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https://stats.stackexchange.com/questions/50013/reconstructing-matched-data-set-from-rs-matching-package
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# reconstructing matched data set from R's matching package
I am using Mebane and Sekhon's Matching package for R, and my goal is to make casual inferences about a proportion and a mean. The proportion is straight forward, but the mean has missing values, which Match does not accept. My approach is trying to get access to the matched records through the row indexes, but the results are not quite right.
Example code:
require(Matching)
demo(DehejiaWahba)
# mean before matching
by(lalonde$u75, lalonde$treat, mean)
# mean after matching
matched <- rbind(lalonde[rr$index.treated,], lalonde[rr$index.control,])
by(matched$u75, matched$treat, mean)
The output of the demo shows the matched means for u75 are 0.6 and 0.62072:
***** (V14) u75 *****
Before Matching After Matching
mean treatment........ 0.6 0.6
mean control.......... 0.68462 0.62072
However, the reconstructed data set has different means:
matched$treat: 0 [1] 0.7861272 --------------------------------------------------------------------------------- matched$treat: 1
[1] 0.7543353
See that matched has 692 observations. Now take a look at summary(rr). You'll see that there are 346 unweighted matched pairs--that is, several of the treated observations were matched to several control observations. You can see using summary(rr$weights) that there is at least one treatment observation that is matched to 12 controls. Without using the weights in your last line, you're getting the wrong answer. As Charlie suggested, using the weights does give means that "match Match." weighted.mean(lalonde[rr$index.control,]$u75, rr$weights)
weighted.mean(lalonde[rr$index.treated,]$u75, rr\$weights)
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2020-10-20 23:40:47
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|
https://stats.stackexchange.com/questions/485200/how-do-i-perform-a-hypothesis-test-comparing-the-mean-of-two-statistical-variabl
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# How do I perform a hypothesis test comparing the mean of two statistical variables?
I am trying to learn about statistical hypothesis testing. As an example problem I want to study the effect of rep range on muscle growth. N subjects will be randomly assigned into one of two groups:
• High (H) load: each workout consists of 3 sets x 5 repetitions of leg press.
• Low (L) load: each workout consists of 3 sets x 10 repetitions of leg press.
The percentwise increase in cross sectional area of the leg muscles over the training period will be recorded.
My hypotheses are:
• H_0: there will be no difference in percentwise increase across group.
• H_A: the Low group will have larger percentwise increase: $$\mu_L >= 1.1 \mu_H$$
I choose a 5% significance level.
What is the minimum value of N?
How do I perform the the test?
I just need some pointers.
First, I suppose your data will be normal. You have said you want to do a one-sided test at the $$\alpha = 5\%$$ level, hoping to detect a difference in group means of size $$\Delta = 0.1.$$ That is, you will test $$H_0: \mu_H - \mu_L = 0$$ against $$H_a: \mu_H - \mu_L < 0.1.$$ [I think I understand your intentions, but your statement of null and alternative hypotheses is not quite right.]
In order to find the required sample size $$n$$ for each group, you would need to state the desired power of the test and to estimate the variance of the observations.
• Because you are willing to make Type I error (falsely rejecting when $$H_0$$ is true) with probability $$\alpha = 0.05 = 5\%,$$ perhaps you want Type II error (failing to reject when $$\mu_a = 1.1)$$ with probability $$\beta = 0.05$$ also, which means you want power $$1 = \beta = 0.95 = 95\%.$$ (That is, you want to be $$95\%$$ sure to detect a difference as large as $$\Delta.$$
• Unless you have previous experience with such experiments it may be difficult to estimate the variance of the observations. The variability may be smaller if the subjects are of roughly equal fitness going into the experiment. For purposes of illustration, I will take $$\sigma^2 = (0.2)^2 = 0.04.$$
A common practice is to provide (at least tentatively) values of $$\alpha, \Delta,$$ and $$\sigma^2$$ and then to use a 'power and sample size' procedure to balance affordable sample size $$n$$ (for each group) with achievable power. For pooled 2-sample t tests, an exact computation requires use of a _noncentral Student's t distribution. [There are also 'power and sample size' procedures (of varying degrees of reliability) available online.]
_ However, required sample sizes are often above $$n = 30$$ and then the following approximate formula gives a useful approximate result. For my speculative values, $$n \approx 87.$$
$$n \approx \frac{2\sigma^2(z_\alpha + z_\beta)^2}{\Delta^2} =\frac{2(0.2^2)(1.645+1.645)^2}{0.1^2} \approx 87.$$
The discussion above is for pooled 2-sample t tests, which assume that the two groups have equal variances. Unless you have prior knowledge or experience with such measurements, it will be best to use a Welch 2-sample t test. If the two groups do have equal variances, then power will be about the same as for the pooled two-sample t test. Otherwise, power may be a little less and you will be protected against systematically incorrect results.
Using two normal samples simulated to the specifications discussed above, here is how a Welch two-sample, one-sided t test would look in R. [Because I'm using a Welch t test I increased the sample sizes to 100 in each group---as a precaution.]
set.seed(829) # for reproducibility
x1 = rnorm(100, 1, .2)
x2 = rnorm(100, 1.1, .2)
summary(x1); length(x1); sd(x1)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.5226 0.8466 0.9983 1.0005 1.1275 1.5506
[1] 100
[1] 0.2068055
summary(x2); length(x2); sd(x2)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.4899 0.9561 1.0734 1.0572 1.1858 1.5258
[1] 100
[1] 0.185094
boxplot(list(x1,x2), col="skyblue2", label=T)
t.test(x1, x2, alt="less")
Welch Two Sample t-test
data: x1 and x2
t = -2.0403, df = 195.61, p-value = 0.02133
alternative hypothesis:
true difference in means is less than 0
95 percent confidence interval:
-Inf -0.0107568
sample estimates:
mean of x mean of y
1.000535 1.057161
The following simulation in R shows that with means $$\mu_1 = 1, \mu_2 = 1.1$$ and other parameters specified above, the Welch two-sample, two-sided t test rejects with power about 97%, so perhaps I was a little too cautious using sample sizes $$n = 100$$ instead of $$n = 87$$ as estimated by my approximate sample-size equation.
set.seed(2020)
pv = replicate(10^5, t.test(rnorm(100,1,.2), rnorm(100,1.1,.2),alt="less")\$p.val)
mean(pv <= 0.05)
[1] 0.97027
A similar simulation with sample sizes $$n = 87$$ does give about 95% power---with no adjustment needed.
Addendum per Comments: If you have reason to believe your data might not be normal, you should consider the use of nonparametric tests. However, you asked about comparing population 'means', and nonparametric tests often do not compare means. To assume routinely from the start that data are not normal may sometimes be prudent, but may sometimes be foolish and counterproductive.
• Not clear why you started out with the normality assumption. Aug 29, 2020 at 21:12
• Chapter 7 of Biostatistics for Biomedical Research hbiostat.org/bbr Aug 30, 2020 at 13:35
• Full document is at hbiostat.org/doc/bbr.pdf Aug 30, 2020 at 17:20
• "In case data are not normal" assumes that the sample size is large enough that non-normality would be detected. Best to just allow for non-normality. Sep 1, 2020 at 2:19
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2022-09-26 05:20:56
|
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|
http://www.koreascience.or.kr/article/ArticleFullRecord.jsp?cn=DBSHBB_2012_v49n4_795
|
GENERAL LAWS OF PRECISE ASYMPTOTICS FOR SUMS OF RANDOM VARIABLES
Title & Authors
GENERAL LAWS OF PRECISE ASYMPTOTICS FOR SUMS OF RANDOM VARIABLES
Meng, Yan-Jiao;
Abstract
In this paper, we obtain two general laws of precise asymptotics for sums of i.i.d random variables, which contain general weighted functions and boundary functions and also clearly show the relationship between the weighted functions and the boundary functions. As corollaries, we obtain Theorem 2 of Gut and Spataru [A. Gut and A. Sp$\small{\check{a}}$taru, Precise asymptotics in the law of the iterated logarithm, Ann. Probab. 28 (2000), no. 4, 1870-1883] and Theorem 3 of Gut and Sp$\small{\check{a}}$taru [A. Gut and A. Sp$\small{\check{a}}$taru, Precise asymptotics in the Baum-Katz and Davids laws of large numbers, J. Math. Anal. Appl. 248 (2000), 233-246].
Keywords
precise asymptotics;general law;weighted function;boundary function;
Language
English
Cited by
1.
Convergence and Precise Asymptotics for Series Involving Self-normalized Sums, Journal of Theoretical Probability, 2016, 29, 1, 267
2.
Asymptotic results for hybrids of empirical and partial sums processes, Statistical Papers, 2014, 55, 4, 1121
References
1.
L. E. Baum and M. Katz, Convergence rates in the law of large numbers, Trans. Amer. Math. Soc. 120 (1965), 108-123.
2.
P. Billingsley, Convergence of Probability Measures, Wiley, NewYork, 1968.
3.
F. Y. Cheng and Y. B. Wang, Precise asymptotics of partial sums for iid and NA sequences, Acta Math. Sinica (Chin. Ser.) 47 (2004), no. 5, 965-972.
4.
P. Erdos, On a theorem of Hsu and Robbins, Ann. Math. Statist. 20 (1949), 286-291.
5.
P. Erdos, Remark on my paper "On a theorem of Hsu and Robbins", Ann. Math. Statistic 21 (1950), 138-142.
6.
D. H. Fuk and S. V. Nagaev, Probability inequalities for sums of independent random variables, Theory Probab. Appl. 16 (1971), 643-660.
7.
A. Gut and A. Spataru, Precise asymptotics in the law of the iterated logarithm, Ann. Probab. 28 (2000), no. 4, 1870-1883.
8.
A. Gut and A. Spataru, Precise asymptotics in the Baum-Katz and Davis laws of large numbers, J. Math. Anal. Appl. 248 (2000), no. 1, 233-246.
9.
C. C. Heyde, A supplement to the strong law of large numbers, J. Appl. Probab. 12 (1975), 173-175.
10.
P. L. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 25-31.
11.
W. D. Liu and Z. Y. Lin, Precise asymptotics for a new kind of complete moment convergence, Statist. Probab. Lett. 76 (2006), no. 16, 1787-1799.
12.
T. X. Pang and Z. Y. Lin, Precise rates in the law of logarithm for i.i.d. random variables, Comput. Math. Appl. 49 (2005), no. 7-8, 997-1010.
13.
Q. M. Shao, A comparison theorem on maximum inequalities between negatively associated and independent random variables, J. Theoret. Probab. 13 (2000), 343-356.
14.
A. Spataru, Precise asymptotics in Spitzer's law of large numbers, J. Theoret. Probab. 12 (1999), no. 3, 811-819.
15.
W. F. Stout, Almost Sure Convergence, Academic Press, NewYork, 1974.
16.
Y. B.Wang, On asymptotic for class of small parameters sequences of B-value dependent random variables, Acta Math, Appl. Sinica 18 (1995), no. 3, 344-352 (in Chinese).
17.
Y. Zhang, X. Y. Yang, and Z. S. Dong, A General law of precise asymptotics for the complete moment convergence, Chin. Ann. Math. Ser. B 30 (2009), no. 1, 77-90.
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2018-10-21 23:56:41
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https://math.stackexchange.com/questions/2734229/why-are-irreducible-elements-prime-in-euclidean-domain
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# Why are irreducible elements prime in Euclidean domain?
I am trying to understand some notes from my algebra course, one of which says (it's basically a proof of that all irreducibles are prime in Euclidean domain) :
......Suppose $x = ab$ and $x$ does not divide $a$. Let $d$ be a highest common factor for $x$ and $a$. Then $d$ is not $xu$ for any unit $u$. But x is irreducible, and so d is a unit. So, in fact, $1$-element is a highest common factor for x and a. By Bézout's Lemma, $\exists s, t \in \mathbf{R}$ with $xs + at = 1$ ......
I am confused with the bolded step and you can take it for granted that I understand other sentences in this proof. Why does 'x is irreducible' imply 'd is a unit'? I know that it would be necessary to find an appropriate inverse for d in order to identify it as a unit. But I can hardly find any conditions here to convince me.
I've read other answers for this proof but I think it would be constructive if I also knew this method. Many thanks if any expert can help me.
• If $d$ is not a unit, then $x=dq$ with $N(d)<N(x)$ and $N(q)<N(x)$ forcing $x$ to be reducible. – David Hill Apr 12 '18 at 17:30
$x$ is irreducible means: If $x=de$ then one of $d,e$ is a unit. So if $d$ were not a unit, $e$ would be, makeing $a$, which is a multiple of $d$, also a multiple of $de^{-1}=x$, contrary to assumption.
By definition of $d$, $d|x$, so $dr=x$ for some $r$. By definition of an irreducible, either $d$ or $r$ is a unit. But the line previous to that prevents $r$ from being a unit. Therefore $d$ is a unit.
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2021-06-15 23:38:12
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https://www.physicsforums.com/threads/uncorrelated-vs-independent-variables.322469/
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# Uncorrelated Vs. Independent variables
1. Jun 29, 2009
### musicgold
Hi,
I am confused with respect to these two terms. In a book on regression analysis, I read the following statements.
1. For two normally distributed variables, zero covariance / correlation means independence of the two variables.
2. With the normality assumption, the following equation means that $$\mu_i$$ and $$\mu_j$$ are NOT ONLY uncorrelated BUT ALSO independently distributed.
$$\left \mu_i - N (0, \sigma^2 \right)$$
Not able to get the wiggly line (~) after ui
I am trying to understand if it is possible to have two variables that are
(a) uncorrelated, and not-independent.
(b) uncorrelated and independent
(c) correlated and not-independent
(d) correlated and independent
I would appreciate it if you could explain each type with one example.
Thanks
MG.
Last edited: Jun 29, 2009
2. Jun 29, 2009
If the variables are normally distributed, then correlation is zero if and only if they are independent. (By the way, instead of not-independent you should say dependent .
In general, if $$X, Y$$ are independent, their correlation is zero, since
$$E[(X-\mu_X)(Y-\mu_Y)] = E[X-\mu_X] \cdot E[Y - \mu_Y] = 0$$
so the correlation will be zero.
For uncorrelated but dependent, consider this somewhat classic example. Assume $$X$$ has a standard normal distribution, let $$W$$ be independent of $$X$$ and $$P(W=1) = 1/2 = P(W = -1)$$. Set
$$Y = W X$$
With a little work you can find that
a) $$Y$$ and $$X$$ are not correlated
b) $$Y$$ has a standard normal distribution (calculate $$P(Y \le y) = E[P(Y \le y \mid W)] =E[P(X \le y \mid W)]$$, and use both the definition of W and the fact that W, X are independent
For correlated and dependent - look at any multivariate normal distribution with non-zero correlations.
Correlated and independent. Let $$X$$ be uniformly distributed on $$[-1, 1]$$ and let $$Y = X^2$$.
These two variables are not independent, since $$Y$$ is determined by $$X$$, but they are uncorrelated.
c) $$X$$ and $$Y$$ are dependent.
3. Jun 30, 2009
### g_edgar
Summary ... (d) is impossible. If X and Y are independent, then X and Y are uncorrelated.
The other three are all possible.
However, when the RVs are normal, (a) is also impossible. For normal random variables X and Y, we have: X and Y are independent if and only if X and Y are uncorrelated.
4. Jun 30, 2009
### musicgold
Thanks.
I thought the term 'independent' here was the opposite of 'joint', as in 'jointly distributed'.
Also, in terms of examples, I was looking for more simple explanations. For example, can we say
the Height and Weight variables for a certain population are correlated but independent?
I found some discussion at the end of http://www.ccl.rutgers.edu/~ssi/thesis/thesis-node53.html" web page, but it is not very clear to me.
Thanks,
MG.
Last edited by a moderator: Apr 24, 2017
5. Jun 30, 2009
### g_edgar
I would not expect them to be independent, since taller people tend to weigh more than shorter people.
6. Jun 30, 2009
No, variables that are jointly distributed may or may not be independent.
No - if you take look at a group of people, and measure (say) each person's height and weight, those measured variables will be correlated - as another says, taller people tend to weigh more, but the more central point is that the measurements are taken from the same person.
Those are good notes, but seem to be (may be - I'm not sure of your mathematical background) more advanced than your current investigations.
Last edited by a moderator: Apr 24, 2017
7. Jun 30, 2009
### gel
No, that's not right. It is not necessary for two uncorrelated and normal variables to be independent. I added a counterexample myself to planetmath website a while ago, http://planetmath.org/encyclopedia/SumsOfNormalRandomVariablesNeedNotBeNormal.html" [Broken]. Are you sure that your book doesn't add an extra requirement that they are "joint normal"? (which is more than just saying that they are normal.)
Edit: I see statdad's example also showed this, but his post started with "If the variables are normally distributed, then correlation is zero if and only if they are independent." which is wrong, unless by 'normally distributed' he meant 'joint normal'.
Last edited by a moderator: May 4, 2017
8. Jul 2, 2009
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2017-12-15 14:29:28
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https://agenda.infn.it/event/20775/
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Theory Group Seminars
# Carlo Giunti "Neutrino and Nuclear Properties from Coherent Elastic Neutrino-Nucleus Scattering"
Europe/Rome
248 (Ed. C)
### 248
#### Ed. C
Description
I will review the process of coherent elastic neutrino-nucleus
scattering, with emphasis on its recent first observation in the
COHERENT experiment with a CsI target. I will discuss the determination
of the radius of the neutron distribution in CsI from the analysis of
the COHERENT data. I will also discuss the constraints on non-standard
neutrino properties: neutrino magnetic moments, charges, charge radii,
and non-standard interactions.
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2020-07-13 01:51:51
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http://tex.stackexchange.com/questions/49741/getting-arguments-underneath-min-in-an-align-environment
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# Getting arguments underneath \min in an align environment
I am wondering how can I ensure that an argument gets placed underneath \min when I use an align environment.
When I use math mode and write
$min_{x_1,\dots x_T}$
the {x_1,\dots x_T} is placed directly underneath min.
However when I use an align environment and write
\begin{align*}
min_{x_1\dots x_T}
\end{align*}
the {x_1,\dots x_T} is placed to the bottom left of \min.
-
Welcome to TeX.SE. While code snippets are useful in explanations, it is always best to compose a fully compilable MWE that illustrates the problem including the \documentclass and the appropriate packages so that those trying to help don't have to recreate it. – Peter Grill Mar 28 '12 at 1:58
Also, did you mean to use $...$ in the first example instead of $...$? Or perhaps you just meant \min instead of min? – Peter Grill Mar 28 '12 at 1:59
The macro is \min, not min.
When you use \min in display mode (ie, within $\min_{<subscript>}$, or within the align environment), the subscript is placed underneath by default.
When you use \min in inline math mode (ie, with $\min_{<subscript>}$), then you need to specify \displaystyle, or \limits to get the subscript underneath.
All four below produce:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
Inline mode:
$\displaystyle \min_{x_1,\dots x_T}$
$\min\limits_{x_1,\dots x_T}$
\bigskip
Display mode:
$\min_{x_1,\dots x_T}$
%
\begin{align*}
\min_{x_1\dots x_T}
\end{align*}
\end{document}
-
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2014-04-21 04:50:30
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https://www.physicsforums.com/threads/poisson-bracket-significance-classical-mechanics.169573/
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# Poisson bracket significance (Classical Mechanics)
1. May 9, 2007
### deadringer
We have to show that [Lx,Ly] = Lz
[Ly,Lx] = -Lz
[Lx,Lx] = 0
and I have done this. We then need to comment on the significance of these results, which I'm not sure of. I know in QM you get similar results for commutators of these quantities, and it means that you can't simultaneously know e.g Lx and Ly, but I'm not sure what happens in CM.
2. May 9, 2007
### lalbatros
Good question. I have no good answer yet.
The correspondance principle associates any QM commutator with a CM Poisson bracket. If there is a meaning for the first in QM, what could be the meaning for the second in CM? quite a good question.
As a first naïve strategy to answer it, I imagine to put one of the L's as a pertubation in an Hamiltonian.
Without the perturbation, Lx and Ly and Lz could be constants of motion, all simultaneously.
Now, if Lx perturbs the hamiltonian, we can deduce from the equations of motion that Lx can remain a constant of motion, but not Ly nor Lz. This would be quite natural as the result of a magnetic field along the x axis.
Would that not be a way to give some physical meaning to the bracket commutation relations?
I would also draw your attention on the fact that measurements in QM always imply an interaction, even if this does not appear explicitely in the infamous QM postulates. This tends to indicate that the analogy is actually more than a simple analogy.
It would be very nice and exciting if you could help me clarify these raw ideas.
Thanks for this question.
3. May 9, 2007
### nrqed
Good question. Someone else will probably do better than what I can say here, but let me mention two applications. One is that one can test whether a transformation between two parametrizations of phase space is a canonical transformation is to check if the Poisson brackets between the phase space coordinates obey the fundamental brackets, $\{ q_i , p_j \} = \delta_{ij}$ and the other being zero.
But another, maybe more relevant application is that the time evolution of a quantity "A" is given by the Poisson bracket of A with the Hamiltonian (plus a partial derivative of A if it has explicit time dependence), viz.
$$\frac{ dA }{dt} = \{ A,H \}_{class} + \frac{\partial A}{\partial t}$$
The connection with qm is therefore the most direct in the Heisenberg picture where the same equation appears with quantum commutators.
Going back to CM, your result shows, for example, that if a Hamiltonian contains only one angular momentum component, the other two components will not be conserved in time.
I hope someone will add more information.
Patrick
4. May 9, 2007
### Physics Monkey
Hi deadringer,
The connection between the Poisson bracket and the quantum commutator is really quite astounding. As you know, the interpretation of [Lx,Ly] = i Lz in quantum theory is that one cannot label physical states by simultaneous eigenvalues of Lx and Ly. The interpretation of {Lx,Ly} = Lz in classical mechanics is that one cannot use both Lx and Ly as canonical variables. In other words, any set of phase space variables containing both Lx and Ly cannot be a set of canonical variables. So we have a sort of correspondence where a maximal set of commuting operators (QM) is related to a canonical set of phase space variables (CM). In both cases there is a notion of the "correct" description of a system. Of course, in the classical case one can still compute the value of the Lx and Ly from a good canonical set of phase space variables, but there is a real sense in which using both Lx and Ly at the same time is the "wrong" way to describe the system. This is one of many possible interpretations of the Poisson bracket. Does this make sense to you?
Last edited: May 9, 2007
5. May 9, 2007
### deadringer
Yes this does make sense, since for a set of canonical coordinates we should get [qi, qj] = zero
Thanks to everybody for helping.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook
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2017-04-27 20:51:24
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https://www.fachschaft.informatik.tu-darmstadt.de/forum/viewtopic.php?f=513&t=35293&p=172974
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## Assignment 7: Moving Mark and Sweep
MrGumby
Mausschubser
Beiträge: 65
Registriert: 16. Apr 2013 15:07
### Assignment 7: Moving Mark and Sweep
Hi there,
am I allowed to further change the method signatures?
(Further as in "the stack is not only passed to mark, but also to sweep".)
Ragnar
Mausschubser
Beiträge: 63
Registriert: 21. Okt 2009 19:15
### Re: Assignment 7: Moving Mark and Sweep
The methods should all already be changed so that the necessary data structures are available.
Usually we are very explicit if we want you to change something, and changing signatures otherwise may lead to non working tests, and is also more often than not an indication, that you did not read the tasks carefully
MrGumby
Mausschubser
Beiträge: 65
Registriert: 16. Apr 2013 15:07
### Re: Assignment 7: Moving Mark and Sweep
Hm, and can I add variables to the MovingMarkAndSweepStore-class. Somewhere I have to save the movements in the store...
Ragnar
Mausschubser
Beiträge: 63
Registriert: 21. Okt 2009 19:15
### Re: Assignment 7: Moving Mark and Sweep
As the task description states, you are supposed to update the sweep method. Please do not change the signature, and also do not add more state to the memory (there is already more than we would like).
However, there is no reason for you not to use some helper functions which are called by sweep.
MrGumby
Mausschubser
Beiträge: 65
Registriert: 16. Apr 2013 15:07
### Re: Assignment 7: Moving Mark and Sweep
Ok, though I have to say that it is not clearly stated what we are allowed/supposed to change here in the task description. But thank you for clarifying.
PS: Will there be a task over the winter pause? It would be awesome if there wasn't These tasks are getting increasingly complex and it would be nice having a pause for some time...
Talaron
Mausschubser
Beiträge: 85
Registriert: 26. Apr 2012 11:34
### Re: Assignment 7: Moving Mark and Sweep
MrGumby hat geschrieben:Will there be a task over the winter pause? It would be awesome if there wasn't These tasks are getting increasingly complex and it would be nice having a pause for some time...
Rest is for the dead! The next assignment will be just one big task that is quite a bit of coding work, but not overly complex, and had a very high average grade last year. I'm sure you could get it done before the Christmas break even starts if you just give it a try.
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2019-12-06 17:06:16
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https://www.math.kit.edu/ianmip/seite/forschungsgebiete/
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# Direct and Inverse Scattering Problems
Work Group Inverse Problems
Prof. Dr. A. Kirsch, Dr. T. Arens, PD. Dr. F. Hettlich
## Scattering problems
Wave phenomena occur in various situations for instance as acustic waves at sound sources, as electromagnetic waves in tele communications or as elastic waves propagating from earthquakes. A common feature of all of these waves is, that they will be scattered, absorbed and/or transmitted by different media, by scattering objects'.
The mathematical modelling is done by partial differential equations like the wave equation
with spatial variable and time variable . A plane monochromatic wave with frequency and incident direction has the form
where denotes the wave number and the velocity in the medium.
The scattering of leads to a scattered field and the total field as a superposition of the incident and the scattered wave. If the scattering obstacle is constant in time, it holds
where and satisfy the reduced wave equation, or Helmholtz equation , in the exterior of the scattering obstacle. Assuming a bounded scattering object the scattered field will be of the asymptotic form
in large distance to the obstacle. Here and denote the polar coordinates of .
The picture shows level lines of far field pattern and with respect to the angles given by and in to (for two dimensional examples).
## Which object belongs to which far field pattern?
• The direct scattering problem consists in showing existence, uniqueness, stability, and the numerical computation (and its graphical illustration) of the fields, if the scattering object is known.
• The invers scattering problem consists in the identification of the scattering object, if far field patterns for directions are known by measurements (i.e. if such plots are given).
## Research of the work group
The direct problems can be written as integral equations using fundamental solutions, which can be helpful for theoretical questions on existence and stability as well as for numerical approximations. Currently in the working group algorithms for numerical solution of three dimensional scattering problems in case of biperiodic gratings are developed and investigated.
The fast and efficient evaluation of solutions of the direct problems is essential for using iterative methods (see below) in solving the corresponding inverse problems. Additionally, by the direct solver we obtain simulated data, which can be used to verify and compare various inversion schemes. The influence of parameter, which describe the shape or the material, can be analysed systematically by such data.
Iterative Methods: Already in case of the scattering of only one incident field at an obstacle the inverse problem can be considered. It consists in solving a non-linear and ill posed equation of the form
Iterative Newton type methods like
will require the domain derivative of the operator. Additionally a regularization is necessary, since otherwise the linearised equation has no stable inversion. By stopping the iteration early enough a good reconstruction from a far field pattern is possible. The picture shows the best, a mean, and the worst reconstruction from experiments with random noise in the data and with computed by a modified regularization scheme, which uses also the second domain derivative.
The factorization method: Iterative algorithm are all-purpose methods and lead still to the best reconstruction results. But they cost a high computational effort (in any step a direct boundary value problem has to be solved) and admit at most local convergence. Therefore, recently different approaches were established, which avoid these drawbacks. Various reconstruction algorithms based on the factorization method have been developed in the work group.
The far field pattern gives the kernel of the far field operator , defined by
with the unit sphere im . The far field operator is compact and normal in case of non-absorbing scattering objects (i.e. ) and can be factorised in the form
with certain operators and , where is compact and satisfies a Garding inequality. This is considerably used in representing the characteristic function of the set in the form
where , , and a spectral system of .
The following reconstructions are comupted by the factorization method from data: (The picture with two obstacles corresponds to the lower one of the two presented far field pattern above.)
---
Department of Mathematics,
Institut for Algebra and Geometry,
Work Group Inverse Problems
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2021-02-25 02:32:58
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https://www.physicsforums.com/threads/taylor-expansion.139785/
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# Taylor expansion
1. Oct 23, 2006
### bemigh
Hey Everyone.
I'm ALMOST finished this problem...
To spare you the long story, I need to take the difference between an gravitational acceleration, and the same gravitational acceleration at a slightly larger height.
The two functions are a(r) and a(r+d), where d is very small
Now... VERY SMALL tells me one thing... Taylor expansion. And this is what i have been advised to do.
I have the function f(a) = constant/r^2 which is just Newtons inverse square law of gravitation.
Now, i know that the function for a Taylor Series is going to be something like this:
F(x) = f(a) + xf'(a) + x^2/2 * f''(a) + ....
But how do i go about differentiating f(a), and what is x???
Thanks for the help
2. Oct 23, 2006
### quasar987
You seem to have lost yourself in the sea of variables. Let's start by clearing that up. You know that the acceleration 'g' as a function of the distance r from the center of the earth is of the form
$$g(r) = -Kr^{-2}$$
for K>0 a constant.
You want to calculate $g(r+d)-g(r)$, for d<<r. Since g(r+d) can be write as
$$g(r+d)=-K(r+d)^{-2}=-\frac{K}{r^2}\left(1+\frac{d}{r}\right)^{-2}$$
You will want to develop the function $f(x)=(1+x)^{-2}[/tex] in a Taylor series and find its radius of convergence (hint: it's gonna be 1, so as soon as d<r, the series converges), and then substitute back x=r/d to get the Taylor expansion of g(r+d). 3. Oct 23, 2006 ### quasar987 Upon reflexion, since this is a physics HW, you will not want to find the series of f(x), but rather you will want to just look it up on wiki and thurst that it converges to f(x) for |x|<1: http://en.wikipedia.org/wiki/Binomial_series ;p 4. Oct 23, 2006 ### tim_lou i guess you just need the fist and second terms of talyor series. stare at $$1/r^2$$, it's derivative is $$-2/r^3$$ since you only want the difference... its quite easy, derivative=df/dx, so df=df/dx * dx, and the difference is approximately: $$-2d/r^3$$ 5. Oct 23, 2006 ### quasar987 What tim_lou is saying is that the easiest approach to this problem is simply to say, ok since the derivative of a function is $$\frac{df}{dx}(x)=\lim_{\Delta x\rightarrow 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}$$, it should be a reasonable approximation to say that for [itex]\Delta x$<<1,
$$f(x+\Delta x)-f(x) \approx \frac{df}{dx}(x)\Delta x$$
Incidentally, this is just a Taylor approximation of first order to $f(x+\Delta x)$ and is also sometimes refered to as "Euler's approximation".
6. Oct 23, 2006
### bemigh
Thanks for the input,
but what good would the radius of convergence give me? Couldnt I just truncate the expansion, and solve for the difference between g(r)?
7. Oct 23, 2006
### quasar987
I guess you have a point!
8. Oct 24, 2006
### quasar987
But I think it's important to know the radius of convergence. Take for exemple the (geometric) series
$$\sum_{n=0}^{\infty} x^n$$
which we know without knowledge about Taylor series to converge to $f(x)=1/(1-x)$ for |x|<1 and diverge otherwise. Now say we want to get an approximation of $f(-2)$ (which is 1). The first term approximation is 1. the second is 1-2=-1, third is -1+4=3, etc. The first order approx is right on, while the other terms make the approximation worse.
Whereas when we want to approximate a value inside the interval of convergence, we know that the more term we take, the better the approximation. ...well, I think!*
So it matters to know the radius of convergence even though we will troncate the series. If you know the series to diverge, it might not be such a good idea to take many terms to your approximation.
*At least we know that no matter how small a number 'h' we take, we can always find an interger N such that for all n>N, the error of nth taylor approximation is lesser than h.
Last edited: Oct 24, 2006
9. Oct 24, 2006
### quasar987
But I'd be interested in a formal result concerning the behavior of the "error function"
$$E(x,n) = \left|\sum_{i=1}^n \frac{f^{(i)}(0)}{i!}x^i - f(x) \right|$$
Is the sequence {$E(x_0,n)$} stricly decreasing for x_0 in the radius of convergence?
I'll ponder on it tomorrow. In the meantime if someone wants to make an input, please do.
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2016-10-27 23:29:26
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https://cran.microsoft.com/snapshot/2020-09-17/web/packages/precommit/vignettes/why-use-hooks.html
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Why use hooks?
The goal of pre-commit hooks is to improve the quality of commits. This is achieved by making sure your commits meet some (formal) requirements, e.g:
• that they comply to a certain coding style (with the hook style-files).
• that you commit derivatives such as README.md or .Rd files with their source instead of spreading them over multiple commits.
• and so on.
As all changes enter a repository history with a commit, we believe many checks should be performed at that point, and not only later on a CI service. For example, creating auto-commits at a CI service for styling code creates unnecessary extra commits, as styling can be checked at the time of committing and is relatively inexpensive.
Why use the pre-commit framework?
Implementing hooks in a framework such as pre-commit.com has multiple benefits compared to using simple bash scripts in .git/hooks:
• Easily use hooks other people have created, in bash, R, python and other languages. There are a wealth of useful hooks available, most listed here. For example, check-added-large-files prevents you from committing big files, other hooks validate json or yaml files and so on.
• No need to worry about dependencies, testing, different versions of hooks, file filtering for specific hooks etc. It’s all handled by pre-commit.
• Hooks are maintained in one place, and you just need a .pre-commit-config.yaml file. No need to c/p hooks from one project to another.
Have an idea for a hook? Please file an issue.
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2023-02-05 09:25:44
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https://cs.stackexchange.com/tags/regular-languages/new
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# Tag Info
0
Suppose that $w = ncm$, where $n \neq m^R$, say $n$'th $i$-th letter from the left, $\sigma$, differs from $m$'s $i$-th letter from the right, $\tau$. Then $$w \in \Sigma^{i-1} \sigma \Sigma^* c \Sigma^* \tau \Sigma^{i-1},$$ where $\Sigma = \{a,b\}$. Conversely, every $w$ of this form is in your language. You take it from here.
0
This answer is for the original version of the question, in which "$k$" was missing. Your language contains all non-empty words. Indeed, if $w \neq \epsilon$ then you can write $w = nm$, where $m = \epsilon$ and $n = w \neq \epsilon = m^R$. In contrast, if $\epsilon = nm$ then $n=m=\epsilon$ and so necessarily $n=m^R$.
1
See this paper for an extended discussion which includes the old Chomskyan center-embedding arguments that English, for example, is not regular. See this answer for an argument that natural languages are not context-free and therefore not regular. Moreover, there is no agreement as to what a syntactic theory of natural languages would look like. The ...
1
In order to show that $f$ is regularity preserving, it suffices to show that $f^{-1}(U)$ is eventually periodic for $U = \{ n : n \equiv b \pmod{a} \}$, where $a$ is a prime power (here we are using the Chinese remainder theorem and the fact that the eventually periodic sets are closed under intersection). For $f(n) = 2^n$, we consider two cases: If $a = 2^... 1 Hint: 5 The answer by @YuvalFilmus is perfectly fine, and points you to the import notion of star height. But let me add a little bit more. We will show that languages of your form give a proper subset of the languages of star height one. But first, some musings what might come close to your form. General Regular Languages First, probably the closest form to yours ... 0 I'll explain my thought process behind thinking about this problem here: -> With inequalities, I first think at the equality constraint. So I assume n = m+3 -> Now, n is always 3 more than m. -> I split the problem further. I think to myself okay, let's have one production handle equal production of a and b. -> How many more b's do we need after ... 1 The best way is to learn is to look at examples, and see how they work. One of the simplest "real" context-free languages is$\{\; a^mb^n \mid n = m \;\}$Its grammar is$S\to aSb\mid \varepsilon$. Now add in steps, the extra 3, and the more than ...$\{\; a^mb^n \mid n = m+3 \;\}\{\; a^mb^n \mid n \le m+3 \;\}$0 As you mention, if$n$was fixed, then this is not too difficult to prove. So, the idea would be to show that in fact,$n$can be bounded a-priori, depending only on$A$, and not on$x$. To this end, consider some word$x\in \Sigma^*$, and suppose$x^m\in A$for some$m$. Let$k$be the number of states in some DFA$D$for$A$(e.g., minimal DFA). Suppose$m&...
0
Assume the language is regular, i.e., there is an automaton that recognize the language with a finite set of states. Therefore there are $i \neq j$ such that processing $a^{i +1}$ and $a^{j + 1}$ reach the same state X. Processing $4i + 2$ b's in state X always ends up in the same state Y. State Y must be accepting because $a^{i + 1} b^{4i + 2}$ is in the ...
1
Arden's theorem states that $A^*\,B$ is the least fixed point of the equation: $$X = A\,X\,\cup B$$ and that $A\,B^*$ is the least fixed point of the equation: $$X = X\,B\,\cup A$$ In your case, $R = Q\,P^* = a^* (a b)^*$.
3
Since I see questions about the pumping lemma on this site quite often, I decided to write a bit of a longer answer hoping that it helps people "get" the PL rather than just treating it as a "plug-n-chug" tool given to us by the gods of math. Understanding the PL I think the best way to go about it is to basically (re-)derive the lemma. ...
1
You want to prove that if $\equiv_S$ has infinite index, then $L$ is not a regular language, or, equivalently that if $L$ is regular, then $\equiv_S$ has finite index. This is an immediate consequence of the following result. Theorem. Let ${\cal A} = (Q, \Sigma, \cdot, i, F)$ be the minimal complete deterministic automaton of $L$. Then $u \equiv_S v$ if and ...
0
(a) Let $\Sigma$ be the alphabet of $L$ and $\Sigma^*/\equiv_L$ the set of equivalence classes of words over $\Sigma$ according to the equivalence relation $\equiv_L$. Define the DFA to have one state for each element of $\Sigma^*/\equiv_L$ (we could think of the states as the classes themselves). Define the initial state to be the class of the empty word $\... 0 Don't know exactly what you mean, but a is an element of L(a). Actually the only element of L(a). (while a* is not an element of L(a*) because none of the elements contain the symbol *). 1 Your question is unclear. However "a language (that has strings of infinite length)" cannot exist. By definition a language only contains words of finite length. Let$\Sigma$be a (finite) alphabet and$\epsilon$denote the empty word. A language is a subset of$\Sigma^*$, where$\Sigma^*$is defined as$\Sigma^* = \cup_{i=1}^{\infty} \Sigma^i$,$\...
1
After a bit more thought I believe this is indeed true and that I've got a proof of it. The idea is to proceed by contrapositive and instead prove that if $L$ is regular, then $\equiv_S$ has only finitely many equivalence classes. We can see this by pulling in Brzozowski derivatives. Given the language $L$ and any string $x \in \Sigma^*$, we define the ...
1
The basic idea is that if a regular language is infinite, then it contains a word of infinite length. Indeed, the pumping lemma shows that the set of lengths of words in the language contains an arithmetic progression, and every arithmetic progression contains a composite integer. We can check whether the language accepted by an NFA is infinite as follows: ...
1
(This is an attempt to an answer, I hope the details are right.) Your language consists of all strings in $(aa+bb)^*$ with an even number of $bb$. We are allowed to use complementation, so we start by looking at the complement of the language. I think we can split the complement into two (overlapping) parts strings not of the form $(aa+bb)^*$, that language ...
0
Let's recall the Pumping Lemma statement: For all regular language $L$, exists a positive constant called $p$ (i.e. $p \geq 1$) such that every string $w$ in $L$ with length $|w| \geq p$ exist strings $x, y, z$ such that $w = xyz$ and that statisfying the following conditions: $|y| \geq 1$ $|xy| \leq p$ $xy^iz \in L, \: \forall i \geq ... 3 Here is a simple example. Take any non-regular language$N$contained in$(aa)^+$and consider the language$L = 1 + a(aa)^* + N$. Then$L$is not regular since$L \cap (aa)^+ = N$is not regular. On the other hand,$L^2 = a^*$is regular. 3$(a^+b \mid b^+a)^*$. I am not sure there is a "simple" description of your language in plain English, but directly from the regex you get that it is the language that has the empty string and all strings that can be partitioned in such a way that each part is either multiple$a$'s (at least one) followed by one$b$, or vice versa. In my opinion ... 5 Your claim is false. Indeed, it is equivalent to prove that if a language$L$is not regular, then also$L^2$is not regular, but this is not true. Here Yuval Filmus gives (possibly) two examples of a non regular language whose "square" is regular, namely$L = \{ 1^p \mid p \text{ is an odd prime}\}$, under the Goldbach conjecture, and$L' = \{ 1^...
7
Nice question! This is a very nontrivial problem involving regular languages. First of all: no, you cannot run an automaton on every substring of a string skipping other letters, you are supposed to run the automaton only once on the target string. In this case it is simpler to reason on the complementary of the given language, namely on L^C = \{ w \in (...
Top 50 recent answers are included
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2020-09-20 20:54:45
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https://discourse.julialang.org/t/julia-is-ranked-35th-on-the-tiobe-index/7026
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# Julia is Ranked 35th on the TIOBE Index
#1
Last month we had a pretty massive blogging campaign, getting quite a few posts to the top of Hacker News in a month. The results of the most recent TIOBE index shows that this has made a sizable dent in the rankings:
https://www.tiobe.com/tiobe-index/
We were 43rd before, and now we are at 35! In terms of the search percentages, that’s 0.2%, or 50% more than what we had before. This means that our writing about GPU computing, differential equations, and machine learning has a measurable impact on language visibility and adoption. I hope this is encouraging for those who have already started showing what Julia can do, and if you haven’t yet, give blogging a try! You can get started by posting links to here and by submitting your feed to JuliaBloggers.com:
Also, remember to use #julialang on Twitter to spread it around, and put a post in to the Julialang Reddit:
The big outlet is then Hacker News, where a post can hit the front page if it grabs enough buzz. Feel free to let others know what to search for on Hacker News to find your thread by alerting people in the chatrooms:
https://slackinvite.julialang.org/
Don’t be afraid to plug into the community: we love to hear what you’re up to!
#2
I would like to contribute to that, but I don’t have a blog or want to start one…
If I make a big markdown file, can I somehow send it to juliabloggers.com?
I checked the page submit rss feed, but if I understood correctly that requires me to already have a blog?
#3
Here are a few ways to get started. The easiest way is to make an account with something like Wordpress.com or Medium.com which are big blogging sites and you just make your articles in them. Simon’s GPU computing article is an example of this: https://medium.com/@sdanisch/writing-extendable-and-hardware-agnostic-gpu-libraries-b21c145a8dad . If you want more control, you can also create a Wordpress blog on your own host (which is what I did for StochasticLifestyle.com), I recommend Bluehost.com’s cloud hosting because you can adjust your computing power to deal with surges (I had to do this when a few posts went to the top of Hacker News since that can get you >10,000 views in a few hours).
Another way to do it is through Github. The JuliaDiffEq blog is hosted through a simple Jekyll page:
The repo is just the organization’s repo site:
To setup an RSS feed, see this commit: (https://github.com/JuliaDiffEq/juliadiffeq.github.io/commit/41b6185b9d9f460bdfa666eb0526275c20fdbf9a) and you’ll be ready to submit to JuliaBloggers.com. With this setup, anyone can make a pull request to the blog (https://github.com/JuliaDiffEq/juliadiffeq.github.io/tree/master/_posts) which is helpful. Note that the Julialang blog is setup the same way: https://github.com/JuliaLang/julialang.github.com/tree/master/blog/_posts (though I am not sure that it has an RSS feed?).
You then just need a host if you want to setup this with a domain, which I use Bluehost. Then you just need to setup the domain forwarding, which is described here: https://help.github.com/articles/setting-up-an-apex-domain-and-www-subdomain/ . There’s a tab in CPanel to do this kind of stuff, and this is how JuliaPlots, JunoLab, etc. all use a special domain name yet are simply a Github repo.
#4
While blogging is indeed a great way to spread the word, some minor things about JuliaBloggers.com are broken (eg some blogs have broken lines in the RSS feed, MathJax support is flaky because delimiters are not escaped properly, etc).
I tried contacting Randy Zwitch about them repeatedly, with concrete suggestions for solutions, but got no replies after a while. Perhaps as the language community grows we should rethink blogging infrastructure — this is a problem that many communities have robust solutions for, eg using an aggregator like Planet, which I am not going to link because the website seems to be down. Looking at feed aggregators, pluto seems to be maintained.
#5
Hugo is another great static website generator, it is lightning fast, with Mmark support which I find very convenient for blogging about technical issues (seamless math, code integration). The Hugo docs has detailed instructions about setting up your blog, it will probably take a few hours. If that helps, you can find the source of my blog in this repo.
#6
The TIOBE index measures the number of hits for +"<language> programming". For Julia, the <language> could be Julia, Julialang or julia-lang. This is described in the TIOBE definition.
It is interesting that the query "JuliaBloggers" + "Julia language" gives 865 hits in Google, while "JuliaBloggers" + "Julia programming" gives 527 hits. In Google, "Julia programming" has 177,000 hits and "Julia language" has 46,000. Interestingly, "Julia programming language" has 104,000 hits.
Is our use of Julia language instead of Julia programming lowering our TIOBE score?
#7
I imagine this is consistent across languages — all would get a higher score if they included other variants.
#8
They might be amenable to including things like that, for all languages. I think it would be useful for all of us in the Julia community to sent e-mails to the people at TIOBE, requesting these changes:
From their site:
This is the top 5 of most requested changes and bugs. If you have any suggestions how to improve the index don’t hesitate to send an e-mail to tpci@tiobe.com.
Apart from " programming", also other queries such as “programming with “, " development” and " coding” should be tried out.
We also need to let them know that esp. for languages like Julia, Go, Rust, Mumps (or Lua in Portuguese) where it’s a common word (unlike C#, Erlang, Perl, C++) that people often differentiate by having " language", and that really should be taken into consideration.
#9
December 2017 - 47th
(from November: 0.600% -> 0.439%)
#10
Well, we had a good run.
(I think <1% has a lot of measurement error, so I am not giving a lot of weight to fluctuations in either direction.)
#11
January 2018 - 47th (0.439% -> 0.226%)
February 2018 - 50th (0.226% -> 0.189%)
Please don’t shoot messenger! Truth is probably important also in our postfactual era.
#12
Let’s get those blogs and news articles churning again then.
#13
Tiobe index is improving:
February 2018 - 50th (0.226% -> 0.189%)
March 2018 - 37th (0.189% -> 0.301%)
https://www.tiobe.com/tiobe-index/
#14
Julians were all rushing to get v0.7/v1.0 together in Dec/Jan/Feb, that must be why it dropped!
Julia ranking trend, TIOBE, RedMonk
#15
As I indicated on the other thread, I don’t think obsessively following these things with bated breath is good for anyone’s sanity. The fact that we see such wild fluctuations seems indicative of huge statistical uncertainties.
Fear not, Julia will stand on its own intrinsic merits. It’ll take a while, but things seem on track to me.
#16
In the last month we had 4 videos added to the Julialang Youtube which got a pretty good number of views, and there were quite a few podcasts:
The searches look pretty linked to “marketing”. So that means we should keep it up, but also that the rankings aren’t that robust.
#17
I’m not at all obsessed by it, I think it’s funny. The TIOBE index has a ton of problems with it’s ranking mechanisms - besides being a popularity contest, I’ve seen that it’s bad at miscounting languages whose names are hard to distinguish, and I don’t think it deals well with things not in English (since it looks for words like “language” and “programming” to distinguish).
IEEE has an index that I think is much better for gaining insight about languages.
#18
I’m not looking for sanity. I just want to win.
#19
Was this not something I fixed? I’m not a MathJax person, and I am reading everyone’s RSS feed using a stock WordPress plugin, so it’s not something I’m completely attuned to. The main limitation is someone with PHP experience (or, moving to a different blogging software)
#20
They really need to use some modern NL processing on this! There are so many good ways finding out if a text contains a certain concept rather than this. They don’t really show themselves to be very good hackers, IMO!
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2018-07-17 01:55:29
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https://bitbucket.org/sjl/learnvimscriptthehardway/src/efff67c5b7535d01087fb386f939cca56dca292a/chapters/26.markdown
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# Strings
The next type of variable we'll look at is the String. Since Vim is all about manipulating text you'll be using this one quite a bit.
Run the following command:
:echom "Hello"
Vim will echo "Hello". So far, so good.
## Concatenation
One of the most common things you'll want to do with strings is adding them together. Run this command:
:echom "Hello, " + "world"
What happened? Vim displayed "0" for some reason!
Here's the issue: Vim's + operator is only for Numbers. When you pass a string to + Vim will try to coerce it to a Number before performing the addition. Run the following command:
:echom "3 mice" + "2 cats"
This time Vim displays "5", because the strings are coerced to the numbers "3" and "2" respectively.
When I said "Number" I really meant Number. Vim will not coerce strings to Floats! Try this command to see prove this:
:echom 10 + "10.10"
Vim displays "20" because it dropped everything after the decimal point when coercing "10.10" to a Number.
To combine strings you need to use the concatenation operator. Run the following command:
:echom "Hello, " . "world"
This time Vim displays "Hello, world". . is the "concatenate strings" operator in Vim, which lets you combine strings. It doesn't add whitespace or anything else in between.
Coercion works both ways. Kind of. Try this command:
:echom 10 . "foo"
Vim will display "10foo". First it coerces 10 to a String, then it concatenates it with the string on the right hand side. Things get a bit stickier when we're working with Floats, though. Run this command:
:echom 10.1 . "foo"
This time Vim throws an error, saying we're using a Float as a String. Vim will happily let you use a String as a Float when performing addition, but won't let you use a Float as a String when concatenating.
The moral of this story is that Vim is a lot like Javascript: it allows you to play fast and loose with types sometimes, but it's a really bad idea to do so because it will come back to bite you at some point.
When writing Vimscript, make sure you know what the type of each of your variables is. If you need to change that type you should use a function to explicitly change it, even if it's not strictly necessary at the moment. Don't rely on Vim's coercion because at some point you will regret it.
## Special Characters
Like most programming languages, Vimscript lets you use escape sequences in strings to represent hard-to-type characters. Run the following command:
:echom "foo \"bar\""
The \" in the string is replaced with a double quote character, as you would probably expect. Escape sequences work mostly as you would expect. Run the following command:
:echom "foo\\bar"
Vim displays foo\bar, because \\ is the escape sequence for a literal backslash, just like in most programming languages. Now run the following command (note that it's an echo and not an echom):
:echo "foo\nbar"
This time Vim will display two lines, "foo" and "bar", because the \n is replaced with a newline. Now try running this command:
:echom "foo\nbar"
Vim will display something like "foo^@bar". When you use echom instead of echo with a String Vim will echo the exact characters of the string, which sometimes means that it will show a different representation than plain old echo. ^@ is Vim's way of saying "newline character".
## Literal Strings
Vim also lets you use "literal strings" to avoid excessive use of escape sequences. Run the following command:
:echom '\n\\'
Vim displays \n\\. Using single quotes tells Vim that you want the string exactly as-is, with no escape sequences. The one exception is that two single quotes in a row will produce one single quote. Try this command:
:echom 'That''s enough.'
Vim will display That's enough.. Two single quotes is the only sequence that has special meaning in a literal string.
We'll revisit literal strings when they become most useful, later in the book (when we dive into regular expressions).
## Truthiness
You might be wondering how Vim treats strings when used in an if statement. Run the following command:
:if "foo"
: echo "yes"
:else
: echo "no"
:endif
Vim will display "no". If you're wondering why this happens you should reread the chapter on conditionals, because we talked about it there.
## Exercises
Read :help expr-quote. Review the list of escape sequences you can use in a normal Vim string. Find out how to insert a tab character.
Try to figure out a way to insert a tab character into a string without using an escape sequence. Read :help i_CTRL-V for a hint.
Read :help literal-string.
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2015-09-02 07:18:09
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http://www.mammal.cn/CN/Y2020/V40/I6/595
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• 研究论文 •
### 黑线仓鼠断乳后能量代谢和脂肪累积的适应性调节
1. （温州大学生命与环境科学学院，温州325035）
• 出版日期:2020-12-01 发布日期:2020-12-03
• 通讯作者: 赵志军 E-mail: zhaozj@wzu.edu.cn
• 基金资助:
国家自然基金（31670417, 31870388）；温州大学研究生创新基金项目（3162019052）；温州大学学生科研课题立项（2019kx171）
### The adaptive regulations of energy metabolism and fat accumulation during post-lactation in striped hamster
YU Jingxin, DENG Guangmin, BAO Yufan, ZHAO Zhijun#br#
1. (College of Life and Environmental Science, Wenzhou University, Wenzhou 325035, China)
• Online:2020-12-01 Published:2020-12-03
Abstract:
Physiological variations of energy metabolism and body fat accumulation are the main energy budgets in small mammals to cope with natural environmental changes. However, the energy mechanisms underpinning the adaptive regulations in different stages of lifespan remain unclear. The present study was aimed to examine the changes in energy metabolism, fat accumulation and the endocrine mechanisms in striped hamsters (Cricetulus barabensis) during lactation and post-lactation. The food intake, fat depots mass, serum leptin levels and the gene expression of leptin receptor (Ob-Rb) and neuropeptides related to food intake regulation in hypothalamus were measured. The results showed that the fat depots were almost decreased to zero at peak lactation, and then were increased significantly during post-lactation. The masses of subcutaneous fat, perirenal fat and abdominal fat were 1.5, 37.1 and 1.9 fold higher in post-lactating females than that in non-reproductive controls. Food intake and serum leptin level of post-lactating females were significantly higher than that of non-reproductive controls, while the gene expression of Ob-Rb was significantly down-regulated in post-lactating females. The gene expression of orexigenic and anorexigenic neuropeptides did not differ between the two groups. The litter size raised during lactation had no significant effects on food intake, resting metabolic rate and body components in post-lactating females. These findings suggest that body fat accumulation is adaptively regulated in the different stages of reproduction.
