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# What is SAMPLING DISTRIBUTION FOR PROPORTIONS?

Figure 1. The sampling distribution of p. Vertical bars are the probabilities; the smooth curve is the normal approximation.
http://onlinestatbook.com/2/sampling_distributions/samp_dist_p.html
This lesson covers sampling distributions. How to compute the variance of a sampling distribution for means and proportions. Includes problems with solutions.
http://stattrek.com/sampling/sampling-distribution.aspx
Prerequisite Introduction to Sampling Distributions, Binomial Distribution, Normal Approximation to the Binomial Learning Objectives 1. Compute the mean and standard deviation of the sampling distribution of p
http://statisticshelp.com/sampling-distribution-of-a-proportion
Assume that 0.80 of all third grade students can pass a test of physical fitness. A random sample of 20 students is chosen: 13 passed and 7 failed.
http://davidmlane.com/hyperstat/A106463.html
Introduction . The sampling distribution of a statistic is the distribution of that statistic, considered as a random variable, when derived from a random sample of size n.
http://en.wikipedia.org/wiki/Sampling_distribution
The Sampling Distribution of Up: Sampling Distribution of the Previous: Sampling Distribution of the The Sample Proportion Suppose a student guesses at the answer on every question in a 300-question exam.
http://www.stat.wmich.edu/s216/book/node68.html
There are many samples that can be drawn from a population. That means that the proportion of successes of the sample, p̂ will vary depending on which sample is picked.
http://mathnstats.com/index.php/category-blog/78-introductory-statistics/distributions/110-sampling-distribution-of-means-and-proportions.html
Sampling distribution of sample proportions . In these notes you will see how to apply the result known as the Central Limit Theorem to sample proportions.
Topic Index > Other Distributions > Mean of Sampling Distribution of the Proportion. What is the Mean of Sampling Distribution of the Proportion? The mean of sampling distribution of the proportion, P, is a special case of the sampling distribution of the mean.
http://www.statisticshowto.com/mean-sampling-distribution-proportion/
Best Answer: p̂ is the ubiased estimate of the population proportion p (sometimes denoted as π for those who like to use Greek letters only for parameters.) a) Since n is so large (n=1000), the sampling distribution is approximately normal. Its mean is p=0.68 and its variance is p(1–p)/n b ...
Chapter 5 Sampling Distribution of the Proportion J.C. Wang Goal and Objectives of Chapter 5 To learn about the sampling distribution of the proportion
http://www.stat.wmich.edu/wang/216/notes/DistrProp_handout.pdf
Topic Index > Other Distributions > Standard Deviation of Sampling Distribution of the Proportion. What is the Standard Deviation of Sampling Distribution of the Proportion?
http://www.statisticshowto.com/standard-deviation-sampling-distribution-proportion/
The standard deviation of the sampling distribution is the "average" deviation between the k sample proportions and the true population proportion, P. The standard deviation of the ... we choose the sample proportion (0.40) as the sample ...
http://stattrek.com/estimation/confidence-interval-proportion.aspx
Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used ...
http://en.wikipedia.org/wiki/Sample_size_determination
Sampling Distributions of Sample Means and Sample Proportions Applied Statistics Dr. Rachel Hall Tips. The techniques for nding the distribution of a sample mean and nding
http://people.sju.edu/~rhall/Biostats/samplingdist.pdf
The sampling distribution of p 1 - p 2 is approximately normal as long as the proportions are not too close to 1 or 0 and the sample sizes are not too small. As a rule of thumb, ...
http://davidmlane.com/hyperstat/A111955.html
