you’d need someone like John Baez for […]
6. Tobias Fritz, a postdoc at the Perimeter Institute, is working with me on category-theoretic aspects of information theory. We published a paper on entropy with Tom Leinster, and we’ve got a followup on relative entropy that’s almost done. I should be working on it right this instant! But for now, read the series of posts here on Azimuth: Relative Entropy Part 1, Part 2 and Part 3. […]
7. Now Tobias Fritz and I have finally finished our paper on this subject:
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https://aimsciences.org/article/doi/10.3934/dcdss.2015.8.723 | # American Institute of Mathematical Sciences
August 2015, 8(4): 723-747. doi: 10.3934/dcdss.2015.8.723
## The Souza-Auricchio model for shape-memory alloys
1 Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria
Received November 2013 Revised March 2014 Published October 2014
Shape-memory alloys are active materials, their amazing thermo-electromechanical behavior is at the basis of a variety of innovative applications. Many models have been set forth in order to describe this complex behavior. Among these the so-called Souza-Auricchio model appears as remarkably simple in terms of mechanical assumptions yet accurate in the description of three-dimensional experiments and robust with respect to approximations. Our aim is to survey here the current literature on the Souza-Auricchio model, with a specific focus on modeling.
Citation: Diego Grandi, Ulisse Stefanelli. The Souza-Auricchio model for shape-memory alloys. Discrete & Continuous Dynamical Systems - S, 2015, 8 (4) : 723-747. doi: 10.3934/dcdss.2015.8.723
##### References:
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https://surprise.readthedocs.io/en/v1.0.5/reader.html | class surprise.reader.Reader(name=None, line_format=u'user item rating', sep=None, rating_scale=(1, 5), skip_lines=0)
The Reader class is used to parse a file containing ratings.
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For each built-in dataset, Surprise also provides predefined readers which are useful if you want to use a custom dataset that has the same format as a built-in one (see the name parameter).
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http://comunidadwindows.org/confidence-interval/standard-error-of-odds-ratio.php | Home > Confidence Interval > Standard Error Of Odds Ratio
# Standard Error Of Odds Ratio
## Contents
Clinically, that often means that the researcher measures the ratio of the odds of a disease occurring or a death from a specific injury or illness happening to the odds of Indeed, for a rare disease, we will have D E ≪ H E , {\displaystyle D_{E}\ll H_{E},} and so D E + H E ≈ H E ; {\displaystyle D_{E}+H_{E}\approx H_{E};} Is extending human gestation realistic or I should stick with 9 months? The latter test would use the SE(ORb) from the delta rule. this contact form
For example, we may not have the population-wide data on who did or did not have the childhood injury. Boca Raton: Chapman & Hall /CRC. Now you have everything to do a meta-analysis. If L is the sample log odds ratio, an approximate 95% confidence interval for the population log odds ratio is L±1.96SE.[5] This can be mapped to exp(L−1.96SE),exp(L+1.96SE) to obtain a 95% https://en.wikipedia.org/wiki/Odds_ratio
## Odds Ratio Confidence Interval Crosses 1
On the other hand, when the disease is rare, using a RR for survival (e.g. The odds for Y within the two subpopulations defined by X = 1 and X = 0 are defined in terms of the conditional probabilities given X, i.e., P(Y|X): Y = This would make it impossible to compute the RR.
Obstetrics and Gynecology, 98(4): 685–688. ^ "The trouble with odds ratios". JSTOR3582428. ^ a b "On the use, misuse and interpretation of odds ratios". However, some diseases may be so rare that, in all likelihood, even a large random sample may not contain even a single diseased individual (or it may contain some, but too Odds Ratio Confidence Interval P Value Calculator The odds ratio is given by with the standard error of the log odds ratio being and 95% confidence interval Where zeros cause problems with computation of the odds ratio or
Veterinary Research 2009;40:15. 4. Etter JF. Odds Ratio Confidence Interval Calculator Odds ratios should be avoided when events are common [letter]. Features Disciplines Stata/MP Which Stata is right for me? If there is a single distinct value, it is converted to 0's if it is less than 0.5 and to 1's if it is greater than or equal to 0.5.
Thus the odds ratio equals one if and only if X and Y are independent. How To Report Odds Ratios And Confidence Intervals An odds ratio greater than 1 indicates that the condition or event is more likely to occur in the first group. Chi-Square (c2) assumes that the numbers in the cells represent counts and not proportions or averages, and it assumes that the value of the expecteds is 5 or greater in 80% Based on these results the researcher would recommend that all males aged 30 to 60 diagnosed with bacterial endocarditis caused by SA be prescribed the new drug.
## Odds Ratio Confidence Interval Calculator
http://dx.doi.org/10.11613/BM.2009.011 School of Nursing, University of Indianapolis, Indianapolis, Indiana, USA Corresponding author: mchughm [at] uindy [dot] edu Abstract The odds ratio (OR) is one of several statistics that Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the Odds Ratio Confidence Interval Crosses 1 This is known as the 'invariance of the odds ratio'. Risk Ratio Confidence Interval The formula is as follows: Where “PG1” represents the odds of the event of interest for Group 1, and “PG2” represents the odds of the event of interest
doi:10.1097/SMJ.0b013e31817a7ee4. weblink Journal of the National Cancer Institute. 11: 1269–1275. You can solve for it numerically very easily using an MCMC sampler. Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. Confidence Interval Crosses 0
The test against 0 is a test that the coefficient for the parameter in the fitted model is negative infinity and has little meaning. PMID12377421. ^ Nurminen, Markku (1995). "To Use or Not to Use the Odds Ratio in Epidemiologic Analyses?". In both these settings, the odds ratio can be calculated from the selected sample, without biasing the results relative to what would have been obtained for a population sample. http://comunidadwindows.org/confidence-interval/standard-error-odds-ratio-formula.php let p = 0.3 let y1 = binomial rand numb for i = 401 1 500 let p = 0.1 let y2 = binomial rand numb for i = 401 1
For example, we may choose to sample units with X=1 with a given probability f, regardless of their frequency in the population (which would necessitate sampling units with X=0 with probability Confidence Interval For Odds Ratio Logistic Regression But, in practice, the CI produced from the more normal estimate (i.e., b rather than exp(b)) will likely yield slightly better CIs for coverage probability. In both these settings, the odds ratio can be calculated from the selected sample, without biasing the results relative to what would have been obtained for a population sample.
## Members of the national psoriasis foundation: more extensive disease and better informed about treatment options.
Applications to Cancer of the Lung, Breast, and Cervix". Why does Deep Space Nine spin? Addictive Behaviors 2009;34:246-51. 5. Natarajan S, Santa Ana EJ, Liao Y, Lipsitz SR, McGee DL. Confidence Interval For Odds Ratio In R Privacy policy About Wikipedia Disclaimers Contact Wikipedia Developers Cookie statement Mobile view Warning: The NCBI web site requires JavaScript to function.
How do really talented people in academia think about people who are less capable than them? In this case I was looking at the difference in children's BMI percentile group (80th and above or below 80th) from a control and experimental group, pre and post intervention treatment. Dependence on the nicotine gum in former smokers. his comment is here A method of correcting the odds ratio in cohort studies of common outcomes".
doi:10.2307/2283825. The degree to which the first group’s odds are lower than that of the second group is not known. The only information available is the odds ratio and the p-value for the first data set. First, when you transform a standard error of an ML estimate using the delta method, you get the same standard error that you would have obtained had you performed the maximization
Frequently, however, the available data only allows the computation of the OR; notably, this is so in the case of case-control studies, as explained below. Contents 1 Definition and basic properties 1.1 A motivating example, in the context of the rare disease assumption 1.2 Definition in terms of group-wise odds 1.3 Definition in terms of joint Patients may decide to accept or forego painful or expensive treatments if they understand what their odds are for obtaining a desired result from the treatment. If there are two distinct values, the minimum value is converted to 0's and the maximum value is converted to 1's.
For example, Friese et al. (10) conducted a study to find out if there were different probabilities for having a larger number of surgeries for breast cancer for women whose initial Numerical examples The following four contingency tables contain observed cell counts, along with the corresponding sample odds ratio (OR) and sample log odds ratio (LOR): OR=1, LOR=0 OR=1, LOR=0 OR=4, LOR=1.39 Blackwell Publishing. 126 (1): 109–114. Statistical inference A graph showing the minimum value of the sample log odds ratio statistic that must be observed to be deemed significant at the 0.05 level, for a given sample
The standard error of this bias corrected odds ratio is then $$\hat{SE}(o') = o' \sqrt{\frac{1}{n_{11} + 0.5} + \frac{1}{n_{21}+ 0.5} + \frac{1}{n_{12}+0.5} + \frac{1}{n_{22}+0.5}}$$ where o' is the bias Often we may overcome this problem by employing random sampling of the population: namely, if neither the disease nor the exposure to the injury are too rare in our population, then There are three reasons for this. A method of correcting the odds ratio in cohort studies of common outcomes". | {"extraction_info": {"found_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": 0.8944896459579468, "perplexity": 1231.6997524385756}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806620.63/warc/CC-MAIN-20171122175744-20171122195744-00529.warc.gz"} |
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# What is x if x=19.2/cos(46)?
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What is x if x=19.2/cos(46°)?
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What is x if x=19.2/cos(46°)?
Hello Guest!
$$x=\frac{19.2}{cos(46°)}=\frac{19.2}{0.694658370459}\\ \color{blue}x=27.6394855608$$
!
asinus Sep 15, 2017
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What is x if x=19.2/cos(46°)?
Hello Guest!
$$x=\frac{19.2}{cos(46°)}=\frac{19.2}{0.694658370459}\\ \color{blue}x=27.6394855608$$
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asinus Sep 15, 2017
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http://en.wikipedia.org/wiki/Table_of_Newtonian_series | # Table of Newtonian series
In mathematics, a Newtonian series, named after Isaac Newton, is a sum over a sequence $a_n$ written in the form
$f(s) = \sum_{n=0}^\infty (-1)^n {s\choose n} a_n = \sum_{n=0}^\infty \frac{(-s)_n}{n!} a_n$
where
${s \choose k}$
is the binomial coefficient and $(s)_n$ is the rising factorial. Newtonian series often appear in relations of the form seen in umbral calculus.
## List
The generalized binomial theorem gives
$(1+z)^{s} = \sum_{n = 0}^{\infty}{s \choose n}z^n = 1+{s \choose 1}z+{s \choose 2}z^2+\cdots.$
A proof for this identity can be obtained by showing that it satisfies the differential equation
$(1+z) \frac{d(1+z)^s}{dz} = s (1+z)^s.$
The digamma function:
$\psi(s+1)=-\gamma-\sum_{n=1}^\infty \frac{(-1)^n}{n} {s \choose n}$
The Stirling numbers of the second kind are given by the finite sum
$\left\{\begin{matrix} n \\ k \end{matrix}\right\} =\frac{1}{k!}\sum_{j=0}^{k}(-1)^{k-j}{k \choose j} j^n.$
This formula is a special case of the kth forward difference of the monomial xn evaluated at x = 0:
$\Delta^k x^n = \sum_{j=0}^{k}(-1)^{k-j}{k \choose j} (x+j)^n.$
A related identity forms the basis of the Nörlund–Rice integral:
$\sum_{k=0}^n {n \choose k}\frac {(-1)^k}{s-k} = \frac{n!}{s(s-1)(s-2)\cdots(s-n)} = \frac{\Gamma(n+1)\Gamma(s-n)}{\Gamma(s+1)}= B(n+1,s-n)$
where $\Gamma(x)$ is the Gamma function and $B(x,y)$ is the Beta function.
The trigonometric functions have umbral identities:
$\sum_{n=0}^\infty (-1)^n {s \choose 2n} = 2^{s/2} \cos \frac{\pi s}{4}$
and
$\sum_{n=0}^\infty (-1)^n {s \choose 2n+1} = 2^{s/2} \sin \frac{\pi s}{4}$
The umbral nature of these identities is a bit more clear by writing them in terms of the falling factorial $(s)_n$. The first few terms of the sin series are
$s - \frac{(s)_3}{3!} + \frac{(s)_5}{5!} - \frac{(s)_7}{7!} + \cdots\,$
which can be recognized as resembling the Taylor series for sin x, with (s)n standing in the place of xn.
In analytic number theory it is of interest to sum
$\!\sum_{k=0}B_k z^k,$
where B are the Bernoulli numbers. Employing the generating function its Borel sum can be evaluated as
$\sum_{k=0}B_k z^k= \int_0^\infty e^{-t} \frac{t z}{e^{t z}-1}d t= \sum_{k=1}\frac z{(k z+1)^2}.$
The general relation gives the Newton series
$\sum_{k=0}\frac{B_k(x)}{z^k}\frac{{1-s\choose k}}{s-1}= z^{s-1}\zeta(s,x+z),$[citation needed]
where $\zeta$ is the Hurwitz zeta function and $B_k(x)$ the Bernoulli polynomial. The series does not converge, the identity holds formally.
Another identity is $\frac 1{\Gamma(x)}= \sum_{k=0}^\infty {x-a\choose k}\sum_{j=0}^k \frac{(-1)^{k-j}}{\Gamma(a+j)}{k\choose j},$ which converges for $x>a$. This follows from the general form of a Newton series for equidistant nodes (when it exists, i.e. is convergent)
$f(x)=\sum_{k=0}{\frac{x-a}h \choose k} \sum_{j=0}^k (-1)^{k-j}{k\choose j}f(a+j h).$ | {"extraction_info": {"found_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": 24, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9837039113044739, "perplexity": 323.59747705484864}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1404776435842.8/warc/CC-MAIN-20140707234035-00093-ip-10-180-212-248.ec2.internal.warc.gz"} |
https://www.oreilly.com/library/view/latex-beginners-guide/9781847199867/ch05s10.html | # Time for action – adding a caption to our font table
Now it's time to complete our table. We shall list the remaining font commands. We'll use the first column to describe the category of the font commands: Family, Weight, Shape, and so on. Then we will add another column to show the effect of combining font commands.
To finish, we shall center the table and provide a number and a caption:
1. Put a table environment around our example table, use `\centering` inside, and insert a `\caption` command at the end of the `table` environment. Add more font commands and add another column at the right containing more examples:
`\documentclass{article} \usepackage{array} \usepackage{booktabs} \usepackage{multirow} \newcommand{\head}[1]{\textnormal{\textbf{#1}}} \newcommand{\normal}[1]{\multicolumn{1}{l}{#1}} ...`
Get LaTeX Beginners Guide now with O’Reilly online learning.
O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers. | {"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": 0.9795858263969421, "perplexity": 2639.7242139985883}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057615.3/warc/CC-MAIN-20210925082018-20210925112018-00515.warc.gz"} |
https://help.algebrakit.com/2020/algebra/algebra-settings/student-variable/ | # Student variable
One of the settings in the algebra interaction type is that you can change the type of the step to student variable.
By default, a step name is only used by the author and not visible to the student. In case you check the student variable setting, the student will be able to use the step name as variable name for the calculations in the interaction related to that step.
In questions that involve algebra or physics such a step often relates to a variable that the student uses. Examples are:
• the variables $a$ and $b$ in the linear formula $y=a x+b$, which represent the slope and the offset.
• the symbols $\angle{A}$, $\angle{B}$ and $\angle{C}$ in the formula $\angle{A}+\angle{B}+\angle{C}=180 \degree$
• the physical quantities $E$, $m$ and $v$ in the formula $E=\frac{1}{2}m v^2$, which represent energy, mass and velocity.
By declaring the step name a student variable, the student can write such algebraic expressions and AlgebraKiT will evaluate it as a correct step.
Example
As an example, we will create the exercise:
Find the formula of the straight line through the points $(0,4)$ and $(2,8)$.
• Create a new exercise and enter $y=a x+b$ as task for the solution step.
• Create a new step with the following settings
• name ‘a’
• description ‘the slope’
• task simplify $(8-4)/2$
• Create another step with settings:
• name is ‘b’
• description ‘the offset’
• task simplify $4$
The resulting interaction behaves as follows:
Note the following:
• variables $a$ and $b$ do not occur in the worked out solution
• the student input $y = a x+b$ is not accepted
Let’s now make variables $a$ and $b$ so-called student variables.
Check the box student variable for both steps in the step menu (by clicking the triangle next to the step name).
Run the exercise again and see how variable $a$ and $b$ show up in the worked-out solution and how they can be used by the student.
Note that a student is now able to use the step names as variables, both in the student input for the steps as well as for the definition of the solution step.
0 / 0
However, you can’t simply use this setting for each task. It only works when the task result is a simple, single answer.
Note: when selecting a task like solving equations, you are not able to make the step a student variable in case the solution of the step has multiple answers. An answer of form $p=0 \vee p=2$ can never be the result of a student variable step $p$. In that case either a domain has to be added to restrain the result to a single answer, or the stepname has to be changed to a regular stepname and the student variable checkbox needs to be deselected.
In case you have checked the student variable checkbox and the result of the task is not a simple single answer, we can not guarantee a correct working of AlgebraKiT.
Note 2: It is not possible to use a student variable for a step which is using a variable that is already used in a task definition of another step, for which that step again is used in the task definition of the new student variable. For example: when student variable step $f(x)$ is defined as $x^2+a$, you can not define student variable step $a$ as solving equations $f(3)=0$ for $a$. This gives a solution model loop ($a$ needs to be resolved before $f(x)$ can be determined, but $f(x)$ needs to be resolved before $a$ can be determined). | {"extraction_info": {"found_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": 34, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6737632751464844, "perplexity": 510.5854247901727}, "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/1637964358786.67/warc/CC-MAIN-20211129164711-20211129194711-00099.warc.gz"} |
https://infoscience.epfl.ch/record/218313 | Study of scandium targets for production of monoenergetic neutron fields with energies below 100 keV
In order to develop reference low-energy monoenergetic neutron fields, the 45Sc(p,n) reaction is being studied within the framework of a scientific cooperation between NPL, PTB, IRMM and IRSN. The first study is dedicated to the selection of the most suitable backing material for scandium targets. It must be able to sustain high proton beam currents to compensate for the low cross section of the 45Sc(p,n) reaction. Targets with backings made of Mo, Al,W, Ag, Pt and Ta were irradiated during several hours at a few tens of mA at the NPL neutron reference facility. Target thickness and composition were analysed with the RBS method at the AIFIRA facility before and after NPL irradiations leading to the selection of tantalum as the best choice for backing material.
Published in:
Radiation Measurements, 45, 10, 1116-1119
Year:
2010
Publisher:
Elsevier
ISSN:
1350-4487
Keywords:
Laboratories:
Note: PRIVATE | {"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": 0.8134616017341614, "perplexity": 4240.815213228094}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676593302.74/warc/CC-MAIN-20180722135607-20180722155607-00453.warc.gz"} |
https://infoscience.epfl.ch/record/172203 | Infoscience
Journal article
# Observation of Bs0 -> Ds(*)+ Ds(*)- using e+e- collisions and a determination of the Bs-Bsbar width difference Delta Gamma_s
We have made the first observation of B-s(0) -> D-s(()*()+) D-s(()*()-) decays using 23.6 fb(-1) of data recorded by the Belle experiment running on the Y(5S) resonance. The branching fractions are measured to be B(B-s(0) -> Ds+Ds-) = (1.03(-0.32-0.25)(+0.39+0.26))% B(B-s(0) -> Ds*D-+/-(s)-/+) = (2.75(-0.71)(+0.83) +/- 0.69)%, and B(B-s(0) -> D-s*(+) D-s*(-)) = (3.08(-1.04-0.86)(+1.22+0.85))%; the sum is B[B-s(0) -> D-s(()*()+) D-s(()*()-)] = (6.85(-1.30-1.80)(+1.53+1.79))%. Assuming B-s(0) -> D-s(()*()+) D-s(()*()-) saturates decays to CP-even final states, the branching fraction determines the ratio Delta Gamma(s)/cos phi, where Delta Gamma(s) is the difference in widths between the two B-s-(B) over bar (s) mass eigenstates, and phi is a CP-violating weak phase. Taking CP violation to be negligibly small, we obtain Delta Gamma(s)/Delta Gamma(s) = 0.147(-0.030)(+0.036)(stat)(-0.041)(+0.042)(syst), where Gamma(s) is the mean decay width. | {"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": 0.9970663785934448, "perplexity": 24304.120330388214}, "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-2017-04/segments/1484560280410.21/warc/CC-MAIN-20170116095120-00416-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://indico.ipmu.jp/indico/event/7/contributions/1635/ | # Open Meeting for the Hyper-Kamiokande Project
21-23 August 2012
Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), The University of Tokyo
Asia/Tokyo timezone
## Atmospheric Neutrino Oscillations at Hyper-Kamiokande
22 Aug 2012, 15:20
25m
Lecture Hall (Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), The University of Tokyo)
### Lecture Hall
#### Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), The University of Tokyo
5-1-5 Kashiwanoha, Kashiwa city, Chiba, 277-8583 JAPAN
### Speaker
Dr Roger Wendell (ICRR)
### Description
Recently experimental measurements of reactor, atmospheric, and solar neutrinos have provided an increasingly clear picture of neutrino oscillations. However, several open issues including the nature of the neutrino mass hierarchy, the octant of $\theta_{23}$, and whether or not neutrinos are CP-violating, remain. Atmospheric neutrinos are capable of addressing these questions due to the sizeable matter effects they experience as they traverse the Earth. With 25 times the fiducial volume of the Super-Kamiokande detector, Hyper-Kamiokande will have unprecedented access to these oscillations. This talk will focus on the sensitivity of atmospheric neutrinos at Hyper-Kamiokande to open questions in oscillation physics, particularly in the era of large $\theta_{13}$ now favored by reactor experiments.
### Primary author
Dr Roger Wendell (ICRR)
### Presentation Materials
Slides
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× | {"extraction_info": {"found_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": 0.41531533002853394, "perplexity": 4384.083201201852}, "config": {"markdown_headings": true, "markdown_code": false, "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-2020-40/segments/1600400206763.24/warc/CC-MAIN-20200922192512-20200922222512-00424.warc.gz"} |
http://mathhelpforum.com/algebra/227649-mathematical-induction.html | # Math Help - Mathematical induction
1. ## Mathematical induction
using the Mathematical induction method to prove this ,
$\Sigma_{r=1}^{n}n(n+2r)=n(2n+1)$ In this problem can i start with substitute n=1 and continue or substitute r=1 and continue...
2. ## Re: Mathematical induction
substitute n=1 and do summation for r and then it is true for n so prove it for n+1 using n
3. ## Re: Mathematical induction
There is no "r" to substitute 1 for! The "r" is a "dummy"- it takes on values of 1 up to n so it would not make sense to "substitute 1" for it.
4. ## Re: Mathematical induction
Originally Posted by srirahulan
using the Mathematical induction method to prove this ,
$\Sigma_{r=1}^{n}n(n+2r)=n(2n+1)$ In this problem can i start with substitute n=1 and continue or substitute r=1 and continue...
as with most induction problems show that $P(1)=True$ and that $P(n) \Rightarrow P(n+1)$
$P(1) = \left\{\displaystyle{\sum_{r=1}^1}1(1+2r)=1(2\cdot 1 + 1)\right\}=\left\{3=3\right\}=True$
I leave it to you to show that $P(n) \Rightarrow P(n+1)$ i.e. that
$\left\{\displaystyle{\sum_{r=1}^n}n(n+2r)=n(2n+1) \right\} \Rightarrow \left\{\displaystyle{\sum_{r=1}^{n+1}}(n+1)((n+1)+ 2r)=(n+1)(2(n+1)+1)\right\}$
5. ## Re: Mathematical induction
Originally Posted by srirahulan
using the Mathematical induction method to prove this ,
$\Sigma_{r=1}^{n}n(n+2r)=n(2n+1)$ In this problem can i start with substitute n=1 and continue or substitute r=1 and continue...
$\Sigma_{r=1}^{n}n(n+2r)=n^2(2n+1)$
Is easier to prove
6. ## Re: Mathematical induction
when i show n=p is true then what do i add both side L.H.S and R.H.S to shoe n=p+1 is true?????
7. ## Re: Mathematical induction
hint:for n=p+1 in summation break it into summation for p and then for 1 term and then use substitution for 2rn term from p(n)
8. ## Re: Mathematical induction
If n=p then,
$\Sigma_{r=1}^{p}(p+2r)=p(2p+1)$
Then i write like this
$\Sigma_{r=1}^{p}P+2\Sigma_{r=1}^{p}r=p(2p+1)$
Then add 2(p+1) both side then i comes like this,
$\Sigma_{r=1}^{p}p+2\Sigma_{r=1}^{p+1}r=p(2p+1)+2(p +1)$
But what about this >> $\Sigma_{r=1}^{p}p$
9. ## Re: Mathematical induction
substitute summation of p from r=1 to p with the eqn u get in n=p
10. ## Re: Mathematical induction
$\displaystyle \sum_{r = 1}^n\{n(n + 2r)\} = n\left\{\sum_{r = 1}^n(n + 2r)\right\} = n\left\{\left(\sum_{r=1}^nn\right) + 2\left(\sum_{r=1}^nr\right)\right\} = n\left(n^2 + 2 * \dfrac{n(n + 1)}{2}\right) =$
$n\left(n^2 + 2 * \dfrac{n^2 + n}{2}\right) = n(n^2 + n^2 + n) = n(2n^2 + n) = n^2(2n + 1) \ne n(2n + 1)\ unless\ n = 0\ or\ n = 1.$
$\displaystyle n = 2 \implies \sum_{r = 1}^2\{2(2 + 2r)\} = 2(2 + 2 * 1) + 2(2 + 2 * 2) = 2 * 4 + 2 * 6 = 8 + 12 = 20 =$
$4 * 5 = 2^2(2 * 2 + 1)\ne 2(2 * 2 + 1).$
$\displaystyle n = 3 \implies \sum_{r = 1}^3\{3(3 + 2r)\} = 3(3 + 2 * 1) + 3(3 + 2 * 2) + 3(3 + 2 * 3) = 3(5 + 7 + 9) = 3 * 21 = 3 * 3 * 7 =$
$3^2(2 * 3 + 1) \ne 3(2 * 3 + 1).$
The student is trying to prove a falsity and so is understandably having trouble. I suggest we ask the student to check what the actual proposition to be proven is.
EDIT: Romsek is correct. RL Brown identified that what was trying to be proved is false several posts back. I am leaving my post up, however, because this student needs it spelled out.
11. ## Re: Mathematical induction
I believe RLBrown identified it in post #5
12. ## Re: Mathematical induction
I think this student is struggling enough to warrant an answer.
The intuition behind proofs by induction is this: if something is true for the next integer if it is true for this integer and if that something is also true for 1, then it is true for 2, which means it is true for 3, which means it is true for 4, and so on forever and ever and ever. Got the intuition?
Now for the proof that a proposition P(n) is true for every positive integer n, the structure of a proof by weak mathematical induction is this:
Step 1: Prove P(1) is true.
Now this means that there is at least one positive integer for which P is true. Choose an arbitrary one of such positive integers (call it k). So P(k) is true. This is frequently called the "induction hypothesis." It is not a mere assumption. You have proved in step 1 that such numbers exist.
Step 2: Prove P(k + 1) is true given that P(1) and P(k) are true and k is a positive integer.
Let's do this for your problem.
$\displaystyle Prove\ by\ induction\ that\ n\ is\ any\ positive\ integer \implies \left\{\sum_{r = 1}^nn(n + 2r)\right\} = n^2(2n + 1).$
Now as a practical matter I like to see whether the proposition is true for 2 and 3 before I do the proof so I don't waste time on trying to prove a falsity, but that is NOT part of a formal proof. OK Formal proof
Step 1
$\displaystyle n = 1 \implies \left\{\sum_{r = 1}^nn(n + 2r)\right\} = 1(1 + 2 * 1) = 1(2 * 1 + 1) = 1^2(2 * 1 + 1) = n^2(2n + 1).$
Thus there exists a positive integer k such that $\displaystyle \left\{\sum_{r = 1}^kk(k + 2r)\right\} = k^2(2k + 1) = 2k^3 + k^2.$
Step 2
$\displaystyle \left\{\sum_{r = 1}^{k+1}(k + 1)(\{k + 1\} + 2r)\right\} = \left\{\sum_{r = 1}^k(k + 1)(\{k + 1\} + 2r)\right\} + (k + 1)\{(k + 1) + 2(k + 1)\} =$
$\displaystyle \left\{\sum_{r = 1}^k(k + 1)(\{k + 1\} + 2r)\right\} + 3k^2 + 6k + 3 =$
$\displaystyle \left\{\sum_{r = 1}^kk\{1 + (k + 2r)\right\} + \left\{\sum_{r = 1}^k1(\{k + 1\} + 2r)\right\} + 3k^2 + 6k + 3 =$
$\displaystyle \left\{\sum_{r = 1}^kk\right\} + \left\{\sum_{r = 1}^kk(k + 2r)\right\} + \left\{\sum_{r = 1}^k(k + 1 + 2r)\right\} + 3k^2 + 6k + 3 =$
$\displaystyle k^2 + (2k^3 + k^2) + \left\{\sum_{r = 1}^k(k + 1 + 2r)\right\} + 3k^2 + 6k + 3 =$
$\displaystyle 2k^3 + 5k^2 + 6k + 3 + \left\{\sum_{r = 1}^k(k + 1 + 2r)\right\}=$
$\displaystyle 2k^3 + 5k^2 + 6k + 3 + \left\{\sum_{r = 1}^kk\right\} + \left\{\sum_{r = 1}^k1\right\} + \left\{\sum_{r = 1}^k2r\right\}=$
$\displaystyle 2k^3 + 5k^2 + 6k + 3 + k^2 + k + 2 * \left\{\sum_{r = 1}^kr\right\}=$
$\displaystyle 2k^3 + 6k^2 + 7k + 3 + 2 * \left\{\sum_{r = 1}^kr\right\}=$
$2k^3 + 6k^2 + 7k + 3 + 2 * \dfrac{k(k + 1)}{2} =$
$2k^3 + 6k^2 + 7k + 3 + k^2 + k=$
$2k^3 + 7k^2 + 8k + 3= (k + 1)(2k^2 + 5k + 3) = (k + 1)(k + 1)(2k + 3) = (k + 1)^2(2k + 2 + 1) =$
$(k + 1)^2\{(2(k + 1) + 1\}.$ QED
QED indeed! | {"extraction_info": {"found_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": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9333994388580322, "perplexity": 1031.5486194189587}, "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/1427131300472.97/warc/CC-MAIN-20150323172140-00268-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://ru.overleaf.com/articles/pca/njcpgktggzvj | Author
Prabhat Soni
Last Updated
6 years ago
Abstract Name: sthlm Beamer Theme :: HEAVILY based on the hsrmbeamer theme Author: Mark Hendry Olson :: Original Author of the hsrmbeamer theme is Benjamin Weiss Email: sayhi@hendryolson.com Website: http://hendryolson.com License This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see . Description This presentation is a demonstration of the sthlm beamer theme, which is HEAVILY based on the HSRM beamer theme which can be found on WriteLaTeX. Description This presentation is a demonstration of the sthlm beamer theme, which is HEAVILY based on the HSRM beamer theme created by Benjamin Weiss (benjamin.weiss@student.hs-rm.de), which can be found on GitHub . Created: 20130731-102346 Log 2014-07-08 -Redesigned for pdfLaTeX using the New PX font -Removed all IEGS logos and backgrounds -Released as a WriteLaTeX template 2013-08-01 - Added overlay effect thanks to: 2013-07-31 - Replaced HSRM beamer theme title page background pdf - Replaced HSRM beamer theme logo with IEGS apple logo - Redefined HSRM color theme with an ios7 inspired color scheme - Changed how mini-frames show subsection progress | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 1, "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": 0.4961070418357849, "perplexity": 5288.843748119184}, "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-2023-14/segments/1679296949533.16/warc/CC-MAIN-20230331020535-20230331050535-00331.warc.gz"} |
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https://www.allaboutcircuits.com/projects/rfid-technology-using-arduino-mega/ | Project
# Build Your Own RFID Technology Using an Arduino MEGA
July 20, 2016 by Joseph Corleto
## In this article, we are going to learn some basics about RFID technology and use an Arduino MEGA to a play around with a popular RFID module, the ID12LA.
In this article, we are going to learn some basics about RFID technology and use an Arduino MEGA to a play around with a popular RFID module, the ID12LA.
RFID stands for Radio Frequency IDentification. If you haven’t noticed yet, it is found in many places. This technology is near you right now!
RFID technology is commonly found in hotels, offices, banks, stores, etc. RFID chips are even implanted in pets to make sure that they can be identified and returned home if lost. It is often compared to a barcode. But even if it has the same use as a barcode, the two differ in a few ways.
In this article, we are going to learn some basics about RFID technology and use an Arduino MEGA to a play around with a popular RFID module, the ID12LA. You will be surprised by how easy it will be to incorporate this technology into your next electronics project!
### BOM
#### Hardware
• Arduino MEGA
• You don't have to use a MEGA, but this will do!
• ID12LA
• ID12LA Breakout PCB
• The pins to the ID12LA are a bit weird so I suggest the breakout PCB from Sparkfun or any other reputable dealer.
• Some jumper wires
• Solder and soldering iron
• Arduino IDE
### Theory
Before we can start any kind of software or hardware planning, it is essential to have an understanding of the very basics of RFID.
In any RFID system, there will be a device that will have information, typically called a tag or transponder, and another device that will “look” or “sense” this information, typically called a reader or interrogator. Both components will need to have their own antenna to communicate and, depending on the type of RFID technology, they can exchange information one or both ways.
To understand this better, we need to understand the two distinctly different types of RFID technology: passive and active.
#### Passive RFID
Let’s start with passive. In a passive system, the tag consists of an antenna and circuitry to house a unique code. But there is no power source (no battery), so how does the circuitry inside get powered?
The answer lies in the reader. In a passive RFID system, the reader will have an antenna that will emit RF energy that will induce a current in the tag’s circuitry. So whenever the tag is moving through the reader’s electromagnetic field, it gets powered and then immediately broadcasts its unique code. At the same time, the reader is also listening for this code.
At what range does all this happen? It depends on the reader and tag, but it is largely dependent on the frequency on which the code is broadcasted. The three main frequencies for passive RFID are:
• Low frequency: ~125 kHz. Typically has a range of a few centimeters
• High frequency: 13.56 MHz. Has a range of up to a meter
• Ultra-high frequency: ~865 MHz. Has a range of about 30 meters
With all this being said, the ID12LA in our project is a passive type reader that consists of a built-in antenna and circuitry that can decode the tag and spit out serial data that our Arduino can understand. It is also 125 kHz which means we need tags that can be interrogated on that frequency.
Passive RFID may seem like it would have its shortcomings due to its short read range but these systems are generally inexpensive. Also, since the tags have no batteries, they can last a long time without service.
Below is a type of 125 kHz, passive tag that the ID12LA can interrogate:
#### Active RFID
Now for active RFID.
As you might have guessed, these tags are always powered and thus have an onboard battery to transmit their code.