Leptin resistance may be one of the most important endocrine mechanisms underpinning the fat accumulation during post-lactation. This is of significance for the mothers to restore fat accumulation and to cope with the periods of high energy demands and food shortage, increasing the fitness.
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2022-10-02 10:43:46
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https://forum.allaboutcircuits.com/threads/very-inexpensive-way-to-operate-relay-from-speaker-output.65893/
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# VERY inexpensive way to operate relay from speaker output .
#### gramparich
Joined Feb 8, 2012
7
Hey folks,
I'm one of those old folks that know a little about a lot of things, so be nice.
I have a project that requires what the title says.
"I need to turn on something when there is sound coming from a speaker."
One of the first considerations is cost, as I am hoping to manufacture a sizable quantity of devices utilizing this function.
My first thought was to utilize the speaker voltage directly, and then I turned to the sound itself being detected and amplified to the point of firing the relay.
Am I missing something ?
Is there a simpler solution that could cost less ?
Thanx,
Grampa Rich (not Rich Grampa as my kids think)
#### PaulEE
Joined Dec 23, 2011
423
Hey folks,
I'm one of those old folks that know a little about a lot of things, so be nice.
I have a project that requires what the title says.
"I need to turn on something when there is sound coming from a speaker."
One of the first considerations is cost, as I am hoping to manufacture a sizable quantity of devices utilizing this function.
My first thought was to utilize the speaker voltage directly, and then I turned to the sound itself being detected and amplified to the point of firing the relay.
Am I missing something ?
Is there a simpler solution that could cost less ?
Thanx,
Grampa Rich (not Rich Grampa as my kids think)
May I (we) ask what the overall goal of this project is? Or, is it top secret?
There are approximately 298459823498 ways to do this, but your project specifications are going to narrow it down to a handful...at which point, we can do the cost-cutting.
#### gramparich
Joined Feb 8, 2012
7
Hey there PaulEE,
Yup - top secret
However, basic voltage available is 12vdc
- lookin' to keep overall device as small as possible
- will need to drop 12v to 5vdc for another little sub device (will gut a $.99 usb to 12v doodad for the 5v) - said little sub device will have 10 second timer to turn speaker off (relay to turn off too) - very low volume of audio is needed HALP Thanx, Grampa - Thread Starter #### gramparich Joined Feb 8, 2012 7 Anybody that likes golden's can't be all bad. grampa Thread Starter #### gramparich Joined Feb 8, 2012 7 I just read over what I forwarded, and I need to change "I want to manufacture----------etc" to "I would like to patent the idea--------etc" #### joeyd999 Joined Jun 6, 2011 4,477 I just read over what I forwarded, and I need to change "I want to manufacture----------etc" to "I would like to patent the idea--------etc" Well, if your intention is to patent the idea of: "I need to turn on something when there is sound coming from a speaker." You've already given it up to the public domain by posting it here! Hopefully, there is more to your invention than that, but, in the future, *be careful*! #### Audioguru Joined Dec 20, 2007 11,249 There is an Instructable that blinks an LED when music plays. It was designed by a 10 years old kid so it is missing two current-limiting resistors and a diode. It is just one TIP31 transistor. It is missing a series base resistor so its forward-biased base-emitter junction blows up and might blow up the audio amplifier. Its emitter is missing a series diode so when its reverse-biased emitter-base junction has avalanche breakdown at about 5V then it blows up and might blow up the audio amplifier. Its LED is missing a series current-limiting resistor so the LED will probably blow up. Thread Starter #### gramparich Joined Feb 8, 2012 7 Well, if your intention is to patent the idea of: You've already given it up to the public domain by posting it here! Hopefully, there is more to your invention than that, but, in the future, *be careful*! Oh yeah, there is much more than this one function, and I appreciate the "be careful", but I have been down this road before and know the bumps. Thanx---------- #### MrChips Joined Oct 2, 2009 23,253 Unless you have$100 grand to spend on a patent application you might as well forget that idea. In any case, if someone knowledgeable in the field of electronics can come up with the same idea in the normal course of practice that kills your patent.
But you can still build a simple sound activated switch, just not patentable.
#### Audioguru
Joined Dec 20, 2007
11,249
Haven't you heard about "The Clap Switch" that is being sold today?
It turns something on when you clap your hands quickly two times (or if your dog barks quickly two times). Then it turns off when you clap your hands quickly two times again (or your dog ...).
How can you patent something that is already used all over the place? How can you sell yours when everybody already has a few?
#### c0de3
Joined May 1, 2009
50
Oh yeah, there is much more than this one function, and I appreciate the "be careful", but I have been down this road before and know the bumps.
Thanx----------
So you are saying the sub-circuit would get power from a separate power source, you just want to switch it on and off with the speak line voltage? Do you care if this device causes issues with said speaker line? ie. does the speaker still need to work with this device inserted?
#### gramparich
Joined Feb 8, 2012
7
OK,
Let me start over here-----------
I have a neat idea for a gadget that needs the aforementioned function.
It might be patentable, it might not, I really don't care.
I just want to make one for my own use, and maybe it might interest someone who had the wherewith all to take it and run.
So, does anyone have an idea how to operate a relay with speaker audio voltage, or the sound itself ? cheap ?
thanx
#### Audioguru
Joined Dec 20, 2007
11,249
A problem with using audio from the output of an amplifier to turn on a relay is that a relay needs a certain DC voltage and audio is AC at many voltages.
The audio must be at least 4.1W into 8 ohms for a duration a little longer than the relay's turn-on time plus the duration tthat you need. Rectify the audio then filter it. The resulting voltage will be at least 5VDC. Use a 5V voltage regulator to turn on a 5V relay.
#### gramparich
Joined Feb 8, 2012
7
WOW,
thanks for all your help !
#### Ctenom
Joined Nov 1, 2010
59
Hey there PaulEE,
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2021-05-15 17:29:27
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https://math.stackexchange.com/questions/3676161/a-is-a-ring-m-a-left-noetherian-a-module-fm-to-m-is-a-left-homomorph?noredirect=1
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# $A$ is a ring, $M$ a left noetherian $A$-module, $f:M \to M$ is a left homomorphism of modules. 2 part question. [duplicate]
$$A$$ is a ring, $$M$$ a left noetherian $$A$$-module, $$f:M \to M$$ is a left homomorphism of modules.
Part A -- Suppose $$Ker f^n=Ker f^{2n}$$, then prove $$Ker f^n \cap Im f^n = \{0\}$$.
Suppose that $$a \in Ker f^n$$ and $$a\ne0$$. Then $$f^n(a)= 0$$. But since $$Ker f^n = Ker f^{2n}$$ then $$f^{2n}(a)=f^n(f^n(a))=f^n(0)=0$$, so $$0\in ker f^n$$ a contradiction. So, if $$a \in Ker f^n$$, then $$a = 0$$. Also\, $$Im f^n$$ must be a module, so must obey the criteria of an abelian group under addition, so $$0\in Im f^n$$.
Since $$Ker f^n = {0}$$, and $$0\in Im f^n$$, then $$Ker f^n \cap Im f^n = \{0\}$$.
This seems like a good proof to me, however it doesn't seem to use any properties of noetherian modules. To me it seems to be just a property of homomorphic maps in general.
Part B -- Suppose $$f$$ is surjective and $$M$$ is noetherian, then show $$f$$ is an isomorphism.
The only thing we need to show is that $$f$$ is injective. So, let's supposed that $$f$$ is not injective, that is, for $$a,b \in M$$, $$f(a) = f(b)$$. Its seems clear here that then if $$M$$ is finite, then the cardinality of $$f(M)$$ must be strictly less that $$M$$, so $$f$$ could not be surjective, a contradiction. The only remaining possibility is that $$M$$ is infinite.
However, here I have a problem, I am not finding the contradiction here. Again, I am not really seeing how to use the fact that $$M$$ is noetherian, ie. every chain of submodules terminates. I see an example of an infinite set that is a noetherian module ( the integers ).
• In Part A, you say that $0 \in Ker(f^n)$ is a contradiction. What exactly do you think does this contradict? Also, you claim that this would imply $Ker(f^n) = \{0\}$ and I do not see how this follows. In fact, this is not true in general (take a nontrivial idempotent endomorphism of some vector space). To show that $Ker(f^n) \cap Im(f^n) = \{0 \}$, take an arbitrary element $a \in Ker(f^n) \cap Im(f^n)$ and use the given assumptions to show that $a = 0$. You will not need $M$ to be noetherian for this. For the second part, you need it. Consider $Ker(f) \subseteq Ker(f^2) \subseteq \dots$ – Matthias Klupsch May 15 '20 at 13:23
• Additional thing to link for the first question that I can't link as a dupe since people chose to answer in the comments: math.stackexchange.com/q/428760/29335 – rschwieb May 15 '20 at 13:35
• @MatthiasKlupsch thanks for your help. I see me my mistake. I was trying to supposed that $0 \notin Ker f^n$, and the contradiction still follows from this, showing that $0 \in Ker f^n$, however the conclusion that $Ker f^n = \{0\}$ does not follow direction from that. – jeffery_the_wind May 15 '20 at 13:45
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2021-01-20 23:01:43
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https://www.physicsforums.com/threads/half-life-decay-question.535059/
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# Half-Life decay question
1. Sep 29, 2011
### onqun
Hello, I am curious. Eventhough, the half-time of an element is always the same. Why not we can't find quarter of elements vanish time, because; half life is directly proportional, 10gr 10 min -> 5gr 20min. if 10 gr vanishes in 10 min, 2.5gr vanishes in 2.5 min for 20gr radioactive material.
2. Sep 29, 2011
### kurros
I am a little unclear what you are asking, but your numbers are wrong. Your numbers imply some kind of linear decay, which is weird, i.e. that everything would be gone after 20 minutes.
We are talking about something that undergoes exponential decay, so to find the amount left after a certain amount of time you need this formula (see http://en.wikipedia.org/wiki/Exponential_decay for info about where this comes from):
$N(t)=N_0 2^{-t/t_{1/2}}$
where N0 is the original number of "things" you have which are decaying, N(t) is the number left after time t and t_1/2 is the half life. For a 20 gram sample with half life of 10 minutes, i.e. N0=20 (mass is proportional to particle number) and t_1/2=10, then after 2.5 minutes you have 16.82 grams left, after 10 minutes you have 10 grams (duh) and after 20 minutes you have 5 grams left (two half lives), 30 minutes->2.5 grams, etc.
3. Sep 29, 2011
### Staff: Mentor
See the discussion on half-life here.
http://hyperphysics.phy-astr.gsu.edu/Hbase/nuclear/halfli2.html
As kurros indicated, it represents a decaying exponential function based on a first order differential equation which indicates that the rate of decay is proportional to the amount of the particular substance (radionuclide) existent (still remaining).
Code (Text):
0 1
1 0.933
1.9265 0.87500 1/8 initial amt decayed
2 0.871
3 0.812
4 0.758
4.1504 0.75000 1/4 initial amt decayed
5 0.707
6 0.660
7 0.616
8 0.574
9 0.536
10 0.500 1/2 initial amt decayed
one half-life
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2017-09-23 07:46:45
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https://www.cut-the-knot.org/pythagoras/HeronsDerivative.shtml
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Derivative in Heron's Formula
Heron's formula gives an expression for the area $A$ of a triangle in terms of its side lengths $a$, $b$, $c$:
$A = (1/4)\sqrt{(a + b + c)(a + b - c)(a - b + c)(-a + b + c)}.$
Have you ever tried to differentiate the right hand side? To give my goal out, I declare this at the outset that we'll be looking for the zeros of the derivative. If so, it would be easier to differentiate the square of the expression on the right, as the two have the same zeros. The derivative we are concerned with is with respect to c (an explanation will be given shortly.)
So consider the function
\begin{align} f(c) &= (a + b + c)(a + b - c)(a - b + c)(-a + b + c) \\ &= ((a + b)^{2} - c^{2})(c^{2} - (a - b)^{2}). \end{align}
Compute its derivative $((gh)' = g'h + gh')$:
$f'(c) = -2c(c^{2} - (a - b)^{2}) + 2c((a + b)^{2} - c^{2}) = 4c(a^{2} + b^{2} - c^{2})$,
such that when it is zero we get $a^{2} + b^{2} - c^{2} = 0$, i.e., the Pythagorean theorem. What is the meaning of it? A coincidence, pure luck? Or is there an explanation?
A mechanical explanation has been offered by Aleksey Kuzmenko from Moscow who kindly drew my attention to his 2009 post at a Russian forum.
Imagine two rods of lengths a and b hinged at endpoints, with their free ends joined by an elastic tube capable of varying its length but rigid otherwise. Imagine further filling such a triangle with a (2-dimensional) gas. Such a configuration will be stable when the area of the (variable) triangle is at its maximum. This happens when the two rods are perpendicular; and the rest follows.
Now, several questions can legitimately be asked as to the validity of this argument.
1. Can a derivative be used in a proof of the Pythagorean Theorem?
We had a chance to establish that at least a good chunk of Calculus - including derivatives - can be derived without a recourse to the Pythagorean theorem.
2. How do we know that the configuration of the three rods has maximum area when the angle between the hinged two is right?
This follows from the Law of Sines. From a previous discussion we know that some aspects of trigonometry can also be obtained without the Pythagorean theorem. The Law of Sines is based merely on the definition of the sine and the formula for the area of a triangle as half the product of a base times altitude.
Note that by answering the two question we actually supply a basis for the proof that eschews the mechanical introduction.
John Molokach additionally observed that, from the area formula $\displaystyle f(C)=\frac{ab\text{ sin}(C)}{2}$, the area - as a function of angle $C$ - attains its maximum exactly at $\displaystyle C = \frac{π}{2}$.
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2019-06-24 17:56:04
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https://www.nextgurukul.in/questions-answers-forum/question/discussion/hello-everyone-i-and-39am-ishaan-from-class-9-i-am-new-to-bo/63699
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##### Get a free home demo of LearnNext
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Aug 16, 2014
# Hello Everyone I'am Ishaan from class 9 . I am new to board exams . I am having a tough time in Hindi. Other Subjects I can Manage . So..
Hello EveryoneI'am Ishaan from class 9 . I am new to board exams . I am having a tough time in Hindi. Other Subjects I can Manage . So , Could some one please teach me how to learn hindi for the Board Exams CBSE Class 9 . Like from where should i learn and how to .... :p Please Enlighten me Asap. Your consideration will be appreciated.Your's Sinceraly ,Ishaan 9-ADunes International School , KSA
Gaurav Teharpuria
Ishaan don't be afraid of hindi its just really easy in board exams... For hindi literature u should read the chapter thoroughly and just read the exersise questions only nt answers... and try to solve the questions in ur mind by keeping the story in ur brain... for hindi grammer and writing part just understand the concept, definations, read some examples related to those topics and understand the topic... At last solve a sample board exam paper... Hope this help.... CHEERS...
Manikandan
THNX guys got relieved when i saw ur answers ... but the question and answers and the paragraph writing .... :p . The main problem i am having i think is the HINDI was not so vast in the past years and like i dont understand it so well ..... if i cant understand the story ,how can i .. u know Keep it in my Mind ! :p Regards Wish All Good Luck For The Board Exams ISHAAN
K jyothi
the problem with many of us is dat v do not write nd learn hindi i think if u write and learn nd read the chapters regularly u wont face a problem
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2019-10-18 02:29:45
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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": 4, "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": 0.22753873467445374, "perplexity": 3886.4428874081837}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986677412.35/warc/CC-MAIN-20191018005539-20191018033039-00127.warc.gz"}
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https://blog.yourlabs.org/posts/2016-03-04-django-responsediff-030/
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# django-responsediff 0.3.0
django-responsediff 0.3.0 has been released !
It now also checks the status_code, and has a cute mixin:
from responsediff.test import ResponseDiffTestMixin
class MixinTest(ResponseDiffTestMixin, test.TestCase):
self.assertResponseDiffEmpty(test.Client().get('/admin/'))
The above will fail on the first time with FixtureCreated to indicate that it has written responsediff/tests/response_fixtures/MixinTest.test_admin/{content,status_code}.
This file is meant to be added to version control. So next time this will run, it will check that response.status_code and response.content is the same, in future version, or in other configurations (ie. py35, py27, pypy, etc …).
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2020-02-28 12:46:49
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http://math.sns.it/paper/2215/
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# Metastability and dynamics of discrete topological singularities in two dimensions: a $\Gamma$-convergence approach
created by ponsiglio on 30 Jul 2013
modified by alicandr on 03 Mar 2015
[BibTeX]
Published Paper
Inserted: 30 jul 2013
Last Updated: 3 mar 2015
Journal: Archive Rational Mech. Anal.
Volume: 214
Pages: 269-330
Year: 2014
Abstract:
This paper aims at building a variational approach to the dynamics of discrete topological singularities in two dimensions, based on $\Gamma$-convergence.
We consider discrete systems, described by scalar functions defined on a square lattice and governed by periodic interaction potentials. Our main motivation comes from $XY$ spin systems, described by the phase parameter, and screw dislocations, described by the displacement function. For these systems, we introduce a discrete notion of vorticity. As the lattice spacing tends to zero we derive the first order $\Gamma$-limit of the free energy which is referred to as renormalized energy and describes the interaction of vortices.
As a byproduct of this analysis, we show that such systems exhibit increasingly many metastable configurations of singularities. Therefore, we propose a variational approach to depinning and dynamics of discrete vortices, based on minimizing movements. We show that, letting first the lattice spacing and then the time step of the minimizing movements tend to zero, the vortices move according with the gradient flow of the renormalized energy, as in the continuous Ginzburg-Landau framework.
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2018-02-19 04:17:06
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https://math.stackexchange.com/questions/3313672/what-test-should-i-use-to-prove-the-convergence-of-the-following-series
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# What test should I use to prove the convergence of the following series?
Prove the convergence or divergence of the following series
A) $$\sum_{n=1}^\infty \frac{1}{2^n +n}$$
B) $$\sum_{n=1}^\infty \frac{ln(n)}{n}$$
C) $$\sum_{n=1}^\infty tan(\frac{1}{n \sqrt (n)})$$
In A) I tried using the direct comparison test: I wrote $$2^n +n>2^n$$ so $$\frac{8}{2^n +n} < \frac{8}{2^n}$$. And as $$8. \frac{1}{2^n}$$ converges, the other one converges. Is it ok?
In B) I also thought about direct comparison test, but I don't know what series I should use to compare.
In C) I don't know what test to use.
For B use $$\frac{\ln{(n)}}{n}\gt\frac1n$$ Then for C use $$\tan\left(\frac1{n^{3/2}}\right)\lt\frac2{n^{3/2}}$$
• But $\frac{ln(n)}{n}$ is not always bigger than $\frac{1}{n}$ does it matter? Aug 4, 2019 at 22:23
• As long as it is true for infinitely many $n$ (above a certain number) then the comparison test works. Aug 4, 2019 at 22:25
Your method for A) is good. You don't have to use $$\frac{8}{2^n}$$, you can just use $$\frac{1}{2^n}$$
For B), you can use direct comparison with $$\sum_{n=1}^{\infty}\frac{1}{n}$$
For C), you can use direct comparison with $$\sum_{n=1}^{\infty}\frac{2}{n\sqrt{n}}$$ which is then a p-series.
First one is correct!
For second one, we have $$\ln(x) > 1$$ after $$x = e$$, so we can start the sum from $$n>e$$ or $$n \geq 3$$.So, $$\sum_{n=3}^{\infty} \frac{\ln(n)}{n} > \sum_{n=3}^{\infty} \frac{1}{n}$$, so by limit comparision test the series diverges!, also you can work out the same using integral test, approximating the sum as the integral as $$\sum_{n=1}^{\infty} \frac{\ln(n)}{n} \approx \int_{1}^{\infty} \frac{\ln(x)}{x}dx$$.
For the third we have for large $$n$$, $$\tan(\frac{1}{n\sqrt{n}})$$ is smaller and we can use the approximation $$\tan(x) \approx x$$ for small $$x$$. After this you can use the limit comparision test to show the convergence of the sum of the series!
Your answer to part $$A$$ is correct
For part $$B$$ use integral test
For part $$C$$ use limit comparison test with $$\sum _1^{\infty} \frac {1}{n\sqrt n}$$
Note first that a necessary condition for convergence of a series $$\sum_{n=1}^{\infty}a_{n}$$ is that the sequence $$a_{n}$$ tends to zero for $$n\to \infty$$.
Once you observe that $$|a_{n}|$$ doesn't become arbitrarily small as n increases you already know that the series must diverge.
In A,B the necessary condition for convergence is satisfied
In A the comparison $$\frac{1}{2^n+n}<\frac{1}{2^n}$$ works just fine since we know that the series $$\sum_{n=1}^{\infty}\frac{1}{2^n}$$ converges to 1. In case you might not know or remember,the last fact is due to the following fact about geometric series $$\sum_{n=0}^{\infty}q^n=\frac{1}{1-q}\ \text{for all}\ 0 and follows from this formula we can derive for the partial sums $$\sum_{k=0}^{n}q^k=\frac{1-q^{n+1}}{1-q}$$.
For part B note that the comparison test works in two directions
If $$0\leq a_{n}\leq b_{n}$$ for $$n\geq k$$ for some k ,then
1) Convergence of $$\sum_{n=1}^{\infty}b_{n}$$ implies convergence of $$\sum_{n=1}^{\infty}a_{n}$$
2) Divergence of $$\sum_{n=1}^{\infty}a_{n}$$ implies divergence of $$\sum_{n=1}^{\infty}b_{n}$$
And then consider the harmonic series $$\sum_{n=1}^{\infty}\frac{1}{n}$$,
which is a series which satisfies the necessary condition for convergence but is divergent.
If k is choosen sufficiently large $$\frac{1}{n}\leq \frac{ln(n)}{n}$$ for all $$n\geq k$$
This implies that the series $$\sum_{n=1}^{\infty}\frac{ln(n)}{n}$$ must diverge.
https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)
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2022-08-12 02:49:55
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http://googology.wikia.com/wiki/User_blog:Dhacorrea/Sumselfgogopyr
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## FANDOM
10,818 Pages
Sumselfgogopyr is defined as the summation of the n-th n-gonal pyramidal numbers with n from 3 to gogopyr, the term was coined by Daniel Corrêa.
Sumselfgogopyr is computed as described below:
$$Sumselfgogopyr = \sum^{gogopyr}_{n=3} \frac{3 \cdot n^{2} + n^{3} \cdot (n-2) - n \cdot (n-5)}{6}$$
Sumselfgogopyr has 1995 digits, and according to the calculations using BCalc to convert gogopyr to power of 10 notation, and using WolframAlphato perform the calculation with the maximum input length, the approximated form of sumselfgogopyr is:
$$Sumselfgogopyr \approx 4.28669410150... \times 10^{1994}$$
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2017-08-16 23:40:20
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https://math.stackexchange.com/questions/2189065/a-curious-summation-question-from-pre-rmo-2016
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# A curious summation question from pre-RMO 2016
This problem came in the Pre-RMO (Regional Mathematics Olympiad) - Delhi Region (INDIA). I've been solving these questions, and this particular summation question is proving to be quite difficult.
The question:
Consider the 50 term sums:
$$S = \frac{1}{1 \times 2} +\frac{1}{3\times 4} + \dots + \frac{1}{99 \times 100}$$ $$T = \frac{1}{51 \times 100} + \frac{1}{52 \times 99} + \dots + \frac{1}{100 \times 51}$$ The ratio $\frac{S}{T}$ is written in the lowest form $\frac{m}{n}$ where $m, n$ are relatively prime natural numbers. Find the value of $m + n$.
This is what I've tried so far:
We can re-write $S$ and $T$ as: $$S = \sum_{i=1}^{50}\frac{1}{(2i-1)\times(2i)}$$ $$= \sum_{i=1}^{50}\frac{1}{2i-1} - \frac{1}{2i}$$ $$T = \sum_{i=1}^{50}\frac{1}{(50+i)\times(101-i)}$$ $$= \frac{1}{151}\sum_{i=1}^{50}\frac{1}{50+i} + \frac{1}{101-i}$$
I expected these to be telescopic sums, and thus the terms could be cancelled out. But apparently not.
I've only reached this far. What are the next steps, or is there an easier way to find the ratio?
Thanks!
The answer is 153. Write $A=\sum_{i=1}^{50} \dfrac{1}{i}$ and $B=\sum_{i=1}^{50} \dfrac{1}{2i-1}$. Then $S=B-A/2$ and you can simplify $T$ as $T=\dfrac{2}{151}(B-A/2)$. Thus $S/T=151/2$.
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2019-06-26 22:20:15
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https://tex.stackexchange.com/questions/347327/section-title-above-table-in-landscape-mode
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# Section title above table in landscape mode
Like in this post (here) I would like to put the name of the appendix on the top of the page which is in landscape mode. In deviation of the one who started that topic, I would like to have the title of the page at the shortest side of the paper (so, at your right side if it is in landscape mode). I tried something similar as the one who answered that topic, but that does not work.
\documentclass[11pt]{article}
\usepackage[textwidth=155mm,top=23.5mm,bottom=23.5mm,
footskip=40pt,heightrounded, showframe]{geometry}
\usepackage[skip=0.33\baselineskip]{caption}
\usepackage[table,xcdraw]{xcolor}
\usepackage[flushleft]{threeparttable}
\usepackage{booktabs, makecell}
\usepackage{pdflscape}
\usepackage{appendix}
\begin{document}
\newgeometry{left=3cm,bottom=0.1cm, top=1cm}
\begin{landscape} \section{Appendix}
\setcounter{table}{0}
\renewcommand*\thetable{\Alph{section}.\arabic{table}} \subsection{Unit root tests}
\leavevmode\vfill
\begin{table}[ht]
\centering\setlength{\tabcolsep}{3pt}
\begin{threeparttable}
\caption{P-values of Augmented Dickey-Fuller Test}
\label{my-label}
\begin{tabular}{@{}llllllllllllll@{}}
\toprule
Variable & Austria & Belgium & Finland & France & Germany & Netherl. & Greece & Italy & Ireland & Portugal & Spain & All eurozone & US \\ \midrule
\textit{Yield-OIS (10y)} & 0.1807 & 0.1912 & 0.1255 & 0.3142 & 0.1641 & 0.1995 & 0.4182 & 0.4180 & 0.5964 & 0.6333 & 0.4743 & & \textbf{0.0437} \\
\textit{CDS } & 0.0779 & 0.2706 & 0.3143 & 0.2230 & 0.0938 & 0.2775 & 0.7790 & 0.1399 & 0.2852 & 0.3403 & 0.2272 & & \\
\textit{Redom} & \textbf{0.0005} & 0.1273 & \textbf{0.0001} & \textbf{0.0287} & & 0.0718 & 0.6975 & 0.2210 & 0.6008 & 0.5033 & 0.4064 & & \\
\textit{BAS }& \textbf{0.0000} & \textbf{0.0111} & \textbf{0.0012} & \textbf{0.0000} & \textbf{0.0000} & 0.0021 & \textbf{0.0026} & 0.0000 & 0.3094 & 0.4802 & 0.0000 & & \\
\textit{OIS rate (10y)} & \multicolumn{1}{c}{} & & & & & & & & & & & 0.8880 & 0.0907 \\
\textit{VSTOXX} & \multicolumn{1}{c}{\textbf{}} & & & & & & & & & & & \textbf{0.0009} & \\
\textit{CESI} & \multicolumn{1}{c}{\textbf{}} & & & & & & & & & & & \textbf{0.0246} & \textbf{0.0146} \\ \bottomrule
\end{tabular}
\begin{tablenotes}[para,flushleft] \footnotesize{
\item \textbf{Notes}: This table shows the p-values of the Augmented Dickey-Fuller (ADF) test. The null hypothesis is that the variable has a unit root. This hypothesis is rejected when the p-value < 0.05 (highlighted in bold). The ADF with trend and intercept has been performed if variables have a clear trend. The column ''All eurozone'' shows the p-values for the time series observations. All variables in this test are measured in level values.}
\end{tablenotes}
\end{threeparttable}
\end{table}
\vfill
\end{landscape}
\restoregeometry
\end{document}
• Are all those packages really necessary in your minimal working example? – totera Jan 5 '17 at 20:59
• Sorry, my bad. I forgot to delete the ones that are not relevant anymore. I edited my MWE. – peter Jan 5 '17 at 21:38
• sorry, where the section title should be? now it is in landscape orientation on the left top page corner. do you like that it is at right page corner, or that it stay in place where it is in portrait orientation? if latter is the case, than page should stay in portrait orientation and be only table rotated. – Zarko Jan 5 '17 at 22:47
• can you show a hand drawn sketch, which show page layout , table position on section title position? – Zarko Jan 5 '17 at 22:49
• Yes it is what you referred to as the latter. So, I would like to have the titles (section and subsection) on the right page corner (which is the same as on the top corner in portrait mode). I have tried to do this with the rotate environment. However, the titles than do not fit on the page and the table is not centered. Especially the first is important. – peter Jan 6 '17 at 0:39
Do you want this?
Note that you should not use ' for an opening quotation mark. Use instead.
\documentclass[11pt]{article}
\usepackage[textwidth=155mm,top=23.5mm,bottom=23.5mm,footskip=40pt,heightrounded, showframe]{geometry}
\usepackage[skip=0.33\baselineskip]{caption}
\usepackage[flushleft]{threeparttable}
\usepackage{booktabs,rotating}
\begin{document}
\newgeometry{left=3cm,bottom=0.1cm, top=1cm}
\section{Appendix}
\setcounter{table}{0}
\renewcommand*\thetable{\Alph{section}.\arabic{table}}
\subsection{Unit root tests}
\begingroup
\vfill
%\centering % uncomment to centre the table horizontally as well as vertically
\begin{sideways}
\setlength{\tabcolsep}{3pt}
\begin{threeparttable}
\caption{P-values of Augmented Dickey-Fuller Test}
\label{my-label}
\begin{tabular}{@{}llllllllllllll@{}}
\toprule
Variable & Austria & Belgium & Finland & France & Germany & Netherl. & Greece & Italy & Ireland & Portugal & Spain & All eurozone & US \\ \midrule
\textit{Yield-OIS (10y)} & 0.1807 & 0.1912 & 0.1255 & 0.3142 & 0.1641 & 0.1995 & 0.4182 & 0.4180 & 0.5964 & 0.6333 & 0.4743 & & \textbf{0.0437} \\
\textit{CDS } & 0.0779 & 0.2706 & 0.3143 & 0.2230 & 0.0938 & 0.2775 & 0.7790 & 0.1399 & 0.2852 & 0.3403 & 0.2272 & & \\
\textit{Redom} & \textbf{0.0005} & 0.1273 & \textbf{0.0001} & \textbf{0.0287} & & 0.0718 & 0.6975 & 0.2210 & 0.6008 & 0.5033 & 0.4064 & & \\
\textit{BAS }& \textbf{0.0000} & \textbf{0.0111} & \textbf{0.0012} & \textbf{0.0000} & \textbf{0.0000} & 0.0021 & \textbf{0.0026} & 0.0000 & 0.3094 & 0.4802 & 0.0000 & & \\
\textit{OIS rate (10y)} & \multicolumn{1}{c}{} & & & & & & & & & & & 0.8880 & 0.0907 \\
\textit{VSTOXX} & \multicolumn{1}{c}{\textbf{}} & & & & & & & & & & & \textbf{0.0009} & \\
\textit{CESI} & \multicolumn{1}{c}{\textbf{}} & & & & & & & & & & & \textbf{0.0246} & \textbf{0.0146} \\ \bottomrule
\end{tabular}
\begin{tablenotes}[para,flushleft]
\footnotesize
\item \textbf{Notes}: This table shows the p-values of the Augmented Dickey-Fuller (ADF) test. The null hypothesis is that the variable has a unit root. This hypothesis is rejected when the p-value < 0.05 (highlighted in bold). The ADF with trend and intercept has been performed if variables have a clear trend. The column All eurozone'' shows the p-values for the time series observations. All variables in this test are measured in level values.
\end{tablenotes}
\end{threeparttable}
\end{sideways}
\vfill
\restoregeometry
\endgroup
\end{document}
If you want the table centred horizontally, as Zarko suggests, simply uncomment the line indicated:
EDITED in light of Zarko's suggestions/corrections.
• For caption in threeparttable should be caption sufficient . From OP comment I understand, that the table should be vertical and horizontal centered. Horizontal centering can be achieved by adding of \hfil after first \vfill . – Zarko Jan 6 '17 at 2:52
• @Zarko Thanks :-). I didn't know that about threeparttable. Seems odd to me, but handy, perhaps. I would just use \centering for the horizontal centring, if that's needed, but you're obviously right that \hfill` would work. – cfr Jan 6 '17 at 23:39
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2020-06-04 05:04:41
|
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https://www.zigya.com/previous-year-papers/ssccgl/12/Reasoning/2017/SSCCGL2017070
|
## Test Series
Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.
## Test Yourself
Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
# SSCCGL Reasoning Solved Question Paper 2017
#### Multiple Choice Questions
5.
In the following question, find the odd letter from the given alternatives.
• KQ
• DJ
• SZ
• RX
C.
SZ
8.
A series is given with one term missing. Select the correct alternative from the given ones that will complete the series.
A, C, E, G, ?
• H
• I
• J
• F
B.
I
$\mathrm{A}\stackrel{+2}{\to }\mathrm{C}\stackrel{+2}{\to }\mathrm{E}\stackrel{+2}{\to }\mathrm{G}\stackrel{+2}{\to }\overline{)\mathrm{I}}$
10.
Hitesh, Sunny, Vicky, Nitin and Bharat are arranged in ascending order of the height from the top. Hitesh is at third place. Bharat is between Nitin and Hitesh while Nitin is not at the bottom. Who has the maximum height among them?
• Hitesh
• Sunny
• Vicky
• Nitin
D.
Nitin
4.
In the following question, find the odd word from the given alternatives.
• Venus : Planet
• Moon : Satellite
• Jupiter : Black Hole
• Sun : Star
C.
Jupiter : Black Hole
Option (3) is odd as 'Jupiter' is a planet not a 'black hole'.
9.
A series is given with one term missing. Select the correct alternative from the given ones that will complete the series.
2, 4, 13, 41, 106, ?
• 172
• 191
• 219
• 232
D.
232
3.
In the following question, select the related numbers from the given alternatives.
50 : 65 : : 122 : ?
• 157
• 145
• 147
• 155
B.
145
50 : 65
The logic is:
(7)2 + 1 = 50
(8)2 + 1 = 65
Similarly,
122 : ?
(11)2 + 1 = 122
(12)2 + 1 = 145
2.
In the following question, select the related letter from the given alternative.
HMPU : IOSY : : GMRF : ?
• FKOB
• HOUJ
• HPUJ
• HOJU
B.
HOUJ
6.
In the following question, find the odd number from the given alternatives.
• 361
• 441
• 784
• 876
C.
784
Except '876' all are perfect square numbers.
7.
Arrange the given words in the sequence in which they occur in the dictionary.
1. Herbivorous
2. Harmony
3. House
4. Honour
5. Helm
• 12543
• 25143
• 21534
• 12354
B.
25143
Harmony → Helm → Herbivorous → Honour → House
1.
In the following question, select the related word from the given alternatives.
Vacant : Empty : : Dearth : ?
• Descend
• Scarcity
• Squander
• Abundant
B.
Scarcity
As 'Vacant' and 'Empty' are synonyms to each other. Similarly, 'Dearth' and 'Scarcity' are synonyms to each other.
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2021-10-25 16:39:42
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https://blog.biyeta.com/bbwh5/a1d01c-arecibo-observatory-construction
|
# arecibo observatory construction
Over 100,000 visitors come per year to the new facility, about 30% of them school children. American astronomers Russell Hulse and Joseph H. Taylor, Jr., used Arecibo to discover the first binary pulsar. Three years later the Arecibo Ionospheric Observatory (AIO) was in operation under the direction of Gordon. Given that we didn't really expect to lose Arecibo for more than about a year $^{\dagger}$ , … Arecibo Observatory Construction ( page 1 ) *images may be downloaded for non-profit / non commercial use ( 300dpi ) Please acknowledge all photos with following credit: courtesy of the NAIC - Arecibo Observatory, a facility of the NSF The Arecibo Observatory is a facility of the National Science Foundation operated under cooperative agreement by the University of Central Florida. That was the dream that built Puerto Rico’s Arecibo Observatory, which collapsed earlier this week. Image: Location Arecibo Observatory Route 625 Bo. They showed that it was losing energy through gravitational radiation at the rate predicted by physicist Albert Einstein’s theory of general relativity, and they won the Nobel Prize for Physics in 1993 for their discovery. This article was most recently revised and updated by, https://www.britannica.com/topic/Arecibo-Observatory, Federation of American Scientists - The Arecibo Ionospheric Observatory, Laser Interferometer Gravitational-Wave Observatory. we'll have to spread out the observing. The platform that collapsed was original to the 1960s construction but became significantly heavier in the 1990s, when new instruments were added. . On December 1, 2020, days after the NSF’s announcement, the cables broke, and the central platform collapsed into the dish. Video has emerged of the collapse of the world-famous Arecibo Observatory in Puerto Rico. The antenna structures could be moved in any direction, making it possible to track a celestial object in different regions of the sky. Following a review of engineering assessments that found damage to the Arecibo Observatory cannot be stabilized without risk to construction workers and staff at the facility, the U.S. National Science Foundation will begin plans to decommission the 305-meter telescope, which for 57 years has served as a world-class resource for radio astronomy, planetary, solar system, and geospace … The new transmitter combined with the telescope forms the world's most powerful radar system. Unless someone was to build an identical observatory at the same latitude as Arecibo, with the same frequency range, receiver options and field of view . The instrument platform of the 305-meter telescope at Arecibo Observatory in Puerto Rico collapsed overnight, according to the National Science Foundation. The platform is … The 305-metre (1,000-foot) radio telescope at the Arecibo Observatory, Puerto Rico. The Arecibo Observatory's radio telescope was built in a natural sinkhole in Puerto Rico, construction was completed in 1963. An engineering survey found the damage to the observatory cannot be stabilized without risk to construction workers and staff. Omissions? Arecibo Observatory’s telescope consists of a radio dish 305m in diameter with a 900-ton instrument platform hanging 137m above. Be on the lookout for your Britannica newsletter to get trusted stories delivered right to your inbox. Gordon's persistence culminated in the construction of the AO which began in the Summer of 1960. June 1960, Before Construction Began. All the bright (radar-reflective) features are believed to be deposits of frozen volatile substances, likely water ice, at least several metres thick in the permanently shaded floors of craters. After a second cable broke in November 2020, the National Science Foundation (NSF) announced that the telescope was in danger of collapse and the cables could not be safely repaired. In August 2020 a cable holding up the central platform snapped and made a hole in the dish. Corrections? Gordon’s persistence culminated in the construction of the Arecibo Observatory which began in the summer of 1960. Esperanza Arecibo, PR 00612 Map Contact info@naic.edu 787.878.2612. The largest number of observatories are…. This instrument, built in the early 1960s, employed a 305-metre (1,000-foot) spherical reflector consisting of perforated aluminum panels that focused incoming radio waves on movable antenna structures positioned about 168 metres (550 feet) above the reflector surface. Even if the repairs could be done safely, the engineering team determined the structure would present long-term stability issues. . Therefore, the NSF will decommission Arecibo Observatory’s 1,000-foot telescope. Mercury's north polar region, in a radar image obtained with the Arecibo radio telescope. More recently, Arecibo detected organic molecules in a distant galaxy and discovered the first repeating fast radio burst. The NSF thus planned to decommission the observatory. It was the site of the world’s largest single-unit radio telescope until FAST in China began observations in 2016. By signing up for this email, you are agreeing to news, offers, and information from Encyclopaedia Britannica. Following a review of engineering assessments that found damage to the Arecibo Observatory cannot be stabilized without risk to construction workers … …(1,600-foot-) diameter dish at the Five-hundred-metre Aperture Spherical Telescope in China and its receivers, is employed and if identical equipment is employed on some transmitting planet, how far apart could the transmitting and receiving planets be for intelligible signals to be passed? The Arecibo dish was damaged following a series of cable failures, and the National Science Foundation (NSF) has decided it would be too dangerous to repair. Updates? Construction of Arecibo Observatory] [field_categories_portfolios] Location Arecibo Observatory Route 625 Bo. Beginnings: Arecibo Observatory was built in 1963 by the U.S. Air Force under the initiative of Professor William Gordon in the Department of Electrical Engineering and his colleagues at Cornell. Let us know if you have suggestions to improve this article (requires login). aug24-1962 1496 Kb : sep71962 1533 Kb: sep14-1962 1428 Kb : oct30-1962 1297 Kb: This can result in images of remarkable resolution: about one-half mile (1 km) for the surface of Venus, down to 50 feet (15 meters) for asteroids and comets. The formal opening ceremony took place on November 1, 1963. Following a review of engineering assessments that found damage to the Arecibo Observatory cannot be stabilized without risk to construction workers … The U.S.’s famed Arecibo Observatory survived all manners of threats since its construction in a bowl-shaped natural sinkhole in the forested hills of Puerto Rico in 1963. Completed in 1963 and stewarded by U.S. National Science Foundation since the 1970s, Arecibo Observatory has contributed to many important scientific discoveries, including the demonstration of gravitational waves from a binary pulsar, the first discovery of an extrasolar planet, composition of the ionosphere, and the characterization of the properties and orbits of a number of potentially hazardous … It is interesting to note that controversy has often followed the construction of large astronomy facilities. The Arecibo Observatory in Puerto Rico suffered serious damage to its giant radio telescope dish when a support cable broke on Aug. 10, 2020. Scientists using the Arecibo Observatory discovered the first extrasolar planets around the pulsar B1257+12 in 1992. The observatory, which … ... eg during construction - … The Arecibo Observatory is a facility of the National Science Foundation operated under cooperative agreement by the University of Central Florida. The observatory also produced detailed radar maps of the surface of Venus and Mercury and discovered that Mercury rotated every 59 days instead of 88 days and so did not always show the same face to the Sun. Observatories can be classified on the basis of the part of the electromagnetic spectrum in which they are designed to observe. The rather astonishing answer is about 2,500 light-years.…, Astronomical observatory, any structure containing telescopes and auxiliary instruments with which to observe celestial objects. According to the journal Nature, the cable that failed in November, setting up Arecibo’s ultimate demise, dates all the way back to the telescope’s construction in 1963. History On March 1, 1997, after eight years of fund-raising, planning and construction, the Observatory inaugurated its "Angel Ramos Foundation" Visitor Center. The planetary astronomer Frank Drake, who conducted the first radio SETI search the same year that construction on Arecibo began, served as the observatory’s director for years. NSF officials said Dec. 3 it was too early to determine whether, and how, it may be rebuilt. Arecibo Observatory, astronomical observatory located 16 km (10 miles) south of the town of Arecibo in Puerto Rico.It was the site of the world’s largest single-unit radio telescope until FAST in China began observations in 2016. Our editors will review what you’ve submitted and determine whether to revise the article. Arecibo Observatory Construction ( page 2 ) *images may be downloaded for non-profit / non commercial use ( 300dpi ) Please acknowledge all photos with following credit: courtesy of the NAIC - Arecibo Observatory, a facility of the NSF. With its 305m (1000ft) diameter dish constructed in 1963, the Arecibo Observatory continuously provides valuable data for the scientific community and the world.” From the beginning there were certain requirements for the site. At 1,000 feet (305 meters) across, Arecibo Observatory was the largest single radio dish in the world until 2016, when China completed its Five-hundred-meter … That is sensitive enough to detect a steel golf ball at the distance of the moon. Radar: The 1997 upgrade includes a doubling of the power of the transmitter, to 1 million watts from about 420,000 watts, used for radar studies of the solar system. 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2021-05-12 17:11:57
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https://khipu.ai/posters-2/
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# posters-2
## Poster session 2
2 - 1
A Budged-Balanced Tolling Scheme for Efficient Equilibria under Heterogeneous Preferences
Gabriel de O. Ramos, Roxana Radulescu, Ann Nowé
Gabriel de Oliveira Ramos
Multiagent reinforcement learning has shown its potential for tackling real world problems, like traffic. We consider the toll-based route choice problem, where self-interested drivers need to repeatedly choose routes that minimise their travel times. A major challenges here is to deal with agents' selfishness when competing for a common resource, as they tend to converge to a substantially far-from-optimum equilibrium. In traffic, this translates into higher congestion levels. Road tolls have been advocated as a means to tackle this issue, though typically assuming that (i) drivers have homogeneous preferences, and that (ii) collected tolls are kept for the traffic authority. In this paper, we propose Generalised Toll-based Q-learning (GTQ-learning), a multiagent reinforcement learning algorithm capable of realigning agents' heterogeneous preferences with respect to travel time and monetary expenses. GTQ-learning neutralises agents' preferences, thus ensuring that congestion levels are minimised regardless of agents' selfishness levels. Furthermore, GTQ-learning achieves approximated budget balance by redistributing a fraction of the collected tolls. We perform a theoretical analysis of GTQ-learning, showing that it leads agents to a system-efficient equilibrium, and provide empirical results, evidencing that GTQ-learning minimises congestion on realistic road networks.
multiagent reinforcement learning, route choice, marginal-cost tolling
2 - 2
A Hierarchical Two-tier Approach to Hyper-parameter Optimization in Reinforcement Learning
Juan Cruz Barsce, Jorge Palombarini, Ernesto Martínez
Juan Cruz Barsce
Optimization of hyper-parameters in reinforcement learning (RL) algorithms is a key task, because they determine how the agent will learn its policy by interacting with its environment, and thus what data is gathered. In this work, an approach that uses Bayesian optimization to perform a two-step optimization is proposed: first, categorical RL structure hyper-parameters are taken as binary variables and optimized with an acquisition function tailored for such variables. Then, at a lower level of abstraction, solution-level hyper-parameters are optimized by resorting to the expected improvement acquisition function, while using the best categorical hyper-parameters found in the optimization at the upper-level of abstraction. This two-tier approach is validated in a simulated task.
reinforcement learning, hyper-parameter optimization, bayesian optimization
2 - 3
A Novel Deviation Bound via Mutual Information for Cross-Entropy Loss
Matias Vera, Pablo Piantanida and Leonardo Rey Vega
Matias Alejandro Vera
Machine learning theory has mostly focused on generalization to samples from the same distribution as the training data. Whereas a better understanding of generalization beyond the training distribution where the observed distribution changes is also fundamentally important to achieve a more powerful form of generalization. In this paper, we attempt to study through the lens of information measures how a particular architecture behaves when the true probability law of the samples is potentially different at training and testing times. Our main result is that the testing gap between the empirical cross-entropy and its statistical expectation (measured with respect to the testing probability law) can be bounded with high probability by the mutual information between the input testing samples and the corresponding representations, generated by the encoder obtained at training time. These results of theoretical nature are supported by numerical simulations showing that the mentioned mutual information is representative of the testing gap, capturing qualitatively the dynamic in terms of the hyperparameters of the network.
mutual information, deviation bound, generalization
2 - 4
Anatomical Priors for Image Segmentation via Post-Processing with Denoising Autoencoders
Agostina Larrazabal, César Martinez, Enzo Ferrante
Agostina
"We introduce Post-DAE, a post-processing method based on denoising autoencoders to improve the anatomical plausibility of arbitrary biomedical image segmentation algorithms. Some of the most popular segmentation methods still rely on post-processing strategies like conditional random fields to incorporate connectivity constraints into the resulting masks. Even if it is a valid assumption in general, these methods do not offer a straightforward way to incorporate more complex priors like convexity or arbitrary shape restrictions. Post-DAE leverages the latest developments in manifold learning via denoising autoencoders. We learn a low-dimensional space of anatomically plausible segmentations, and use it to impose shape constraints by post-processing anatomical segmentation masks obtained with arbitrary methods. Our approach is independent of image modality and intensity information since it employs only segmentation masks for training. We performed experiments in segmentation of chest X-ray images. Our experimental results show that Post-DAE can improve the quality of noisy and incorrect segmentation masks obtained with a variety of standard methods, by bringing them back to a feasible space, with almost no extra computational cost."
anatomical segmentation, autoencoders, post-processing
2 - 5
Asistente de velocidad vehicular como agente de control en entornos urbanos
Rodrigo Velázquez
Rodrigo Manuel Velázquez Galeano
El trabajo busca plantear el modelo de un sistema asistente de velocidad vehicular que sea capaz de identificar coordenadas, en el vehículo y compararlas con las coordenadas almacenadas, por medio de una webApp implementando API’S de google maps, en una base de datos de marcas de velocidad de zonas urbanas, y alertar al conductor si excede en alguna de ellas a medida que vaya avanzando en su recorrido, lo que puede contribuir de gran manera al desarrollo de esta línea de investigación y a mejorar de forma notable las posibilidades de implementar en un futuro no muy lejano en un automóvil que pueda ser completamente asistido por un computador, teniendo en cuenta estos principios aquí mencionados.