To help illustrate the sampling distribution of the sample proportion, consider a student survey that accompanies the ACT test each year asking whether the student would like some help with math skills.
http://www.dummies.com/how-to/content/how-to-find-the-sampling-distribution-of-a-sample-.html
RELATED DOCUMENTS. Sampling distribution of proportions; Sampling and Sampling Distribution; Sampling distribution proportions; Sampling Distributions for Counts and Proportions
http://www.docstoc.com/docs/157863271/Sampling-distribution--proportions
Lecture 10: Depicting Sampling Distributions of a Sample Proportion Chapter 5: Probability and Sampling Distributions 2/10/12 Lecture 10 1
http://www.stat.purdue.edu/~xuanyaoh/stat350/xyFeb10Lec11.pdf
15 Sampling Distribution of a Proportion 1. Sampling Distribution of a Proportion In the last lecture we introduced the concept of a sampling distribution of sample means, i.e. the probability distribution that characterizes the fluctuation of means of samples
http://www.john-uebersax.com/stat312/15%20Sampling%20Distribution%20of%20a%20Proportion.pdf
Sampling Distributions of Proportions The dotplot is a partial graph of the • and record Toss a penny 20 timesall sample sampling distribution of number of sample theproportionsof heads.size 20.
http://www.docstoc.com/docs/115434012/Sampling-distribution-proportions
Announcements: • Midterm 2 is Wed. Review sheet is on class webpage (in the list of lectures) and will be covered in discussion on Monday. Two sheets
http://www.ics.uci.edu/~jutts/8/Lecture19Compact.pdf
Introduction: Statistics More Details: What makes up the data for the sampling distribution of proportions? What is its mean and standard deviation.
http://www.thephysics.org/73018/what-makes-data-sampling-distribution-proportions-what-its
Sampling distribution is a theoretical idea which form the basis for estimating the population parameters from sample statistics. ... The Sampling distribution of proportions approach normality as the sample size is increased.
http://www.mathcaptain.com/probability/sampling-distribution.html
Sampling Distributions for Sample Proportion, p-hat. ... To get an idea of how such a random variable behaves we consider this variable's sampling distribution which we discussed previously in this lesson.
https://onlinecourses.science.psu.edu/stat200/book/export/html/42
The solution provides step by step method for the calculation of sampling distribution for proportions . Formula for the calculation and Interpretations of the results are also included.
https://brainmass.com/statistics/normal-distribution/234528
Figure 1. A simulation of a sampling distribution. The parent population is uniform. The blue line under "16" indicates that 16 is the mean.
http://onlinestatbook.com/2/sampling_distributions/samp_dist_mean.html
Sampling Distribution of Proportion (Statistics)? ? asked 4 years ago; After constructing anew manufacturing machine, 5 items are produced and it is found that 2 are defective (D) and 3 are acceptable (3).
The sampling distribution for counts and proportions Suppose we ask a random sample of size n a yes/no question. Let the RV X denote the number of individuals
http://www.stat.osu.edu/~ekaizar/courses/528/notes/9_counts_proportions.pdf
Sampling Distribution of a Sample Proportion. From earlier material remember that if X is the count of successes in a sample of n trials of a binomial random variable then the proportion of success is given by = X/n.
http://oxfordmath.wikispaces.com/file/view/Sampling+Distribution+of+a+Sample+Proportion.pdf
1 NOTES: sample proportions sampling distributions A Simple Random Sample used to obtain pˆ provides an unbiased estimator of p. In other words, the
http://faculty.valenciacollege.edu/pmurphy2/STA_2023/NOTES_p-hat_sampling_distributions.pdf
Answer to What makes up the data for the sampling distribution of proportions? What is its mean and standard deviation....