Because of this, along with the option of operating at either 433 MHz or 915 MHz, they have a very long read range—up to a couple of hundred meters! And since they have onboard batteries, they can be coupled with other technologies like temperature sensors and GPS tracking modules that can tailor to many different types of applications.
Finally, there are two types of tag styles you can purchase: transponder (like in passive RFID) and beacon.
A transponder tag is similiar to the passive system in terms of the communication protocol. The reader will send a signal to the tag to ask for its code.
A beacon tag will do the opposite and send a signal every so often on its own—but this really cuts down on battery life.
In either passive or active systems, you can have a tag that is read-only or writable. Read-only means just that, you cannot change the tag's data. Writable means that you can choose what data to place within the tag.
Active RFID tags can also get pretty big. Below is one type of form factor; specifically, a ruggedized one:
### Communicating with the ID12LA with an Arduino
Phew! Now that we got that out of the way, let’s figure out how to get the ID12LA to communicate with the Arduino.
To follow along, I strongly suggest having the ID12LA's datasheet (PDF) handy.
So with our newfound RFID knowledge, we know that a tag will send a code to the reader, but then what happens? Well, if we study the datasheet, page 4 gives us information on the data output:
This means that once a tag is read, information can be sent out of the reader in serial format, at 9600 baud, No Parity Bit, and 1 Stop Bit. This is a pretty common asynchronous serial communication setup and will make connecting to the Arduino a snap.
Once the reader sends out the data to the Arduino, we need a way to know when to start capturing data. Looking at how the reader spits out data, we find that it uses a Start of Text controller character. Basically, when the serial buffer has some data in it, we can first look to see if this control character is in the queue. If so, then we can go ahead and record the next. If not, we will keep reading until we see it or until the serial buffer is empty.
Assuming we read in the Start of Text controller character, we can go and blindly read in the next 10 ASCII characters from the serial buffer. Then, for the next 5 ASCII characters (2 for checksum, 1 for carriage return, 1 for line feed, and 1 for End of Text controller character), we will read them in but not save it anywhere in our program.
However, to ensure that our transmission was correct, we will double check to see that the End of Text controller character is seen. Though it may rarely be the case, the transmission might fail and we should throw everything we did out the window for the sake of system integrity.
Once the tag is read and saved somewhere in our program, we can use this data for whatever we want! A typical application is access control. You take your saved tag and compare it to a database of tags that are considered to be valid (in our case, we only use one saved tag). The problem is, how do we know what the tag’s code is before we save it to a database? It is not like the tag comes with a paper with its code scribbled on it from the manufacturer.
To work around this and begin to make a database for ourselves, we will need to read in the code and spit it out to the serial monitor. In the Arduino code section, I will provide easy-to-follow comments on where this occurs. When this happens, we will need to write this code down and then alter our program to store this code upon compilation. This is rather a manual way of doing it but this is for the sake of learning the basics of RFID.
Once that is achieved, I would encourage experimenting with programming a simple program sequence that could save RFID tag to EEPROM while the code is running, as well as a way to save and validate more than one tag.
Okay, so let us summarize what the Arduino code must do:
1. Monitor the serial buffer for available data.
2. When data is present, read and save it with some validation ensuring communication integrity.
3. Spit out the data to a serial monitor (primarily for initial setup) and compare this tag to our saved tags.
4. Perform an action (we will spit out a message to the serial terminal to illustrate this).
### Wire it Up
If we turn to page 3 on the datasheet, we see the pinouts to what is essentially a giant IC:
The ID12LA has some nice features such as an output (pin 6) that indicates when a tag is in range and a beeper output (pin 10). However, we don’t use these features in our baseline interface.
For our application, we are using ASCII output. For this to happen, the datasheet tells us (on page 6) that we need to set the format selector input (pin 7) to ground. The data pin we will use is D0 (pin 9). For controlling the reader’s status, we will connect RES (pin 2) to +5V that way the reader is always on.
Refer to the schematic below for the complete overview:
You can also refer to the ID12LA’s pin descriptions:
##### Click to enlarge.
As for getting the ID12LA onto a breadboard, there's a reason that I suggested buying a breakout board from Sparkfun.com or some other reputable shop. The spacing on the ID12LA is not breadboard-friendly, and, unless you have female-to-male jumpers, will be impossible to connect easily.
For an example on how to wire on a breadboard, please take a look at my wiring setup below:
My tip is to try and be as neat as possible as it is easy to get lost while wiring. But whatever you do, please ensure the power and ground pins are where they are supposed to be! Follow the schematic!
The capacitor is not optional—it provides important high-frequency power-supply bypassing for the ID12LA.
### Arduino Code
As promised, here is the heavily commented code to guide you through all of the logic. This code shows you how to compare the detected tag to one stored tag. The same general techniques can be used to extend the code to compare the detected tag against a database that includes multiple valid tags.
If you have any questions, leave me a comment below or run to the forums and someone will be happy to assist you!
If you are still new at Arduino programming, however, I suggest reading up on some basic syntax to help with this code.
/*
================================================================================
File........... ID12LA RFID Test Code
Purpose........ To demonstrate how to interface to a ID12LA RFID module
Author......... Joseph Corleto
E-mail......... corleto.joseph@gmail.com
Started........ 06/28/2016
Finished....... 07/02/2016
Updated........ --/--/----
================================================================================
Notes
================================================================================
================================================================================
================================================================================
*/
//===============================================================================
//===============================================================================
//===============================================================================
// Constants
//===============================================================================
// Here is where we save valid tags. When you see the example video
// of this working, I will first show the invalid tag. Then I will comment this
// line and uncomment the valid tag. This shows you how to manually set your own
// valid tag. Only difference is you will need to manually type this in. I
// was able to uncomment because I have done this prior to making the video.
// Bogus tag
char tag1[10] = {'X','X','X','X','X','X','X','X','X','X'};
// Good tag
//char tag1[10] = {'3','6','0','0','6','6','0','0','5','C'};
//===============================================================================
// Variables
//===============================================================================
char ourTag[10]; // We will use this to hold the interrogated tag's data.
boolean tagDetected; // We can use this to continue program action if our
// reading seems like a real tag was detected.
//===============================================================================
// Pin Declarations
//===============================================================================
//Inputs:
// Serial1 (pin 19) will be used to grab serial data from buffer which is given
// by the ID12LA
//Outputs:
// Serial (pin 2) will be used to output serial data as user feedback to see
// what is going on
//===============================================================================
// Initialization
//===============================================================================
void setup()
{
// Initialize serial port speed for the serial terminal.
// We will use Serial1 on our MEGA for RFID data and the Serial for messages
// to the terminal.
Serial.begin(9600);
Serial1.begin(9600);
// Initialize data flags
tagDetected = false;
}
//===============================================================================
// Main
//===============================================================================
void loop()
{
// This function call will return the interrogated tag's data in form of a char
// array. If there was an error in the integrity of the transmission, it will
// return "0000000000". Of course, this only happens unless there is something
// in the serial buffer. All the while, we also
// set a flag if there was data there. This comes into use later on.
if (Serial1.available() > 0)
{
// Give some time for all data to arrive safe and sound into the buffer.
delay(250);
// The if statement below ensures that the beginning of a tag is seen.
// Remember that a Start of Text is the decimal value of 2. If we do not
// see this, all bets are off in even continuing to look further into the
// buffer. I use peek simply because I don't like touching data until I
// decide to process it.
if (Serial1.peek() != 2)
{
// Log that we did not have a true tag detected.
tagDetected = false;
// Flush the buffer to bring it back to an initial, known state.
flushSerial1Buffer();
}
else
{
// Looks like the serial data starts with a valid Start of Text character,
// let mark that we detected a potential tag.
tagDetected = true;
// Go and process the tag in the serial1 buffer.
fetchTagData(ourTag);
// NOTE: The fetchTagData function actually alters the ourTag array
// declared earlier before. Nothing is returned because if an array's name
// pass along into a function, it is actually passing by reference, not by
// value. That means we are changing the array's contents in the function
// so nothing needs to be returned! There are other spots in this program
// where this happens so please keep this in mind.
// While we're at it, why not print out the tag's ID.
Serial.print("Your tag says it is: ");
Serial.flush();
printTag(ourTag);
}
}
else
{
// We don't flush the buffer here since we know the buffer is zero.
tagDetected = false;
}
// If no tag was detected, then the below code will never execute. But, if
// there is a tag, then we will see if it belongs to our database.
if (tagDetected)
{
// Now here is the part where we do the database comparison with our handy
// isValidTag function. And this where you may perform an action
// if it is or is not valid.
if (isValidTag(ourTag))
{
Serial.println("Come on in and have some freshly baked cookies!!!\n");
Serial.flush();
}
else
{
Serial.println("No idea who you are but I have released the hounds!!!\n");
Serial.flush();
}
}
}
//===============================================================================
// Functions
//===============================================================================
////////////////////////
// flushSerial1Buffer //
////////////////////////
void flushSerial1Buffer()
{
// Now there is a function on the Arduino that is called Serial1.flush
// keep on plucking data off of the serial buffer until it is empty!
while (Serial1.available() > 0)
{
}
}
//////////////////
// fetchTagData //
//////////////////
void fetchTagData(char tempTag[])
{
// First, pluck off the Start of Text character
// Second, read off the tag's actual ID data
for (int counter = 0; counter < 10; counter++)
{
}
// Third, pluck off two checksum, one CR, and one LF characters
// Fourth, pluck off what should be the End of Text character. And
// while we are plucking, why not throw in a sanity check (mentioned in
// the article)
{
// If for some odd reason the transmission was faulty and we only read
// in partial information, just throw in dummy data for the tag
for (int counter = 0; counter < 10; counter++)
{
tempTag[counter] = '0';
}
}
else
{
// But if it all looks good, flush the buffer and keep the previously
// acquired data
flushSerial1Buffer();
}
}
////////////////
// isValidTag //
////////////////
boolean isValidTag(char tempTag[])
{
boolean result;
// Compare all of the tags by OR-ing all of the compared tag results. If at
// least one matches, then it is a valid tag.
result = compareTags(tempTag, tag1);
return result;
}
/////////////////
// compareTags //
/////////////////
boolean compareTags(char tagA[], char tagB[])
{
boolean result = true;
// Basically, we will just compare each character in corresponding array
// cells until we hit something that does not match. But if it does all
// match, then our initial state of result will be true.
for (int counter = 0; counter < 10; counter++)
{
if (tagA[counter] != tagB[counter])
{
result = false;
break;
}
}
return result;
}
/////////////////
// printTag //
/////////////////
void printTag(char tag[])
{
// This function just helps identify what the tag ID is so that you
// may initially read this in, hard code into your program, compile,
// and then run to have a valid tag in your database.
for (int counter = 0; counter < 10; counter++)
{
Serial.print(tag[counter]);
}
Serial.println("");
}
If you've followed all of these steps successfully, you should have your own working passive RFID system. Here's mine in action:
### RFID Applications
RFID with access control is a pretty natural and straightforward application— but with some imagination, you can tailor it to different ideas.
For example, if you are familiar with Geocaching, you can hide RFID tags that can open to give clues to other treasures. Or maybe try something like what pet owners do and use an RFID to track your dog.
If you want to go even further, I highly encourage trying out active RFID to broaden the horizon. One application that sticks in my head is someone tagging all of their food and creating a database that gives recipes on what to make for dinner depending on what tags were in the fridge; overkill, but definitely cool!
Give this project a try for yourself! Get the BOM.
ID12LA_RFID_Test_Code_(2).zip
• Share
• W
Warren Winters July 21, 2016
I think a really useful opportunity has been missed here.
This would have been an ideal opportunity to code a ‘State Machine’, and see how useful that form of coding can be to a Real-Time task.
But, as the code stands, it doesn’t demonstrate much, and I’m quite disappointed.
Personally, I found that Comment Lines made reading the Code harder. Take a look at this segment:
https://gist.github.com/anonymous/301c8ccb12d92cddfa11d8d93e784937
This is what I chose to do:
- Line up the Closing “}” of the If & Else, so that they stick out (On the Arduino IDE, matching Braces get highlighted, and this helps to ensure the Logic is complete)
- Put the “//” into Columns 1 & 2, so that they don’t get in the way of the Eye reading the words
- Use the “//” comment text in line with the Code, so that you read it to know what the next segment of code is about to do
- The next 2 “//” comments are on the same line as the code they are talking about (To me, this is an Assembler thing, which is what I was taught with. Let’s not try to fool ourselves into thinking that this is a High Level Language, so it’s not really Assembler-style coding - This code is talking to a Machine, not handling a Business problem, which is why - IMHO - a State Machine style of coding would have been superior)
- Then, there is a slab of Text, so use the /* ... */ technique - With Indentation - to avoid unnecessary Characters for the eye to process (Again, the Arduino IDE will put this Block of Comments in a different colour to the Code, and the “//” Comments - Another way to help the Comprehension of the whole code)
- Let’s not forget the whole Indentation method. By lining up all the code, then the brain can understand what is related, and what is different, or related in a different manner.
- Lastly, the If uses Negative Logic:
if (Serial1.peek() != 2)
I was taught never to use Negative Logic, but to instead write
if (Serial1.peek() == 2)
This way, the brain can understand more easily, and so you can avoid Double Negatives.
This is just my 2 cents worth, and there are probably an infinite number of different styles that could be used here - Mine is just one. All I’m saying is let’s try to be the best we can be, and have the code reflect that.
OK, now everyone can comment on my comments.
Like.
• J
Joseph Corleto July 22, 2016 | {"extraction_info": {"found_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": 0.22207817435264587, "perplexity": 1058.848333116854}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988774.96/warc/CC-MAIN-20210507025943-20210507055943-00534.warc.gz"} |
http://clay6.com/qa/23253/a-mixture-of-ethane-c-2h-6-and-ethene-c-2h-4-occupies-40-litre-at-1-00atm-a | Browse Questions
# A mixture of ethane $(C_2H_6)$ and ethene $(C_2H_4)$ occupies 40 litre at 1.00atm and at 400k.The mixture reacts completely with 130g of $O_2$ to produce $CO_2$ and $H_2O$.Assuming ideal gas behavior ,Calculate the mole fractions of $C_2H_4$ and $C_2H_6$ in the mixture.
$\begin{array}{1 1}(a)\;1.2,3.2&(b)\;0.66,0.34\\(c)\;0.1,0.2&(d)\;2.2,3.1\end{array}$
Mixture of $C_2H_6$ and $C_2H_4$
$PV=nRT$
$1\times 40=n\times 0.082\times 400$
Total mole of $(C_2H_6+C_2H_4)=1.2195$
$C_2H_6+C_2+H_4=1.2195$
$a+b=1.2195$-------(1)
$C_2H_6+\large\frac{7}{2}$$O_2\rightarrow 2CO_2+3H_2O C_2H_4+3O_2\rightarrow 2CO_2+2H_2O \large\frac{7a}{2}$$+3b=\large\frac{130}{32}$------(2)
From (1) & (2)
$a=0.808$
$b=0.4115$
Mole fraction of $C_2H_6=\large\frac{0.808}{1.2195}=$$0.66$
Mole fraction of $C_2H_4=0.34$
Hence (b) is the correct answer. | {"extraction_info": {"found_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": 0.919560432434082, "perplexity": 6772.111194835059}, "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-2017-04/segments/1484560280761.39/warc/CC-MAIN-20170116095120-00132-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://gvanderzwan.nl/history/william-the-conqueror/ | # William the Conqueror
But to the extent that ancestry is considered in genealogical rather than genetic terms, our findings suggest a remarkable proposition: no matter the languages we speak or the colour of our skin, we share ancestors who planted rice on the banks of the Yangtze, who first domesticated horses on the steppes of the Ukraine, who hunted giant sloths in the forests of North and South America, and who laboured to build the Great Pyramid of Khufu.
One of the things in Dan Brown’s book The Da Vinci Code that really ground my gears to a complete stop was the ‘revelation’ that Sophie Neveu and her little brother are descendants of Jesus and Mary Magdalene. At the time I thought the whole concept was ridiculous, because in every one of the 67 generations between the year zero and the present Jesus’ and Maria’s genes were halved, and nothing would be left, not even a base pair3. I never read another of his books.
So what’s the deal, did they have a Jesus gene that gave them the ability for turning water into wine? The book does not tell us what spectacular properties these kids have that made them so important. But I would like to know, because I almost certainly would also have those capabilities.
After reading the section ‘The Tasmanian’s Tale’ in Richard Dawkins’ highly recommended The Ancestors Tale I realized that if Jesus and Mary Magdalen had any living descendants, everyone of us would be among their successors, in other words, they would be Common Ancestor (CA) to all of us.
I descend from William the Conqueror as the picture on the left shows4. I also descend from Charlemagne, who lived some ten generations before William, but so far I found no direct link between William and Charlemagne5. The tree on the left spans thirty one generations (I included my son), so let’s think for a second about the thirty generations that have elapsed. I have two parents, four grandparents, eight great grandparents and so on. By the time I get to William, I should have more than 1 billion (great)27-grand parents, but the world population at that time is estimated at only 300 million6. At Charlemagnes time I would have had 1012 (a thousand billion) ancestors, probably more people than ever lived. Clearly this doesn’t work. And footnote 4 already shows why not. I have a common ancestor with Willem Meier, and with at least ten other people I don’t know, on geneanet alone, who all have Klaasje van Winkel in their family tree (because that is what I searched for on that site). And there are many sites devoted to genealogy nowadays — what else can a pensioner (mainly men I get the impression) do with all his free time — so there are likely quite a few more. But this is the crux of the matter: at a certain time we must all have a common ancestor (CA). And of course if there is a CA there is also a most recent common ancestor (MRCA).
And here is the funny thing: this MRCA is much closer in time than you think, or at least than what I thought before reading Dawkins book7 and Chang’s papers2,8, and although William maybe is not, Charlemagne could well be a CA. Or they could both be.
As Dawkins explains ([7], p 39):
Pick any two people and go backwards and, sooner or later, we hit a most recent common ancestor. You and me, the plumber and the queen. Any set of us must converge on a single concestor (or couple). But unless we pick close relatives, finding the concestor requires a vast family tree, and most of it will be unknown. This applies a fortiori to all humans alive today. Dating concestor 0, the most common recent ancestor of all living humans, is not a task that can be undertaken by a practising genealogist. It is a task in estimation: a task for a mathematician.
That mathematician is J.T. Chang. The mathematical model Chang presents8 is simple and amenable to statistical analysis. But it is not too simple, later improvements show2,9 that the main conclusions hold. The model is, in Chang’s own words ([8], p. 1003):
We assume the population size is constant at n. Generations are discrete and non overlapping. The genealogy is formed by this random process: in each generation, each individual chooses two parents at random from the previous generation. The choices are made just as in the standard Wright–Fisher model—randomly and equally likely over the n possibilities—the only difference being that here each individual chooses twice instead of once. All choices are made independently. Thus, for example, it is possible that when an individual chooses his two parents, he chooses the same individual twice, so that in fact he ends up with just one parent; this happens with probability 1/n.
That last probability becomes of course vanishingly small when the population is large (in the millions).
On the basis of this model Chang proves two theorems. The first one gives the probability of finding the MRCA at a certain generation in the past:
Theorem 1. Let $$\mathcal{T}_n$$ denote the number of generations, counting back from the present, to an MRCA of all present-day individuals, in a population of size n. Then
$\frac{\mathcal{T}_n}{^2\log n} \to 1\quad \mbox{as} \quad n\to \infty$
What this means is that for large populations the number of generations $$\mathcal{T}_n$$ to the MRCA becomes proportional to 2log n where 2log n is the base 2 logarithm of n. In other words, this is approximately how many generations are needed on average to find the MRCA. Now, the population of Europe in the year 1000 was about 60 million, and $$^2\log 6\times10^7 \approx 26$$ so there is a reasonably probability that the MRCA of all Europeans lived as few as 26 generations ago. It is a statistical result (the ratio approaches 1 in the infinite population limit), so it is not certain, but you can be pretty damn sure that Charlemagne, who lived forty generations ago, is in the bloodline of the vast majority of people in Europe, and absolutely certain that Jesus (67 generations) is one of my ancestors. If Sophie Neveu is his progeny, so am I.
Actually that does not mean very much, as the second theorem of Chang shows, because by that time a large proportion of the population is my ancestor. It is a little more complicated, so I won’t quote it in full, but give merely the numerical result. It is based on the obvious consequence that all ancestors of a CA also become CA, so pretty soon everybody living in the world a number of generations before the MRCA is my ancestor and of everybody else. Chang proves that this takes, on average and in the large population limit, 1.77 2log n generations. It is a little dangerous to think in terms of genes in a genealogical context, but I have the feeling that it means that pretty much everybody living at the time of Jesus in Europe and the middle east contributed to my genome. The world as a whole is more complicated, and you need to take into account groups of people living more or less isolated from the rest, but even so Chang et al. argue that the MRCA of all current humans lived only a few thousands of years ago ([2], p. 565).
Of course not everybody contributes, since there is always a proportion of the population that leaves no offspring at all, and some, maybe even most, genealogical lines do come to an end. Consequently, a person living some four or five millenia ago either has no current relatives at all, or is everybody’s ancestor. Some of these considerations are nicely illustrated by a simple simulation of Chang’s model consisting of just five people per generation ([8], p. 1005).
The bottom line is generation 0 and every individual from that generation chooses two parents at random. In the case of person 1 this is twice 5, but for larger populations that possibility becomes negligible, and does not alter the results in any essential way. Person 2 has 2 and 5 in generation -1 as parents, 3 has 1 and 2, and so on. Thus, in generation -1 number 1 has 3 and 5 as children, 2 has 2 and 3, well, you get the idea. The next step illustrates what can also happen: number 5 is not chosen at all, and this ends the contribution of 5 at generation -2 to all future generations. This is indicated by the symbol ∅. Also, already in generation -2 person 4 becomes CA, indicated by an S. You can follow lines originating from that person to all persons in generation 0. $$\mathcal{T}_5=^2\log5\approx 2.3$$, so theorem 1 states that this should happen between generation -2 and -3, but the numbers are so small that it does not really apply to this situation10. In any case , the MRCA is identified. A generation before that 1 and 2 become ancestors to 4, thus becoming also a CA of generation 0, and two generations before that a person is either a CA to generation 0, or has no offspring at all. You can also note that common ancestors in different generations need not be related. Number 4 in generation -2 (William the Conqueror) is a CA, as is number 2 in generation -4 (Charlemagne), but William does not have Charles as ancestor.
Should I be surprised that William the Conqueror is in my ancestry: not at all. In fact it would be very surprising if he were not. And even more so for Charlemagne. In fact there are probably many more paths leading to the same people. Does it mean anything? I don’t think so, the link between genetics and genealogy is complicated. I can share an ancestor but none of his/her genetic material. Chang, in a response to one of his critics states:11
The descendants of a common ancestor need not share any particular DNA from that ancestor, and it is even possible that none of the descendants has inherited any DNA from the ancestor. If you and I were investigating our common ancestry, we might conceive of an extreme case in which your mother’s father is the same as my mother’s father, but our common grandfather passed along no genes to either of us. Our ability to detect this common ancestor may be affected by these genetic circumstances, but the fact that we have a common grandfather would remain.
Does the idea of being a descendant of Jesus have any meaning? For me even less so than before. Not only is the likelihood of having the gene for holiness infinitesimally small, but almost everybody else has him as an ancestor as well. Could Dan Brown have known this? The Da Vinci Code was published in 2003, Chang’s paper in 1999, so yes! But in view of the historical accuracy of many of the other things in the book, it does not surprise me that he was not up to date on the statistical literature either.
Everybody will either become a common ancestor, or leave no trace at all. The probability of me becoming a common ancestor to all people in the year 4000 is currently zero. My parents have a marginally better chance.
[1] He is still alive in almost all of us. Picture taken from https://en.wikipedia.org/wiki/William_the_Conqueror
[2] D.L.T. Rohde , S. Olson, and J.T. Chang, Modelling the recent common ancestry of all living humans, Nature, 431, (2004), 562. doi
[3] Every generation the number of base pairs coming from Jesus (or Mary) is halved. In 67 generations this dilutes the original genome by a factor of 10-20. You only have 3×109 base pairs. It would already be very surprising if one of Jesus’s original base pairs is still in us. About the same probability as winning the lottery ten thousand times.
[4] Most of the work is done by a Willem Meier, whose family tree I found on https://gw.geneanet.org/ and with whom I apparently share a set of ancestors six generations ago (Hendrik van Winkel and Marijtje van Noort). There are a few other trees with which I could check some of the generations before that, and the first ten or so generations following William the Conqueror can be found on wikipedia and readily available documents of English heritage societies. Obviously this all becomes rather useless, some of the information is missing or unreliable, and it is extremely likely that the visiting milkman is not just a recent development, despite the risks https://www.youtube.com/watch?v=s4nSt0q_Jfo
[5] There is a website http://www.kareldegrote.nl/ where you can submit your bloodline to Karel de Grote (as Charlemagne is called in the Netherlands). Given the number of generations gone by, the amount of wives (6) and known concubines (4) he had children with, we can safely conclude that the majority of people in Europe could produce a link. And probably even more than that, since Charlemagne was also a guest of Haroen al-Rasjid, and considering his fondness of women, it would be very surprising if he had not grabbed some pussy in the middle east as well.
[7] Richard Dawkins, The Ancestor’s Tale, A pelgrimage to the Dawn of Life, Weidenfeld & Nicholson, (2004). Rendezvous 0, All Humankind. ISBN: 0-618-00583-8
[8] J.T. Chang, Recent Common Ancestor of All Present-day Individuals, Adv. Appl. Prob., 31, (1999) 1002. doi
[9] There are a number of critical papers and discussions following his publications. Ask me if you are interested, and can’t find them yourself.
[10] Also Theorem 1 is a statistical result, and the simulation is just one realization of the model for a population of 5. Other realizations will give a different generation for the MRCA. The theorem only tells us what happens when we average over all of these.
[11] J.T. Chang, Reply to discussants: recent common ancestors of all present-day individuals, Adv, Appl. Prob., 31, (1999), 1036. | {"extraction_info": {"found_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": 0.5917124152183533, "perplexity": 1129.6137883401157}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988802.93/warc/CC-MAIN-20210507181103-20210507211103-00588.warc.gz"} |
https://stats.stackexchange.com/questions/188762/which-statistical-test-is-appropriate-for-my-data | # Which statistical test is appropriate for my data?
First 5 rows of my data are as follows:
before after exercise_type
17.4 16.74 1
17.5 18.74 2
17.2 25.62 1
18.0 16.65 3
18.0 16.60 1
where before is the weight before the exercise, after is the weigh after the exercise and exercise_type is the exercise that was applied. I want to investigate which exercise type led to more weight lose. I have 50 observations. Which test should I use?
You should use ANOVA and a Tukey Range Test.
The top google result for ANOVA is:
https://statistics.laerd.com/statistical-guides/one-way-anova-statistical-guide.php
Which is captioned with:
The one-way analysis of variance (ANOVA) is used to determine whether there are any significant differences between the means of three or more independent (unrelated) groups. This guide will provide a brief introduction to the one-way ANOVA, including the assumptions of the test and when you should use this test.
This will tell you whether there is a difference in means between the treatment groups.
Then, post-hoc, you can use a Tukey Range Test, as Kevin rightly suggested in another answer, to help you determine which treatments differ.
• But my data are repeated. Does that make any difference? I suppose I should use Factorial Repeated Measures ANOVA. Am I right? – Günal Dec 30 '15 at 21:24
• Sure, you could either use repeated measures ANOVA and consider before and after $T_1$ and $T_2$ or ANOVA and consider after-before as the value. – Thomas Cleberg Dec 30 '15 at 21:29
If somebody would correct me, please do, but I believe one analysis would be Tukey's HSD. Here is a link for more information.
https://en.wikipedia.org/wiki/Tukey%27s_range_test
Basically, when you have more than two levels (exercise type), it becomes more difficult to do a proper test without taking into consideration the # of levels you have. Do you only have 3 levels?
edit @Thomas Cleberg is probably right but we'll see I guess!
• I have 5 levels. I am interested in the sharpest decrease in the weight. – Günal Dec 30 '15 at 21:23
• Actually, given that you're looking for the highest effect of exercise treatments, the answer is both ANOVA and a Tukey Range Test. That is, you'd use ANOVA to test if there is a difference and Tukey post hoc to find the highest effect. – Thomas Cleberg Dec 30 '15 at 21:38
• As answers can change position, and other answers can be added, references to answers "above" or "below" can be wrong or ambiguous. I've edited to specify the author in question. That would remain valid if there are other answers (and would only be rendered invalid if the answer was deleted). – Nick Cox Dec 31 '15 at 2:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.5946702361106873, "perplexity": 850.4071239918106}, "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/1570986655735.13/warc/CC-MAIN-20191015005905-20191015033405-00446.warc.gz"} |
http://tex.stackexchange.com/users/16855/christian-clason?tab=activity | # Christian Clason
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# 73 Actions
May28 awarded Enlightened May28 awarded Nice Answer Mar17 revised LaTeX Editors/IDEsadd link to MacVim, code completion Feb3 reviewed Excellent How can I draw nucleosomes with wrapped DNA in tikz or pstricks? Feb3 reviewed Excellent In biblatex, make title sentence case but not journal name Feb3 reviewed Satisfactory How do I change the basic font into 'Corbel'? Feb3 reviewed Excellent Back references for shorthandlist Feb3 reviewed Excellent Link enumerate item to subsection Feb3 reviewed Excellent In-row table page break Feb3 reviewed Excellent Improve a fraction's appearance Feb3 reviewed Excellent How to indent the whole text and float environment? Feb2 awarded Custodian Feb2 reviewed Excellent TikZ shadings and printing incompatibility Jan17 awarded Informed Jan14 comment Sorted list of publications in moderncv from bibtex@Katuyci - In this case, I would indeed suggest asking a new question (use the link at the bottom of this page) and describing exactly what you want. This will have a much greater chance of getting the attention of the bibtex experts here. Jan13 comment Sorted list of publications in moderncv from bibtex@Katuyci - Sorry, I don't have a quick solution. The problem is that moderncv patches into the thebibliography environment, and that messes up the indentation of the labels. My quick suggestion would be to simply insert the subheadings by hand (as subsections). Dec18 comment $\epsilon$ undefined using Minion Pro with pdftex@NunoNunes - You are very welcome. Do ask that followup question; it would be very useful to have somewhere a set of instructions for using the new scripts on Windows. Dec16 reviewed Reviewed How do I forward a length from a command into a column specifier? Dec16 comment $\epsilon$ undefined using Minion Pro with pdftex@NunoNunes - If the package is already installed, you should not have to do anything (except possibly setting the path to include the corresponding directory). Unfortunately, I'm not very familiar with MiKTeX and Windows. I think it would be a good idea to ask a new question on "Using FontPro with MiKTeX" (with a link to the new scripts); that way you have a much better chance of getting the experts to help you (who wouldn't necessarily see these comments). Dec14 comment $\epsilon$ undefined using Minion Pro with pdftexWhich version of the MinionPro font do you have? (You can check with otfinfo.) My (working) version is Version 2.103;PS 2.000;hotconv 1.0.67;makeotf.lib2.5.29150, which I got from (IIRC) Adobe Reader 10 under MacOS X. | {"extraction_info": {"found_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": 0.6914530992507935, "perplexity": 5265.169424342058}, "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/1368709224828/warc/CC-MAIN-20130516130024-00012-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://pos.sissa.it/358/349/ | Volume 358 - 36th International Cosmic Ray Conference (ICRC2019) - CRI - Cosmic Ray Indirect
The results and future prospects of the LHCf experiment
H. Menjo*, O. Adriani, E. Berti, L. Bonechi, M. Bongi, G. Castellini, R. D'Alessandro, M. Haguenauer, Y. Itow, K. Kasahara, Y. Matsubara, Y. Muraki, K. Ohashi, P. Papini, S. Ricciarini, T. Sako, N. Sakurai, K. Sato, Y. Shimizu, T. Tamura, A. Tiberio, S. Torii, A. Tricomi, B. Turner, M. Ueno and K. Yoshidaet al. (click to show)
Full text: pdf
Pre-published on: July 22, 2019
Published on: July 02, 2021
Abstract
The LHCf forward (LHCf) experiment measures the production cross sections of neutral particles emitted to the very forward region of an LHC interaction point in order to test the hadronic interaction models used in air-shower simulations. In this proceedings, we present the neutron and $\pi^0$ spectra measured in $pp$ collisions at $\sqrt{s}$ = 13 TeV. In addition to them, many results will be delivered from currently on-going analyses of data obtained at LHCf-ATLAS common operation, and at the RHICf experiment with $pp$ collisions at $\sqrt{s}$ = 510 GeV, as well as from future LHCf operations with $pp$ and $p\mathrm{O}$ collisions at LHC.
DOI: https://doi.org/10.22323/1.358.0349
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access | {"extraction_info": {"found_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": 0.9157659411430359, "perplexity": 3941.5872234215917}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301720.45/warc/CC-MAIN-20220120035934-20220120065934-00615.warc.gz"} |
http://mathhelpforum.com/differential-geometry/135503-trouble-uniform-continuity-calculation.html | # Math Help - Trouble with Uniform continuity calculation
1. ## Trouble with Uniform continuity calculation
So i have to prove that $f(x)=\frac{1}{\sqrt{x}}$ is uniformly continuous using the definition of uniform continuity...
aka I have to start with $|\frac{\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{c}}}{x-c} + \frac{1}{2\sqrt{c^3}}|$
and knowing that $|x-c|<\delta$, I have to make the first inequality less than $\epsilon$.
I am getting so lost in the calculation and this problem is due tomorrow, someone please help....
2. Uniformly continuous on what domain?
3. $x>0$
4. Does anyone have any idea??
5. Well, it is NOT uniformly continuous on $(0,\infty)$, and it's easy to show this as follows: Consider the sequence $s_{n} = \frac{1}{n^{2}}$, which is Cauchy, but $f(s_{n}) = n$ is not Cauchy, and so $f$ cannot be uniformly continuous. Not exactly sure how to show this using the $\epsilon - \delta$ definition though.