2 - 6
Assisted Optimal Transfer of Excitation Energy by Deep Reinforcement Learning
Joseph Vergel-Becerra and Leonardo A. Pachón
Joseph Vergel
"The high efficiency of energy transfer is one of the main motivations in the study of light-harvesting systems. The accurate description of these complexes can be formulated in the framework of open quantum systems which comprises the interaction among their fundamental units called chromophores and the interaction with the environment. Maximizing energy transfer involves optimally controlled system dynamics and at the same time, getting optimal configurations that achieve this objective. Therefore, this research proposes the implementation of reinforcement learning (RL) as a mechanism for quantum optimal control of excitation energy transfer (EET) in light-harvesting systems and, in turn, obtaining configurations that maximize efficiency through a classical agent that even can tolerate environments with high noise levels. "
reinforcement learning, open quantum systems, excitation energy
2 - 7
Bert's behavior evaluation using Stress test
"Recently, several machine learning based models have been proposed for Natural Language Processing (NLP), achieving outstanding results, by using powerful architectures like “Transformer” (Vaswani et al., 2017) and pretraining on large text corpus, as is the case of BERT (Devlin et al., 2018). However, it has been shown that language models are fragile (they are easily broken) and biased (instead of an actual comprehension of the text, they tend to take advantage of data biases). To the best of our knowledge, this is the first time a Transformer-based model is systematically put to test."
natural language processing, language models, evaluation
2 - 8
Biomarker discovery on multi-omic data using Kernel Learning and Autoencoders
Martin Palazzo, Patricio Yankilevich, Pierre Beauseroy
Martin Palazzo
Molecular data from cancer patients is characterized by tens of thousands of gene features and also by different modalities or ‘omics’ like Genomics, Transcriptomics and Proteomics. These systems are also labeled by clinical information like patient survival, tumor stage and tumor subtype. The initial high dimensional input space is noisy and makes complicated to find useful patterns like similarities between tumor types and sub-types. For clinical reasons this work aims to learn meaningful and lower dimensional representations of tumors which keeps biological signals and contribute to classify tumor subtype or stage by using Variational Autoencoders (VAE) and Kernelized Autoencoders (KAE) . Then a feature selection strategy based on Multiple Kernel Learning is executed with the objective to approximate as much as possible the resulting representation based on the selected features to the one learned by the autoencoders. Selected features are also evaluated to classify tumor samples based on clinical labels and also to discover tumor subtypes. Preliminary results show that the learned representations drive the selection of meaningful genes associated to the clinical outcome of the patient and thus provide evidence for potential biomarkers.
kernel learning, autoencoders, cancer genomics
2 - 9
Bottom-Up Meta-Policy Search
Luckeciano C Melo, Marcos Máximo, Adilson Cunha
Luckeciano
Despite of the recent progress in agents that learn through interaction, there are several challenges in terms of sample efficiency and generalization across unseen behaviors during training. To mitigate these problems, we propose and apply a first-order Meta-Learning algorithm called Bottom-Up Meta-Policy Search (BUMPS), which works with two-phase optimization procedure: firstly, in a meta-training phase, it distills few expert policies to create a meta-policy capable of generalizing knowledge to unseen tasks during training; secondly, it applies a fast adaptation strategy named Policy Filtering, which evaluates few policies sampled from the meta-policy distribution and selects which best solves the task. We conducted all experiments in the RoboCup 3D Soccer Simulation domain, in the context of kick motion learning. We show that, given our experimental setup, BUMPS works in scenarios where simple multi-task Reinforcement Learning does not. Finally, we performed experiments in a way to evaluate each component of the algorithm.
imitation learning, meta-learning, robotics
2 - 10
Classification of SAR Images using Information Theory
Eduarda T. C. Chagas, Alejandro C. Frery and Heitor S Ramos
Eduarda Tatiane Caetano Chagas
The Classification of regions, especially urban areas, on synthetic aperture polarimetric radar (PolSAR) data is a challenging task. We know that texture analysis has a great informational power of the spatial properties of the main elements of the image, being one of the most important techniques in image processing and pattern recognition. The first task of this analysis is the extraction of discriminant features capable of efficiently incorporating information about the characteristics of the original image. Based on this principle, in this paper, we propose a new classification technique. Through the analysis of the textures of these images, ordinal pattern transition graphs, and information theory descriptors, we achieved a high discriminatory power in the characterization and classification of the regions under study.
sar image, classification, theory information
2 - 11
Clustering of climate time series
Y. Barrera, M. Jonckheere, V. Lefieux, D. Picard, A. Umfurer , E. Smucler,
Matthieu Jonckheere
The fluctuations in the temperature have a strong influence in the electric consumption. As a consequence, identifying and finding groups of possible climate scenarios is useful for the analysis of the electric supply system. The scenarios data that we are considering are time series of hourly measured temperatures over a grid of geographical points in France and neighboring areas, used by the French company RTE . Clustering techniques are useful for finding homogeneous groups of times series but the challenge is to find a suitable data transformation and distance metric. In this work, we used several transformations (fourier, wavelets, autoencoders) and distance metrics (DTW and euclidean among others) and found consistent groups of climate scenarios using clustering techniques. We give several performance indicators and we findd that k-shape performs the best according to some of them.
clustering, performance, time series
2 - 12
Complex Data Relevance Analysis for Event Detection
Caroline Mazini Rodrigues, Luis Pereira, Anderson Rocha, Zanoni Dias
Caroline Mazini Rodrigues
Considering the occurrence of an event with high social impact, it is important to establish a space-time relation of available information and so, answer some questions about the event as“who”, “how”, “where” and “why”. This work is part of the thematic FAPESP project “DéjàVu: Feature-Space-Time Coherence from Heterogeneous Data for Media Integrity Analytics and Interpretation of Events” and it proposes, from social network collected data, to determine the relevance of them for the analyzed event, allowing the correct construction of relationships among these data during an analysis phase later on. The main challenges of this work are the characteristics of the data which will be used: heterogeneity, as they come from different sources; multi-modality, such as texts, images and videos; unlabeled data, as they do not present label of straightforward relevance for the event; and unstructured data, as they do not possess characteristics which could be used directly during the learning.
event detection, data mining, features engineering
2 - 13
Conceptual Attention Networks for Action Recognition
Andrés Espinosa, Alain Raymond, Julio Hurtado
Alain Raymond
"We introduce Concept Attention Networks (CAN) for Action Recognition. CANs seek to provide more interpretability by providing attention for both visual features as well as concepts associated to the action we want to recognize. CANs are modelled on the MAC architecture - which has produced great results on VQA through the use of sequential reasoning- with two main differences: 1) The knowledge base is modified to take video features. 2) We introduce attention over concepts via an auxiliary task that tries to guess the concepts associated to the predicted class on each reasoning step. We expect that taking visual features and word features to the same space might provide both similar accuracy as well as greater interpretability; since CAN - as the MAC architecture on which it is based- divides its reasoning in steps, we are able to see on which parts of the video and on which concepts the model is focusing to generate its predictions. We present results on the Something to Something v2 dataset against a C3D baseline. "
attention, action recognition, sequential reasoning
2 - 14
Deep Reinforcement Learning for Humanoid Walking
Dicksiano Carvalho Melo, Adilson Marques da Cunha, Marcos Ricardo Omena de Albuquerque Máximo
Dicksiano Carvalho Melo
"The work consists in applying Deep Reinforcement Learning algorithms in order to the improve a robot's walking engine. Therefore, the final goal is to implement a Push Recovery Controller, which is a bio-inspired controller that stabilizes the agent under external perturbations in order to achieve a more stable and also faster walking movement. Proximal Policy Optimization algorithm has already been used in different domains and had success to solve many Continuous Control problems, being considered one of the state-of-art techniques of Deep Reinforcement Learning, therefore this is the main technique used in this work. Given the nature of Policy Gradient methods, we applied distributed training in order to Speed Up the learning process. We have used Intel AI DevCloud Cluster in order to have many agents running in parallel."
deep reinforcement learning, humanoid walking, robotics
2 - 15
Multitask Learning on Graph Neural Networks: Learning Multiple Graph Centrality Measures with a Unified Network
Pedro HC Avelar, Marcelo OR Prates, Henrique Lemos, Luis C Lamb
Pedro Henrique da Costa Avelar
The application of deep learning to symbolic domains remains an active research endeavour. Graph neural networks (GNN), consisting of trained neural modules which can be arranged in different topologies at run time, are sound alternatives to tackle relational problems which lend themselves to graph representations. In this paper, we show that GNNs are capable of multitask learning, which can be naturally enforced by training the model to refine a single set of multidimensional embeddings and decode them into multiple outputs by connecting MLPs at the end of the pipeline. We demonstrate the multitask learning capability of the model in the relevant relational problem of estimating network centrality measures, focusing primarily on producing rankings based on these measures. We then show that a GNN can be trained to develop a lingua franca of vertex embeddings from which all relevant information about any of the trained centrality measures can be decoded. The proposed model achieves 89% accuracy on a test dataset of random instances with up to 128 vertices and is shown to generalise to larger problem sizes. The model is also shown to obtain reasonable accuracy on a dataset of real world instances with up to 4k vertices, vastly surpassing the sizes of the largest instances with which the model was trained ($n=128$). Finally, we believe that our contributions attest to the potential of GNNs in symbolic domains in general and in relational learning in particular.
graph neural networks, graph networks, centrality measures, network centrality
2 - 16
End-To-End Imitation Learning of Lane Following Policies Using Sum-Product Networks
Renato Lui Geh, Denis Deratani Mauá
Renato Lui Geh
Recent research has shown the potential of learning lane following policies from annotated video sequences through the use of advanced machine learning techniques. They however require high computational power, prohibiting their use in low-budget projects such as educational robotic kits and embedded devices. Sum-product networks (SPNs) are a class of deep probabilistic models with clear probabilistic semantics and competitive performance. Importantly, SPNs learned from data are usually several times smaller than deep neural networks trained for the same task. In this work, we develop an end-to-end imitation learning solution to lane following using SPNs to classify images into a finite set of actions. Images are obtained from a monocular camera, which is part of the low-cost custom made mobile robot. Our results show that our solution generalizes training conditions with relatively few data. We investigate the trade-off between computational and predictive performance, and conclude that sacrificing accuracy for the benefit of faster inference results in improved performance in the real world, especially in resource constrained environments.
machine learning, robotics, sum-product networks
2 - 17
Friend or Foe: Studying user trustworthiness for friend recommendation in the era of misinformation
Antonela Tommasel
Antonela Tommasel
" The social Web, mainly represented by social networking sites, enriches the life and activities of its users by providing new forms of communication and interaction. Even though most of the time, the use of Internet is safe and enjoyable, there are risks that involve communication through social media. The unmoderated nature of social media sites often results in the appearance and distribution of unwanted content or misinformation. Thus, although social sites provide a great opportunity to stay informed about events and news, it also produces skepticism among users, as not every piece of shared information can be trusted. Moreover, the potential for automation and the low cost of producing fraudulent sites, allows the rapid creation and dissemination of unwanted content. Thus, current information dissemination processes pose the challenge of determining whether it is possible to trust on recommendations. The goal of this work is to define a profile to describe and estimate the trustworthiness or reputation of users, to avoid making recommendations that could favour the propagation of unreliable content and polluting users. The final aim is to reduce the negative effects of the existence and propagation of such content, and thus improving the quality of the recommendations."
recommender systems, trusworthiness, misinformation
2 - 18
Global Sensitivity Analysis of MAP inference in Selective Sum-Product Networks
Julissa Villanueva Llerena and Denis deratani Mauá
JulissaVillanueva
"Sum-Product Networks (SPN) are deep probabilistic models that have exhibited state-of-the-art performance in several machine learning tasks. As with many other probabilistic models, performing Maximum-A-Posteriori (MAP) inference is NP-hard in SPNs. A notable exception is selective SPNs, that allows MAP inference in linear time. Due to the high number of parameters, SPNs learned from data can produce unreliable and overconfident inference. This effect can be partially detected by performing a Sensitivity Analysis of the model predictions to changes in the parameters. In this work, we develop efficient algorithms for global quantitative analysis of MAP inference in selective SPNs. In particular, we devise a polynomial-time procedure to decide whether a given MAP configuration is robust with respect to changes in the model parameters. Experiments with real-world datasets show that this approach can discriminate easy- and hard-to-classify instances, often more accurately than criteria based on the probabilities induced by the model."
sensitivity analysis, sum-product networks, tractable probabilistic models.
2 - 19
Graph Feature Regularization: Combining machine learning models with graph data
Federico Albanese, Esteban Feuerstein, Leandro Lombardi
Federico Albanese
"In recent years, the amount of available data has drastically increased. However, labelling such data is hugely expensive. In this scenario, semi-supervised learning emerge as a vitally important tool, which combines labelled data (supervised machine learning) and unlabelled data (unsupervised learning) in order to make better predictions. In particular, graph based algorithms takes into account the relationships between the instances of the data and the underlying graph structures to make those predictions. In addition, in the context of data analysis, there are scenarios that can be naturally think as graphs. This occurs in situations where in addition to individual properties, connectivity between the elements of the data set is also important. Therefore, it is logical that machine learning models include information from both a node and its neighbours when making a prediction. This works propose adding graph feature regularization terms (GFR) to the the objective function to maximize. This new regularization terms depends on the structure of the network, the weight of the edges and the features of the node. We conclude that adding this terms to gradient boosted trees can outperform complex network architectures such as the Graph Convolutional Networks."
graph, machine learning, regularization
2 - 20
IA and HPC Convergence
Mariza Ferro, Vinícius Klôh, Felipe Bernardo, Bruno Schulze
Mariza Ferro
The convergence of High-Performance Computing (HPC) and Artificial Intelligence (AI) has become a promissing approach to major performance improvements. This combination has much to offer from each other and it’s giving to the users unprecedent capabilities of research. In this interaction HPC could be used by AI (HPC for AI) to execute and enhance the performance of its algorithms. It involves using and evaluating different HPC architectures to train AI algorithms, understand and optimize their performance on different architectures. IA for HPC can be further subdivided in IA after HPC and autotune. In the first, ML algorithms are used to understand and analyze the results of simulations on HPC. It involves using ML to understand scientific applications, how they are relate to different HPC architectures, and the impact of this relationship on performance and power consumption. It is more related to knowledge discovery and its result can be used in autotune. In autotune, IA is used to configure HPC, to choose the best set of computation and parameters to achieve some goal, for example energy saving. Also, ML is used to the prediction of performance and energy consumption, job scheduling and frequency and voltage scaling.
hpc, performance, autotune
2 - 21
l0-norm feature LMS algorithms
Hamed Yazdanpanah, José A. Apolinário Jr., Paulo S. R. Diniz, Markus V. S. Lima
Hamed Yazdanpanah
A class of algorithms known as feature least-mean-square (F-LMS) has been proposed recently to exploit hidden sparsity in adaptive filter parameters. In contrast to common sparsity-aware adaptive filtering algorithms, the F-LMS algorithm detects and exploits sparsity in linear combinations of filter coefficients. Indeed, by applying a feature matrix to the adaptive filter coefficients vector, the F-LMS algorithm can revealand exploit their hidden sparsity. However, in many cases the unknown plant to be identified contains not only hidden but also plain sparsity and the F-LMS algorithm is unable to exploit it. Therefore, we can incorporate sparsity-promoting techniques into the F-LMS algorithm in order to allow the exploitation of plain sparsity. In this paper, by utilizing the l0-norm, we propose the l0-norm F-LMS (l0-F-LMS) algorithm for sparse lowpass and sparse highpass systems. Numerical results show that the proposed algorithm outperforms the F-LMS algorithm when dealing with hidden sparsity, particularly in highly sparse systems where the convergence rate is sped up significantly.
lms algorithm, hidden sparsity, plain sparsity
2 - 22
Learning to Solve NP-Complete Problems
Marcelo Prates, Pedro Avelar, Henrique Lemos, Luis Lamb, Moshe Vardi
Marcelo Prates
Graph Neural Networks are a promising technique for bridging differential programming with combinatorial domains. In this paper we show that GNNs can learn to solve, with very little supervision, the decision variant of the Traveling Salesperson Problem.
graph neural networks, np-complete, traveling salesperson problem
2 - 23
Loco: A toolkit for RL research in locomotion
Wilbert Santos Pumacay Huallpa
Wilbert Santos Pumacay Huallpa
Recent advances in the field of Deep Reinforcement Learning have achieved impressive results in various tasks. One key component for these achievements are the simulated environments used to train and test DeepRL based agents, and for locomotion tasks there are various benchmarks that can be used, which are built on top of popular physics engines. However, these locomotion benchmarks do not offer the functionality required to train and evaluate agents in more diverse and complex tasks, exposing only relatively simple tasks, e.g. traversing flat terrain. This work presents an engine-agnostic toolkit for locomotion tasks that provides such functionality, allowing users to create a wide range of diverse and complex environments. We provide support for various physics engines via a physics abstraction layer, allowing users to easily switch between engines as required.
locomotion benchmarks, deeprl, simulated environments
2 - 24
Machine Learning-Based Pre-Routing Timing Prediction with Reduced Pessimism
E. Carvajal, N. Shukla, Y. Chen, J. Hu.
Erick Carvajal Barboza
Optimizations at placement stage need to be guided by timing estimation prior to routing. To handle timing uncertainty due to the lack of routing information, people tend to make very pessimistic predictions such that performance specification can be ensured in the worst case. Such pessimism causes over-design that wastes chip resources or design effort. In this work, a machine learning-based pre-routing timing prediction approach is introduced. Experimental results show that it can reach accuracy near post-routing sign-off analysis. Compared to a commercial pre-routing timing estimation tool, it reduces false positive rate by about 2/3 in reporting timing violations.
integrated circuit design, static timing analysis, machine learning
2 - 25
Memory in Agents
Meire Fortunato, Melissa Tan, Ryan Faulkner, Steven Hansen*, Adrià Puigdomènech Badia, Gavin Buttimore, Charlie Deck, Joel Z Leibo, Charles Blundell
Meire Fortunato
Memory is an important aspect of intelligence and plays a role in many deep reinforcement learning models. However, little progress has been made in understanding when specific memory systems help more than others and how well they generalize. The field also has yet to see a prevalent consistent and rigorous approach for evaluating agent performance on holdout data. In this paper, we aim to develop a comprehensive methodology to test different kinds of memory in anagent and assess how well the agent can apply what it learns in training to a holdout set that differs from the training set along dimensions that we suggest are relevant for evaluating memory-specific generalization. To that end, we first construct a diverse set of memory tasks that allow us to evaluate test-time generalization across multiple dimensions. Second, we develop and perform multiple ablations on an agent architecture that combines multiple memory systems, observe its baseline models, and investigate its performance against the task suite.
memory, rl, generalization
2 - 26
Model-Based Reinforcement Learning with Deep Generative Models for Industrial Applications
Ângelo Gregório Lovatto, Thiago Pereira Bueno, Leliane Nunes de Barros
Ângelo Gregório Lovatto
Industrial applications, such as those in process industry like or power generation, could benefit from reinforcement learning (RL) agents to reduce energy consumption and lower emissions. However, the systems involved in these applications usually have high usage costs, while RL algorithms generally require too many trials to learn a task. A promising approach to the inefficiency problem is the model-based RL method, which allows agents to learn a predictive model of the environment to extract more information from available data. Given that industrial applications generally feature complex stochastic behavior, we propose investigating novel integration schemes between the model-based approach and deep generative models, a class of neural networks specially designed to handle sophisticated probability distributions. We will test these interventions in existing and novel benchmark tasks aimed at assessing a learning system's capacity of handling state changes governed by complex conditional probability distributions. We expect that our approach will lead to better model predictions and faster learning.
reinforcement learning, generative models, deep learning
2 - 28
On the optimization of the regularization parameters selection in sparse modeling
Victoria Peterson and Rubén D. Spies
Victoria Peterson
Tikhonov functionals are commonly used as regularization strategies for severely ill-posed inverse problems. Besides the type of penalization induced into the solution, the proper selection of the regularization parameters is of utmost importance for accurate estimation. In this work, we analyze several data-driven regularization parameters estimation methods in a mixed-term discriminative framework. Numerical results for P300 detection in Brain-Computer Interfaces classification are presented, showing the impact of regularization parameter estimation into classification performance.
generalized tikhonov regularization, tunning parameter selection, sparse modeling
2 - 29
Pajé - End-to-End Machine Learning
Edesio Alcobaça, Davi Pereira-Santos, André Carvalho
Edesio Alcobaça
"The number, variety, and complexity of Data Science applications are rapidly increasing along with automated solutions. This kind of solution, called automated machine learning, makes data science accessible to non-specialists. On the other hand, from the specialist standpoint, automated machine learning can spare him/her manual and repetitive work, speeding up research. In the last years, there has been a strong interest in the development of tools able to automate data science. While the existing frameworks mainly focus on inducing accurate models through hyperparameter tuning, they disregard or forgo, for instance, the data preprocessing step, reproducibility, and explainability. Nevertheless, this kind of task expends the majority of human resources. In this paper, we present an overview of ideas behind Pajé, an open tool for automated data science. Pajé includes all the core processes of the data science pipeline, from data acquisition to model interpretation, and at the same time, addresses important aspects of machine learning, such as reproducibility and explainability."
automl, meta-learning, machine learning
2 - 30
Preliminary results of supervised models trained with charge density data from Cruzain-inhibitors complexes.
Villafañe, Roxana Noelia; Luchi, Adriano Martín; Angelina, Emilio Luis; Peruchena, Nélida María.
Roxana Noelia Villafañe
"Proteins are the most versatile biological molecules, with diverse functions. Recently, the AI community have developed interest in specific topics related to proteins as: protein folding, structural analysis, protein-ligand affinity estimation, among others. Cruzain is a cysteine protease involved in chagas disease with several Cz-inhibitor complexes deposited in the Protein Data Bank (PDB). Unfortunately, the number of structures solved up-to-date is scarce for the requirements of a machine learning optimization algorithm. Another issue is the high dimensionality of the data involved in structure-based approaches for drug design. In this work, charge density-based data was employed as input for a classification algorithm with the protein-ligand interactions as columns and ligands as rows. A support vector machine with recursive feature elimination was employed to uncover the most relevant features involved in the protein-inhibitor complexes. This approach is the first step for further analysis of topological data of Cz-ligand complexes under study. We hope that results will shed light to understand the inhibition mechanism of Cruzain."
support vector machines, qtaim, feature selection
2 - 31
Probability distributions of maximum entropy on Wasserstein balls and their applications
Luis Felipe Vargas and Mauricio Velasco
Mauricio Velasco
We introduce a cutting plane method for efficiently finding the probability distribution of maximum entropy contained in a Wasserstein ball. Such distributions are the most general (i.e. minimizers of the amount of prior information) in the ball and are therefore of central importance for statistical inference. We generalize these results to the problem of minimizing cross-entropy from a given prior distribution and use them to propose 1-parameter families of learning algorithms that are naturally resilient to biases.
wasserstein metric, maximum entropy, minimum cross-entropy
2 - 32
Random Projections and $\alpha$-shape to Support the Kernel Design
"Daniel Moreira Cestari Rodrigo Fernandes de Mello"
Daniel CestarI
We automatically design kernels from data by projecting points into either random hyperplanes or onto the boundaries forming the $\alpha$-shape. We interpret such transformation as an explicit strategy a kernel uses to extract features from data, thus SVM applied on this transformed space should be capable of correctly separating class instances. We firstly applied this method on two different synthetic datasets to assess its performance and parameter sensitivity. Those experimental results confirmed a considerable improvement over the original input space, robustness in the presence of noise and parameter changes. Secondly, we applied our approach on well-known image datasets in order to evaluate its ability to deal with real-world data and high dimensional spaces. Afterwards, we discuss how this novel approach could be plugged to Convolutional Neural Networks, helping to understand the effects and the impact of adding units to layers. Our proposal has a low computational cost and it is parallelizable to work directly on the transformed space and, when memory constraints hold, its resultant kernel matrix might be used instead. Such approach considerably improved the classification performance in almost all scenarios, supporting the claim that it could be used as a general-purpose kernel transformation.
random projections; alpha-shape; kernel design
2 - 33
Regular Inference over Recurrent Neural Networks as a Method for Black Box Explainability
Franz Mayr, Sergio Yovine
Franz Mayr
This work explores the general problem of explaining the behavior of recurrent neural networks (RNN). The goal is to construct a representation which enhances human understanding of an RNN as a sequence classifier, with the purpose of providing insight on the rationale behind the classification of a sequence as positive or negative, but also to enable performing further analyses, such as automata-theoretic formal verification. In particular, an active learning algorithm for constructing a deterministic finite automaton which is approximately correct with respect to an artificial neural network is proposed.
recurrent neural networks, regular inference, explainability
2 - 34
Scalable methods for computing state similarity in deterministic Markov Decision Processes
Pablo Samuel Castro
Pablo Samuel Castro
We present new algorithms for computing and approximating bisimulation metrics in Markov Decision Processes (MDPs). Bisimulation metrics are an elegant formalism that capture behavioral equivalence between states and provide strong theoretical guarantees on differences in optimal behaviour. Unfortunately, their computation is expensive and requires a tabular representation of the states, which has thus far rendered them impractical for large problems. In this paper we present a new version of the metric that is tied to a behavior policy in an MDP, along with an analysis of its theoretical properties. We then present two new algorithms for approximating bisimulation metrics in large, deterministic MDPs. The first does so via sampling and is guaranteed to converge to the true metric. The second is a differentiable loss which allows us to learn an approximation even for continuous state MDPs, which prior to this work had not been possible.
markov decision processes, reinforcement learning, bisimulation metrics
2 - 35
See and Read: Detecting Depression Symptoms in Higher Education Students Using Multimodal Social Media Data
Paulo Mann, Aline Paes, Elton H. Matsushima
Paulo Mann
Mental disorders such as depression and anxiety have been increasing at alarming rates in the worldwide population. Notably, major depressive disorder has become a common problem among higher education students. While the reasons for this alarming situation remain unclear (although widely investigated), the student already facing this problem must receive treatment. To that, it is first necessary to screen the symptoms. The traditional way for that is relying on clinical consultations or answering questionnaires. However, nowadays, the data shared at social media is a ubiquitous source that can be used to detect the depression symptoms even when the student is not able to afford or search for professional care. In this work, we focus on detecting the severity of the depression symptoms in higher education students, by comparing deep learning with feature engineering models induced from Instagram data. The experimental results show that students presenting a BDI score higher than 20 can be detected with 0.92 of recall and 0.69 of precision in the best case, reached by a fusion model. Our findings show a potential of help on further investigation of depression, by bringing students at-risk to light, to guide them to access adequate treatment.
deep learning, depression, students
2 - 36
Solving Linear Inverse Problems by Joint Posterior Maximization with a VAE Prior
Mario González, Andrés Almansa, Mauricio Delbracio, Pablo Musé
Mario González
"We address the problem of solving ill-posed inverse problems in imaging where the prior is a neural generative model. Specifically we consider the decoupled case where the prior is trained once and can be reused for many different degradation models without retraining. Whereas previous MAP-based approaches to this problem lead to highly non-convex optimization algorithms, our approach computes the joint (space-latent) MAP that naturally leads to alternate optimization algorithms and to the use of a stochastic encoder to accelerate computations. We show theoretical and experimental evidence that the proposed objective function may be quite close to bi-convex, which would pave the way to show strong convergence results of our optimization scheme. Experimental results also show the higher quality of the solutions obtained by our approach with respect to non-convex MAP approaches."
inverse problems, variational autoencoder, maximum a posteriori
2 - 37
Stream-based Expert Ensemble Learning for Network Measurements Analysis
Juan Vanerio, Pedro Casas, Federico Larroca
Juan Vanerio
"The application of machine learning to Network Measurements Analysis problems has largely increased in the last decade; however, it remains difficult to say today which is the most fitted category of models to address these tasks in operational networks. We work on Stream-GML2, a generic stream-based (online) Machine Learning model for the analysis of network measurements. The model is a stacking ensemble learning algorithm, in which several weak or base learning algorithms are combined to obtain higher predictive performance. In particular, Stream-GML2 is an instance of a recent model known as Super Learner, which performs asymptotically as good as the best input base learner. It provides a very powerful approach to tackle multiple problems with the same technique while minimizing over-fitting likelihood during training, using a variant of cross-validation. Additionally, stream-GML2 copes with concept drift and performance degradation by relying on Reinforcement Learning (RL) principles, no-regret learning and online-convex optimization. The model resorts to adaptive memory sizing to retrain the system when required, adjusting its operation point dynamically according to distribution changes in incoming samples or performance degradation over time."
stream learning; ensemble learning; network attacks
2 - 39
Synthesizing Atmospheric Radar Images from IR Satellite Channel Using Generative Deep Neural Networks
Sacco, Maximilliano A. ;Scheffler, Guillermo ; Ruiz, Juan
Maximiliano Sacco
We present a novel application to infer atmospheric radar reflectivity images using infrared satellite images. Given the high cost of radar instruments, data oriented image reconstruction appears as an attractive option. We compared output from fully connected networks, convolutional-deconvolutional networks and generative adversarial networks trained with synthetically generated radar/satelite image pairs from numerical weather model simulations. Results are comparable with state of the art statistical methods. The application shows promising results for short term weather prediction.
2 - 40
Towards self-healing SDNs for dynamic failures
Cristopher G. S. Freitas, André L. L. Aquino
Cristopher Gabriel de Sousa Freitas
Legacy IP networks are currently a huge problem for Internet Service Providers, as the demand grows exponentially, the profit doesn't follow. With the emergence of the Software-Defined Networks (SDN), providers are hoping to improve their service while lowing the operational expenses. In this work, we focus on self-healing SDNs, that requires fault-tolerant mechanisms and intelligent network management for enabling the system to perceive its incorrect states and acting to fix it. As fault tolerance is a huge issue, we narrow our proposal for only dynamic failures, as these are usually the best target for machine learning approaches as deterministic solutions are sub-optimal or too complex. Thus, we develop a solution using Deep Reinforcement Learning (DRL) for routing and load balancing, considering highly dynamic traffic, and we show the viability of a model-free solution and its efficiency.
deep reinforcement learning, fault tolerance, software-defined networks
2 - 41
Towards the Education of the Future: Challenges and Opportunities, for AI?
Germán Capdehourat, Federica Bascans, Fabián Frommel, María Catalina Piana, Fiorella Nahmias, Cecilia Bisogno, Cecilia Marconi, Alessia Zucchetti, Fiorella Haim, Enrique Lev.
Germán Capdehourat
As in other verticals, the application of data science to education opens up new possibilities. An example is the growing research community in learning analytics. Different goals, such as looking for tools for a more personalized education and the detection of particular difficulties at early ages, are relevant challenges that are being addressed in the area. In this context, we present the case of Plan Ceibal, an institution that assists the education system in Uruguay, providing technological solutions for the support of education.
education, learning analytics, ai literacy
2 - 42
Transfer in Multiagent Reinforcement Learning
Silva, Felipe Leno da; Costa, Anna Helena Reali
Felipe Leno da Silva
Reinforcement learning methods have successfully been applied to build autonomous agents that solve challenging sequential decision-making problems. However, agents need a long time to learn a task, especially when multiple autonomous agents are in the environment. This research aims to propose a Transfer Learning framework to accelerate learning by combining two knowledge sources: (i) previously learned tasks; and (ii) advice from a more experienced agent. The definition of such a framework requires answering several challenging research questions, including: How to abstract and represent knowledge, in order to allow generalization and posterior reuse?, How and when to transfer and receive knowledge in an efficient manner?, and How to consistently combine knowledge from several sources?
machine learning, multiagent reinforcement learning, transfer learning
2 - 43
Transformers are Turing Complete
Jorge Pérez, Javier Marinkovic, Pablo Barceló
Jorge Perez
"Alternatives to recurrent neural networks, in particular, architectures based on attention, have been gaining momentum for processing input sequences. In spite of their relevance, the computational properties of these alternatives have not yet been fully explored. We study the computational power of one of the most paradigmatic architectures exemplifying the attention mechanism, the Transformer (Vaswani et al., 2017). We show that the Transformer is Turing complete exclusively based on their capacity to compute and access internal dense representations of the data. Our study also reveals some minimal sets of elements needed to obtain these completeness results."
attention, transformers, turing completeness
2 - 44
Uncovering differential equations
Agustin Somacal
Many branches of science and engineering require differential equations to model the dynamics of the systems under study. Traditionally, the identification of the appropriate terms in the equation has been done by experts. Brunton, Proctor, and Kutz 2016 developed a method to automate this task using the data itself. In this work, we extend the applicability of this method to situations where not all variables are observed by adding higher-order derivatives to the model space search. We first test the results using only one variable of the Lorenz system and then apply the same methodology to temperature times series. We found that the proposed approach is enough to recover equations with R²>0.95 in both cases. We also propose an algebraic method to get future values of the system and compare it with traditional integrative methods finding that our approach is more stable giving high accuracy prediction results in the case of the Lorenz system.
differential equations, dynamical systems
2 - 45
Aurea Soriano-Vargas, Bernd Hamann, Maria Cristina F. de Oliveira
Aurea Soriano-Vargas
We present an integrated interactive framework for the visual analysis of time-varying multivariate datasets. As part of our research, we performed in-depth studies concerning the applicability of visualization techniques to obtain valuable insights. We consolidated the considered analysis and visualization methods in one framework, called TV-MV Analytics. It effectively combines visualization and data mining algorithms providing the following capabilities: i) visual exploration of multivariate data at different temporal scales; and ii) a hierarchical small multiples visualization combined with interactive clustering and multidimensional projection to detect temporal relationships in the data. We demonstrate the value of our framework for specific scenarios, by studying three use cases that were validated and discussed with domain experts.
visual analytics, time-varying multivariate data, visual feature selection
2 - 46
AI-enabled applications with social and productivity impact
Digital Sense Technologies
Álvaro Pardo
dSense is a specialized R&D Studio that provides consultancy and development services in Computer Vision, Machine Learning and Image Processing for projects with an important component of innovation. Our team of 4 PhDs, 5 MScs and experienced engineers authored more than 175 papers and 4 US patents. By taking advantage of our research background, we have been able to develop valuable custom AI-enabled solutions across industries with a positive social and productivity impact. We introduce some of the most recent in this poster.
Computer Vision, Machine Learning, Image Processing
2 - 47
FLambé: A Customizable Framework for Machine Learning Experiments
Jeremy Wohlwend, Nicholas Matthews, Ivan Itzcovich
Carolina Rodriguez Diz
Flambé is a machine learning experimentation framework built to accelerate the entire research life cycle. Flambé's main objective is to provide a unified interface for prototyping models, running experiments containing complex pipelines, monitoring those experiments in real-time, reporting results, and deploying a final model for inference. Flambé achieves both flexibility and simplicity by allowing users to write custom code but instantly include that code as a component in a larger system which is represented by a concise configuration file format. We demonstrate the application of the framework through a cutting-edge multistage use case: fine-tuning and distillation of a state of the art pretrained language model used for text classification.
Pytorch Experiment Research
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2022-11-27 09:11:22
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https://math.stackexchange.com/questions/1784613/another-hockey-stick-identity
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Another Hockey Stick Identity
I know this question has been asked before and has been answered here and here.
I have a slightly different formulation of the Hockey Stick Identity and would like some help with a combinatorial argument to prove it. First I have this statement to prove: $$\sum_{i=0}^r\binom{n+i-1}{i}=\binom{n+r}{r}.$$ I already have an algebraic solution here using the Pascal Identity: \begin{align*} \binom{n+r}{r}&=\binom{n+r-1}{r}+\binom{n+r-1}{r-1}\\ &=\binom{n+r-1}{r}+\left[\binom{n+(r-1)-1}{(r-1)}+\binom{n+(r-1)-1}{r-2}\right]\\ &=\binom{n+r-1}{r}+\binom{n+(r-1)-1}{(r-1)}+\left[\binom{n+(r-2)-1}{r-2}+\binom{n+(r-2)-1}{(r-2)-1}\right]\\ &\,\,\,\vdots\\ &=\binom{n+r-1}{r}+\binom{n+(r-1)-1}{(r-1)}+\binom{n+(r-2)-1}{(r-2)-1}+\binom{n+(r-3)-1}{r-3}+\cdots+\left[\binom{n+1-1}{1}+\binom{n+1-1}{0}\right]\\ &=\binom{n+r-1}{r}+\binom{n+(r-1)-1}{(r-1)}+\binom{n+(r-2)-1}{(r-2)-1}+\binom{n+(r-3)-1}{r-3}+\cdots+\binom{n+1-1}{1}+\binom{n-1}{0}\\ &=\sum_{i=0}^r\binom{n+i-1}{i}. \end{align*}
I have read both combinatorial proofs in the referenced answers above, but I cannot figure out how to alter the combinatorial arguments to suit my formulation of the Hockey Stick Identity. Basically, this formulation gives the "other" hockey stick. Any ideas out there?
Note that $\binom{n+r}{r}=\binom{n+r}{n}$ is the number of subsets of $\{1,2,\ldots,n+r\}$ of size $n$. On the other hand, for $i=0,1,2,\ldots,r$, $\binom{n+i-1}{i}=\binom{n+i-1}{n-1}$ is the number of subsets of $\{1,2,\ldots,n+r\}$ of size $n$ whose largest element is $n+i$.
• This is exactly what I was hoping for. Thanks. – Laars Helenius May 14 '16 at 12:47
Suppose that the Diophantine inequality $x_1 + x_2 + ... + x_n \le r$ has $A(n, r)$ non-negative integer solutions. (Or one has to disturb at most $r$ objects into $n$ bins and this task is possible in $A(n, r)$ ways. Note that one distinguishes the bins but one does not wish to distinguish the objects)
We will calculate $A(n, r)$ in two ways.
$$x_1 + x_2 + ... + x_n \le r \\ \Rightarrow \exists x_{n+1} \in \mathbb{Z^+}\cup\{0\}: x_1 + x_2 + ... + x_n + x_{n+1} = r$$
According to stars and bars problem,
$$A(n, r) = \left(\!\!{n + 1 \choose r}\!\!\right) = {n + r \choose r} \qquad \mathcal{\color{navy}{(I)}}$$
Hence wee seek integer solutions (and $r$ is also an integer), by the rule of sum, $A(n, r)$ would be the sum of non-negative integer solutions to these equations:
$$x_1 + x_2 + \cdots + x_n = 0\\or\\ x_1 + x_2 + \cdots + x_n = 1\\or\\ x_1 + x_2 + \cdots + x_n = 2\\or\\ \vdots\\or\\ x_1 + x_2 + \cdots + x_n = r$$
For all $0 \le i \le r$, the equation $x_1 + x_2 + ... + x_n = i$ would have $\left(\!\!{n \choose i}\!\!\right) = {n + r - 1 \choose r}$ non-negative integer solutions. Hence,
$$A(n, r) = \sum_{i=0}^r\left(\!\!{n \choose i}\!\!\right) = \sum_{i=0}^r{n+i-1 \choose i} \qquad \mathcal{\color{navy}{(II)}} \\ {\color{navy}{(I)}}, {\color{navy}{(II)}} \Rightarrow {n + r \choose r} = \sum_{i=0}^r\left(\!\!{n \choose i}\!\!\right) = \sum_{i=0}^r{n+i-1 \choose i}$$
• Thank you for your help. This is an original way of looking at it from what I've seen. – Laars Helenius May 14 '16 at 12:49
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2019-05-19 08:24:03
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https://www.gamedev.net/forums/topic/122937-array-boundaries-in-cc/
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#### Archived
This topic is now archived and is closed to further replies.
# Array boundaries in C/C++
This topic is 5732 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
Is there any way to specify negative boundaries for a built-in C array? Say I wanna do Screen[-20 to 20] or something like that, is it possible? Thanks in advance There are 10 kinds of people: those who know binary and those who don''t
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char array_thingy[41];char *ptr_thingy = array_thingy[20];for (int i = -20; i <= 20; ++i) { ptr_thingy[i] = something;}
i think something like that would work but it's probably not the best idea in the world. why don't you want to go from 0 to 40 (or whatever value, as the case may be)?
scott
edit: square bracket thingies...
[edited by - LizardAl on November 7, 2002 10:12:41 AM]
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That´s what I had thought myself. The reason I want to do this is... I don´t remember anymore! I know there was a reason, but can´t remember! Anyway, thanks for the reply
There are 10 kinds of people: those who know binary and those who don''t
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quote:
Original post by LizardAl
i think something like that would work
No it won't. It will invoke undefined behaviour. The -ve index will be converted to an unsigned value of high magnitude, meaning you will be well off the end of the array. The simple answer to the OP's question is: no it can't be done. The more esoteric answer is: it can be simulated via a level of indirection. I.e. you write a layer of abstraction around the array which accepts -ve indices and correctly translates them into the corresponding unsigned value.
[edited by - SabreMan on November 7, 2002 10:35:31 AM]
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template< class T>class TWeirdArray{T *m_theTs;int m_startBound, m_endBound;public:TWeirdArray( int startBound, int endBound ) : m_startBound( startBound ), m_endBound( endBound ){ m_theTs = new T[ m_endBound - m_startBound + 1 ]; // Note: if you don''t want this to go bananas on you, you // should add checking to see if endbound > startbound etc.}T& operator[]( int idx ){return m_theTs[ idx - m_startBound ];}};
Quick hack Not perfect, but it shows the possibilities.
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it''s a feature of ruby
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quote:
Original post by SabreMan
[quote]Original post by LizardAl
i think something like that would work
No it won''t. It will invoke undefined behaviour. The -ve index will be converted to an unsigned value of high magnitude, meaning you will be well off the end of the array. The simple answer to the OP''s question is: no it can''t be done. The more esoteric answer is: it can be simulated via a level of indirection. I.e. you write a layer of abstraction around the array which accepts -ve indices and correctly translates them into the corresponding unsigned value.
[edited by - SabreMan on November 7, 2002 10:35:31 AM]
But it would work if the [ ] operator was replaced with a plain old ptr + offset (because the -ve offset points at valid memory)? So you are saying the indexing operator casts to unsigned?
"Most people think, great God will come from the sky, take away everything, and make everybody feel high" - Bob Marley
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quote:
But it would work if the [ ] operator was replaced with a plain old ptr + offset (because the -ve offset points at valid memory)?
How do you figure that one out?
quote:
So you are saying the indexing operator casts to unsigned?
Yes.
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if you want, have a function
int translateIndex(int index)array[translateIndex(index)];
i wouldn''t bother trying to be clever with indexing, it''ll just put an overhead on people understanding your code (that includes you in a fortnight''s time)
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quote:
Original post by SabreMan
But it would work if the [ ] operator was replaced with a plain old ptr + offset (because the -ve offset points at valid memory)?
How do you figure that one out?
... if we have
T array[ 100 ];
isn''t this valid...
T* midptr = array + 50;
* ( midptr - 50 ) = 0; // same as array [ 0 ] = 0;
(I did miss out the * earlier).
quote:
So you are saying the indexing operator casts to unsigned?
Yes.
"Most people think, great God will come from the sky, take away everything, and make everybody feel high" - Bob Marley
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2018-07-18 22:42:37
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https://projecteuclid.org/euclid.dmj/1077245466
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## Duke Mathematical Journal
### A characterisation of the tight three-sphere
#### Article information
Source
Duke Math. J., Volume 81, Number 1 (1995), 159-226.
Dates
First available in Project Euclid: 19 February 2004
https://projecteuclid.org/euclid.dmj/1077245466
Digital Object Identifier
doi:10.1215/S0012-7094-95-08111-3
Mathematical Reviews number (MathSciNet)
MR1381975
Zentralblatt MATH identifier
0861.57026
#### Citation
Hofer, H.; Wysocki, K.; Zehnder, E. A characterisation of the tight three-sphere. Duke Math. J. 81 (1995), no. 1, 159--226. doi:10.1215/S0012-7094-95-08111-3. https://projecteuclid.org/euclid.dmj/1077245466
#### References
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• [17] J. Franks, Geodesics on $S^{2}$ and periodic points of annulus homeomorphisms, Invent. Math. 108 (1992), no. 2, 403–418.
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• [21] H. Hofer and D. Salamon, Floer homology and Novikov rings, The Floer Memorial Volume, Progr. Math., vol. 133, Birkhäuser, Basel, 1995, pp. 483–524.
• [22] H. Hofer and C. Viterbo, The Weinstein conjecture in the presence of holomorphic spheres, Comm. Pure Appl. Math. 45 (1992), no. 5, 583–622.
• [23] H. Hofer, K. Wysocki, and E. Zehnder, The dynamics on a strictly convex energy surface in $R^{4}$, preprint.
• [24] H. Hofer, K. Wysocki, and E. Zehnder, Properties of pseudoholomorphic curves in symplectisations I: Asymptotics, to appear in Analyse Nonlinéaire, May 1996.
• [25] H. Hofer, K. Wysocki, and E. Zehnder, Properties of pseudoholomorphic curves in symplectisations II: Embedding controls and algebraic invariants, to appear in Geom. Funct. Anal. 5, 1995.
• [26] H. Hofer, K. Wysocki, and E. Zehnder, Properties of pseudoholomorphic curves in symplectisations III: Fredholm theory, preprint.
• [27] H. Hofer and E. Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks], Birkhäuser Verlag, Basel, 1994.
• [28] J. Martinet, Formes de contact sur les variétés de dimension $3$, Proceedings of Liverpool Singularities Symposium, II (1969/1970), Springer, Berlin, 1971, 142–163. Lecture Notes in Math., Vol. 209.
• [29] D. McDuff, The local behaviour of holomorphic curves in almost complex $4$-manifolds, J. Differential Geom. 34 (1991), no. 1, 143–164.
• [30] D. McDuff and D. Salamon, Introduction to Symplectic Topology, Oxford University Press, Oxford, to be published.
• [31] D. McDuff and D. Salamon, $J$-Holomorphic Curves and Quantum Cohomology, University Lecture Series, vol. 6, Amer. Math. Soc., Providence, 1994.
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• [34] T. H. Parker and J. G. Wolfson, Pseudo-holomorphic maps and bubble trees, preprint, 1991.
• [35] J. Robbin and D. Salamon, The spectral flow and the Maslov index, to appear in J. London Math. Soc.
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• [38] R. Ye, Filling by holomorphic disks in symplectic $4$-manifolds, preprint.
• [39] R. Ye, Gromov's compactness theorem for pseudo holomorphic curves, Trans. Amer. Math. Soc. 342 (1994), no. 2, 671–694.
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2019-10-18 14:26:52
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https://stats.stackexchange.com/questions/405550/is-it-possible-to-specifiy-the-components-to-use-in-pcr-in-r
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# Is it possible to specifiy the components to use in PCR (in R)?
For a class project, my group and I are looking to play around with PCR since we didn't get a chance to dive into much details in class. We were going to look at a few different ways to select the principal components used in PCR beyond the default way R does. One of these that we wanted to look at was just a couple random samples, and seeing how they compare to the default R method. However, I can't find anything in tutorials or the R functions for pcr that let you specify the components themselves - only the number of components used (Right now I'm mainly using the pcr function from the pls package). Is there any package or function that will allow me to specify the components, or will I have to make my own function?
Thank you!
• What different ways did you have in mind? It's not clear to me if you want to select particular PCs to explore, or if you want to make different linear combinations (which wouldn't really be PCs then). – Aaron - Reinstate Monica Apr 29 at 1:53
The best way that I'm aware of is to apply the standard linear model function against the selected PCA scores. See example below, assuming your independent variables are held in data and dependent variable is found in yVector, and z is the number of columns you want to sample.
pca <- princomp( ~ ., data=data, cor=T)
sample <- pca$$scores[, sample(ncol(pca$$scores), z)])
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2019-11-19 07:37:40
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http://www.logic.univie.ac.at/2016/Talk_10-13_a.html
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# 2016 seminar talk: Some graph theory from the Rockies
Talk held by Daniel Soukup (KGRC) at the KGRC seminar on 2016-10-13.
### Abstract
The goal of this talk is to describe two projects I have been involved with at the University of Calgary in the last 8 months. First, we will look at the problem of finding independent partial transversals in sparse infinite graphs: we show that if $G$ is an infinite $K_n$-free graph and $m$ is finite then there is a finite $r=r(G,m)$ so that whenever the vertices of $G$ are partitioned into $r$ sets of equal size then there is an independent set $A$ which meets at least $m$ classes in a set of size of $G$. We determine the exact value of $r(G,m)$ for a few examples, in particular for Henson's homogeneous, universal $K_n$-free graphs. Joint work with C. Laflamme, A. A. Lopez, and R. Woodrow.
Second, we look at the following conjecture of S. Thomasse: for any digraph $D$, there is an appropriate set $C$ of cycles so that after reversing the orientation along members of $C$ the resulting digraph can be covered by two acyclic vertex sets. We will summarize the current knowledge on this question in the finite and infinite case. Joint work with C. Laflamme and A. A. Lopez.
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2017-12-15 00:40:39
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https://www.physicsforums.com/threads/limits-of-trig-functions.553016/
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Limits of trig functions
Homework Statement
lim(x -->0) (1-cos(14x))/(xsin(18x))
None?
The Attempt at a Solution
The hint tells me to use L'hopital's rule through which I got
lim(x-->0) (sin(14x))/(18xcos(18x)+sin(18x)) (I factored out the 14 in the numerator)
That gave me a 0/0 so I did L'hopital's rule again, through which I got
lim(x-->0) (cos(14x))/(cos(18x)-9xsin(18x)) (I factored out 14/2)
This gives me 98, which is wrong. (As x-->0, the function becomes 1, leaving what I factored out as 98)
I'm not sure what to do here. Help? :(
Last edited:
Answers and Replies
Related Calculus and Beyond Homework Help News on Phys.org
Dick
Science Advisor
Homework Helper
I think it's the things you are factoring out. I don't think you factor out 14/2 to get the expression you showed at the end. Can you show how you did that? Try showing your expressions without the 'factoring out'.
Last edited:
lim(x-->0) (1-cos14x)/(xsin(18x)), this gives 0/0
L'hopital's
lim(x-->0) (14sin14x)/(sin(18x) + 18x(cos(18x))), Gives 0/0
L'hopital's
lim(x-->0) (196cos(14x))/(36cos(18x)-324xsin(18x)) This gives 49/9 which is right...
Thanks, it seems I just screwed up the calculations. Sorry for the bother
Dick
Science Advisor
Homework Helper
lim(x-->0) (1-cos14x)/(xsin(18x)), this gives 0/0
L'hopital's
lim(x-->0) (14sin14x)/(sin(18x) + 18x(cos(18x))), Gives 0/0
L'hopital's
lim(x-->0) (196cos(14x))/(36cos(18x)-324xsin(18x)) This gives 49/9 which is right...
Thanks, it seems I just screwed up the calculations. Sorry for the bother
You are welcome. No problem.
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2020-04-01 12:41:26
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http://phenotiki.com/faq.html
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### Device FAQ
Where can I find the list of items to build-up a Phenotiki Acquisition Device?
You can find a complete list of the equipment needed to build your sensor in the Getting Started page.
I followed all the steps in the Phenotiki Device Guide, but the web server will not start after entering the “../bin/pserve development.ini” command.
Firstly, make sure if you are connected to the Internet. Secondly, make sure that the network you are connected to allows hosting a local webserver. If everything is fine with the Internet, you may be missing some required packages. Use the following commands and then go through the installation guide again.
$sudo apt-get install libxml2-dev libxslt-dev$ cd ~/phenotiki/env/ $bin/pip install requests-toolbelt How can I found out the IP address of my Raspberry PI? It is possible to find out the IP address using the command ifconfig in the terminal. If you are connected to WiFi the address will be displayed in the wlan0 section. If you are connected via Ethernet cable the address will be displayed in the eth0 section. In either case, you need to look for a line similar to inet addr: 10.99.78.101. I get error(s) when accessing to the webserver interface. If there is an error you can go back to the home page by typing in the webserver address in your browser again. If the error persists, go through the installation steps again as there may be a package missing. The camera flat cable is too short. Is there anyway I can get a longer cable? My Raspberry Pi restarted and now the webserver is not working. If the Raspberry Pi restarts the raspistillWeb application needs to be initialized again from the command line as follows:$ cd /home/pi/Development/env/bin/pserve development.ini
There is the a way to have the raspistillWeb application start automatically with the following steps.
1. Create a startup script
$sudo nano /etc/init.d/raspistillweb 2. Type in the following lines save and exit. 3. #!/bin/bash cd /home/pi/Development/env/raspistillWeb ../bin/pserve development.ini 4. Make the script executable:$ sudo chmod 755 /etc/init.d/raspistillweb
5. Register the script to be run at startup:
$sudo update-rc.d /etc/init.d/raspistillweb defaults Is it possible to access the web interface outside our University/Laboratory/Institute? Generally speaking, it is possible. If your institute has some firewall blocking any access from the outside, you need to contact your IT service and ask how to configure a VPN in your computer. By configuring a VPN, you can access your Raspberry Pi using the local IP address. Another way we recommend is to install TeamViewer on your Raspberry Pi and your computer. How do I remove raspstillWeb from my Raspberry PI? You can remove raspstillWeb by using the following command:$ sudo rm -rf /home/pi/phenotiki
If you have also the start-up script (see above), you may also run the following commands:
$sudo update-rc.d /etc/init.d/raspistillweb remove$ rm /etc/init.d/raspistillweb
### Analysis Software FAQ
Phenotiki is telling me that libsvm was successfully installed, but I get some errors in the Matlab console. How can I fix it?
Generally, this problem appears when you do not have a suitable C compiler installed and/or configured in your system. Please, follow this instruction for your operating system to solve the issue. If you believe the problem is something else, do not hesitate to contact us.
How can I move the data to/from another workstation?
If you wish to share data with colleagues or move the them to another workstation, you simply need to copy the plant's image files and the database file with .mat extension that was generated by the modules. When you load your data on the new workstation, the software will ask you to provide the path where images are located. Please, provide the new location of the images on the new workstation.
Some computations take too long. How can I abort them?
Unfortunately, it is not possible to abort a computation. Since our software is based on MATLAB and it is single-threaded, we could not add any mechanism to cancel long computations. However, if you are running Phenotiki from the Source Code, you may press CTRL+Z, as you would do for any computation in MATLAB, to abort.
I am experiencing problems with mclmcr.dll. How can I solve it?
If you have errors saying \textit{mclmcr.dll not found}, it could be either of the following: (i) MCR not installed, (ii) MCR installation corrupted, (iii) Older version of the library installed in a different directory. Specifically, we suggest:
1. Download the Installer of Phenotiki and/or make sure you are installing MCR
2. Different solutions can be found on-line. Search for MCR on your system and delete all the files related to it. Then, go to the point (i)
3. Search on your system for the mclmcr.dll. It can happen it is located within the System32 directory of Windows. Locate and remove it. Then, go to the step (ii)
I downloaded Phenotiki and I cannot unzip the provided zip file. How can I decompress it?
Sometimes on Linux systems, you may experience the error "An error occurred while extracting files". If you have the zip file containing Phenotiki in your Desktop folder, try to move it file in any other folder different than the Desktop and try again.
Phenotiki does not work properly under Linux virtual machines. How can I work this around?
We experienced issues using MATLAB/Phenotiki on Parallels (for Mac), depending on MATLAB and we were unable to fix them. We do not recommend using Parallels with Phenotiki on a virtual Linux Operating System.
Using the Pot Tray Analysis, I cannot find suitable parameters. What can I do?
Finding good parameters for the plant segmentation may not be immediate for challenging datasets. If you have fair results and you want to improve them, then we suggest to select a few images to trial different configurations. In the unluckily case that segmentation results are not accurate enough, we suggest to run a grid search. With this method, the software will automatically test a range of parameters and find optimal ones according to some supervision. First, segment manually a few of plant images using an external image editing software (e.g., GIMP, Photoshop). Create a black-and-white (also known as binary) image with just 0's and 1's, where 0 (black) marks background area and 1 (white) marks plant area. When you are done with this, open the Phenotiki Analysis Software and go to Pot Tray Analysis tool and load your dataset. Then, from the list of images, select one plant image for which you have manually created the foreground/background segmentation and press the right-button of your mouse, then select Set ground-truth. When the file selection window appears, select the corresponding mask for this image and repeat this operation for all the plant images for which you have manually obtained the segmentation mask. Then press on the Setting button in the bottom part of the Pot Tray Analysis Tool and press on Advanced Options. The full list of parameters will appear and you may choose the ones you want to include in the grid search, by ticking the check-boxes in the list. When you choose a parameter, you may define a range of values that the software will test against the ground-truth you have provided before. Ranges can be set in the following way.