Sampling Distribution of a Sample Proportion Lecture 26 Section 8.4 Robb T. Koether Hampden-Sydney College Mon, Oct 10, 2011 Robb T. Koether (Hampden-Sydney College) Sampling Distribution of a Sample Proportion Mon, Oct 10, 2011 1 / 33
http://people.hsc.edu/faculty-staff/robbk/Math121/Lectures/Fall%202011/Lecture%2026%20-%20Sampling%20Distribution%20Proportion.pdf
Part 2: The Sampling Distribution of the Sample Proportion. Suppose that the variable of interest is Gender. We would like to know the true proportion p of women in a population.
http://www-personal.umich.edu/~johnpj/stat/module_sampling_distribution.htm
The Central Limit Theorem for Proportions Theorem (The Central Limit Theorem for Proportions) For any population and any sample size, the sampling distribution
http://people.hsc.edu/faculty-staff/robbk/Math121/Lectures/Spring%202012/Lecture%2026%20-%20Sampling%20Distribution%20Proportion.pdf
©2011 Brooks/Cole, Cengage Learning Elementary Statistics: Looking at the Big Picture 1 Lecture 19: Chapter 8, Section 1 Sampling Distributions: Proportions
http://www.pitt.edu/~nancyp/stat-0200/slides/bpX1textfieldslecture19-samplingproportion.pdf
Printer-friendly version. If numerous repetitions of samples are taken, the distribution of $$\hat{p}$$ is said to approximate a normal curve distribution.
http://onlinecourses.science.psu.edu/stat200/node/43
The Sampling Distribution Model for a Proportion Provided that the sampled values are independent and the sample size is large enough, the sampling distribution of Öp is modeled by a Normal model with mean S SÖ ...
http://isites.harvard.edu/fs/docs/icb.topic1232542.files/Sampling%20Distributions%20%20-%20F13.pdf
Edit Proportion Edit Data Show Data Table Choose samples of size n = Reset Plot
http://lock5stat.com/statkey/sampling_1_cat/sampling_1_cat.html
Sampling Distribution of Sample Proportions We can measure elements of a population in terms of a qualitative property but looking at the proportion of the population that has the specific quality.
Answer to For the sampling distribution for proportions, where x is the observed number of successes, n trials and p is the true p...
Explain the sampling distribution of the sample proportion in this case. The sampling distribution of p is the distribution that would result by repeatedly sampling 50 observations and determined the proportion (p) that.
http://blog.tutorvista.com/2010/12/sample-proportion-in-statistics/
Page 1 of 6 Chapter 7: Sampling Distributions Distributions of the Sample Mean and the Sample Proportion • Distribution of the Sample Mean: - We usually estimate the population mean µ by the sample mean x.
http://www.apsu.edu/sites/apsu.edu/files/alzaatreha/Chapter_7_Fall_13.pdf
Distribution of the Sample Proportion Page 1 Robert A. Powers University of Northern Colorado Distributions of Sample Proportions The goal of this activity is to use a graphics calculator investigate the distributions of sample
http://www.unco.edu/nhs/mathsci/facstaff/Powers/M550/SamplingDistributions/pdf/8.2.1%20Distribution%20of%20Sample%20Proportions.pdf
THE SAMPLING DISTRIBUTION DEFINITION. The sampling distribution is a distribution of a sample statistic. ... When the sample button is pressed, the computer generates 100 samples of the sample size selected, computes the mean for each sample, ...
http://www.psychstat.missouristate.edu/introbook/SBK19.htm
Sampling Distributions of the Sample Mean and Sample Proportion. Douglas M. Andrews Department of Mathematics and Computer Science
http://www.causeweb.org/repository/StarLibrary/activities/andrews_2003/
In statistics, a sampling distribution is the probability distribution, ... The distribution of these means is the "sampling distribution of the sample mean" (for the given sample size). This distribution will be normal since the population is normal.