6. yea sorry the problem says for x>0
7. Yes, and for that interval it is NOT uniformly continuous and to somehow use the epsilon-delta definition, you have to show that $\forall \, \delta > 0, \exists \, \epsilon > 0$ such that for some $x,y \in (0,\infty ), |x-y| < \delta$ and $|f(x) - f(y)| \ge \epsilon$. | {"extraction_info": {"found_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": 0.987939715385437, "perplexity": 168.1542379003567}, "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-2015-32/segments/1438042990112.50/warc/CC-MAIN-20150728002310-00281-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://link.springer.com/article/10.1007%2Fs12665-013-2431-y | Environmental Earth Sciences
, Volume 71, Issue 1, pp 277–286
# Variation of cadmium uptake, translocation among rice lines and detecting for potential cadmium-safe cultivars
• Zhang Hongjiang
• Zhang Xizhou
• Li Tingxuan
• Huang Fu
Original Article
## Abstract
Cadmium (Cd) pollution highly threats to rice consumption for humans. This study aims to investigate the variation of Cd uptake and translocation among rice lines and to screen cadmium-safe cultivars (CSCs). Total of 146 rice lines were grown in artificially Cd pollution hydroponics within 30 day followed by a pot culture in which 17 rice lines were planted and treated with different Cd levels until maturity. The results showed that Cd tolerance and Cd accumulation significantly (p < 0.05) varied among 146 rice lines in the hydroponics experiment as well as among the 17 rice lines in the followed pot culture. Cd contents of brown rice significantly correlated with Cd accumulations in plant and their translocation from vegetative organs to edible parts, implying that extremely attention should paid to Cd translocation and its influence factors for CSCs selection. IRBN95-90 and D26B of maintainer lines and Lu5278-I332, Lu17-T21712, Lu17-I2R60 of restorer lines were detected to be potential CSCs under 2 and 10 mg kg−1 Cd level, which confirmed the feasibility of selection of CSCs from rice lines. Therefore, the study confirmed the variations of Cd uptake and translocation among rice lines and a combinatorial and recursive selection process is feasible and affordable to screen CSCs to reduce Cd risk for rice consumption.
## Keywords
Cadmium-safe cultivar (CSC) Rice line Genetic variation Cadmium (Cd)
## Introduction
Pollution with heavy metals has become a critical problem worldwide as a result of mining, disposal of industrial waste, application of fertilizers and metal contaminated sewages (Gupat and Gupta 1998; Liang et al. 2005; Sun et al. 2008). As a non-essential trace element, cadmium (Cd) is fully considered as one of the most hazardous heavy metals due to its toxicity (Arasimowicz-Jelonek et al. 2011; Järup and Åkesson 2009; Zhou et al. 2007; Zhou 2003). Throughout the world, the background content of soil Cd is in the range of 0.01–2 mg kg−1 with a median of 0.35 mg kg−1 (Zhao et al. 2009), unfortunately, more than 2.2 × 107 kg Cd was dumped into soil and water per year (Liu et al. 2009a), leading health risks to humans and animals through the soil biology chain. Therefore, reducing Cd pollution has been an urgent issue for environmental and agro-scientists (Liu et al. 2010).
Over the past period of time, soil remediation, such as topsoil replacement and extraneous matter addition was applied to remove Cd from soil or limit its activity (Chehregani et al. 2009), yet, popularization and application was limited by its high costs and the induced secondary damage (Bidar et al. 2007; Zhou and Song 2004). Recently, more concerns have been reversed to phyto remediation and more than 400 hyper accumulators, which accumulate heavy metal ions in their shoots or roots, have been gradually reported to be suitable for growing in different metalliferous soils (Brooks et al. 1998). It is disappointing that low biomass and unsuitability of applications have questioned their importance (Liu et al. 2008; Qadir et al. 2004), therefore, only paying attention to soil bodies is insufficient to ensure Cd-safe food production. Based on the theory that Cd tolerance and accumulation varied among species and among cultivars within species, attention should be paid to the selection of pollution-safe plant species and the technology to restrict Cd transportation from Cd-polluted soil to plants for food safety (Kurz et al. 1999; Wang et al. 2007; Yu et al. 2006).
Stable crops have been main diets of human beings for thousands of years. In the last decades, reports have confirmed the existence of potential low-Cd cultivars in conventional crops, such as rice (Oryza sativa L.) (Kurz et al. 1999; Xu et al. 2009), wheat (Triticum sestivum L.) (Li et al. 2003) and maize (Zea mays L.) (Zhang et al. 2000). As one of the important stable crops, the paddy rice is wildly cultivated and consumed all over the world, especially in East Asia. In some regions of Asia, the paddy rice has been reported to be heavily exposed to Cd (Sun et al. 2010). Recently, rice cultivars with low Cd content in brown rice were identified (Yu et al. 2006; Li et al. 2012), which confirmed the possibility of seeking for low-Cd cultivars. To reduce the risk of Cd contamination for rice consumption, the health risk of heavy metal and method of cultivating Cd-safety crop were measured and maximum allowable Cd content (0.2 mg kg−1) in paddy rice was emerged according to NFHSC (National Food Hygienic Standard of China 2010). Although several low-Cd cultivars or cadmium-safe cultivars (CSCs) of rice have been reported (He et al. 2006; Yu et al. 2006; Xu et al. 2009), there is few reports about the selection of CSCs from rice lines. As basic materials for rice breeding, rice lines transmit genetic information to their hybridized rice cultivars and selection of CSCs of rice lines can be a basic, but efficacious mode to minimize Cd risk for rice consumption.
In this study, the 146 rice lines, including 33 maintainer lines and 113 restorer lines, were tested to identify characteristic of Cd accumulation and tolerance of rice lines and to screen CSCs as referring to NFHSC limit (Cd content ≤0.2 mg kg−1). Furthermore, whether differences in Cd accumulation between maintainer line and restorer line exist and relationship between Cd accumulation in plant and Cd content in brown rice were also to be concerned.
## Materials and methods
### Experimental design
Experiments were carried out in the experimental areas of Sichuan agricultural university at Ya’an, Sichuan province, China (29°54′E, 103°01′N). Two differential and recursive trials (here after referred to as exp. 1 and exp. 2) were conducted in 2009 (exp. 1) and 2010 (exp. 2) for acquiring CSCs from quantities of Chinese rice lines. In the exp. 1, the artificially Cd pollution hydroponics was conducted to select potential CSCs from a large amount of rice lines. In this experiment, the rice lines treated with 0 and 1 mg L−1 Cd were cultivated 30 days, then growth traits, Cd contents of all the rice line seedlings were detected. Thereafter, the pot culture (exp. 2) was designed in the next year to test the variations of Cd uptake and translocation; more importantly, whether CSCs exist or not was tested as well. In this experiment, the tested rice lines were treated Cd within 0, 2 and 10 mg kg−1, respectively, and the samples of root, stem, leaf, grain and brown rice were collected at the maturity stage. Both of the experiments were conducted in the greenhouse within natural illumination and temperature.
### Rice lines preparation and hydroponics culture (exp. 1)
The 146 rice lines (provided by College of agriculture, Sichuan agricultural university) were used as experimental materials to test the variation of Cd tolerance and accumulation among cultivars and to acquire low-Cd rice lines at seedling stage. All seeds were surface-sterilized by submerged in H2O2 (10 %) for 30 min and in 0.1 % NaClO for 10 h, then, rinsed thoroughly with deionized water and germinated in an incubator at 30 °C for 24 h. The germinated seeds were sown broadcast and cultivated in trays filled with quartz sands. During the seedling period, rice plants were paced in the artificial climate box, in which the intensity of illumination, illumination time, temperature and humidity were set to 30,000 lx, 14 h, 28/20 °C and 75 %. When the third leaf emerged, the seedlings of uniform size were transferred to 40 L (80 × 50 × 10 cm) hydroponics containers, which were assorted with plastic plates with 30 smoothly round holes (three holes for each cultivars and two plants were cultivated into one hole). The composition of the basic nutrient solution was the same as the International Rice Research Institute recommended formula (Wang and Gong 2006). After the plants had been cultivated in complete nutrient solution for 1 week, Cd treatments with three replications were arranged consisting (1) 0 (CK, control) and (2) 1 mg L−1 Cd (prepared by dissolving analytical grade CdCl2∙2.5H20). The nutrient solution was continuously renewed every 4 days and pH in the solution was adjusted to 5–5.5 daily using HCl or NaOH. After 30 days of Cd treatments, samples were harvested. The roots were dipped in 0.1 μmol L−1 EDTA for 30 min to remove the heavy metal ions absorbed at the surface of roots, then, all samples were rinsed four times with distilled water, oven-dried at 75 °C for 48 h, finally, all samples were weighed and ground to sieve through a 100 mesh nylon sieve.
### Soil culture and Cd treatment (exp. 2)
This experiment was conducted to study Cd accumulation and to determine whether potential CSCs existed among 17 rice lines with low or high Cd accumulation selected from exp. 1. The soil was air-dried, sieved through a 6 mm sieve and 10 kg of the soils were placed into each pot. The pots (30 cm in diameter and 40 cm in height) were mixed thoroughly with three levels of Cd in solution: 0 (CK), 2 and 10 mg kg−1, respectively. All pots were ranged in a completely randomized design and submerged in water (2–3 cm above the soil surface) for a month, in the following, the physicochemical properties of the soil were analyzed (Table 1) and five healthy uniform size seedlings of the tested Chinese rice lines (cultivated according to exp. 1) were transplanted into soil culture pots with three replicates for each treatment on May 31, 2010. Pots received N, P and K fertilizers three times i.e., 2.17 g urea and 4 g potassium hydrogen phosphate when the day Cd added and 1 g urea were applied when the 30th day and the 90th day emerged after transplantation. During the rice growing seasons, about 2–3 cm water was maintained above the soil surface. The samples of root, stem, leaf and grain were harvested at maturity during the period of September 28–October 2, 2010. The grain of each treatment was air-dried, weight and then divided into two equal parts. The chaff of one part was removed with sheller machine (JLGJ-45, Zhengzhou, China) according to the standard of “The Testing Methods of Rice Qualities” issued by China Ministry of Agriculture (NY147-88), hereafter brown rice samples were oven-dried and ground through 100 mesh nylon sieve as well as samples of root, stem, leave and grain.
Table 1
Basic physicochemical property of soil used in exp. 2
Soil pH
Org C (g kg−1)
CEC (cmol kg−1)
Total N (g kg−1)
Available P (mg kg−1)
Available K (mg kg−1)
Total Cd (mg kg−1)
CK
6.62
14.0 ± 0.93
11.8 ± 1.39
1.31 ± 0.17
8.63 ± 0.57
69.7 ± 2.72
0.31 ± 0.03
Cd2
1.98 ± 0.17
Cd10
8.99 ± 0.31
### Chemical analysis
Plant samples were digested in a 5:1 (v/v) mixture of HNO3–HClO4 and Cd contents of samples in exp. 1 were determined with FAAS (wavelength 228.8 nm, slit 0.7 nm, AAnalyst 800, Perkin Elmer, USA) and Cd contents of root, stem, leaf, grain and brown rice in exp. 2 were determined with GAAS (wavelength 228.8 nm, slit 0.7 nm, AAnalyst 800, Perkin Elmer, USA) (Zou et al. 2011). Analytical procedure control was synchronously performed fourteen times by measuring the reference materials GBW08503b with Cd content of 0.15 mg kg−1 purchased from the National Center for Certificate Reference Materials, China. The relative standard deviations were 1.56 % in exp. 1 and 0.134 % in exp. 2 and the average recoveries were 106.59 % in exp. 1 and 97.33 % in exp. 2, respectively.
Soil pH, organic matter content, total N, available P, available K in exp. 2 were measured following the method of Bao (2007), total Cd of soil after treatment was determined by GAAS (wavelength 228.8 nm, slit 0.7 nm, AAnalyst 800, Perkin Elmer, USA) following a 5:1:1 (v:v:v) mixture of HNO3–HClO4–HF digestion (Zou et al. 2011).
### Statistical analysis
To explore the relative response of rice lines to different Cd level, the formula of “Growth Traits Response to Stress (GRS)” was applied and calculated as follow.
$${\text{GRS (\% ) }} = \, (G_{\text{Cd}} - \, G_{\text{CK}} ) \, / \, G_{\text{CK}} \times { 1}00$$
where G Cd and G CK are the growth traits i.e., root lengths, root-shoot ratios, plant heights and grain yields under Cd exposures and controls, respectively.
To figure out the translocation of Cd, the indicators of “distribution ratio of Cd to aboveground” and “distribution ratio of Cd from aboveground to grain” were calculated. We calculated the distribution of Cd to aboveground and the distribution of Cd from aboveground to grain as follows:
$${\text{Distribution ratio of Cd to aboveground\,(\%) }} = \frac{\text{Cd accumulation aboveground}}{\text{Cd accumulation in total}} \times 100$$
$${\text{Distribution ratio of Cd from aboveground to grain\,(\%) }} = \frac{\text{Cd accumulation in grain}}{\text{Cd accumulation aboveground }} \times 100$$
where Cd accumulation aboveground is the sum of Cd accumulations of stem, leaf and grain, and Cd accumulation in total is the sum of Cd accumulations of root, stem, leaf and grain.
Data were analyzed with statistical software of SPSS 17.0, Origin 8.0 and Excel 2007 for windows. An one-way ANOVA was performed for the various of cultivars, where cultivar and its linked cultivar type (maintainer or restorer line) was considered as a random factor, followed by presenting the results at the 0.05 confidence interval.
## Results
### Cd tolerance and accumulation of 146 rice lines
Growth response to stress (GRS) can be used to evaluate the tolerance of plant when exposed to heavy metals. GRSs of root shoot ratio, plant height and root length (GRS-SRSs, GRS-PHs, GRS-RLs) were in great variation among 146 rice lines as well as GRSs of dry weight (GRS-DWs), however, such situation was not detected between maintainer line and restorer line, i.e., the response characteristic of all tested growth traits of restorer lines were in consistent with those of maintainer lines (Table 2). This suggested that the tolerance of rice lines to Cd stress should be cultivar dependent.
Table 2
Growth responses to Cd stress (GRS %) of 146 rice lines in exp.1
Traits
GRS-RSR
GRS-PH
GRS-RL
GRS-DW
ML
RL
ML
RL
ML
RL
ML
RL
Minimum
12.8
8.4
−43.4
−52.4
−38.8
−48.4
−61.7
−67.1
Maximum
85.9
98.1
−15.1
−17.7
57.3
71
27.7
35.6
Average
46.4
47.5
−29.5
−38.7
4.6
4.1
−24.6
−39.5
Standard deviation
26.7
4
10.1
9.9
29.5
29.7
26.6
24.4
Coefficient of variation
57.4
49.2
34.2
25.5
640.2
610.2
108.5
61.7
F value
2.28**
3.04**
2.32**
2.69**
8.40**
7.84**
2.28**
1.78**
GRS-RSR, GRS-PH, GRS-RL and GRS-DW symbolize the responses of growth traits i.e., RSR root-shoot ratio, PH plant height, RL root length and DW plant dry weight to Cd stress
ML and RL indicate rice maintainer lines (n = 33) and restorer lines (n = 113), respectively.* and ** means significant difference at 0.05 and 0.01 level by using LSD test, respectively
Under 1 mg L−1 of Cd exposure, Cd contents in plant of 146 rice lines were in the range of 44.43–124.02 mg kg−1 and averaged 71.07 mg kg−1, Cd accumulation ranged from 12.02 to 59.86 μg plant−1 and averaged 26.82 μg plant−1. Even though restorer line and maintainer line are in different function for rice breeding, the ability of Cd absorption was somewhat in the same level (Fig. 1). That is to say, it is possible for selecting potential rice CSCs from the tested materials.
Based on the concept of CSCs, 14 rice lines (including six maintainer lines and eight restorer lines) were selected as potential CSCs using cluster analysis (by taking the growth responses to Cd stress of all tested traits (GRS-SRSs, GRS-PHs, GRS-RLs and GRS-DWs) and Cd contents in plant as standard factors). Especially, three of high Cd accumulation rice materials were observed, whose Cd contents were almost twofold higher than average Cd contents of those 14 rice lines.
### Cd distribution in plants of the 17 tested rice lines
Cd content and Cd accumulation in different organs i.e., roots, stems, leaves and grains of the 17 rice lines are in Table 3. On one hand, significant (p < 0.0.5) difference of Cd content and accumulation in each organ was detected among the 17 rice lines under either level of Cd exposure. Especially, the grain Cd contents ranged from 0.03 to 0.49 mg kg−1 under Cd treatments 2 mg kg−1 (Cd2) and from 0.11 to 1.00 mg kg−1 under Cd treatments 10 mg kg−1 (Cd10), while Cd accumulation were 0.26–4.36 μg plant−1 for Cd2 and 0.81–5.53 μg plant−1 for Cd10, respectively. On the other hand, with regard to Cd content and distribution ratio among different organs, large variation were observed both in Cd2 and Cd10, overall, the average ratios of Cd content in root:stem:leaf:grain were 95.2:6:3.6:1 under Cd2 and 180.3:8.2:3.0:1 under Cd10 with the average Cd distribution in root:stem:leaf:grain 42:6.5:3.2:1 for Cd2 and 44:5.8:2:1 for Cd10. However, Cd contents and accumulations in root, stem, leaf and grain of restorer lines were similar with those of maintainer lines.
Table 3
Variations among 17 rice lines on Cd content (mg kg−1) and quantity accumulation (μg plant−1) in different organs of rice plants exposed to Cd at maturity in exp. 2
Cd content
In root
In stem
In leaf
In grain
Cd2
Cd10
Cd2
Cd10
Cd2
Cd10
Cd2
Cd10
Minimum
6.16
107.66
0.63
2.38
0.32
0.80
0.06
0.11
Maximum
30.41
640.58
1.72
9.34
1.25
2.46
0.49
1.00
Average
16.97
246.93
1.07
3.67
0.64
1.32
0.18
0.45
Standard deviation
6.49
152.89
0.35
1.72
0.29
0.44
0.12
0.30
Coefficient of variation
38.27
61.92
33.15
46.78
45.55
32.99
66.57
66.82
F value
239.5**
262.4**
235.5**
162.5**
129.4**
48.9**
41.4**
284.2**
Cd accumulation
In root
In stem
In leaf
In grain
Cd2
Cd10
Cd2
Cd10
Cd2
Cd10
Cd2
Cd10
Minimum
13.50
63.47
1.27
6.07
0.50
2.30
0.26
0.81
Maximum
42.47
188.93
13.91
49.11
6.85
14.23
4.36
7.57
Average
25.90
127.50
4.61
18.11
2.20
5.68
1.38
3.12
Standard deviation
8.70
40.87
3.22
11.61
1.56
3.21
1.02
2.01
Coefficient of variation
33.58
32.05
69.77
64.09
71.02
56.42
73.72
64.39
F value
15.0**
9.5**
63.0**
35.6**
91.7**
57.7**
29.9**
34.7**
** Means significant difference at 0.05 and 0.01 level by using LSD test, respectively
### Yields and Cd accumulations of brown rice
Either under Cd stress or not, brown rice yields were highly variable among the tested 17 Chinese rice lines (Table 4), which seemed to imply that the effects of Cd on yield were both genetic and Cd level dependent. Yield response to Cd stress (YRS) was calculated to evaluate Cd tolerance of brown rice yield and variations in YRS were highly significant among cultivars in spite of those between types both under Cd2 and Cd10 (Table 4). Meanwhile, average YRSs in maintainer line and restorer line were similarly below 0 either under Cd2 or Cd10. That is to say, Cd decreased brown rice yields differently among cultivars, but similarly between types.
Table 4
The brown rice yields (g plant−1) and yield response to Cd stress (YRS, %) of 17 rice cultivars in exp.2
Type
Cultivars
Brown rice yield
YRS
CK
Cd2
Cd10
Cd2
Cd10
ML
DiguB
17.4bc
17.0bc
16.3ab
−2.46
−3.84
Zhong9B
13.7def
15.3cd
15.1 cd
11.16
−1.03
IRBN95-90
20.8a
20.2a
19.3a
−2.72
−4.80
Wujin4B
9.9 g
11.8e
11.3ef
19.78
−4.48
D26B
12.6ef
12.4de
12.8de
−1.67
3.70
Xiang2B
13.2ef
11.8e
11.4ef
−10.48
−3.67
Mian5B
19.4ab
17.8ab
13.8 cd
−8.37
−22.64
KangfengB
20.1ab
18.3ab
16.2abc
−9.06
−11.09
RL
Lu5278-I332
12.4f
12.9de
14.0 cd
4.20
8.26
Lu17-T2171
12.4f
12.1e
10.2f
−2.66
−15.88
Lu17-T21712
16.9bc
16.5bc
18.8ab
−2.04
13.63
Lu17-IR199
16.7bc
17.3ab
17.6ab
3.70
1.69
Luhui602
16.6bc
16.1bc
15.6bc
−3.03
−3.14
Lu5274-I332
19.6ab
17.6ab
12.9de
−10.11
−26.74
Lu17-I2R60
15.3 cd
13.8de
11.2ef
−9.83
−18.89
Luhui17
15.2de
13.8de
12.6de
−9.20
−8.55
R527-M63
14.2def
14.5 cd
15.5bc
1.99
7.35
The same letters of each column indicate no significant difference at 0.05 level by using LSD test. YRS2 and YRS10 symbolize the brown rice yield response to 2 and 10 mg kg−1 Cd stress, respectively
Brown rice Cd contents were significant different (p < 0.01) among the tested 17 Chinese rice lines under Cd treatments (Cd2 and Cd10). Cd contents were 0.028–0.486 mg kg−1 (average of 0.164 mg kg−1) for Cd2 and 0.073–0.962 mg kg−1 (average of 0.427 mg kg−1) for Cd10 (Fig. 2). Cd contents in brown rice of the eleven Chinese rice lines (including five maintainer lines and six restorer lines) were below the safe limits according to the NFHSC standard in a low Cd contaminated soil, remarkably, some of the tested Chinese rice lines (IRBN95-90, D26B of maintainer lines and Lu5278-I332, Lu17-T21712 and Lu17-I2R60 of restorer lines) produced safe brown rice for rice consumption even when soil Cd contamination approached 10 mg kg−1 (Fig. 2). In addition, brown rice Cd content was detected to be little difference between maintainer and restorer lines. The results indicated that variation of Cd content in brown rice was cultivar and Cd contamination level dependent, while not submit to rice line types.
### Relationship between brown rice Cd content and plant Cd accumulation and distribution
Cd contents in brown rice showed positive and significant correlation with Cd total accumulation in rice plant in exp. 1 (p < 0.01), Cd total accumulation in whole plants (p < 0.01) and Cd distribution ratios to aboveground parts in exp. 2 (p < 0.01) (Figs. 3 and 4). Meanwhile, Cd accumulation in plant in exp. 1 and in exp. 2 were in a positive and significant relationship (p < 0.01) (Fig. 3), which symbolized that the results in exp. 2 were excellently consistent with those in exp. 1. In contrast, the brown rice Cd content correlated significantly, but negatively with Cd distribution proportion of grain in shoot (p < 0.05) (Fig. 5). These demonstrated whether Cd level in edible part exceed safety standard not only subject to Cd accumulation ability but also to Cd transport capacity of plant.
## Discussion
Cd is one of the most toxic metallic pollutants, and it enters bodies of plant and animal through the soil–plant–animal system. Cd affects photosynthesis and antioxidant enzymes, resulting in growth inhibition and reduction in food production. Liu et al. (2007a) found that plant dry matters and grain yields of six rice cultivars were in great variation under 100 mg kg−1 soil Cd stress. Yu et al. (2006) also figured out that brown rice yields of 43 rice cultivars varied significantly (threefold in most) either under low Cd level or high Cd level. The results in the present hydroponics experiment showed that biomasses of rice lines exposed to 1 mg L−1 Cd were reduced. When respecting the Cd toxicity, significant variation was found among the 146 rice lines (Table 2), which, to a certain extent, suggested that variation of Cd tolerance was due to genotype. Meanwhile, when respecting the yields among rice lines, significant difference was detected both under CK and Cd treatments, when compared with CK, yields of brown rice were averagely and slightly reduced under Cd treatments (Table 4), such phenomenon has been previously observed in paddy rice (Yu et al. 2006; Wu et al. 1999). This phenomenon indicated that the influence of Cd on rice lines was existed but differing in cultivars.
It is publicized that Cd accumulation varied greatly among species and cultivars within a species (Kurz et al. 1999; Liu et al. 2007b). In Japan, Arao and Ae (2003) figured out that large difference in Cd content was explored among 49 cultivars of rice grown in containers. Although in China, paddy rice has been reported to be greatly variable in Cd uptake and transport as well as Cd tolerance among cultivars and between types (i.g., normal type and hybrid) (Yu et al. 2006; Xu et al. 2009; Liu et al. 2003a, b, 2005; Wu et al. 1999). In the present study, visible variation was observed among 146 rice lines both in Cd tolerance and Cd accumulation (Fig. 1), while Cd contents in root, stem and leaf of the 17 rice lines in exp. 2 were significant different, which was consistent with the results of exp. 1 (Table 2). However, Cd accumulation between maintainer line and restorer line was not significant different, that is to say, although the usage of maintainer line and restorer line is different, their genetic characteristics of anti-cadmium in relatively independent and consistent. This phenomenon confirmed the repeatability of Cd accumulation of rice plant and suggested that selection of CSCs from either maintainer lines or restorer lines could be feasible.
Partial distribution of Cd in plants has been reported to be derived by the translocation of Cd from shoot to grain (Arao and Ishikawa 2006). Former reporter accounted that Cd content of edible part was governed by the translocation of Cd from vegetative to generative parts of plant (Morghan 1993) and Cd content in brown rice were significantly correlated with Cd accumulation in rice plant and Cd distribution ratio to aboveground parts (Liu et al. 2007b). Presently, brown rice Cd content correlated significantly (p < 0.01) with total Cd accumulation in plant, Cd distribution ration aboveground and Cd distribution ratio from aboveground to grain (Figs. 3, 4 and 5). It demonstrated that Cd content in generative parts were somehow (maybe genetic) governed by Cd absorption ability and its translocation. Therefore, we should not only focus on Cd accumulation at vegetative stage, but also on Cd translocation for evaluating crop response to Cd and selecting CSCs.
With regard to CSCs selection, NFHSC, in which the maximum permissible Cd content is 0.2 mg kg−1, was frequently applied to be the standard for measuring the safety of rice consumption. Under this standard, paddy rice cultivars produced safe grain or brown rice were selected from the tested rice cultivars in the soil culture experiments, where pots were exposed to Cd at a low level under waterlogging condition (Xu et al. 2009; Yu et al. 2006). On the contrary, no CSC was found under a high level of Cd exposure. Therefore, Yu et al. (2006) pointed that CSCs-selection was highly attached to the level of soil Cd. In this study, eleven rice lines were safe for human feeding under the low level soil Cd treatment (2 mg kg−1), when soil Cd approached to 10 mg kg−1, there were still five rice lines whose Cd content were below 0.2 mg kg−1 in brown rice (Fig. 2). Therefore, two conclusions can be summed up based on our experiments. First, CSCs selection was somewhat both genetic regulated and pollution level dependent. On one hand, although Cd level differed fivefold, five rice lines could be identified as potential CSCs both under low soil Cd level and the higher soil Cd level, which confirmed the genotype advantage to minimize Cd accumulation. On the other hand, Brown rice Cd content of 6 cultivars, which produced safe brown rice for food consumption under Cd treatment Cd2, exceeded 0.2 mg kg−1 under Cd treatment Cd10. Second, slightly variation of Cd content between maintainer line and restorer line was observed in edible parts. The variation of Cd content in rice plant was repeatable and extremely consistent between the recursive two experiment (exp. 1 and 2), which symbolized the consistency of Cd uptake and transportation between rice line types.
Cd accumulation in plant is convinced to be governed by genes and environment influence (Nwugo and Huerta 2008). Increasing Cd content in environment enhances security risks of human feeding. Khan et al. (2008) reported that Cd contents of food crops grown in soil irrigated with wastewater were much higher those in the uncontaminated soil. Feng et al. (2011) studied on the relationship between crop (paddy rice) Cd content and traffic-related contamination in Eastern China and significant correlation was found. He also pointed that heavy metal contents in rice plants were different caused by the distance from rice planted to the road edge. The results in our study showed that Cd contents differed in Cd levels. When Cd was 2 mg kg−1 soil, almost 65 % of the tested rice lines produced safe brown rice for human feeding (Cd contents were below 0.2 mg kg−1), when Cd added to fivefold of the low Cd level, Cd contents of all of the rice lines increased (Fig. 2). Meanwhile, Cd uptake and translocation were also genetic governed and its affection may be higher than environment influence. Liu et al. (2009b) reported that a dose of 0.25 and 0.5 mg L−1 directly leaded to expression of DNA MMR genes in the Arabidopsis seedling, suggesting its function of genetic control. Similarly, QTLs analysis directed by Chen et al. (2009) suggested that Cd contents in brown rice were connected with 2 QTLs, which are both located on the eleventh chromosome. He also pointed out that Cd content in brown rice was a relative independent, but genetic governed trait. Therefore, breeding CSCs can be a widespread approach to reduce Cd risk for food consumption. Yu et al. (2006) pointed that pollution-safe rice cultivars could be found from a large amount of rice cultivars. Liu et al. (2007b) figure out that brown rice Cd content was not only subject to Cd uptake but also translocation. In our study, the Cd ions in brown rice content came from root absorption and the translocation from other parts, which was similar with theirs. Thus, the selection of CSCs of rice lines could be an effective method to breeding cadmium-safe rice cultivars.
Concept of cultivar selection provides an option for farmer to minimize Cd risk in the human food chain. As basic materials for rice breeding, rice lines carrying the low-Cd trait must be embedded the acceptable characteristics for yield, quality, farming-suitability and pest and disease resistance. Therefore, constraints in breeding and developing applicable and acceptable CSCs for breeders are still on the horizon. Consequently, as long as the Cd risk exists, selection and application of CSCs is in large and serious demand (i.g., stabilities of low-Cd traits after hybridization and qualities and yields of CSCs) and environmental effects (i.g., management practices, role of radial oxygen loss (ROL) in the regulation of anti-cadmium) are eager to be exposed in further studies.
## Conclusion
The present work demonstrates that Cd uptake and translocation are significant variation among rice lines. With the conception of CSCs, Cd uptake as well as Cd translocation should be concerned. Under the controlled condition, IRBN95-90, D26B (maintainer line) and Lu5278-I332, Lu17-T21712 and Lu17-I2R60 (restorer line) were verified as potential CSCs. It exhibited that Cd accumulation is consistent between maintainer line and restorer line and a combinatorial and recursive selection process is feasible and affordable to screen CSCs. Furthermore, to reduce Cd risk, the application of CSCs and appropriate farming management are both important because of its genetic and environment dependent.
## Notes
### Acknowledgments
This work was financially supported by the National Natural Science Foundation of China (No. 30230250), Keystone Program from the Office of Education in Sichuan Province (No. 2006A008) and the State Key Laboratory of Soil and Sustainable Agriculture (No. 055124).
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© Springer-Verlag Berlin Heidelberg 2013
## Authors and Affiliations
• Zhang Hongjiang
• 1
• Zhang Xizhou
• 1
• Li Tingxuan
• 1
• Huang Fu
• 2
1. 1.College of Resource and Environmental ScienceSichuan Agricultural UniversitySichuanPeople’s Republic of China
2. 2.Rice Research InstituteSichuan Agricultural UniversitySichuanPeople’s Republic of China | {"extraction_info": {"found_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": 0.7627989649772644, "perplexity": 14213.032707517083}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156096.0/warc/CC-MAIN-20180919083126-20180919103126-00344.warc.gz"} |
https://lost-stats.github.io/Contributing/Contributing.html | # HOW TO CONTRIBUTE
1. Get a GitHub account. You do not need to know Git to contribute to LOST, but you do need a GitHub account.
2. Read the Guide to GitHub Markdown which will show the syntax that is used on LOST pages.
3. Read the below LOST Writing Guide, which shows what a good LOST page looks like from top to bottom. Even if you are just adding another language to an existing page, be sure to read the Implementations section at the bottom.
4. Explore LOST using the navigation bar on the left, find a page that needs to be expanded, and add more content. Or find one that doesn’t exist but should (perhaps on the Desired Nonexistent Pages list, and write it yourself! Go to the GitHub Repository for LOST to find the appropriate file to edit or folder to create your new file in.
5. If you are a “Contributor” to the project, you can make your edits and changes directly to the repository. If not, you will need to issue a pull request to get your work on LOST. We will add you as a contributor after your first accepted pull request. If you don’t know Git or how to do a pull request, please post in Issues asking to be added as a contributor so you can edit LOST directly.
6. If you’ve made a new page, make sure it’s saved as a .md file, put it in the appropriate folder, and add Navigation Information at the top (see below). If you’ve written a Desired Nonexistent Page, be sure to remove it from the list. Or, if your page links to some new nonexistent pages, add those to the list! Also, try to see if other pages have attempted to link to the page you’re working on, and update their links so they go to the right place.
# LOST WRITING GUIDE
A LOST page is intended to be a set of instructions for performing a statistical technique, where “statistical technique” is broadly defined as “the things you do in statistical software”, which includes everything from loading data to estimating models to cleaning data to visualization to reproducible notebooks.
After someone reads a LOST page, they should have a decent idea of:
• How to implement at least a basic version of what they want to do in the language/software they’re using
• What common pitfalls there might be in what they’re doing
• What are the pros and cons of meaningfully-different ways of doing the same thing, if relevant
• Given what they’re doing, what else should they consider doing (for example, if they’re running a regression discontinuity design, you might suggest they also run a test for bunching on either side of the cutoff)
Things to remember while writing:
• Be as clear as possible. You’re writing a set of instructions, in effect. People should be able to follow them.
• The technical ability of the reader may vary by page. People reading a LOST page about how to calculate a mean probably have little experience with their software and will need a lot of hand-holding. You can assume that people reading a LOST page about Markov-Chain Monte Carlo methods probably already have a fairly solid background.
## Markdown
LOST pages are written in Markdown. Markdown is a lightweight and easy-to-use syntax for styling your writing. It includes conventions for
Syntax highlighted code block
- Bulleted
- List
1. Numbered
2. List
**Bold** and _Italic_ and Code text
Note that links in LOST are relative links - when linking to another LOST page, don’t use the full URL. Instead of regular-markdown
[Page](url)
instead do, for example:
/Category/page.html
For more details see GitHub Flavored Markdown.
## Math
Math is rendered with MathJax, which provides support for $$\LaTeX$$ math formatting. To use on a specific page, make sure that the YAML at the top on the underlying Markdown (i.e. .md) file includes a line saying mathjax: true. This should already be the default on most existing pages, but it is worth emphasising. For example, here is a screenshot of the “Contributing.md” file that you are reading right now.
After that, equations and other math sections can be delimited with two dollar symbol pairs. For example, $$x = \frac{1}{2}$$ is rendered inline as $$x = \frac{1}{2}$$. Similarly, we can render math in display mode (i.e. as a distinct block) by wrapping the dollar symbol pairs on separate lines. For example,
$$y = \beta_0 + \beta_1 x + \beta_2 x^2 + \epsilon$$
is rendered as display math:
$y = \beta_0 + \beta_1 x + \beta_2 x^2 + \epsilon$
While we don’t include such examples here, note that standard $$\LaTeX$$ math environments such as $$...$$ (for numbered equations) and \begin{align} ... \end{align} (for aligned equation systems) are all supported. Just remember to wrap them between a pair of dollar symbols. More information about MathJax can be found here.