• Numeric values: MATLAB syntax is accepted. For example:
• explicit list of values to test: [0, 10, 20, 30, 40, 50];
• all the values between 0 and 50 with a step of 10: 0:10:50;
• Text values: cell array MATLAB syntax is accepted. Some examples are:
• {Feature1, Feature2}: the software will use Feature1 and Feature2 separately;
• {Feature1,Feature2}, {Feature1,Feature3}: the software will test the best combination between Feature1 and Features2, or Feature1 and Feature3.
• Boolean values: for Boolean values you do not need to specify range of values, as they can be either 0 or 1.
What are the allowed values for the paramters?
Whilst integers parameters may accept any value, we suggest you to vary them by small amounts. For further details on the pararemters selection, we reccomand to read the corresponding sections in the user manual.
A leaf is split in half by another leaf. What should I do?
We suggest to add an annotation with the same label to the different part of the leaf. Once you annotated one part, select from the annotation list the label corresponding to the newly created label and annotated the other part of the leaf. This will result with two annotations with the same label. Once you are finished, select the <new label> to annotate a new leaf.
In the leaf labeling tool, is it possible to keep the labels consistent accross time
If you want to assign the same label to the same leaf across time, we recommend to start the annotation from the first time instant (or the last). Then, move to the next time instant and, from the list of labels, click with the right-button of your mouse and select Copy from the previous plant (or Copy from the next plant). In this way, annotations are copied with consistent numeric identifiers. Then, adapts the copied labels to adjust to growth and movement of the plant and add new labels if necessary.
Part of a leaf is assigned to another leaf. How can I make the leaf segmentation more precise?
Use more refined annotation (such as lines or freehand scribbles) to better delineate the image region of each leaf.
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2018-03-19 10:18:24
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https://www.vcalc.com/wiki/JustinLiller/Alveolar+Ventilation+Volume
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# Alveolar Ventilation Volume
Not Reviewed
V_A =
Tags:
Rating
ID
JustinLiller.Alveolar Ventilation Volume
UUID
6432ac18-efff-11e3-b7aa-bc764e2038f2
This equation computes the alveolar ventilation volume which is the volume of gas per unit time that reaches the alveoli.
## APPLICATIONS
Used by pulmonologists, doctors who specialize in treating pulmonary conditions, to measure a patients ventilation.
## INPUTS
The following describes the inputs to this equation:
• Tidal Ventilation Volume = the volume of air moved in and out of the lungs during breathing
• Dead Space Volume = the volume of inhaled air that does take part in the gas exchange
## EXAMPLES
Va = Vt - Vt = 10 - 5 = 5 L
## REFERENCE
<Any reference that follows the Creative Common Attribution ShareAlike License model …>
[1] Ventilation
Source: Wikipedia
URL: http://en.wikipedia.org/wiki/Ventilation_%28physiology%29
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2019-05-19 15:16:34
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http://www.geomerics.com/blogs/quaternions-rotations-and-compression/
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• Thursday April 16th, 2015
• Blogs
This blog was generated by a question from Glenn Fiedler regarding good schemes for compressing the relative rotation between two near-by configurations. Before we look at that problem we start with some background.
As an aside, this blog is also a first experiment with a Latex plug-in for WordPress, the WP Latex package. The results are ok, but I’m happy to hear suggestions for improvements.
## Unit quaternions and rotors
To fully understand quaternions it is my belief that you should see them in their natural setting of the geometric algebra of three-dimensional space. In this context you can see how they arise naturally as the generators of rotations, and how they act on vectors. There are also some neat tie-ins with quantum mechanics, that I hope to get to in a later post.
For now the key idea we need is that a rotation can be represented by a unit quaternion. In geometric algebra we refer to unit quaternions as rotors, a concept that then extends to arbitrary spaces. Here I will stick with the term unit quaternion.
$q = w + x \mathbf{i} + y \mathbf{j} + z \mathbf{k}$
A unit quaternion is normalised to 1:
$qq^* = w^2 + x^2 + y^2 + z^2=1.$
A unit quaternion defines a rotation matrix through a simple two-to-one relation. The mapping is two-to-one because both q and -q specify the same rotation.
Unit quaternions can be thought of as unit vectors in a 4-dimensional space, so they lie on the surface of a 3-sphere. The 3-sphere can therefore be thought of as the space of group of unit quaternions, and it is an example of a Lie group manifold. There is some fascinating geometry behind this idea, which again will have to wait for another post.
The reason unit quaternions form a group is that the product of any two unit quaternions results in a third unit quaternion. This proof is quite simple:
$(q_1 q_2) (q_1 q_2)^* = q_1 q_2 q_2^* q_1^* = q_1 q_1^* = 1.$
This multiplicative behaviour is the way we expect to combine rotations.
The fact that the group manifold is a 3-sphere helps us understand how to interpolate between rotations. The shortest path between two unit quaternions is a great circle on the 3-sphere. To find points on this path we can just linearly interpolate between the two unit quaternions and normalise the result. Quaternions get close to linearising many relationships involving rotations, which makes them so much more convenient than rotation matrices and Euler angles.
One further result is useful when studying unit quaternions. Every unit quaternion can be written as the exponentional of a quaternion vector (a quaternion with no w component),
$q = e^{B/2}$
The factor of two here ensures that the magnitude of B is precisely the angle of rotation. The direction of the quaternion vector is the rotation axis. In the language of geometric algebra we would call a quaternion vector a bivector and think of it as representing a plane.
## Relative rotations
The problem posed by Glenn concerns network physics, where you want to update the state of an object each frame. Rotating objects cannot rotate that much between frames so each new unit quaternion is close to its predecessor, which should allow for a good compression scheme.
Suppose that our base quaternion is q0, and the next unit quaternion in sequence is q1. We write
$q_1 = q_1 q_0^* q_0 = R q_0$
and focus attention on the relative rotation defined by R. Essentially we have rotated q0 back to the identity, so that the relative rotation is guaranteed to be small. We can now write
$R=\exp(B) = \cos|B| + \sin|B| \frac{B}{|B|}$
and with some simple trig functions we can recover the quaternion vector B, which is guaranteed to have a small magnitude. If f is the frequency of update, then the angular velocity is given by
$\omega = 2 |B| f$
A typical physics solver would have an upper limit on the angular velocities present in a system and typically we find |B| around 0.1, though this would depend on the update rate.
At this point you can fall back to your favourite compression scheme for small vectors in three dimensions. Glenn Fiedler’s original problem contained a number of axis-aligned boxes, which meant most updates took place along the three axial directions, allowing for further compression. But this is a bit of an accident of his set-up, and in general you would expect B to be fairly evenly distributed.
## The Cayley transform
The preceding scheme is fine, but the trig functions in both the encode and decode step are a bit of an overhead. There is an alternative way to represent a rotation in terms of a quaternion vector that dates back to Cayley and is quite useful here. Instead of the exponential form we write
$R = \frac{1+B}{1-B} = \frac{1-|B|^2}{1+|B|^2} + \frac{2B}{1+|B|^2}.$
This inverts simply to give
$B_i = \frac{R_i}{1+R_0}$
where the subscript i denotes the component of the vector part of the quaternion. These relations ensure that both the encode and decode steps are simple.
The end result is much the same as the previous scheme: a quaternion vector with small overall magnitude. This can be compressed aggressively with little loss of accuracy.
The geometry behind the Cayley transform is interesting. The transform is performing a stereographic projection of the 3-sphere to a 3-dimensional Euclidean space. Near the identity this is a good way of linearising the space, which is appropriate for handling small rotations.
## Rigid-body dynamics
The preceding schemes both assume that we only know the preceding value of a unit quaternion, and use this as a basis for computing the next one. But for most physics applications this is probably a bad idea. You can do a lot better if you keep the preceding two orientations, and use these to compute the next orientation assuming that no torques are present. This is the same as using position and velocity to update the position, assuming no forces are present. In most situations the rigid body will behave like a free particle, or subject to a force like gravity that only induces small variations. Bigger changes only come about due to collisions, which should be resolved within one or two frames.
To see what the evolution looks like in the absence of torques, we need to form the angular velocity for a time-varying unit quaternion. This is given by
$B = 2\dot{q}q^*$
In the absence of external torques B is constant, and the motion is described by
$q = e^{Bt/2}q_0.$
Now let’s assume that our time-step is δ, and we keep the values at two previous values, q0 and
$q_{-1} = e^{-B\delta/2} q_0.$
Our predicted value at q1 is
$q_1 = e^{B\delta/2} q_0 = (q_{-1} q_0^*) q_0 = q_0 q_{-1} q_0.$
Geometrically what this does is reflect the point q-1 through the point q0 to give the new predicted point. In fact, the quaternion products here are achieving the geometric product of vectors in 4 dimensions!
In most cases q1 will give a better base prediction for the actual value than q0 allowing for even more aggressive compression.
The original Latex version of this blog is available here: PDF
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2017-01-23 08:24:56
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https://www.physicsforums.com/threads/is-it-possible-to-calculate-the-prices-of-stock-market-trends-with-calculus.92214/
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# Is it possible to calculate the prices of stock market trends with calculus?
1. Oct 4, 2005
### QuantumTheory
My grandpa is an investor . I heard some people get rich off the stock market.
Is it possible to predict stock market prices?
thank you
2. Oct 4, 2005
### Pengwuino
It is not possible to predict stock market prices and it is DEFINITELY not possible to calculate them using calculus.
The problem with mathematically deducing what a stock will do is that the stock market does not follow equations or anything like that. The "variables" in the stock market are beliefs, feelings, instincts, etc instead of ratios and constants and such. It is kind of like asking if you can mathematically predict love using calculus. Is there an equation that will tell you if someone will fall in love with you? No. Same with the stock market.
People get rich off the stock market for various reasons. An extremely extremely extremely small # of people get lucky and throw money into a stock and become rich because the stock just happens to take off. A majority of people however, get out after losing or gaining a few dollars/share. A lot of people throw their money in and the stock falls and they just think its going to go back up one day but it never does and they lose a large portion of their money. A small number of people center their lives around the market however. They look at tremendous amounts of information related to specific stocks they are researching to determine how the stock might turn out and make various judgement calls and act on those calls. Those are the people who really get rich off the stock market.
Another group of people that gets rich however, are corporation presidents/CEO's. For example, we'll use Bill Gates. The reason he is rich is because Microsoft was his company. Once they went public and offered shares, Bill Gates had a large portion of the shares of the company; a large % to be exact. As Microsoft grew to have a networth higher then many countries do, Gates effectively became worth the $50 billion or whatever he's worth now (or is it 10, i dunno). This is because say, if he had stock of 50% of the company and the company was worth$100 billion, he is effectively worth \$50 billion. The thing is however... he doesn't really have this cash accessible. He would have to sell his stock which means he sells off portions of his ownership in the company.
There is one good example of what the real stock market works off of, beliefs. If Bill Gates started selling off large # of stocks, people will start believing and speculating that something is wrong with the company. This will mean that the stock share will command a lower price on wall street because it is no longer as good of a company as people think it is. Conversely, if some big wall street brokerage starts buying up shares of Microsoft, people will start thinking Microsoft is becoming a better company and closer to achieving its goals of world-wide domination. Thus, a good stock to get into.
Another implication of this system is that brokerage houses can literally destroy companies or pull failing companies out of the grave. For example, I believe Krispee Kreme went through this. Brokerage houses and investors had large amounts of money in the company (I may be wrong as to which company im thinking of though). They said they were going to expand and everything was going to be great. Well they hit the west coast and they weren't successful. The investors, who held tremendous amounts of stock in KK, realized the company wasn't worth it so they all sold off. KK's stock price then tumbled. For many companies, this action could very well destroy them. Converseley, a company can be pulled out of the ground because of a large brokerage house or large investors. I can't really think of an example right now but what basically might happen is that a brokerage house might start buying up shares of a company like crazy. This would mean the company has a larger networth now. They could also see this and issue more stock and raise capital to expand the company. Since the brokerages think its a good company, they can gain a large amount of money through stock issuance (the company that is).
3. Oct 4, 2005
### FredGarvin
Don't you think if it were possible, there would be some very very wealthy people out there?
4. Oct 4, 2005
### Anttech
Most brokerages are using Mathimatical alogriths to help them deside when to invest and when to withdraw stocks...Also when assembeling your portfolio mathimatics can help you minimise risk on a certain gain. Investors also look at GARP to determine what is a wise investment and what isnt.
Last edited by a moderator: May 2, 2017
5. Oct 4, 2005
### Tom Mattson
Staff Emeritus
Yeah, jeez, if it were possible to do that, I wouldn't be sitting around here talking to you people. :tongue2:
6. Oct 4, 2005
### Lisa!
We had a very knowledgable professor who hardly spent time to answer students' questions out of the class( I was an exception of course ). he was always sitting in front of his computer and we thought he was sutudying physics articles, but once 1 of his student had discovered that actually he was visiting a stock market site! And I should tell you he was really rich ,although he was only 35! So yes, it might be possible and you...:tongue2:
7. Oct 4, 2005
### vanesch
Staff Emeritus
I know some people who TRY to do this. In fact, this business used to be an attraction pole for physicists-out-of-their-25th-postdoc. Of course it is difficult to predict individual stock prices, but they try to find some correlations between stocks in order to be able to predict short-term moves. I knew some people (I don't know if they were very successful) who just tried to fit big neural networks onto a lot of stock data, with the hope that the neural network would fit onto the correlations. But of course, major events are never included into this. The result of elections or so cannot be foreseen. You can only hope to find some short range correlated dynamics (if the course of oil companies goes up, then maybe a few days later, the course of car manufacturers goes down or something like that). That can be enough to make small margins, and if you have enough money to bet onto your model, you can make bucks with it.
However, another known truth is that such a model cannot be generally known. If it were, the market would ALREADY correct for it by all those greedy nerds all over using their model, and as such, no margin would be left.
8. Oct 4, 2005
### Physics_wiz
I read somewhere that stock prices are chaotic, which implies that they are very sensitive to initial conditions. If anyone figured out a pattern and tried to draw a profit out of it, they would fail because they would change the initial conditions.
9. Oct 4, 2005
### QuantumTheory
Thanks for the great post Pengwuino
PHysics whiz, do you know alot about physics?
I'm 17 and dont know what to do yet, and I hope this will help me decide,thanks!
Pengwuino I will ask you more questions on stock by PM, is that ok with you?
10. Oct 4, 2005
### Physics_wiz
It looks like we have some stuff in common . Well ok, first, I don't really know much about physics. I created this account when I was in high school and was pretty good at my AP physics class. Right now, I'm in engineering...still know some physics but not much. I recently got interested in stocks and the stock market too and got a few books. I even decided on buying a few SPY shares for now until I read up more on the stock market. If you have stock questions, post them here! I'd be happy to discuss them or learn something new from the thread. Guess what? When I first started, I downloaded a few spreadsheets of data to check for any trends...I was a bit stupid. Anyways, read a few books on the stock market, they help a lot. Also, I found "Fooled by Randomness" to be an awesome book. It won't teach you much, but the author makes some very good points (pay attention to what he says) that most 17 years old or 19 years old (me) people don't know about.
11. Oct 5, 2005
### fourier jr
ya if it were possible to use calculus to get rich off the stockmarket wouldn't literally everybody who follows that stuff make a killing? it's like asking if statisticians & probabilists know any tricks to use at a casino.
12. Oct 5, 2005
### QuantumTheory
Heh I am interested in alot of things right now. mostly numismatics, and physics (time dilation and general and special relativity) its one of those things i just want to know without having to understand all the complex equations (if you think this is possible, let me know) and economics. Are there any jobs you can do with a degree in economics? do you know of any good books on stocks for beginners?
thanks
13. Oct 5, 2005
### Pengwuino
Sure, i'll try to do my best to not screw up your understanding :D
14. Oct 5, 2005
### Pengwuino
But there is tricks to use at the casino!!!
Except that its a bit difficult and casinos look for people who are doing it and kick them out.
15. Oct 5, 2005
### cronxeh
There are a few tools like Stochastic models and derivative pricing, Ito calculus, Black-Scholes partial diff eq model, Heath-Jarrow-Morton (HJM), Hull-White (HW), Monte Carlo, Black-Karasinski (BK), Cox-Ross-Rubinstein (CRR) for option pricing, Equal Probabilities Tree, Crank-Nicolson, Black-Derman-Toy (BDT), Brace-Gatarek-Musiela, Ho-Lee
16. Oct 7, 2005
### fuzzyfelt
Hi Guys - this is Husband Of Fi: darling wife brought this thread to my attention since i have only ever worked in stock markets, and thats for 15 years now.
I think the biggest issue for modelling markets is the almost infinite number of variables (each participant is a variable in themselves!). Somebody with out-math me here i am sure, but there is a big cause and effect problem with economics, ecascerbated by the fact the most of the variables are organic and emotive rather than rational. Thus, its always been my view that the best discipline to possess is psychology rather than economics. Now i, like many of you perhaps, would have thought that human nature (being the driver) was modelable, but long story short, its not! There are a few "natural number" (what is the term??) rules that certainly do get you somewhat ahead of the pack, eg, Fibonacci levels, Stochastic Oscillators, but the bulk of the analysis we use is of a statistical nature. The bulk of predictive modelling as traded by traders (eg hedge funds, rather than long only investors, eg Franklin, Fidelity etc) is one way or another based around mean reversion, this is a better than average sort of modelling too, and somewhat organic in its origins. The best rules are the simple ones, and the emotive ones, the market is driven by only two basic principles: Fear and Greed. I think for markets a 5 year view isnt too hard (thats macro economic stuff) and a 5 min view isnt so hard (thats trend and momentum) the tough views, and the ones that really pay to get right, are the 6 mth and 1 year views: splitting a chicken is probably as valid a method as any for that!
The interesting thing about bubbles is - everyone knows its a bubble, therefore the only value is picking the catalyst for the correction, not seeing the bubble itself! In the market there is intellectual snobbery associated with being bearish, becuase the great unwashed masses are always bullish and optimistic - i enjoy the irony of the fact that all charts basically start in the bottom left and corner and finish in the top right: therefore, the unwashed masses ploughs over the intellectual bears every time! yay the common man!
Re the question on books: a couple that i and a few others i know in the market have enjoyed; Market Wizards, there was 1 and 2 at least, this is a book of traders anecdotes as is interesting, and, Irrational Exhuberance by Robert Schiller which is an interesting look at late 1990s equity valuations.
Get into the markets, its fun! and even more fun with somebody elses money!!
17. Oct 13, 2007
### math dunce
I came across this question by accident, and although I agree that you probably couldnt be accurate 100% of the time, you could use math to outperform the market. Before I start, I have to admit that I am mathematically challenged. That said, I believe that by picking a small group of stocks (5-25) and assigning numeric value to certain attributes, you would increase your chances of being profitable. I trade stocks daily and average 5% a month. It wont make you a millionaire overnight but you should be able to double your money every 14.4 months. I do this without any algorithms, but, I think if you used math you could make a fortune! At the very least you would lower the risk that the market would slaughter you. I would do it but I can only do so much with my abacas.
18. Jul 22, 2010
### elfboy
I have done work on this this for awhile and have derived equations that describe the mechanics stocks market based on empirical observations. it works by breaking buy & sell orders into individual 'electrons' and 'positrons' and then there are other variables like volume
19. Jul 22, 2010
### cronxeh
god damnit.
20. Jul 22, 2010
### edward
THE ALCHEMISTS OF WALL STREET
An in depth look at Quants. Don't be fooled by the beginning the man is a multi-millionaire.
Last edited by a moderator: Sep 25, 2014
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2017-07-24 04:56:29
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https://www.overleaf.com/help/30-what-packages-do-you-support
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What packages do you support?
We use TeX Live 2016 on our servers, which provides about 4000 packages, including:
For more details please see this blog post.
Also note that you can upload .sty files for other packages. If you need a particular package from CTAN installed, please contact us, and we'll be happy to help.
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2017-11-19 04:58:45
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https://forum.allaboutcircuits.com/threads/wrangling-output-with-macspice.60619/#post-408482
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# Wrangling output with MacSPICE?
#### ctishman
Joined Oct 12, 2011
9
Hey, folks
I'm trying to complete the worksheets shown in the e-book, but they seem to refer to an ancient and arcane version of SPICE that:
a) is no longer available anywhere and
b) seems a heck of a lot more helpful than the 3f5 that's current.
For instance, in the book all the instructor has to do is list a voltage source and a resistor and BAM, out pops a page or two with useful info like voltage at various nodes and most importantly, total power dissipation.
Now let's contrast that with what I get out of SPICE 3:
Rich (BB code):
MacSpice 1 -> source Macintosh\ HD:Users:ctishman:Documents:2011:Electrical\ Study:SPICE\ files:circuit3.cir
Circuit: first example circuit
MacSpice 2 ->
Now, after a day or so of banging my head against the usual impenetrable maze of spaghetti-documentation, I managed to cajole it into printing a DC sweep, but there's still no power dissipation and everything's in scientific notation, including the steps between 0 and 100v. Yeah, it's good practice for mental multiplication but GOD is it annoying to try and make anything useful out of a quick scan of a graph.
Does anybody know a way to make this software use fixed-point notation by default, or at least until it gets to very large or small numbers?
#### charles7
Joined Jan 19, 2011
3
You appear to be referring to
which is using SPICE2.6G for its examples. This was a fortran version of Spice released in 1983. At that time circuit simulation was typically performed by feeding punched cards into a mainframe and waiting many hours. One was expected not to waste a second of precious CPU time so by default it produced a dump of everything onto a bail of line-printer paper to study while waiting for the next place in the queue.
So, here is how to make MacSpice (roughly) reproduce this behaviour:
---- Circuit_spice2.src file starts below this line ----
01 My First Circuit
v 1 0 dc 10
r 1 0 5
.options ACCT LIST NODE OPTS NOPAGE
.dc v 0 100 5
.print dc v(1) i(v)
.plot dc i(v)
.control
destroy all
set nomoremode
run
plot v(1)
.endc
.end
---- Circuit_spice2.src file ends above this line ----
By 1989, when Spice 3 came out, most people would have used a terminal such as a VT100 to review the results of simulations. It was also possible to run (small) simulations interactively in a matter of minutes. Since VT220s could only display 24 lines of 132 characters with no scroll-back having large amounts of data spew out by default was counterproductive so, by default Spice 3 does nothing until asked. To get the results you seek using the Spice 3 as nature intended use:
---- Circuit_spice3.src file starts below this line ----
01 My First Circuit
v 1 0 dc 10
r 1 0 5
.end
---- Circuit_spice3.src file ends above this line ----
And then type the following commands at the command line:
MacSpice 18 -> op
MacSpice 19 -> print all
MacSpice 20 -> dc v 0 100 5
MacSpice 21 -> print v(1) i(v)
MacSpice 22 -> plot v(1)
MacSpice 23 -> plot i(v)
etc. These commands can be stored with the netlist between .control/.endc lines, or in a script file.
Something that people sometimes miss with Spice 3 is the automatic calculation of the power dissipation of a circuit which SPICE2 used to produce. The problem is that the SPICE2 method is okay for simple circuits where adding up the the power supplied by every source is what you want. However, many so-called macro models for devices use virtual sources (and other components) as part of the model. These need to be excluded from the calculation. In practice it is easier to identify the sources representing the power supplies, and just sum the reported dissipation for these.
There is a comprehensive set of documentation, tutorials and examples for MacSpice at www.macspice.com. You can also email developer@macspice.com for additional advice and support.
Best regards
Charles
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2021-10-20 07:04:53
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http://www.mathdoubts.com/d-by-dx-sinx/
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# Derivative of sinx formula
## Formula
$\large \dfrac{d}{dx} \sin{x} \,=\, \cos{x}$
It is read as the derivative (or) differentiation of sine of angle $x$ with respect to $x$ is equal to cosine of angle $x$.
### Proof
Learn how to derive differentiation of $\sin{x}$ formula in calculus.
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2018-06-22 16:56:40
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https://www.physicsforums.com/threads/questions-about-the-speed-of-light.47888/
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# Question's About the Speed of Light
1. Oct 15, 2004
### Gecko
ok, im new to SR and had a couple questions about the speed of light. The first is, i recently read that if 2 beems of light where going towards each other at the speed of light, the distance between them would close only at 1 c instead of 2c. how is it possible that the distance between only closes in at the speed of light? shouldnt it be 2x the speed of light?
the second actually pertains to light traveling faster than 300,000 km/s. there is a site HERE that says that they have recorded light traveling waaaay faster than the speed of light. wouldn't this really screw up SR and GR? also, is this true, or, how would this be worked out in SR and GR?
thanks.
2. Oct 15, 2004
### mijoon
That is incorrect.
I should be and is.
The end of the article says;
William Happer, a physicist at Princeton University argued that several specific problems exist with the experiment, including the fact that pulses get distorted when passed through any media other than a vacuum, or empty space.
In addition, he said Wang and his colleagues performed the experiment in a way that doesn’t tell the whole story, and that it can be interpreted incorrectly. "This is anything but dramatic," said Happer. "If you look at the data, there’s essentially no evidence that [the beam] is going faster than the speed of light."
3. Oct 15, 2004
### Staff: Mentor
Here's an example that may clarify things. Say we have two flashlights 2 lightyears apart (as measured by us on earth; pretend the flashlights are on space stations at rest with respect to the earth). If we turn on the flashlights, how long does the light take to cover the distance and meet in the middle? One year, of course, since each beam travels at the speed of light = 1 lightyear/year. So, in a sense, the relative "separation rate" of the two light beams is 2c, since they get 2 lightyears closer in one year. But note that each light beam always travels at the same speed c with respect to any observer (in this case, us on the earth).
This is no different than having two runners who can run a 4 minute mile sprint towards each other. If they start a mile apart, they will meet in 2 minutes. Does that mean they can run a two-minute mile? Of course not.
What the original statement was probably referring to is this: Say two high-speed rockets are traveling directly towards each other, each moving at 0.99c with respect to the earth. If they are initially about 2 lightyears apart (according to our earth measurements) then they will crash in about one year (again, according to our earth measurements). But what would the pilot of one rocket measure as the speed of the oncoming rocket with respect to him? Special Relativity tells us that the relative speed of Rocket 2 as measured by Rocket 1 is:
$$v = \frac{0.99c + 0.99c}{1 + 0.99 \times 0.99} = 0.99995 c$$
So the relative speed of the oncoming rocket approaches, but never quite reaches, the speed of light. (Of course, for this to make sense, other relativistic effects must also be considered, such as "length contraction".)
4. Oct 15, 2004
### Gecko
yeah, thats the formula i saw. thanks for clearing that up. and i only read about half that article so i never saw the ending -.-' so does the formula you used only work for objects that have mass? which means they couldnt travel faster than light, or that formula only works for speeds less than light.
also, why is it that the speed of rocket 2 relative to rocket one is .99995c instead of almost 2c? arent they both feeling accelerations which would mean that neither could claim to be at rest so they would both have to be traveling at .99c and close in at 1.98c. and judging from your last sentance, this could probably be answered if i where to take into account "length contraction" which judging be the name means that the distance between the 2 ships would be half as long relative to one of the ships, so they would close in at half the speed but have to travel half the distance as well. thats what im guessing anyway ^.^'
5. Oct 15, 2004
### CJames
From any given reference point, it is impossible for anything to travel faster than the speed of light. If we watch these two rockets from Earth, they will both be traveling near the speed of light, and as he said the "separation rate" would be close to 2c. However, from the point of view of the rockets, the other rocket must be traveling slower than the speed of light. And yes, this is due to length contraction or time dilation, depending on whose point of view you take.
6. Oct 15, 2004
### Gecko
ooohhhh, ok i got it now. thanks alot you guys. last question (i think) does what you (CJames) posted also apply to light? like if the referance was from one beam of light that was heading towards another, the beam of light that was coming would only be traveling at c with respect to the other beam of light? but to someone observeing the 2 beams of light, the distance would be closing at a speed of 2c?
7. Oct 15, 2004
### Severian596
Good thought, Gecko, but unfortunately light beams do not have reference frames. It's impossible to define a frame of reference where a light beam (or a photon, for that matter) is at rest. If you attempt it, the photon's spacial axes x, y, and z, and its time axis t, begin merging (during the Lorentz Transformation to velocity v=c). Eventually the photon's "frame of reference" would only have one dimension, time, and one unit of measurement on this axis would be infinitely long.
In summary, things that apply to matter don't apply equally to photons or light beams.
(ps You guys can correct the nuances of my statement. I performed something like this a while ago and got a huge distortion of t' and x', where x' shrunk indefinitely, and t' expanded indefinitely...it looked like an infinity/zero problem, so that's why I assumed it was undefined. Someone else confirmed this at the time, and I believe this fits with current accepted theory)
8. Jul 8, 2009
### Guesser7
This question is irrelevant as the observer is stationary. It is like the relevance of a pedestrian crossing a road with two cars approaching from oposite directions at other at 30mph, the cars are not doing 60mph and he would no have to cross the road any faster.
On the other hand if you could be sitting on one of the beams of light it would also be irrelevant as for you time would stand still and nothing would be observed to move.
As far as two beams of photons where some collide they would convert to mass. However we would have an almost incalculably small amount M=E/C2
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2018-07-15 20:12:51
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https://datascience.stackexchange.com/questions/65545/for-a-square-matrix-of-data-i-achieve-r2-1-for-linear-regression-and-r2-0/65549
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# For a square matrix of data, I achieve $R^2=1$ for Linear Regression and $R^2=0$ for Lasso. What's the intuition behind?
For a square matrix of random data, N columns and N rows. I am fitting two models, linear regression and Lasso.
For the linear regression, I achieve a perfect score in train set, while in the Lasso I achieve a score of 0.
import pandas as pd
import numpy as np
from sklearn import linear_model
N = 100
X = pd.DataFrame(np.random.rand(N,N))
y = np.random.randint(20, size=N)
lin = linear_model.LinearRegression().fit(X,y)
lasso = linear_model.Lasso().fit(X,y)
print('Linear regression score',lin.score(X,y))
print('Lasso score',lasso.score(X,y))
Linear regression score 1.0
Lasso score 0.0 My questions will be:
1. Can someone give me an intuitive idea why for a square matrix, Lasso regression achieve different results from Linear regression?
2. What is the intuition behind the Lasso shrinking?
Note: In this case, the matrix is squared and the data/target is created randomly.
A few things going on here:
1. Your matrix is 100x100. So you have no degrees of freedom left in a linear model, which will cause $$R^2=1$$. See this post.
2. You use random numbers. Thus, they should make little sense in terms of explaining your dependent variable (it's basically noise). Since Lasso "shrinks" parameters which are not useful (and none is useful given perfect noise), all parameters are set to zero. This in turn also gives you an $$R^2=0$$. In this case the model consists only of an intercept (should be equal to 0.5), which is essentially the mean.
Change the matrix to have less columns than rows and you will get a low (but positive) $$R^2$$ for linear regression. Also look at the Lasso coefficients, they are all zero.
Have a look at the predicted values as well. You will see that the linear model does not work well. So the R-squared gives no indication about model fit in this case.
You can also try to change the random pattern to have some trend and you will find that Lasso does not shrink all coefficients to zero.
import pandas as pd
import numpy as np
from sklearn import linear_model
n = 1000
k = 5
X = pd.DataFrame(np.random.rand(n,k))
y = np.random.randint(2, size=n)
lin = linear_model.LinearRegression().fit(X,y)
lasso = linear_model.Lasso().fit(X,y)
print(lin.coef_)
print(lin.intercept_)
print(lasso.coef_)
print(lasso.intercept_)
print('Linear regression score',lin.score(X,y))
print('Lasso score',lasso.score(X,y))
Output:
[-0.00446436 -0.04509905 0.07870413 -0.00165025 -0.03951546]
0.5010650787133537
[-0. -0. 0. -0. -0.]
0.495
Linear regression score 0.003094912043144493
Lasso score 0.0
• Hi! Thanks for the answer. I am looking particularly at the case of a square matrix, same columns and same rows. I am interested in understanding how does the shrinkage works even if for a linear model you have one more degree of liberty and you can fully fit the space. – Carlos Mougan Dec 28 '19 at 10:59
• The use of the random numbers is done with purpose so there is no pattern in data and achieving any positive result is wrong. – Carlos Mougan Dec 28 '19 at 11:04
• I believe that you are answering the question of how to avoid having $R^2=1$ is linear. Not what are the differences bt lasso and linear results for a square matrix. I am looking more for the intuition of shrinkage of the space. – Carlos Mougan Dec 28 '19 at 11:09
• So then post a proper question and make clear what you ask for. I cannot read your mind – Peter Dec 28 '19 at 11:20
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2020-02-26 04:26:17
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https://zbmath.org/?q=an:1092.47027
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# zbMATH — the first resource for mathematics
Fractional powers of the algebraic sum of normal operators. (English) Zbl 1092.47027
The author establishes sufficient conditions governing the following fact: if $$A$$ and $$B$$ are unbounded normal linear operators on a (complex) Hilbert space $$H$$, then for each $$\alpha \in (0,1)$$ ${D}(({\overline{A+B}})^{\alpha}) = {D}(A^{\alpha})\cap {D}(B^{\alpha})= {D}(({\overline{A+B}})^{*\alpha}),$ where $$\overline{A+B}$$ denotes the closure of the algebraic sum $$A+B$$ of $$A$$ and $$B$$. This result is applied to characterize the domains of fractional powers of a large class of the Hamiltonians with singular potentials arising in quantum mechanics through the study of the Schrödinger equation.
##### MSC:
47B25 Linear symmetric and selfadjoint operators (unbounded) 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.) 47B44 Linear accretive operators, dissipative operators, etc.
Full Text:
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2022-01-22 08:03:24
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https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.univar.robust_1var_trimmed.html
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# naginterfaces.library.univar.robust_1var_trimmed¶
naginterfaces.library.univar.robust_1var_trimmed(x, alpha)[source]
robust_1var_trimmed calculates the trimmed and Winsorized means of a sample and estimates of the variances of the two means.
For full information please refer to the NAG Library document for g07dd
https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/g07/g07ddf.html
Parameters
xfloat, array-like, shape
The sample observations, , for .
alphafloat
, the proportion of observations to be trimmed at each end of the sorted sample.
Returns
tmeanfloat
The -trimmed mean, .
wmeanfloat
The -Winsorized mean, .
tvarfloat
Contains an estimate of the variance of the trimmed mean.
wvarfloat
Contains an estimate of the variance of the Winsorized mean.
kint
Contains the number of observations trimmed at each end, .
sxfloat, ndarray, shape
Contains the sample observations sorted into ascending order.
Raises
NagValueError
(errno )
On entry, .
Constraint: .
(errno )
On entry, .
Constraint: .
Notes
robust_1var_trimmed calculates the -trimmed mean and -Winsorized mean for a given , as described below.
Let , for represent the sample observations sorted into ascending order. Let where represents the integer nearest to ; if then is reduced by .
Then the trimmed mean is defined as:
and the Winsorized mean is defined as:
robust_1var_trimmed then calculates the Winsorized variance about the trimmed and Winsorized means respectively and divides by to obtain estimates of the variances of the above two means.
Thus we have;
and
References
Hampel, F R, Ronchetti, E M, Rousseeuw, P J and Stahel, W A, 1986, Robust Statistics. The Approach Based on Influence Functions, Wiley
Huber, P J, 1981, Robust Statistics, Wiley
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2023-01-29 06:31:39
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https://kb.osu.edu/handle/1811/19505?show=full
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dc.creator Olkhov, Rouslan V. en_US dc.creator Nizkorodov, Sergey A. en_US dc.creator Dopfer, Otto en_US dc.date.accessioned 2006-06-15T19:22:20Z dc.date.available 2006-06-15T19:22:20Z dc.date.issued 1999 en_US dc.identifier 1999-TH-13 en_US dc.identifier.uri http://hdl.handle.net/1811/19505 dc.description $^{a}$ R. V. Olkhov, S. A. Nizkorodov and O. Dopfer J. Chem. Phys. 108, 10046, 1998. en_US dc.description Author Institution: Institute for Physical Chemistry, University of Basle en_US dc.description.abstract Rotationally resolved infrared photodissociation spectra of $CH_{3}^{+}$-$Rg_{n}$ ionic complexers (Rg = He,Ne,Ar, n=1,2), have been recorded in a tendem mass spectrometer. The spectra of the dimers are compatible with $\pi$--bonded equilibrium structures where the Rg atoms are attached to the vacant $2p_{z}$ orbital of the central C atom ($C_{3v}$ symmetry). In the case of Ar, partial charge transfer into this orbital leads to a large binding energy of the complex (ca. 0.5 eV), so that only overtones of the CH stretch modes can be observed in the photofragmentation spectra. The strong intermolecular bond induces a massive deformation of the $CH_{3}+$ ion which transforms from $sp^{2}$ towards $sp^{3}$ hybridization. In the $Ar-CH_{3}+$-Ar trimer the second Ar atom is weakly attached to the other side of the $2p^{z}$ orbital of C ($C_{3v}$ symmetry). The two C-Ar bonds are not equivalent: one is strong and short, the other one is long and weak. However, tunneling splittings reveal that they can exchange their role via the intracluster inversion motion of $CH_{3}^{+}$ through a transition state with $D_{3h}$ $symmetry^{a}$. The intermolecular bonds in the He and Ne containing complexes are much weaker and result mainly from induction interactions. The $CH_{3}^{+}$ deformation is smaller and the absence of the tunneling splittings in the $Ne-CH_{3}^{+}$-Ne spectrum suggests that the trimers have $D_{3h}$ equilibrium geometries. The experimental results are supported by ab initio calculations. en_US dc.format.extent 141787 bytes dc.format.mimetype image/jpeg dc.language.iso English en_US dc.publisher Ohio State University en_US dc.title INFRARED SPECTRA OF $CH_{3}^{+}$ -$Rg_{n}$), COMPLEXES ($Rg=He, Ne, Ar, n=1,2$) en_US dc.type article en_US
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2021-09-20 12:31:01
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https://math.stackexchange.com/questions/503025/probability-with-percents
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# Probability with Percents
A local population consist of 80% women and 20% men. If we select a sample of 20 people at random from this population, then how many woman can we expect to be selected in the sample?
Any random sample from the population will still be $80$ percent women and $20$ percent men. What's $80$ percent of $20$?
If X is any one person from the population, then all we know from the problem is. $$p(X = woman) = 0.8$$ so $$E(\sum_{i=1}^{20}\delta(X_i = woman)) = \sum_{i=1}^{20}E(\delta(X_i = woman))$$ $$= \sum_{i=1}^{20}p(X_i = woman) = \sum_{i=1}^{20}0.8 = 16$$
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2019-08-23 05:12:16
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https://www.physicsforums.com/threads/real-analysis-find-sets-e-f-and-f-e-f-f.425016/
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Homework Help: (Real Analysis) Find sets E\F and f(E)\f(F)
1. Aug 28, 2010
phillyolly
1. The problem statement, all variables and given/known data
The problem #11.
3. The attempt at a solution
My partial answer is attached. There, I found E\F. I still don't understand what is f(E) and f(F) and how to derive them from E and F.
Attached Files:
File size:
24 KB
Views:
174
• IMG_0143.jpg
File size:
37.2 KB
Views:
158
2. Aug 29, 2010
From #10 we know that f(E) = f(F). Thus, f(E)\f(F) = {} = $$\emptyset.$$ Can you get the rest?
3. Aug 29, 2010
vela
Staff Emeritus
f(E) = {f(x) | x ∈ E}
Does that make sense?
4. Aug 29, 2010
phillyolly
So f(E\F) is (-1=<x<0), which is NOT a subset of an empty set.
Correct??
5. Aug 29, 2010
Not quite...almost there.
E\F = { -1 =< x < 0 }, not f(E\F). Find f(E\F). The final step's still the same and obvious.
6. Aug 29, 2010
phillyolly
My inability to understand is killing me. I am using this forum non-stop for the last 12 hours for Real Analysis questions. No progress on my part what so ever.
7. Aug 29, 2010
How are you going about teaching this to yourself? Which textbook are you using? Any other resources?
8. Aug 29, 2010
phillyolly
I only have one textbook, which is Real Analysis by Bartle and Sherbert. I've read the chapter many times and continue reading it. Thanks to your, Raskolnikov, comments, I have made some progress, but still very weak.
I also have another online book. I haven't found any helpful online sources for dummies on Real Analysis.
9. Aug 29, 2010
vela
Staff Emeritus
E is a subset of the domain of the function f. f(E) is a subset of the codomain of f. It's the set that f maps elements of E onto.
If y is an element of f(E), then there's some x in E such that f(x)=y.
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2018-09-21 03:50:13
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https://cs.stackexchange.com/questions/113305/is-the-graph-symbol-used-in-dask-a-general-notation
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# Is the graph symbol used in dask a general notation?
Dask is a flexible library for parallel computing in Python.
This piece of code define some simple functions.
def inc(x):
return x + 1
def double(x):
return x + 2
return x + y
data = [1, 2, 3, 4, 5]
output = []
for x in data:
a = inc(x)
b = double(x)
output.append(c)
total = sum(output)
this piece of code wraps the functions above, and defer their execution.
x = dask.delayed(inc)(1)
z.visualize()
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2021-12-09 11:42:07
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https://www.tutorialspoint.com/program-to-find-possible-number-of-palindromes-we-can-make-by-trimming-string-in-python
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Program to find possible number of palindromes we can make by trimming string in Python
PythonServer Side ProgrammingProgramming
Suppose we have a string s, we have to find the number of ways we can obtain a palindrome by trimming the left and right sides of s.
So, if the input is like s = "momo", then the output will be 6, as You can get ["mom", "omo", "o", "o", "m", "m", "o")
To solve this, we will follow these steps −
• Define a function expand() . This will take i, j, s
• c := 0
• while i >= 0 and j < size of s and s[i] is same as s[j], do
• i := i − 1, j := j + 1
• c := c + 1
• return c
• From the main method, do the following
• c := 0
• for i in range 0 to size of s, do
• c := c + expand(i, i, s)
• c := c + expand(i, i + 1, s)
• return c
Let us see the following implementation to get better understanding −
Example
Live Demo
def expand(i, j, s):
c = 0
while i >= 0 and j < len(s) and s[i] == s[j]:
i −= 1
j += 1
c += 1
return c
class Solution:
def solve(self, s):
c = 0
for i in range(len(s)):
c += expand(i, i, s)
c += expand(i, i + 1, s)
return c
ob = Solution()
s = "momo"
print(ob.solve(s))
Input
"momo"
Output
6
Published on 21-Oct-2020 15:47:27
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2021-06-23 11:43:14
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https://math.stackexchange.com/questions/375924/non-central-subgroup-which-is-maximal-among-abelian-normal-subgroups-is-self-cen
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# Non-central subgroup which is maximal among abelian normal subgroups is self-centralizing?
If $G$ is a supersolvabe group, and $A$ is a maximal among abelian normal subgroups of $G$, then the centralizer of $A$ in $G$ is $A$ itself (see link).
My question is about the importance of the hypothesis that "$G$ is supersolvable".
Question: Let $G$ be any group, $Z(G)$ be its center, and $A$ be a maximal among abelian normal subgroups of $G$, such that $Z(G)\neq A$ (i.e. $Z(G)<A$). Prove or disprove: the centralizer of $A$ in $G$ is $A$ itself?
(The examples I found were direct product of an abelian group with a non-abelian simple group; but here we can not have a maximal abelian normal subgroup $A$ such that $Z(G)\neq A$.)
• $S_3\times A_5$?
– user641
Apr 29, 2013 at 7:18
• @Steve: What a simple and NICE answer! Please post the comment in "Answer". Apr 29, 2013 at 7:20
Here is a counterexample of minimal order. Consider the binary octahedral group $2\mathcal{O}$ and let $\langle x \rangle$ be the cyclic subgroup of order $4$ which contains $Z(2\mathcal{O})$ but is not contained in the derived subgroup $2\mathcal{O}^\prime$. (So, $x^2$ generates the center.)
There is a $\sigma\in\operatorname{Aut}\left(2\mathcal{O}\right)$ of order $2$ defined by $\sigma:x\mapsto x^{-1}$. We construct a semidirect product based on that automorphism: let $\langle z \rangle = C_2$ and consider $G=2\mathcal{O}\rtimes \langle z \rangle$ formed by $z\mapsto \sigma$.
We observe that $z$ fixes $x^2$, so this group the same center as $2\mathcal{O}$. Therefore, $A=\langle x^2,z \rangle=Z(2\mathcal{O})\times \langle z \rangle$ is maximal among abelian normal subgroups. However, its centralizer has order $48$ (in fact it is isomorphic to $\operatorname{SL}_2(\mathbb{F}_3)\times \langle z \rangle$). So, this is a counterexample.
To see that this counterexample has minimal order, notice that the binary octahedral group is the smallest counterexample where $A$ is central.
• The group $2\mathcal{O}$ is ${\rm GL}_2(\mathbb{F}_3)$, right? The first line of second paragraph is not clear to me (How a non-abelian group can have automorphism $x\mapsto x^{-1}$) [Also you have used $x$ in automorphism as well as subgroup! I understood the difference, but the automorphism I not understood when looked into the group as a matrix group.] Mar 26, 2018 at 6:34
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2022-05-20 20:16:09
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https://gamedev.stackexchange.com/questions/101647/ping-pong-bat-is-not-detecting-the-collision-with-the-wall
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# Ping Pong bat is not detecting the collision with the wall
I have been learning Unity for last couple of days. I want to make one simple ping pong game. The idea is simple. The game has a Sphere as a ball, a plane as ground, 2 rectangles as bats and 4 rectangles as walls. Look at the image
It is a 2 players game. One player will use 'W' and 'S' key and another player will use 'Up Arrow' and 'Down Arrow' on the keyboard to move the bat up and down.
But I have a problem here. If a player moves the bat at the limit (up or down), the bat does not detect the collision with the wall. It just goes through the wall. Look at the image.
The bats and the walls have Box Collider, but still the problem persists. So what should I do so that the bat detects the collision with the wall.
• make sure you have attached rigidbody componenet – idurvesh May 29 '15 at 18:51
Use Raycast to collider: http://docs.unity3d.com/ScriptReference/Collider.Raycast.html
Just like in example:
void Update() {
if (Input.GetMouseButtonDown(0)) {
Ray ray = Camera.main.ScreenPointToRay(Input.mousePosition);
RaycastHit hit;
if (coll.Raycast(ray, out hit, 100.0F))
transform.position = ray.GetPoint(100.0F);
}
}
Replace input method and use ray pointed from bat to the wall to detect collision with walls. But in your case I DEFENITELY check bat coordinate to not exceed wall bounds (Y or Z coordinate), because it is simple and I suggest do this for you if want to study coding
Good luck!
Oh this... I tried to make a pinball game. There were several methods I tried which included making the hitbox larger, decreasing the time slice for the physics engine (the time in between each physics check was smaller) and a few other things. In the end I had to hand code the physics of the ball to shoot off when it touched the paddles, as long as the paddles weren't at rest. https://www.youtube.com/watch?v=hg3AyHEEGws I will add a link to the project soon. (a reminder wouldnt hurt)
https://www.dropbox.com/s/hraflyt9tj67ikh/ATLATLfinalWithSQL.zip?dl=0
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2020-03-28 09:59:24
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http://mathhelpforum.com/calculus/117947-parametric-trig-curve.html
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# Math Help - parametric trig curve
1. ## parametric trig curve
find the equation of the normal to the curve x= 2cosALPHA, y = 3sinALPHA at the point where ALPHA= pi/4
find the coordinates of the point where this normal cuts the curve again.
i didnt have any problems with the first question; i found the equation of the normal is y = 2x/3 - 2sqrt2/3 + 3sqrt2/2
but from here its hard to find the point where the curve and the normal intersect again. i tried using 3sinALPHA=2x/3 - 2sqrt2/3 + 3sqrt2/2 and replacing ALPHA with arccos(x/2) but that doesnt make sense does it?
2. Another approach is to note
1) (x/2)^2 +(y/3)^2 = 1 using x/2 = cos(a) y/3 = sin(a)
and y = 2/3 x + 5sqrt(2)/6
substitute this into 1)
Still it won't be pretty and I hope you have a computer or calculator to
solve.
See attachment where I have used Mathcad to solve the problem
3. hey but the equation ends up being quadratic, which value is the right one? your explanation is a bit confusing. can you show me step by step?
4. The problem was to find where the curve and the normal line intersect again! Obviously the original point is one solution to that quadratic equation. The other solution is where they intersect again.
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2016-07-31 03:26:48
|
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https://orinanobworld.blogspot.com/2018/05/
|
## Wednesday, May 30, 2018
### Getting Videos to Play in Firefox
I think I've solved a lingering problem I've had playing certain videos in Firefox, and I'm posting the details here mostly so I don't forget them and partly in case anybody else is tripping over this.
I will periodically land on a web page with a video at the top. Usually I don't want to play the video, but sometimes I do ... in which case I have mixed results getting the video to play in Firefox. Typically Chrome has no such problem with the page, which makes sense given that the issue in Firefox relates to a couple of browser extensions I use. What made diagnosing the problem tricky was that (a) results were inconsistent (some videos played, some didn't) and (b) the problem resulted from a combination of two extensions, not just one particular one.
They symptom was that, when I clicked the play button on a video, the player box would turn into a black screen with a spinner that would spin indefinitely, until an error message popped up saying that the video player had hit a time limit waiting for the video to load. Again, this happened on some videos but not others. In particular, I never had a problem with a YouTube video. It was at least consistent in that a video that triggered the error would always trigger the error, regardless of page reloads etc.
The two Firefox extensions involved are HTTPS Everywhere (which tries to force page contents to load using the more secure HTTPS protocol than the ordinary HTTP protocol) and Disable HTML5 Autoplay (which prevents videos from automatically starting to play). The first extension is a security enhancement. (For an opinion piece on why HTTPS is important, read "Why HTTPS Matters".) Unfortunately, many web sites either do not deploy HTTPS for some content or screw up their site configuration. Regarding the second extension, I find video autoplay to be rather annoying, since it frequently involves ads or other videos that I have no interest in, and forces me to play whack-a-mole to shut them the bleep up.
I'm loathe to give up either extension, and fortunately I don't have to. What works for me is a combination of two tweaks. On a site where I get problem videos (time.com is the main source, in my case), I click the toolbar button for the autoplay extension, leave "Disable Autoplay" selected, but deselect "Disable Preloading". That only needs to be done once per site. With a page open containing a problem video, I then disable HTTPS Everywhere (again, by clicking its toolbar button and deselecting the first option). That should automatically cause the page to reload, and the video will play properly. After I'm done watching, I just reenable HTTPS Everywhere. This part has to be repeated for each page containing a video that will not load via HTTPS, but it's a price I'm willing to pay to preserve security.
## Tuesday, May 15, 2018
### Grouping Rows of a Matrix
I spent a large chunk of yesterday afternoon doing something I thought would be simple (relatively speaking) in LaTeX. I wanted to group rows of a matrix (actually, in my case, a vector) with right braces, and label the groups. An example of what I wanted is in the image below.
This seems to me to be a fairly common thing to do, and LaTeX has been around over 35 years (TeX even longer), so by now it must be pretty easy. Right? Um, not so much. I wore out Google looking for packages that would do this. Curiously, it's easy to put braces over and under things:
• $\overbrace{[x_1,\dots,x_n]}$ [\overbrace{[x_1,\dots,x_n]}];
• $\underbrace{[x_1,\dots,x_n]}$ [\underbrace{[x_1,\dots,x_n]}].
There are packages to let you surround matrices, arrays etc. with a variety of delimiters (not just parentheses or square brackets). Nowhere, though, could I find a command or package to do the above.
Fortunately, something pointed me in the direction of the PGF/TiKZ package, which I've used in the past for doing drawings. It's an incredible tool in terms of both what it can do and the outstanding quality of its manual. Because it does so many things, I've never really gotten to know all its capabilities, and in particular its ability to do matrices in a picture environment.
Here is the code to do my illustration. You need to load the TiKZ package and two of its libraries in your document preamble, as follows:
\usepackage{tikz}
\usetikzlibrary{matrix, decorations.pathreplacing}
The code for the drawing is:
\begin{tikzpicture}
\matrix (vec) [matrix of math nodes, left delimiter = {[}, right delimiter = {]}] {
f_1 \\
\vdots \\
f_{a} \\
f_{a + 1} \\
\vdots \\
f_{b} \\
f_{b + 1} \\
\vdots \\
f_{c} \\
};
\node (a) at (vec-1-1.north) [right=20pt]{};
\node (b) at (vec-3-1.south) [right=20pt]{};
\node (c) at (vec-4-1.north) [right=20pt]{};
\node (d) at (vec-6-1.south) [right=20pt]{};
\node (e) at (vec-7-1.north) [right=20pt]{};
\node (f) at (vec-9-1.south) [right=20pt]{};
\draw [decorate, decoration={brace, amplitude=10pt}] (a) -- (b) node[midway, right=10pt] {\footnotesize something};
\draw [decorate, decoration={brace, amplitude=10pt}] (c) -- (d) node[midway, right=10pt] {\footnotesize something else};
\draw [decorate, decoration={brace, amplitude=10pt}] (e) -- (f) node[midway, right=10pt] {\footnotesize something silly};
\end{tikzpicture}
The name of the matrix ("vec") is arbitrary. The amplitude for the brace (10pt) and the offsets (10pt and 20pt) are matters of taste.