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## Trigonometry (10th Edition)

Published by Pearson

# Chapter 1 - Trigonometric Functions - Section 1.4 Using the Definitions of the Trigonometric Functions - 1.4 Exercises - Page 37: 93

positive

#### Work Step by Step

1. With $-90^{\circ}\lt 2\theta\lt 90^{\circ}$, then $-45^{\circ}\lt \theta \lt 45^{\circ}$ 2. This means that $\theta$ is in QI or QIV, where $x\gt0$ 3. Therefore $\\cos( \theta)\gt 0$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.

format: plain


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# Winding number always zero by definition. Help find the mistake.

Can someone point out where the mistake is please.

Let $$\gamma = C(0,1)$$ with $$\gamma : [0,1] \to \mathbb{C}$$. Okay so it is know that $$\int_{\gamma}\frac{dz}{z} = 2\pi i$$. And that the winding number $$n(\gamma,0) = 1$$. However lets try to calculate this from the definition.

$$2\pi i n(\gamma,0)=\int_{\gamma}\frac{dz}{z}=\int_0^1\frac{\gamma\prime(t)dt}{\gamma(t)} = \text{Log}(\gamma(1))-\text{Log}(\gamma(0))$$ $$=\text{ln}|\gamma(1)|-\text{ln}|\gamma(0)| + i(\theta(\gamma(1)) - \theta(\gamma(0))).$$ But we have that $$\gamma(0)=\gamma(1)$$. So is the above expression not just zero? Meaning that this winding number should be zero for any $$\gamma$$ closed curve. Clearly this is wrong but I do not understand why.

• There is a legitimate antiderivative for $1/z$ in the half plane $\mathrm{Re}\;z > 0$. – GEdgar Oct 19 '18 at 21:44
• @pureundergrad, $1/z$ has no singularity at $2$, so the integral is $0$. The point is exactly that there is singularity inside contour around $0$. – Ennar Oct 19 '18 at 21:44


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rivet is hosted by Hepforge, IPPP Durham

## Rivet analyses reference

### ATLAS_2016_I1426695

Track-based minimum bias at 8 TeV
Experiment: ATLAS (LHC)
Inspire ID: 1426695
Status: VALIDATED
Authors:
• Roman Lysak
References:
Beams: p+ p+
Beam energies: (4000.0, 4000.0) GeV
Run details:
• $pp$ QCD interactions at 8 TeV. Diffractive events should be included. Multiple kinematic cuts should not be required.

This paper presents measurements of distributions of charged particles which are produced in proton-proton collisions at a centre-of-mass energy of $\sqrt{s} = 8$ TeV and recorded by the ATLAS detector at the LHC. A special dataset recorded in 2012 with a small number of interactions per beam crossing (below 0.004) and corresponding to an integrated luminosity of 160 $\mu\text{b}^{-1}$ was used. A minimum-bias trigger was utilised to select a data sample of more than 9 million collision events. The multiplicity, pseudorapidity, and transverse momentum distributions of charged particles are shown in different regions of kinematics and charged-particle multiplicity, including measurements of final states at high multiplicity. The results are corrected for detector effects and are compared to the predictions of various Monte Carlo event generator models which simulate the full hadronic final state.