# STRUCTURE OF A LOST PAGE
When starting a LOST page, you should copy the New Page Template. There are four main sections of a LOST page:
Your page will begin with what’s known as YAML, i.e. something that looks like this:
---
title: Observation level
parent: Data Manipulation
has_children: false
nav_order: 1
mathjax: true
---
You don’t need to worry too much about YAML syntax (here’s the Wikipedia entry for those interested). The important thing is that the YAML provides a set of very basic instructions for the website navigation and page structure. Make sure to fill in the title with a relevant and brief title. Also be sure to put the appropriate name for the parent — this will ensure that your page shows up in the appropriate spot in the navigation structure. Options for parent include:
• Data Manipulation
• Geo-Spatial
• Machine Learning
• Model Estimation
• Presentation
• Summary Statistics
• Time Series
• Other
For the most part, you should generally ignore has_children. (An exception is if you are creating a new section that does have new child pages, but then you are probably better off filing an issue with us to make sure this is done correctly.) You can also ignore nav_order — leaving this at 1 for everything will put everything in alphabetical order.
## Introduction
This is an introduction to the technique. Most of the time this will be just a few sentences about what it is and does, and perhaps why it is used. However, in cases of more niche or complex material, there may be a reason to include more detailed information or general non-language-specific instructions here. In general, however, for more detailed explanations or discussions of statistical properties, you can always just link to an outside trusted source like Wikipedia or a (non-paywalled) academic paper.
## Keep in Mind
This is a list of details and reminders for people using the method, especially if they are not yet an expert at it or if the detail is not well-known. This may include:
• Important assumptions that an estimation method makes.
• Notes about interpreting the results.
• Settings where the technique seems like it might be a good idea, but actually isn’t.
• Features of the technique that might surprise users or be unexpected.
• Rules of thumb for use (“you will want to set the number of bootstrap samples to at least 1,000 (citation)”)
## Also Consider
This is a list of other techniques that are commonly used in addition to this page’s technique, or as an alternative to this page’s technique. If not obvious, include a very brief explanation of why you might want to use that other technique in addition to/instead of the current one. Note that you can link to another LOST page even if that page doesn’t exist yet. Maybe it will inspite someone to write it!
For example, pages about estimation techniques might list standard robustness tests to be used in addition to the technique, or adjustments to standard errors they might want to use. A page about a data visualization technique might include a link to a page about setting color palettes to be used in addition.
Or, they might list an alternative technique that might be used if a certain assumption fails (“This technique requires continuous variables. So if your data is discrete, use this other method.”).
To link to other LOST pages (even if they don’t exist yet — don’t forget to add these to Desired Nonexistent Pages!), we ask that you spell the url in a way our markdown renderer understands. Specifically, please write the url as {{ "/Category_name/page.html" | relative_url }}.
For example, if you’d like to link to this page, please write [Guide to Contributing]({{ "/Contributing/Contributing.html" | relative_url}}) which will then be rendered as Guide to Contributing.
## Implementations
Implementations contains multiple subsections, one for each statistical software environment/programming language that the technique can be implemented in.
• Implementations should be listed in alphabetical order of software/language. eViews, then Python, then R, then SAS, then Stata, etc.
• For each language, include well-commented and as-brief-as-reasonably-possible example code that provides an example of performing the technique. Readers should be able to copy the code and have it run the technique from beginning to end, including steps like loading in data if necessary. See existing pages for examples.
• If someone else on the internet has already written a clear, thorough, and general implementation example, then linking to it is perfectly fine! This includes StackOverflow/StackExchange answers, which you can link to using the share button. Extremely long demonstrations for super-complex methods may be better left as links only (perhaps with a tiny example pulled out and put on LOST). If the example is short enough, though, including the example directly in the LOST page is preferable, with link attribution of the source, so readers don’t have to go elsewhere.
• Avoid creating a long list of examples showing every variant or optional setting of the technique. Instead, focus on one main example, with variants included only if they are especially important. If you like, you can mention in comments additional useful options/settings the reader might want to look into and what they do.
• If the technique requires that a package or library be installed, include the code for installing the package in a comment (or if you are using a language where libraries cannot be installed inside the code, include a comment directing the user to install the library).
• If a given language has multiple ways of performing the same technique, ideally report only one “best” method, whatever that might be. If other methods are only different in trivial ways, then you can describe them as being alternatives, but avoid providing examples for them. If other methods are different in important ways, then include an example for each, with text explanations of what is different about them. If two contributors seriously disagree about which way is best, then they’re probably different in some meaningful way so you can include both as long as you can explain what that difference is.
• It is fine to add implementations for software that only has a graphical interface rather than code (such as Excel) using screenshots. Be sure to keep images well-cropped and small so they don’t crowd the page. If your graphical instructions are necessarily very long, consider posting them as a blog post somewhere and just put a link to that post in Implementations.
Images
Images can be added to Implementation sections if relevant, for example if you’re working with GUI-only software, or demonstrating the output of a data visualization technique.
How can you add these images? You can upload the images somewhere on the internet that allows image linking, and include the image in your instructions with . Ideally, upload the image directly to the Images/name-of-your-page/ subfolder of whatever directory you’re working in, and link to the images there.
Please be sure to add alt text to images for sight-impaired users. Image filenames should make reference to the language used to make them, i.e. python_scatterplot.png.
Data
Ideally, the same data set will be uploaded to LOST directly in a format accessible by many languages (like CSV) in the Data/name-of-your-page/ subfolder of whatever directory you’re wokring in, and then that data can be used for implementation in all languages on the page. This is not required, but is encouraged.
# FREQUENTLY ASKED QUESTIONS
• What techniques are important enough to be their own page? This is a little subjective, but if you’re writing about X, which is a minor option/variant of Y, then you can just include it on the Y page. If X is a different technique or a variant of Y that is used in different circumstances or produces meaningfully different output, then give X its own page.
• How should I title my page? Pick a single, concise description of the technique you’re talking about. If there are multiple ways to refer to the technique you’re doing, pick one. You will also need to select a file name, which should be in lower_case_with_underscores.md and you might want to make a bit shorter. So Ordinary Least Squares (Linear Regression) might be the title and H1 heading, and ordinary_least_squares.md might be the file name.
• What languages can I include in Implementations? Any language is valid as long as it’s something people actually do statistical analysis in. Don’t include something just because you can (I mean, you can technically do OLS in assembly but is that useful for anyone?), but because you think someone will find it useful.
• Should I include the output of my code? For data visualization, yes! Just keep the images relatively small so they don’t crowd the page. See the Implementations section above for how to add images. If your output is not visual, there’s probably no need to include output unless you think that it is especially important for some technique.
• How can I discuss what I’m doing with other contributors? Head to the Issues page and find (or post) a thread with the title of the page you’re talking about.
• How can I [add an image/link to another LOST page/add an external link/bold text] in the LOST wiki? See the Markdown section above.
• I want to contribute but I do not like all the rules and structure on this page. I don’t even want my FAQ entry to be a question. Just let me write what I want. If you have valuable knowledge about statistical techniques to share with people and are able to explain things clearly, I don’t want to stop you. So go for it. Maybe post something in Issues when you’re done and perhaps someone else will help make your page more consistent with the rest of the Wiki. I mean, it would be nicer if you did that yourself, but hey, we all have different strengths, right? | {"extraction_info": {"found_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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.31143924593925476, "perplexity": 1075.4380795113618}, "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-2021-10/segments/1614178373761.80/warc/CC-MAIN-20210305214044-20210306004044-00496.warc.gz"} |
http://mathoverflow.net/questions/63526/dualizing-complex-of-the-product-of-two-locally-compact-spaces | # Dualizing complex of the product of two locally compact spaces
Hello!
In the setting of locally compact Hausdorff spaces, I would like to understand the relation between the exterior product ${\mathbb D}_X\boxtimes{\mathbb D}_Y$ of the dualizing complexes of two spaces $X,Y$ and the dualizing complex ${\mathbb D}_{X\times Y}$ of their product.
So far I could only find a morphism ${\mathbb D}_X\boxtimes{\mathbb D}_Y\to{\mathbb D}_{X\times Y}$ from playing with the adjunctions; however, I can't say anything more specific about it, e.g. give criteria for when it is an isomorphism. In their book "Representation Theory and Complex Geometry", Chriss-Ginzburg state that for $F$ a smooth manifold, there is indeed an isomorphism, but they don't elaborate on that.
Do you know criteria for $X,Y$ ensuring that ${\mathbb D}_X\boxtimes{\mathbb D}_Y\cong{\mathbb D}_{X\times Y}$?
Related to this is the question of constructing a cross product in Borel-Moore homology. Using the map from above, one can get such a cross product. On the other hand, at seems to me that since Borel-Moore homology is dual to compactly supported sheaf cohomology, one can also construct a cross product by dualizing the Künneth isomorphism for compactly supported cohomology . Now the second question I have is:
Do these two cross products coincide?
In general, I would be happy to have a detailed reference for these issues, as Chriss-Ginzburg is rather short on Borel-Moore homology.
Thank you!
Hanno
- | {"extraction_info": {"found_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": 0.9276400804519653, "perplexity": 181.46895194518547}, "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-2016-07/segments/1454701165697.9/warc/CC-MAIN-20160205193925-00318-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://scirate.com/arxiv/physics.flu-dyn | # Fluid Dynamics (physics.flu-dyn)
• Plane Poiseuille flow, the pressure driven flow between parallel plates, shows a route to turbulence connected with a linear instability to Tollmien-Schlichting (TS) waves, and another one, the bypass transition, that is triggered with finite amplitude perturbation. We use direct numerical simulations to explore the arrangement of the different routes to turbulence among the set of initial conditions. For plates that are a distance $2H$ apart and in a domain of width $2\pi H$ and length $2\pi H$ the subcritical instability to TS waves sets in at $Re_{c}=5815$ that extends down to $Re_{TS}\approx4884$. The bypass route becomes available above $Re_E=459$ with the appearance of three-dimensional finite-amplitude traveling waves. The bypass transition covers a large set of finite amplitude perturbations. Below $Re_c$, TS appear for a tiny set of initial conditions that grows with increasing Reynolds number. Above $Re_c$ the previously stable region becomes unstable via TS waves, but a sharp transition to the bypass route can still be identified. Both routes lead to the same turbulent in the final stage of the transition, but on different time scales. Similar phenomena can be expected in other flows where two or more routes to turbulence compete.
• We investigate the accuracy and robustness of one of the most common methods used in glaciology for the discretization of the $\mathfrak{p}$-Stokes equations: equal order finite elements with Galerkin Least-Squares (GLS) stabilization. Furthermore we compare the results to other stabilized methods. We find that the vertical velocity component is more sensitive to the choice of GLS stabilization parameter than horizontal velocity. Additionally, the accuracy of the vertical velocity component is especially important since errors in this component can cause ice surface instabilities and propagate into future ice volume predictions. If the element cell size is set to the minimum edge length and the stabilization parameter is allowed to vary non-linearly with viscosity, the GLS stabilization parameter found in literature is a good choice on simple domains. However, near ice margins the standard parameter choice may result in significant oscillations in the vertical component of the surface velocity. For these cases, other stabilization techniques, such as the interior penalty method, result in better accuracy and are less sensitive to the choice of the stabilization parameter. During this work we also discovered that the manufactured solutions often used to evaluate errors in glaciology are not reliable due to high artificial surface forces at singularities. We perform our numerical experiments in both FEniCS and Elmer/Ice.
• Understanding the statistics of ocean geostrophic turbulence is of utmost importance in understanding its interactions with the global ocean circulation and the climate system as a whole. Here, a study of eddy-mixing entropy in a forced-dissipative barotropic ocean model is presented. Entropy is a concept of fundamental importance in statistical physics and information theory; motivated by equilibrium statistical mechanics theories of ideal geophysical fluids, we consider the effect of forcing and dissipation on eddy-mixing entropy, both analytically and numerically. By diagnosing the time evolution of eddy-mixing entropy it is shown that the entropy provides a descriptive tool for understanding three stages of the turbulence life cycle: growth of instability, formation of large scale structures and steady state fluctuations. Further, by determining the relationship between the time evolution of entropy and the maximum entropy principle, evidence is found for the action of this principle in a forced-dissipative flow. The maximum entropy potential vorticity statistics are calculated for the flow and are compared with numerical simulations. Deficiencies of the maximum entropy statistics are discussed in the context of the mean-field approximation for energy. This study highlights the importance entropy and statistical mechanics in the study of geostrophic turbulence.
• We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect; or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely Galilean invariance.
• Internal gravity waves play a primary role in geophysical fluids: they contribute significantly to mixing in the ocean and they redistribute energy and momentum in the middle atmosphere. Until recently, most studies were focused on plane wave solutions. However, these solutions are not a satisfactory description of most geophysical manifestations of internal gravity waves, and it is now recognized that internal wave beams with a confined profile are ubiquitous in the geophysical context. We will discuss the reason for the ubiquity of wave beams in stratified fluids, related to the fact that they are solutions of the nonlinear governing equations. We will focus more specifically on situations with a constant buoyancy frequency. Moreover, in light of recent experimental and analytical studies of internal gravity beams, it is timely to discuss the two main mechanisms of instability for those beams. i) The Triadic Resonant Instability generating two secondary wave beams. ii) The streaming instability corresponding to the spontaneous generation of a mean flow.
• We formulate a general criterion for the exact preservation of the "lake at rest" solution in general mesh-based and meshless numerical schemes for the strong form of the shallow-water equations with bottom topography. The main idea is a careful mimetic design for the spatial derivative operators in the momentum flux equation that is paired with a compatible averaging rule for the water column height arising in the bottom topography source term. We prove consistency of the mimetic difference operators analytically and demonstrate the well-balanced property numerically using finite difference and RBF-FD schemes in the one- and two-dimensional cases.
• We propose a model for the density statistics in supersonic turbulence, which play a crucial role in star-formation and the physics of the interstellar medium (ISM). Motivated by [Hopkins, MNRAS, 430, 1880 (2013)], the model considers the density to be arranged into a collection of strong shocks of width $\sim\! \mathcal{M}^{-2}$, where $\mathcal{M}$ is the turbulent Mach number. With two physically motivated parameters, the model predicts all density statistics for $\mathcal{M}>1$ turbulence: the density probability distribution and its intermittency (deviation from log-normality), the density variance-Mach number relation, power spectra, and structure functions. For the proposed model parameters, reasonable agreement is seen between model predictions and numerical simulations, albeit within the large uncertainties associated with current simulation results. More generally, the model could provide a useful framework for more detailed analysis of future simulations and observational data. Due to the simple physical motivations for the model in terms of shocks, it is straightforward to generalize to more complex physical processes, which will be helpful in future more detailed applications to the ISM. We see good qualitative agreement between such extensions and recent simulations of non-isothermal turbulence.
• The dynamics of interacting quantum vortices in a quasi-2D spatially nonuniform Bose-Einstein condensate is considered in hydrodynamic approximation for the case when equilibrium density of the condensate vanishes at two points of the plane, in each of them the presence of a stationary vortex of several quanta of circulation is possible. A special class of the density profiles is chosen, so that with the help of a conformal mapping of the plane onto a cylinder, analytical calculation becomes possible for the velocity field created by vortices. Equations of motion are presented in a noncanonical Hamiltonian form. The theory is generalized to the case when condensate takes form of a curved quasi-2D shell in the 3D space. | {"extraction_info": {"found_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": 0.9118391871452332, "perplexity": 487.1291440061577}, "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-2017-09/segments/1487501174135.70/warc/CC-MAIN-20170219104614-00178-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://stats.stackexchange.com/questions/178777/density-of-an-empirical-cdf | Density of an empirical cdf
I can figure how the underlying density function of an empirical-cdf looks like? Does it look like a histogram?
It won't have a density, per se. It has a probability mass function, with probability $\frac{1}{n}$ at each sample point.
• (+1) Lest casual readers be misguided, please note that although each data point will get a weight of $1/n$, individual sample values may get greater weights in the pmf, depending on how many data points have those values. – whuber Oct 27 '15 at 0:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6442059874534607, "perplexity": 674.8702759153934}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988725.79/warc/CC-MAIN-20210506023918-20210506053918-00039.warc.gz"} |
https://datascience.stackexchange.com/questions/13191/how-to-compute-conditional-probability-in-code | # How to compute conditional probability in code?
In this paper http://www.aclweb.org/anthology/D13-1176, in "2. Framework" it says
We begin by describing the modelling framework underlying RCTMs. An RCTM estimates the probability $P(f \ | \ e)$ of a target sentence $f = f_1, ..., f_m$ being a translation of a source sentence $e = e_1, ..., e_k$. Let us denote by $f_{i\ : \ j}$ the substring of words $f_i, ..., f_j$. Using the following identity,
$$P(f \ | \ e) = \prod_{i=1}^m P(f_i \ | \ f_{1:i−1}, e)$$
an RCTM estimates $P(f|e)$ by directly computing for each target position $i$ the conditional probability $P (f_i|f_{1:i-1}, e)$ of the target word $f_i$ occurring in the translation at position $i$, given the preceding target words $f_{1:i-1}$ and the source sentence $e$.
I understand the identity that they used, but how is it implemented in terms of code? How can a module calculate such a probability?
For this specific paper, the conditional distribution is calculated as follows:
$P(f_i = v |f_{1:i-1} ) = \frac{\exp(o_{i,v})}{\sum_{v=1}^V\exp(o_{i,v})}$
on page 1702
• You should edit the question? Sep 6 '16 at 6:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.7704610824584961, "perplexity": 650.4594309176541}, "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-2021-39/segments/1631780057018.8/warc/CC-MAIN-20210920040604-20210920070604-00426.warc.gz"} |
https://sea-man.org/lng-carrier-design.html | .
Site categories
The New Generation of Liquefied Natural Gas Carriers – Basic Design Philosophy
Increasing demand of LNG in modern world claims natural gas transportation to be faster. This is why the new generation of Liquefied Gas Carriers should be constructed and designed to carry more LNG, than old natural gas carriers.
Summary
Chantiers de l’Atlantique has built 15 LNG Carriers and is considered as a front runner in terms of innovations. Two vessels (74 000 Cum and 154 000 Cum) now under construction for GAZ DE FRANCE are the achievement of years of R&D and thinking to improve LNG Carriers. They incorporate two major innovations: CS1 new cargo containment system and diesel electric propulsion with dual fuel (DF) engines operated in a lean burn gas mode as priority.
Introduction
Our philosophy for LNG Carriers can be briefly described as follows:
• LNG Carriers as most large cargo ships are of rectangular shape and rectangular cargo tanks fit best in such a shape with optimum use of volumes without large openings in the upper deck. Membrane type cargo containment systems are the adapted solution for hull design and increasing size of tanks on bigger ships.
• Among membrane type systems, priority should be given to those which are the lightest and the thinnest for a given boil-off level. The TGZ mark III system or the new CS1 system which both use PUF (polyurethane foam) as insulation material fulfill such requirements. We have taken an active part to the development of CS1 and are the first yard to apply it.
• LNG Carriers are primarily LNG Carriers. They should be designed to deliver a maximum amount of cargo. This is what owners expect. Any other weight should be minimised.
• There are and there will always be size limitations which result in displacement limitations. To compare correctly LNG Carriers and technical solutions, the same loaded displacement should be the basis. This is how we have made our comparisons.
• For a given displacement which may be limited by existing or new terminals, delivered cargo will be equal to total displacement in loaded condition minus:
• Light ship weight (including tanks insulation and propulsion plant).
• Weight of “fuel” needed for propulsion whatever the “fuel” used: HFO, LNG or a combination of both.
Light ship weight plus “fuel” weight should be as low as possible.
• Propulsion plant efficiency is an important factor as it reduces the weight of fuel needed but it should not be considered alone as used to be done previously when attention was focussed on fuel savings. Propulsion plant is only part of a global solution to deliver economically a maximum of cargo weight. All consequences of choosing the propulsion plant type should be considered.
• Weight and consequently volume of cargo delivered results from above subtractions and not from the volume strictly needed to fit any “compact” propulsion plant. If weight is saved it will be convertible into extra cargo. If no weight is saved, there will be no extra cargo. That is Archimedes’s rule!
• In addition, weights should be correctly positioned within the ship and volume is needed at bow and stern for hydrodynamic efficiency and correct trim.
• LNG is a concentrated fuel (high calories per unit weight). Using LNG in a given plant saves about 20 % on fuel weight. If in addition propulsion plant is more efficient, global “fuel” weight reduction may be about 40 %, leaving more weight for extra cargo.
• LNG is the cheapest fuel available when expressed in $/calorie. Time is also money and if the ship does not need to waste time for refuelling (HFO) more cargo can be delivered and revenues increased. On gas burning ships, loading means also bunkering! • Ecology is a major concern. Solutions such as diesel electric with lean burn gas engines (DF) divide nearly by two CO2 emissions, reject no SOX, are comparable to steam plants for NOX emissions (10 times better than HFO burning diesel engines). Lean burn gas engines are a real break through in terms of ecology. • Economic comparisons of LNG Carriers having same initial displacement should take into account selling price of LNG delivered minus purchase price of LNG loaded and the cost of HFO or DO if such fuels are used for propulsion. • Such comparisons show a clear advantage for diesel electric plants using LNG (natural boil off + forced boil off). They do much better than alternatives such as HFO burning low speed engines and reliquefaction plant. Such plants deliver less cargo even if they do not burn any as they are penalised by extra global initial dead-weight (HFO + low speed engine). • The competition for lower and lower boil-off levels is meaningless on ships which are using natural and forced boil-off as unique fuel taken from cargo tanks. • Insulation need not to be too efficient, hence too thick as on The Liquefied Gas Tanker typesmembrane type ships it reduces volume dedicated to cargo. It should be adapted to offer a safe margin so that natural boil-off does not exceed fuel demand in loaded condition. • Increasing ship’s speed is a way to raise LNG deliveries per ship. An economical compromise can be found between extra cargo delivered and extra cargo owners would accept to burn for propulsion. • Power fitted should be adapted to the highest range of speed expected. Contrarily to steam plants diesel electric plants may be operated efficiently at part loads. • Electric propulsion plant with several diesel generators is the only alternative which offers large flexibility, redundancy and efficiency at any speed and during port operations. It will make the new generation of LNG carriers perfectly adapted to the spot market as well as to classical long term contracts on dedicated routes. • Qualified crews able to operate correctly steam plants are already difficult to find and the problem will become more and more acute in the near future. Using up to date technologies is the right answer to the crew qualification. To summarise, diesel electric propulsion plant using mainly gas from the cargo is a break through which brings a positive answer to all questions related to LNG carriers and is superior in: • Efficiency; • Extra useful cargo capacity; • Savings and extra revenues; • Safety and redundancy; • Ecology; • Crew; • Etc. Soon it will become the new reference for LNG propulsion plants, as it is today on cruise ships. The following detailed comments are related to new ships, not to the existing fleet which is using only steam turbines. Steam ships have been designed to use a combination of natural, forced boil-off and HFO. They do not benefit of the additional cargo capacity which would have resulted from using only LNG as fuel. We have also based all our comparisons of different propulsion plants on same displacements for a given family (size) of ships as this appears as the key parameter for design of large ships. The other main parameters are distances, ship’s speed, cost of fuel, gas prices (buying and selling), boil off level. For each new application an optimum economic compromise may be easily found, provided comparisons are done on clear basis. We are at owner’s disposal for the evaluation of the benefits through Diesel-Electric propulsion for their specific trades. Alternatives to Steam Plants They may be classified as follows according to the main fuels which are used: LNG, HFO, or HFO + LNG. HFO + LNG A Steam plants Until recently it was required to have the possibility to use HFO in addition to available natural boil-off as HFO was supposed to be a cheaper fuel. Steam plants with boilers offer this possibility. It was considered as an economic advantage since steam plants have a low efficiency and complementing with forced boil-off reduced significantly the cargo delivered. However, on some trades, HFO is very expensive or not available. In such cases owners use only LNG with existing ships designed to load HFO. However, they do not take full benefit of using only gas as they cannot load LNG in fuel tanks! For a given displacement and for new projects, loading 4 000 to 6 000 tons of HFO means a reduction of cargo loaded (8 000 to 12 000 cum) and also less cargo delivered. In addition, unit cost of HFO ($/mm Btu) is higher than equivalent cost of LNG loaded (FOB) as can be seen on following table:
Table 1
COST USD/tCOST USD/mm Btu
HFO1503,68
LNG (Fob)1042,00
Owners who will choose to have new ships with steam propulsion designed to load HFO shall be penalised twice:
• Extra cost of HFO compared to LNG;
• Reduction of cargo capacity.
B Dual Fuel Diesel (High pressure injection)
Low speed or medium speed engines may be operated with gas in a diesel mode i. e. injection of gas at the end of compression stroke. The main difference between two stroke low speed and four stroke medium speed engines is that two stroke engines can be operated only in a diesel mode due to scavenging while four stroke engines can also be operated in a lean burn gas mode (OTTO cycle) as described bellow.
In diesel mode, gas has to be compressed to some 350 bar which cancels the benefits expected from a diesel propulsion. In addition to compressing gas, oil qualities may have to be modified according to gas/oil ratio in a combustion chamber which would burn both gas and HFO.
It also means extra weight due to engine (logically a low speed) and due to HFO loaded, no redundancy, high cost of HFO and, at the end, less cargo delivered. High pressure injection may now be considered as obsolete as low pressure engines are available and burning HFO is meaningless.
C Dedicated engines:
To avoid burning fuels so different as gas and HFO in the same engine, it is possible to have dedicated “engines” (diesel engines or gas turbines), some “engines” dedicated to gas combustion, the others dedicated to HFO combustion. As the amount of natural boil-off is very different during laden and ballast voyages, it results in extra power, cost and weight for all the reasons related to having HFO loaded. This is merely complications for a poor economical result.
HFO Only
A Reliquefaction
Reliquefaction plants and a low speed engine burning HFO may have appeared attractive to people who have not examined the problem globally as all cargo loaded is delivered and HFO is supposed to be cheaper than LNG which is wrong (see table 1).
If the question is clearly examined as indicated, (see above), How and For What Liquefied Petroleum Gas Reliquefaction Plants Workreliquefaction plants are the wrong answer:
• Extra weight due to propulsion plant;
• Extra weight due to HFO;
• High electric load which partially cancels the advantages brought by an efficient low speed engine;
• Extra “fuel” cost;
• Less cargo loaded and less cargo unloaded. Comparisons show clearly no economic advantages.
In addition low speed engine and reliquefaction present several weak points:
• No propulsion redundancy except if two shaft lines are fitted (which also means lower hydrodynamic efficiency);
• Maintenance of the main engine should not be allowed at terminals and the ship shall have to be stopped for maintenance;
• An electric power plant is needed for cargo unloading and reliquefaction plant;
• Redundancy is needed for reliquefaction plant (2 plants plus a gas oxidiser);
• High level of pollution with corresponding potential penalties (see above).
What seemed to be attractive is no longer when the question is examined globally.
LNG Only
Using LNG as main fuel for propulsion without any HFO is clearly the right choice for following reasons:
• About 20 % more calories per ton;
• Lower “fuel” cost/calorie (see table 1);
• Fuel and cargo are the same, cargo loading means refuelling;
• “Fuel” is stored in central cargo tanks, not forward and at stern with increased bending moments;
• No heavy fuel storage, heating, treatment;
• Drastic reduction of pollution;
• The only realistic way to replace steam plants by modern and efficient propulsion plants;
• An important reduction of LNG transportation cost due to the combination of fuel savings and increased cargo deliveries;
• More redundancy, safety, flexibility, etc.
A Electric transmission
Power transmission to propeller through frequency converters and synchronous electric motors is a well proven technology on cruise ships. It has become the rule on cruise ships for inherent advantages most of which also apply to LNG:
• An electric power plant with several generators offering redundancy and flexibility of operation and arrangement in the ship;
• Constant speed generators started and stopped automatically according to power demand with driving engines correctly loaded;
• Power plant used for both propulsion and electric load including accommodations, auxiliaries, cargo pumps and auxiliaries;
• Variable speed solid FP propeller driven by two independent electric motors offering each 50 % total torque, redundancy and unequalled torque capacity at any speed;
• Nearly constant transmission efficiency whatever the operating mode (full or reduced power, port operations, etc.).
B Power plant
Gas turbines or lean burn gas engines may be used. Gas engines as described above are the preferred solution.
Gas turbines could be used as electric power generators. We have not chosen them for several reasons:
• Gas turbines alone are not efficient enough, a steam recovery plant is needed (other recovery systems are not proven);
• For efficiency reasons, steam plant should include a vacuum condenser i. e. a steam plant similar to present LNG carriers, which means cost and complexity;
• One gas turbine in a COGES mode offers the power needed. For redundancy and safety reasons a back-up system is needed, logically a spare gas turbine which is again costly;
• Operating flexibility is poor;
• Efficiency drops drastically at part load, port operation or when outside temperature is high;
• Gas fuel has to be compressed to some 30 bar.
Two gas turbines may be used if a high power (large fast ships) is needed. They “save” some 500 tons weight compared to a diesel electric plant. However this advantage is cancelled if the ships are not operated at full speed due to lower efficiency of gas turbines at part load. Such solutions are not adapted to spot market with speed adapted to needs.
Dual Fuel Diesel Electric
Lean Burn Gas Engines
The power plant consists of several medium speed diesel generators feeding electrical power to medium voltage switchboards. Typically, 4 generators (as on cruise ships) are fitted to offer large flexibility.
Medium speed DF engines developed by WARTSILÄ are operated in a lean burn gas mode (OTTO cycle) with low pressure gas feeding (6 bar).
The gas is mixed to air before each inlet valve from a gas common rail by electronically controlled gas valves. At the end of compression stroke, the air/gas mixture is ignited by a pilot fuel of DMA which ensures reliable ignition. The engine is operated in a “lean” burn mode when running on gas i. e. in a narrow window between knocking and misfiring limits. This is possible thanks to electronic control of all cylinders plus individual adjustment of each cylinder for an optimum combustion.
By these means the engine can be operated at 90 % of the output achievable with the classical HFO diesel engine without detonation occurring. Pilot fuel is only 1 % of the total energy consumption which has little incidence on the fuel cost.
In case of abnormal combustion on any cylinder detected by a dedicated combustion sensor, the engine is automatically shifted to a diesel mode as the engine is derived from the diesel version and has all corresponding equipment. Shifting occurs without power modification. Same power is available when operation at 100 % onDMA.
The plant is expected to run on gas in all operating conditions except when starting engines (less than 1′) and when no LNG is available (first voyage or after dry dock, etc.).
Gas Production
Gas has to be fed to engines continuously at correct pressure whatever the power variations (gas demand) and natural boil-off production.
Forced boil-off and natural boil-off are combined and controlled so as to maintain cargo tanks pressure within safe limits. The complete gas chain and related systems and auxiliaries including gas oxydisers, control systems, electric boilers, LNG “fuel” pumps and their suction devices are covered by patents.
Consequences
• Engines are operated at constant speed which makes the control easier;
• Load can be maintained close to optimum power and efficiency as engines are started and stopped automatically according to power demand;
• Thermal efficiency is high and above 46 % according to test bed measurements;
• Emissions are drastically reduced (see below).
Emissions
The emissions are globally divided by two if diesel electric is chosen. This results from the combustion process, higher efficiency and carbon content of HFO and LNG.
CO2
CO2 emissions are strongly reduced for three reasons:
• Higher thermal efficiency of engines;
• Higher energy density (kJ/kg) of gas compared to HFO;
• Carbon content in CH4 is only 75 % when it is about 86 % with HFO.
NOX
NOX emissions depend of the combustion process. They are determined by the peak temperature and the duration of the high temperature.
Lean burn gas engines like steam boilers have low NOX emissions, while diesel engines and especially low speed engines have high levels.
SOX
SOX emissions are a function of the sulphur content of the fuel used. Low sulphur HFO or DO could be used in boilers but cost would be prohibitive. Using gas as the only fuel results in zero SOX emissions.
Following tables show a comparison of CO2, NOX and SO2 emissions expressed in g/kwh on shaft line and tons/year. We have included electric loads and transmission losses. Shaft power is 25 000 kw and sulphur content is 2 % fuel weight.
Above emissions reductions can be expected to be convertible into penalties savings i. e. about 0,5 Million $/year for CO2 emissions only. Economic Aspects When solutions have to be compared, following questions are raised: • What are the savings? • What is the extra cost? • What about maintenance? Savings As indicated above, to make comparisons meaningful, the same loaded displacement should be the basis. Different displacements corresponding to different ship sizes may be examined. The other key parameters are ship’s speed, distances and cost of LNG (buying, selling), cost of HFO. We have done such comparisons for different simulations/scenarios which lead to same clear conclusions. Read also: Weather-related Economics of Natural Gas Transport for Two Propulsion Plant Configurations It can be concluded that the combination of the reduction of energy consumption and extra deliveries results in savings which are much higher than those resulting from fuel savings only as used to be done previously when the comparisons did not consider the global ship design. Extra Cost The extra cost for the highly efficient new technology represents about 5 mill$. This has to be compared to yearly savings. It can be concluded that extra cost shall be recovered within one year or less on ships designed for 40 years operation.
As we expect this technology to become the new standard as it is now on passenger ships, comparison to old steam technologies will become meaningless.
Maintenance Cost
The electric transmission which includes converters, transformers and electric motors are proven technologies with little maintenance, electric cables are used instead of pipes. Gears will be driven by electric motors with limited torque variations. The system is not new and little maintenance is expected.
NOX SO2 CO2 g/kwh t/y g/kwh t/y g/kwh t/y Steam turbines 1 200 12 2 400 900 180 000 Low speed diesel + reliquefaction 20 3 950 9,0 1 800 600 120 000 Lean burn diesel electric 1,2 240 0 0 500 100 000 Gas turbines and COGES 4,3 850 0 0 550 108 000
DF engines are now proven in power plants. Wear will be quite limited due to the clean fuel used. Maintenance cost of these engines cannot be compared to engines operated with HFO. Extra maintenance compared to steam plants should not exceed 50 000 USD/year. This has to be compared to penalty savings on emissions which can be estimated at about 500 000 USD/year i. e. 10 times more and savings resulting from the new technology.
Larger Ships
Size of LNG carriers are mainly limited by terminals (draft, displacement, capacity of terminals, etc.).
Building larger LNG membrane type ships represents no technical difficulty. Membranes are attached to the inner hull at cofferdams perimeters through the Invar tubes (GT NO96 or CS1) or through the PUF insulation panels (TGZ mark III).
Hence they follow the static and dynamic deformations of the ship’s structure. Stresses in membranes are limited from design. Same is true to adjacent hull structure which make membrane type double hull LNG carriers staunch ships. Membranes and structure on larger ships or smaller ships operate in same safe conditions.
The sloshing phenomena has been a major concern on ships using “empty” insulation wooden boxes (old designs GT NO85 and NO88). It has never created problems on “full” PUF panels used today on TGZ mark III or CS1.
Larger upper chamfers have also improved situation. In addition, sloshing phenomena can now be predicted and simulated for safe design of tanks.
Ships up to 220 000 cum and 4 tanks only have been examined and found sloshing risk free. For higher ship’s capacities (250 000 Cum) a five tanks design is proposed.