If you happen to know a faster way of doing this, please do share in a comment.
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2021-01-16 00:15:00
|
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|
https://math.stackexchange.com/questions/3047829/how-do-i-compute-lim-x-to-0-sinx-2x-frac-cos-x-sin-x-without
|
# How do I compute $\lim_{x \to 0}{(\sin(x) + 2^x)^\frac{\cos x}{\sin x}}$ without L'Hopital's rule?
What I've tried so far is to use the exponent and log functions: $$\lim_{x \to 0}{(\sin(x) + 2^x)^\frac{\cos x}{\sin x}}= \lim_{x \to 0}e^ {\ln {{(\sin(x) + 2^x)^\frac{\cos x}{\sin x}}}}=\lim_{x \to 0}e^ {\frac{1}{\tan x}{\ln {{(\sin(x) + 2^x)}}}}$$.
From here I used the expansion for $$\tan x$$ but the denominator turned out to be zero. I also tried expanding $$\sin x$$ and $$\cos x$$ with the hope of simplifying $$\frac{\cos x}{\sin x}$$ to a constant term and a denominator without $$x$$ but I still have denominators with $$x$$.
Any hint on how to proceed is appreciated.
Take the logarithm and use standard first order Taylor expansions: $$\lim_{x\to0} \frac{\log\bigl(\sin(x)+2^x\bigr)}{\tan(x)} =\lim_{x\to0} \frac{\log\bigl(\sin(x)+2^x\bigr)}{x+o(x)} =\lim_{x\to0} \frac{x+\log(2)x+o(x)}{x+o(x)} = 1+\log(2).$$ Then $$\lim_{x\to0} \bigl(\sin(x)+2^x\bigr)^{\cot(x)} = e^{1+\log(2)} = 2e.$$
EDIT
Maybe it's important to clarify why $$\log\bigl(\sin(x)+2^x\bigr)=x+\log(2)x+o(x)$$. I'm using the following facts:
• $$\log(1+t) = t+o(t)$$ as $$t\to0$$,
• $$\sin(x)+2^x = 1+x+\log(2)x+o(x)$$ as $$x\to0$$.
$$\lim_{x \to 0}{(\sin(x) + 2^x)^\frac{\cos x}{\sin x}}= \lim_{x \to 0}{[1+(\sin(x) + 2^x-1)]^\frac{\cos x}{\sin x}}=$$ $$=\lim_{x \to 0} \left[\left[1+(\sin(x) + 2^x-1)\right]^\frac{1}{\sin(x)+2^x-1}\right] ^{\frac{\cos x}{\sin x} (\sin(x)+2^x-1)}=$$ $$=\lim_{x \to 0} \left[\left[1+(\sin(x) + 2^x-1)\right]^\frac{1}{\sin(x)+2^x-1}\right] ^{\cos(x)\left(1+\frac{2^x-1}{\sin(x)}\right)}= e^{\lim_{x\to0}\cos(x)\left(1+\frac{2^x-1}{\sin(x)}\right)}.$$ But $$\lim_{x\to0}\frac{2^x-1}{\sin x} = \lim_{x\to0} \frac{e^{x\log2}-1}{\sin x}=\lim_{x\to0}\frac{x\log2}{x}=\log2.$$ So your limit is equal to $$e^{1+\log2}=2e$$.
PD: We use that $$e^{y}-1\sim y$$ and $$\sin y \sim y$$ when $$y\to0$$.
• How is $${\frac{\cos x}{\sin x} (\sin(x)+2^x-1)}={\cos(x)+\frac{2^x-1}{\sin(x)}}?$$ – E.Nole Dec 20 '18 at 19:14
• sorry, the last fraction must be multiplied by $\cos x$. But this does not affect thhe final result – Tito Eliatron Dec 20 '18 at 19:15
• Now it seems correct. – Tito Eliatron Dec 20 '18 at 19:17
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2019-06-25 10:16:46
|
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|
https://albertometelli.github.io/publication/0008-2020-Truly-Batch-Model-Free-Inverse-Reinforcement-Learning-about-Multiple-Intentions
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Truly Batch Model-Free Inverse Reinforcement Learning about Multiple Intentions
Giorgia Ramponi, Amarildo Likmeta, Alberto Maria Metelli, Andrea Tirinzoni, and Marcello Restelli
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, 2020.
Abstract
We consider Inverse Reinforcement Learning (IRL) about multiple intentions, \ie the problem of estimating the unknown reward functions optimized by a group of experts that demonstrate optimal behaviors. Most of the existing algorithms either require access to a model of the environment or need to repeatedly compute the optimal policies for the hypothesized rewards. However, these requirements are rarely met in real-world applications, in which interacting with the environment can be expensive or even dangerous. In this paper, we address the IRL about multiple intentions in a fully model-free and batch setting. We first cast the single IRL problem as a constrained likelihood maximization and then we use this formulation to cluster agents based on the likelihood of the assignment. In this way, we can efficiently solve, without interactions with the environment, both the IRL and the clustering problem. Finally, we evaluate the proposed methodology on simulated domains and on a real-world social-network application.
[Paper] [Talk] [BibTeX]
@InProceedings{ramponi2020truly,
author = "Ramponi, Giorgia and Likmeta, Amarildo and Metelli, Alberto Maria and Tirinzoni, Andrea and Restelli, Marcello",
editor = "Chiappa, Silvia and Calandra, Roberto",
title = "Truly Batch Model-Free Inverse Reinforcement Learning about Multiple Intentions",
booktitle = "Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics",
pages = "2359--2369",
year = "2020",
volume = "108",
series = "Proceedings of Machine Learning Research",
address = "Online",
publisher = "PMLR",
pdf = "http://proceedings.mlr.press/v108/ramponi20a/ramponi20a.pdf",
url = "http://proceedings.mlr.press/v108/ramponi20a.html"
}
|
2021-10-26 05:12:34
|
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http://experiment-ufa.ru/Prime-factorization-of-57
|
# Prime factorization of 57
If it's not what You are looking for type in the field below your own integer, and You will get the solution.
Prime factorization of 57:
By prime factorization of 57 we follow 5 simple steps:
1. We write number 57 above a 2-column table
2. We divide 57 by the smallest possible prime factor
3. We write down on the left side of the table the prime factor and next number to factorize on the ride side
4. We continue to factor in this fashion (we deal with odd numbers by trying small prime factors)
5. We continue until we reach 1 on the ride side of the table
57 prime factors number to factorize 3 19 19 1
Prime factorization of 57 = 1×3×19= $1 × 3 × 19$
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2018-04-21 19:29:53
|
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|
http://www.researchgate.net/publication/7568198_Charmed-Meson_Decay_Constants_in_Three-Flavor_Lattice_QCD
|
Article
# Charmed-Meson Decay Constants in Three-Flavor Lattice QCD
[more]
Department of Physics, Columbia University, New York, New York, United States
(Impact Factor: 7.51). 10/2005; 95(12):122002. DOI: 10.1103/PhysRevLett.95.122002
Source: OAI
ABSTRACT
We present the first lattice QCD calculation with realistic sea quark content of the ${D}^{+}$-meson decay constant ${f}_{{D}^{+}}$. We use the MILC Collaboration's publicly available ensembles of lattice gauge fields, which have a quark sea with two flavors (up and down) much lighter than a third (strange). We obtain ${f}_{{D}^{+}}=201\ifmmode\pm\else\textpm\fi{}3\ifmmode\pm\else\textpm\fi{}17\text{ }\text{ }\mathrm{MeV}$, where the errors are statistical and a combination of systematic errors. We also obtain ${f}_{{D}_{s}}=249\ifmmode\pm\else\textpm\fi{}3\ifmmode\pm\else\textpm\fi{}16\text{ }\text{ }\mathrm{MeV}$ for the ${D}_{s}$ meson.
### Full-text
Available from: Dru Renner,
• Source
• "We report on progress in the Fermilab Lattice and MILC Collaboration calculation of the D meson decay constants. This work is a continuation of the program that predicted the decay constants: f D + = 201(3)(17) and f D s = 249(3)(16) MeV [1], in good agreement with the CLEO-c value of f D + = 205.8 ± 8.5 ± 2.5 [2] [3]. "
##### Article: The Ds and D+ Leptonic Decay Constants from Lattice QCD
[Hide abstract]
ABSTRACT: We present the leptonic decay constants fDs and fD+ computed on the MILC collaboration's 2+1 flavor asqtad gauge ensembles. We use clover heavy quarks with the Fermilab interpretation and improved staggered light quarks. The simultaneous chiral and continuum extrapolation, which determines both decay constants, includes partially-quenched lattice results at lattice spacings a ~ 0:09, 0:12 and 0:15 fm. We have made several recent improvements in our analysis: a) we include terms in the fit describing leading order heavy-quark discretization effects, b) we have adopted a more precise input r1 value consistent with our other D and B meson studies, c) we have retuned the input bare charm masses based upon the new r1. Our preliminary results are fDs = 260 +/-10 MeV and fD+ = 217 +/-10 MeV. Comment: contribution to LATTICE 2009
• Source
• "In 2005, combined work by the Fermilab Lattice and MILC Collaborations [1] determined the value of the D s decay constant f D s to around 10% before it had been determined to that accuracy by experiment. When the subsequent experimental determination agreed to within one sigma, we claimed that as a successful prediction. "
##### Article: B and D Meson Decay Constants
[Hide abstract]
ABSTRACT: We present an update of our calculations of the decay constants of the D, D_s, B, and B_s mesons in unquenched 2+1 flavor QCD. We use the MILC library of improved staggered gauge ensembles at lattice spacings 0.09, 0.12, and 0.15 fm, clover heavy quarks with the Fermilab normalizations, and improved staggered light valence quarks. Comment: 7 pages; based on talked presented by P. Mackenzie at the XXVI International Symposium on Lattice Field Theory, July 14-19 2008, Williamsburg, Virginia, USA
• Source
• "The same test can obviously be performed with D + → ℓ + ν, although the experiment is more difficult because this decay is Cabibbo-suppressed. Lattice QCD [22] "
##### Article: The Physics of Charm: Recent Experimental Results
[Hide abstract]
ABSTRACT: We review the most recent results from experiments studying systems containing charmed quarks. The selection reflects the presenter's bias, and there is an emphasis on decays of open charm. We discuss precision measurements of various sorts, various new states in the charmonium system, measurements aimed at testing Lattice QCD, and the latest searches for charm mixing. We conclude with a discussion of upcoming experiments at existing and future facilities.
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2015-11-27 08:28:06
|
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|
https://www.atmschools.org/2017/ist/atsi/application-form
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# IST Asymptotic Theory of Statistical Inference (2017) - Application Form
IST Asymptotic Theory of Statistical Inference (2017)
23rd Oct to 04th Nov, 2017
Last date for submission of forms is 30th May , 2017
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2019-06-20 00:50:10
|
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https://iitutor.com/tag/complex-number/
|
# Complex Numbers with Vector Addition
Complex Numbers with Vector Addition is obtained using the sides of triangles, the sum of sides of two sides of a triangle is greater than the other side. Worked Examples of Complex Numbers with Vector Addition Suppose $\displaystyle 0 \lt \alpha, \ \beta \lt \frac{\pi}{2}$ and define complex numbers $z_n$ by z_n = […]
# Complex Number Regions
Regions defined by complex numbers $\displaystyle z = x + yi$ where $x$ and $y$ are real numbers, can be drawn using inequalities for complex number regions. Worked Example of Complex Number Regions Find the inequality of complex region $\displaystyle \Bigg|1+\frac{1}{z}\Bigg| \le 1$. \( \begin{aligned} \displaystyle \require{color} \frac{|z+1|}{|z|} &\le 1 \\ […]
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2022-07-06 00:48:38
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http://www.maa.org/meetings/mathfest/program-details/2013/invited-paper-sessions?device=desktop
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# Invited Paper Sessions
## Open and Accessible Problems in Knot Theory
Thursday, August 1, 1:00 p.m. – 5:00 p.m., Marriott, Ballroom A
With the increase in undergraduate research there is also an increased need for open and accessible problems for students to tackle. Knot theory is particularly fertile ground for such problems. Each speaker in this session will introduce a topic, pose three open questions that are accessible to undergraduate research, and place the questions in context of the topic. The final time slot in the session will consist of a discussion/reception where faculty and undergraduates can further discuss open problems with the speakers.
Organizers:
Lew Ludwig, Denison University
Turning Knots into Flowers
1:00 p.m. – 1:20 p.m.
Knot Mosaics
1:30 p.m. – 1:50 p.m.
Lew Ludwig, Denison University
The Forbidden Number of a Knot
2:00 p.m. – 2:20 p.m.
Sandy Ganzell, St. Mary’s College of Maryland
Folded Ribbon Knots in the Plane
2:30 p.m. – 2:50 p.m.
Elizabeth Denne, Washington & Lee University
Graphs that are Intrinsically Linked with an Unused Vertex
3:00 p.m. – 3:20p.m.
Joel Foisy, SUNY Potsdam
Sequences, Spiral Knots, and the Elephant in the Room
3:30 p.m. – 3:50 p.m.
Problems in Virtual Knot Theory
4:00 p.m. – 4:20 p.m.
Louis Kauffman, University of Illinois at Chicago
4:30 p.m. – 5:00 p.m.
## Developments in Commutative Algebra
Thursday, August 1, 2:00 p.m. – 5:50 p.m., Marriott, Ballroom B
Commutative algebra may be thought of as studying solutions of many equations in many unknowns when, typically, the solution is not unique. The set of solutions could then be viewed geometrically, but one can instead encode all the relevant information about the equations in algebraic objects called commutative rings. Study of the resulting ring structure can then give information about the geometric object, or can be pursued in its own right. In this Invited
Paper Session, current research results in commutative algebra will be presented in a way that will be inviting to a non-expert audience.
Organizers:
Susan Loepp, Williams College
Janet Striuli, Fairfield University
Zero-Divisor Graphs of Certain Semigroups Associated to Commutative Rings
2:00 p.m. – 2:20 p.m.
Neil Epstein, George Mason University
An Introduction to Path Ideals
2:30 p.m. – 2:50 p.m.
Leah Gold, Cleveland State University
Associated Primes of the Third Power of Cover Ideals
3:00 p.m. – 3:20 p.m.
Cameron Bishop, Fairfield University
Totally Reflexive Modules
3:30 p.m. – 3:50 p.m.
Janet Striuli, Fairfield University
Hilbert Series, H-Vectors, and the Fibonacci Sequence
4:00 p.m. – 4:20 p.m.
Branden Stone, Bard College
Going to Great Lengths…
4:30 p.m. – 4:50 p.m.
Hans Schoutens, New York City College of Technology
## Complex Geometry Research and Accessible Problems
Friday, August 2, 2:00 – 4:50 p.m., Marriott, Ballroom A
Complex geometry continues to be an area of fruitful research at all levels, from undergraduates to professional researchers. Areas as diverse as algebraic geometry and complex dynamics make use of the structure that complex analysis provides. In this session the speakers will highlight areas of current research related to complex geometry and point out opportunities for research involving undergraduates.
Organizers:
Lynette Boos, Providence College
Su-Jeong Kang, Providence College
Locating and Counting the Zeros of the Polynomials $$p(z) = z^n + z^k-1$$
2:00 p.m. – 2:20 p.m.
Michael Brilleslyper, US Air force Academy
Minimal Surface and Harmonic Mappings
2:30 p.m. – 2:50 p.m.
Composition Operators and the Geometry of the Unit Disk
3:00 p.m. – 3:20 p.m.
Christopher Hammond, Connecticut College
Complex Variables and Gravitational Lensing by a Spiral Galaxy
3:30 p.m. – 3:50 p.m.
Erik Lundberg, Purdue University
Connecting Real and Imaginary Parts of Complex Quadratic Functions to Julia Sets
4:00 p.m. – 4:20 p.m.
Julia Barnes, Western Carolina University
Complex Analysis and Soap Films
4:30 p.m. – 4:50 p.m.
Michael Dorff, Brigham Young University
## AMS-MAA Special Session: Coding Theory and ...
Friday, August 2, 2:00 – 4:50 p.m., Marriott, Ballroom B
Whenever information is transmitted or stored, errors are bound to occur. It is the goal of coding theory to devise efficient methods of adding redundancy to the information so that these errors can be detected and corrected. By its very nature, coding theory lies at the intersection of mathematics, computer science, and electrical engineering. Many different areas of mathematics have found applications in coding theory, including linear algebra, combinatorial designs, number theory, group theory, algebraic geometry, and graph theory, just to name a few. Each talk in this session will highlight a connection between coding theory and some area of mathematics, either by discussing how that branch of mathematics was used to obtain a recent coding theoretic result or by discussing how coding theory can be incorporated into an undergraduate-level course in that branch of mathematics.
Organizers:
Katherine Morrison, University of Northern Colorado
Judy L. Walker, University of Nebraska – Lincoln
Using Coding Theory for Quantum Cryptography
2:00 p.m. – 2:20 p.m.
Susan Loepp, Williams College
Coding Theory, Designs, and Finite Geometries
2:30 p.m. – 2:50 p.m.
David Clark, University of Minnesota
Coding Theory and Elementary Number Theory
3:00 p.m. – 3:20 p.m.
Justin Peachey, Davidson College
Coding Theory and Neuroscience
3:30 p.m. – 3:50 p.m.
Nora Youngs, University of Nebraska - Lincoln
Coding Theory and Graph Search Algorithms
4:00 p.m. – 4:20 p.m.
Elizabeth Weaver, Indiana University Southeast
Coding Theory and Instrumentation
4:30 p.m. – 4:50 p.m.
Jonathan Hall, Michigan State University
## Recent Developments in Mathematical Finance
Saturday, August 3, 1:00 – 4:45 p.m., Marriott, Ballroom B
This invited paper session will address recent challenges and solutions in Mathematical Finance. In particular, presentation themes will cover the theories of optimal investment, options pricing, risk management and price impact for large investors. The mathematical methods used herein are primarily from the field of Stochastic Analysis, but also branch out to include results from general Probability Theory, Partial Differential Equations, Convex and Harmonic Analysis, as well as Game Theory.
While the chief objective of the session is to provide results from the forefront of research into Mathematical Finance, a significant secondary goal is to make the talks accessible to a broader audience. Special attention will be paid to undergraduate and graduate students, as well as those researchers with a basic working knowledge of Probability and Stochastic Processes. Indeed, this session hopes to convince those who attend it that there are many interesting and challenging open problems in Mathematical Finance, both from a Mathematical and “Real World” perspective.
Organizers:
Tomoyuki Ichiba, University of California Santa Barbara
Scott Robertson, Carnegie Mellon University
Static Fund Separation of Long Term Investments
1:00 p.m. – 1:30 p.m.
Scott Robertson, Carnegie Mellon University
Occupation Times, Drawdowns, and Drawups for One-Dimensional Regular Diffusions
1:45 p.m. – 2:15 p.m.
Hongzhong Zhang, Columbia University
Volatility – A Key Concept in Mathematical Finance
2:30 p.m. – 3:00 p.m.
Stephan Sturm, Worcester Polytechnic Institute
Portfolios Under Rank-Based Equity Market Models
3:15 p.m. – 3:45 p.m.
Tomoyuki Ichiba, UCSB
4:00 p.m. – 4:30 p.m.
## Climate and Geophysical Modeling
Saturday, August 3, 2:00 – 3:50 p.m., Marriott, Ballroom A
Mathematical models of the atmosphere, oceans, and other geophysical systems and are a key part of understanding Earth system dynamics and the effects of climate change. The Earth system is immensely complex and mathematical and computational techniques are vital to analyzing and studying the dynamics. In honor of the 2013 Mathematics of Planet Earth initiative, this session will highlight role of mathematics in modeling, predicting, and explaining behavior in areas such as hydrodynamics, atmospheric and oceanic circulation, sea ice, and biogeochemical processes. It will focus research involving computational models of geophysical systems and the integration of data into these models.
Organizer:
Matthew J. Hoffman, Rochester Institute of Technology
Improving Climate Models Using Non-Global Data Assimilation and Parameter Estimation
2:00 p.m. – 2:20 p.m.
Lewis Mitchell, University of Vermont
A Hybrid Ensemble Kalman Filter / Variational Method for Data Assimilation of the Ocean
2:30 p.m. – 2:50 p.m.
Steven Penny, University of Maryland
Numerical Modeling of Vegetation-Climate Feedbacks: An Example over Western Africa
3:00 p.m. – 3:20 p.m.
Clement Alo, Montclair State University
Quasi-Periodic Fluctuations in Climate Due to Sea Ice
3:30 p.m. – 3:50 p.m.
Raj Saha, Bowdoin College
Tags:
Year:
2013
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2015-01-29 23:11:06
|
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http://mathhelpforum.com/trigonometry/78879-solving-trigonometric-equations.html
|
# Math Help - solving trigonometric equations
1. ## solving trigonometric equations
I've been stuck trying to figure this one out for a while...
sin(2A) + sin(4A) = 0
2. Originally Posted by nathanand
I've been stuck trying to figure this one out for a while...
sin(2A) + sin(4A) = 0
Let $u = 2A$
$sin(u) + sin(2u) = 0$
$2sin(u)cos(u) + sin(u) = 0$
$sin(u)(2cos(u)+1) = 0$
Either sin(u) = sin(2A) = 0 so A=0
or $2cos(u) = -1 \rightarrow cos(u) = -\frac{1}{2}$
and so $u = \frac{2\pi}{3}$ thus $2A = \frac{2\pi}{3}
\rightarrow A = \frac{\pi}{3}$
bear in mind this graph will repeat every $\pi$ radians instead of every $2\pi$ radians
3. Thanks for the help!
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2016-05-24 19:19:48
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http://spongebob.wikia.com/wiki/Message_Wall:Itsshehahnbro
|
# ChocolateBrownieBoy
## aka IDK
3,722 Edits since joining this wiki
June 8, 2014
My favorite wikis
• I live in IDK
• My occupation is IDK
• I am IDK
(Redirected from Message Wall:Itsshehahnbro)
Hey lads, feel free to post anything you want here unless it's spam. I'm an admin here so if there is any sort of problem going on, feel free to tell me right away.
• You participated in a discussion's voting stage that wasn't properly created, so you are going to have to revote: ESB:Discussions/Highlight administrative and bureaucratic requests/voting
• Alright, done. Thanks for notifying me.
• Why did you intend to switch accounts and then decide to switch back?
Nevermind.
13:33, August 18, 2016
• How you get to be an admin? And what admins do?
• View all 5 replies
• Im one of the assistants.
• CBB I tough you in ESB chat?
• http://spongebob.wikia.com/wiki/File:7736434.jpg Please delete that image, as I think it will frighten younger users.
• Done.
• So, I made a new account that I want to use here. Since the ESB Policy states that you are permitted only one account (bot exemption), can I be blocked just for the current one I'm using?
• Yes.
• Okay.
(this is kelpy g)
• Okay. I have blocked the other account.
• Could you add this to the emoticons page? Here are the two emojis in the code I'm requesting:
```*http://vignette2.wikia.nocookie.net/mismagiusstar/images/7/7a/Mockingjayyyy.png/revision/latest?cb=20160721144959
** (mockingjay)
** (Mockingjay)
** (dance2)
** (dance 2)
```
• Done.
• On ESB:Discussions, on the instructions it says "replace 'TOPIC' with 'topic of proposal to be discussed' or 'topic of proposal to be voted', depending on the stage of the discussion.
I am unsure about the directions. Do I literally replace "Topic" with "topic of proposal to be discussed", or do I put in what I want to discuss?
Don't worry, I have something to discuss. It's not spam or anything.
Yours,
Snowstripe (M •C •E)| Sunday, September 25, 2016
• Hi. Replace the topic with what is wanted to be discussed. For example, if you want to talk about adding a category, replace the "topic" with "Adding _____Category." I'm not an admin or anything, just wanted to answer.
• Thank you.
• Sorry for the late response. But yeah, per Cans.
• Ever since i left in May, things have changed here a lot. I don't remember you being admin (no offense) or Navus being an assistant.
• View all 9 replies
• JackTheRipper5210 wrote: I wonder when Navus became assistant.
Navus's old name is Ryujo111.
• Never seen Ryujo111 anywhere either.
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2016-09-25 22:32:30
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https://www.linuxjournal.com/article/8590
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# Build a Home Terabyte Backup System Using Linux
## Linux Journal
by Duncan Napier
A terabyte-plus backup and storage system is now an affordable option for Linux users. This article discusses options for building and configuring an inexpensive, expandable, Linux-based backup server.
Server Design
High-capacity disk drives are now widely available at prices that are incredibly cheap compared to those of only a few years ago. In addition, with so many Linux users now ripping CDs to disk, saving images from their digital cameras and recording video using digital camcorders and DVRs, such as MythTV, the need for backing up and archiving large amounts of data is becoming critical. Losing pictures and videos of your kids—or your audio music library—because of a disk crash would be a catastrophe. Fortunately, a high-capacity, Linux-based backup server can be built easily and cheaply using inexpensive disk drives and free software.
Virtually any home PC can meet the basic requirements for a backup server. If you have long backup windows or relatively small amounts of data, a slow computer is not an obstacle. Make sure your network is fast enough to transfer data within your backup window. For older equipment, the bottleneck for backups can be the disk data transfer bandwidth (30-150Mbps depending on disk technology).
Many consumer-level computers do not have cooling capacity for more than two internal hard disks. Most motherboards support a maximum of four onboard disks (often four ATA/IDE devices, but the two ATA/IDE and two SATA combination is becoming common). External USB high-capacity drives are also available. If your computer is older and has USB1, purchase an inexpensive USB2 PCI expansion card, which is ten times faster.
SCSI has fewer limitations, but it is expensive and has tended to lock purchasers in to “flavor-of-the-month” SCSI technologies. One option for disk expansion and upgrade is the Host Bus Adaptor (HBA), such as those made by Promise Technology. An HBA is a disk controller on a PCI expansion card. HBAs typically require no additional software, have their own BIOS and are not constrained by PC BIOS limits on disk size. HBAs let you put large disks (more than 120GB) into systems with legacy BIOSes, upgrade from ATA-33 to ATA-150 or mix ATA and SATA disks.
You may want to consider purchasing a dedicated fileserver. A bare-bones server capable of holding six disks (fully preassembled, no disks or OS) can cost less than $1,500 US. With this initial investment, you can expand disk space as needed for less than$0.80 per GB or grow by plugging in USB disks. Once you have decided how many disks you need, consider their space, cooling and noise requirements. Figure 1 shows an example of a backup system build from an old server. The system has well over a terabyte of storage capacity.
Figure 1. Storage array build from an old server (capacity of nine IDE disks, including five in a converted SCSI RAID stack). Additional IDE spots added with Promise HBA.
Even if you choose to build a server from scratch and populate it with high-capacity disks, you can expect costs for your terabyte-plus backup server still to be minimal in terms of its per-gigabyte price. This is because storage costs have decreased so dramatically. Table 1 provides a variety of different configurations for a backup server, along with estimated prices per gigabyte for each (note: prices are estimates and do not include taxes or shipping costs). As you can see from the table, costs for a new server equipped with more than two terabytes of storage can be built for a cost of less than $1.50 per gigabyte. That will back up a lot of home movies, digital pictures and music files! Table 1. Some Backup Options, with Estimated per-GB Costs TypeConfigurationCapacity (TB)Cost per GB ($)
ATA/SATA DiskInternal disk0.40.56
Linux Desktop*Three internal disks1.20.84
Linux Desktop*Three internal disks plus two USB external2.00.73
LaCie 2TB StorageNetwork server appliance21.15
Linux Server**Six internal disks2.41.21
Linux Server**Six internal plus two USB external3.21.08
*Intel Celeron D 478 325 2.53GHz, 256MB of RAM. **Intel SC5275 chassis, Intel ATX Motherboard, dual-3GHz Xeon CPUs, 2GB of RAM.
During the past few years, I have built backup servers using Red Hat Linux 9, but you can use any flavor of Linux. I use Red Hat 9 because it is stable, free, currently maintained (Fedora Legacy Project) and simple to install and configure. If you buy a new computer, you may have to use a more current version of Linux. I generally do not use RAID for low-budget systems where cost is paramount, but it is worth considering.
Software requirements for a Linux backup server are minimal. Basic network administration utilities (including the secure shell, SSH, and secure shell daemon, sshd) and rsync are required. rsync is a fast, incremental duplication/synchronization utility that comes with most Linux distributions. With SSH and rsync, you can carry out virtually all basic backup tasks. It is advantageous for a backup server also to be a fileserver, so I install Samba, the SMB fileserver as well. I use Samba because it is the default fileserver for MS Windows clients, and it also is readily accessible by any UNIX system (including Mac OS X) using a Samba client. If you have a homogenous UNIX network, you can use NFS, which I will not discuss here.
If you need to attach additional disks to your server, begin by making sure you have enough data (IDE/SATA/SCSI) cables and power lines to accommodate the expansion. Ensure that your drive is Linux-compatible (although most are). Turn off the power to your computer and disconnect the power cable. Physically attach the disk(s) to your computer. Linux should recognize the new disk(s) on boot. If your drive is not recognized, your disk is incompatible or you need to locate and install a driver for it. Check boot messages for new drives using the dmesg command. The boot message for an IDE drive may look like this:
hdb: ST3400832A, ATA DISK drive
All IDE/ATA (and some SATA) drives have the designation hdx, where the x is replaced with a letter of the alphabet (b in this case). Similarly, adding new USB or SCSI (and some SATA) disks gives boot messages indicating a new drive designation sdx, where the x is replaced by the appropriate letter.
Most Linux distributions come with a GUI disk manager. These disk managers let you define and format partitions (I generally use one partition per backup disk), assign mountpoints (for example, /data1, /data2) and mount the partition. The process also can be done from the command line using fdisk to create partitions.
Creating New Partitions
To create new partitions on hdb (above), type:
fdisk /dev/hdb
Type m at the fdisk prompt for a help summary. Typing n at the prompt asks about the new partition we are creating:
Command action
e extended
p primary partition (1-4)
p
For a single primary partition, type in p:
Partition number (1-4):1
You are then prompted for a partition number (type 1 for a single partition). Next, set the partition size by determining the first and last cylinder. Because we are using the whole disk, you should be able to select the default values (the first and last cylinders):
First cylinder (1-48641, default 1):
Using default value 1
Last cylinder or +size or +sizeM or +sizeK (1-48641, default 48641):
Using default value 48641
Type w to write the partition table. You now have a partition, /dev/hdb1, that occupies the whole disk.
Next, format the partition in the filesystem of choice (mine is in the ext3 format) using the mkfs command:
mkfs -t ext3 /dev/hdb1
Create a mountpoint for the new partition of your new disk (I'll call it /data1):
mkdir /data1
Mount the newly created ext3 partition:
mount -t ext3 /dev/hdb1 /data1
And, test reading and writing. Finally, add a line in /etc/fstab, the mount table, to mount automatically during the boot process:
# Device mountpoint fstype options freq pass_no
/dev/hdb1 /data1 ext3 defaults 1 2
Software Configuration—rsync and SSH
rsync is included in most Linux distributions. You need rsync and SSH on both your backup client and server. Check to see whether rsync installed by typing rsync at the command prompt or check your list of installed packages. If you cannot find a binary distribution for your package, you can download the source code for rsync by following links on the rsync home page (see the on-line Resources).
The simplest way to run rsync over a network is as a standalone application using SSH for authentication. You can run rsync as a daemon with more features, but you won't need to in this case. I illustrate this here with a backup client named foo and a server named bar.
To replicate the directory /home on Linux machine foo with directory /data1/foo of backup server bar from client foo using rsync and SSH, type:
rsync -az /home -e ssh bob@bar:/data1/foo
You will be prompted for user bob's password, and then the foo /home directories are replicated to /data1/foo/home on bar (bob needs an account on the server and write permission for /data1/foo).
To avoid having to type bob's password each time, create a private/public key pair for SSH authentication without a password. This allows you to automate the login process.
Generating the Key Pair
On the machine you want to log in to (logged on as bob on bar in this case), type ssh-keygen -d to generate the key pair. Enter a password if the key will be accessible/readable to other users. Otherwise, press Return. Change into the .ssh directory and copy the public key to the allowed list:
cd ~/.ssh
cp id_dsa.pub authorized_keys2
Copy the private key to the .ssh directory of the account on the machine you will be logging in from (for example, root user on foo). Remove the private key from bar (the machine you want to log on to):
scp id_dsa root@foo:~/.ssh/id_dsa
rm id_dsa
On the machine you're logging in from, start the SSH agent, and add the key to the agent's list (ssh-add asks for a password if you typed one in the first step above):
eval ssh-agent
ssh bob@foo
You can run a script on foo to replicate foo on bar using bob's account on bar. You should read the documentation for rsync, which has numerous features (more than 70 command-line options). In particular, the -delete option can have disastrous consequences if misused. Listing 1 shows a seven-day incremental backup. Files altered or deleted on each day of the week are deposited in directories named for the day (set by -backup-dir). The most recent backup is stored in the directory current.
Listing 1. Full and Incremental rsync
#!/bin/sh
# This script does backups of foo to the backup server bar
# in a 7 day rotating incremental backup.
# Based on script by Andrew Tridgell
# directory to backup
BDIR=/home
# Remote directory on backup server
BACKUP_HOME=/data1/foo
# Backup login account on remote server
# the name of the backup server
BSERVER=bar
BACKUPDIR=date +%A
OPTS="--force --ignore-errors --delete --backup
-backup-dir=$BACKUP_HOME/$BACKUPDIR -av"
export PATH=$PATH:/bin:/usr/bin:/usr/local/bin # Dump output to backup file date > /var/log/backup.$BACKUPDIR.log
# the following line clears the last week's incremental directory
[ -d /tmp/emptydir ] || mkdir /tmp/emptydir
rsync --delete -a /tmp/emptydir/
BACKUP_LOGIN@$BSERVER:$BACKUP_HOME/$BACKUPDIR/ rmdir /tmp/emptydir # now the actual transfer rsync$OPTS $BDIR BACKUP_LOGIN@$BSERVER:$BACKUP_HOME/current >> /var/log/backup.$BACKUPDIR.log
If you prefer a compressed archive format, you still can run tar for a full backup over the network:
tar cvfz - /home | ssh bob@bar dd of=/data1/foo/current.tar.gz
and use the -newer option for an incremental tar backup.
rsync is more efficient than the tar command, because rsync copies only the differences between the current and previous copy of the data.
You can get by with rsync and SSH on most platforms (including MS Windows), but in reality, a fileserver setup is preferable, especially if you are running MS Windows clients. For MS Windows machines, a Windows backup application is preferable. The easiest way to do this is to run the backup to write to a share on the Samba server.
Software Configuration—Samba
If your Linux installation supports SMB file sharing, Samba is probably installed. If not, binaries are included with virtually all distributions. If this isn't the case with your distribution, or if you prefer to use the very latest Samba version, download the source code and compile and install. Official Samba distributions are available from the Samba home page (see Resources). Refer to the documentation there for installing and initially configuring Samba.
Once your backup server has Samba server installed, all Samba configurations are made by editing the smb.conf file, which is usually in /etc/samba/smb.conf or /usr/local/samba/lib/smb.conf. Graphical configuration utilities like SWAT usually are included with Samba. See your documentation for information about starting or stopping Samba. You should configure your server to ensure that Samba starts when the server initially boots up.
Following our backup example above, on server bar, set up a simple smb.conf file or try appending the section below to the existing smb.conf file to define a share called bob:
[bob]
comment = foo backup account
path = /data1/foo
valid users = bob
public = no
writable = yes
Next, add bob with any secure password as a Samba user (bob must have a Linux account as well as permission to read/write the /data1/foo directory):
smbpasswd -a bob
For MS Windows clients, map the share \\bar\bob as a network drive in MS Windows using the user name bob and the SMB password for the bob Samba account. You then should be able to run backups to the mapped network drive. I typically use the free ntbackup software and set it up to write .bkf files to network storage. ntbackup comes free with Windows 2000 and XP and can run automated, regularly scheduled backups from the Windows client. Windows client-based backups have the advantage of backing up the entire state of the system (including the Windows registry).
You also can use Samba to serve files to most UNIX or Mac OS X clients. The smb client is installed by default in Mac OS X. In Linux distributions, make sure that the smb client package is installed. The smb share should be mounted onto the /backup mountpoint of machine foo:
mount -t smbfs -o username=bob,password=somepassword //bar/foo /backup
To have the backup drive mount when the system boots, place a line such as the following in /etc/fstab:
//bar/data1/foo /backup smbfs rw,username=bob,password=somepassword 0 0
To add an additional level of security, you may consider adding a second server to your overall backup plans consisting of a server that exists off-site, away from the home or office location where your primary backup server is located. This allows you to mirror your backup server to an off-site location once a week. That way, if you have a fire or some other catastrophe at your primary location, your data still will be available. Figure 2 shows a sample configuration for this setup.
Figure 2. Example backup scenario with client foo, backup server bar and off-site mirror baroffsite.
Listing 2 is a basic script that mirrors the server bar with an off-site mirror baroffsite using rsync. Always set up backups to run automatically and on a regular schedule. Always keep logs of your backups, and always check the backup logs.
Listing 2. rsync Mirroring bar to baroffsite
#!/bin/sh
# Mirror /data1 on bar to /data1/bar on baroffsite.
#Backup directory on bar
BACKUP=/data1
#Backup directory on baroffsite
BACKUP_OFF=/data1/bar
# Give the day of week as name of backup
BACKUPNAME=date +%A
# Offsite server
BSERVER=baroffsite
# Backup account on backup server
BAC_ACC=backup
date > /var/log/backup.$BACKUPNAME.log /usr/bin/rsync -avz --delete -e ssh$BACKUP $BAC_ACC@$BSERVER:$BACKUPOFF >> /var/log/backup.$BACKUPNAME.log
# Email the log to administrator
cat /var/log/backup.$BACKUPNAME.log | mail -s 'Mirror Check' backup_guy@mycompany.com Monitoring Your Backup Server In order to monitor your backup process and make sure your backups are running as scheduled (and that your backup server hasn't run out of disk space), it's important to put some automated monitoring and reporting into place. Listing 3 is a simple script that can be set up to run periodically via cron and send you a summary of the backups that have occurred and how much disk space is remaining on each of your partitions. Listing 3. Simple Timestamp and Disk Space Lister #!/bin/sh # Check space on partitions # List timestamps in chronological order BACKUPS=/data1 #Identify directories to check # Give the day of week as name of backup BACKUPNAME=date +%A #Timestamp date > /var/log/backup.$BACKUPNAME.log
# Disk space on partitions
df -k > /var/log/backup.$BACKUPNAME.log echo ' ' >> /var/log/backup.$BACKUPNAME.log
#List timestamps on backup server
# ls -lRt is much more verbose
ls -lt $BACKUPS/* >> /var/log/backup.$BACKUPNAME.log
# Email the log to administrator
cat /var/log/backup.\$BACKUPNAME.log | mail -s 'Backup Check'
backup_guy@mycompany.com
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2021-10-27 03:35:33
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https://socratic.org/questions/how-do-you-find-the-product-q-r-2-q-r
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# How do you find the product (q+r)^2(q-r)?
Jan 20, 2017
${q}^{3} + {q}^{2} r - q {r}^{2} - {r}^{3}$
#### Explanation:
We are asked to find the product of two numbers ${\left(q + r\right)}^{2}$ and $\left(q - r\right)$. The algebraic expressions $\left(q + r\right)$ and $\left(q - r\right)$ reflect the internal structure of each number.
We can think of ${\left(q + r\right)}^{2}$ as equal to $\left(q + r\right)$$\left(q + r\right)$
So ${\left(q + r\right)}^{2}$$\left(q - r\right)$ = $\left(q + r\right)$$\left(q + r\right)$ $\left(q - r\right)$
We should be familiar with the result
$\left(q + r\right)$$\left(q - r\right)$= $\left({q}^{2} - {r}^{2}\right)$
So $\left(q + r\right)$$\left(q + r\right)$ $\left(q - r\right)$= $\left({q}^{2} - {r}^{2}\right)$$\left(q + r\right)$
And multiplying out in full
$\left({q}^{2} - {r}^{2}\right)$$\left(q + r\right)$= ${q}^{3} + {q}^{2} r - q {r}^{2} - {r}^{3}$
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2019-09-21 02:40:42
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https://im.kendallhunt.com/HS/students/1/3/7/index.html
|
# Lesson 7
The Correlation Coefficient
• Let’s see how good a linear model is for some data.
### 7.1: Which One Doesn’t Belong: Linear Models
Which one doesn’t belong?
### 7.2: Card Sort: Scatter Plot Fit
Your teacher will give you a set of cards that show scatter plots of data. Sort the cards into 2 categories of your choosing. Be prepared to explain the meaning of your categories. Then, sort the cards into 2 categories in a different way. Be prepared to explain the meaning of your new categories.
### 7.3: Matching Correlation Coefficients
1. Take turns with your partner to match a scatter plot with a correlation coefficient.
2. For each match you find, explain to your partner how you know it’s a match.
3. For each match your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
1. $$r = \text-1$$
2. $$r = \text-0.95$$
3. $$r = \text-0.74$$
4. $$r = \text-0.06$$
5. $$r = 0.48$$
6. $$r = 0.65$$
7. $$r = 0.9$$
8. $$r = 1$$
Jada wants to know if the speed that people walk is correlated with their texting speed. To investigate this, she measured the distance, in feet, that 5 of her friends walked in 30 seconds and the number of characters they texted during that time. Each of the 5 friends took 4 walks for a total of 20 walks. Here are the results of the first 20 walks.
distance (feet) number of characters texted distance (feet) number of characters texted 105 142 95 138 125 110 125 110 115 120 160 80 140 98 175 64 145 102 130 106 160 89 140 95 170 72 150 95 140 100 155 90 130 107 160 74 105 113 135 108
Over the next few days, the same 5 friends practiced walking and texting to see if they could walk faster and text more characters. They did not record any more data while practicing. After practicing, each of the 5 friends took another 4 walks. Here are the results of the final 20 walks.
distance (feet) number of characters texted distance (feet) number of characters texted 140 140 165 151 150 155 170 136 160 151 190 143 155 170 205 132 180 125 205 128 205 130 210 140 225 95 215 109 175 161 220 105 195 108 230 126 155 142 225 138
1. What do you notice about the 2 scatter plots?
2. Jada noticed that her friends walked further and texted faster during the last 20 walks than they did during the first 20 walks. Since both were faster, she predicts that the correlation coefficient of the line of best fit for the last 20 walks will be closer to -1 then the correlation coefficient of the line of best fit for the first 20 walks. Do you agree with Jada? Explain your reasoning.
3. Use technology to find an equation of the line of best fit and the correlation coefficient for each data set. Was your answer to the previous question correct?
4. Why do you think the correlation coefficients for the 2 data sets are so different? Explain your reasoning.
### Summary
While residuals can help pick the best line to fit the data among all lines, we still need a way to determine the strength of a linear relationship. Scatter plots of data that are close to the best fit line are better modeled by the line than scatter plots of data that are farther from the line.
The correlation coefficient is a convenient number that can be used to describe the strength and direction of a linear relationship. Usually represented by the letter $$r$$, the correlation coefficient can take values from -1 to 1. The sign of the correlation coefficient is the same as the sign of the slope for 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.
While it is possible to try to fit a linear model to any data, you should always look at the scatter plot to see if there is a possible linear trend. The correlation coefficient and residuals can also help determine whether the linear model makes sense to use to estimate the situation. In some cases, another type of function might be a better fit for the data, or the two variables you are examining may be uncorrelated, and you should look for other connections using other variables.
### Glossary Entries
• 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.
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2022-01-22 10:46:29
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https://www.aakash.ac.in/important-concepts/physics/angular-momentum
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• Call Now
1800-102-2727
•
# Angular momentum, definition and mathematical representation, angular momentum for system of particles and rigid body, practice problems, FAQs
Why does the Earth keep on spinning? What started it spinning to begin with? And how does an ice skater manage to spin faster and faster simply by pulling her arms in? Why does she not have to exert a torque to spin faster? Questions like these have answers based on angular momentum.
Do you know why the earth keeps on spinning for thousands of years? And how the ice skater increases and decreases its rotational speed without applying any external torque. She can manage to do this only by her hands. This all can be explained by the angular momentum. Let's see what angular momentum is !
• Angular momentum
• Angular momentum in component form
• Angular Momentum of a System of Particles
• Angular Momentum of a Rigid Body Angular Momentum of Rigid Body
• Practice problems
• FAQs
## Angular momentum
Angular momentum is the rotational analogue of linear momentum. It is also known as the moment of linear momentum.
Let us consider a particle is moving in x-y plane and r is the position vector of that particle at a particular point. It is moving with a translational velocity and the velocity is making an angle 0 with the position vector.
Thus, the angular momentum (moment of linear momentum) of this particle about point O is given as follows:
$\stackrel{\to }{{L}_{o}}=\stackrel{\to }{r}×\stackrel{\to }{p}$
Since $\stackrel{\to }{p}=m\stackrel{\to }{v}$
$\stackrel{\to }{{L}_{o}}=m\left(\stackrel{\to }{r}×\stackrel{\to }{v}\right)$
Using the right-hand thumb rule for the cross product, we get the direction of the angular momentum as going upwards in the positive z-direction.
We can calculate the angular momentum in two ways, either by taking the perpendicular component of the velocity vector or by taking the perpendicular component of the position vector.
On taking the perpendicular component of the velocity vector, we get the following:
$|\stackrel{\to }{{L}_{o}}|=m|\stackrel{\to }{r|}|\stackrel{\to }{v}|sin\theta$
$|\stackrel{\to }{{L}_{o}}|=m|\stackrel{\to }{r|}|\stackrel{\to }{{v}_{\perp }}|$
$|\stackrel{\to }{{L}_{o}}|=|\stackrel{\to }{r|}|\stackrel{\to }{{p}_{\perp }}|$
On taking the perpendicular component of the position vector, we get the following:
$|\stackrel{\to }{{L}_{o}}|=m|\stackrel{\to }{v|}|\stackrel{\to }{r}|sin\theta$
$|\stackrel{\to }{{L}_{o}}|=m|\stackrel{\to }{v|}|\stackrel{\to }{{r}_{\perp }}|$
$|\stackrel{\to }{{L}_{o}}|=|\stackrel{\to }{p|}|\stackrel{\to }{{r}_{\perp }}|$
## Angular Momentum in Component Form
$\stackrel{\to }{L}=\stackrel{\to }{r}×\stackrel{\to }{p}$
$\stackrel{\to }{r}={r}_{x}\stackrel{^}{i}+{r}_{y}\stackrel{^}{j}+{r}_{z}\stackrel{^}{k}$
$\stackrel{\to }{p}={p}_{x}\stackrel{^}{i}+{p}_{y}\stackrel{^}{j}+{p}_{z}\stackrel{^}{k}$
$\stackrel{\to }{L}=\stackrel{\to }{r}×\stackrel{\to }{p}=\left({r}_{y}{p}_{z}-{r}_{z}{p}_{y}\right)\stackrel{^}{i}+\left({r}_{z}{p}_{x}-{r}_{x}{p}_{z}\right)\stackrel{^}{j}+\left({r}_{x}{p}_{y}-{r}_{y}{p}_{x}\right)\stackrel{^}{k}$
$\stackrel{\to }{L}=\stackrel{\to }{{L}_{x}\stackrel{^}{i}}+\stackrel{\to }{{L}_{y}\stackrel{^}{j}}+\stackrel{\to }{{L}_{z}\stackrel{^}{k}}$
## Angular momentum of particle in circular path
Consider a particle of mass moving in a circle of radius r at an angular speed ω about the z-axis in a plane parallel to the x-y plane passing through the origin O.
The velocity of the particle is given by
The vector from the centre of the circle (the point O ) to the object is given by
The angular momentum about the centre of the circle is the vector product
${\stackrel{\to }{L}}_{o}={\stackrel{\to }{r}}_{O}×\stackrel{\to }{p}={\stackrel{\to }{r}}_{O}×m\stackrel{\to }{v}=rmv\stackrel{^}{k}=rmr\omega \stackrel{^}{k}=m{r}^{2}\omega \stackrel{^}{k}$
The magnitude is and the direction is in the -direction. Angular Momentum of a System of Particles Let us consider a system of particles with masses m1, m2, m3,.....mn having position vectors , respectively, and rotating about the axis of rotation with velocities , respectively.
The net angular momentum of this system of particles will be the vector sum of all the angular momentum of all the individual particles.
$\stackrel{\to }{L}=\stackrel{\to }{{L}_{1}}+\stackrel{\to }{{L}_{2}}+\stackrel{\to }{{L}_{3}}+..........+\stackrel{\to }{{L}_{n}}$
$\stackrel{\to }{L}={m}_{1}\left(\stackrel{\to }{{r}_{1}}×\stackrel{\to }{{v}_{1}}\right)+{m}_{2}\left(\stackrel{\to }{{r}_{2}}×\stackrel{\to }{{v}_{2}}\right)+{m}_{3}\left(\stackrel{\to }{{r}_{3}}×\stackrel{\to }{{v}_{3}}\right)..........+{m}_{n}\left(\stackrel{\to }{{r}_{n}}×\stackrel{\to }{{v}_{n}}\right)$
## Angular Momentum of a Rigid Body Angular Momentum of Rigid Body
The angular momentum of a rigid body rotating about a fixed axis can be viewed as many small particles moving in a circular motion about the axis with different velocities. All the particles have the same angular velocity as they are a part of the same body.
A rigid body rotating about the axis can be considered as the combination of different particles having the circular motion about the same axis of rotation. So the angular momentum of the body is equal to the sum of the angular momentum of all particles present in the body. As they are on same body to angular velocity will be the same for all particles.
Let us consider the particles with masses m1, m2, m3,.....mn, having position vectors , respectively, and rotating about the axis of rotation AB with velocities , respectively.
The angular momentum of the system of particles about the axis AB is given as follows:
${\stackrel{\to }{L}}_{AB}=\stackrel{\to }{{L}_{1}}+\stackrel{\to }{{L}_{2}}+\stackrel{\to }{{L}_{3}}+..........+\stackrel{\to }{{L}_{n}}$
${\stackrel{\to }{L}}_{AB}={m}_{1}\left(\stackrel{\to }{{r}_{1}}×\stackrel{\to }{{v}_{1}}\right)+{m}_{2}\left(\stackrel{\to }{{r}_{2}}×\stackrel{\to }{{v}_{2}}\right)+{m}_{3}\left(\stackrel{\to }{{r}_{3}}×\stackrel{\to }{{v}_{3}}\right)..........+{m}_{n}\left(\stackrel{\to }{{r}_{n}}×\stackrel{\to }{{v}_{n}}\right)$
For all particles,
${L}_{AB}={m}_{1}{r}_{1}{v}_{1}+{m}_{2}{r}_{2}{v}_{2}+{m}_{3}{r}_{3}{v}_{3}.............+{m}_{n}{r}_{n}{v}_{n}$
Since
${L}_{AB}={m}_{1}\omega {r}_{1}^{2}+{m}_{2}\omega {r}_{2}^{2}+{m}_{3}\omega {r}_{3}^{2}.............+{m}_{n}\omega {r}_{n}^{2}$
${L}_{AB}=\omega \sum _{i=1}^{n}{m}_{i}{r}_{i}^{2}$
Since $I=\sum _{i=1}^{n}{m}_{i}{r}_{i}^{2}$
${L}_{AB}=I\omega$
The angular momentum of a rigid body about a particular axis of rotation is the moment of inertia of that rigid body about that axis multiplied by the angular velocity of that rigid body.
The angular momentum is similar to its linear counterpart in terms of the following formula:
$\stackrel{\to }{L}=I\stackrel{\to }{\omega }$
$\stackrel{\to }{p}=m\stackrel{\to }{v}$
Where the moment of inertia is the rotational equivalent of the mass and the angular velocity is the rotational equivalent of the linear velocity.
## Practice problems
Q. Two particles A and B, each of mass m, are attached rigidly to the ends of a light rod of length l. The rod is clamped at the centre such that the system rotates about the perpendicular bisector of the rod at an angular speed 𝜔. Calculate the angular momentum of the individual particles and of the system about the axis of rotation.
A.
As the axis of rotation is fixed, the particles are performing pure rotational motions.
The angular momentum of particle A is:
${L}_{A}=mvr=m\left(\omega \frac{l}{2}\right)\left(\frac{l}{2}\right)=\frac{m\omega {l}^{2}}{4}$
As the rotation is clockwise, the orientation of the angular momentum is also clockwise.