Source code: ATLAS_2016_I1426695.cc
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 // -*- C++ -*- #include "Rivet/Analysis.hh" #include "Rivet/Projections/ChargedFinalState.hh" namespace Rivet { /// @brief Add a short analysis description here class ATLAS_2016_I1426695 : public Analysis { public: //phase space regions enum regionID { k_pt100_nch2 = 0, k_pt500_nch1, k_pt500_nch6, k_pt500_nch20, k_pt500_nch50, kNregions }; /// Constructor DEFAULT_RIVET_ANALYSIS_CTOR(ATLAS_2016_I1426695); /// @name Analysis methods //@{ /// Book histograms and initialise projections before the run void init() { for (int iR=0; iR < kNregions; ++iR) { _sumW[iR] = 0.; } // Initialise and register projections declare(ChargedFinalState(Cuts::abseta < 2.5 && Cuts::pT > 100*MeV), "CFS_100"); declare(ChargedFinalState(Cuts::abseta < 2.5 && Cuts::pT > 500*MeV), "CFS_500"); // Book histograms for (int iR=0; iR < kNregions; ++iR) { if (iR == k_pt100_nch2 || iR == k_pt500_nch1) { _hist_nch [iR] = bookHisto1D ( 2 + iR, 1, 1); _hist_ptnch[iR] = bookProfile1D(14 + iR, 1, 1); } _hist_pt [iR] = bookHisto1D(4 + iR, 1, 1); _hist_eta[iR] = bookHisto1D(9 + iR, 1, 1); } } void fillPtEtaNch(const Particles particles, int nMin, int iRegion, double weight) { //skip if event fails multiplicity cut int nch =particles.size(); if (nch < nMin) return; //fill event weight info _sumW[iRegion] += weight; // Fill nch if (iRegion == k_pt100_nch2 || iRegion == k_pt500_nch1) { _hist_nch[iRegion]->fill(nch, weight); } for (const Particle&p : particles) { // Loop over particles, fill pT, eta and ptnch const double pt = p.pT()/GeV; const double eta = p.eta(); _hist_pt [iRegion]->fill(pt , weight/pt); _hist_eta[iRegion]->fill(eta, weight); if (iRegion == k_pt100_nch2 || iRegion == k_pt500_nch1) { _hist_ptnch[iRegion]->fill(nch, pt, weight); } } //end loop over particles } /// Perform the per-event analysis void analyze(const Event& event) { // Get charged particles, omitting some strange heavies const Cut& pcut = ( (Cuts::abspid!=PID::SIGMAMINUS) && (Cuts::abspid!=PID::SIGMAPLUS) && (Cuts::abspid!=PID::XIMINUS) && (Cuts::abspid!=PID::OMEGAMINUS)); const Particles& p_100 = apply(event, "CFS_100").particles(pcut); const Particles& p_500 = apply(event, "CFS_500").particles(pcut); fillPtEtaNch(p_100, 2, 0, event.weight()); fillPtEtaNch(p_500, 1, 1, event.weight()); fillPtEtaNch(p_500, 6, 2, event.weight()); fillPtEtaNch(p_500, 20, 3, event.weight()); fillPtEtaNch(p_500, 50, 4, event.weight()); } void finalize() { for (int iR = 0; iR < kNregions; ++iR) { if (_sumW[iR] > 0) { if (iR == k_pt100_nch2 || iR == k_pt500_nch1) { scale(_hist_nch[iR], 1.0/_sumW[iR]); } scale(_hist_pt [iR], 1.0/_sumW[iR]/TWOPI/5.); scale(_hist_eta[iR], 1.0/_sumW[iR]); } } } //@} private: double _sumW[kNregions]; /// @name Histograms Histo1DPtr _hist_nch [kNregions]; Histo1DPtr _hist_pt [kNregions]; Histo1DPtr _hist_eta [kNregions]; Profile1DPtr _hist_ptnch [kNregions]; }; // The hook for the plugin system DECLARE_RIVET_PLUGIN(ATLAS_2016_I1426695); }


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# JFK Assassination

#### DS86DS

Staff member
Member
Who killed JFK?

I personally believe that the CIA and the banking establishment colluded to have the president killed, for one, John F. Kennedy was known for his stance against the Vietnam War and had stated on occasion that he sought to end a war which had caused the deaths of thousands of American soldiers and military personnel. This would not bode well with the CIA or the Military Industrial Complex who had power and money at stake for this to be allowed happen. The CIA also understood that Lyndon Johnson was a lot more hawkish on Vietnam and if they could get rid of Kennedy, they would have the man they wanted in the White House.

President Kennedy, like Andrew Jackson before him had promised to smash the corrupt banking system into a million pieces and thus bring the American economy back under the control of the country and out of the hands of the Federal Reserve banking cartel - who to this day dominate the American and World economy by holding governments to ransom while printing money out of thin air. What Kennedy had in mind policy-wise would have benefitted US society and the American people as a whole and not simply a few shady Central Bankers at the top of the pyramid. To this day, the authorities and Mainstream Media do all they can to convince us of the lone gunman Oswald theory, yet it should always be considered that President Kennedy had made dangerous enemies in high places, including within the CIA and banking system.

All opinions and thoughts welcome.

Member
Who killed JFK?

I personally believe that the CIA and the banking establishment colluded to have the president killed, for one, John F. Kennedy was known for his stance against the Vietnam War and had stated on occasion that he sought to end a war which had caused the deaths of thousands of American soldiers and military personnel. This would not bode well with the CIA or the Military Industrial Complex who had power and money at stake for this to be allowed happen. The CIA also understood that Lyndon Johnson was a lot more hawkish on Vietnam and if they could get rid of Kennedy, they would have the man they wanted in the White House.