Footnotes
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SOC.MEDIA | {"extraction_info": {"found_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": 0.5591543912887573, "perplexity": 4684.904324899767}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499899.9/warc/CC-MAIN-20230201013650-20230201043650-00209.warc.gz"} |
https://math.stackexchange.com/questions/2160180/solve-lim-x-rightarrow-2-fracxex-1-2ex-2-without-using-lhopitals/2160206 | Solve $\lim_{x \rightarrow 2} \frac{xe^{x-1}-2e}{x-2}$ without using L'Hopital's rule
I tried:
$$\lim_{x \rightarrow 2} \frac{xe^{x-1}-2e}{x-2} = \frac{(x-2)?}{x-2}$$
I feel like I can factor $xe^{x-1}-2e$ into $(x-2)y$, but I am not sure what y is.
I tried figuring it out and the closes I got was $$(x-2)(xe^{x-1}e) = xe^{x-1}+xe-2e^{x-1}-2e$$
Am I on the right track? How do I solve this?
• Hint: Use the taylor expansion of $e^{x-1}$ – mrnovice Feb 25 '17 at 0:30
• @RRL Perhaps he cannot take such derivatives yet. However, though, I think this is fine as long as he continues to provide his own efforts and such, as he has done sufficiently well in my opinion. – Simply Beautiful Art Feb 25 '17 at 0:48
Simply use the definition of derivative. Let $f(x)=xe^{x-1}$, then $f(2)=2e$.
Also, $f'(x)=(x+1)e^{x-1}$
So the limit becomes
$\lim_{x \to 2} \frac {f(x)-f(2)}{x-2} =f'(2)=3e$
Algebra solution:
Let $x=u+2$.
\begin{align}\frac{xe^{x-1}-2e}{x-2}&=\frac{xe^{x-1}-2e^{x-1}+2e^{x-1}-2e}{x-2}\\&=\frac{(x-2)e^{x-1}+2e(e^{x-2}-1)}{x-2}\\&=e^{x-1}+2e\frac{e^u-1}u\end{align}
We know that $\frac{e^u-1}u\to1$, thus,
$$\lim_{x\to2}\frac{xe^{x-1}-2e^{2-1}}{x-2}=e+2e=3e$$
Taylor series solution:
Let $x=u+2$ and $e^u=1+u+\mathcal O(u^2)$.
\begin{align}\frac{xe^{x-1}-2e}{x-2}&=e\frac{(u+2)e^u-2}u\\&=e\frac{(u+2)(1+u+\mathcal O(u^2))-2}u\\&=e\frac{3u+\mathcal O(u^2)}u\\&=3e+\mathcal O(u)\\&\to3e\end{align}
• Was expecting some taylor expansion :( – bigfocalchord Feb 25 '17 at 0:38
• @dydxx I suppose I can go overkill and wrap all the answers up :P – Simply Beautiful Art Feb 25 '17 at 0:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8677346110343933, "perplexity": 867.7072855676415}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999964.8/warc/CC-MAIN-20190625233231-20190626015231-00320.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/college-algebra-6th-edition/chapter-5-systems-of-equations-and-inequalities-exercise-set-5-5-page-571/17 | ## College Algebra (6th Edition)
1. The inequality sign is $<$, so we draw a dashed border 2. The border, $(x-2)^{2}+(y+1)=3^{2}$, is a circle, centered at $(2,-1)$, radius=$3$ 3. Test the point $(2,-1)$, the center: $(2-2)^{2}+(-1+1) ^2<9\quad ?$ $0 < 9\quad ?$ Yes. 4. Shade the region that the center, $(2,-1)$, belongs to (the region inside the circle) | {"extraction_info": {"found_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": 0.982646107673645, "perplexity": 1055.6357447388389}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267866926.96/warc/CC-MAIN-20180624083011-20180624103011-00455.warc.gz"} |
https://www.lmfdb.org/Genus2Curve/Q/8281/b/405769/1 | # Properties
Label 8281.b.405769.1 Conductor $8281$ Discriminant $405769$ Mordell-Weil group $$\Z \times \Z$$ Sato-Tate group $E_6$ $$\End(J_{\overline{\Q}}) \otimes \R$$ $$\mathrm{M}_2(\R)$$ $$\End(J_{\overline{\Q}}) \otimes \Q$$ $$\mathrm{M}_2(\Q)$$ $$\End(J) \otimes \Q$$ $$\mathsf{CM}$$ $$\overline{\Q}$$-simple no $$\mathrm{GL}_2$$-type yes
# Related objects
Show commands for: SageMath / Magma
## Simplified equation
$y^2 + (x^3 + x + 1)y = -3x^5 + 9x^4 - 7x^3 - 2x^2 + x$ (homogenize, simplify) $y^2 + (x^3 + xz^2 + z^3)y = -3x^5z + 9x^4z^2 - 7x^3z^3 - 2x^2z^4 + xz^5$ (dehomogenize, simplify) $y^2 = x^6 - 12x^5 + 38x^4 - 26x^3 - 7x^2 + 6x + 1$ (minimize, homogenize)
sage: R.<x> = PolynomialRing(QQ); C = HyperellipticCurve(R([0, 1, -2, -7, 9, -3]), R([1, 1, 0, 1]));
magma: R<x> := PolynomialRing(Rationals()); C := HyperellipticCurve(R![0, 1, -2, -7, 9, -3], R![1, 1, 0, 1]);
sage: X = HyperellipticCurve(R([1, 6, -7, -26, 38, -12, 1]))
magma: X,pi:= SimplifiedModel(C);
## Invariants
Conductor: $$N$$ $$=$$ $$8281$$ $$=$$ $$7^{2} \cdot 13^{2}$$ magma: Conductor(LSeries(C)); Factorization($1); Discriminant: $$\Delta$$ $$=$$ $$405769$$ $$=$$ $$7^{4} \cdot 13^{2}$$ magma: Discriminant(C); Factorization(Integers()!$1);
### G2 invariants
$$I_2$$ $$=$$ $$2596$$ $$=$$ $$2^{2} \cdot 11 \cdot 59$$ $$I_4$$ $$=$$ $$375193$$ $$=$$ $$7^{2} \cdot 13 \cdot 19 \cdot 31$$ $$I_6$$ $$=$$ $$248614093$$ $$=$$ $$7^{2} \cdot 13 \cdot 390289$$ $$I_{10}$$ $$=$$ $$51938432$$ $$=$$ $$2^{7} \cdot 7^{4} \cdot 13^{2}$$ $$J_2$$ $$=$$ $$649$$ $$=$$ $$11 \cdot 59$$ $$J_4$$ $$=$$ $$1917$$ $$=$$ $$3^{3} \cdot 71$$ $$J_6$$ $$=$$ $$-1907$$ $$=$$ $$-1907$$ $$J_8$$ $$=$$ $$-1228133$$ $$=$$ $$-1228133$$ $$J_{10}$$ $$=$$ $$405769$$ $$=$$ $$7^{4} \cdot 13^{2}$$ $$g_1$$ $$=$$ $$115139273278249/405769$$ $$g_2$$ $$=$$ $$524030063733/405769$$ $$g_3$$ $$=$$ $$-803230307/405769$$
sage: C.igusa_clebsch_invariants(); [factor(a) for a in _]
magma: IgusaClebschInvariants(C); IgusaInvariants(C); G2Invariants(C);
## Automorphism group
$$\mathrm{Aut}(X)$$ $$\simeq$$ $C_6$ magma: AutomorphismGroup(C); IdentifyGroup($1); $$\mathrm{Aut}(X_{\overline{\Q}})$$ $$\simeq$$$D_6$magma: AutomorphismGroup(ChangeRing(C,AlgebraicClosure(Rationals()))); IdentifyGroup($1);
## Rational points
Known points
$$(1 : 0 : 0)$$ $$(1 : -1 : 0)$$ $$(0 : 0 : 1)$$ $$(0 : -1 : 1)$$ $$(1 : -1 : 1)$$ $$(1 : -2 : 1)$$
$$(1 : -1 : 3)$$ $$(3 : -6 : 2)$$ $$(-2 : -13 : 1)$$ $$(-2 : 22 : 1)$$ $$(1 : -36 : 3)$$ $$(3 : -41 : 2)$$
magma: [C![-2,-13,1],C![-2,22,1],C![0,-1,1],C![0,0,1],C![1,-36,3],C![1,-2,1],C![1,-1,0],C![1,-1,1],C![1,-1,3],C![1,0,0],C![3,-41,2],C![3,-6,2]];
Number of rational Weierstrass points: $$0$$
magma: #Roots(HyperellipticPolynomials(SimplifiedModel(C)));
This curve is locally solvable everywhere.
magma: f,h:=HyperellipticPolynomials(C); g:=4*f+h^2; HasPointsEverywhereLocally(g,2) and (#Roots(ChangeRing(g,RealField())) gt 0 or LeadingCoefficient(g) gt 0);
## Mordell-Weil group of the Jacobian
Group structure: $$\Z \times \Z$$
magma: MordellWeilGroupGenus2(Jacobian(C));
Generator $D_0$ Height Order
$$D_0 - (1 : -1 : 0) - (1 : 0 : 0)$$ $$x^2 - 4xz + 2z^2$$ $$=$$ $$0,$$ $$y$$ $$=$$ $$-6xz^2 + 3z^3$$ $$0.086938$$ $$\infty$$
$$D_0 - (1 : -1 : 0) - (1 : 0 : 0)$$ $$2x^2 - z^2$$ $$=$$ $$0,$$ $$2y$$ $$=$$ $$-4xz^2 + z^3$$ $$0.086938$$ $$\infty$$
## BSD invariants
Hasse-Weil conjecture: verified Analytic rank: $$2$$ Mordell-Weil rank: $$2$$ 2-Selmer rank: $$2$$ Regulator: $$0.005668$$ Real period: $$19.78540$$ Tamagawa product: $$3$$ Torsion order: $$1$$ Leading coefficient: $$0.336475$$ Analytic order of Ш: $$1$$ (rounded) Order of Ш: square
## Local invariants
Prime ord($$N$$) ord($$\Delta$$) Tamagawa L-factor Cluster picture
$$7$$ $$2$$ $$4$$ $$3$$ $$1 + 5 T + 7 T^{2}$$
$$13$$ $$2$$ $$2$$ $$1$$ $$1 + 2 T + 13 T^{2}$$
## Sato-Tate group
$$\mathrm{ST}$$ $$\simeq$$ $E_6$ $$\mathrm{ST}^0$$ $$\simeq$$ $$\mathrm{SU}(2)$$
## Decomposition of the Jacobian
Splits over the number field $$\Q (b) \simeq$$ 6.6.891474493.2 with defining polynomial:
$$x^{6} - x^{5} - 31 x^{4} + 4 x^{3} + 162 x^{2} - 81 x - 27$$
Decomposes up to isogeny as the square of the elliptic curve:
$$y^2 = x^3 - g_4 / 48 x - g_6 / 864$$ with
$$g_4 = \frac{1574069}{6561} b^{5} + \frac{13576892}{6561} b^{4} - \frac{56218393}{6561} b^{3} - \frac{17230402}{243} b^{2} + \frac{2496578}{243} b + \frac{81063052}{243}$$
$$g_6 = -\frac{655459038871}{531441} b^{5} + \frac{100362384668}{531441} b^{4} + \frac{20455326360833}{531441} b^{3} + \frac{543846776200}{19683} b^{2} - \frac{3528969869152}{19683} b - \frac{1057160135213}{19683}$$
Conductor norm: 1
## Endomorphisms of the Jacobian
Of $$\GL_2$$-type over $$\Q$$
Endomorphism ring over $$\Q$$:
$$\End (J_{})$$ $$\simeq$$ $$\Z [\frac{1 + \sqrt{-3}}{2}]$$ $$\End (J_{}) \otimes \Q$$ $$\simeq$$ $$\Q(\sqrt{-3})$$ $$\End (J_{}) \otimes \R$$ $$\simeq$$ $$\C$$
Smallest field over which all endomorphisms are defined:
Galois number field $$K = \Q (a) \simeq$$ 6.6.891474493.2 with defining polynomial $$x^{6} - x^{5} - 31 x^{4} + 4 x^{3} + 162 x^{2} - 81 x - 27$$
Not of $$\GL_2$$-type over $$\overline{\Q}$$
Endomorphism ring over $$\overline{\Q}$$:
$$\End (J_{\overline{\Q}})$$ $$\simeq$$ an Eichler order of index $$3$$ in a maximal order of $$\End (J_{\overline{\Q}}) \otimes \Q$$ $$\End (J_{\overline{\Q}}) \otimes \Q$$ $$\simeq$$ $$\mathrm{M}_2($$$$\Q$$$$)$$ $$\End (J_{\overline{\Q}}) \otimes \R$$ $$\simeq$$ $$\mathrm{M}_2 (\R)$$
### Remainder of the endomorphism lattice by field
Over subfield $$F \simeq$$ $$\Q(\sqrt{13})$$ with generator $$\frac{4}{243} a^{5} - \frac{1}{243} a^{4} - \frac{145}{243} a^{3} - \frac{32}{243} a^{2} + \frac{316}{81} a - \frac{11}{27}$$ with minimal polynomial $$x^{2} - x - 3$$:
$$\End (J_{F})$$ $$\simeq$$ $$\Z [\frac{1 + \sqrt{-3}}{2}]$$ $$\End (J_{F}) \otimes \Q$$ $$\simeq$$ $$\Q(\sqrt{-3})$$ $$\End (J_{F}) \otimes \R$$ $$\simeq$$ $$\C$$
Sato Tate group: $E_3$
Of $$\GL_2$$-type, simple
Over subfield $$F \simeq$$ 3.3.8281.2 with generator $$-\frac{1}{27} a^{5} - \frac{2}{27} a^{4} + \frac{34}{27} a^{3} + \frac{71}{27} a^{2} - \frac{49}{9} a - \frac{7}{3}$$ with minimal polynomial $$x^{3} - x^{2} - 30 x - 27$$:
$$\End (J_{F})$$ $$\simeq$$ $$\Z [\frac{1 + \sqrt{-3}}{2}]$$ $$\End (J_{F}) \otimes \Q$$ $$\simeq$$ $$\Q(\sqrt{-3})$$ $$\End (J_{F}) \otimes \R$$ $$\simeq$$ $$\C$$
Sato Tate group: $E_2$
Of $$\GL_2$$-type, simple | {"extraction_info": {"found_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": 0.8198876976966858, "perplexity": 4449.759355140808}, "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-2021-10/segments/1614178358033.38/warc/CC-MAIN-20210226234926-20210227024926-00525.warc.gz"} |
http://mymathforum.com/calculus/32030-evaluating-integral-interpreting-form-area.html | My Math Forum Evaluating the integral by interpreting it in form of area.
Calculus Calculus Math Forum
November 25th, 2012, 12:39 PM #1 Newbie Joined: Jun 2012 Posts: 15 Thanks: 0 Evaluating the integral by interpreting it in form of area. For question a), I know from the book that the area can be found by taking the area of the trapezoid yielding 4. But if 0 and 2 are the domain of the integral wouldn't it just be the area of the triangle? I am sorry for my articulation, English is not my native language. http://img210.imageshack.us/img210/6359 ... reting.png Regards, MP
November 25th, 2012, 12:47 PM #2 Newbie Joined: Jun 2012 Posts: 15 Thanks: 0 Re: Evaluating the integral by interpreting it in form of ar I also have one more quick question if you are in will to engage towards. What do I do when the question requests that I evaluate an integral by interpreting it in terms of area? Such as: let S= integral symbol (tell me how to add the integral symbol) let IxI be absolute value of x. S(1-x)dx and S(IxI)dx
November 26th, 2012, 07:55 AM #3 Senior Member Joined: Aug 2012 From: New Delhi, India Posts: 157 Thanks: 0 Re: Evaluating the integral by interpreting it in form of ar The integral of a function from a limit of $x=a$to $x=b$ is equal to the area enclosed by the curve between the x-axis under those points. For the image question $\int^2_0 f(x)\,dx=\text{Area of rectangle + area of triangle}$ $=2*1+\frac{1}{2}\,2*2 =2+2 =4$ Similarly, you can find other areas.
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http://events.berkeley.edu/index.php/calendar/sn/?view=summary&timeframe=month&date=2019-02-28&tab=academic | << February 2019 >>
## Friday, February 1, 2019
### Labor Lunch Seminar: Tuition subsidies and overeducation
Seminar | February 1 | 12-1 p.m. | 648 Evans Hall
Ciprian Domnisoru, Carnegie Mellon University
Center for Labor Economics
### Solid State Technology and Devices Seminar: Ultrafast Spintronics
Seminar | February 1 | 1-2 p.m. | Cory Hall, The Hogan Room, 521
Jeffery Bokor, Professor, Electrical Engineering and Computer Sciences Department, UC Berkeley
Magnetic nanodevices are receiving great attention these days due to their non-volatility and
potential for extremely low energy dissipation. The field is rapidly evolving from rotating
magnetic disks for mass storage to on-chip magnetic random access memory (MRAM).
MRAM is in the advanced product development phase in a number of companies and is
expected to be in widespread commercial... More >
### Magnetism in Amorphous Alloys: Nano Seminar Series
Seminar | February 1 | 2-3 p.m. | 4 LeConte Hall
Prof. Frances Hellman, UC Berkeley, Physics & MSE
Most condensed matter textbooks start by introducing crystal symmetries and the periodic lattice as foundational to the field. Yet, it has long been known that the amorphous structure supports ferromagnetism, superconductivity, and a host of other condensed matter properties.
Superconductivity theory was famously expanded from the original Bloch wave pairing to be described as pairing of... More >
### Student Probability/PDE Seminar: Hydrodynamics for ASEP with Open Boundaries
Seminar | February 1 | 2:10-3:30 p.m. | 891 Evans Hall
Dan Daniel Erdmann-Pham, UC Berkeley
Department of Mathematics
Rezakhanlou has shown that the hydrodynamic behaviour of ASEP and other attractive asymmetric particle processes on $R^d$ is governed by a class of conservation laws. That is, macroscopic particle density profiles are given by entropy solutions of these conservation laws. In this talk, we will discuss Bahadoran’s recent extension of these results to bounded domains with particle reservoirs at... More >
### Job Market Seminar (Joint with Haas School): "Outside Options, Bargaining, and Wages: Evidence from Coworker Networks"
Seminar | February 1 | 2:10-3:30 p.m. | Haas School of Business, N270 Chou Hall
Sydnee Caldwell, MIT Economics
Department of Economics
Field(s): Labor Economics, Applied Econometrics, Personnel Economics, Public Finance
### Composition Colloquium: Etienne Charles
Colloquium | February 1 | 3 p.m. | 250 Morrison Hall
Department of Music
Over its century-plus history, jazz has forged its shape-shifting identity by encompassing a rainbow of musical dialects in an improvisation-infused setting. While jazz's potency launched into popular appeal based on the integration of the European classical music sensibility and the grassroots of African-American cultural heritage, it has not remained a static idiom. Indeed, jazz has become... More >
### Book Talk: The Feminist Awakening in China
Colloquium | February 1 | 3-5 p.m. | UC Berkeley Extension (Golden Bear Center), IEAS Conference Room (510A)
Leta Hong Fincher
Lü Pin
Center for Chinese Studies (CCS)
On the eve of International Women’s Day in 2015, the Chinese government arrested five feminist activists and jailed them for 37 days. The Feminist Five became a global cause célèbre, with Hillary Clinton speaking out on their behalf, and activists inundating social media with #FreetheFive messages. But the Feminist Five are only symbols of a much larger feminist movement of university students,... More >
### MENA Salon: 60,000 Political Prisoners and a New Cathedral: Is Sisi's Egypt Sustainable?
Workshop | February 1 | 3-4 p.m. | 340 Stephens Hall
January 25 marked the 8th anniversary of the Egyptian revolution. On Coptic Christmas Eve, January 6, Egyptian President Abdel Fattah Al-Sisi was interviewed by 60 Minutes' Scott Pelley in which he denied the existence of over 60,000 political prisoners in the country's prisons. The Egyptian government tried to block the interview from airing, to no avail. The interview was aired the same evening... More >
### The Times They Are A-Changin’: The Influence of Scandal and Experience on Users’ Attitudes to Social Media Data Control
Seminar | February 1 | 3:10-5 p.m. | 107 South Hall
Catherine Marshall
Information, School of
Has widespread news of abuse made people more protective of their personal data?
### Raga Gopalakrishnan - Integrating Behavior, Economics, and Operations in Urban Mobility: Ridesharing and Multi-Modal Travel
Seminar | February 1 | 3:30-4:30 p.m. | 1174 Etcheverry Hall
Raga Gopalakrishnan, Cornell University
Abstract: In today’s urban mobility marketplaces, both operational policies (e.g., matching, routing) and economic mechanisms (e.g., pricing, incentives) affect perceptions of Quality of Service (QoS) and users’ mobility choices. These, in turn, affect both operational objectives (e.g., utilization, vehicle-miles travelled) and economic objectives (e.g., profit, welfare). We study these complex... More >
### Dynasties and Democracy in Japan
Colloquium | February 1 | 4 p.m. | 180 Doe Library
Daniel M. Smith, Associate Professor, Harvard University
Political dynasties exist in all democracies, but have been conspicuously prevalent in Japan, where over a third of legislators and two-thirds of cabinet ministers come from families with a history in parliament. In his new book, Dynasties and Democracy: The Inherited Incumbency Advantage in Japan, Daniel M. Smith introduces a comparative theory to explain the persistence of dynastic... More >
### Chemical Tools for Investigating Reactive Sulfur Species
Seminar | February 1 | 4-5 p.m. | 120 Latimer Hall
College of Chemistry
Reactive sulfur species, such as H2S and sulfane-sulfur compounds, play key roles in different (patho)physiological processes. In addition, these small molecules are also key targets for new donor motifs that function both as important research tools and pharmacological agents. Aligned with this importance, our lab has recently developed a palette of new donor motifs, including H2S- and... More >
### Student Arithmetic Geometry Seminar: Etale Homotopy Obstructions for Rational Points Applied to Open Subvarieties
Seminar | February 1 | 4:10-5 p.m. | 891 Evans Hall
David Corwin, UCB
Department of Mathematics
In 2008, Bjorn Poonen announced the construction of a variety without rational points but no étale-Brauer obstruction to the existence of rational points. We attempt to create a new obstruction that explains Poonen s example by applying the étale-Brauer obstruction to a Zariski open cover of a variety. On the one hand, we prove a general result stating that this new obstruction explains every... More >
## Monday, February 4, 2019
### EH&S 403 Training Session
Course | February 4 | 10:30-11:30 a.m. | 331 University Hall | Note change in date
Jason Smith, UC Berkeley Office of Environment, Health, & Safety
This session briefly covers the UC Berkeley specific radiation safety information you will need to start work. In addition, dosimeter will be issued, if required.
Seminar | February 4 | 11:10 a.m.-12:30 p.m. | 489 Minor Hall
Michael Telias, Postdoc in Richard Kramer's Lab; Joseph Leffler, PhD Candidate
Michael Telias's Abstract
Retinoic acid is the trigger for neural hyperactivity in retinal degeneration and
blocking its receptor unmasks light responses and augments vision
Light responses are initiated in photoreceptors, processed by interneurons, and synaptically transmitted to retinal ganglion cells (RGCs), which send information to the brain. Retinitis pigmentosa (RP) is a blinding... More >
### Machine Learning Data-Driven Discretization Theories, Modeling and Applications: SEMM Seminar
Seminar | February 4 | 12-1 p.m. | 502 Davis Hall
Wing Kam Liu, PhD, PE, Northwestern University/Global Center on Advanced Material Systems and Simulation
An open problem in data-driven methods for mechanical science is the efficient and accurate description of heterogeneous material behavior that strongly depends on complex microstructure. To explore the future development and the adaptation of data-driven methods, new mathematical and computational paradigms and broad flexible frameworks are needed.
### UCB-UCSF Joint Medical Program Head of Foundational Medical Science Job Talk
Conference/Symposium | February 4 | 12-1 p.m. | 5101 Berkeley Way West
Lee HangFu, M.D., MBA
UCB-UCSF Joint Medical Program
It has been nearly half a century since the McMaster University introduced the Problem-Based Learning (PBL) pedagogy in medical education. Since then, hundreds of reviews and study reports have identified many critical issues affecting the success of the PBL unit. Nonetheless, we are still debating the efficacy and success of the PBL program. In his presentation, Dr. HangFu will be discussing the... More >
### Combinatorics Seminar: Varieties of signature tensors
Seminar | February 4 | 12:10-1 p.m. | 939 Evans Hall | Note change in date
Bernd Sturmfels, UC Berkeley and Max Planck Institute
Department of Mathematics
We discuss recent developments in combinatorial algebraic geometry that were motivated by the study of rough paths in stochastic analysis. Every path in a real vector space is encoded in a signature tensor whose entries are iterated integrals. As the path varies over a nice family, we obtain an algebraic variety with interesting properties. Combinatorialists will especially enjoy the role played... More >
### PERL Seminar: “Voting for Quality? The Impact of School Performance Information on Electoral Outcomes”
Seminar | February 4 | 12:30-1:30 p.m. | 223 Moses Hall
Marina Dias, UC Berkeley-ECON
BCEP
Political Economy Research Lunch:PERL is an opportunity for PhD students to present work in progress and receive valuable feedback from faculty and peers.
### Seminar 231, Public Finance:
Seminar | February 4 | 2-4 p.m. | 597 Evans Hall
Isabela Manelici, UCB; Francis Wong, UCB
Isabela Manelici - "The Distributional Effects of Multinationals' Entry"
Francis Wong - "The Property Tax as a Tax on Leveraged Committed Consumption"
### Seminar 211, Economic History: Eight Centuries if Global Real Rates and the `Suprasecular Decline’, 1311-2018
Seminar | February 4 | 2-3:30 p.m. | 639 Evans Hall
Paul Schmelzing, Harvard University
Department of Economics
### Probabilistic Operator Algebra Seminar: Conditionally free random variables: the two-states framework
Seminar | February 4 | 2-4 p.m. | 736 Evans Hall
Jorge Garza Vargas, UC Berkeley
Department of Mathematics
In non-commutative probability the notion of stochastic independence is not unique. Therefore an extension of free probability which produces a larger variety of limit laws is certainly of interest. In this seminar we will review the notion of conditional freeness, introduced by Bozejko and Speicher. We will survey some of the combinatorial and analytic tools that are used in this setting and... More >
### String-Math Seminar: Magnificent Four with color
Seminar | February 4 | 2-3 p.m. | 402 LeConte Hall
Nicolo' Piazzalunga, Stony Brook & SCGP
Department of Mathematics
I will present the rank $$N$$ magnificent four theory, which is the supersymmetric localization of $$U(N)$$ super-Yang-Mills theory with matter on a Calabi-Yau fourfold, and conjecture an explicit formula for the partition function $$Z$$: it has a free-field representation, and surprisingly it depends on Coulomb and mass parameters in a simple way. Based on joint work with N.Nekrasov.
### Northern California Symplectic Geometry Seminar: Contact submanifolds in higher dimensions
Seminar | February 4 | 2:30-3:30 p.m. | 740 Evans Hall
Roger Casals, UC Davis
Department of Mathematics
In this talk, I will discuss our understanding of contact submanifolds in higher dimensions. First, I will introduce the problems we are interested in and the current techniques we have to address them. In the main focus of the talk, I will present the construction of contactomorphic (and smoothly isotopic) contact submanifolds which are actually not contact isotopic. This resolves one of the... More >
### Differential Geometry Seminar: Cone spherical metrics
Seminar | February 4 | 3:10-4 p.m. | 939 Evans Hall
Bin Xu, University of Science and Technology of China
Department of Mathematics
Cone spherical metrics are conformal metrics with constant curvature one with finitely many conical singularities on compact Riemann surfaces. The existence problem of such metrics has been open over twenty years. I will introduce the respectful audience some progress on this problem joint with Qing Chen, Xuemiao Chen, Yiran Cheng, Bo Li, Lingguang Li, Santai Qu, Jijian Song, Yingyi Wu and Xuwen... More >
### Canceled - to Be Postponed: Lifeworlds of Indigenous Languages
Colloquium | February 4 | 3:10-5 p.m. | 370 Dwinelle Hall
Beth Piatote, UC Berkeley
Department of Linguistics
How do the underlying structures, epistemologies, and cultural practices associated with Indigenous languages in North America enrich the study of disciplines beyond linguistics? Drawing on my own work in Nez Perce language and literature, as well as examples from other scholars, I will present some of the current influences of Indigenous language “lifeworlds” shaping scholarship in law,... More >
### Northern California Symplectic Geometry Seminar: H-principle for complex contact structures on Stein manifolds
Seminar | February 4 | 4-5 p.m. | 740 Evans Hall
Franc Forstneric, University of Ljublana
Department of Mathematics
The aim of this talk is to present a first attempt towards homotopy classification of holomorphic contact structures on Stein manifolds. We introduce the notion of a formal complex contact structure and show that any such structure on an odd dimensional Stein manifold $X$ is homotopic (through formal contact structures) to a genuine holomorphic contact structure on a Stein domain in X which is... More >
### Statistical inference for infectious disease modeling
Seminar | February 4 | 4-5 p.m. | 1011 Evans Hall
Department of Statistics
We discuss two recent results concerning disease modeling on networks. The infection is assumed to spread via contagion (e.g., transmission over the edges of an underlying network). In the first scenario, we observe the infection status of individuals at a particular time instance and the goal is to identify a confidence set of nodes that contain the source of the infection with high probability.... More >
### IB Seminar: Decoupling tooth loss from the origin of baleen in whales
Seminar | February 4 | 4-5 p.m. | 2040 Valley Life Sciences Building
Carlos Peredo, George Mason University
### Dare to Repair: From DNA Chemistry to Cancer and back again
Seminar | February 4 | 4-5 p.m. | 106 Stanley Hall
Sheila David, University of California, Davis
College of Chemistry
### Job Market Seminar: "Machine Learning for Set-Identified Linear Models"
Seminar | February 4 | 4:10-5:30 p.m. | 648 Evans Hall
Vira Semenova, MIT Economics
Department of Economics
Field(s): Econometrics, Industrial Organization
### The Paris Review: Women at Work with Emily Nemens
Presentation | February 4 | 6:30 p.m. | Berkeley Art Museum and Pacific Film Archive
What does it mean to be a woman at work in the creative arts in 2019? The Paris Review’s new editor, Emily Nemens, reflects on this question through the lens of the storied literary quarterly’s Writers at Work interview series, the work of contemporary contributors, and her own creative practice as a writer and illustrator.
## Tuesday, February 5, 2019
### Workplace Civility: Respect in Action
Workshop | February 5 | 9 a.m.-12 p.m. | 24 University Hall
Ombuds
Learn practical steps for promoting civility at work, including guidelines for considerate conduct and ideas for creating a more inclusive work environment. Participants will also learn how to help their unit establish group norms and effective ways to respond to rudeness.
### Street Story: A Platform for Community Engagement
Presentation | February 5 | 10-11 a.m. | Webex platform online
Kate Beck, UC Berkeley SafeTREC
Please join Kate Beck, program lead at UC Berkeley Safe Transportation Research and Education Center (SafeTREC) for a demonstration and discussion of Street Story, a web-based community engagement tool designed for people to report transportation safety issues they see and experience. The Street Story tool aims to help agencies and community groups collect information that can create a fuller... More >
### Clayton Heathcock Lectureship: Studies Related to the ATP-Adenosine Pathway
Seminar | February 5 | 11 a.m.-12 p.m. | 120 Latimer Hall
Terry Rosen, Arcus Biosciences
College of Chemistry
Tumor cell death induced by hypoxia or chemotherapy releases large amounts of ATP (adenosine triphosphate) into the extracellular environment. ATP is rapidly converted to AMP (adenosine monophosphate) which, in turn, is converted by hypoxia-induced CD73 into adenosine (ADO). ADO suppresses immune responses, including those of T cells, NK cells and dendritic cells through activation of adenosine... More >
### Seminar 217, Risk Management: Endogenous risk, indirect contagion and systemic risk
Seminar | February 5 | 11 a.m.-12:30 p.m. | 1011 Evans Hall
Speakers: Rama Cont, University of Oxford
Deleveraging by financial institutions in response to losses may lead to contagion of losses across institutions with common asset holdings. Unlike direct contagion via counterparty exposures, this channel of contagion -which we call indirect contagion- is mediated through market prices and does not require bilateral exposures or relations.
### Dynamic Neural Fields: the embodiment of neural computation
Seminar | February 5 | 12-1:30 p.m. | 560 Evans Hall
Yulia Sandamirskaya, Institute of Neuroinformatics, University of Zurich and ETH Zurich
Activity of neuronal populations in several cortical regions can be described by a Dynamic Neural Field (DNF) equation. A DNF is a continuous in time and in space activation function defined over a metric space spanned over perceptual (e.g., color, retinal location, orientation) or motor (e.g., orientation of the head, direction of movement) dimensions, in which neurons in the underlying... More >
### Evaluating the impact and outcomes of STEM programs: A common sense approach
Workshop | February 5 | 12-1:30 p.m. | 290 Hearst Memorial Mining Building
Are your STEM programs, activities, events, courses, curricula really reaching their intended audiences? In this moderated panel presentation, you will learn how to measure and assess the impacts and outcomes of STEM programs.
### Student Faculty Macro Lunch - Inflation and Capital Misallocation
Presentation | February 5 | 12-1 p.m. | 639 Evans Hall
Amir Kermani, Assistant Professor, Department of Economics and Haas School of Business
Clausen Center
This workshop consists of one-hour informal presentations on topics related to macroeconomics and international finance, broadly defined. The presenters are UC Berkeley PhD students, faculty, and visitors.
** MUST RSVP**
RSVP by emailing jgmendoza@berkeley.edu by February 1.
### Webnet: The future of content delivery
Workshop | February 5 | 12-1:30 p.m. | 303 Doe Library
Tor Haugan, Writer/Editor, Library Communications Office
Director of Staff Learning and Development
### Seminar 218, Psychology and Economics: Selling Fast and Buying Slow: Heuristics and Trading Performance of Institutional Investors
Seminar | February 5 | 2-3:30 p.m. | 648 Evans Hall
Alex Imas, Carnegie Mellon University
Department of Economics
### Two-Year Home Country Physical Presence Requirement Workshop
Workshop | February 5 | 2-4 p.m. | International House, Sproul Rooms
J-1 and J-2 visitors subject to this requirement must return to their country of legal permanent residence for two years or obtain a waiver before being eligible for certain employment visas such as H (temporary employment), L (intra-company transfer), or Permanent Resident status ("green card"). Not all J visitors are subject as it depends on specific factors.