Similarly, the angular momentum of particle B is:
${L}_{B}=mvr=m\left(\omega \frac{l}{2}\right)\left(\frac{l}{2}\right)=\frac{m\omega {l}^{2}}{4}$
Angular momentum of the system,
${L}_{sys}={I}_{sys}\omega =\left[\frac{m\omega {l}^{2}}{4}+\frac{m\omega {l}^{2}}{4}\right]=\frac{m\omega {l}^{2}}{2}$
Q. A particle of mass m is projected on the horizontal ground with an initial velocity of u, making an angle 𝜃 with the horizontal. Find out the angular momentum of the particle about the point of projection when it is at the highest point of the path.
A.
At this point, Hmax is the perpendicular distance of the line of motion from the point of projection.
Velocity of the particle at this point is,
We know that, ${H}_{max}=\frac{{u}^{2}{sin}^{2}\theta }{2g}$
Thus, the angular momentum is as follows:
$L={r}_{\perp }p$
$⇒L=\left({H}_{max}\right)m\left(ucos\theta \right)$
$⇒L=\frac{{u}^{2}{sin}^{2}\theta }{2g}×m\left(ucos\theta \right)$
$⇒L=\frac{m{u}^{3}{sin}^{2}\theta cos\theta }{2g}$
As the direction of the angular momentum is along axis, we can write
$⇒\stackrel{\to }{L}=\frac{m{u}^{3}{sin}^{2}\theta cos\theta }{2g}\left(-\stackrel{^}{k}\right)$
Q. Calculate the angular momentum of the Earth about its axis considering Earth as a uniform density sphere of mass and radius
A.
Time period of rotation,
Angular velocity, $\omega =\frac{2\pi }{T}=\frac{2\pi }{86400}$
Moment of inertia, $I=\frac{2}{5}M{R}^{2}$
Angular momentum,
Q. A meteor of mass enters Earth’s atmosphere and is observed by someone on the ground before it burns up in the atmosphere. The vector gives the position of the meteor with respect to the observer. At the instant the observer sees the meteor, it has velocity , and it is accelerating at a constant along its path, which for our purposes can be taken as a straight line.
What is the angular momentum of the meteor about the origin, which is at the location of the observer?
A.
The meteor is entering Earth’s atmosphere at an angle of 90.0° below the horizontal, so the components of the acceleration in the x- and y-directions are
We write the velocities using the kinematic equations.
At the instant observer sees the meteor,
Position of meteor, $\stackrel{\to }{r}=\left(25×{10}^{3}\stackrel{^}{i}+25×{10}^{3}\stackrel{^}{j}\right)$
The angular momentum is
$\stackrel{\to }{L}=\stackrel{\to }{r}×\stackrel{\to }{p}$
$=\left(25×{10}^{3}\stackrel{^}{i}+25×{10}^{3}\stackrel{^}{j}\right)×\left[15.\left(-2000\stackrel{^}{j}\right)\right]$
## FAQs
Q. Write the dimensional formula for Angular momentum.
A. The dimensional formula is $\left[M{L}^{2}{T}^{-1}\right]$.
Q. When a mass is rotating in plane about a fixed point, Its angular momentum is directed along the
a. Radius Tangent to the orbit
b. Line at angle of to the
c. plane of rotation
d. Axis of rotation
A. When a mass is rotating in a plane about a fixed point, its angular momentum is directed along the axis of rotation.
Q. Is angular momentum a scalar quantity or a vector quantity
A. Angular momentum has both direction and magnitude and hence is a vector quantity.
Q. Suppose the angular momentum of a body is zero at about some point. Is it necessary that it will be zero at a different point?
A. No, it is not necessary that angular momentum will be zero about all the points if it is zero about any point. Assume a body travelling along the x−axis with some velocity. Now the angular momentum of the body about the origin will be zero (${r}_{\perp }=0$) It will be zero about every point lying on the x−axis. But the value of angular momentum will be non-zero about any other point having non zero y-coordinate value.
Q. For a body the angular momentum is zero about a point. Is it required that it will be zero about all the points?
A. No, it is not necessary. For example if a body is moving along y- axis the angular momentum of body will be zero about the origin as (${r}_{\perp }=0$) but about the point which is not on the y- axis the angular momentum will be non- zero.
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2023-01-29 21:40:10
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|
https://stats.stackexchange.com/questions/455561/error-fitting-random-slopes-with-glmmpql
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# Error fitting random slopes with glmmPQL
I am currently trying to fit a GLM to to describe the following data with both random slopes and intercepts:
The following code with no random slope works:
PQL <- glmmPQL(TorqueT ~ twist, random = ~ 1| BrainID, family = gaussian(link = "log"), data = Cplane)
summary(PQL)
And provides the appropriate output however when I attempt to incorporate random slopes with the following code:
PQL <- glmmPQL(TorqueT ~ twist, random = ~ twist| BrainID, family = gaussian(link = "log"), data = Cplane)
iteration 1
iteration 2
Error in chol.default((value + t(value))/2) : the leading minor of order 2 is not positive definite
|
2020-04-04 19:47:49
|
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|
https://www.albert.io/ie/gmat/adam-beth-and-carrie-join-together-to-build-puzzles
|
Free Version
Difficult
Adam, Beth and Carrie Join Together to Build Puzzles
GMAT-9ARE9C
Adam, Beth, and Carrie enjoy building puzzles. Adam can build $8$ puzzles an hour, Beth can build $6$ an hour, and Carrie can build $5$ an hour. Assume that if the three friends work simultaneously on the same puzzle, there is no loss in production speed.
To the nearest minute, how long will it take Adam, Beth, and Carrie working together to build $1$ puzzle?
A
$1$ minute
B
$2$ minutes
C
$3$ minutes
D
$4$ minutes
E
$5$ minutes
|
2017-03-01 20:14:21
|
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https://ghc.haskell.org/trac/ghc/ticket/9907
|
Opened 4 years ago
Closed 3 years ago
## #9907 closed bug (fixed)
# "Unknown PEi386 section name .text$printf'" error in GHCi on Windows Reported by: Owned by: mmikolajczyk Phyx- normal 7.10.3 GHCi 7.8.3 hvr, Phyx-, igloo Windows x86 GHCi crash #7103, #10051, #7056, #8546 Phab:D1244 ### Description I work on a Haskell library interfacing with foreign C++ library. While trying to use it in GHCi on Windows 8.1 64bit, I encountered an error message that said: <loading other libraries> Loading package library-0.1.0.0 ... <interactive>: Unknown PEi386 section name .text$_ZNSt6vectorIcSaIcEED1Ev' (while processing: c:\path\to\file.o)
ghc.exe: panic! (the 'impossible' happened)
(GHC version 7.8.3 for i386-unknown-mingw32):
I've prepared a minimal example triggering this bug and attached it to this bug report. On Linux (Arch 64bit), after cabal build and cabal repl it behaves as intended:
GHCi, version 7.8.3: http://www.haskell.org/ghc/ :? for help
[1 of 1] Compiling Example ( Example.hs, interpreted )
λ: foo
Test
GHCi, version 7.8.3: http://www.haskell.org/ghc/ :? for help
n name .text\$printf' (while processing: dist\build\cbits\ex.o)
ghc.exe: panic! (the 'impossible' happened)
(GHC version 7.8.3 for i386-unknown-mingw32):
Crashing in GHCi means that I cannot use it with programs that contain TH splices, what is important for me.
### Changed 4 years ago by mmikolajczyk
Minimal cabal project triggering this bug
### comment:1 Changed 3 years ago by kdmadej
I've encountered a similar error while working on windows myself. Checked with the attached example and it also crashes. Is there a chance this matter will get looked into?
### comment:2 follow-up: 3 Changed 3 years ago by rwbarton
Related Tickets: → #7103, #10051
### comment:3 in reply to: 2 Changed 3 years ago by danilo2
Replying to rwbarton: Hello rwbarton! I'm working with both kdmadej as well as mmikolajczyk and this bug is some kind of blocker for us. I would love to ask you if can we discuss possible solutions / workarounds to make our use case work? We would like to collaborate with you guys as strong as we are able, we can try to investigate it further if you provide any hints for us - anything.
As a side-note: we are using GHCi (or more strictly GHC API) under the hood and GHCi is some kind of interpreter our product bases on - because of that and because the release deadline is in very narrow time from now, we are worrying about that issue. I would be very thankful for any help! :)
### comment:4 follow-up: 5 Changed 3 years ago by rwbarton
I would love to ask you if can we discuss possible solutions / workarounds to make our use case work?
Use Linux? :)
Sorry, I have no Windows experience and no access to a Windows machine.
### comment:5 in reply to: 4 Changed 3 years ago by danilo2
Use Linux? :) Sorry, I have no Windows experience and no access to a Windows machine.
I hope that was not offensiwe (although I feel it was). We cannot convert all the people, who we address our software to, to use Linux, can we? Additional I thought GHC is ment to be serious - cross-platform compiler, so I think solving this bug is somewhat important for everybody.
We've got some windows expirence and people that can help you (but they are not haskellers) additional I can provide you any time remote machine on Amazon with everything configured - you could connect to it and check the things out. We will help you as much as we can also - what do you think?
Last edited 3 years ago by danilo2 (previous) (diff)
### comment:6 Changed 3 years ago by thoughtpolice
Related Tickets: #7103, #10051 → #7103, #10051, #7056, #8546
Basically, the check for these debugging symbol sections is a real hack. See https://github.com/ghc/ghc/blob/master/rts/Linker.c#L4388-L4407 for the relevant code. GHC tries to ignore sections containing debugging information in its own linker code, but this has proven pretty painful for us in the long run, because MinGW/binutils changes mean we frequently hit sections we didn't know about before, so things like this fail (even though those sections are almost certainly harmless).
I suspect the best thing to do honestly is remove this code, or at least rework it. It is probably better to add a message which is printed out when linked with -debug (and using a debugging runtime flag) about what unknown sections we found, instead of always erroring out when an unknown section is found like we do today.
This fix would be pretty simple and also fix the root issue of most of the related tickets (since they're basically all dupes of different colors). If someone would submit a (tested!) patch, that would be excellent!
### comment:7 Changed 3 years ago by Phyx-
Architecture: x86_64 (amd64) → x86 set to Phyx-
### comment:8 Changed 3 years ago by Phyx-
Differential Rev(s): → D671 new → patch
### comment:9 Changed 3 years ago by Austin Seipp <austin@…>
rts/linker: ignore unknown PE sections
Summary: Currently the linker tries to see if it understands/knows every section in the PE file before it continues. If it encounters a section it doesn't know about it errors out. Every time there's a change in MinGW compiler that adds a new section to the PE file this will break the ghc linker. The new sections don't need to be understood by ghc to continue so instead of erroring out the section is just ignored. When running with -debug the sections that are ignored will be printed.
Test Plan:
See the file ghcilinkerbug.zip in #9907.
1) unzip file content.
2) open examplecpp.cabal and change base <4.8 to <4.9.
3) execute cabal file with cabal repl.
Applying the patch makes cabal repl in step 3) work.
Note that the file will fail on a ___mingw_vprintf not being found. This is because of the cc-options specifying -std=c++0x, which will also require libmingwex.a to be linked in but wasn't specified in the cabal file. To fix this, remove the cc-options which defaults to c99.
Reviewers: austin
Reviewed By: austin
Subscribers: thomie
GHC Trac Issues: #9907, #7103, #10051, #7056, #8546
### comment:10 Changed 3 years ago by thoughtpolice
Differential Rev(s): D671 → Phab:D671 → 7.10.1 patch → merge
Merged, thanks!
### comment:11 Changed 3 years ago by thoughtpolice
Resolution: → fixed merge → closed
Merged to ghc-7.10 (via ad628657cd56362964d17677728f4ae4d6868613).
### comment:12 Changed 3 years ago by ezyang
Owner: Phyx- deleted fixed closed → new
I am reopening this ticket, because by suppressing these errors we have opened up users to a more pernicious situation: GHC silently ignores a section it doesn't understand (failing to map it into memory) when a program ACTUALLY needs it to function. Previously, it was pretty obvious that something bad had happened and it was because GHC didn't support a section, but now the errors can be a lot more obscure, e.g. #10672 and #10563.
Is there any reason we can't take an alternate approach, where by default we attempt to map in ALL sections in an object file, except ones we've specifically blacklisted?
### comment:13 Changed 3 years ago by Phyx-
I have been trying something similar, but then I encountered another error: unhandled PEi386 relocation type 3. Looking at the code there is indeed no case for relocation type 3 which unless I'm mistaken is:
But curiously while trying to understand what the linker is doing (and I may have the wrong idea since I'm new to this part) I see under the x86_64 cases this case 17: /* R_X86_64_32S */.
However in the PE doc I can't find any relocation type 0x0011. So am I looking at the wrong place or should this have been 0x0003?
### comment:14 Changed 3 years ago by ezyang
Ian Lyangh would be able to say better, having authored the patch, but what I think happened was, because the PE spec doesn't actually say how to process relocations, the code was written by cross-referencing against relocations in ELF. But it does look like R_X86_64_32S was given the wrong constant...
### comment:15 Changed 3 years ago by Phyx-
Owner: set to Phyx-
### comment:16 Changed 3 years ago by thoughtpolice
Milestone: 7.10.1 → 7.10.3
Moving to 7.10.3, in case there's a fix. Thanks Phyx-!
### comment:17 Changed 3 years ago by Phyx-
@thoughtpolice Yes there will be a fix :) I have changed the code to identify most of the sections based on the flags in the PE file instead of the section names. So we don't have to keep a list of white-listed sections, so it should be much more resilient to changes.
The only sections still being ignored by names are a few debugging ones, but it's fine since those are reserved names and currently we don't do debug section relocations.
I'm just trying to find where the constant 17 comes from, but from looking at the generated .s files, I think this might be a bug in GAS. I'll submit a diff this weekend after I finish checking if the related bug reports are also fixed :)
### comment:18 Changed 3 years ago by Phyx-
Differential Rev(s): Phab:D671 → Phab:D1244 new → patch
### comment:19 Changed 3 years ago by Thomas Miedema <thomasmiedema@…>
In 620fc6f9/ghc:
Make Windows linker more robust to unknown sections
The Windows Linker has 3 main parts that this patch changes.
1) Identification and classification of sections
2) Adding of symbols to the symbols tables
3) Reallocation of sections
1.
Previously section identification used to be done on a whitelisted
basis. It was also exclusively being done based on the names of the
sections. This meant that there was a bit of a cat and mouse game
between GCC and GHC. Every time GCC added new sections there was a
good chance GHC would break. Luckily this hasn't happened much in the
past because the GCC versions GHC used were largely unchanged.
The new code instead treats all new section as CODE or DATA
sections, and changes the classifications based on the Characteristics
flag in the PE header. By doing so we no longer have the fragility of
changing section names. The one exception to this is the .ctors
section, which has no differentiating flag in the PE header, but we know
we need to treat it as initialization data.
The check to see if the sections are aligned by 4 has been removed.
The reason is that debug sections often time are 1 aligned but do have
relocation symbols. In order to support relocations of .debug sections
this check needs to be gone. Crucially this assumption doesn't seem to
be in the rest of the code. We only check if there are at least 4 bytes
to realign further down the road.
2.
The second loop is iterating of all the symbols in the file and trying
to add them to the symbols table. Because the classification of the
sections we did previously are (currently) not available in this phase
we still have to exclude the sections by hand. If they don't we will
load in symbols from sections we've explicitly ignored the in # 1. This
whole part should rewritten to avoid this. But didn't want to do it in
this commit.
3.
Finally the sections are relocated. But for some reason the PE files
contain a Linux relocation constant in them 0x0011 This constant as
far as I can tell does not come from GHC (or I couldn't find where it's
being set). I believe this is probably a bug in GAS. But because the
constant is in the output we have to handle it. I am thus mapping it to
the constant I think it should be 0x0003.
Finally, static linking *should* work, but won't. At least not if you
want to statically link libgcc with exceptions support. Doing so would
require you to link libgcc and libstd++ but also libmingwex. The
problem is that libmingwex also defines a lot of symbols that the RTS
automatically injects into the symbol table. Presumably because they're
symbols that it needs. like coshf. The these symbols are not in a
section that is declared with weak symbols support. So if we ever want
to get this working, we should either a) Ask mingw to declare the
section as such, or b) treat all a imported symbols as being weak.
Though this doesn't seem like it's a good idea..
Test Plan:
Running ./validate for both x86 and x86_64
Also running the specific test case for #10672
make TESTS="T10672_x86 T10672_x64"
Reviewed By: ezyang, thomie, austin
GHC Trac Issues: #9907, #10672, #10563`
|
2018-07-20 06:49:20
|
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|
http://jcwc.com.sg/fsgw/magnitude-of-high-pass-filter.html
|
Magnitude of high pass filter
Conversely, if it passes low frequencies and rejects high ones, it is a low-pass filter. The graph is unable to plot below 1Hz at the moment. frequency is shown in Figure 5 (right axis). An example of an analogue electronic band-pass filter is an RLC circuit (a resistor–inductor–capacitor circuit). There are many kinds of highpass filters that can appear at various stages in the signal path (e. 79 shows the first order high pass Butterworth filter. Simple Band Pass Filter with Op Amp This circuit will attenuate low frequencies ( w <<1/R 2 C 2 ) and high frequencies ( w >>1/R 1 C 1 ), but will pass intermediate frequencies with a gain of -R 1 /R 2 . The design equations for low pass, high pass, band pass, and notch filters are given. For example, a low-pass filter may have a transfer function that is inversely proportional to frequency in the limit of high-frequency. By default, this check box is cleared. A high pass filter is such a filter which only allows frequencies with high magnitude to pass through them and block the lower frequencies as the name suggests. Algorithms. 6. FIGURE of a second (4) A sketch of Eq. High-pass filtering with a 10th order Butterworth filter applied only to the spectral magnitudes (acausal filter) was found to yield better displacements than those calculated using lower order Butterworth filters (e. • Therefore, the frequency response of a bandpass filter is: 2 1 2 1 0 ( ) 1 Mar 02, 2020 · Pass-band Ripple 1 − Ap: Amount of variation (fluctuation) in the magnitude response of the filter. Several examples of bandpass amplitude response curves are shown in Figure 5 Nov 12, 2018 · How do you chose a filter for your particular analysis goals? Digital filtering is a common preprocessing step when analyzing EEG data. Problem Obtain the complex transfer function H(ω) for the circuit shown below over the range 0 < ω < ∞. Four commonly used ideal-filter frequency responses are the (1) lowpass filter, (2) highpass filter, (3) bandpass filter, and (4) bandstop filter, as shown in Figure 14. e. In a low pass filter, frequency values higher than the frequency A novel and miniature high-pass filter (HPF) based on a hybrid-coupled microstrip/nonuniform coplanar waveguide (CPW) resonator is proposed in this article, in which the designed CPW has exhibited a wideband dual-mode characteristic within the desired high-pass frequency range. Ideally, the frequency output of a high pass filter is like this, An 8th order Butterworth filter with a high pass corner frequency of 0. The following diagram shows the signal flow for a general FIR A band-pass filter can be characterized by its Q factor. None Review Count Popularity Average rating Also called a Bass-cut filter, it (high pass filter) attenuates signals that fall below cutoff frequency (stop-band) as well as enabling signals over the . Aug 24, 2018 · As can be seen, application of high pass filter, blocked all the low frequencies in the center and allowed only the high frequencies to pass through. Common Names: Laplacian, Laplacian of Gaussian, LoG, Marr Filter Brief Description. P. b) Magnitude response of a high-pass filter. FDATool also provides tools for filters analysis, such as; magnitude and phase response and pole-zero plots. The function of pushing the gain of a filter at every frequency is the amplitude response (or magnitude frequency response). Active Filters 4 ) Single op amp second order active filters KRC or Sallen-Key filters The second order passive low pass filter has an asymptotic Slope of 40 dB / dec at high frequencies. [ ] Some authors have chosen to include the ts factor in the discrete h(n) impulse response in the above Step 4, that is, make h(n) = tshc(nts) [14, 18]. freqz determines the transfer function from the (real or complex) numerator and denominator polynomials you specify and returns the complex frequency response, H(e jω), of a digital filter. 2-2b. 2. , the mic, the preamp, the equalizer/EQ plug-in, etc guide. , but does not have Sufficient flexibility to control the magnitude of the filter Around ω = ω 0 The attenuation of high frequency is due to the reactance of capacitor, which decreases with the increasing frequency. One would expect an ideal low pass filter to leave low frequencies unchanged (to "pass" them) and to significantly decrease the amplitude of high frequencies (to "stop" them). Steps 1, 2, and 3 are Prelab activities. It can. A physical LPF filter, however, might pass all frequencies below 1 kHz but also partially pass frequencies above 1 kHz. Figure 1. The frequencies of these guitar chords are filtered based on the high/low pass filter above. 1 The low-pass filter specification panel intoduced in FAZA. 4 Voltage drop at high frequencies (in decibels) in single low-pass filter II. (3), i. How could we create a high-pass lter ( lter out low frequencies, pass high frequencies). To calculate Resistor values for High pass filter Equation 2 is used. Gaussian high pass filter. **Low Pass Filtering** A low pass filter is the basis for most smoothing methods. 5 Dual-stage low–pass filter II. Example: Audio filter (band pass filter) Audio filter is matched to the frequency range of the ear (20-20,000 Hz). 3. When you turn down the volume control on your stereo, you are “attenuating” the signal being sent to the speakers. • Filters may be classified as passive or active , depending on whether the filter has any internal sources of energy. On a high pass filter, values lower than the frequency cutoff (~f_c~) point will be filtered out - you will see the magnitude of their waveforms decrease as they pass the frequency cutoff. For the low-frequency asymptote, take f!0 as usual, so that 1 ˛Bfand 1 ˛Cf. For example, taking the voltage over the inductor results in a high-pass filter, while taking the voltage over the resistor makes a band-pass filter. 4. Figure-1 shows the circuit of first order high pass Butterworth filter using RC network and operational amplifier The simulation results of the high-pass and low-pass filter effect on the quality of informative low-amplitude of the heart biopotential by the order of magnitude. In this study, a high-pass (HP) filtering technique was applied in the Fourier domain of the magnitude data to enhance the signal of venous vasculature through background suppression. 4 c J. Element Values for Butterworth (Maximally Flat) Low-Pass Filter Prototypes (g o=1,w c=1,N=1 to 10) N g1 g2 g3 g4 g5 g6 g7 g8 g9 g10 g11 Notes 18 largely plagiarized by %khc 1 Pole-Zero Diagram to Magnitude/Phase Plot For particular arrangements of the poles and zeros, we can arrive at various magnitude and phase responses. A high-pass filter is usually modeled as a linear time-invariant system. High pass filter adalah lawan dari Practical Filter Specification L4. Shown below is a LPF(left) and a BPF(right): 1. That means, it rejects (blocks) all low frequency components. as many derivatives of the magnitude of the transfer function as possible are equal to zero at some specified frequency. (8 points) The source is a sinusoidal voltage with some amplitude and frequency. High pass filter as the name suggests, it allows (passes) only high frequency components. 1. The phase shifts 16 Nov 2017 In a s plane, pole and zero allow to locate where the magnitude of the transfer high pass filter, a first order low pass filter transfer function. The main feature of the Chebyshev filter is a ripple in the pass-band. Aspects of a high pass filter schematic follow. An RLC circuit has a resistor, inductor, and capacitor connected in series or in parallel. The formula of Phase shift is not same as Low Pass filter as in low pass filter the phase became negative, but in high pass filter it is a positive phase shift, so the formula implies as:-Phase shift φ = arctan (1 / 2πfRC) Let’s see the phase shift curve of the circuit:-This is the Phase shift of the circuit, used as practical example. High pass filter. 41. HdB 0. The general rule that was applied during the This magnitude of one frequency of one hertz sin wave is applied to the high pass filter. it attenuates the plot the magnitude frequency responses of the analysis and synthesis filters. Use this utility to simulate the Transfer Function for filters at a given frequency or values of R and C. 1 and frequency 1. 0. Figure 2-2 - Ideal magnitude responses of (a. Another way of considering the transfer function is to say that the high-pass filter response is the low-pass filter response subjected to the transformation RCs = 1/RCs', so that the response of the high-pass filter at angular frequency 1/RC equals that of the low-pass filter at the same frequency, and at angular frequency 2/RC it equals that Active Low Pass Filter. The amplitude response of the ideal lowpass filter is shown in Fig. Fig 4. A high-pass filter also has a slope associated with it. 36 • note the concentration of image energy inside the inner circle. For simplicity, in the following we assume the frequency is normalized by the cut-off frequency, i. An RL high pass filter is a filter circuit, composed of a resistor and an inductor, which passes high-frequency signals and blocks low frequency signals. For Ω >> Ωc, the magnitude response can be approximated by 2 a 2n c 1 H(j ) (/ ) Ω≈ ΩΩ. [] In a low-pass filter design, for example, the filter type (Chebyshev, Butterworth, elliptic), filter order (number of poles), and the cutoff frequency are parameters to be defined in this step. 01 micro Farads. Earlier on this page we hinted that the 11 degree bit could be simplified. Connect the STEMlab board to your circuit: Connect the Oscilloscope & Signal generator probes as is shown in figure 7. Figure: Circuit for High pass filter. a band-pass filter will be \$>1\$ in the central part, delimiting a band of frequencies allowed to pass. This type of filter is called an Infinite-Impulse Response (IIR) filter, because if you give it an impulse input, the output takes an infinite time to go down to exactly zero. 09 Hz was used to approximate the Ormsby filter used by CSMIP, which ideally removed all frequency content below 0. CheungSlide 21. These are respectively referred to as narrow-band and wide-band filters. , Figure FigureA1 A1 in Appendix), and excessive pass-band ripple including non-unity gain at DC (the step response never returns to one). The Sallen-Key filters are second-order active filters (low-pass, high-pass, and band-pass) that can be easily implemented using the configuration below: We represent all voltages in phasor form. Spartan-6 FPGA board, System Generator is then used for the appropriate FIR FPGA filter implementation for low-pass, high-pass, band-pass filter as shown in Figures 5-9. This page is a web application that design a RC high-pass filter. 5 capacitor and a… For high pass filters, the magnitude of the step function gets its minimum value at frequency approaches to infinity, the inductor behaves like wi component. In Fig. HighpassFilter[data, High - pass filter - pass high frequencies and reject low frequencies. Cookbook Filter Guide 4 To design a filter of a particular response (i. Sometimes it is desirable to only pass a certain range of frequencies that do not begin at 0 Hz, (DC) or end at some upper high frequency point but are within a certain range or band of frequencies, either narrow or wide and attenuate other frequencies on both sides of this pass band. Terkadang filter ini disebut low cut filter, bass cut filteratau rumble filter yang juga sering digunakan dalam aplikasi audio. The second order passive low pass filter has an asymptotic Slope of 40 dB / dec at high frequencies. Blocking capacitor and 2nd resistor in biasing network acts as an high pass filter in a CE amplifier. g. Powerline interference (50 or 60 Hz noise from mains supply) can be removed by using a notch filter of 50 or 60 Hz cut-off frequency. Simulation Results for Low-Pass FIR Filter Figure 6(b) and Figure 6(c) verified the comparison between the pass filter lowsimulation from Matlab and - A band pass filter can in principle be constructed by combining a low and high pass filter in cascade. Let me take the same input signal, same input signal with the same frequency spectrum, and instead I'm going to put it through high pass filter. , a 4th order filter is common). I found the transfer function of a high pass filter as $$\frac{V_{out}(j\omega)}{V_{in}(j\omega)}=\frac{j\omega}{j\omega+\frac{1}{RC}}$$ Amplitude and phase response curves for the high-pass filter are shown in Figure 4. When an input is passed through a low-pass filter, the output is delayed by some fraction. The Laplacian of an image highlights regions of rapid intensity change and is therefore often used for edge detection (see zero crossing edge Band Pass Filter - A circuit that allows a range of frequency signals to pass through a circuit but attenuates low and high frequency signals. 4). A block diagram is shown in Figure 1. This diagram conveys the generic characteristics of the frequency response of an RC low-pass filter. 2 Single-stage low–pass filter Output voltage (magnitude and phase) II. Model the filter in MatLab, 3. RC High-Pass Filter Circuit In such circuit, the output is taken across the resistor and practically reactance of the capacitor decrease with increasing frequency. Oct 06, 2016 · RC Low Pass Filter pole and 3dB frequency calculation. By emphasizing the high frequencies, the P waves from the main shock earthquake and from several aftershocks are enhanced. In addition, it graphs the bode plot for magnitude in decibels and the phase in radians. Plot the magnitude of H and the phase angle as a function of ω on a log scale. The behavior of the system in the transition band is not specified. 74), the positions of R and C are changed in the high pass circuit shown in Fig. 1(C). 3. The amplitude of signals outside this range of frequencies (called stop band) is reduced (ideally reduced to zero). It can be observed that as compared to first order low pass filter (Fig. Now since edges are usually made of low frequencies, that's we see in the resultant image. 2Simulate the design with PSpice, and 4. First and Second Order Low/High/Band-Pass filters. The phase plot is linear except for discontinuities at the two frequencies where the magnitude goes to zero. Its principle of operation and frequency response is exactly the same as those for the previously seen passive filter, the only difference this time is that it uses an op-amp for amplification and gain control. Several examples of bandpass amplitude response curves are shown in Figure 5 Dec 04, 2016 · The topology of the of the circuit is a first order high pass filter followed by a second order Sallen and key. Bode Plot of a High-Pass Filter ( ) ( ) out c 1 j / j / j L R j L V V H( ) The Phase shift is same as seen in Passive high pass filter. FFT Algorithm and Spectral Analysis Windows RC High-pass Filter Design Tool. Now, all of the above theory can also be applied to the design of a High Pass Filter. 14. However, as Figure 16– 6 shows, the passband gain is not monotone, but contains ripples of constant magnitude instead. In this work, design of digital FIR high pass filter using FDATools using: 1)Equiripple method (The filters are set according to the following options The circuit implementation of the Operational Amplifier based High pass filter is shown below: The frequency response of the Operational Amplifier high pass filter is shown in the following figure: As you must have noticed that the above circuit for the high pass filter is designed to have the cut-off frequency of 40 kilo Hertz. The transfer function of ideal high pass filter is as shown in the equation below: The Bode Plot or Frequency Response Curve above for a passive high pass filter is the exact opposite to that of a low pass filter. Filter E. Just take the fourier transform of Laplacian for some higher size of FFT. The gain (also called the transfer function) of a filter is the ratio of the phasor output voltage to the phasor input voltage. They don't absolutely pass some frequencies and absolutely reject others. Figure 1-2 - Passive, RLC, low-pass filter. High-Pass Filter . In the asymptotic limit, a filter has a gain characteristic of 20 n decibels per In this blog post, I will use np. 4 Solution for What are magnitude and frequency scale factor will transform the prototype high pass filter into a high pass filter with a 0. A simple example of a Butterworth filter is the third-order low-pass design shown in the figure on the right, with C 2 = 4/3 F, R 4 = 1 Ω, L 1 = 3/2 H, and L 3 = 1/2 H. 2 Tschebyscheff Low-Pass Filters The Tschebyscheff low-pass filters provide an even higher gain rolloff above f C. 2 Design of FIR Filters An FIR lter of length M is an LTI system with the following difference equation1: y[n] = Why Laplacian is a High Pass Filter? A similar question was asked in a forum. We know that the active high pass filter can be designed by using either inverting terminal or the non-inverting terminal of an operational amplifier. The filter used in the example in the previous section was a bandpass. Analyze it: the magnitude of the FRF of an nth order high-pass Butterworth filter with cut-off frequency is Now we consider the implementation of a Butterworth filter. order low pass transfer function: RL High Pass Filter - Frequency and Bode Plot Calculator. The concatenation of these and other higher-order (more poles and zeros) linear systems can give rise to a large expression, but always with the factorization of poles and zeros as in the expression above. The number of possible bandpass response characteristics is infinite, but they all share the same basic form. Even though this article shows a low pass filter, the same principles apply to a high pass filter where the output is taken over the resistor. Try a cut-off period of 2 s for the high pass filter. The low pass filter magnitude response is shown in Figure 2. ricker (points, a) Return a Ricker wavelet, also known as the “Mexican hat wavelet”. Aug 16, 2011 · A high-pass filter (hpf) is an audio frequency filter that cuts (filters out) frequencies below a set level. So far, our transfer equation has been specified in terms of voltage gain, but we are actually interested in the half- power (-3dB) point. harmonics of high magnitude in the source voltage. They also read how a Bode plot is developed through simple approximation techniques for both the magnitude and phase. , so that . Let's design an audio filter using low and high pass RC circuits. A simple mathematical design procedure is derived for the passive high pass filter. • We call ω co1 the lower (or low) cutoff frequency and ω co2 the upper (or high) cutoff frequency. Ideal Band Pass Filter • This filter only passes frequencies above a value ω co1 and below a value ω co2 and attenuates all other frequencies outside this range. However it's not a very successful highpass filter either. Till now we saw the high pass filter circuit and response curves of the non-inverting active high pass filter. RC Low Pass Filter – Magnitude Response. If a filter passes high frequencies and rejects low frequencies, then it is a high-pass filter. The all-pass filters are also called delay equalizers or phase correctors. The Set to Lowpass to implement a low-pass filter, set to Highpass to implement a high-pass filter. High pass filters: pass high frequencies, filter out low frequencies filter. Students view the development of the transfer function for a RC high pass filter. This results in a high The functions AG(ω), φG(ω) form the frequency response of a filter Example: Low-pass filter magnitude specs. Band Stop Filter circuit using R, L and C. For Arduino, the is simply the original analog input and is the analog pin of Arduino. ) low-pass, (b. 1 uF R2 200K Vi +-OUT + R1 20 K Vo 2 1 10 R K R == 2 1 c 500 RC ω== Transfer function in jω • Find R 2 and R 1 values in the above active High-pass filter for gain of 10 and cutoff frequency of 500 rad/s. c) Frequency response of an ideal filter. The ideal high-pass filter is shown in Fig. Ideal version of these filters are described below and their magnitude response are shown in Figure Ideal LPF An ideal low-pass filter transmits, without any distortion, all of the signals of frequencies The attenuation for high quality low-pass filters can be 60 - 80 db. If a capacitor and a resistor are connected in series to an AC source they have the same current. , Low-Pass Filter High pass filter adalah jenis filter yang melewatkan frekuensi tinggi, tetapi mengurangi amplitudo frekuensi yang lebih rendah daripada frekuensi cutoff. a) Magnitude response of a low-pass filter. As simple high pass filter is shown in the figure below. The question is, why Laplacian is a high pass filter? Why Sobel is a HPF? etc. Background Suppression Using a High-Pass Filter. Butterworth Filter - A type of filter that is "maximally flat", i. A filter will have a transfer function whose magnitude is less than or equal to 1 for all frequencies. If x is a matrix, the function filters each column independently. Discussion of Bode Plot and frequency response. , 2011) with default settings exhibits excessive filter ringing (cf. Typically in I am stuck trying to determine the phase response of a high pass filter. An idealized band pass filter is shown in Figure 8. The output frequency is rounded to the second decimal place. Our discussion begins with high-pass and low-pass filters. 1 Magnitude response of a typical Chebyshev filter. A band-pass filter is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range. It blocks most low frequencies & DC component. The low pass filter cutoff frequency can be adjusted to 107 Hz, 257 Hz, and 537 Hz. An image is smoothed by decreasing the disparity between pixel values by averaging nearby pixels (see Smoothing an Image for more information). Because of the location of zeros, the frequency response magnitude is larger towards frequencies $\pm \pi$ and smaller at low frequencies and for this reason it is classified as a highpass filter. RL High Pass Filter - Frequency and Bode Plot Calculator. Gain: Gain is a measure of the increase in signal amplitude. 75 kHz. Figure 1(a) clearly shows the approximation. After passing through the band-pass filter, the output amplitudes at ω 1 and ω 3 are significantly decreased because they fall outside the desired frequency range, while the frequency at ω 2 is within the desired range, so its signal amplitude passes through unaffected. This is a low-pass lter. Stop-band attenuation As is the maximum attenuation to the frequencies in stop-band. The basic first-order high-pass filters use the same components as the low-pass filters we just studied. An idealized magnitude plot of a high-pass filter is shown as the second 20 Jan 2019 Here is 1st, 2nd and higher order active high pass filter circuits, frequency The magnitude of the pass band gain is equal to 1 + (R3/R2). A high-Q filter will have a narrow passband and a low-Q filter will have a wide passband. Start PSpice 2. Band-pass filters can be made by stacking a low-pass filter on the end of a high-pass filter, or vice versa. The magnitude plot indicates that the moving-average filter passes low frequencies with a gain near 1 and attenuates high frequencies, and is thus a crude low-pass filter. The magnitude response of filters can be characterized in terms of the frequency bands the filter will pass or reject. H0. • Simplest high-pass amplifier is described by • ω L = lower cutoff If a high-pass filter and a low-pass filter are cascaded, a band pass filter is created. An electrical load consisting series connected capacitor (100 uF), inductor (0:25 H) and resistor (4 ohm) is fed by a sinusoidal voltage source. Fessler,May27,2004,13:18(studentversion) 8. 10 p455 Low-pass Filter High-pass Filter Band-pass Filter Band-stop Filter PYKC 8-Feb-11 E2. This is a highpass filter. Sep 08, 2016 · The Fig. Expressing magnitudes in decibels Actual magnitude Magnitude in dB 1/2 8. The high-pass filter is realized using a ladder of one-port URCO and URCS networks, and the band-pass filter is realized using the "cascade and stub" technique as explained by Wyndrum. What is electronic filter: The electronic filter is the circuit, which passes some (Figure below) This high impedance in series tends to block low-frequency signals from getting to load. The magnitude in decibels is G dB = 20 log10 f f0 n =20nlog10 f f0 (4) Table 1. capacitive highpass filter v1 1 0 ac 1 sin c1 1 2 0. And the first answer given to it was in terms of Fourier Transform. Various frequency normalizations can be chosen for best magnitude and polar response, although the linear phase approximation in the passband of the low-pass is not maintained at higher frequencies. Also calculate the 3dB Frequency and sketch the approximate bode plot. Fundamentals of Low-Pass Filters Active Filter Design Techniques 16-7 16. R R C Vs C Vo a b Figure 6 High Pass Filter: passes high-frequency signals and reduces the amplitude of signals with frequencies lower than the threshold frequency. We may obtain a band pass filter by combining a low pas and a high pass filter. Frequencies that \pass" are between lower and upper frequency limits, ! Land ! Those factors are then used to approximate high--pass and band-pass filter characteristics. Follow-ing this corner frequency, the filter response falls off at a rate of –40 dB/decade. The source voltage, as a function of time, is shown on the next page. The preferred structure is a high-pass/low-pass bit. Therefore, an ideal high pass filter has a flat magnitude characteristic. Gain is expected to be greater An ideal lowpass filter, for example, might pass frequencies below 1 kHz and completely stop (reject, eliminate) all frequencies above 1 kHz. Low Pass Filter This is a filter that reduces (attenuates) high frequency signals and lets low frequency signals through with little modification. • The key is to determine a transformation function that maps the normalized, low-pass design into the appropriate (low-pass, high-pass, etc. At very high frequencies, the capacitor acts as short circuit and therefore, the output drops to zero. The capacitor has the abbreviation $$C$$ and the resistor $$R$$, which is why the abbreviation $$RC$$ high pass is often used. The third-order harmonic distortion (HD3) of the filter is 51 dB for 20 mVp−p at 100 Hz sinusoidal input 4. 9 the ideal magnitude responses of the four most frequently used filter types are illustrated as a function of ω in radians per second. (1-2) Butterworth Filter Design Procedure Electronics Tutorial about Passive High Pass Filter Circuit the Passive RC The circuit gain, Av which is given as Vout/Vin (magnitude) and is calculated as:. , the filters shown in Fig. For example, two second-order low pass filters can be cascaded together to produce a fourth-order low pass filter, and so on. If you analyse the high pass filter network, when the value of capacitor impedance and resistor configuration a high-pass filter, a low-pass filter, a band-pass filter or a band-reject filter? Explain your answer. Understanding Bode Plots. The following diagram shows the signal flow and coefficients for the high-pass filter. Figure 2 and Figure 4 use single curves because the high-pass and the low-pass phase responses are similar, just shifted by 90° and 180° (π/2 and π radians). The simplest band-pass filter can be made by combining the first order low pass and high pass filters that we just looked at. 2. Electronics Tutorial about Active High Pass Filter including its High Pass Filter For a non-inverting amplifier circuit, the magnitude of the voltage gain for the A high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies The magnitude curve and phase curve of the bode plot for high pass filter is as shown in the below figure. The most common and easily understood active filter is the Active Low Pass Filter. 4 Band Pass Filter (BPF) We can make a band pass lter by appropriately cascading a high-pass and low-pass lter. ✖. % This also demonstrates the effect of using a window function like % the Kaiser window to reduce the side lobes of the filter. Example: Magnitude response of an ideal low pass filter at 8 KHz. A high pass RL filter is a filter composed of a resistor and inductor which passes through high-frequency signals. Filter Products Showing 1 - 12 of 18 results. RLC series band-pass filter (BPF) You can get a band-pass … Gunness/Chauhan Optimizing the Magnitude Response of Matched Z Transform Filters (“MZTi”) for Loudspeaker Equalization necessary antialias filter drives the response of the system toward zero at Nyquist, rendering moot the precise match of the filter at that frequency. This was referred to as the inverted, second-order, high-pass response. 35 Chapter 4 Image Enhancement in the Frequency Domain 4. Mathematically, the magnitude of the transfer function is the magnitude of the top divided by the magnitude of the bottom. 1 -40 1 10 100 ω • Active Low-Pass Filter, • Passive High-Pass Filter, and • Active High-Pass Filter. Our example is the simplest possible low-pass filter. If you analyse the high pass filter network, when the value of capacitor impedance and resistor There are five basic filter types (bandpass, notch, low-pass, high-pass, and all-pass). Ideal low-pass filter ⎩ ⎨ ⎧ ≤ = 0 0 ( ) 1 ( , ) ( , ) if D u v D if D u v D H u v, f 0 D0is the cutoff frequency and D(u,v) is the distance between (u,v) and the frequency origin. • New values for L and C are obtained by maintaining the same Z through the transformation. Jan 20, 2019 · Active High Pass Filter using Inverting Operational Amplifier. 10. May 21, 2019 · Transfer function and Bode plot for a 2nd order low pass filter . morlet2 (M, s[, w]) Complex Morlet wavelet, designed to work with cwt. Using phasor analysis, the transfer function of a first-order RC Low Pass filter as a function of frequency is given by the equations below. The Butterworth Low-Pass Filter 10/19/05 John Stensby Page 2 of 10 the derivative of the magnitude response is always negative for positive Ω, the magnitude response is monotonically decreasing with Ω. Normalising these to correspond with the normalised pole tables gives: Figure 2. 3 Bode-plots and the 3dB breakpoint II. Write out the mathematical High-order filters, such as third, fourth, and fifth-order are usually formed by cascading together single first-order and second-order filters. Test the design in the Lab. To maximise the magnitude, minimise the bottom part. Design the filter for a specified cut-off frequency, 2. Oct 26, 2015 · Band Pass Filter. This can be achieved by applying a high-pass remove it, a high-pass filter of cut-off frequency 0. 1 Hz or often even 1 Hz and a low-pass filter to filter out frequencies above 40 or 50 Hz Hz. function for a RC high pass filter. A processor is configured to iteratively select an optimal high pass filter for the The signal spectra 102 and 104 are normalized in magnitude such that the A second order low pass filter blocks high pass frequencies more effectively due This is the frequency at which the magnitude of the transfer function is 0. (f s = 48 kHz) In the following sections low-pass and high-pass filters will often be referred to as LP or HP filters. ) bandpass, and (d. A High Pass Filter or HPF, is the exact opposite to that of the previously seen circuit gain, Av = which is given as Vout/Vin (magnitude) and is calculated as:. 16 Dec 2005 Their frequency response (mostly the magnitude part but the phase A high pass filter is a circuit whose amplitude response increases with as Strona główna Atrybut produktu: Filtry High Pass Filter. Now, I got this high pass filter by just rearranging the output. Notes: As in all the ALM labs we use the following terminology when referring to the connections to the M1000 connector and configuring the hardware. If, for example, f s = 2000 Hz, f = 40 Hz, and N = 201, the magnitude response of the filter will be as in the graph below. Here's the corresponding high-pass filter: xfilt = filter([1-a a-1],[1 a-1], x); If you need to design a filter, and have a license for the Signal Processing Toolbox, there's a bunch of functions , look at fvtool and fdatool . 3: Х 1. 79. highpass uses a minimum-order filter with a stopband attenuation of 60 dB and compensates for the delay introduced by the filter. Figure 5 Bode magnitude (top) and phase (bottom) plots. 18. In a low pass filter, frequency values higher than the frequency Dec 15, 2015 · We now have an equation that describes the output magnitude of the RC low pass filter. fft. This tool calculates the crossover frequency for a RL high pass filter. Set the oscilloscope attenuation Apr 29, 2017 · It is a low pass filter, So far I have made calculations and used Multisim to confirm my answers to make sure they are correct. If this is a low pass filter how do i convert it to a Jan 26, 2019 · The pass band gain must be equal to low pass filter and high pass filter. Figure 4 shows such a filter. Note the smooth curve transition, due to which at each point, the value of Do, can be exactly defined. 2, where the maximum gain, , and the frequency at which it occurs, , RC Low-pass Filter ω H = 1 (R 1R 2)C V o =V s R 2 sC R 2 + 1 sC R 1 + R 2 sC R 2 + 1 sC V o V s = R 2 R 1 +R 2! " # $% & 1 1+ s ω H! " # # # #$ % & & & & Impedance of capacitor = 1 sC 8 High-pass Amplifiers • Combines a single pole with a zero at the origin. The maximum potential difference across the resistor is proportional to the resistance, while the maximum potential difference across the capacitor is proportional to the capacitive reactance. Frequency Responses of and simple Low-pass filter and Band-pass filter My task is to draw two filters in PSpice and do simulations to get the frequency responses (both magnitude and phase responses). The typical practice in EEG signal processing is to apply a high-pass filter to filter out slow frequencies less than 0. The bandwidth is equal to the –3 dB frequency. For each of the configurations you will 1. Copy to clipboard. This is a fourth-order Butterworth low-pass filter with a cutoff frequency of 500 Hz and a passband gain of 10 (20 dB); this circuit was taken from [1]. The filter impulse response is [1/9 1/9 1/9;1/9 1/9 1/9;1/9 1/9 1/9]. Taking the impedance of the capacitors C to be 1/(Cs) and the impedance of the inductors L to be Ls, where s = σ + jω is the complex frequency, the circuit equations yield the transfer function for this device: The input signal of the filter shown here has equal amplitude at frequencies ω 1, ω 2, and ω 3. We say, H(ω) ∼ ω-1. The top part is trivial. On the simplest level, a highpass filter is just a filter (sometimes called a low-cut) that attenuates low frequencies below a certain cutoff frequency and allows frequencies above to pass. The implementation of the BS-MRV technique includes the following steps. A CR high pass is also often Thus, the Bode magnitude plot of a first-order low-pass filter is approximated by two straight lines intersecting at ω 0. In general H (ω) ∼ωn, where n is a negative number for a low-pass filter. To build a high pass RL filter, the inductor is placed in parallel to the power source signals entering the circuit, as shown below in the following circuit: A high pass filter is such a filter which only allows frequencies with high magnitude to pass through them and block the lower frequencies as the name suggests. A low pass filter is one that does not affect the low frequencies and rejects high frequencies. The band pass filter passes a band of frequencies between a lower cutoff frequency, f l, and an upper cutoff frequency, f h. Given below is a sample high pass filter circuit using op-amp. ) bandstop filter. It gives the equations used to generate IIR filters from the s domain coefficients of analog filters using the Bilinear Transform. The standard form of a second-order, low-pass filter is given as TLP(s) = TLP(0)ω 2 o s2 + ωo Q s + ω 2 o (1-3) where TLP(0) is the value of TLP(s) at dc, ωo is the pole frequency, and Q is the pole Q or the pole quality factor. d) Edge detector in image processing. ) high-pass, (c. Bode magnitude plots: RC High pass Filter, One zero, One Pole, Magnitude, Phase and That is, a low pass filter is said to pass frequencies lower than !c and reject those that are higher than !c. , but does not have Sufficient flexibility to control the magnitude of the filter Around ω = ω 0 • We use positive feedback to bolster the magnitude of the filter response around ω 0 The Gaussian low pass filter can be represented as. frequencies to pass through while rejecting others. Low Pass Filter High Pass Filter Figure 5 The transition frequency which indicates that range of frequencies that are allowed and those that are rejected is given by the cutoff frequencyω0. The frequency at which the passband and stopband meet is called the cutoff frequency. A low-pass filter is one which does not affect low frequencies and rejects high frequencies. These magnitude and phase responses can be divided into five major classes: all pass band pass high pass low pass band stop or notch Figure 6: Low pass RC filter response at 500Hz. The simplest filter is an ideal filter with zero phase. 2-pole, multiple-feedback (MFB), high-pass filter. Time constant (s) — Filter time constant 10e-3 (default) | positive scalar First-order filter time constant, specified in seconds. Active Filter Circuits C 0. FM modulators and noise-reduction circuits also use pre-emphasis (high-pass) and de-emphasis (low For example, a simple first-order low pass filter has a single pole, while a first-order high pass filter has a pole and a zero. First Order Low Next, high pass filter is designed to attenuate frequencies from 0 to 9. This tool calculates the crossover frequency for a RC high pass filter. When a sinusoidal input V i is applied to it, then the output V o is Next, high pass filter is designed to attenuate frequencies from 0 to 9. pass filter (LPF), high- pass filter (HPF), band-pass filter (BPF) and band-elimination or band stop or band reject filter (BEF, BSF, BRF). 1 except The magnitude and phase plots are shown below. Passive Filters References: Hayes & Horowitz (pp 32-60), Rizzoni (Chapter 6) Frequency-selective or lter circuits pass to the output only those input signals that are in a desired range of frequencies (called pass band). 01 micro Farads D The objective of this Lab activity is to study the characteristics of passive filters by obtaining the frequency response of low pass RC filter and high pass RL filter. It has been shown that a simple RC Low Pass filter has the transfer function. The frequency response is the same as that for P. The equation for the cutoff frequency, ωc, of an RC high pass filter is the same as for In this lab we will explore the low and high-‐pass filters. Filters, like most things, aren't perfect. High-frequency asymptote. morlet (M[, w, s, complete]) Complex Morlet wavelet. May 24, 2019 · In both cases, we have a pole at s = –ω O, meaning that both the low-pass filter and the high-pass filter will have the following characteristics: The magnitude response at ω O will be 3 dB below the maximum magnitude response; with a passive filter, the maximum magnitude response is unity, in which case the value at ω O is –3 dB. ) at the desired frequency. applies a highpass filter with a cutoff frequency ωc to an array of data. Gaussian high pass filter has the same concept as ideal high pass filter, but again the transition is more smooth as compared to the ideal one. The circuit is just 1 resistor, 1 capacitor built on breadboard that will be programmed and powered through Arduino Uno. RC High Pass Filter - Frequency and Bode Plot Calculator. Only the bottom varies with frequency. The actual Bode magnitude plot is 3 dB lower than the approximate plot at ω = ω o , the cutoff frequency. 6 Hz can be used. Similarly, a simple RC High Pass filter has the transfer function . Analyze the qualitative response of the building blocks that compose the bandpass filter (i. A physical filter can be designed to closely approximate an ideal filter if needed. The function giving the gain of a filter at every frequency is called the amplitude response (or magnitude frequency response). A high pass filter is used in circuits that only require high frequencies to operate. For example, if you set a high-pass filter at 300hz, you’d lose a lot of the bass sound from instruments that have frequencies in that lower range. Ideally, the frequency response is flat over 20-20,000 Hz, and rolls off sharply at frequencies below 20 Hz and above 20,000 Hz. . characteristic is simple. 5u rload 2 A highpass filter does exactly the opposite to a lowpass filter, i. As shown in the plot, the As shown in the plot, the actual simulated value of the cutoff frequency is within 0. 75 kHz Cs = 0. I was able to find the transfer function for the high pass filter and the magnitude but I am stuck finding the phase. Response rolls off at -20dB/decade, or -6dB/octave above . But it's now in the stop band of the of high pass filter, where it's attenuated by a factor of 0. 1 Hz, and scaled the magnitude of the frequency content linearly between these two frequencies. So at the output of the high pass filter, we have a sin wave of amplitude 0. 4 of the text. Therefore, the magnitude of transfer function of Low pass filter will vary from 1 to 0 as ω varies from 0 to ∞. f) Frequency response of a filter with finite impulse response Passive Low Pass Filter. Bode plots are very useful for understanding how a filter or amplifier affects an AC signal at a specific frequency. High-Pass RL filter: Set up the RL circuit as shown in figure 2 on your solderless breadboard, with the component values R1 = 1 KΩ, L1 = 22 mH. Butterworth low-pass filter. High-Pass Digital Filter Implementation Using PGA _____ 45 deleting poles and zeros. Apr 19, 2016 · Magnitude Response of First Order High-Pass Filter. e) Transfer function of a filter with infinite impulse response. Arduino Connection Diagram of High Pass RC Filter 1. In practical situations the design of a High pass or Low pass filter is guided by the value of the cutoff or corner frequency ω0. An example of schematic is shown below, with LM35 Temperature Sensor as the analog signal input. 