At this workshop, you will... More >
### Seminar 237/281: Macro/International Seminar - "Household Debt Revaluation and the Real Economy": Evidence from a Foreign Currency Debt Crisis
Seminar | February 5 | 2-4 p.m. | 597 Evans Hall
Emil Verner, Assistant Professor of Finance, MIT
Department of Economics
Joint 237/281 Macro and International Trade Seminar
RSVP by emailing Joseph G. Mendoza at jgmendoza@berkeley.edu
### Clinical Science Colloquium
Colloquium | February 5 | 3:30-5 p.m. | 1104 Berkeley Way West
Amit Etkin MD PhD
Department of Psychology
Over the past two decades, neuroimaging studies have defined a set of distributed brain systems that contribute to cognition, emotion, mood and other mental processes. Perturbations in these circuits have been identified in different ways across psychiatric disorders. The challenge ahead of us is how to use these insights to: 1) understand the nature of neural circuit deficits in mental illnesses... More >
### 3-Manifold Seminar: Special cube complexes
Seminar | February 5 | 3:40-5 p.m. | 736 Evans Hall
Larsen Linov, UC Berkeley
Department of Mathematics
A cube complex is a cell complex in which each n-cell is a n-dimensional cube. We'll define "special" cube complexes and explain their relationship to right-angled Artin groups. We'll also discuss some results about separability in their fundamental groups.
### 3-Manifold Seminar: Special cube complexes
Seminar | February 5 | 3:40-5 p.m. | 736 Evans Hall
Larsen Linov, UC Berkeley
Department of Mathematics
A cube complex is a cell complex in which each n-cell is a n-dimensional cube. We'll define "special" cube complexes and explain their relationship to right-angled Artin groups. We'll also discuss some results about separability in their fundamental groups.
### 2019 William Main Seminar Series: Fire Science, Policy and Management in California Wildlands
Seminar | February 5 | 4-5:30 p.m. | 125 Li Ka Shing Center
Mark Finney, U.S. Forest Service
William Main Seminar Endowment
The 2019 William Main Seminar Series examines the confluence of environmental science, policy and management in contending with the spate of recent fire outbreaks in California. We are excited to welcome Mark Finney, USFS Research Forester, who will kick off the series with his presentation, "Understanding Wildlife Spread through Experiments and Modeling".
### Single Molecule Probes and Single Particles Probed
Seminar | February 5 | 4-5 p.m. | 120 Latimer Hall
Laura Kaufman, Department of Chemistry, Columbia University
College of Chemistry
I will describe two projects in which we characterize complex systems – supercooled liquids and conjugated polymer aggregates – through single molecule or single particle fluorescence imaging. First, in supercooled liquids – systems that display behaviors consistent with the presence of heterogeneous dynamics – we investigate the time scales over which heterogeneities persist using “ideal” single... More >
### Representation Theory and Mathematical Physics Seminar: Temperley-Lieb algebra action on the category of representations of periplectic supergroup
Seminar | February 5 | 4-5 p.m. | 748 Evans Hall
Vera Serganova, UC Berkeley
Department of Mathematics
We define the action of infinitely generated Temperley-Lieb algebra on the category of representations of the supergroup $$P(n)$$. The supergroup in question is an interesting super analogue of the orthogonal and symplectic groups. As an application of this construction we get algorithm computing characters of irreducible representation of $$P(n)$$ and some other esults. As n tends to infinity,... More >
### How to Email a Professor to Get a Positive Response: Workshop
Workshop | February 5 | 4-5 p.m. | 9 Durant Hall
Leah Carroll, Haas Scholars Program Manager/Advisor, Office of Undergraduate Research and Scholarships
Do you need to email a professor you've never met before to ask for their help, but you don't know where to start? Have you ever written a long email to a professor, only to receive no response, or not the one you hoped? If so, this workshop is for you! We will discuss how to present yourself professionally over email to faculty and other professionals ... More >
### Art for Your Apartment: and dorm
Presentation | February 5 | 5-6 p.m. | Doe Library, Morrison Room
Library
Come see and learn about the Graphic Arts Loan Collection.
This is framed art prints you can bring home and hang on your wall for the school year. Prints comprise a survey of movements and artists - from Impressionism to Cubism, and from Rembrandt to Miro.
This all takes place in the historic Morrison Room. A brief presentation will be followed by ample time to browse representative works... More >
Note: borrowing from the Graphic Arts Loan Collection is limited to UCB students, faculty and staff and is free
## Wednesday, February 6, 2019
### No BioE Department Seminar
Seminar | February 6 | 106 Stanley Hall
Bioengineering (BioE)
### Educational Integration Across Generations among Mexicans and Other Origin Groups: A Brown Bag Talk
Colloquium | February 6 | 12-1 p.m. | 2232 Piedmont, Seminar Room
Jennifer Van Hook, Professor, Sociology, Penn State University
A lunch time talk and discussion session, featuring visiting and local scholars presenting their research on a wide range of topics of interest to demography.
### KUSTU ENDOWED LECTURE: "Mechanisms and Consequences of Biofilm Formation"
Seminar | February 6 | 12-1 p.m. | 101 Barker Hall
Fitnat Yildiz, University of California, Santa Cruz
Dr. Yildiz's lab at UCSC focuses on understanding molecular mechanisms of biofilm formation, c-di-GMP signaling, and environmental stress response. Dr. Yildiz received her B.S. from Hacettepe University, Turkey followed by her Ph.D. from Indiana University. She was a recipient of the Ellison Medical foundation New Scholar Award in Global Infectious Disease and is a Fellow of the American Academy... More >
### MVZ LUNCH SEMINAR - Jennifer Smith: Evolutionary ecology of social networks in free-living mammals: From hyenas to ground squirrels
Seminar | February 6 | 12-1 p.m. | Valley Life Sciences Building, 3101 VLSB, Grinnell-Miller Library
Jennifer Smith
Museum of Vertebrate Zoology
MVZ Lunch is a graduate level seminar series (IB264) based on current and recent vertebrate research. Professors, graduate students, staff, and visiting researchers present on current and past research projects. The seminar meets every Wednesday from 12- 1pm in the Grinnell-Miller Library. Enter through the MVZ's Main Office, 3101 Valley Life Sciences Building, and please let the receptionist... More >
### Computer Vision Beyond Recognition
Seminar | February 6 | 12-1:30 p.m. | 560 Evans Hall
Stella Yu, UC Berkeley
Computer vision has advanced rapidly with deep learning, achieving super-human performance on a few recognition benchmarks. At the core of the state-of-the-art approaches for image classification, object detection, and semantic/instance segmentation is sliding-window classification, engineered for computational efficiency. Such piecemeal analysis of visual perception often has trouble getting... More >
### Greg Crutsinger on "Drones and data: aftermath of California's wildfires"
Conference/Symposium | February 6 | 12-1 p.m. | Sutardja Dai Hall, 310 Banatao Auditorium
CITRIS and the Banatao Institute
Drone technology has been increasingly used by public agencies for emergency and disaster response, including the recent devastating wildfires in California. However, the volume of information drones can collect quickly has resulted in a pressing need for rapid data processing and visualization. This lecture will walk through the use of drone imagery following three major... More >
### Reclaiming Childhood in a Digital Age (BEUHS370)
Workshop | February 6 | 12:10-1:30 p.m. | Tang Center, University Health Services, Section Club
Richard Freed, Ph.D.
Be Well at Work - Work/Life
Dr. Richard Freed will speak on raising happy, healthy kids in the digital age. Learn how a virtually unknown merger between the tech industry and psychology is leading to video games, social media, and smartphones that kids can’t put down. And, why this means children and teens need our help to navigate this digital landscape.
This interactive talk will explore key questions:
• How... More >
### Pan-Africanism - A History
Colloquium | February 6 | 12:30-2 p.m. | 223 Moses Hall
Hakim Adi, Professor of the History of Africa & the African Diaspora, University of Chichester
Professor Hakim Adi will introduce his latest book, Pan-Africanism – A History, in which he provides a history of the individuals and organizations that have sought the unity of all those of African origin as the basis for advancement and liberation.
### EE Seminar: Manipulating interfacial physics for novel multimodal and multiphase insect-scale robots
Seminar | February 6 | 1-2 p.m. | Soda Hall, Wozniak Lounge, 430
Several insect species, such as diving flies and diving beetles, exhibit remarkable locomotive capabilities in aerial, aquatic, and terrestrial environments, inspiring the development of similar capabilities in robots at the centimeter scale. In this talk I will present two insect-scale robots capable of multimodal and multiphase locomotion. I will start by presenting a 175mg, flapping wing robot... More >
### Harmonic Analysis Seminar: Introduction to Fourier restriction via polynomial partitioning
Seminar | February 6 | 1:10-2 p.m. | 736 Evans Hall
Michael Christ, UC Berkeley
Department of Mathematics
Introduction to the work of L. Guth on application of the method of polynomial partitioning to Fourier restriction inequalities. This will be the first of a series of seminar meetings devoted to the 2016 article of Guth on this topic. Key concepts will be introduced. The method will be illustrated through an application to a simpler problem.
### Experimental design in an oligonucleotide synthesis factory using numerical simulations in Python and pandas
Seminar | February 6 | 1:30-2:45 p.m. | 775A Tan Hall
Aaron Wiegel, Data Scientist, Synthego
Department of Chemistry
Abstract: Regardless of the application, calculating a particular statistic and associated p-value is not necessarily the biggest challenge in designing an experiment, especially given the availability of open source software packages such as scipy and statsmodels in Python. Instead, ensuring that the assumptions required for a statistical test are actually satisfied by the data is far more... More >
### Advances and Challenges in Computational Modeling of Dynamic Material Failure: From Single to Multi-Scale Simulations and Their Industrial Applications
Seminar | February 6 | 2-3 p.m. | 3110 Etcheverry Hall
Dr. C.T. Wu, Livermore Software Technology Corporation (LSTC)
Numerical modeling of material failure remains a formidable challenge to the computational mechanics community. Apparently, the pure continuum-based numerical methods are not able to accurately predict the material failure takes place at the finer scale. In other words, the C1-continuity assumption in most finite element methods is inadequate to describe the kinematic discontinuity of... More >
### Topology Seminar (Introductory Talk): Involutive Heegaard Floer homology
Seminar | February 6 | 2:10-3 p.m. | 740 Evans Hall
Matthew Stoffregen, MIT
Department of Mathematics
We'll review the definition of Ozsvath-Szabo's Heegaard Floer homology, and then define the involutive version constructed by Hendricks and Manolescu.
### A phase transition in a spatial permutation model on infinite trees
Seminar | February 6 | 3-4 p.m. | 1011 Evans Hall
Milind Hegde, UC Berkeley
Department of Statistics
Abstract: Spatial random permutation models are of physical interest due to connections to representations of certain gases such as helium as well as of the quantum Heisenberg ferromagnet. Physical phase transitions in these contexts correspond to the appearance of macro or infinite cycles in the permutation model. We study a spatial random permutation model on infinite trees with a time... More >
### Race—The Power of an Illusion
Panel Discussion | February 6 | 3-6 p.m. | Sutardja Dai Hall
Larry Adelman, executive producer of RACE and co-director of California Newsreel, California Newsreel; john a. powell, UC Berkeley Faculty and Director of the Haas Institute, Haas Institute for a Fair and Inclusive Society; Michael Omi, Series Advisor and UC Berkeley faculty, Asian American and Asian Diaspora Studies; Jason Corburn, UC Berkeley faculty, City/Regional Planning and Public Health; Darlene Francis, UC Berkeley Faculty, School of Public Health and Neuroscience; Victoria Robinson, UC Berkeley Faculty and Director of the American Cultures Center, The Department of Ethnic Studies
Lulu Matute, Haas Scholar, Haas Scholars Program
A public event celebrating the launch of a new companion website for the groundbreaking documentary series, 'Race—The Power of an Illusion.'
### Number Theory Seminar: Absolute Hodge cycles
Seminar | February 6 | 3:40-5 p.m. | 748 Evans Hall
Koji Shimizu, UC Berkeley
Department of Mathematics
### UROC (Underrepresented Researchers of Color): Putting finishing touches to your research applications: A Practical hands-on workshop
Workshop | February 6 | 4-5:30 p.m. | 9 Durant Hall
Andrea Ramirez, UROC; Ife Okeke, UROC
For anyone who is applying to the Haas Scholars Program or to the SURF Program, we will be holding a workshop space for students to get feedback on their proposals. Please stop by at whatever stage you're in.If you're unable to make this workshop, but want an extra set of eyes, please email uroc@berkeley.edu to set up a time to meet. We will have food for y'all. Excited to see you there!
### Encapsulation of metal nanoparticles within microporous zeotypes via hydrothermal synthesis in the presence of ligand-protected metal cations
Colloquium | February 6 | 4-6 p.m. | 180 Tan Hall
Trenton Otto, Ph.D. student in the Iglesia Group
### Proteostasis, Sexual Dimorphism and Declining Adaptive Homeostasis in Ageing
Seminar | February 6 | 4-5 p.m. | 114 Morgan Hall
Kelvin Davies, USC
### Thematic Seminar: The tautological ring of the moduli space of curves
Seminar | February 6 | 4:10-5 p.m. | 740 Evans Hall
Aaron Pixton, Massachusetts Institute of Technology
Department of Mathematics
Let Mg be the moduli space of smooth curves of genus g. The tautological ring is a subring of the cohomology of Mg that was introduced by Mumford in the 1980s in analogy with the cohomology of Grassmannians. Work of Faber and Faber-Zagier in the 1990s led to two competing conjectural descriptions of the structure of the tautological ring. After reviewing these conjectures, I will discuss some of... More >
### Center for Computational Biology Seminar: Dr. Beth Shapiro, Professor, UC Santa Cruz
Seminar | February 6 | 4:30-5:30 p.m. | 125 Li Ka Shing Center
Center for Computational Biology
Genomics, genetic rescue, and the future of conservation
Abstract: New technologies, including complete genome sequencing and genome engineering, promise to revolutionize conservation and slow the pace of the ongoing extinction crisis. However, the value of these technologies to conservation remains unclear. Using mountain lions from across their range and wolves from Isle Royale as examples,... More >
### Religion: A Mellon Foundation Sawyer Seminar
Seminar | February 6 | 5-7 p.m. | 370 Dwinelle Hall
Niklaus Largier, UC Berkeley; Michael Warner, Yale; Mayanthi Fernando, UC Santa Cruz
Michael Lucey, UC Berkeley
These public talks continue the series of events connected to the Sawyer Seminar in Linguistic Anthropology & Literary and Cultural Studies that began in Fall 2018. Many of the studies taken up so far in the seminar depend on religious objects, rituals, or encounters to help illuminate those pragmatic aspects of discourse that might be more easily concealed in our everyday routines. Perhaps the... More >
### Linguistic Anthropology and Literary and Cultural Studies: A Mellon Foundation Sawyer Seminar: Session 4: Religion
Conference/Symposium | February 6 – 7, 2019 every day | 5-7 p.m. | 370 Dwinelle Hall
Niklaus Largier, UC Berkeley; Michael Warner, Yale University; Mayanthi Fernando, UC Santa Cruz; Michael Allan, University of Oregon; Courtney Handman, University of Texas at Austin; Charles Hirschkind, UC Berkeley; Webb Keane, University of Michigan
This is the fourth of seven two-day meetings of a Mellon Foundation Sawyer Seminar taking place throughout 2018-2019. The seminar aims to explore the potential of a set of concepts, tools, and critical practices developed in the field of linguistic anthropology for work being done in the fields of literary and cultural criticism.
### Topology Seminar (Main Talk): An infinite-rank summand of the homology cobordism group
Seminar | February 6 | 5:10-6 p.m. | 3 Evans Hall | Note change in time
Matthew Stoffregen, MIT
Department of Mathematics
We explain a generalization of the techniques that Hom introduced to construct an infinite-rank summand of the topologically slice knot concordance group. We generalize Hom's epsilon-invariant to the involutive Heegaard Floer homology constructed by Hendricks-Manolescu. As an application, we see that there is an infinite-rank summand of the homology cobordism group. This is joint work with Irving... More >
### We the People: Justice for Some
Panel Discussion | February 6 | 6:30-7:30 p.m. | JCC East Bay, Berkeley Branch
1414 Walnut Street, Berkeley, CA 94709
JCC East Bay
Featuring GSPP professors Jack Glaser and Steve Raphael, prisoner's rights attorney Margot Mendelson, and moderated by Abbie VanSickle of the Marshall Project.
Join us for a guided conversation about the most pressing and complex issues in the criminal justice system today. This discussion will examine professors Glaser, Raphael, and Mendelson's research on inequality in the criminal justice... More >
$20 Non-Member,$15 Member
## Thursday, February 7, 2019
### Special Seminar: Effective Arithmetic Geometry
Seminar | February 7 | 11 a.m.-12 p.m. | Calvin Laboratory (Simons Institute for the Theory of Computing), Main Lecture Hall | Note change in location
Yuri Tschinkel, Simons Foundation and NYU
Department of Mathematics
Tschinkel will discuss effectivity issues in several problems in arithmetic geometry, the study of solutions of systems of polynomial equations with integral coefficients.
### Applied Math Seminar: Adjoint sensitivity analysis of chaotic dynamical systems via shadowing methods
Seminar | February 7 | 11 a.m.-12 p.m. | 891 Evans Hall
Angxiu Ni, UC Berkeley
Department of Mathematics
In this talk we discuss how to compute derivatives of long-time-averaged objectives with respect to multiple system parameters in chaotic systems, via the recently developed non-intrusive least-squares adjoint shadowing (NILSAS) algorithm.
First we review how to compute such derivatives via comparing the base trajectory and a shadowing trajectory, which is a new trajectory with perturbed... More >
### Econ 235, Financial Economics Seminar: No Seminar
Seminar | February 7 | 11:10 a.m.-12:30 p.m. | C330 Haas School of Business
Department of Economics
Joint with Haas Finance Seminar
### Oliver E. Williamson Seminar: "Common Values, Unobserved Heterogeneity, andEndogenous Entry in U.S. Offshore Oil Lease Auctions∗"
Seminar | February 7 | 12-1:30 p.m. | C325 Haas School of Business
Phil Haile, Yale
Department of Economics
The Oliver E. Williamson Seminar on Institutional Analysis, named after our esteemed colleague who founded the seminar, features current research by faculty, from UCB and elsewhere, and by advanced doctoral students. The research investigates governance and its links with economic and political forces. Markets, hierarchies, hybrids, and the supporting institutions of law and politics all come... More >
### The Berkeley Network's Webinar Series: Fundamentals for Successful Career Change: 3 Effective Strategies and How to Prepare
Workshop | February 7 | 12-1 p.m. | Virtual
Joy Lin, Quarter Life Joy
Cal Alumni Association
This webinar is designed to give you the fundamentals of preparing for a career change and effective strategies you can explore. You will walk away with a more realistic idea of what to expect, how to prepare, and what strategies can help make your career change possible.
### Back Talk: Less Stress on Your Back (BEUHS404)
Workshop | February 7 | 12:10-1:30 p.m. | Tang Center, University Health Services, Class of '42
Mallory Lynch, Campus Ergonomist, Ergonomics@Work
Ergonomics@Work
Learn new ways of performing daily activities with less stress to your back. Practice some useful stretching and strengthening exercises. Wear comfortable clothing.
### Research Colloquium: Dr. Jerry Brandell "Psychoanalysis in the Halls of Social Work Academe: Can this patient be saved?"
Colloquium | February 7 | 12:10-1:30 p.m. | Haviland Hall, Commons/116
Social Welfare, School of
Psychoanalytic theory is not a unified body of knowledge, but rather, composed of multiple theories, models, and schemata pertaining to development, psychopathology, and clinical method and technique. It is a literature of vast scope whose evolution now spans 125 years. This history is actually fraught with points of convergence and dissonance; important issues and controversies surrounding the... More >
### The California Housing Crisis and Potential Solutions
Panel Discussion | February 7 | 12:15-1:30 p.m. | 250 Goldman School of Public Policy
Join us for a new lunch series to discuss the housing crisis in California and potential solutions. Prominent leaders in state policy alongside real estate professionals will lead panel discussions followed by time for Q&A. Free lunch provided!
### Econ 235, Financial Economics Student Seminar: No Meeting
Seminar | February 7 | 1-2 p.m. | 597 Evans Hall
Department of Economics
### How to Write a Research Proposal Workshop
Workshop | February 7 | 2-3 p.m. | 9 Durant Hall
Leah Carroll, Haas Scholars Program Manager/Advisor, Office of Undergraduate Research and Scholarships
Need to write a grant proposal? This workshop is for you! You'll get a head start on defining your research question, developing a lit review and project plan, presenting your qualifications, and creating a realistic budget.
Open to all UC Berkeley students.
### ESPM Seminar Series, Spring 2019
Seminar | February 7 | 3:30 p.m. | 132 Mulford Hall
David Ackerly
David Ackerly, Dean of the College of Natural Resources at UC Berkeley, will present: "Topography, species distributions and impacts of climate change on California native plants." Hosted by George Roderick. Meet the speaker and enjoy refreshments after the talk in 139 Mulford Hall.
### Higher Education Careers for PhDs
Panel Discussion | February 7 | 3:30-5 p.m. | Sproul Hall, Room 309
Dr. Lilia Chavez, Dean of Special Projects and Grants, Merritt College; Dr. Brooke Hessler, Director of Learning Resources, California College of the Arts; Mackenzie Smith MFA Communications Specialist, UC Berkeley College of Natural Resources
Dr. Colette Plum, Deputy Director Study Abroad, UC Berkeley
Career Center
This panel program will introduce career options in higher education. Learn about the paths of PhD professionals as they discuss their work in Learning Resources, Student Life, International Education and Science Communication.
### Seminar 242, Econometrics: "Deep Neural Networks for Estimation and Inference: Application to Causal Effects and Other Semiparametric Estimands".
Seminar | February 7 | 4-5 p.m. | 597 Evans Hall
Max Farell, University of Chicago Booth
Department of Economics
### Inverse RNA folding and Computational Riboswitch Detection
Seminar | February 7 | 4-5 p.m. | 1011 Evans Hall
Professor Danny Barash, Department of Computer Science, Ben-Gurion University
Department of Statistics
The inverse RNA folding problem for designing sequences that fold into a given RNA secondary structure was introduced in the early 1990's in Vienna. Using a coarse-grain tree graph representation of the RNA secondary structure, we extended the inverse RNA folding problem to include constraints such as thermodynamic stability and mutational robustness, developing a program called RNAexinv. In the... More >
### Mathematics Department Colloquium: Fukaya categories with coefficients and spectral networks
Colloquium | February 7 | 4:10-5 p.m. | 60 Evans Hall
Carlos Simpson, Université de Nice
Department of Mathematics
A conjecture of Kontsevich says that the Fukaya category of a symplectic manifold having an additional volume form, should have a stability condition where the stable objects are represented by possibly singular "special Lagrangians". This statement has a nice expression, in the case where we look at the Fukaya-Seidel category of a Riemann surface with coefficients in a fiber category. The... More >
### Religion: A Mellon Foundation Sawyer Seminar
Seminar | February 7 | 5-7 p.m. | 370 Dwinelle Hall
Michael Allan, University of Oregon; Courtney Handman, UT Austin; Webb Keane, University of Michigan
Michael Lucey, UC Berkeley
These public talks continue the series of events connected to the Sawyer Seminar in Linguistic Anthropology & Literary and Cultural Studies that began in Fall 2018. Many of the studies taken up so far in the seminar depend on religious objects, rituals, or encounters to help illuminate those pragmatic aspects of discourse that might be more easily concealed in our everyday routines. Perhaps the... More >
### Linguistic Anthropology and Literary and Cultural Studies: A Mellon Foundation Sawyer Seminar: Session 4: Religion
Conference/Symposium | February 6 – 7, 2019 every day | 5-7 p.m. | 370 Dwinelle Hall
Niklaus Largier, UC Berkeley; Michael Warner, Yale University; Mayanthi Fernando, UC Santa Cruz; Michael Allan, University of Oregon; Courtney Handman, University of Texas at Austin; Charles Hirschkind, UC Berkeley; Webb Keane, University of Michigan
This is the fourth of seven two-day meetings of a Mellon Foundation Sawyer Seminar taking place throughout 2018-2019. The seminar aims to explore the potential of a set of concepts, tools, and critical practices developed in the field of linguistic anthropology for work being done in the fields of literary and cultural criticism.
## Friday, February 8, 2019
### Berkeley Linguistics Society Workshop: Countability Distinctions
Conference/Symposium | February 8 | 370 Dwinelle Hall
David Barner, UC San Diego; Suzi Lima, University of Toronto
Department of Linguistics
See the Workshop Program.
### Sarah Pinto | The Arts of Counter-Ethics
Workshop | February 8 | 10 a.m.-12 p.m. | Barrows Hall, H. Michael and Jeanne Williams Seminar Room, Social Science Matrix, (8th Floor) | Note change in location
Sarah Pinto, Professor of Anthropology, Tufts University
Lawrence Cohen, Professor in Anthropology and South and Southeast Asian Studies, UC Berkeley
A workshop led by Professor Sarah Pinto, Professor of Anthropology at Tufts University.
### Vive Center Seminar - Computer Vision at Magic Leap
Seminar | February 8 | 10:30 a.m.-12 p.m. | Cory Hall, 337 Cory
Jean-Yves Bouguet, Senior Director of Computer Vision at Magic Leap
Vive Center
Jean-Yves will be presenting past, present and future research and development work in the computer vision group at Magic Leap leading to the Magic Leap One. He will provide some insights on the technical challenges that Magic Leap's team of researchers and engineers are tackling to make computer vision work for a see-through wearable Mixed Reality device.
### UROC (Underrepresented Researchers of Color): research proposal and application draft-reading: Get feedback from an experienced undergraduate researcher
Workshop | February 8 | 11:30 a.m.-1:30 p.m. | 14 Durant Hall
Andrea Ramirez, UROC
### Seminar 237/281: ARE/Macro/International Seminar - "Border Walls"
Seminar | February 8 | 12-2 p.m. | 597 Evans Hall
Melanie Morten, Assistant Professor of Economics, Stanford University
Department of Economics
ARE/237/281 Macro and International Trade Seminar
RSVP by emailing Joseph G. Mendoza at jgmendoza@berkeley.edu
### Border Walls
Seminar | February 8 | 12:10-1:30 p.m. | 597 Evans Hall
Melanie Morten, Stanford
### Dancing for Fun and Fitness (BEUHS605)
Workshop | February 8 | 12:10-1 p.m. | 251 Hearst Gymnasium
Be Well at Work - Wellness
Fit some fun and fitness into your day with these free, beginner dance classes. Zumba will be 9/7, Salsa will be 10/19, Hula / Polynesian will be11/2, and Zumba / Salsa will be 12/7. No partner required. Comfortable clothing and athletic shoes recommended.
### Solid State Technology and Devices Seminar: Light based Sound Extraction:Remote Photonic Bio-Sensing and Disease Diagnosis
Seminar | February 8 | 1-2 p.m. | Cory Hall, The Hogan Room, 521
Zeev Zalevsky, Professor, Engineering and the Nanotechnology Center, Bar-Ilan University, Israel
I will present a photonic technological sensing platform that can be used for remote and simultaneous sensing of many biomedical parameters as well as for serving as highly directional hearing aid device. The technology is based upon illuminating a light scattering surface (skin) with a laser and then using a camera with its special optics to perform temporal and spatial tracking of the back... More >
### GRASP seminar: Introduction to D-modules via Bernstein-Sato polynomials
Seminar | February 8 | 2-3 p.m. | 732 Evans Hall
Aaron Brookner, UCB
Department of Mathematics
Given a real polynomial $p$ in $n$-variables, we define a family of distributions over $\{\lambda \in \mathbb C | \text {Re}\lambda >0\}$, generalizing the Γ-function. We claim that it is possible to analytically continue this family, exactly the same way as is traditionally done for the Γ-function, using the existence of the so-called Bernstein-Sato polynomial, $b_p$, of $p$.
We compute some... More >
### Discrete Microfluidics for More Efficient Pharmaceutical Compound Testing: Nano Seminar Series
Seminar | February 8 | 2-3 p.m. | 4 LeConte Hall
Prof. Melinda Simon, San Jose State University, Biomedical Engineering
In 2012, the declining efficiency and increasing cost of pharmaceutical research was noted in a phenomenon termed “Eroom’s law”, to distinguish it from the efficiency of “Moore’s law” in transistor development.
Though the reasons for this phenomenon are myriad and varied, the efficiency of drug development and commercialization could be greatly improved by the development of better paradigms... More >
### MENA Salon: Western Arms Sales and Human Rights in the Middle East
Workshop | February 8 | 3-4 p.m. | 340 Stephens Hall
Every Friday the CMES hosts an informal guided discussion of current events in the Middle East and North Africa, open to all.
On January 27, French President Emmanuel Macron began his first official visit to Egypt. The meeting of Macron and Egyptian President Abdel Fattah Al-Sisi solidified a strategic relationship between France, as one of Egypt's main arms suppliers, and Egypt, described by... More >
### Composition Colloquium: Michael Pisaro
Colloquium | February 8 | 3 p.m. | 250 Morrison Hall
Department of Music
MICHAEL PISARO was born in Buffalo in 1961.
He is a composer and guitarist, a member of the Wandelweiser Composers Ensemble and founder and director of the Experimental Music Workshop, Calarts.
His work is frequently performed in the U.S. and in Europe, in music festivals and in many smaller venues.
It has been selected twice by the ISCM jury for performance at World Music Days... More >
### Information Flows and Cultural Disruption
Seminar | February 8 | 3:10-5 p.m. | 107 South Hall
Michael Buckland
Information, School of
A change to a societyâs pattern ofÂcommunication, coordination, trust, and coercion is culturally disruptive.
### Sébastien Martin - From School Buses To Start Times: Driving Policy With Optimization
Seminar | February 8 | 3:30-4:30 p.m. | Etcheverry Hall
Sébastien Martin, Massachusetts Institute of Technology
Abstract: Maintaining a fleet of buses to transport students to school is a major expense for U.S. school districts. In order to reduce costs by reusing buses between schools, many districts spread start times across the morning. However, assigning each school a time involves estimating the impact on transportation costs and reconciling additional competing objectives. Facing this intricate... More >
### Logic Colloquium: Some applications of model theory in computer science
Colloquium | February 8 | 4-5 p.m. | 60 Evans Hall
Szymon Toruńczyk, University of Warsaw
Department of Mathematics
I will present a few basic applications of model theory in theoretical computer science, e.g. in verification, databases, and algorithms. I will also briefly discuss some links between notions from graph theory and stability theory.
### Neil Bartlett Lectureship: The close and loose relationship between Carbon and Phosphorus
Seminar | February 8 | 4-5 p.m. | 120 Latimer Hall
Manfred Scheer, Institute of Organic Chemistry, Universitat Regensburg
College of Chemistry
Polyphosphorus units are an important class of compound and isolobal to carbon-based relatives. Because of the lone pairs at the phosphorus atoms, the five-fold symmetric cyclo-P5 ring of the pentaphosphaferrocenes [CpRFe(η5-P5)] enables the use of these complexes in unique supramolecular aggregations with Lewis acidic transition metal moieties to form unprecedented giant spherical molecules... More >
### Student 3-Manifold Seminar: The loop theorem and Dehn's lemma
Seminar | February 8 | 4-5:30 p.m. | 939 Evans Hall
Kyle Miller, UC Berkeley
Department of Mathematics
Simplified, the loop theorem states that if the induced map $\pi _1(\partial M)\to \pi _1(M)$ for a $3$-manifold $M$ is not injective, then there is a nullhomotopy of an essential loop in $\partial M$ that can be represented by an embedded disk. We will go through the proof of Stalling's formulation of the loop theorem using Papakyriakopoulos's tower construction and discuss some applications.
### Student Arithmetic Geometry Seminar: Etale Homotopy Obstructions for Rational Points Applied to Open Subvarieties
Seminar | February 8 | 4:10-5 p.m. | 891 Evans Hall
David Corwin, UCB
Department of Mathematics
Last week, I explained the (etale) Brauer-Manin obstruction and Poonen's counterexample. I also stated my result that the Brauer-Manin obstruction on Zariski open covers is enough to (theoretically) determine the existence of rational points. This week, I will say more about how to prove this result. I will also explain the idea behind the etale homotopy obstruction to the local-global principle... More >
### Hungry for Change: Emerging Food Systems Leaders
Panel Discussion | February 8 | 5-7:30 p.m. | 112 Wurster Hall
Berkeley Food Institute
Across California, an emerging generation of food system leaders is advancing food equity, justice, and health in new and transformative ways. The stories of these champions of change highlight our collective struggle and aspiration to reimagine how to feed communities fairly while healing the planet.
The evening will begin with a reception and tasty food before we sit down to listen to ten... More > | {"extraction_info": {"found_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": 0.20454278588294983, "perplexity": 10496.03066415283}, "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-2019-30/segments/1563195526799.4/warc/CC-MAIN-20190720235054-20190721021054-00282.warc.gz"} |
https://blog.csdn.net/Leftmumu/article/details/79957916 | # Abstract Methods and Classes
An abstract class is a class that is declared abstract—it may or may not include abstract methods. Abstract classes cannot be instantiated, but they can be subclassed.
An abstract method is a method that is declared without an implementation (without braces, and followed by a semicolon), like this:
abstract void moveTo(double deltaX, double deltaY);
If a class includes abstract methods, then the class itself must be declared abstract, as in:
public abstract class GraphicObject {
// declare fields
// declare nonabstract methods
abstract void draw();
}
When an abstract class is subclassed, the subclass usually provides implementations for all of the abstract methods in its parent class. However, if it does not, then the subclass must also be declared abstract.
Note: Methods in an interface (see the Interfaces section) that are not declared as default or static are implicitly abstract, so the abstract modifier is not used with interface methods. (It can be used, but it is unnecessary.)
## Abstract Classes Compared to Interfaces
Abstract classes are similar to interfaces. You cannot instantiate them, and they may contain a mix of methods declared with or without an implementation. However, with abstract classes, you can declare fields that are not static and final, and define public, protected, and private concrete methods. With interfaces, all fields are automatically public, static, and final, and all methods that you declare or define (as default methods) are public. In addition, you can extend only one class, whether or not it is abstract, whereas you can implement any number of interfaces.
Which should you use, abstract classes or interfaces?
• Consider using abstract classes if any of these statements apply to your situation:
• You want to share code among several closely related classes.
• You expect that classes that extend your abstract class have many common methods or fields, or require access modifiers other than public (such as protected and private).
• You want to declare non-static or non-final fields. This enables you to define methods that can access and modify the state of the object to which they belong.
• Consider using interfaces if any of these statements apply to your situation:
• You expect that unrelated classes would implement your interface. For example, the interfaces Comparable and Cloneable are implemented by many unrelated classes.
• You want to specify the behavior of a particular data type, but not concerned about who implements its behavior.
• You want to take advantage of multiple inheritance of type.
An example of an abstract class in the JDK is AbstractMap, which is part of the Collections Framework. Its subclasses (which include HashMapTreeMap, and ConcurrentHashMap) share many methods (including getputisEmptycontainsKey, and containsValue) that AbstractMap defines.