2 The subject is treated in detail beginning with section 15. From this, we can apply some algebraic manipulation to solve for the -3dB cutoff frequency. You can expect the pass-band frequencies of your signal to be attenuated by a factor within the pass-band ripple. That means the output voltage amplitude is smaller than the input voltage amplitude and the network attenuates the input signal. how do i determine whether it is an Low pass filter or a high pass filter. In other words, the pass(ing) band is ! < !c. low-pass filter. As a low-pass filter contains a capacitor, the phase angle of the output may lag behind that of the input signal and out of phase by a certain angle. This article describes a low-pass filter, but the same principles apply to high and band pass filters and can even be extended to to resonators. From the drawing, it is clear that the circuit represents a low-pass lter (LPF). A simple band stop filter circuit with passive components is shown below. Low-frequency asymptote. Solution for What are magnitude and frequency scale factor will transform the prototype high pass filter into a high pass filter with a 0. Frequency 13 Oct 2016 Calcuate Magnitude and Phase of Output from Transfer function for a RC High Pass Filter. qmf (hk) Return high-pass qmf filter from low-pass. , the log-magnitude of $H(j\omega_c)$ 12 Mar 2018 If we add an Amplifier across passive high pass filter, we can easily create We can calculate the magnitude gain by converting the op-amp A high pass filter prevents frequencies below its cut-off frequency from passing and lets through signals above it. 1 High Pass RL Filter. The filter selected in VanRullen's simulation was a bad choice as it results in artifacts not related to filtering per se. Such is the case in the passive low-pass filter considered thus far. 4B Roll off per decade II. From the gain From the cutoff frequency 1 1 20 500 RK C = =Ω RR K 21= 10 200=Ω 10500 (1 ) 500 j Hj j ω ω There are many applications for an RLC circuit, including band-pass filters, band-reject filters, and low-/high-pass filters. This calculator allows a user to select the magnitude of the units of the capacitor, For example, right here whenever the frequency response, the magnitude of the frequency Let's look at a little bit more specific at lowpass and highpass filters. 1 First-Order Low-Pass and High-Pass Filters ( ) ( ) ( ) Where Note: With an op amp the gain and cut-off frequency can be determined independently Frequency Response Plots: 𝑖 𝑅 ; 𝑅 𝐶 For the circuit, when the frequency changes only the impedance of the capacitor is affected. The simplest band pass filter one can create has a frequency response function: 2 12 1j G(j ) K 1 j 1 j (11) For example, a simple first-order low pass filter has a single pole, while a first-order high pass filter has a pole and a zero. The transfer function of a second-order high-pass filter is given by (3) The gain of the second-order high-pass filter is the magnitude of Eq. , Another common name for the amplitude response is magnitude frequency response . Sort By. To build a high pass RL filter, the inductor is placed in parallel to the power source signals entering the circuit, as shown below in the following circuit: Ideal Low Pass Filter Ideal High Pass Filter filter. If you look at the documentation, it says: "in order to measure the real acceleration of the device, the contribution of the force of gravity must be eliminated. Like most engineers, I use them at many points in my mixes to clean up woofy signals and tighten up arrangements. As the first part is an RC high pass buffered circuit, I believe the TF can be cascaded (multiplied). forms a filter whose frequency response is a function of the magnitude of the control voltage. 707 A voltage-controlled low-pass high-pass filter is described. Thus, the RC high-pass filter has the capacitor in series with the signal and the resistor across the output, as shown in the first diagram to the right. Cutoff frequency: In another way, the frequency when the signal magnitude is Vpp/sqrt(2). The op-amp is connected inversely. Adding two poles close to those zeros would make it a strong notch filter. The FIR filter generated by EEGLAB (Delorme et al. In this article, you will learn how to calculate the And magnitude of the voltage gain is: (7). High Pass Filter. The figure is simple four-terminal RC Apr 19, 2018 · The frequency response of the filter is a complex function whose magnitude gives the gain of the system. Ideal transfer function of low-pass filter with 1-kHz corner frequency The filter-response DC gain in Figure 2 is equal to 0 dB. Laplacian/Laplacian of Gaussian. For the high-frequency asymptote, take f!1as usual, so that 1 ˝Bf and 1 ˝Cf. The magnitude response in the pass-band, where , varies from 1 to , following cosine function. The amplitude response of an LTI filter is defined as the magnitude (or modulus) of the (complex) filter frequency response, i. Butterworth, or Bessel) there is a unique ratio of components to be used. Chapter 15: Active Filter Circuits 15. 01 micro Farads D This article describes a low-pass filter, but the same principles apply to high and band pass filters and can even be extended to to resonators. A band pass lter essentially sets both an lower and upper limit of input signal frequency components that are allowed to pass through the BPF. design of a High pass or Low pass filter is guided by the value of the cutoff or corner frequency ω0. B. 0547 normalized frequency), as an example. May 12, 2019 · The term bandwidth refers to the width of a filter’s passband, and in the case of a low-pass filter, the bandwidth is equal to the –3 dB frequency (as shown in the diagram below). Audio Filters: Along with the CW band-pass filter mentioned above, audio filters are also used to get rid of hum (50 or 60 Hz signals caused by magnetic fields), buzz (caused by 120 Hz rectified AC and ac neutral currents), and high-frequency hiss. 75 kHz and standard capacitor value for audio circuit design chosen to be 0. Figure 7 RC high-pass filter. 5 capacitor and a… High-pass filter. Magnitude curve is flat for low frequency and rolls off at high frequency. fft2 to experiment low pass filters and high pass filters. The implemented filter consists of the top microstrip coupled patches and the bottom modified nonuniformly short the magnitude of the FRF of an nth order high-pass Butterworth filter with cut-off frequency is Now we consider the implementation of a Butterworth filter. A band pass filter can be created by putting a high pass filter in series with a low pass filter, although one must be careful in the design to avoid significant loading effects. So, remember, I get rid of low frequencies, and I pass through high frequencies. The Circuits. The high-level implementation provides better compatibility across various filter structures, especially filters that would contain algebraic loops when constructed using basic elements. Think of it as the rate of Clear the check box to implement the filter as a high-level subsystem. For our example RC circuit, with R=10kΩ and C=47nF, the cutoff frequency is 338 Hz. 1st . When , the Chebyshev function increases rapidly with no ripples, and monotonically decreases and tends to zero. Also calculate the 3dB Frequency and sketch the 23 Aug 2017 In this video, passive RC High Pass Filter has been discussed. When H is smaller than unity, HdB is a negative number. Cut-off frequency is set to 9. The second category of ideal filter is the high-pass filter and has a gain of 0 from 0 to ωT and a gain of 1 for all frequencies greater than or equal to ωT. For example, suppose that the magnitude of a dimensionless quantity G(f) is G = f f0 n (3) where f0 and n are constants. 5 to 0. High Pass RL Filter. Set the oscilloscope attenuation A high-pass filter will pass the high-frequency Fourier components, but not those components at lower frequencies. High Pass Filter :- The basic operation of an active high pass filter is exactly the Above the cut - off frequency, the magnitude of the output voltage is constant. So the magnitude as a function of frequency shows which frequencies are attenuated and which are not. This Windowed FIR Filter C Code has two parts, the first is the calculation of the impulse response for a rectangular window (low pass, high pass, band pass, or notch). 5 Now denormalise the frequency-domain transfer function H(s) of the Butterworth filter, with the corresponding low-pass to low-pass frequency transformation of Equation 5. This is a low-pass filter. At very high frequencies the capacitor acts as a short circuit and all the input appears at the output. basic filter without using them. 2 High Pass Filter A high pass filter is a circuit whose amplitude response increases with ! as shown in fig. Figure 6: Low pass RC filter response at 500Hz. Consider the arrangement shown on Figure 6. Figure 1: RC Low pass filter circuit Sinusoidal Input. For a 180 bit, you must cascade to 90s, or use an alternate structure. 4A Roll off per octave II. Passive first order high pass filter. When an resistor is placed in series with the power source of the circuit and an inductor is placed in parallel to that same power source, as shown in the diagram circuit above, this type of First Order Low-Pass Filter Magnitude Phase EE40 Fall 2009 Prof. Intuitively, when frequency is high, $Z_2(j\omega)$ is small i. Horizontal line in the “EEE305”, “EEE801 Part A”: Digital Signal Processing Chapter 5: Design of IIR Filters University of Newcastle upon Tyne Page 5. Response rolls off at -20dB/decade, or There are five basic filter types (bandpass, notch, low-pass, high-pass, and all-pass). The amount of attenuation for each frequency depends on the filter design. Nilai-nilai pengurangan untuk frekuensi berbeda-beda untuk tiap-tiap filter ini . Note that, once again, it is possible to define a cutoff frequency at ω 0 = 1/ RC in the same way as was done for the low-pass filter. frequency of a filter, the impedances of all its elements will be of the same order of magnitude. The shorter the transition band, the better the practical filter is. Formally, it is the ratio of the output amplitude to the input amplitude. Figure 6. You will use AC Analysis to determine its frequency response. % This demonstration shows the magnitude and phase response for an FIR filter % of 2M+1 elements whose ideal response is a low pass filter with cutoff % frequency of fs/4. The corner frequency of this low-pass filter occurs at 1 kHz, and the gain magnitude at 1 kHz is equal to –3 dB. However, their positions are swapped. In this blog post, I will use np. 1 Add a high-frequency disturbance e(n), . Where: m = magnitude coefficient f c = 9. One of the ways that a crossover may be constructed from a Bessel low-pass filter employs the standard low-pass to high-pass transformation. This filter is a high pass filter with a cutoff frequency f as it allows frequencies above f to pass and as it attenuates frequencies below f. • what happens if we Fundamentals of Low-Pass Filters Active Filter Design Techniques 16-7 16. The Laplacian is a 2-D isotropic measure of the 2nd spatial derivative of an image. An all-pass filter with the output lagging behind the input is illustrated in figure. View FIR IIR Filter EXAM from EL EL 6183 at New York University. For high pass filters, the magnitude of the step function gets its minimum value at frequency approaches to infinity, the inductor behaves like wi component. II. Here is the circuitry implementation of inverted active High pass filter:-It is an active High pass filter in inverted configuration. And there is some range of frequencies where the magnitude of the fft of data is too high (in red circle). Consider the circuit shown in Figure 1. A Low Pass Filter is a circuit that can be designed to modify, reshape or reject all unwanted high frequencies of an electrical signal and accept or pass only those signals wanted by the circuits designer Mar 13, 2019 · A high-pass filter is a simple, but effective EQ curve that scoops out unwanted low frequencies from an audio source. The scale of decibels Comparison of signal amplitudes R RE Ru M Vin RI I on Vin om Von (a)Low-pass filter (b) High-pass-filter. These ratios are usually kept is handy tables like the one below. High-pass filter definition: a filter that transmits all frequencies above a specified value , substantially | Meaning, pronunciation, translations and examples a high [frequency]-pass filter will be \$>1\$ in the high frequency region, the right side of the plot. The FIR filter. Frequencies below f l and above f h are in the stop band. 05 Hz, passed all frequency content above 0. The bottom part is the square root of the sum of the imaginary part squared and the real part squared. • All of the different filter types are derived from the low-pass filter. Oct 13, 2016 · Calcuate Magnitude and Phase of Output from Transfer function for a RC High Pass Filter. Set 3 dB points as follows: Jul 09, 2012 · Filter Selection. Filling in the gaps (in the same spirit as the low-pass and high-pass lters above) is left as an exercise. 4 An all-pass filter is that which passes all frequency components of the input signal without attenuation but provides predictable phase shifts for different frequencies of the input signals. A high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The schematic of a multiple-feedback, high-pass filter is shown in Figure 13, and its ideal phase shift vs. The damping factor, ζ, which may be better known to the reader, is The coefficients for the FIR low-pass filter producing Daubechies wavelets. Figure 3. The response of the filter is displayed on graphs, showing Bode diagram, Nyquist diagram, Impulse response and Step response. From a 2nd order low pass filter we can get a 2nd order high pass filter: () 0 2 2 0 2 let / then for a 2nd order LPF: 21 1/ 12 n LP LP HP qj H Hq qq Hq Hq Hq qq ωω ζ ζ = = ++ == ++ If the components of a filter are replaced so that any impedance dependence on ωis replaced by a similar dependence on 1/ωthe filter changes from low pass to Following up on John Lahr's recent email on filtering, it's interesting to filter the Kuril seismogram with a high pass filter. The size of the discontinuities is π, representing a sign reversal. 1% of the specified value. 0156 normalized frequency), F_pass = 7 kHz (0. 5 Signals & Linear Systems Lecture 9 Slide 11 Butterworth Filters (1) Let us consider a normalised low-pass filter (i. Those factors are then used to approximate high--pass and band-pass filter characteristics. These plots have been normalized to have the filter cutoff frequency ω 0 = 1 rad/s. Low-Pass Filter Figure 4. The Q-factor is the reciprocal of the fractional bandwidth. The simple high pass of the 1st order is built up with a capacitor and a resistor connected in series. The frequency response of a digital filter can be interpreted as the transfer function evaluated at z = e jω. Switched filter phase shifter bits, either high pass, or low pass, are not useful above 90 degrees of phase shift. The magnitude Bode plots of functions equal to powers of f are linear. For the active bandpass filter shown in Figure 6. Due to the virtual ground assumption, at non-inverting input is virtually the same as that at the inverting input, which is connected to the output . The first part (C 1 R 1 ) will pass high frequency signals while the second part (C 2 R 2 ) will pass the low frequencies (or rejects high frequency signals). 4: Building blocks of the bandpass filter shown in Fig. Fig 2. An ideal low pass filter then could have the magnitude response shown at the graph below. Butterworth 1 st order 1 kHz high-pass filter flowchart. Apr 22, 2020 · And the amplitude will completely zero for signals which have a lower frequency than the cutoff frequency. If we plot the magnitude of the ratio of the output and input voltages, we see that f jv outj jv inj Figure 1: Magnitude of the transfer function. one that has a cut-off frequency at 1) with an amplitude characteristic given by the equation: • Active Low-Pass Filter, • Passive High-Pass Filter, and • Active High-Pass Filter. This is equivalent to a change of the sign of the phase, causing the outputs of the low-pass filter to lag and the high-pass filter to lead. Then a window (Kaiser, Hanning, etc) is applied to the impulse response. (4) is shown in Fig. Alternate 11 degree bit. “Attenuate” means to reduce or diminish in amplitude. The frequency response of band stop filter is shown below and green line indicates the practical response in the below figure. It calculates the range of high frequency signals that a filter passes through. It is +45 degree at the cutoff frequency of fc. Figure 13. Ideally, the frequency output of a high pass filter is like this, pass filters and high pass filters. • The type of filter can readily be determined by the magnitude plot of the TF relating the filter input to the filter output. A) FIR Filter Design Fig 1 represents the magnitude response of a digital ideal low pass filter with cut-off frequency of f 1 . You can use series and parallel RLC circuits to create band-pass and band-reject filters. Here the signal is attenuated or damped at low frequencies with the output increasing at +20dB/Decade (6dB/Octave) until the frequency reaches the cut-off point ( ƒc ) where again R = Xc. The second is after applying high pass filter with F_stop = 2 kHz (0. IIR Filters See this page for IIR Filter Design Equations and C Code. Although the magnitude (or gain) is not plotted on a logarithmic scale, it is not A high-pass filter is a transfer function that removes low frequency content so Abstract: A new and simple method is given for transforming a low-pass filter maximum attenuation rate of the HPF magnitude response near \omega = 0 is 6 It is important to notice that mag is the magnitude of the transfer function. magnitude of high pass filter
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2020-07-10 13:05:39
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https://leanprover-community.github.io/archive/stream/113488-general/topic/lawful.20classes.html
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## Stream: general
### Topic: lawful classes
#### Simon Hudon (Mar 23 2018 at 16:30):
I'm having a look at the new is_lawful_functor. I just realized that it does not extend functor. That makes some signatures pretty verbose. Is there a plan to make shortcuts like lawful_functor that would combine both?
#### Mario Carneiro (Mar 23 2018 at 18:37):
I think it used to be bundled and was later unbundled. Of course you should ask Sebastian for the full story
#### Sebastian Ullrich (Mar 23 2018 at 19:50):
I'm not convinced of the useful of such shortcut classes. You cannot have class inference convert both to and from the class without risking cycles, which would make their usage quite clunky, I'd imagine.
Last updated: May 17 2021 at 22:15 UTC
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2021-05-17 23:15:54
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https://wiki2.org/en/Category_of_sets
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# Category of sets
In the mathematical field of category theory, the category of sets, denoted as Set, is the category whose objects are sets. The arrows or morphisms between sets A and B are the total functions from A to B, and the composition of morphisms is the composition of functions.
Many other categories (such as the category of groups, with group homomorphisms as arrows) add structure to the objects of the category of sets and/or restrict the arrows to functions of a particular kind.
## Properties of the category of sets
The axioms of a category are satisfied by Set because composition of functions is associative, and because every set X has an identity function idX : XX which serves as identity element for function composition.
The epimorphisms in Set are the surjective maps, the monomorphisms are the injective maps, and the isomorphisms are the bijective maps.
The empty set serves as the initial object in Set with empty functions as morphisms. Every singleton is a terminal object, with the functions mapping all elements of the source sets to the single target element as morphisms. There are thus no zero objects in Set.
The category Set is complete and co-complete. The product in this category is given by the cartesian product of sets. The coproduct is given by the disjoint union: given sets Ai where i ranges over some index set I, we construct the coproduct as the union of Ai×{i} (the cartesian product with i serves to ensure that all the components stay disjoint).
Set is the prototype of a concrete category; other categories are concrete if they are "built on" Set in some well-defined way.
Every two-element set serves as a subobject classifier in Set. The power object of a set A is given by its power set, and the exponential object of the sets A and B is given by the set of all functions from A to B. Set is thus a topos (and in particular cartesian closed and exact in the sense of Barr).
Every non-empty set is an injective object in Set. Every set is a projective object in Set (assuming the axiom of choice).
The finitely presentable objects in Set are the finite sets. Since every set is a direct limit of its finite subsets, the category Set is a locally finitely presentable category.
If C is an arbitrary category, the contravariant functors from C to Set are often an important object of study. If A is an object of C, then the functor from C to Set that sends X to HomC(X,A) (the set of morphisms in C from X to A) is an example of such a functor. If C is a small category (i.e. the collection of its objects forms a set), then the contravariant functors from C to Set, together with natural transformations as morphisms, form a new category, a functor category known as the category of presheaves on C.
## Foundations for the category of sets
In Zermelo–Fraenkel set theory the collection of all sets is not a set; this follows from the axiom of foundation. One refers to collections that are not sets as proper classes. One cannot handle proper classes as one handles sets; in particular, one cannot write that those proper classes belong to a collection (either a set or a proper class). This is a problem because it means that the category of sets cannot be formalized straightforwardly in this setting. Categories like Set whose collection of objects forms a proper class are known as large categories, to distinguish them from the small categories whose objects form a set.
One way to resolve the problem is to work in a system that gives formal status to proper classes, such as NBG set theory. In this setting, categories formed from sets are said to be small and those (like Set) that are formed from proper classes are said to be large.
Another solution is to assume the existence of Grothendieck universes. Roughly speaking, a Grothendieck universe is a set which is itself a model of ZF(C) (for instance if a set belongs to a universe, its elements and its powerset will belong to the universe). The existence of Grothendieck universes (other than the empty set and the set ${\displaystyle V_{\omega }}$ of all hereditarily finite sets) is not implied by the usual ZF axioms; it is an additional, independent axiom, roughly equivalent to the existence of strongly inaccessible cardinals. Assuming this extra axiom, one can limit the objects of Set to the elements of a particular universe. (There is no "set of all sets" within the model, but one can still reason about the class U of all inner sets, i.e., elements of U.)
In one variation of this scheme, the class of sets is the union of the entire tower of Grothendieck universes. (This is necessarily a proper class, but each Grothendieck universe is a set because it is an element of some larger Grothendieck universe.) However, one does not work directly with the "category of all sets". Instead, theorems are expressed in terms of the category SetU whose objects are the elements of a sufficiently large Grothendieck universe U, and are then shown not to depend on the particular choice of U. As a foundation for category theory, this approach is well matched to a system like Tarski–Grothendieck set theory in which one cannot reason directly about proper classes; its principal disadvantage is that a theorem can be true of all SetU but not of Set.
Various other solutions, and variations on the above, have been proposed.[1][2][3]
The same issues arise with other concrete categories, such as the category of groups or the category of topological spaces.
## Notes
1. ^ Mac Lane 1969
2. ^ Feferman 1969
3. ^ Blass 1984
## References
• Blass, A. The interaction between category theory and set theory. Contemporary Mathematics 30 (1984).
• Feferman, S. Set-theoretical foundations of category theory. Springer Lect. Notes Math. 106 (1969): 201–247.
• Lawvere, F.W. An elementary theory of the category of sets (long version) with commentary
• Mac Lane, S. One universe as a foundation for category theory. Springer Lect. Notes Math. 106 (1969): 192–200.
• Mac Lane, Saunders (September 1998). Categories for the Working Mathematician. Springer. ISBN 0-387-98403-8. (Volume 5 in the series Graduate Texts in Mathematics)
• Pareigis, Bodo (1970), Categories and functors, Pure and applied mathematics, 39, Academic Press, ISBN 978-0-12-545150-5
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.
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2021-12-03 02:27:51
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http://math.stackexchange.com/questions/319442/show-sum-a-1-1n-sum-a-2-1a-1-sum-a-3-1a-2-sum-a-m-1a-m-1
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# Show $\sum_{a_1=1}^n\sum_{a_2=1}^{a_1}\sum_{a_3=1}^{a_2}…\sum_{a_m=1}^{a_{m-1}}a_m=\frac 1 {(m+1)!}\prod_{k=0}^m(n+k)$.
When playing around Wolfram Alpha, I find something interesting:
$\displaystyle \sum_{a_1=1}^n a_1=\frac 1 2 n(n+1)$
$\displaystyle \sum_{a_1=1}^n\sum_{a_2=1}^{a_1} a_2=\frac 1 6 n(n+1)(n+2)$
$\displaystyle \sum_{a_1=1}^n\sum_{a_2=1}^{a_1}\sum_{a_3=1}^{a_2} a_3=\frac 1 {24} n(n+1)(n+2)(n+3)$
I then deduce that $\displaystyle \sum_{a_1=1}^n\sum_{a_2=1}^{a_1}\sum_{a_3=1}^{a_2}...\sum_{a_m=1}^{a_{m-1}}a_m=\frac 1 {(m+1)!}\prod_{k=0}^m(n+k)$. But I don't know how to prove or disprove this. Please help. Thank you.
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Try to prove by induction.
Take
$S_m(n) = \sum_{a_1=1}^n\sum_{a_2=1}^{a_1}\sum_{a_3=1}^{a_2}...\sum_{a_m=1}^{a_{m-1}}a_m$,
$S_{m+1}(n)= \sum_{a_0=1}^n\sum_{a_1=1}^{a_0}\sum_{a_2=1}^{a_1}\sum_{a_3=1}^{a_2}...\sum_{a_m=1}^{a_{m-1}}a_m=\sum_{a_0=1}^n S_m(a_0)$.
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induction, I believe? – Vincent Tjeng Mar 3 '13 at 14:28
@VincentTjeng oops...thanks. – Yimin Mar 3 '13 at 14:29
Note that$a_m=\sum_1^{a_m}1$
Your question is now that of finding the size of the set;
$n\geq a_m \geq a_{m-1}\geq...\geq a_1 \geq 1$
Note that this is the same as finding no.s $x_i$ such that $n\geq x_i\geq0$ and $\sum x_i=n$ ( Think differences). Now can you do it? I may have made a mistake , here or there but the idea's fine I think.
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2014-09-23 22:25:44
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https://math.stackexchange.com/questions/2297649/is-this-a-valid-proof-of-lagranges-theorem-finite-case
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# Is this a valid proof of Lagrange's theorem (finite case).
Let $$G$$ be finite and $$H$$ be a subgroup. We will show that the left cosets of $$H$$ partition $$G$$ and each coset has the same size.
1) Each element $$g \in G$$ belongs to the coset $$gH$$ since $$g1=g$$ and $$1\in H$$.
So every element lies in at least one coset.
2) We know show that each $$g \in G$$ lies in exactly one coset.
Suppose for a contradiction $$g$$ lies in more than one coset then $$g \in aH$$ and $$g \in bH$$ where $$aH,bH$$ are distinct left cosets. Then $$g=ah_1$$ and $$g=bh_2$$ so $$ah_1=bh_2$$ for some $$h_1,h_2 \in H$$.
Now $$aH \subseteq bH$$ since if $$ah \in aH$$ then $$ah=bh_2h_1^{-1}h \in bH$$. Likewise $$bH \subseteq aH$$ so $$aH=bH$$ a contradiction.
So each $$g \in G$$ lies in exactly one coset.
Hence the cosets form a partition of $$G$$.
3) For each $$g \in G$$ the coset $$gH$$ has the same order as $$H$$.
To see this establish a function $$\phi:gH \rightarrow H$$ by $$\phi(gh)=h$$. This is clearly a bijection.
So $$|G|=\text{Number of cosets} \times \text{Size of each coset}=[G:H]|H|$$ and so $$|H| \mid |G|$$.
Is this proof valid?
• What do you mean "finite case"? Lagrange's theorem is only applicable to finite groups, since "divides the order" only makes sense when "order" is a number. – Adam Hughes May 26 '17 at 14:11
• There's just a small issue with your argument that $aH\subseteq bH$. You wrote $ah = bh_2h_{1}^{-1}$, where I think it should be $ah = bh_2h_{1}^{-1}h$. – James May 26 '17 at 14:22
• By finite case I meant there is some kind of extension that the index is infinite for infinite groups. – Ben B May 26 '17 at 15:36
• @James Yes you are correct that was just a mistake when writing it out. Is everything else sound though? Thanks! – Ben B May 26 '17 at 15:37
• Everything sounds good to me. Though it may be easier to justify the last point by considering $\phi : H\to gH$ defined by $\phi(h)= gh$. It would then be easier to justify that :1. It is well-defined, 2. It is bijective – Maxime Ramzi May 26 '17 at 17:08
Your proof is fine, except that I recommend you consider \begin{align} \varphi: H&\to gH \\ h&\mapsto gh, \end{align}
then justify that $$\varphi$$ is a well-defined bijection; it's much easier than your $$\phi$$.
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2020-06-04 02:28:05
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http://www.show-my-homework.com/
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## Effective Charge Laboratory
The definition of the effective charge In this paper we will determine the effective charge of an electron. The effective charge is by definition the ratio (e/m). Background Information and History Thomson was the first scientist that used a selection of different gases to determine the ratio of the electric charge of a particle to
## Spherical shell potential (Griffiths)
The charged sphere A spherical shell has spherical symmetry and because of this we write its potential as $V(R,\theta)=V_0(\theta)$ ($\theta$ is the “polar” angle of the spherical coordinate system). a) When $V_0(\theta)=V_0(1-\theta^2)$ find the equation of definition for $V(R,\theta)$ if $r>R$. b) When $V_0(\theta)=V_0(\cos^2 \theta +2)$ please evaluate the potential of this spherical shell at
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2017-07-25 10:42:44
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http://crypto.stackexchange.com/questions?page=3&sort=active&pagesize=15
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2015-04-28 07:04:28
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http://math.stackexchange.com/questions/278522/finding-a-limit-without-using-lh%c3%b4pital
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# Finding a limit without using l'Hôpital
Can somebody help me find this limit without using the l'Hôpital's rule. I'm probably overseeing something really simple but all I can get are $0/0$ forms or such:
$$\lim_{x\to -\infty}\left(\frac{-2}{\pi}\cdot\arctan{x}\right)^x$$
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Since $x\lt0$, $\arctan x=-\arctan(1/x)-\pi/2$ hence you are looking at $(1+u(x))^x$ with $u(x)=(2/\pi)\arctan(1/x)\sim2/(\pi x)$. For every $a$, $(1+a/x)^x\to\mathrm e^a$ when $x\to\infty$ hence the quantity you are looking at converges to $\mathrm e^{2/\pi}$.
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Let $\frac{-2}{\pi}\cdot\arctan x=1-y$ $\implies \arctan x=-(\frac\pi2-\frac\pi 2y)$ $\implies x=\tan \{-(\frac\pi2-\frac\pi 2y)\}=-\tan(\frac\pi2-\frac\pi 2y)=-\cot \frac\pi2y$
and as $x\to-\infty\implies\cot \frac\pi2y=\infty\implies y\to 0$
$$\lim_{x\to -\infty}\left(\frac{-2}{\pi}\cdot\arctan{x}\right)^x$$
$$=\lim_{y\to0}(1-y)^{-\cot \frac{\pi y}2}$$ $$=(\lim_{y\to0}(1-y)^{-y})^{\frac{\lim_{y\to0}\cos\frac{\pi y}2}{\lim_{y\to0}\frac{\sin \frac{\pi y}2}y}}=e^{\frac2\pi}$$
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Let $\arctan x=y-\frac\pi2\implies x=\tan(y-\frac\pi2)=-\tan(\frac\pi2-y)=-\cot y$
and $x\to-\infty, \cot y=\infty\implies y\to 0$
$$\lim_{x\to -\infty}\left(\frac{-2}{\pi}\cdot\arctan{x}\right)^x$$
$$=\lim_{y\to 0}\{\frac{-2}{\pi}(y-\frac\pi2)\}^{-\cot y}=\lim_{y\to 0}\left(1-\frac y{\frac\pi2}\right)^{-\cot y}$$
$$z=\left(1-\frac y{\frac\pi2}\right)^{-\cot y}$$
$$\implies \log z=-\cot y\log\left(1-\frac y{\frac\pi2}\right)=\frac{\cos y}{\left(\frac{-\sin y}{-y}\right)}\frac{\log\left(1-\frac y{\frac\pi2}\right)}{\frac{-y}{\frac\pi2}}\frac2\pi$$
So, $$\lim_{y\to 0}\log z=\frac2\pi \frac{\lim_{y\to 0}\cos y}{\lim_{y\to 0}\left(\frac{-\sin y}{-y}\right)}\cdot \lim_{y\to 0}\frac{\log\left(1-\frac y{\frac\pi2}\right)}{\frac{-y}{\frac\pi2}}=\frac2\pi$$
So, $$\lim_{y\to 0}z=e^{\frac2\pi}$$
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2015-05-25 14:35:04
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https://www.physicsforums.com/threads/what-alternative-kind-of-government-do-you-support.53432/
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# News What Alternative kind of Government do you Support?
1. Nov 20, 2004
### Smurf
In this thread everyone get's to express what kind of alternative Government you think we should have?
Rules are:
No arguing for Democracy
No arguing for Republic
No arguing for Fascism
No arguing for Communism
Why:
Because we've tried those before, (except maybe communism according to some, but whatever) and this thread is to find an Alternative, a New Shiny idea of a Government.
http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/List_of_forms_of_government [Broken]
Last edited by a moderator: May 1, 2017
2. Nov 20, 2004
### Smurf
I personally support http://www.wordlist.org/an/Anarcho-syndicalism.html [Broken].
Last edited by a moderator: May 1, 2017
3. Nov 20, 2004
### loseyourname
Staff Emeritus
Well, that's about exactly the opposite of what I would propose.
Ideally, I would eliminate just about every role of government outside of foreign relations, contract enforcement, currency printing, and national defense, although even here I would like the military to rely more on the production of technology that can be applied to civilian use rather than on taxation and deficit spending. I'd like to see the majority of decisions made locally and see federal government just about completely abolished, sort of a town-hall approach to government, with each municipality deciding for itself how to spend its own money and what rules it will live by. I'd like to see public services provided by private investment and user fees wherever possible, again in lieu of taxation. All taxation that does exist would ideally be applied only to transactions between private entities and public entities, eliminating income and corporate taxes. An important part of privatizing most government functions, and also allowing the market to operate under the best conditions, would be full disclosure of business activities, including expense reports, for all companies, not just those listed on public stock exchanges. I'd probably leave this function to the government as well. This way, we can bring about the only true democracy, one based on the principals of capitalism, where you vote with your dollar, giving it to whoever does the job best, instead of giving half to a public beast that misspends it without repercussion.
4. Nov 20, 2004
### Smurf
Why Capitalism?
5. Nov 20, 2004
### loseyourname
Staff Emeritus
Because when it operates under ideal conditions, it is the only fair system of exchange of goods and services ever devised.
6. Nov 20, 2004
### Smurf
That is simply untrue.
Ever tried in the west? True.
Most Successfull in exploiting the world? True.
But there are a million and one economic systems that have been devised that just havn't been tried yet because they would take power away from the corporations.
7. Nov 20, 2004
### BobG
Interesting list.
Wouldn't doulocracy (rule by slaves) be problematic? What if they outlawed slavery? Or would political candidates sell themselves into slavery to raise campaign funds? (Reminds of the SNL skit about how Dole's resignation from the Senate might affect the Clinton/Dole Presidential campaign :rofl: )
A strumpetocracy (rule by strumpets) or a pornocracy (rule by harlots) would make for an interesting campaign. :tongue2:
I'd lean towards a mesocracy. Better than the stochastic foolocracy we have today.
8. Nov 20, 2004
### wasteofo2
What are ideal conditions for capitalism?
Around the time of the industrial revolution, the government had very few restrictions on buisness. As a result, the wages workers were paid were ridiculously low, children as young as 4 were working to help support their families, there was no reason for buisnesses to spend any extra money to protect their employees from work-related accidents, buisnesses had no accountability for their actions, and thus they took no precautions to protect the environment.
I think you need a strong/fair central government to keep corporations in check. Without government mandating minimum wage, environmental restraints, work place safety etc., corporations have no reason to not exploit people if it'll make them more money.
9. Nov 20, 2004
### loseyourname
Staff Emeritus
Fair competition standards and full disclosure of all business practices.
Sure they do. The only way for any company to remain in existence is for them to sell their product or service. When they operate according to fair competition standards (no collusion, kickbacks, etc., all strictly regulated by an impartial third-party committee that is not politicized) and under full disclosure, they have every reason not to exploit anybody.
I suppose this depends on what you mean by fair. By fair, I mean that this is the least coercive and aggressive of any economic system.
10. Nov 20, 2004
### plover
How do you get companies that see this as in their best interest? The ones we have now fight transparency kicking and screaming.
And how do economies of scale operate? If governmental decisions are all local and but corporate decisions can be global, you'd end up with a kind of corporate feudalism, with your proposed central governments sort of serving the role the church played in medieval feudalism.
11. Nov 20, 2004
### franznietzsche
Technocracy with capitalist economic philosophy (as opposed to socialist).
If your IQ is over 140, you matter, if not, get back to work.
12. Nov 21, 2004
### vanesch
Staff Emeritus
A favorite goes to random technocracy, where people with the right competences in the domain are given political responsability by random choice (lottery). It is actually very close to the actual way of functioning of the European administration. Legislation comes out, but there are no faces on it, no parties on it. It just happens
13. Nov 21, 2004
### vanesch
Staff Emeritus
I'd like to see both, actually. No matter what capitalists (or socialists for that matter) say, a simplistic ideology never works optimally in all circumstances. Some things work better with a capitalist ideology, others with a socialist ideology, and sometimes you'll have to think up another alternative. There's no magic rule that solves all problems in one sentence.
14. Nov 21, 2004
### franznietzsche
I'll rephrase:
Technocracy: But you don't get what you don't earn. Period.
15. Nov 21, 2004
### vanesch
Staff Emeritus
Do you do the same thing to your kids ?
16. Nov 21, 2004
### franznietzsche
If i had kids, yes. They don't get allowances for chores, they do chores because they are alive. They have to learn that nothing is free. If they choose to do extra things for money, then so be it, but nothing in this world is free,and they have to learn that.
I've seen nine year olds with $200 cd players (not so common now that they are cheaper) listening to someofthe fouestl music, becuase their parents just give them what they want. I have a friend who works at best buy and routinely has parents who come and pick things up, at their child's request while the kid is at school so they kid can have it when he gets home. Heck no. You have to earn your keep in this world, and learn to not expect it to be given to you by anyone, the government least of all. Now back to more political territory: Before one of themore vapid liberals trys it, i will jsut say that no, if one is mentallyretarded or parapalegic or otherwise genuinely disabled i don'tthink that they should starve because they cannot function. But a normal healthy person who does nothing but wait to be given something without working, does deserve to starve. 17. Nov 21, 2004 ### vanesch Staff Emeritus Glub ! :yuck: Can you imagine he/she's maybe between a rock and a hard place ? Like after having been beaten up by her man, left alone with 4 children, on the street, of which two are ill and nothing to live off ? Things like that ? 18. Nov 21, 2004 ### franznietzsche I'm speaking in generalities. General rules. You are dealing with exceptions. As i made the point about people genuinely disabled there are exceptions, but the rule is you earn what you get, you don't go to others looking for handouts and freebies just because you're lazy. 19. Nov 21, 2004 ### Smurf Franz, I think it is a common misconcenption that Socialism is going to give people everything for free, I don't know the dictionary definition off the top of my head but I've been called a socialist more often than not and I don't think people should get money for not doing anything either. My socialism is about exceptions. 20. Nov 21, 2004 ### vanesch Staff Emeritus Well, then we agree. But if there is not some form of social coverage organised by the state, there's no way to handle these "exceptions". (that is what a long discussion with Aquamarine was about) It is typically one of the problems that pure, hard capitalism handles badly. However, you'd be surprised what is the fraction of people in "socialist states" according to a typical US view, like many Western European ones who are supported by social wellfare, that are of the "exceptional case". It is true, however, that there is also a fraction based on laziness, or even downright abuse (in that they DO work, undeclared, and get their allowances on top of that, making easily$6000 a month cash). There should be a strong crackdown on that.
But nevertheless, there's more honest misery out there than you think, and it is often not the fault of the people (they just had bad luck for one or another reason, often one of the factors being born in the wrong place).
21. Nov 21, 2004
### franznietzsche
Well, since you bring up bad luck, your example of the woman fleeingher abusive "man," thats not bad luck. Thats the culmination of bad choices. The situation her kids are in, that is bad luck. The situation she's in, is the result of her bad judgement.
You say we agree, in principle. The difference is, and smurf brings this up, is that you want to serve the exceptions first. I do not. The government is a failure when it comes to this sort of thing, because too many people who should not be helped, get helped, and too many people who should not be helped have lobbyists that are far to powerful, and i'msick of it.
My mother works at bank. She has people come in every other week to cash disability checks. More than half are for carpal tunnel syndrome. She has yet to see even one who has any difficulty driving to the bank, opening the door, walking to her desk, signing paper work, or any thing else. Now i'm sure a few might have just been able to conceal genuine pain, but you cannot tell me, a bunch of people, obviously healthy enough to still work, if they can go to the bank on their own they can work, deserve anything from the government.
22. Nov 21, 2004
### Smurf
I think this is an example of the Government's inefficiency in dealing with scammers than the failure of the system in general. We have the same problems in Canada.
23. Nov 21, 2004
### franznietzsche
The government is the system. The failure of the government is the failure of the system.
24. Nov 21, 2004
### Aquamarine
Does the industrial age argument never die?
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2018-06-21 12:50:23
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https://electronics.stackexchange.com/questions/56193/clock-period-using-verilog-code
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# Clock Period using Verilog code
I want to calculate time period by using Verilog code. Is this the correct way to get time period of clock of a particular frequency? Please suggest to me some better Verilog code. The code is not working.
I have written this sample code:
module clk(reg gsclk, output reg time1,output time2,output gs_clk_period)
always@(posedge gsclk)time1=$current_time; always@(negedge gsclk)time2=$current_time;
always@(posedge gsclk)gs_clk_period = (time2 - time1)*2;
$display("%clock %b",gs_clk_period); endmodule I have to use time period for synthesize and want to run in real device. • Could you explain more why you are doing this? Are you trying to determine how fast your simulation is running or do you want something you can synthesize and run in a real device? – The Photon Jan 26 '13 at 16:55 • I have to use time period for synthesize and want to run in real device.This will be use like for example , Vout(n) T = gsclk*2, Vout(n)=gsclk*3 like wise in my program. – Manzer Jan 26 '13 at 17:04 ## 3 Answers Verilog offers three system tasks related to the simulation timestep: $time returns the current time as a 64-bit integer, in units of the timestep defined by the timescale directive.
$stime returns the same value as a 32-bit integer. $realtime returns the same value as a real number.
However none of these system directives are likely to be useful for synthesis. They would normally be implemented by special code in the simulator that accesses variables in the simulator program.
To keep track of time in a real circuit, you need to start with an input clock with a known frequency. For good accuracy you'd generate this with a crystal oscillator circuit, which would be entirely outside your device if you're working on an FPGA.
Then you simply build a counter to keep track of ticks of your clock (note code not tested):
module time_counter(input clk, input rst, output reg [31:0] ticks)
always @(posedge clk or posedge rst) begin
if (rst) begin
ticks <= 32'h00000000;
end
else begin
ticks <= ticks + 1;
end
end
endmodule
There is a limit to how fast a counter like this can operate, and various tricks to build faster counters if needed.
If you need to find the period of an input with an unknown period, you need to compare it to a clock with a known period. It's simplest conceptually to make the known clock much faster than the unknown clock and count ticks of the known clock for each period of the unknown clock. If that's not possible, you can divide the unknown clock by some factor (say 16 or 128 or 1024) and count ticks of the known clock for each cycle of the divider to work out the unknown period.
• But my question is how to get time period of clock?I mean frequency calculation.If the frequency of clock is 10 mhz, i want to calculate in timeperiod in ns in verilog code?? – Manzer Jan 26 '13 at 18:11
• You need to have another clock with known period. Count how many periods of the known clock make one (or 16 or 128 or 1024) period of the unknown clock. But the details of how to do it, beyond what I've already answered, depend on knowing more about your application --- what frequency range are you trying to measure? What technology are you using? etc. – The Photon Jan 26 '13 at 18:27
For it to be synthesize you need a reference clock that you already know the real period (e.g. ref_clk), then you can estimate the period of any other clock.
You'll need an counter (e.g. gs_cnt) that is incremented by gsclk. Let the counter run for ref_cnt number of ref_clk cycles. The period of gsclk can be estimated as ref_period*ref_cnt/gs_cnt.
It is a good idea to prevent the counter from rolling back to 0 while incrementing. This also lets you know that the gsclk is to fast to be measured in the ref_cnt window.
Your code assumes that the clock has 50% duty cycle. Instead you should sample twice in an always block:
module clk(reg gsclk, output reg time1,output time2,output gs_clk_period)
time rising_edge;
always @(posedge gsclk)
begin
rising_edge = $time; @(posedge gsclk) gs_clk_period =$time - rising_edge;
end
endmodule
`
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2020-03-30 12:48:48
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https://www.bartleby.com/questions-and-answers/or-fx-dx-1-or-fxx-dx-a-0.-j-xx-dx-a-0./eb94da1b-36be-4d16-8041-48d2fcfd72e1
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# | f{x) dx = 1 | f(x)x dx = a 0. J (x)x² dx = a² 0.
Question
Find all the continuous positive functions f(x), for 0 ≤ x ≤ 1, such that where α is a given real number
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2021-05-19 04:04:44
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https://robertmarks.org/REPRINTS/2020-Notched.html
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# Impedance Tuning with Notched Waveforms for Spectrum Sharing in Cognitive Radar
Publisher: IEEE
12
Author(s)
Abstract: In a congested radio spectrum, radar systems must be capable of sharing spectrum in real time. Two possible radar transmission approaches involve either avoiding interfer...
Abstract:
In a congested radio spectrum, radar systems must be capable of sharing spectrum in real time. Two possible radar transmission approaches involve either avoiding interferers or placing a notch in the sub-bands of interference. Impedance tuning allows the radar transmitter power amplifier to maximize its output power while adjusting its linearity to meet notch and/or out-of-band spectral requirements. In real-time spectrum sharing, the system controller decides whether to provide a waveform that notches around the interference or to avoid the interference altogether. Considerations in this decision include the maximum detection range obtainable from a tuned amplifier versus the finest achievable range resolution, based on transmitted bandwidth. This paper describes a comparison of real-time impedance tuning for notched, random FM waveforms versus a contiguous-band chirp used for avoidance. Comparisons are made between the range (calculated from output power) and the range resolution (calculated from bandwidth) obtained by the optimized circuits in these two cases.
Date of Conference: 28-30 April 2020
Date Added to IEEE Xplore: 11 June 2020
ISBN Information:
ISSN Information:
INSPEC Accession Number: 19688635
Publisher: IEEE
Conference Location: Washington, DC, USA, USA
No metrics found for this document.
SECTION I.
## Introduction
The re-allocation of radar S-band spectrum for sharing with wireless communications is only the most recent example of an ongoing trend that is driving research on radar spectrum sharing [1][2][3][4][5][6][7]. One method of sharing is for the radar to transmit in a contiguous band of frequencies that changes based on the radio frequency interference (RFI) gleaned from the environment. In such scenarios, a tunable matching network can be placed after the transmitter power-amplifier device and tuned in real-time to operate between the RFI frequencies [8]. Real-time tuning of the amplifier is useful because the output power, the power-added efficiency (PAE), and the adjacent-channel power ratio (ACPR) of an amplifier all depend on the load impedance presented to the amplifier [9], which is also affected by changing antenna impedance due to mutual coupling in arrays [10]. Real-time circuit tuning under control of a cognitive radio platform can therefore improve output power in frequency/beam agility scenarios. Kirk [11] likewise demonstrates the use of a software-defined radio (SDR) platform to maximize bandwidth, signal-to-interference-plus-noise ratio (SINR), and target-to-clutter ratio for spectrum sharing by sensing the spectrum, and then choosing the band for transmission.
In some sharing scenarios, rather than change the contiguous band of operation, spectral notches [12][13][14][15] can be placed within the transmitted radar bandwidth at the particular sub-bands occupied by RFI. A recent approach has relied upon the inherent maneuver freedom of random FM waveforms [16] to incorporate notches. Specifically, Jakabosky [17] demonstrates Tukey windowing to taper the range sidelobes otherwise induced by sharp notch edges, and Mohr [18] uses a spectral frequency-template error (FTE) metric for optimization of notched waveforms. Ravenscroft [19] provides an holistic perspective on the use of notched random FM waveforms for radar detection in an environment with stationary and dynamic RFI, integrating this approach into a cognitive radio platform using a perception-action cycle for spectrum sensing, decision making, and adaptation. Valette [20] subsequently discusses the interaction of notched waveforms with power amplifier nonlinearities.
In [21] Semnani demonstrates a 90 W evanescent-mode (EVA) cavity impedance tuner that provides the capability to reconfigure within hundreds of milliseconds by adjusting the positions of discs atop its two cavities, with loss of only ∼0.75 dB across most of the Smith Chart. This tuner is likewise shown by Alcala-Medel [8] to be frequency-agile over the S-band radar allocation using fast tuning algorithms developed by Dockendorf [22]. Here we demonstrate the use of this cavity tuner to perform impedance tuning for spectrally notched waveforms, providing the capability to optimize the power amplifier nonlinearities to obtain desirable notch depth and out-of-band spectral performance while maximizing the radar range.
SECTION II.
## Measurement Results: Impedance Tuning Implications on the Decision to Notch or Avoid
With the availability of notched waveforms (e.g. [12][13][14][15][16][17][18][19]), a cognitive radar may either notch around RFI frequencies or avoid the interference by selecting a smaller contiguous bandwidth. The impedance tuning considerations contribute to an engineering trade-off that must be negotiated between these two operating conditions. If a “notch” decision is made, the matching circuit can be tuned to maximize the power under the stringent consideration of meeting the sharp notch roll-off. If nonlinearities in the power amplifier cause intermodulation that fills the notch, then the load impedance must be tuned to focus on linearizing the amplifier device rather than improving the output power. As such, the greater bandwidth available from the notched waveform, and accompanying improvement in range resolution, might come at a sacrifice of output power and a related undesirable decrease in radar range.
In performing experiments to investigate the trade-off between range and range resolution for the “notch” and “avoid” cases, the Baylor research team performed measurements on two versions of notched random FM from the University of Kansas, which inherently possess constant amplitude. Because their generation involves spectral shaping optimization, both to ensure good spectral roll-off in the out-of-band region and to initiate spectral notches, the deployment-ready version of each waveform exists in a discretized form that must be appropriately implemented as a continuous waveform in hardware. For example, [24] discusses the process required to realize spectrally notched waveforms on the modest fidelity available on an SDR platform.
For high-fidelity implementations such as can be achieved with an arbitrary waveform generator (AWG) it is necessary to up-sample the waveform to the DAC rate of the AWG. However, if these waveforms are sinc-interpolated when upsampling, which would seem to be the obvious approach, significant amplitude modulation (AM) in the time-domain can arise. Consequently, AM to phase modulation (AM-PM) nonlinearities in the power amplifier can cause spectral spreading, thus resulting in significant degradation of notch depth [23].
On the other hand, constant amplitude can be preserved by performing interpolation solely in the phase domain. As such, AM-PM conversion does not become an issue, and impedance tuning can be used to maximize output power rather than being traded to improve linearity and thereby maintain notch depth.
We shall herein show two examples of using real-time impedance tuning with notched waveforms for radar applications. The trade-off between range and range resolution is examined for sinc-interpolated (non-constant modulus) and phase-interpolated (constant-modulus) notched waveforms. The benefit of using phase-interpolated waveforms is confirmed through these experiments to benefit both range and range resolution.
Fig. 1.
Random FM contiguous-band waveform with 15 MHz bandwidth: “avoid low” case
### A. Sinc-Interpolated Notched Waveforms
A simplified spectrum sharing scenario is constructed involving an overall bandwidth of 60 MHz at a center frequency of 3.3 GHz (3.27–3.33 GHz). RFI having 15 MHz bandwidth is assumed to reside within the sub-band between 3.285 and 3.3 GHz (i.e. 15 MHz from the lower end of the band and 30 MHz from the upper end). Consequently, the cognitive radar controller has three options to operate without interference: “avoid low”, “avoid high”, or “notch”. A comparison of these three options based on best performance obtainable through impedance tuning is examined.
Figure 1 shows the “avoid left” possibility, where a contiguous-band random FM waveform is synthesized to be lower than the 15 MHz RFI (indicated by the center red line). Likewise Fig. 2 shows the “avoid high” possibility where a contiguous-band random FM waveform is synthesized higher than the RFI. This case achieves a wider bandwidth than Fig. 1 because there is more available spectrum as specified by the mask. Finally, Fig. 3 shows a notched random FM waveform that has been sinc-interpolated, thus realizing a notch depth of about 30 dB. Clearly, a notched waveform provides more total bandwidth than the avoidance-based waveforms, thereby providing better range resolution, because it can make use of the available spectrum on both sides of the RFI.
Fig. 2.
Random FM contiguous-band waveform with 30 MHz bandwidth: “avoid high” case
For each of these waveforms and their corresponding spectral mask, a full load-pull measurement was performed using the Purdue University Generation 2 EVA cavity tuner over the combinations of the two cavity position numbers (n1,n2$n_{1}, n_{2}$) [25]. Figures 4, 5, and 6 show the load-pull measurement results for the “avoid low”, “avoid high”, and “notch” cases, respectively. The output power contours are shown, along with a shaded region representing the range of (n1,n2$n_{1}, n_{2}$) combinations for which the spectral mask is violated. Table I delineates the maximum constrained output power and detectable range for each waveform, as well as the calculated approximate range resolution based on the bandwidth of the waveform.
Fig. 3.
Random FM waveform over 60 MHz band containing a 15 MHz notch
Table I: Constrained optimum values for avoid and notch cases at constrained optimum load impedance
Fig. 4.
Output power load-pull measurement results in tuner cavity position number combinations (n1,n2$n_{1}, n_{2}$) for the “avoid low” waveform of fig. 1. The region causing violation of the spectral mask is shaded.
Figure 6 shows that the sinc-interpolated implementation of the notched, random FM waveform causes very little of the (n1,n2$n_{1}, n_{2}$) plane to be available for impedance matching. As such, the constrained optimum Pout$P_{\text{out}}$ is much lower than the global optimum. While the contours look similar in all three cases, the two “avoid” cases in Figs. 4 and 5 show a greater spectrally acceptable region of the (n1,n2$n_{1}, n_{2}$) plane, which results in higher constrained optimum Pout$P_{\text{out}}$. Of course, sinc-interpolation is not the appropriate way to implement a notched waveform on a AWG because, as noted earlier, doing so introduces AM that invalidates the transmitter-ready FM nature.
Fig. 5.
Output power load-pull measurement results in tuner cavity position number combinations (n1,n2$n_{1}, n_{2}$) for the “avoid high” waveform of fig. 2, with the constrained optimum shown with ‘x’. The region causing violation of the spectral mask is shaded.
Fig. 6.
Output power load-pull measurement results in tuner cavity position number combinations (n1,n2$n_{1}, n_{2}$) for the notched, sinc-interpolated random FM waveform of fig. 3, with the constrained optimum shown with ‘x’. The region causing violation of the spectral mask is shaded.