An example of a class in the JDK that implements several interfaces is HashMap, which implements the interfaces SerializableCloneable, and Map<K, V>. By reading this list of interfaces, you can infer that an instance of HashMap (regardless of the developer or company who implemented the class) can be cloned, is serializable (which means that it can be converted into a byte stream; see the section Serializable Objects), and has the functionality of a map. In addition, the Map<K, V> interface has been enhanced with many default methods such as merge and forEach that older classes that have implemented this interface do not have to define.
Note that many software libraries use both abstract classes and interfaces; the HashMap class implements several interfaces and also extends the abstract class AbstractMap.
## An Abstract Class Example
In an object-oriented drawing application, you can draw circles, rectangles, lines, Bezier curves, and many other graphic objects. These objects all have certain states (for example: position, orientation, line color, fill color) and behaviors (for example: moveTo, rotate, resize, draw) in common. Some of these states and behaviors are the same for all graphic objects (for example: position, fill color, and moveTo). Others require different implementations (for example, resize or draw). All GraphicObjects must be able to draw or resize themselves; they just differ in how they do it. This is a perfect situation for an abstract superclass. You can take advantage of the similarities and declare all the graphic objects to inherit from the same abstract parent object (for example, GraphicObject) as shown in the following figure.
Classes Rectangle, Line, Bezier, and Circle Inherit from GraphicObject
First, you declare an abstract class, GraphicObject, to provide member variables and methods that are wholly shared by all subclasses, such as the current position and the moveTo method. GraphicObject also declares abstract methods for methods, such as draw or resize, that need to be implemented by all subclasses but must be implemented in different ways. The GraphicObject class can look something like this:
abstract class GraphicObject {
int x, y;
...
void moveTo(int newX, int newY) {
...
}
abstract void draw();
abstract void resize();
}
Each nonabstract subclass of GraphicObject, such as Circle and Rectangle, must provide implementations for the draw and resize methods:
class Circle extends GraphicObject {
void draw() {
...
}
void resize() {
...
}
}
class Rectangle extends GraphicObject {
void draw() {
...
}
void resize() {
...
}
}
## When an Abstract Class Implements an Interface
In the section on Interfaces, it was noted that a class that implements an interface must implement all of the interface's methods. It is possible, however, to define a class that does not implement all of the interface's methods, provided that the class is declared to be abstract. For example,
abstract class X implements Y {
// implements all but one method of Y
}
class XX extends X {
// implements the remaining method in Y
}
In this case, class X must be abstract because it does not fully implement Y, but class XX does, in fact, implement Y.
## Class Members
An abstract class may have static fields and static methods. You can use these static members with a class reference (for example, AbstractClass.staticMethod()) as you would with any other class.
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http://stackoverflow.com/questions/13991893/create-an-epub-file-from-markdown-with-math | # Create an ePub file from markdown with math
I've spent a considerable about of time trying to figure out how I can take a markdown file, which contains TeX math and convert it into an ePub file where the math is rendered properly.
For example:
This is a markdown file. Here is a [link](www.example.com).
Here is some inline math: $\sigma_{i=1}^n \frac{\mu}{100}$
Here is an equation:
$$y = mx + b$$
How can I convert a markdown file with the above text into an ePub file?
I've experimented with different methods of conversion using Pandoc; however, I still can not find a solution which renders the math even 50% correct.
Can anyone provide any help as to how I can do this?
I've tried this solution as well as other Pandoc option without success. Thanks in advance for the help.
-
I see ePub supports vector images. So, isn't this only a matter of running pdflatex on the equations on page without decorations, crop the PDF, convert to SVG, and inline the result in the ePub file ? After you get that working, then you will need some way to determine a correct base height for each inlined equation to get a consistent layout. – mmgp Dec 21 '12 at 15:44
Here's a read: Use LaTeX to produce Epub – Werner Dec 21 '12 at 16:58
## 1 Answer
The development version of pandoc has an epub3 writer. It renders latex math into mathml, which epub3 readers are supposed to support. This will be in the next release. If you like to live on the edge, you can try installing it from source. Instructions are here. Once you've installed pandoc, you can use -t epub3 to force epub3 output.
Of course, this isn't much help if you want epub2 output. For that, your best bet is to write a script that replaces latex math with embedded images. You can use the techniques described here. You might try posting to the pandoc-discuss list on Google Groups to see if anyone has already done something like this.
-
John, thanks for taking the time to reply. pandoc-1.10 failed during the building phase, but I can wait until the next version now that I know what to do. Thanks for all your work on Pandoc, it's fantastic! – drbunsen Dec 21 '12 at 21:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8906840085983276, "perplexity": 1283.6958179679582}, "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-2015-06/segments/1422115855561.4/warc/CC-MAIN-20150124161055-00090-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://brilliant.org/problems/10-sec-challenge-10/ | # 10-seconds challenge-10
Calculus Level 4
Find the order of given differential equation:
$\left (\dfrac{d^{2}y}{dx^{2}} \right )^{4}+\int y\, dx=\cos x$
This is a part of 10-seconds challenge.
× | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "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": 0.8983442187309265, "perplexity": 9963.938480703513}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573735.34/warc/CC-MAIN-20190919204548-20190919230548-00213.warc.gz"} |
https://www.leehodgkinson.com/blog/onion-routing-under-the-hood/ | This is an attempt of a mid-level overview of how Tor combines public-key encryption and symmetric-key cryptography to allow it to function. I should make it clear that, I’m not an expert and these ideas really are just a compendium of things I’ve read here and there, and how I believe it to function. I’d be more than happy to edit the post if someone has a better idea and wants to correct the article.
# High-level overview
First a high-level overview. I’m not going to talk at all about what Tor is, the history of Tor or what it’s used for – there are plenty of other resources where you can read about that. You should know roughly how Tor operates (connecting nodes in a circuit between your computer and it's ultimate destination) and other high-level things about it before continuing.
This image was directly pilfered from Wikipedia. What this image represents is the layers of the “onion”. The data-packet is wrapped in successive layers of encryption, and each time the message traverses a node in the circuit, the outer layer is decrypted (or “peeled” to keep inline with onion nomenclature and analogy). The key feature of this is that no single node knows both the origin of the packet (client’s computer) and destination of the packet (e.g. some web-server). A single node knows only the address of the previous node and the following node. Of course if the packet is ever to reach its ultimate destination, the IP of this destination must be there somewhere in the bundle, but the key is that is it buried under the layers of the onion.
Of course the final node, or “exit node”, could see the contents of the message itself if that message wasn’t also encrypted (for example if the client does not establish a HTTPS connection with the webserver), so it’s important to keep that in mind when using Tor and ensure HTTPS everywhere.
Another feature is that no node knows whether the previous node was the client or whether it was just another node in the chain like itself.
The nodes that form a circuit or chain are mandated by what is known as the directory authority nodes. These also provide the client with the public key for each of the nodes in the chain, but more about that later.
# Asymmetric key cryptography
One of the pre-requisites to understanding how Tor works is understanding how asymmetric-key cryptography works. A full account would be beyond the scope of this article, but the basic idea is that we have a pair of keys different from each other – a public key and private key. As the names suggest, the public key is available to the world and the private key must be kept secret.
Using the public key anyone can encrypt a given message (or given block of data), and then only the holder of the private key can decrypt it.
Contrarily, the private key could also be used to encrypt some msg that the public key could decrypt. This is a feature of the mathematics. However given that the public key is public, this kind of usage would be pointless for encryption purposes. However when it is used in this manner we call it "signing" as it is useful to prove the authenticity of the message if only the originator has the private key.
One feature of asymmetric-key encryption is that it is computationally much slower than symmetric-key encryption.
Some examples of asymmetric key algorithms are RSA and ECC. Here is a nice guide to the maths of RSA and another here
# Symmetric key cryptography
This is where both parties have the same (secret) key for both encrypting and decrypting messages.
One of the main challenges is how to share such a secret between two physically distant parties without a third-party, who is listening in, also obtaining this secret key. Diffie-Hellman (DH) key exchange provides a solution to this.
I'm going to include an example here (again stolen from Wikipedia) just to make this concrete so we can talk more concretely when it comes to Tor by referring back to this.
The simplest and the original implementation of the protocol uses the multiplicative group of integers modulo p, where p is prime, and g is a primitive root modulo p. These two values are chosen in this way to ensure that the resulting shared secret can take on any value from 1 to p–1.
Here is an example of the protocol:
1) Alice and Bob agree to use a modulusp = 23 and baseg = 9 (which is a primitive root modulo 23). Both of these things are public info that Eve can also note down.
2) Alice chooses a secret integer a =4, then sends Bob A = g^a mod p which for the values chosen means A= 6. Note Eve can see this, but if we're using big enough numbers then because of the discrete log problem then Eve cannot simply invert to get a.
3) Likewise, Bob chooses a secret integer b = 3, then sends Alice B = g^b mod p, which for these values gives B = 16.
4) Alice computes s = B^a mod p, which gives s = 9
5) Bob computes s = A^b mod p, which gives s = 9 also.
6) Alice and Bob now share a secret (the number 9).
They got the same number because of exponentiation is commutative under mod.Mathematically: g^(ab) equiv g^(ba) (under modp).
Note that only ab, and (g^ab mod p = g^ba mod p) are kept secret. All the other values – pg,A, B – are sent in the clear. Once Alice and Bob compute the shared secret they can use it as an encryption key, known only to them, for sending messages across the same open communications channel.
Take a look also at the video
# Tor Steps :
## Step 1:
The client has the public key of node 1 (N1) the first node in the circuit; it has obtained this from the directory server. Since we already have the public key of N1 we are able to send messages to N1 that N1, and only N1, can decrypt and read. You may wonder if since RSA private keys can be used to “encrypt” a message, which the public key can decrypt, can’t N1 also send us back encrypted messages? Well yes, mathematically speaking, but they wouldn’t be secure because the public key is well, public. Using the keys that way around therefore is only good for signing. We would like to establish a session with N1. In other words, establish a shared secret between us (CLIENT) and N1 so we may use symmetric-key-exchange crypto.
To do this we will use Diffie-Hellman (DH) techniques. Taking the (toy) example from the previous section, we agree (publically) to use modulus p=23 and base g=9. Then we (CLIENT) pick a secret integer a=4. We then compute A=(g^a)modp = (9^4)mod23.
So far just like regular DH, but this time we use PKN1 (N1’s public key) to encrypt A, and we send encPKN1(A) to N1. Just like in regular DH, N1 now picks his random integer b, and computes B=(g^b)modp. It sends this to us in plain text as the image above shows, no envelope. This however is not an issue because of the initial request being encrypted with the public key, as I hope the following aside will make clear. The rest now proceeds as in regular DH exchange. N1 now computes the secret s = A^b, and CLIENT now computes the secret s=B^a.
### Aside on why the public key encryption is needed at all.
You may wonder why we need to encrypt our message to N1 with the public key at all, since isn’t DH supposed to be immune to eavesdroppers and a way to establish a secret even when someone is watching? The caveat however is that this is only true when the eavesdropper is passive and does nothing but listen; if we have an active eavesdropper, then MITM attacks could thwart our initial establishment of a secret without using the public key to encrypt the CLIENT→N1 component of the setup.
You can imagine Eve sat in the middle of CLIENT AND N1 as in the image
She intercepts A=g^a(modp), and instead of simply reading it passively then forwarding it on to N1, she decides to choose her own secret, c, and actually forwards A’=g^c(modp). N1 has no idea that this came from Eve and not the client. Now N1 will compute s’=(A’)^b, a different secret. Also, when Eve received B she will compute the same s’=(B)^c. In other words it is now Eve who has used DH techniques to establish a secret with N1, but N1 thinks this is a secret between himself and CLIENT. In the exact same way, Eve can pick another random integer on the return journey, d, to compute B’=g^d(modp) and pass this back to the client instead of B. Eve can then compute s’’=A^d and the client will compute the same s’’=(B’)a. In other words with an active snooper, DH would be vulnerable to MITM style attacks without using public key encryption for at least one leg of the journey. The client would think it has a session key with N1 and N1 would think is has a session key with the client, but really we’d have 2 sessions, CLIENT<→ EVE and EVE<→N1. Not good! Also check out this video explaining an active DH attack in more detail.
But what about the return trip being in plain-text? It’s true that active Eve could intercept and modify this data too right? Yes, but it would do her little good. N1 would have still received the intended A=g^a(modp) from the client and using it N1 will compute a shared secret s=A^b, where b is N1’s random private number. Now if Eve had tampered with the return packet B=(g^b)modp and made it say B’=(g^d)modp, then when CLIENT tried to compute the same shared secret that N1 holds he’d do (B’)^a=(g^da)modp, which is not the same as (g^ab)modp. In this manner, CLIENT and N1 would end up with different secrets, and they wouldn’t be able to communicate at all. Eve has therefore the ability to disrupt the communications in this manner, but not the ability to snoop on them.
I imagine one more layer of protection that public key encryption is giving us is that N1 will sign the return message with its private key, which the CLIENT (or of course anyone else), using the public key, can verify the message came from N1 not someone else.
## Step 2
Now CLIENT and N1 have established a session (they have a shared secret) and can efficiently communicate with the faster methods of symmetric-key exchange and dispense with the slow and weighty computational expense of public-key crypto. This is the first layer of our onion!
What we’d like to do next is extend the circuit to the second node (N2) that the directory server had chosen for us.
Again we have N2’s public key (PKN2) and we can use it to encrypt a message that N2, and only N2, can read. This is important, not even N1 can read that message nor Eve.
We once again begin the DH dance. We choose our random number, a, (different from the first time we did this with N1!), and we need to find a way to send our A=g^amodp to N2. We only want N2 to be able to read this so once again we encrypt it using the public key: encPKN2(g^amodp), and then we use our shared secret (SS1) with N1 to further wrap it, i.e. SS1(encPKN2(g^amodp)). This means Eve has 2 layers of encryption between her and the juicy data now.
When N1 receives this data, it can unwrap the SS1 layer using the shared secret we established, and find under it encPKN2(A). Note it cannot see what A is itself, so one more precaution against it doing a MITM attack in the manner described in the earlier aside. N1 will just see that the packet should be forwarded to N2 and do so. N2 will receive this packet, encPKN2(A), and it will decrypt it using its private key to obtain A. It will pick a private random number b , and compute the session secret s2=A^b and B=g^bmodp, the latter which it will send back to N1. It may sign the message with B using it’s private key to authenticate the messages origin, however Eve or anyone else could use the public key to read that message, but just like explained earlier, this does not matter.
N1 will encypt B with SS1 before sending it back to CLIENT (not that it really matters as the N2→N1 was in clear text anyway).
CLIENT can now decrypt using SS1 to get B, and compute s2=B^a.
Now the CLIENT and N2 have a shared secret that N1 (nor anyone else) doesn’t know.
## Step 3
Hopefully it’s obvious how this could be extended to the third node and so on if desired. The client would send SS1(SS2(encPK3(g^amodp))). N1 would peel SS1 and forward to N2. N2 would peel the remaining SS2 and forward encPK3(g^amodp) to N3 who could decrpyt it using it's private key PK3. In this way CLIENT and N3 would end up establishing a secret, s3, that both N1 and N2 did not know nor anyone else.
## Step 4
By now we have extended the circuit to include a given number of nodes (probably at least three). We, the CLIENT, have established shared secrets with multiple nodes, N1, N2, N3 by leveraging a combination of public key cryptography and DH key exchange techniques, and now we can communicate with each using symmetric key exchange with these secrets in a manner than only that particular node can read.
If we want to send a message to some web-server, then what we can do, therefore, is take our message (and message header that will contain the destination IP address of the message, e.g. IP for google.com), then we first encrypt it (wrap it) using SS3 (the secret with the exit node node N3) Next we wrap it with SS2 (the secret with exit node N2) and add an intermediary header containing the IP address of N3. Next we wrap it with SS1 (the secret with exit node N1) and add an intermediary header containing the IP address of N2. In this way we have SS1(SS2(SS3(msg)))….and the layers of encryption are stacked up like an onion.
N1 gets this onion and strips off the outer later SS1. It can see the header that tells it to pass it N2’s IP and obviously know the IP of the previous node, but it doesn’t know that the previous node was the originator and not just another node in the circuit. Nor can is break the other 2 layers of encryption remaining to read the message or lower-level forwarding information. It forwards accordingly SS2(SS3(msg)) to N2. N2 now strips away SS2 leaving SS3(msg). Note again it can’t read the msg. It can read the header to tell it to forward the package to N3 and it knows the previous node N1 but nothing about the client.
Finally, N3 gets SS3(msg). It strips the final layer, to show the message. Note that if the message itself isn’t encrypted (between the client and web-server) then N3 can read the message in plain-text. This is why it's still important to use HTTPS with Tor.
On the return trip with the message from the webserver, rmsg, the exit node wraps it in SS3(rmsg) and passes to N2, which wraps in SS2(SS3(msg)) before passing to N1, which wraps as SS1(SS2(SS3(rmsg))) before passing back to the client. The client has all these secrets so can unwrap the full onion to get rmsg.
Note that the exit could read the response from the server, but N2 and N1 cannot because it has again been wrapped in SS3 and SS2 successively at each hop.
Note the return message, doesn’t contain any information in the header (or headers) that can be used to route it back to the client (not even encrypted ones), it’s simply a case of each node forwarding the data to the place that made the request to it initially, and them playing pass the pacel parcel back (I believe anyway).
Currently unrated | {"extraction_info": {"found_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": 0.33077138662338257, "perplexity": 1217.2830385107063}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247504594.59/warc/CC-MAIN-20190221111943-20190221133943-00373.warc.gz"} |
http://math.stackexchange.com/users/54402/ryan?tab=summary | Ryan
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### Questions (54)
46 Show that $\int_{0}^{\pi/2}\frac {\log^2\sin x\log^2\cos x}{\cos x\sin x}\mathrm{d}x=\frac14\left( 2\zeta (5)-\zeta(2)\zeta (3)\right)$ 18 A log improper integral 18 A series involves harmonic number 17 Find the infinite sum $\sum_{n=1}^{\infty}\frac{1}{2^n-1}$ 16 How to evaluate $\int_{0}^{1}{\frac{{{\ln }^{2}}\left( 1-x \right){{\ln }^{2}}\left( 1+x \right)}{1+x}dx}$
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+5 Evaluate $\int_{0}^{+\infty }{\left( \frac{x}{{{\text{e}}^{x}}-{{\text{e}}^{-x}}}-\frac{1}{2} \right)\frac{1}{{{x}^{2}}}\text{d}x}$ +5 A improper integral with Glaisher-Kinkelin constant +5 Show that $\int_{0}^{\pi/2}\frac {\log^2\sin x\log^2\cos x}{\cos x\sin x}\mathrm{d}x=\frac14\left( 2\zeta (5)-\zeta(2)\zeta (3)\right)$ +5 A log improper integral
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### Tags (31)
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Mathematics 1,523 rep 618 | {"extraction_info": {"found_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": 0.9249385595321655, "perplexity": 12990.593400546859}, "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/1464049288709.66/warc/CC-MAIN-20160524002128-00048-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://testbook.com/question-answer/a-3-m-thick-clay-layer-is-subjected-to-an-initial--58d37b9f0328215c466ff431 | # A 3 m thick clay layer is subjected to an initial uniform pore pressure of 145 kPa as shown in the figure.For the given ground conditions the time (in days, rounded to the nearest integer) required for 90% consolidation would be ________
This question was previously asked in
GATE CE 2017 Official Paper: Shift 1
View all GATE CE Papers >
## Answer (Detailed Solution Below) 1765 - 1775
Free
CT 1: Ratio and Proportion
2672
10 Questions 16 Marks 30 Mins
## Detailed Solution
Concept:
The time required for any degree of consolidation is given by Taylor's formula
$$\left( {{{\rm{T}}_{\rm{v}}}} \right) = \frac{{{{\rm{C}}_{\rm{v}}}{\rm{t}}}}{{{{\rm{d}}^2}}}$$
Tv - Time factor
Cv - Coefficient of consolidation
t - Time taken for consolidation
d - Drainage path
Drainage path represents the maximum distance the water particles have to travel to reach the free drainage layer.
Calculation:
Given:
Since the bottom is impermeable water can drain only through top sand layer
It is one way drainage case so
H = 3 m = 3000 mm
$$\begin{array}{l} {T_v} = \frac{{{c_v}t}}{{{H^2}}}\\ t = \frac{{0.85 \times {{3000}^2}}}{3} = 2250000\;minutes \end{array}$$
⇒ 1770.83 days ≈ 1771 days
Double drainage condition refers to the situation when both faces are permeable and pore water can dissipate through both faces but in single drainage only one face is permeable and hence it takes a longer time in single drainage.
Single drainage d = H
Double drainage d = H/2 | {"extraction_info": {"found_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": 0.6517232656478882, "perplexity": 5238.310761504529}, "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/1634323587623.1/warc/CC-MAIN-20211025030510-20211025060510-00262.warc.gz"} |
http://crm.sns.it/course/5411/ | Celebrating the 25th anniversary of "Calculus of Variations and Partial Differential Equations"
# Quantum field theory and geometric analysis
speaker: Jürgen Jost (Max Planck, Leipzig)
abstract: I shall describe how models from quantum field theory, like the (supersymmetric) nonlinear sigma model, can be converted into geometric variational problems. Since these problems typically possess a noncompact invariance group, standard variational schemes do not apply. On the other hand, however, via Noether's theorem, these symmetries provide us with additional structure that help us with the analytical treatment. I shall argue that these problems, because of their rich and difficult structure, can play a pioneering for the development of new techniques in geometric analysis.
timetable:
Fri 18 May, 9:30 - 10:10, Aula Dini
<< Go back | {"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": 0.8348276019096375, "perplexity": 1002.8291816400256}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202635.43/warc/CC-MAIN-20190322054710-20190322080710-00009.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/dcdss.2018038 | # American Institute of Mathematical Sciences
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August 2018, 11(4): 631-641. doi: 10.3934/dcdss.2018038
## Symmetries and conservation laws of a KdV6 equation
Department of Mathematics, University of Cádiz, PO.BOX 40, 11510 Puerto Real, Cádiz, Spain
* Corresponding author: M.S. Bruzón.
Received December 2016 Revised May 2017 Published November 2017
In the present work we make an analysis of the Korteweg-de Vries of sixth order. We apply the classical Lie method of infinitesimals and the nonclassical method, due to Bluman and Cole, to deduce new symmetries of the equation which cannot be obtained by Lie classical method. Moreover, we obtain ten different conservation laws depending on the parameters and we conclude that potential symmetries project on the infinitesimals corresponding to the classical symmetries.
Citation: María Santos Bruzón, Tamara María Garrido. Symmetries and conservation laws of a KdV6 equation. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 631-641. doi: 10.3934/dcdss.2018038
##### References:
show all references
##### References:
[1] Wen-Xiu Ma. Conservation laws by symmetries and adjoint symmetries. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 707-721. doi: 10.3934/dcdss.2018044 [2] M. S. Bruzón, M. L. Gandarias, J. C. Camacho. Classical and nonclassical symmetries and exact solutions for a generalized Benjamin equation. Conference Publications, 2015, 2015 (special) : 151-158. doi: 10.3934/proc.2015.0151 [3] María-Santos Bruzón, Elena Recio, Tamara-María Garrido, Rafael de la Rosa. Lie symmetries, conservation laws and exact solutions of a generalized quasilinear KdV equation with degenerate dispersion. Discrete & Continuous Dynamical Systems - S, 2020, 13 (10) : 2691-2701. doi: 10.3934/dcdss.2020222 [4] Stephen Anco, Maria Rosa, Maria Luz Gandarias. Conservation laws and symmetries of time-dependent generalized KdV equations. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 607-615. doi: 10.3934/dcdss.2018035 [5] Chaudry Masood Khalique, Muhammad Usman, Maria Luz Gandarais. Nonlinear differential equations: Lie symmetries, conservation laws and other approaches of solving. Discrete & Continuous Dynamical Systems - S, 2020, 13 (10) : i-ii. doi: 10.3934/dcdss.2020415 [6] María Rosa, María de los Santos Bruzón, María de la Luz Gandarias. Lie symmetries and conservation laws of a Fisher equation with nonlinear convection term. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1331-1339. doi: 10.3934/dcdss.2015.8.1331 [7] Zhijie Cao, Lijun Zhang. Symmetries and conservation laws of a time dependent nonlinear reaction-convection-diffusion equation. Discrete & Continuous Dynamical Systems - S, 2020, 13 (10) : 2703-2717. doi: 10.3934/dcdss.2020218 [8] Alexander V. Bobylev, Sergey V. Meleshko. On group symmetries of the hydrodynamic equations for rarefied gas. Kinetic & Related Models, 2021, 14 (3) : 469-482. doi: 10.3934/krm.2021012 [9] Juan Belmonte-Beitia, Víctor M. Pérez-García, Vadym Vekslerchik, Pedro J. Torres. Lie symmetries, qualitative analysis and exact solutions of nonlinear Schrödinger equations with inhomogeneous nonlinearities. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 221-233. doi: 10.3934/dcdsb.2008.9.221 [10] Carsten Collon, Joachim Rudolph, Frank Woittennek. Invariant feedback design for control systems with lie symmetries - A kinematic car example. Conference Publications, 2011, 2011 (Special) : 312-321. doi: 10.3934/proc.2011.2011.312 [11] José F. Cariñena, Fernando Falceto, Manuel F. Rañada. Canonoid transformations and master symmetries. Journal of Geometric Mechanics, 2013, 5 (2) : 151-166. doi: 10.3934/jgm.2013.5.151 [12] Miriam Manoel, Patrícia Tempesta. Binary differential equations with symmetries. Discrete & Continuous Dynamical Systems, 2019, 39 (4) : 1957-1974. doi: 10.3934/dcds.2019082 [13] Olivier Brahic. Infinitesimal gauge symmetries of closed forms. Journal of Geometric Mechanics, 2011, 3 (3) : 277-312. doi: 10.3934/jgm.2011.3.277 [14] Marin Kobilarov, Jerrold E. Marsden, Gaurav S. Sukhatme. Geometric discretization of nonholonomic systems with symmetries. Discrete & Continuous Dynamical Systems - S, 2010, 3 (1) : 61-84. doi: 10.3934/dcdss.2010.3.61 [15] L. Bakker, G. Conner. A class of generalized symmetries of smooth flows. Communications on Pure & Applied Analysis, 2004, 3 (2) : 183-195. doi: 10.3934/cpaa.2004.3.183 [16] Michael Baake, John A. G. Roberts, Reem Yassawi. Reversing and extended symmetries of shift spaces. Discrete & Continuous Dynamical Systems, 2018, 38 (2) : 835-866. doi: 10.3934/dcds.2018036 [17] Michael Hochman. Smooth symmetries of $\times a$-invariant sets. Journal of Modern Dynamics, 2018, 13: 187-197. doi: 10.3934/jmd.2018017 [18] Davi Obata. Symmetries of vector fields: The diffeomorphism centralizer. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021063 [19] Júlio Cesar Santos Sampaio, Igor Leite Freire. Symmetries and solutions of a third order equation. Conference Publications, 2015, 2015 (special) : 981-989. doi: 10.3934/proc.2015.0981 [20] Robert I. McLachlan, Ander Murua. The Lie algebra of classical mechanics. Journal of Computational Dynamics, 2019, 6 (2) : 345-360. doi: 10.3934/jcd.2019017
2019 Impact Factor: 1.233 | {"extraction_info": {"found_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": 0.49551650881767273, "perplexity": 6883.675063224908}, "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/1623488552937.93/warc/CC-MAIN-20210624075940-20210624105940-00536.warc.gz"} |
https://physionet.org/content/osv/1.0.0/ | Database Open Access
# Pattern Analysis of Oxygen Saturation Variability
Published: Sept. 27, 2017. Version: 1.0.0
When using this resource, please cite the original publication:
Amar S. Bhogal and Ali R. Mani. Pattern Analysis of Oxygen Saturation Variability in Healthy Individuals: Entropy of Pulse Oximetry Signals Carries Information about Mean Oxygen Saturation. Frontiers in Physiology, 8, 555. DOI:10.3389/fphys.2017.00555.
Goldberger, A., Amaral, L., Glass, L., Hausdorff, J., Ivanov, P. C., Mark, R., ... & Stanley, H. E. (2000). PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals. Circulation [Online]. 101 (23), pp. e215–e220.
### Abstract
This database contains one hour oxygen saturation measurements of 36 patients, used for the analysis of oxygen saturation variability.
### Background
Pulse oximetry is routinely used for monitoring patients' oxygen saturation levels with little regard to the variability of this physiological variable. There are few published studies on oxygen saturation variability (OSV), with none describing the variability and its pattern in a healthy adult population. The aim of this study was to characterise the pattern of OSV using several parameters: the regularity (sample entropy analysis), the self-similarity (detrended fluctuation analysis (DFA)), and the complexity (multiscale entropy (MSE) analysis). Secondly, to determine if there were any changes that occur with age.
The study population consisted of 36 individuals. The 'young' population consisted of 20 individuals [Mean age = 21.0 (SD = 1.36 years)] and the 'old' population consisted of 16 individuals [Mean age = 50.0 (SD = 10.4 years)]. Through DFA analysis, OSV was shown to exhibit fractal-like patterns. The sample entropy revealed the variability to be more regular than heart rate variability and respiratory rate variability. There was a significant inverse correlation between mean oxygen saturation and sample entropy in healthy individuals. Additionally, the MSE analysis described a complex fluctuation pattern, which was reduced with age (p < 0.05). These findings suggest partial "uncoupling" of the cardio-respiratory control system that occurs with ageing. Overall, this study has characterized OSV using pre-existing tools. We have showed that entropy analysis of pulse oximetry signals carries information about body oxygenation. This may have the potential to be used in clinical practice to detect differences in diseased patient subsets.
### Data Collection
Before starting the recording, the participants are interviewed to obtain:
• Age
• BMI (use their weight and height on the NHS BMI calculator tool)
• Gender
• Smoking history and/or current smoking status
• Any significant medical conditions that could affect reading
Measurement Setup:
1. In the LabChart software, switch off all input sources except input 1,2, and 3.
2. Set the sampling frequency to 1KHz.
3. Plug Pulse Oximeter into Power Lab input 1.
4. Plug the Pulse pressure transducer into Power Lab input 2.
5. Attach Respiratory band into Power Lab input 3.
6. Connect personal computer to the PowerLab data acquisition system.
Procedure for recording:
1. Clean the pulse oximeter and place on finger of participants choosing
2. Place the pulse pressure transducer on the adjacent finger
3. Wrap the Respiratory band around the umbilicus of the participant
4. Preferably have participant sitting with the fingers relatively still
5. Test equipment to ensure correct readings
6. Once the equipment has been checked stop the test and start the official recording
7. Add a comment to show when the data collection has started and once again when it has ended
8. After the hour has passed stop the recording, then remove and clean the equipment
9. Save the file ensuring complete anonymity by using the date of collection (i.e if 1st participant on January 1st 2017, then save file as 010117A)
Extracting Oxygen Saturation Data for Analysis:
1. Select the 1 hour recorded segment
2. File > Export As – select LabChart Text FIle
3. Choose channel 1 and select the option for current selection
4. Down sample by 1000 and remove comments
5. Save file in a separate file with the other samples
### Data Files
The oxygen saturation data files are provided in standard WFDB format. The sampling frequency of the measurements is 1Hz as specified in the header files.
### Contributors
This data was contributed by Amar S. Bhogal and Ali R. Mani from the UCL Division of Medicine, University College London.
##### Access
Access Policy:
Anyone can access the files, as long as they conform to the terms of the specified license.
##### Corresponding Author
You must be logged in to view the contact information.
## Files
Total uncompressed size: 969.2 KB.
##### Access the files
• Access the files using the Google Cloud Storage Browser here. Login with a Google account is required.
• Access the data using the Google Cloud command line tools (please refer to the gsutil documentation for guidance):
gsutil -m -u YOUR_PROJECT_ID cp -r gs://osv-1.0.0.physionet.org DESTINATION
wget -r -N -c -np https://physionet.org/files/osv/1.0.0/
Visualize waveforms
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https://dispatchesfromturtleisland.blogspot.com/2018/01/ | ## Wednesday, January 31, 2018
### Yes, Particle Physics Is That Weird
A new comic from xkcd accurately illustrates how weird particle collider physics is in a way that the average person can understand.
Alt text:
The most delicious exotic fruit discovered this way is the strawberry banana. Sadly, it's only stable in puree form, so it's currently limited to yogurt and smoothies, but they're building a massive collider in Europe to search for a strawberry banana that can be eaten whole.
Actually, plain old organic chemistry is almost as remarkable. One of my most memorable high school experiences (while I was a high school student in New Zealand) was producing esters from noxious seeming chemicals in the lab that smelled exactly like familiar fruits and other smells, because those smells, at their most essential levels, are these chemicals.
For example, pineapple smell is partially allyl hexanoate and ethyl butyrate is a chemical in the smell of pineapple, strawberry and banana.
## Tuesday, January 30, 2018
### European Population History In a Nutshell
You too can watch European population figures, by country, unfold with video maps and dramatic music for every year since 400 BCE, over a little less than twelve minutes.
One insight is how thinly populated places like Britain were until quite recently.
Another is that political boundaries are anything but static in the long run.
It also brought to my attention the Novgorod Republic in what is now Northern Russia, that lasted nearly three centuries in the late Middle Ages and was one of the earliest and most successful democratic experiments which is often overlooked.
UPDATE January 31, 2018: Today at sister blog Wash Park Prophet, I made the 9000th post from the combined Wash Park Prophet and Dispatches From Turtle Island blogs since I began the Wash Park Prophet blog on July 3, 2005.
### An Elite Dominance Model Of Beaker Pottery
A paper reviewed by Bell Beaker blogger assembles evidence that local people who encountered Bell Beaker elites at first tried to copy Bell Beaker pottery using their own techniques until their pottery had fully assimilated into the Bell Beaker approach.
This also suggests that people who copy one aspect of Bell Beaker culture might copy others in a similar elite dominance fashion, resulting in heavy borrowing from, or even language shift to, the language spoken by the newly arrived Bell Beaker people.
### Atoms Or Ripples?
4Gravitons has a nice little riff explaining the perspective that fundamental particles are excited ripples in fields (which are more fundamental) rather than truly being fundamental particles. From the closing stanza:
This is Quantum Field Theory, the universe of ripples. Democritus said that in truth there are only atoms and the void, but he was wrong. There are no atoms. There is only the void. It ripples and shimmers, and each of us lives as a collection of whirlpools, skimming the surface, seeming concrete and real and vital…until the ripples dissolve, and a new pattern comes.
### New Results From KLOE-2 And LHCb
The KLOE-2 experiment has released some new results.
1. It confirmed Standard Model predictions regarding the running of the electromagnetic coupling constant at energy scales from 0.6 GeV to 1.0 GeV.
2. It expanded the range in which the carrier boson for dark matter interactions (a.k.a. a dark photon) is ruled out. The exclusions are the most strict of any experiment in the 0.7 GeV to 1 GeV boson mass range. Such a boson could also explain muon anomalies if they existed.
3. It searched for CPT violation in neutral kaon systems and ruled them out to high precision, with considerable room for improvement simply by continuing to run the experiment to reduce statistical error.
The KLOE-2 results reach the sensitivity at the level of 10^−18 GeV 20, which is several orders of magnitude more precise than results obtained with other neutral meson systems a . The results were obtained with the data sample corresponding to the 1.7 fb^−1 integrated luminosity, and is mainly limited by the statistical errors[.]
The total amount of data collected will be about three times as great as the amount collected so far.
Meanwhile, at the LHC, charm quark properties (mainly determined through studies of neutral D mesons which made made up of charm quarks and antiup quarks, or up quarks and anticharm quarks) have not found any sign of CP violation in the system (where the Standard Model prediction is that CP violation be less strong than the experiment is capable of distinguishing). The most recent paper on this topic from LHCb concludes that:
The measurement of the mixing parameters and the searches of CPV in the charm sector provide a precise tests of the SM and probes of New Physics effects, complementary to analogous searches with B and K mesons. The LHCb experiment has used a world-leading sample of charm particles to provide a set of measurements based on the Run 1 data which confirmed the SM predictions. The no-mixing hypothesis for D0 system has been excluded at more than 10 σ level, based on data gathered in Run 1. Results based on both prompt and double-tagged candidates are in agreement. All measurements are consistent with the no-CP violation hypothesis. The current precision reached is of order of 10−4 for the indirect searches. The majority of the measurements are statistically limited, and some of the systematics factors are expected to reduce with signal yields. Currently, several Run 1 and Run 2 based analyses are ongoing. The Run 2 measurements benefits not only from the higher statistics but also from the optimized trigger.
## Monday, January 29, 2018
### Alternative Dark Energy Theories Further Tighten Bound On Neutrino Masses
Many investigators favor a form of dark energy that can vary over time to the cosmological constant, although both theories can fit the evidence within the bounds of statistical significance. A varying dark energy cosmology, when applied to available data, more tightly bounds the upper limit to the sum of the neutrino masses.
We explore cosmological constraints on the sum of the three active neutrino masses Mν in the context of dynamical dark energy (DDE) models with equation of state (EoS) parametrized as a function of redshift z by w(z)=w0+waz/(1+z), and satisfying w(z)1 for all z. We perform a Bayesian analysis and show that, within these models, the bounds on Mν\textit{do not degrade} with respect to those obtained in the ΛCDM case; in fact the bounds are slightly tighter, despite the enlarged parameter space. We explain our results based on the observation that, for fixed choices of w0,wa such that w(z)1 (but not w=1 for all z), the upper limit on Mν is tighter than the ΛCDM limit because of the well-known degeneracy between w and Mν. The Bayesian analysis we have carried out then integrates over the possible values of w0-wa such that w(z)1, all of which correspond to tighter limits on Mνthan the ΛCDM limit. We find a 95\% confidence level (C.L.) upper bound of Mν<0.13eV. This bound can be compared with Mν<0.16eV at 95\%~C.L., obtained within the ΛCDM model, and Mν<0.41eV at 95\%~C.L., obtained in a DDE model with arbitrary EoS (which allows values of w<1). Contrary to the results derived for DDE models with arbitrary EoS, we find that a dark energy component with w(z)1 is unable to alleviate the tension between high-redshift observables and direct measurements of the Hubble constant H0. Finally, in light of the results of this analysis, we also discuss the implications for DDE models of a possible determination of the neutrino mass hierarchy by laboratory searches. (abstract abridged)
Sunny Vagnozzi, et al., "Constraints on the sum of the neutrino masses in dynamical dark energy models with w(z)≥−1 are tighter than those obtained in ΛCDM" (January 25, 2018). | {"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": 0.801464855670929, "perplexity": 1974.5359900153421}, "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/1627046153966.60/warc/CC-MAIN-20210730122926-20210730152926-00289.warc.gz"} |
https://www.researchgate.net/profile/Hueseyin-Merdan | # Hüseyin MerdanTOBB University of Economics and Technology · Department of Mathematics
Professor of Mathematics
48
Publications
6,812
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
384
Citations
July 2013 - August 2014
Position
• Professor
September 2005 - present
Position
• Professor of Applied Mathematics
## Publications
Publications (48)
Article
Full-text available
We analyze Hopf bifurcation and its properties of a class of system of reaction-diffusion equations involving two discrete time delays. First, we discuss the existence of periodic solutions of this class under Neumann boundary conditions, and determine the required conditions on parameters of the system at which Hopf bifurcation arises near equilib...
Article
Full-text available
We present a mathematical model for a market involving two stocks which are traded within a single homogeneous group of investors who have similar motivations and strategies for trading. It is assumed that the market consists of a fixed amount of cash and stocks (additions in time are not allowed, so the system is closed) and that the trading group...
Article
Full-text available
We consider a general first-order scalar difference equation with and without Allee effect. The model without Allee effect represents asexual reproduction of a species while the model including Allee effect represents sexual reproduction. We analyze global stabilities of both models analytically and compare the results obtained. Numerical simulation...
Article
Full-text available
We present an algorithm for determining the existence of a Hopf bifurcation of a system of delayed reaction–diffusion equations with the Neumann boundary conditions. The conditions on parameters of the system that a Hopf bifurcation occurs as the delay parameter passes through a critical value are determined. These conditions depend on the coeffici...
Article
Full-text available
We study stability and Hopf bifurcation analysis of a model that refers to the competition between the immune system and an aggressive host such as a tumor. The model which describes this competition is governed by a reaction-diffusion system including time delay under the Neumann boundary conditions, and is based on Kuznetsov-Taylor's model. Choos...
Article
Full-text available
We study the stability and Hopf bifurcation analysis of a coupled two-neuron system involving both discrete and distributed delays. First, we analyze stability of equilibrium point. Choosing delay term as a bifurcation parameter, we also show that Hopf bifurcation occurs under some conditions when the bifurcation parameter passes through a critical...
Research
Full-text available
We present an algorithm for determining the existence of Hopf bifurcations of a system of general delayed reaction-diffusion equations with the Neumann boundary conditions. The conditions on parameters of the system that a Hopf bifurcation occurs as the delay parameter passes through a critical value are determined. These conditions depend on the c...
Article
We study the stability and Hopf bifurcation analysis of an asset pricing model that is based on the model introduced by Caginalp and Balenovich, under the assumption of a fixed amount of cash and stock in the system. First, we analyze stability of equilibrium points. Choosing the momentum coefficient as a bifurcation parameter, we also show that Ho...
Article
In this paper, we give a detailed Hopf bifurcation analysis of a recurrent neural network system involving both discrete and distributed delays. Choosing the sum of the discrete delay terms as a bifurcation parameter the existence of Hopf bifurcation is demonstrated. In particular, the formulae determining the direction of the bifurcations and the...
Chapter
Full-text available
We investigate bifurcations of the Lengyel-Epstein reaction-diffusion model involving time delay under the Neumann boundary conditions. We first give stability and Hopf bifurcation analysis of the ODE models including delay associated with this model. Later, we extend these analysis to the PDE model. We determine conditions on parameters of both mo...
Book
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear disc...
Article
Full-text available
The model analyzed in this paper is based on the model set forth by Aziz Alaoui et al. [Aziz Alaoui & Daher Okiye, 2003; Nindjin et al., 2006] with time delay, which describes the competition between the predator and prey. This model incorporates a modified version of the Leslie-Gower functional response as well as that of Beddington-DeAngelis. In...
Article
In this paper we give a detailed Hopf bifurcation analysis of a ratio-dependent predator–prey system involving two different discrete delays. By analyzing the characteristic equation associated with the model, its linear stability is investigated. Choosing delay terms as bifurcation parameters the existence of Hopf bifurcations is demonstrated. Sta...
Article
Full-text available
We investigate bifurcations of the Lengyel-Epstein reaction-diffusion model involving time delay under the Neumann boundary conditions. Choosing the delay parameter as a bifurcation parameter, we show that Hopf bifurcation occurs. We also determine two properties of the Hopf bifurcation, namely direction and stability, by applying the normal form t...
Article
Full-text available
The aim of this paper is to give a detailed analysis of Hopf bifurcation of a ratio-dependent predator-prey system involving two discrete delays. A delay parameter is chosen as bifurcation parameter for the analysis. Stability of the bifurcating periodic solutions is determined by using the center manifold theorem and the normal form theory introdu...
Article
Full-text available
The effect of the high/low liquidity in the market on the asset price forecasting is studied by deriving a system of ordinary differential equations. The model is an extension of that introduced by Caginalp and Merdan for the system involving a single asset traded by heterogenous groups. Derivation is based on the finiteness of assets (rather than...
Article
In this paper, we have considered a system of delay differential equations. The system without delayed arises in the Lengyel–Epstein model. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. Linear stability is investigated and existence of Hopf bifurcation is demonstrated via analyzing the associated characteristic...
Article
This work represents Hopf bifurcation analysis of a general non-linear differential equation involving time delay. A special form of this equation is the Hutchinson–Wright equation which is a mile stone in the mathematical modeling of population dynamics and mathematical biology. Taking the delay parameter as a bifurcation parameter, Hopf bifurcati...
Article
Full-text available
The aim of this paper is to investigate bifurcations of the Lengyel- Epstein reaction di¤usion model involving delay under Neumann bound- ary conditions. The bifurcation analysis of the model shows that Hopf bifurcation occurs by regarding the delay as the bifurcation parameter. Using the normal form theory and the center manifold reduction for par...
Article
Full-text available
In this paper, we investigate stability conditions of equilibrium points of a general delay difference population model with and without Allee effects which occur at low population density. The analysis demonstrates that Allee effects have both stabilizing and destabilizing effects on population dynamics including time delay.
Article
The stability conditions of equilibrium points of the population model Xt+1 = lambda X(t)f(Xt-3) with and without Allee effects are investigated. It is assumed that the Allee effect occurs at low population density. Analysis and numerical simulations show that Allee effects have both stabilizing and destabilizing effects on population dynamics with...
Data
The stability conditions of equilibrium points of the population model Xt+1 = λXtf (Xt−3) with and without Allee effects are investigated. It is assumed that the Allee effect occurs at low population density. Analysis and numerical simulations show that Allee effects have both stabilizing and destabilizing effects on population dynamics with delay.
Data
The stability conditions of equilibrium points of the population model Xt+1 = λXtf (Xt−3) with and without Allee effects are investigated. It is assumed that the Allee effect occurs at low population density. Analysis and numerical simulations show that Allee effects have both stabilizing and destabilizing effects on population dynamics with delay.
Data
The stability conditions of equilibrium points of the population model Xt+1 = λXtf (Xt−3) with and without Allee effects are investigated. It is assumed that the Allee effect occurs at low population density. Analysis and numerical simulations show that Allee effects have both stabilizing and destabilizing effects on population dynamics with delay.
Article
Full-text available
The stability conditions of equilibrium points of the population model Xt+1 = λXtf (Xt−3) with and without Allee effects are investigated. It is assumed that the Allee effect occurs at low population density. Analysis and numerical simulations show that Allee effects have both stabilizing and destabilizing effects on population dynamics with delay.
Article
Asset price dynamics is studied by using a system of ordinary differential equations which is derived by utilizing a new excess demand function introduced by Caginalp [4] for a market involving more information on demand and supply for a stock rather than their values at a particular price. Derivation is based on the finiteness of assets (rather th...
Article
We present a stability analysis of steady-state solutions of a continuous-time predator– prey population dynamics model subject to Allee effects on the prey population which occur at low population density. Numerical simulations show that the system subject to an Allee effect takes a much longer time to reach its stable steady-state solution. This...
Article
Full-text available
We present a stability analysis of steady-state solutions of a continuous-time predator–prey population dynamics model subject to Allee effects on the prey population which occur at low population density. Numerical simulations show that the system subject to an Allee effect takes a much longer time to reach its stable steady-state solution. This r...
Article
This paper presents the stability analysis of equilibrium points of a general continuous time population dynamics model involving predation subject to an Allee effect which occurs at low population density. The mathematical results and numerical simulations show that the system subject to an Allee effect takes much longer time to reach its stable s...
Article
This paper presents the stability analysis of equilibrium points of a general discrete-time population dynamics involving predation with and without Allee effects which occur at low population density. The mathematical analysis and numerical simulations show that the Allee effect has a stabilizing role on the local stability of the positive equilib...
Article
This paper presents the stability analysis of equilibrium points of a continuous population dynamics with delay under the Allee effect which occurs at low population density. The mathematical results and numerical simulations show the stabilizing role of the Allee effects on the stability of the equilibrium point of this population dynamics. Editor...
Article
In this paper, we study the stability analysis of equilibrium points of population dynamics with delay when the Alice effect occurs at low population density. Mainly, our mathematical results and numerical simulations point to the stabilizing effect of the Allee effects on population dynamics with delay. (C) 2006 Elsevier Ltd. All rights reserved.
Article
A system of ordinary differential equations is used to study the price dynamics of an asset under various conditions. One of these involves the introduction of new information that is interpreted differently by two groups. Another studies the price change due to a change in the number of shares. The steady state is examined under these conditions t...
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We study the temporal evolution of an interface separating two phases for its large-time behavior by adapting renormalization group methods and scaling theory. We consider a full two-phase model in the quasi-static regime and implement a renormalization procedure in order to calculate the characteristic length of a self-similar system, R(t), that i...
Article
Renormalization group and scaling theory have been used to determine the large time growth exponent for the characteristic length, R(t), of an interface in the form R(t) ∼ tβ. The exponent β is different in the two cases: quasi-static, in which the time derivative in the heat equation is suppressed, and the fully dynamic system. This paper examines...
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Renormalization group (RG) methods are described for determining the key ex- ponents related to the decay of solutions to nonlinear parabolic dierential equations. Higher order (in the small coecient of the nonlinearity) methods are developed. Exact solutions and theorems in
Article
Full-text available
The application of renormalization techniques to interface problems is considered after a brief review of the methodology. We study the standard sharp interface problem in the quasi-static limit (time derivative set to zero in the heat equation) for large time. The characteristic length, R(t), behaves as t β where β has values in the continuous spe...
Article
Full-text available
Scaling and renormalization group (RG) methods are used to study parabolic equations with a small nonlinear term and find the decay exponents. The determination of decay exponents is viewed as an asymptoti-cally self similar process that facilitates an RG approach. These RG methods are extended to higher order in the small coefficient of the nonlin...
Article
Scaling and renormalization group (RG) methods are used to study parabolic equations with a small nonlinear term and find the decay exponents. The determination of decay exponents is viewed as an asymptotically self similar process that facilitates an RG approach. These RG methods are extended to higher order in the small coe#cient of the nonlinear...
Article
Full-text available
The stability conditions of equilibrium points of the population model Xt+1 = Xtf(Xt−3) with and without Allee effects are investigated. It is assumed that the Allee effect occurs at low population density. Analysis and numerical simulations show that Allee effects have both stabilizing and destabilizing effects on population dynamics with delay.
Article
Full-text available
In this paper, we have considered a system of delay differential equations. The system without delayed arises in the Lengyel–Epstein model. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. Linear stability is investigated and existence of Hopf bifurcation is demonstrated via analyzing the associated characteristic...
Cited By
## Projects
Projects (4)
Project
Analysis of a ratio-dependent reaction-diffusion predator-prey model involving two discrete maturation time delays
Project
Our goal is to construct an algorithm for determining the existence and direction of the Hopf bifurcation of a class of reaction–diffusion system including discrete delays with the Neumann boundary conditions. | {"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": 0.9325730800628662, "perplexity": 568.5530898636467}, "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/1656103037089.4/warc/CC-MAIN-20220626040948-20220626070948-00631.warc.gz"} |
https://iacr.org/cryptodb/data/author.php?authorkey=4317 | ## CryptoDB
### Ittai Abraham
#### Publications
Year
Venue
Title
2021
TCC
Secure computation enables $n$ mutually distrustful parties to compute a function over their private inputs jointly. In 1988 Ben-Or, Goldwasser, and Wigderson (BGW) demonstrated that any function can be computed with perfect security in the presence of a malicious adversary corrupting at most $t< n/3$ parties. After more than 30 years, protocols with perfect malicious security, with round complexity proportional to the circuit's depth, still require sharing a total of $O(n^2)$ values per multiplication. In contrast, only $O(n)$ values need to be shared per multiplication to achieve semi-honest security. Indeed sharing $\Omega(n)$ values for a single multiplication seems to be the natural barrier for polynomial secret sharing-based multiplication. In this paper, we close this gap by constructing a new secure computation protocol with perfect, optimal resilience and malicious security that incurs sharing of only $O(n)$ values per multiplication, thus, matching the semi-honest setting for protocols with round complexity that is proportional to the circuit depth. Our protocol requires a constant number of rounds per multiplication. Like BGW, it has an overall round complexity that is proportional only to the multiplicative depth of the circuit. Our improvement is obtained by a novel construction for {\em weak VSS for polynomials of degree-$2t$}, which incurs the same communication and round complexities as the state-of-the-art constructions for {\em VSS for polynomials of degree-$t$}. Our second contribution is a method for reducing the communication complexity for any depth-1 sub-circuit to be proportional only to the size of the input and output (rather than the size of the circuit). This implies protocols with \emph{sublinear communication complexity} (in the size of the circuit) for perfectly secure computation for important functions like matrix multiplication.
2017
PKC
2008
TCC | {"extraction_info": {"found_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": 0.6172930002212524, "perplexity": 1093.4521036328986}, "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-2021-43/segments/1634323588284.71/warc/CC-MAIN-20211028100619-20211028130619-00657.warc.gz"} |
https://zbmath.org/?q=an%3A1247.65138 | ×
## Variational iteration method for the time-fractional Fornberg-Whitham equation.(English)Zbl 1247.65138
Summary: We present the approximate analytical solutions to solve the nonlinear Fornberg-Whitham equation with fractional time derivative. By using initial values, explicit solutions of the equations are solved by using a reliable algorithm like the variational iteration method. The fractional derivatives are taken in the Caputo sense. The present method performs extremely well in terms of efficiency and simplicity. Numerical results for different particular cases of $$\alpha$$ are presented graphically.
### MSC:
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 35R11 Fractional partial differential equations 45K05 Integro-partial differential equations
Full Text: | {"extraction_info": {"found_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": 0.5464366674423218, "perplexity": 616.1810779144112}, "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/1656103033925.2/warc/CC-MAIN-20220625004242-20220625034242-00481.warc.gz"} |
http://stackoverflow.com/questions/9069990/mathml-is-rendered-poorly-with-firefox-on-windows-xp-but-rendered-well-on-linux?answertab=active | # MathML is rendered poorly with Firefox on Windows XP but rendered well on Linux
Here is a MathML sample code I am using to test MathML rendering.
Demo URL: http://jsfiddle.net/3ak4P/
<!DOCTYPE html>
<html lang="en">
<title>MathML demo</title>
<style type="text/css">
math {
display: block;
font-size: 16px;
}
</style>
<body>
$<mrow> <munder> <mo>∑</mo> <mrow> <mi>p</mi> <mtext> prime</mtext> </mrow> </munder> <mi>f</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mo stretchy="false">∫</mo> <mrow> <mi>t</mi> <mo>></mo> <mn>1</mn> </mrow> </msub> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo> </mo> <mo mathvariant="italic">d</mo> <mi>π</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow>$
</body>
</html>
Output with Firefox 8 on Windows XP:
Output with Firefox 8 on Debian GNU/Linux:
Now, considering that one can't insist the users of a website to install new fonts, etc. what are the possible ways to ensure that Windows users also have a good experience browsing math formulas written with MathML?
- | {"extraction_info": {"found_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": 0.678419828414917, "perplexity": 11295.160655944417}, "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-2013-48/segments/1386163052949/warc/CC-MAIN-20131204131732-00063-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://intomath.org/simplifying-expressions-with-exponents/ | Simplifying expressions with exponents is an important skill that is required to comfortably work with different types of functions and their equations. It is especially useful when solving polynomial and rational equations.
We already looked at the concept of exponent in previous grades. However, we only operated integer exponents.
In this lesson we are moving further and learning about rational exponents and their properties.
A rational exponent is an exponent expressed as a fraction m/n.
A power containing a rational exponent can be transformed into a radical form of an expression, involving the n-th root of a number.
The n-th root of a number a is another number, that when raised to the exponent n produces a.
We are also practicing how to use negative exponents in this lesson and discussing the difference between even and odd exponents.
In addition, we are analyzing the base of 0 raised to a rational exponent.
Simplifying expressions with exponents requires us to use a variety of exponent laws and properties. We may start with a really complex expression that, when simplified, could result in one variable or a number.
For example, in order to simplify the following expression, it makes sense to express what we can in terms of the same base and use exponent laws:
As you can see, we used the Power law of exponents, as well as the quotient law to simplify this expression. It is not uncommon that these simplifying expressions with exponents requires us to think a little bit outside of the box, see ways that we can express and transform numbers in order to apply laws to them. | {"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": 0.8746227025985718, "perplexity": 290.539949282008}, "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/1634323587963.12/warc/CC-MAIN-20211026231833-20211027021833-00171.warc.gz"} |
https://im.kendallhunt.com/HS/students/1/glossary.html | ### Glossary
• absolute value
The absolute value of a number is its distance from 0 on the number line.
• association
In statistics we say that there is an association between two variables if the two variables are statistically related to each other; if the value of one of the variables can be used to estimate the value of the other.
• average rate of change
The average rate of change of a function $$f$$ between inputs $$a$$ and $$b$$ is the change in the outputs divided by the change in the inputs: $$\frac{f(b)-f(a)}{b-a}$$. It is the slope of the line joining $$(a,f(a))$$ and $$(b, f(b))$$ on the graph.
• bell-shaped distribution
A distribution whose dot plot or histogram takes the form of a bell with most of the data clustered near the center and fewer points farther from the center.
• bimodal distribution
A distribution with two very common data values seen in a dot plot or histogram as distinct peaks. In the dot plot shown, the two common data values are 2 and 7,
• categorical data
Categorical data are data where the values are categories. For example, the breeds of 10 different dogs are categorical data. Another example is the colors of 100 different flowers.
• categorical variable
A variable that takes on values which can be divided into groups or categories. For example, color is a categorical variable which can take on the values, red, blue, green, etc.
• causal relationship
A relationship is one in which a change in one of the variables causes a change in the other variable.
• coefficient
In an algebraic expression, the coefficient of a variable is the constant the variable is multiplied by. If the variable appears by itself then it is regarded as being multiplied by 1 and the coefficient is 1.
The coefficient of $$x$$ in the expression $$3x + 2$$ is $$3$$. The coefficient of $$p$$ in the expression $$5 + p$$ is 1.
• completing the square
Completing the square in a quadratic expression means transforming it into the form $$a(x+p)^2-q$$, where $$a$$, $$p$$, and $$q$$ are constants.
Completing the square in a quadratic equation means transforming into the form $$a(x+p)^2=q$$.
• constant term
In an expression like $$5x + 2$$ the number 2 is called the constant term because it doesn't change when $$x$$ changes.
In the expression $$5x-8$$ the constant term is -8, because we think of the expression as $$5x + (\text-8)$$. In the expression $$12x-4$$ the constant term is -4.
• constraint
A limitation on the possible values of variables in a model, often expressed by an equation or inequality or by specifying that the value must be an integer. For example, distance above the ground $$d$$, in meters, might be constrained to be non-negative, expressed by $$d \ge 0$$.
• correlation coefficient
A number between -1 and 1 that describes the strength and direction of a linear association between two numerical variables. The sign of the correlation coefficient is the same as the sign of the slope of the best fit line. The closer the correlation coefficient is to 0, the weaker the linear relationship. When the correlation coefficient is closer to 1 or -1, the linear model fits the data better.
The first figure shows a correlation coefficient which is close to 1, the second a correlation coefficient which is positive but closer to 0, and the third a correlation coefficient which is close to -1.
• decreasing (function)
A function is decreasing if its outputs get smaller as the inputs get larger, resulting in a downward sloping graph as you move from left to right.
A function can also be decreasing just for a restricted range of inputs. For example the function $$f$$ given by $$f(x) = 3 - x^2$$, whose graph is shown, is decreasing for $$x \ge 0$$ because the graph slopes downward to the right of the vertical axis.
• dependent variable
A variable representing the output of a function.
The equation $$y = 6-x$$ defines $$y$$ as a function of $$x$$. The variable $$x$$ is the independent variable, because you can choose any value for it. The variable $$y$$ is called the dependent variable, because it depends on $$x$$. Once you have chosen a value for $$x$$, the value of $$y$$ is determined.
• distribution
For a numerical or categorical data set, the distribution tells you how many of each value or each category there are in the data set.
• domain
The domain of a function is the set of all of its possible input values.
• elimination
A method of solving a system of two equations in two variables where you add or subtract a multiple of one equation to another in order to get an equation with only one of the variables (thus eliminating the other variable).
• equivalent equations
Equations that have the exact same solutions are equivalent equations.
• equivalent systems
Two systems are equivalent if they share the exact same solution set.
• exponential function
An exponential function is a function that has a constant growth factor. Another way to say this is that it grows by equal factors over equal intervals. For example, $$f(x)=2 \boldcdot 3^x$$ defines an exponential function. Any time $$x$$ increases by 1, $$f(x)$$ increases by a factor of 3.
• factored form (of a quadratic expression)
A quadratic expression that is written as the product of a constant times two linear factors is said to be in factored form. For example, $$2(x-1)(x+3)$$ and $$(5x + 2)(3x-1)$$ are both in factored form.
• five-number summary
The five-number summary of a data set consists of the minimum, the three quartiles, and the maximum. It is often indicated by a box plot like the one shown, where the minimum is 2, the three quartiles are 4, 4.5, and 6.5, and the maximum is 9.
• function
A function takes inputs from one set and assigns them to outputs from another set, assigning exactly one output to each input.
• function notation
Function notation is a way of writing the outputs of a function that you have given a name to. If the function is named $$f$$ and $$x$$ is an input, then $$f(x)$$ denotes the corresponding output.
• growth factor
In an exponential function, the output is multiplied by the same factor every time the input increases by one. The multiplier is called the growth factor.
• growth rate
In an exponential function, the growth rate is the fraction or percentage of the output that gets added every time the input is increased by one. If the growth rate is 20% or 0.2, then the growth factor is 1.2.
• horizontal intercept
The horizontal intercept of a graph is the point where the graph crosses the horizontal axis. If the axis is labeled with the variable $$x$$, the horizontal intercept is also called the $$x$$-intercept. The horizontal intercept of the graph of $$2x + 4y = 12$$ is $$(6,0)$$.
The term is sometimes used to refer only to the $$x$$-coordinate of the point where the graph crosses the horizontal axis.
• increasing (function)
A function is increasing if its outputs get larger as the inputs get larger, resulting in an upward sloping graph as you move from left to right.
A function can also be increasing just for a restricted range of inputs. For example the function $$f$$ given by $$f(x) = 3 - x^2$$, whose graph is shown, is increasing for $$x \le 0$$ because the graph slopes upward to the left of the vertical axis.
• independent variable
A variable representing the input of a function.
The equation $$y = 6-x$$ defines $$y$$ as a function of $$x$$. The variable $$x$$ is the independent variable, because you can choose any value for it. The variable $$y$$ is called the dependent variable, because it depends on $$x$$. Once you have chosen a value for $$x$$, the value of $$y$$ is determined.
• inverse (function)
Two functions are inverses to each other if their input-output pairs are reversed, so that if one functions takes $$a$$ as input and gives $$b$$ as an output, then the other function takes $$b$$ as an input and gives $$a$$ as an output.
You can sometimes find an inverse function by reversing the processes that define the first function in order to define the second function.
• irrational number
An irrational number is a number that is not rational. That is, it cannot be expressed as a positive or negative fraction, or zero.
• linear function
A linear function is a function that has a constant rate of change. Another way to say this is that it grows by equal differences over equal intervals. For example, $$f(x)=4x-3$$ defines a linear function. Any time $$x$$ increases by 1, $$f(x)$$ increases by 4.
• linear term
The linear term in a quadratic expression (In standard form) $$ax^2 + bx + c$$, where $$a$$, $$b$$, and $$c$$ are constants, is the term $$bx$$. (If the expression is not in standard form, it may need to be rewritten in standard form first.)
• maximum
A maximum of a function is a value of the function that is greater than or equal to all the other values. The maximum of the graph of the function is the corresponding highest point on the graph.
• minimum
A minimum of a function is a value of the function that is less than or equal to all the other values. The minimum of the graph of the function is the corresponding lowest point on the graph.
• model
A mathematical or statistical representation of a problem from science, technology, engineering, work, or everyday life, used to solve problems and make decisions.
• negative relationship
A relationship between two numerical variables is negative if an increase in the data for one variable tends to be paired with a decrease in the data for the other variable.
• non-statistical question
A non-statistical question is a question which can be answered by a specific measurement or procedure where no variability is anticipated, for example:
• How high is that building?
• If I run at 2 meters per second, how long will it take me to run 100 meters?
• numerical data
Numerical data, also called measurement or quantitative data, are data where the values are numbers, measurements, or quantities. For example, the weights of 10 different dogs are numerical data.
• outlier
A data value that is unusual in that it differs quite a bit from the other values in the data set. In the box plot shown, the minimum, 0, and the maximum, 44, are both outliers.
• perfect square
A perfect square is an expression that is something times itself. Usually we are interested in situations where the something is a rational number or an expression with rational coefficients.
• piecewise function
A piecewise function is a function defined using different expressions for different intervals in its domain.
• positive relationship
A relationship between two numerical variables is positive if an increase in the data for one variable tends to be paired with an increase in the data for the other variable.
An equation that is equivalent to one of the form $$ax^2 + bx + c = 0$$, where $$a$$, $$b$$, and $$c$$ are constants and $$a \neq 0$$.
A quadratic expression in $$x$$ is one that is equivalent to an expression of the form $$ax^2 + bx + c$$, where $$a$$, $$b$$, and $$c$$ are constants and $$a \neq 0$$.
The formula $$x = {\text-b \pm \sqrt{b^2-4ac} \over 2a}$$ that gives the solutions of the quadratic equation $$ax^2 + bx + c = 0$$, where $$a$$ is not 0.
A function where the output is given by a quadratic expression in the input.
• range
The range of a function is the set of all of its possible output values.
• rational number
A rational number is a fraction or the opposite of a fraction. Remember that a fraction is a point on the number line that you get by dividing the unit interval into $$b$$ equal parts and finding the point that is $$a$$ of them from 0. We can always write a fraction in the form $$\frac{a}{b}$$ where $$a$$ and $$b$$ are whole numbers, with $$b$$ not equal to 0, but there are other ways to write them. For example, 0.7 is a fraction because it is the point on the number line you get by dividing the unit interval into 10 equal parts and finding the point that is 7 of those parts away from 0. We can also write this number as $$\frac{7}{10}$$.
The numbers $$3$$, $$\text-\frac34$$, and $$6.7$$ are all rational numbers. The numbers $$\pi$$ and $$\text-\sqrt{2}$$ are not rational numbers, because they cannot be written as fractions or their opposites.
• relative frequency table
A version of a two-way table in which the value in each cell is divided by the total number of responses in the entire table or by the total number of responses in a row or a column.
The table illustrates the first type for the relationship between the condition of a textbook and its price for 120 of the books at a college bookstore.
$10 or less more than \$10 but less than $30$30 or more
new 0.025 0.075 0.225
used 0.275 0.300 0.100
• residual
The difference between the $$y$$-value for a point in a scatter plot and the value predicted by a linear model. The lengths of the dashed lines in the figure are the residuals for each data point.
• skewed distribution
A distribution where one side of the distribution has more values farther from the bulk of the data than the other side, so that the mean is not equal to the median. In the dot plot shown, the data values on the left, such as 1, 2, and 3, are further from the bulk of the data than the data values on the right.
• solutions to a system of inequalities
All pairs of values that make the inequalities in a system true are solutions to the system. The solutions to a system of inequalities can be represented by the points in the region where the graphs of the two inequalities overlap.
• solution to a system of equations
A coordinate pair that makes both equations in the system true.
On the graph shown of the equations in a system, the solution is the point where the graphs intersect.
• standard deviation
A measure of the variability, or spread, of a distribution, calculated by a method similar to the method for calculating the MAD (mean absolute deviation). The exact method is studied in more advanced courses.
• standard form (of a quadratic expression)
The standard form of a quadratic expression in $$x$$ is $$ax^2 + bx + c$$, where $$a$$, $$b$$, and $$c$$ are constants, and $$a$$ is not 0.
• statistic
A quantity that is calculated from sample data, such as mean, median, or MAD (mean absolute deviation).
• statistical question
A statistical question is a question that can only be answered by using data and where we expect the data to have variability, for example:
• Who is the most popular musical artist at your school?
• When do students in your class typically eat dinner?
• Which classroom in your school has the most books?
• strong relationship
A relationship between two numerical variables is strong if the data is tightly clustered around the best fit line.
• substitution
Substitution is replacing a variable with an expression it is equal to.
• symmetric distribution
A distribution with a vertical line of symmetry in the center of the graphical representation, so that the mean is equal to the median. In the dot plot shown, the distribution is symmetric about the data value 5.
• system of equations
Two or more equations that represent the constraints in the same situation form a system of equations.
• system of inequalities
Two or more inequalities that represent the constraints in the same situation form a system of inequalities.
• two-way table
A way of organizing data from two categorical variables in order to investigate the association between them.
has a cell phone does not have a cell phone
10–12 years old 25 35
13–15 years old 38 12
16–18 years old 52 8
• uniform distribution
A distribution which has the data values evenly distributed throughout the range of the data.
• variable (statistics)
A characteristic of individuals in a population that can take on different values
• vertex form (of a quadratic expression)
The vertex form of a quadratic expression in $$x$$ is $$a(x-h)^2 + k$$, where $$a$$, $$h$$, and $$k$$ are constants, and $$a$$ is not 0.
• vertex (of a graph)
The vertex of the graph of a quadratic function or of an absolute value function is the point where the graph changes from increasing to decreasing or vice versa. It is the highest or lowest point on the graph.
• vertical intercept
The vertical intercept of a graph is the point where the graph crosses the vertical axis. If the axis is labeled with the variable $$y$$, the vertical intercept is also called the $$y$$-intercept.
Also, the term is sometimes used to mean just the $$y$$-coordinate of the point where the graph crosses the vertical axis. The vertical intercept of the graph of $$y = 3x - 5$$ is $$(0,\text-5)$$, or just -5.
• weak relationship
A relationship between two numerical variables is weak if the data is loosely spread around the best fit line.
• zero (of a function)
A zero of a function is an input that yields an output of zero. If other words, if $$f(a) = 0$$ then $$a$$ is a zero of $$f$$.
• zero product property
The zero product property says that if the product of two numbers is 0, then one of the numbers must be 0. | {"extraction_info": {"found_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": 0.8820605874061584, "perplexity": 286.6002375342709}, "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-2019-47/segments/1573496668910.63/warc/CC-MAIN-20191117091944-20191117115944-00040.warc.gz"} |