### B. Phase-Interpolated Notched Waveforms
In contrast to the sinc-interpolated implementation considered above, now consider a phase-interpolated implementation that preserves constant amplitude (per [19]). Consequently, the possibility of AM-PM conversion from amplifier nonlinearities is eliminated. Figure 7(a) shows the normalized spectrum for a phase-interpolated random FM waveform, with and without an amplifier terminated in an impedance resulting in significant nonlinearities. For comparison, Fig. 7(b) shows the sinc-interpolated waveform for the same conditions.
The former case, where the contant amplitude is preserved, realizes negligible difference with or without the amplifier in Fig. 7(a). This result is expected because, by maintaining the FM structure, the waveform is well-suited to a high power amp. Alternatively, the sinc-interpolated case in Fig. 7(b) shows roughly 20 dB of degradation in notch depth due to the distortion that is ultimately caused by AM imposed on the signal that translates into AM-PM nonlinearity in the amplifier.
Simply put, the even seemingly innocuous details of the implementation become quite important when high power and high fidelity are both required.
Fig. 7.
(a) Phase-interpolated random FM waveform with and without power amplifier and (b) Sinc-interpolated random FM waveform with and without power amplifier. Both waveforms were measured at the same tuner (n1,n2$n_{1}, n_{2}$) setting (same load impedance).
Figures 8 and 9 compare use of an “avoid high” LFM chirp and a notched, random FM waveform (phase-interpolated), respectively, to determine the best range and range resolution that can be obtained given a set of spectral constraints that dictate the out-of-band roll-off and avoidance of a 1 MHz RFI source (with acceptable transmit power of −57 dBm). Here the former case has a 6 MHz bandwidth to (mostly) achieve the desired spectral constraints, while the latter employs all of the available 20 MHz, aside from the 1 MHz notch. Further, the LFM does not meet the RFI avoidance criterion, while the notched waveform achieved the required notch depth with room to spare.
Fig. 8.
“Avoid right” chirp for a 1 MHz notch and −57 dBm depth enforcement
Fig. 9.
Random FM waveform with a 1 MHz notch and −57 dBm depth enforcement
Figures 10 and 11 show the output power load-pull contours for the waveforms in Figs. 8 and 9, respectively. The power of the “avoid” chirp must be reduced to meet the depth enforcement aspect of the mask for the 1 MHz RFI. The loadpull result for this waveform (Fig. 10) shows a maximum output power of approximately 4 dBm. However, Fig. 11 shows a maximum output power of approximately 18 dBm for the notched waveform (phase-interpolated), with the entire (n1,n2$n_{1}, n_{2}$) plane meeting spectral requirements.
Table II depicts a comparison of the search results between the “notch” and “avoid” cases for the scenario above. A range of 16.91 km is available with the notched, random FM waveform, while only 7.91 km of range is available with the “avoid” chirp waveform at the optimum output power load impedance. Additionally, the notched waveform provides finer range resolution due to the use of all available bandwidth.
Fig. 10.
Output power load-pull measurement results tuner cavity position number combinations (n1,n2$n_{1}, n_{2}$) for the “avoid left” waveform of fig. 8 after a power back-off is performed, allowing the waveform the possibility of meeting notch-depth spectral mask criteria. The constrained optimum is shown with ‘x’, and the region causing violation of the spectral mask is shaded.
Fig. 11.
Output power load-pull measurement results tuner cavity position number combinations (n1,n2$n_{1}, n_{2}$) for the notched, constant-modulus PRO-FM waveform of fig. 9. The constrained optimum is shown with ‘x’, and the entire viewable region is spectral-mask compliant.
Table II: Constrained optimum values for avoid and notch cases at constrained optimum load impedance
SECTION III.
## Conclusions
An investigation has been presented on the impact of impedance tuning upon the decision of whether to use a notched waveform or contiguous-band waveform when a cognitive radar is contending with in-band RFI. The implementation of (discretely) optimized waveforms on an AWG also plays an important role, with standard sinc-interpolation leading to rather significant degradation due to AM-PM amplifier nonlinearities that necessitate power back-off to compensate. In contrast, phase-interpolation preserves the FM structure of the waveform, thereby avoiding these AM-PM effects altogether. Consequently, both range and range resolution can be optimized through impedance tuning without fear of inducing undesired spreading into the notch. These results are critical in integrating amplifier limitations into cognitive-radar decision making where notching or avoidance of RFI is required.
### ACKNOWLEDGMENT
This work has been funded by the Army Research Laboratory (Grant No. W911NF-16-2-0054 and W911NF-15-2-0063). The views and opinions expressed do not necessarily represent the opinions of the U.S. Government. The authors are grateful to John Clark of the Army Research Laboratory for assistance in development of this paper.
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# References
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12. J.R. Guerci and S.U. Pillai, "Adaptive transmission radar: the next ‘wave’?", IEEE National Aerospace & Electronics Conf., Oct. 2000.
13. I.W. Selesnick and S.U. Pillai, "Chirp-like transmit waveforms with multiple frequency-notches", IEEE Radar Conf., May 2011.
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15. A.W. Doerry, J.M. Andrews and S.M. Buskirk, "Digital synthesis of linear-FM chirp waveforms: comments on performance and enhancements", SPIE Defense & Security vol. 9077 Radar Sensor Technology XVIII, May 2014.
16. S.D. Blunt, J.K. Jakabosky, C.A. Mohr, P.M. McCormick, J.W. Owen et al., "Principles & applications of random FM radar waveform design", IEEE Aerospace & Electronic Systems Magazine.
17. J. Jakabosky, B. Ravenscroft, S.D. Blunt and A. Martone, "Gapped spectrum shaping for tandem-hopped radar/communications & cognitive sensing", IEEE Radar Conf., May 2016.
18. C.A. Mohr, P.M. McCormick, S.D. Blunt and C. Mott, "Spectrally-efficient FM noise radar waveforms optimized in the logarithmic domain", IEEE Radar Conf., Apr. 2018.
19. B. Ravenscroft, J.W. Owen, J. Jakabosky, S.D. Blunt, A.F. Martone and K.D. Sherbondy, "Experimental demonstration and analysis of cognitive spectrum sensing & notching", IET Radar Sonar & Navigation, vol. 12, no. 12, pp. 1466-1475, Dec. 2018.
20. A. Valette, M. Ariaudo, S. Traverso, I. Fijalow and L. Zerioul, "Robustness of filter bank multicarrier signals to power amplifier nonlinearities", 46th European Microwave Conf., Oct. 2016.
21. A. Semnani, M. Abu Khater, D. Peroulis, C. Baylis, L. Hays, C. Kappelmann, et al., "An evanescent-mode cavity-based high-power impedance tuner for adaptive radar applications", USNC-URSI National Radio Science Meeting, Jan. 2018.
22. A. Dockendorf, A. Egbert, E. Langley, C. Calabrese, J. Alcala-Medel, S. Rezayat, et al., "Fast optimization algorithm for evanescent-mode cavity tuner optimization and timing reduction in software-defined radar implementation", IEEE Trans. Aerospace & Electronic Systems.
23. A. Dockendorf, A. Goad, C. Calabrese, B. Adkins, A. Egbert, J. Owen, et al., "The impact of nonlinear power amplifier load impedance on notched waveforms for cognitive radar spectrum sharing", IEEE Radio & Wireless Symp., Jan. 2020.
24. C.A. Mohr, J.W. Owen, S.D. Blunt and C.T. Allen, "Zero-order reconstruction optimization of waveforms (ZOROW) for modest DAC rates", IEEE Intl. Radar Conf., Apr. 2020.
25. A. Semnani, G.S. Shaffer, M.D. Sinanis and D. Peroulis, "High-power impedance tuner utilising substrate-integrated evanescent-mode cavity technology and external linear actuators", IET Microwaves Antennas & Propagation, vol. 13, no. 12, pp. 2067-2072, Oct. 2019.
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2020-09-27 19:06:57
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http://www.newton.ac.uk/event/mqiw05/timetable
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09:00 to 09:45 Pranab Sen (Tata Institute of Fundamental Research)Unions, intersections and a one shot quantum joint typicality lemma A fundamental tool to prove inner bounds in classical network information theory is the so-called conditional joint typicality lemma'. In addition to the lemma, one often uses unions and intersections of typical sets in the inner bound arguments without so much as giving them a second thought. These arguments fail spectacularly in the quantum setting. This bottleneck shows up in the fact that so-called simultaneous decoders', as opposed to `successive cancellation decoders', are known for very few channels in quantum network information theory. In this talk we shall see how to overcome the bottleneck by proving for the first time a one-shot quantum joint typicality lemma with robust union and intersection properties. To do so we develop two novel tools in quantum information theory, which we call tilting and smoothing, which should be of independent interest. Our joint typicality lemma allows us to construct simultaneous quantum decoders for many multiterminal quantum channels and gives a powerful tool to extend many results in classical network information theory to the one-shot quantum setting. We shall see a glimpse of this in the talk by constructing a one shot simultaneous decoder for the quantum multiple access channel with an arbitrary number of senders. Our one shot rates reduce to the known optimal rates when restricted to the asymptotic iid setting, which were previously obtained by successive cancellation and time sharing. INI 1 09:45 to 10:30 Oliver Johnson (University of Bristol)Some entropy properties of discrete random variables It is well-known that Gaussian random variables have many attractive properties: they are maximum entropy, they are stable under addition and scaling, they give equality in the Entropy Power Inequality (and hence give sharp log-Sobolev inequalities) and have good entropy concavity properties. I will discuss the extent to which results of this kind can be formulated for discrete random variables, and how they relate to ideas of discrete log-concavity. INI 1 10:30 to 11:00 Morning Coffee 11:00 to 11:45 Mario Berta (Imperial College London)Partially smoothed information measures Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the sub-systems are often left unchanged and this is not reflected by the standard smoothing of information measures over a ball of close states. We propose to smooth instead only over a ball of close states which also have some of the reduced states on the relevant sub-systems fixed. This partial smoothing of information measures naturally allows to give more refined characterizations of various information-theoretic problems in the one-shot setting. In particular, we immediately get asymptotic second-order characterizations for tasks such as privacy amplification against classical side information or classical state splitting. For quantum problems like state merging the general resource trade-off is tightly characterized by partially smoothed information measures as well. However, for quantum systems we can so far only give the asymptotic first-order expansion of these quantities. INI 1 11:45 to 12:30 Felix Leditzky (University of Colorado)Dephrasure channel and superadditivity of coherent information The quantum capacity of a quantum channel captures its capability for noiseless quantum communication. It lies at the heart of quantum information theory. Unfortunately, our poor understanding of nonadditivity of coherent information makes it hard to understand the quantum capacity of all but very special channels. In this paper, we consider the dephrasure channel, which is the concatenation of a dephasing channel and an erasure channel. This very simple channel displays remarkably rich and exotic properties: we find nonadditivity of coherent information at the two-letter level, a substantial gap between the threshold for zero quantum capacity and zero single-letter coherent information, a big gap between single-letter coherent and private informations. Its clean form simplifies the evaluation of coherent information substantially and, as such, we hope that the dephrasure channel will provide a much-needed laboratory for the testing of new ideas about nonadditivity. INI 1 12:30 to 14:00 Buffet Lunch at CMS 13:55 to 17:30 Afternoon Session: In memory of Dénes Petz (1953-2018) INI 1 14:00 to 14:45 Milan Mosonyi (Budapest University of Technology and Economics)Dénes Petz' legacy in quantum information theory In this talk we give an overview of a subjective selection of Dénes Petz's many results on quantum entropies and their impact on quantum information theory, with a special emphasis on recent results inspired by them. INI 1 14:45 to 15:30 Fumio Hiai (Tohoku University)Quantum f-divergences in von Neumann algebras This talk is a comprehensive survey on recent developments of quantum divergences in general von Neumann algebras, including standard f-divergences, maximal f-divergences, and R\'enyi type divergences, whose mathematical backgrounds are Haagerup's L^p-spaces and Araki's relative modular operator. Standard f-divergences were formerly studied by Petz in a bit more general form with name quasi-entropy, whose most familiar one is the relative entropy initiated by Umegaki and extended to general von Neumann algebras by Araki. We extend Kosaki's variational expression of the relative entropy to an arbitrary standard f-divergence, from which most important properties of standard f-divergences follow immediately. We also go into standard R\'enyi divergences (as a variation of standard f-divergences) in some detail, and touch briefly sandwiched R\'enyi divergences in von Neumann algebras, which have recently been developed by Jen\v cov\'a and Berta-Scholz-Tomamichel. Finally, we treat maximal f-divergences and discuss their definition, integral expression, and comparison with standard f-divergences. This talk is dedicated to the memory of D\'enes Petz. INI 1 15:30 to 16:00 Afternoon Tea 16:00 to 16:45 Anna Jenčová (Slovak Academy of Sciences)Renyi relative entropies and noncommutative L_p-spaces The standard quantum Renyi relative entropies belong to the class of Petz quantum f-divergences and have a number of applications in quantum information theory, including and operational interpretation as error exponents in quantum hypothesis testing. In the last couple of years, the sandwiched version of Renyi relative entropies gained attention for their applications in various strong converse results. While the Petz f-divergences are defined for arbitrary von Neumann algebras, the sandwiched version was introduced for density matrices. In this contribution, it is shown that these quantities can be extended to infinite dimensions. To this end, we use the interpolating family of non-commutative L_p-spaces with respect to a state, defined by Kosaki. This definition provides us with tools for proving a number of properties of the sandwiched Renyi entropies, in particular the data processing inequality with respect to normal unital (completely) positive maps. It is also shown that this definition coincides with the previously introduced Araki-Masuda divergences by Berta et. al.The notion of sufficient (or reversible) quantum channels was introduced and studied by Petz. One of the fundamental results in this context is the fact that equality in the data processing inequality for the quantum relative entropy is equivalent to sufficiency of the channel. We extend this result for sandwiched Renyi relative entropies. See arXiv:1609.08462 and arXiv:1707.00047 for more details. INI 1 16:45 to 17:30 Beth Ruskai (University of Massachusetts Lowell)Using local additivity to find examples of superadditivity of quantum channels The local additivity of minimal output entropy can be extended to local additivity of maximal relative entropy with respect to a fixed reference state. This can be exploited to test channels for superadditivity of Holevo capacity with numerical effort comparable to searching for the minimal output entropy. Local maxima which do not arise from product inputs play a key role. Moreover, evidence of superadditivity can be found even if the additivity violation itself is too small to be seen numerically. A max-min expression for the capacity, dues to Petz, et al, plays a key role. INI 1 19:00 to 22:00 Formal Dinner at Pembroke College (Old Library)
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2019-08-19 05:32:12
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http://mathhelpforum.com/differential-equations/76561-first-order-differential-equation-problem.html
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# Math Help - First order differential equation problem
1. ## First order differential equation problem
I should really know the answer to this but am having trouble seeing it
I have a first order differential
$x\frac{dy}{dx} +\frac{y}{1-x} = (x-1)^2 sinx$
I get the intergrating factor $\frac{x}{1-x}$
but when multiplied through to get:
$\frac{x}{1-x}\frac{dy}{dx} + \frac{1}{(1-x)^2} y = (1-x) sinx$
i do not see the what the left side intergral should be any help would be greatly appreciated
2. $\frac{x}{1-x}\cdot y'+\frac{y}{(1-x)^{2}}=\left( \frac{x}{1-x}\cdot y \right)'.$
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2014-10-20 12:25:14
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https://answers.ros.org/question/350373/ros-quaternion-component-w-not-behaving-as-it-should/
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# Ros quaternion component w not behaving as it should.
The quaternions in ros are supposed to be (x,y,z,w), where w = cos(theta/2) where theta is the angle of the rotation.
I did the following, I used tf_listener to get the position of my robot t_base,r_base = tf_listener.lookupTransform('/map','/base_link',rospy.Time(0))
and then I printed the last component of r_base as I did a 360° continuous turn with the robot. What I get is values between -0.3 and 0.3 with a jump in sign between -0.3 and 0.3. (So I start from -0.3 it goes up to 1 then down to 0.3 where it jumps to -0.3) as if the robot were missing around 30°from the 360°.
What is happening here?
edit retag close merge delete
I prefer to think in euler angles rather than quaternions .. use (r,p,y) = tf.transformations.euler_from_quaternion(quaternion=r_base) to save yourself a headahe
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2021-12-01 07:44:45
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https://im.kendallhunt.com/HS/teachers/3/3/14/preparation.html
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# Lesson 14
More Arithmetic with Complex Numbers
### Lesson Narrative
This lesson is optional because it is an opportunity for extra practice that not all classes may need.
In this lesson, students practice using complex number arithmetic to write expressions in the form $$a+bi$$, where $$a$$ and $$b$$ are real numbers. Students look for and make use of repeated reasoning to analyze the expression $$i^n$$, where $$n$$ is a whole number (MP8). They also construct viable arguments and critique the reasoning of others when they resolve discrepancies during a row game (MP3).
### Learning Goals
Teacher Facing
• Add, subtract, and multiply complex numbers, and represent the solutions in the form $a+bi$.
• Explain reasoning and critique the reasoning of others when writing numbers in the form $a+bi$.
• Generalize patterns in repeated reasoning to show what happens when $i$ is raised to different powers.
### Student Facing
• Let’s practice adding, subtracting, and multiplying complex numbers.
### Student Facing
• I can do arithmetic with complex numbers.
Addressing
### Print Formatted Materials
Teachers with a valid work email address can click here to register or sign in for free access to Cool Down, Teacher Guide, and PowerPoint materials.
Student Task Statements pdf docx Cumulative Practice Problem Set pdf docx Cool Down Log In Teacher Guide Log In Teacher Presentation Materials pdf docx
### Additional Resources
Google Slides Log In PowerPoint Slides Log In
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2023-03-25 00:34:36
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https://www.zbmath.org/?q=an%3A0788.05040
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# zbMATH — the first resource for mathematics
Classes of chromatically unique graphs. (English) Zbl 0788.05040
The authors show that for every $$n \geq 3$$, the graph $$K_{n,n}-rK_ 2$$ with $$0 \leq r \leq n$$, is chromatically unique.
Reviewer: J.Fiamcik
##### MSC:
05C15 Coloring of graphs and hypergraphs
##### Keywords:
chromatically unique graphs
Full Text:
##### References:
[1] Chao, C.-Y.; Whitehead, E.G., Chromatically unique graphs, Discrete math., 27, 171-177, (1979) · Zbl 0411.05035 [2] Chia, G.L., The chromaticity of wheels with a missing spoke, Discrete math., 82, 209-212, (1990) · Zbl 0712.05025 [3] Farrell, E.J., On chromatic coefficients, Discrete math., 29, 257-264, (1980) · Zbl 0443.05041 [4] Harary, F., Graph theory, (1969), Addison-Wesley Reading, MA · Zbl 0797.05064 [5] Koh, K.M.; Goh, B.H., Two classes of chromatically unique graphs, Discrete math., 82, 13-24, (1990) · Zbl 0697.05027 [6] Salzberg, P.M.; López, M.A.; Giudici, R.E., On the chromatic uniqueness of bipartite graphs, Discrete math., 58, 285-294, (1986) · Zbl 0594.05034 [7] Whitehead, E.G.; Zhao, L.-C., Cutpoints and the chromatic polynomial, J. graph theory, 8, 371-377, (1984) · Zbl 0551.05041
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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2021-04-15 16:30:37
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https://www.physicsforums.com/threads/stat-phys-free-energy-from-eq-of-state.637526/
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# Homework Help: Stat phys - free energy from eq of state
1. Sep 20, 2012
### lol_nl
1. The problem statement, all variables and given/known data
Consider a mixture of hard spheres of diameter σ. The potential energy
for a hard sphere system is given by
$\beta U(r) = 0 (r > \sigma)$
$∞ (r ≤ \sigma)$
The packing fraction (η) of the system is the amount of space occupied
by the particles.
(b) The equation of state for the hard sphere fluid is approximately
$\frac{P_{liq}V}{Nk_{B}T}= \frac{1+ \eta + \eta^2 - \eta^3}{ (1 - \eta)^3 }$
What is the corresponding free energy?
2. Relevant equations
Hint: At very low packing
fraction the hard sphere liquid acts like an ideal gas.
3. The attempt at a solution
Frankly, I have no idea how to calculate the free energy from an equation of state like the one given above. Even in the case of the ideal gas ($\eta=0$, I would suppose the free energy would have to calculated in a different manner. The way I learned the calculation for the ideal gas was quite complicated, beginning with a calculation of the partition function of a single molecule by looking at quantum densities. Once given the partition function, it was not difficult to show that the Helmholtz free energy for an ideal gas is given by $F = -k_{B}T Log(Z) \approx N k_{B}T (Log(\frac{N}{V n_Q}) - 1)$ where $n_{Q}$ is a (scaling?) constant.
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2018-09-23 11:52:42
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https://core.ac.uk/display/4443107
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## Transition region spectroscopy of dialkali halides: Sodium(2)chloride and sodium(2) + atomic fluorine going to sodium fluoride + sodium
### Abstract
Molecular beam chemiluminescence from Na$\sb2$ + F $\to$ NaF + Na$\sp\*$ was dispersed and measured with a fast spectrograph. Attention was given to emission wavelengths at and around 388.5 and 342.8 nm, which correspond to the electric dipole forbidden atomic transitions Na 4s $\to$ 3s and 3d $\to$ 3s, respectively. It was hoped that the nascent products NaF and Na$\sp\*$ would interact such that these normally dis-allowed transitions could be observed, thereby constituting a direct glimpse of the three atom system late in the reaction event. A small emission peak was observed at the 3d $\to$ 3s transition wavelength, but its weak intensity could be explained by electric quadrupole radiation of the free atom rather than a reaction-induced breaking of dipole selection rules. No structured emission was observed at the 4s $\to$ 3s wavelength, although interference from Na$\sb2\sp\*$ may be obscuring an otherwise observable peak. In a second experiment, two lines of an argon ion laser are crossed with a single Na/NaCl beam in an effort to observe resolved laser-induced fluorescence of the stable molecule Na$\sb2$Cl. The copious emission from Na$\sb2\sp\*$ precluded any definitive identification of fluorescence from the target molecule. Finally, a detailed description is given of the f/2 spectrograph that was developed in this laboratory. The instrument observes a 100 nm wavelength region simultaneously, images atomic lines to a full-width-half-maximum (fwhm) of 2 nm, has a photocathode quantum efficiency of 3.1% at 800 nm, and exhibits only 36 counts per second dark current
Topics: Physical chemistry
Year: 1990
OAI identifier: oai:scholarship.rice.edu:1911/16392
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2021-06-23 22:18:25
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https://math.stackexchange.com/questions/2769859/linear-independence-of-a-set-implies-linear-independence-of-the-coordinate-vecto/2769884
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# Linear independence of a set implies linear independence of the coordinate vectors
Here's the question:
Let $S$ be a basis for an $n$-dimensional vector space $V$. Show that $\{ v_1, v_2, \dots , v_r \} \subseteq V$ is linearly independent if and only if the coordinate vectors $\{ (v_1)_S, (v_2)_S, \dots , (v_r)_S \} \subseteq \mathbb{R}^n$ is linearly independent.
I saw the answers to a similar (well, essentially the same) question here: Proving linear independence of a basis from coordinate vectors
However, at this point in the text I am using, the facts listed in the answers have not been introduced. And technically, we don't know that we can obtain the set $\{ (v_1)_S, (v_2)_S, \dots , (v_r)_S \}$ via a change of basis.
I'd like to prove this from more elementary means, using the definition of coordinate vectors. This is just the vector of coefficients when each vector in the original set is expressed in terms of the basis vectors.
Approach: I want to prove that
$k_1v_1 + \cdots + k_r v_r = 0 \Longrightarrow k_i=0~ \forall i$ if and only if $l_1(v_1)_S + \cdots + l_r(v_r)_S = 0 \Longrightarrow l_i = 0 ~ \forall i$.
However, if I express the left side as $S$-vectors, the vectors on the right side would be scalars on the left side. How do I translate without invoking a change of basis?
Thanks for your insights, I only need a nudge here.
## 1 Answer
Hint: proceed by contradiction and use the fact that the coordinate mapping is linear.
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2020-06-04 06:37:24
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https://socratic.org/questions/an-object-with-a-mass-of-6-kg-is-on-a-plane-with-an-incline-of-pi-4-if-it-takes--4
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# An object with a mass of 6 kg is on a plane with an incline of - pi/4 . If it takes 24 N to start pushing the object down the plane and 9 N to keep pushing it, what are the coefficients of static and kinetic friction?
##### 1 Answer
Jun 27, 2017
u(static) = 0.58, u(kinetic) = 0.22
#### Explanation:
To start motion, Force down = Opposing Frictional Force
Opposing Frictional Force = u(static) Normal Force.
Weight down = mg = 6 (9.8 m/s^2) = 58.8 N
Normal Force is found with trigonometry = 58.8 cos pi/4 =
58.8 [sqrt 2] / 2 = 41.6 N
So .... 24 = u(static) 41.6 => u(static) = 0.58
Similarly 9 = u(kinetic) 41.6 => u(kinetic) = 0.22
:-))
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2020-05-28 00:35:21
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https://mathoverflow.net/questions/257830/correlation-for-a-discrete-time-markov-chain
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# Question
Let $(X_n)_{n\in \mathbb{N}}$ be an irreducible Discrete Time Markov Chain (DTMC) with finite state space $S$, transition matrix $P$ and steady state $\pi$. Assume that we are ''far enough'' in time that we may assume that for all $n$ $X_n \overset{d}{=} \pi$ then we define: $$\ell_m := \mbox{Corr}(X_{n}, X_{n+m}),$$ since we are working with a Markov chain one would think that for all $m$, $\ell_m$ can be expressed in function of $\ell_1$. My question is : Is there a good way to see this and what this relation is? i.e. find for each $m$ the function $f_m$ s.t. $\ell_m = f_m(\ell_1)$. As show below, for the special case $|S| = 2$ the function $f_m$ is just given by $f_m(x) := x^m$.
# Special Case
In a very special case : a state space with only 2 states we have with $\pi = [\alpha\quad 1-\alpha]$ that for some constant $a \in \left[\max\left(2-\frac{1}{\alpha},0\right),1\right]$: $$P = \begin{pmatrix} a & 1-a\\ \frac{\alpha-\alpha a}{1-\alpha} & \frac{\alpha a - 2\alpha + 1}{1-\alpha}. \end{pmatrix}$$ This allows one to see (by trivial calculations) that $\ell_1 = \mbox{Det}(P)$. But then we see, as $\ell_m$ is just $\ell_1$ for the adapted process $Y_n := X_{n\cdot m}$: $$\ell_m = \mbox{Det}(P^m) = \mbox{Det}(P)^m = \ell_1^m$$
• I know how correlation of real-valued random variables is defined, but how do you define the correlation of random variables taking values in an abstract set $S$? – Nate Eldredge Dec 22 '16 at 19:17
• You may assume $S \subseteq \mathbb{R}$ – HolyMonk Dec 22 '16 at 19:18
• I guess I'm also a little confused by the question. It certainly can't be true that there is a single family of functions $f_m$ that does the job for every possible Markov chain, or even for every possible Markov chain on a given fixed state space $S$. And if you allow the family $f_m$ to depend on the chain, then it is trivially true since you just set $f_m(\ell_1)$ to be whatever $\ell_m$ is for that chain. – Nate Eldredge Dec 22 '16 at 19:25
• Yes you make a very valid point. – HolyMonk Dec 22 '16 at 19:28
• I will reconsider my question. – HolyMonk Dec 22 '16 at 19:28
Here is a simple counterexample that is a bit too long for a comment.
Consider two discrete-time Markov chains on $S=\{1,2,3\}$ with the following two transition matrices: $$P_1 = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{bmatrix} \;, \quad P_2 = \begin{bmatrix} 0 & 1/2 & 1/2 \\ 1/2 & 0 & 1/2 \\ 1/2 & 1/2 & 0 \end{bmatrix}$$ Both chains are irreducible and leave the uniform distribution invariant. The corresponding discrete-time Markov chains have the same lag-$1$ equilibrium autocorrelation, i.e., $\ell_1=-1/2$. However, for $k>1$ their lag-$k$ autocorrelations are quite different since the first chain is periodic with period $3$ while the second chain's lag-$k$ autocorrelation decays to zero with $k$.
This is not quite a counterexample, since the first chain does not have a steady-state or limiting distribution. To correct this deficiency, we break its periodicity by slightly perturbing its entries using a small parameter $\epsilon>0$: $$\tilde P_1 = \begin{bmatrix} 0 & 1-\epsilon & \epsilon \\ \epsilon & 0 & 1-\epsilon \\ 1-\epsilon & \epsilon & 0 \end{bmatrix}$$ The lag-$k$ correlation functions for the chains with transition matrices $\tilde P_1$ (blue line) and $P_2$ (black line) are plotted below with $\epsilon=1/25$ (chosen for visualization purposes only). The inset shows the first few lag correlations. Note that $\ell_1$ is the same for the two chains.
As the OP (HolyMonk) points out in the comments to this answer: for $\tilde P_1$ (given above) and for any $\epsilon>0$, we have $\ell_1 = -1/2$ and $\ell_2 = -1/2−3(−1+ϵ)ϵ$.
• I have done the calculations and in fact we just have $\ell_1 = \frac{-1}{2}$ regardless of the value of $\varepsilon$ whilst for example $\ell_2 = -3 \varepsilon^2 + 3 \cdot \varepsilon - \frac{1}{2}$. – HolyMonk Dec 23 '16 at 9:10
• @HolyMonk That is not quite what I get. For $\tilde P_1$ I get $\pi \propto (1-\epsilon, (1-\epsilon)^{-1}-\epsilon,1)$ and $\ell_1 = (3-4 \epsilon + 3 \epsilon^3 -2\epsilon^4) (-6 + \epsilon (11+(-7+\epsilon) \epsilon))^{-1}$. So for $\epsilon=1/25$ we have $\ell_1 \approx -0.5098$. – Nawaf Bou-Rabee Dec 23 '16 at 11:03
• What do you mean by $\pi$? I usually use this notation for the stationary distribution/steady state but I would think this is just $[\frac{1}{3},\frac{1}{3},\frac{1}{3}]$ here? – HolyMonk Dec 23 '16 at 11:10
• @HolyMonk That's right: I am using your notation for the steady state distribution. The steady distribution for $\tilde P_1$ is no longer uniform when $\epsilon>0$ since $[\frac{1}{3}, \frac{1}{3}, \frac{1}{3}] \tilde P_1 = [ \frac{1-\epsilon}{3}, \frac{1+\epsilon}{3}, \frac{1}{3} ]$. – Nawaf Bou-Rabee Dec 23 '16 at 12:39
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2019-10-19 13:21:46
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https://www.lisenkov.com/publication/2019-mechanical-resonance-enhanced-thin-film-magnetoelectric-heterostructures-for-magnetometers-mechanical-antennas-tunable-rf-inductors-and-filters/
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# Mechanical-Resonance-Enhanced Thin-Film Magnetoelectric Heterostructures for Magnetometers, Mechanical Antennas, Tunable RF Inductors, and Filters
### Abstract
The strong strain-mediated magnetoelectric (ME) coupling found in thin-film ME heterostructures has attracted an ever-increasing interest and enables realization of a great number of integrated multiferroic devices, such as magnetometers, mechanical antennas, RF tunable inductors and filters. This paper first reviews the thin-film characterization techniques for both piezoelectric and magnetostrictive thin films, which are crucial in determining the strength of the ME coupling. After that, the most recent progress on various integrated multiferroic devices based on thin-film ME heterostructures are presented. In particular, rapid development of thin-film ME magnetometers has been seen over the past few years. These ultra-sensitive magnetometers exhibit extremely low limit of detection ($\mathrm{sub-pT/Hz}^{1/2}$) for low-frequency AC magnetic fields, making them potential candidates for applications of medical diagnostics. Other devices reviewed in this paper include acoustically actuated nanomechanical ME antennas with miniaturized size by 1–2 orders compared to the conventional antenna; integrated RF tunable inductors with a wide operation frequency range; integrated RF tunable bandpass filter with dual H- and E-field tunability. All these integrated multiferroic devices are compact, lightweight, power-efficient, and potentially integrable with current complementary metal oxide semiconductor (CMOS) technology, showing great promise for applications in future biomedical, wireless communication, and reconfigurable electronic systems.
Type
Publication
Materials vol. 12 issue: 14 page: 2259
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2020-09-27 17:30:05
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https://indico.cern.ch/event/773049/timetable/?view=indico_weeks_view
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24th International Conference on Computing in High Energy & Nuclear Physics
from Monday, 4 November 2019 (08:00) to Friday, 8 November 2019 (13:00)
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2020-01-19 05:30:50
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http://blog.jpolak.org/
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# On a characterisation of Krull dimension zero rings
Posted by Jason Polak on 21. September 2017 · Write a comment · Categories: modules · Tags:
Here is one characterisation of commutative rings of Krull dimension zero:
Theorem. A commutative ring $R$ has Krull dimension zero if and only if every element of the Jacobson radical ${\rm Jac}(R)$ of $R$ is nilpotent and the quotient ring $R/{\rm Jac}(R)$ is von Neumann regular.
Recall that a ring $R$ is von Neumann regular if for every $x\in R$ there exists a $y\in R$ such that $xyx = x$. This odd property is equivalent to saying that every $R$-module is flat.
Here are two examples of what happens when we drop various assumptions in the “if” direction of the theorem:
1. The ring $\Z_{(p)}$ of integers localised away from the prime $(p)$ is an example of a ring such that $R/{\rm Jac}(R)$ is von Neumann regular but ${\rm Jac}(R)$ has no nontrivial nilpotent elements. The ring $\Z_{(p)}$ has Krull dimension one.
2. Another type of example is given by $\Z[[t]]/t^n$ where $\Z[[t]]$ denotes the power series ring with integer coefficients. Unlike our first example, the Jacobson radical of this ring is the ideal $(t)$, which is also the nilradical (=set of nilpotent elements), but $R/{\rm Jac}(R) = \Z$, which is not von Neumann regular and has Krull dimension one.
Note that we were forced look for counterexamples to dropped assumptions in the class of infinite rings. That’s because every finite commutative ring has Krull dimension zero.
# Dimension zero rings for three types of dimension
Posted by Jason Polak on 20. September 2017 · Write a comment · Categories: homological-algebra, model-theory
There are all sorts of notions of dimension that can be applied to rings. Whatever notion you use though, the ones with dimension zero are usually fairly simple compared with the rings of higher dimension. Here we’ll look at three types of dimension and state what the rings of zero dimension look like with respect to each type. Of course, several examples are included.
All rings are associative with identity but not necessarily commutative. Some basic homological algebra is necessary to understand all the definitions.
## Global Dimension
The left global dimension of a ring $R$ is the supremum over the projective dimensions of all left $R$-modules. The right global dimension is the same with “left” replaced by “right”. And yes, there are rings where the left and right global dimensions differ.
However, $R$ has left global dimension zero if and only if it has right global dimension zero. So, it makes sense to say that such rings have global dimension zero. Here is their characterisation:
A ring $R$ has global dimension zero if and only if it is semisimple; that is, if and only if it is a finite direct product of full matrix rings over division rings.
Examples of such rings are easy to generate by this characterisation:
1. Fields and finite products of fields
2. $M_2(k)$, the ring of $2\times 2$ matrices over a division ring $k$
3. etc.
# How to choose a PhD program
Posted by Jason Polak on 19. September 2017 · Write a comment · Categories: advice
Choosing where to get your PhD is an important decision. If you continue onto academia, your PhD might be the longest time you spend at any one institution until you get a permanent position. The most obvious choice is apply to the high-ranking schools. However, you should consider far more than that. Here, we’ll look at some of the important factors to consider, with the context of mathematics in mind. However, most of what I say applies to some other fields as well.
## Represented research areas
Unlike choosing an undergraduate program, where the curriculum doesn’t differ much around the world (though it certainly can vary greatly in strength or intensity), a PhD will be on a very specialised topic. So, if you go to a school where analysis and statistics are the main topics represented and you like algebra, you probably won’t like it. This can be worse for those places where you don’t have to choose an advisor until the second year. So I suggest you look at the represented research areas on departmental websites and see what catches your interest. Unfortunately, some math department websites look like they were coded on a Super Nintendo, if that were even possible. So:
Make sure someone is actually doing something you’re interested in at prospective schools!
If you’re at the undergraduate level and not sure of your interests yet, it could be a good idea to consider a masters program first before starting a PhD. I enjoyed doing a masters degree first, even though in the long run it is more expensive.
## Total school atmosphere
If you’re lucky enough to be nearby some schools you’re interested in, you should visit them, meet some professors, and even sit in on some classes and departmental seminars. Just walk around and see what it’s like. Some schools have a much nicer atmosphere than others. You should also get a sense of the surrounding city. This is true especially if you are a very independent worker: having an enjoyable city will in fact make working much easier. Conversely, living in a place you dislike for several years is quite draining.
Sadly, living temporarily in cities you don’t like is very probable in at least one stage of climbing the academic ladder.
More »
# Is it a projective module?
Posted by Jason Polak on 19. September 2017 · Write a comment · Categories: homological-algebra, modules
Consider a field $k$. Define an action of $k[x,y]$ on $k[x]$ by $f*g = f(x,x)g(x)$ for all $f\in k[x,y]$ and $g\in k[x]$. In other words, the action is: multiply $f$ and $g$ and then replace every occurrence of $y$ by $x$.
Is $k[x]$ a projective $k[x,y]$-module? Consider first the map $k[x,y]\to k[x]$ given by $f\mapsto f(x,x)$. It’s easy to check that this map is in fact a $k[x,y]$-module homomorphism. It would be tempting to try and split this map with the inclusion map $k[x]\to k[x,y]$. But this doesn’t work: this inclusion is not a $k[x,y]$-module homomorphism.
In fact, the $k[x,y]$-module homomorphism $k[x,y]\to k[x]$ given by $f\mapsto f(x,x)$ cannot split simply because there are no nonzero $k[x,y]$-module homomorphisms $k[x]\to k[x,y]$. Therefore, $k[x]$ is not projective as a $k[x,y]$-module, using the module structure we gave it.
Here are two more ways to see this:
1. Through the notion of separability: by definition, $k[x]$ being a projective $k[x,y]\cong k[x]\otimes_k k[x]$-module under the structure that we have defined means that $k[x]$ is a separable $k$-algebra. However, all separable $k$-algebras are finite-dimensional as vector spaces over $k$, whereas $k[x]$ is infinite-dimensional.
2. Through Seshradi’s theorem: this theorem says that every finitely-generated projective module over $k[x,y]$ is actually free. Therefore, we just have to show that $k[x]$ is not free because $k[x]$ is certainly finitely-generated as a $k[x,y]$-module. But $(x^2y – xy^2)$ annihilates all elements of $k[x]$, which cannot happen in a free module.
# Strong Nilpotence and the Jacobson Radical
Posted by Jason Polak on 01. September 2017 · Write a comment · Categories: ring-theory · Tags:
In the previous post we saw the following definition for a ring $R$: An element $r\in R$ is called strongly nilpotent if every sequence $r = r_0,r_1,r_2,\dots$ such that $r_{n+1}\in r_nRr_n$ is eventually zero. Why introduce this notion?
Well, did you know that every finite integral domain is a field? If $R$ is an integral domain and $a\in R$ is nonzero, then the multiplication map $R\to R$ given by $x\mapsto ax$ is injective. If $R$ is finite, then it must also be surjective so $a$ is invertible!
Another way of stating this neat fact is that if $R$ is any ring and $P$ is a prime ideal of $R$ such that $R/P$ is finite, then $P$ is also a maximal ideal. A variation of this idea is that every prime ideal in a finite commutative ring is actually maximal. Yet another is that finite commutative rings have Krull dimension zero.
More »
# Nilpotent and Strongly Nilpotent
Posted by Jason Polak on 31. August 2017 · Write a comment · Categories: ring-theory · Tags:
Let $R$ be an associative ring. An element $r\in R$ is called nilpotent if $r^n = 0$ for some $n$. There is a stronger notion: an element $r\in R$ is called strongly nilpotent if every sequence $r = r_0,r_1,r_2,\dots$ such that $r_{n+1}\in r_nRr_n$ is eventually zero.
How are these two related? It is always the case that a strongly nilpotent element is nilpotent, because if $r$ is strongly nilpotent then the sequence $r,r^2,r^4,r^8,\dots$ vanishes. However, the element
$$\begin{pmatrix}0 & 1\\ 0 & 0\end{pmatrix}$$
in any $2\times 2$ matrix ring is nilpotent but not strongly nilpotent. Notice how we had to use a noncommutative ring here—that’s because for commutative rings, a nilpotent element is strongly nilpotent!
# Comparing Methods for Finding the Vertex of a Parabola
Posted by guest on 27. August 2017 · Write a comment · Categories: math
A guest Post by Paul Pierce and Ashley Ross
With the advances in calculator technology, some developmental and college-level math courses are restricting the use of any type of graphing or programmable calculators. This is to help students avoid becoming dependent on their calculators for both simple arithmetic and graphing. So, some teachers are going “old school” and forbidding the use of calculators in the classroom. Therefore, it is imperative that students learn efficient methods for finding important values, as well as graphing functions, without the help of their calculator. One type of function that appears in many courses is the quadratic function, and one of the most critical points on the graph of a quadratic function is the vertex.
## Fundamental Concepts of the Graph of a Quadratic Function
For the function $f(x)=ax^2+bx+c$ with $a\not=0$, the graph is a smooth, continuous curve called a parabola. This parabola opens upward if $a > 0$ or opens downward if $a < 0$. The vertex $(h,k)$ of the graph is the only turning point on the parabola, which makes it a critical point. The $y$-coordinate $k$ of the vertex represents the minimum value of the function if $a>0$, or the maximum value of the function if $a<0$.
The point $(h,k)$ may be found using the formulas $h=\frac{-b}{2a}$ and $k=\frac{bh}{2}+c$, which begin to show the importance of the vertex. We give two examples:
Example 1. For $y=x^2+6x+3$, find the vertex $(h,k)$.
First find $h$ using $h=\frac{-b}{2a}=\frac{-6}{2(1)}=-3$.
Next find $k$ using $k=\frac{bh}{2}+c=\frac{(6)(-3)}{2}+3=-9+3=-6$.
So, the coordinates of the vertex of the parabola are $(-3, -6)$. Observe from the graph that this vertex is the lowest point on the parabola, which means that $k = -6$ is the minimum value of the function.
Example 2.For $y=-2x^2+8x-5$, find the vertex $(h,k)$.
First find h using $h=\frac{-b}{2a}=\frac{-8}{2(-2)}=2$.
Next find k using $k=\frac{bh}{2}+c=\frac{(8)(2)}{2}-5=8-5=3$.
So, the coordinates of the vertex of the parabola are $(2, 3)$. Note that this vertex is the highest point on the graph, which illustrates that $k = 3$ is the maximum value of this function.
# Semisimple and Jacobson Semisimple
Posted by Jason Polak on 27. August 2017 · Write a comment · Categories: math, modules
Let $R$ be an associative ring with identity. The Jacobson radical ${\rm Jac}(R)$ of $R$ is the intersection of all the left maximal ideals of $R$. So, ${\rm Jac}(R)$ is a left ideal of $R$. It turns out that the Jacobson radical of $R$ is also the intersection of all the right maximal ideals of $R$, and so ${\rm Jac}(R)$ is also an ideal!
The idea behind the Jacobson radical is that one might be able to explore the properties of a ring $R$ by first looking at the less complicated ring $R/{\rm Jac}(R)$. Since the ideals of $R$ containing ${\rm Jac}(R)$ correspond to the ideals of $R/{\rm Jac}(R)$, the ring $R/{\rm Jac}(R)$ has zero Jacobson radical. Often the rings $R$ for which ${\rm Jac}(R) = 0$ are called Jacobson semisimple.
This terminology might be a tad bit confusing because typically, a ring $R$ is called semisimple if every left $R$-module is projective, or equivalently, if every left $R$-module is injective. How does the notion of semisimple differ from Jacobson semisimple? The Wedderburn-Artin theorem gives a classic characterisation of semisimple rings: they are exactly the rings that are finite direct products of full matrix rings over division rings. Since a full matrix ring over a division ring has no nontrivial ideals, the product of such rings must have trivial Jacobson radical. Thus:
A semisimple ring is Jacobson semisimple.
The converse is false: there exists a ring that is Jacobson semisimple but not semisimple. For example, let $R$ be an infinite product of fields. Then ${\rm Jac}(R) = 0$. However, $R$ is not semisimple. Why not? If it were, by Wedderburn-Artin it could also be written as a finite product of full matrix rings over division rings, which must be a finite product of fields because $R$ is commutative. But a finite product of fields only has finitely many pairwise orthogonal idempotents, whereas $R$ has infinitely many.
Incidentally, because $R$ is not semisimple, there must exist $R$-modules that are not projective. However, $R$ does have the property that every $R$-module is flat!
# Are we running out of problems?
Posted by Jason Polak on 06. August 2017 · Write a comment · Categories: math, opinion
A senior mathematician who will remain nameless recently said in a talk, “there is nothing left to prove”. In context, he was referring to the possibility that we are running out of math problems. People who heard laughed, and first-year calculus students might disagree. Was it said as a joke?
Because of the infinite nature of mathematics, there will always be new problems. On the other hand, there are only finitely many theorems we’ll ever know; only finitely many that we’ll ever be interested in. Are we close to knowing all the interesting theorems? Is the increasing specialisation of the literature a sign of a future with a thousand subfields each with only one or two devotees?
Truthfully, I don’t think math is running out of problems at all. I think it’s more like good, nonspecialist exposition isn’t really keeping up with the rapid development of mathematics and so we know less and less about what our colleagues are doing. So we should attempt to prevent the future where every person is their own research field. Here are some ways we could do that:
1. Make part of your introduction in your paper understandable to a much wider range of mathematicians. This will encourage more collaboration and cross-disciplinary understanding. For example, once I was actually told by a journal to cut out a couple of pages from a paper because it was well-known to (probably ten) experts, even though that material was literally not written down anywhere else! Journals should actually encourage good exposition and not a wall of definition-theorem-proof.
2. Have the first twenty minutes of your talk understandable by undergraduates. Because frankly, this is the only way mathematicians (especially young ones) in other fields will actually understand the motivation of your work. How are we supposed to ask good questions when we can’t figure out where our research fits in with the research of others?
3. Use new avenues of mathematical exposition like blogs and nontechnical articles. Other fields like physics and biology appear in magazines like Scientific American and have an army of people working to make specialised work understandable to the nonspecialist.
4. Encourage new, simplified proofs or explanations of existing results. And by ‘encourage’, I mean count high-quality, expository papers on the level of original results in determining things like tenure and jobs! There are already journals that publish these types of papers. Chances are, any expository paper will actually help at least as many people as an original result, perhaps more. And there are still hundreds of important papers that are very difficult if not impossible to read (even by many experts), with no superior alternative exposition available.
I think it’s been a long-lived fashion in mathematics to hide the easy stuff in favour of appearing slick ever since one dude tried to hide how he solved the cubic from another dude, and it’s probably something we can give up now.
# Check out this preliminary text on cluster algebras
Posted by Jason Polak on 25. July 2017 · Write a comment · Categories: math
Fomin, Williams, and Zelevinsky (posth.) are preparing a new introductory text on cluster algebras. The first three chapters look elementary enough, and it’s worth a look for those interested in learning this topic.
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2017-09-22 15:14:42
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https://physics.stackexchange.com/questions/280043/what-is-the-average-value-of-time-since-last-collision-in-drude-model
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# What is the average value of time since last collision in Drude model?
I have been following Feynman lectures on Physics, lecture 43 — Diffusion.
There he derives the average value of time till next collision over all molecules. He finds it to be equal to the average time between collisions $$\tau$$. This concept is pretty clear.
Then he goes on to derive the drift velocity of molecules (and in my case of interest, electrons). Here he states that the average time between collisions also to be equal to the average number of collisions per second. My doubt lies here:
I'm not able to mathematically prove how the average value of time since last collision to be equal to the average time between collisions.
I checked up some online resources too, none of them explain this properly.
How can it be proved mathematically?
Edit: Another question cropped up in this same topic. The author derives the probability that the molecule survives t seconds without collision is
$$P(t)=\exp\left(\frac{-t}{\tau}\right)$$
Since all these events are independent shouldn't the integral of this probability function from $$t=o$$ to infinity should be equal to $$1$$? But if we evaluate this integral we will actually get $$\tau$$ as the answer. Isn't this a violation of the axioms of probability?
• What makes you think that the event of a molecule surviving from one moment to the next is independent of all of the other previous events/moments? You can't "un-collide" the molecule; once the molecule fails to survive without collision during a particular moment, it also automatically fails to survive without collision for all future moments, since it has already done so. – probably_someone Jan 22 at 0:14
Here he states that the average value of time since last collisions also to be equal to the average number of collisions per second.
I cannot find such a statement in the reference that you have given.
If the average time between collisions is 0.1 seconds then the average number of collisions per second is $\dfrac{1}{0.1} = 10$
The author derives the probability that the molecule survives t seconds without collision is P(t)=exp(-t/τ).
Your integration should not equal 1.
This equation gives you the probability of something happening.
In this case no collisions occurring after a time $t$.
At $t$ increases the probability of such an event decreases which is what one would expect.
This is equivalent to the probability of a radioactive nucleus with decay constant $\lambda$ not decaying in a time $t$.
$P(t) = \exp(-\lambda t)$
From the probability function one can find the average time before a collision $<t>$.
$<t> = \dfrac{\int ^\infty_0 t \; \exp(t/\tau)\; dt}{\int ^\infty_0 \; \exp(t/\tau)\; dt} = \tau$
which in the nuclear context was the average lifetime of a radioactive nucleus with $<t> = \dfrac 1 \lambda$.
• The statement is found in the last lines of the paragraph before equation 43.13 – Danny Sep 14 '16 at 9:17
• Feynman write *"Now the average time since the last collision must be the same as the average time until the next collision, . . . " – Farcher Sep 14 '16 at 9:30
• Which in turn is equal to $\tau$ . Which is the average number of collisions per second – Danny Sep 14 '16 at 11:28
• Where is it stated that tau is the average number of collisions per seconds which would mean that tau would have the units of $\text{time}^{-1}$ whereas tau actually has the units of $\text{time}$? – Farcher Sep 14 '16 at 11:46
• Damn , how couldn't I have though about that? I'm really sorry.Its the average time between collisions. Btw how do we prove that the average time since last collision also equals tau . Thanks for your patience! – Danny Sep 14 '16 at 12:04
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2020-04-05 21:05:22
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https://winvector.github.io/vtreat/reference/BinomialOutcomeTreatment.html
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Hold settings and results for binomial classification data preparation.
BinomialOutcomeTreatment(
...,
var_list,
outcome_name,
outcome_target = TRUE,
cols_to_copy = NULL,
params = NULL,
imputation_map = NULL
)
## Arguments
... not used, force arguments to be specified by name. Names of columns to treat (effective variables). Name of column holding outcome variable. dframe[[outcomename]] must be only finite and non-missing values. Value/level of outcome to be considered "success", and there must be a cut such that dframe[[outcomename]]==outcometarget at least twice and dframe[[outcomename]]!=outcometarget at least twice. list of extra columns to copy. parameters list from classification_parameters map from column names to functions of signature f(values: numeric, weights: numeric), simple missing value imputers.
## Details
Please see https://github.com/WinVector/vtreat/blob/master/Examples/fit_transform/fit_transform_api.md, mkCrossFrameCExperiment, designTreatmentsC, and prepare.treatmentplan for details.
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2020-08-15 02:20:56
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https://www.aimsciences.org/article/doi/10.3934/dcds.2010.26.1073
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# American Institute of Mathematical Sciences
September 2010, 26(3): 1073-1100. doi: 10.3934/dcds.2010.26.1073
## Continuity of global attractors for a class of non local evolution equations
1 Instituto de Matemática e Estatística-Universidade de São Paulo, Rua do Matão, 1010, Cidade Universitária, CEP 05508-090, São Paulo-SP, Brazil 2 Unidade Acadêmica de Matemática e Estatística UAME/CCT/UFCG, Avenida Aprígio Veloso, 882, Bairro Universitrio, Caixa Postal: 10.044, CEP 58109-970, Campina Grande-PB, Brazil
Received February 2009 Revised September 2009 Published December 2009
In this work we prove that the global attractors for the flow of the equation
$\frac{\partial m(r,t)}{\partial t}=-m(r,t)+ g(\beta J$∗$m(r,t)+ \beta h),\ h ,\ \beta \geq 0,$
are continuous with respect to the parameters $h$ and $\beta$ if one assumes a property implying normal hyperbolicity for its (families of) equilibria.
Citation: Antônio Luiz Pereira, Severino Horácio da Silva. Continuity of global attractors for a class of non local evolution equations. Discrete & Continuous Dynamical Systems - A, 2010, 26 (3) : 1073-1100. doi: 10.3934/dcds.2010.26.1073
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2019 Impact Factor: 1.338
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