President Kennedy, like Andrew Jackson before him had promised to smash the corrupt banking system into a million pieces and thus bring the American economy back under the control of the country and out of the hands of the Federal Reserve banking cartel - who to this day dominate the American and World economy by holding governments to ransom while printing money out of thin air. What Kennedy had in mind policy-wise would have benefitted US society and the American people as a whole and not simply a few shady Central Bankers at the top of the pyramid. To this day, the authorities and Mainstream Media do all they can to convince us of the lone gunman Oswald theory, yet it should always be considered that President Kennedy had made dangerous enemies in high places, including within the CIA and banking system.

All opinions and thoughts welcome.
There was a time when I was much younger and much less cynical I would have told you to take off your tinfoil hat. Sadly, today with the hindsight of a lot of experience, I have to say I tend to agree with you.

What John Q. Public does not seem to understand, or even WANT to understand is the difference between Capitalism and Casino Capitalism. Capitalism merely means having wealth in private hands and investing it in business as makes financial sense. This is how wealth is created and held accountable - i.e. the exact opposite of Marxist communism in which the state owns all means of production. Casino Capitalism is what we have once again, as we did in the 1920s - where the world of finance simply creates ways to re-distribute wealth by the simple means of speculative gain. In most textbook economies, that would mean inflation, but in the one VERY special case of Wall Street - where the member PRIVATE banks own the central bank - and pretty much own those within the Beltway, they can simply increase the money supply to cover their gains - passing the bill (the money supply is a liability to the taxpayer) to the public. This works in the USA simply because that central bank is privately owned and secondly that the Greenback has de-facto hegemony, and when the inflationary forces of increasing the money supply are applied, other central banks the world over have to jump in and buy US to keep their US denominated instruments and accounts from crashing and taking THEM down. It is a brilliantly planned system that has taken hundreds of years to evolve to its current extreme where in '08 instead of crashing as it should have, banks declared themselves "too big to fail" and their ringleader - Paulson - started the ball rolling for trillion in bailouts - that was picked up by the Uniparty and continued under Barack Obama without a wiggle of change in direction.

I don't doubt for one minute that Kennedy - threatening to repeat the curiosity that killed the McFadden cat - was an easy target for someone(s) who stood to lose a hundred years of "progress" by returning control of the economy to the people who have to pick up the bills.

OP

#### DS86DS

Staff member
Member
Very good post. Kennedy and his successor Johnson had many policies in the pipeline which would benefit and protect the average person from the harsher outcomes of American Capitalism, including the Great Society Program and Medicare. I cannot imagine that that went down too well with the powers that be. It's no coincidence perhaps that from Nixon onwards, there had been a radical shift in US economic policy even though institutions such as the EPA were brought into existence under his tenure.

The lone nut with a gun and a grudge seems like a plausible scenario, though not so much as that of those with power and wealth getting rid of a man they considered a threat to their interests. It's the oldest story in politics, aka. the protection of wealth, privilege and power at any cost necessary - and God help anybody who decides to get in the way. In that sense, Kennedy had made a lot of powerful enemies within the corridors of power. And not merely powerful enemies, but dangerous enemies.

Member
There is a lot to learn about the Yanks for we outsiders and non-historians.

One take on the Federal Reserve system came from it very founder of its modern format, Sen Louis McFadden
Now, he was in no uncertain terms an anti-semite, but you also have to judge him by the standards of the time where racism, etc. were a significant and fluid part of everyday life and culture. If the banker writing banking legislation felt that his baby had been violated, I tend to want to take him seriously.

At the other extreme of the same balance is how Wall Street (that essentially OWNS not only the Federal Reserve but also the secretariat of anything financial within every administration) financed Hitler and essentially WWII:

The relationship between European banks and bankers has been extremely close from day one because it is the ONLY playground in the world where they can own the central bank and control a superpower's monetary, financial and economic policy.

#### Jennyanydots

Member
I can't say whether there was a conspiracy or not. It happened more than 20 years before I was born. All I have to go on is things such as the Warren Report and Jim Garrison's book "On The Trail Of The Assassins". Note the plural: 'Assassins'.

OK... assuming there was a conspiracy, it was extraordinarily well planned and carried out. However, there was one thing that no amount of preparation could plan for:

Abraham Zapruder standing on a plinth on the grassy knoll with his 16mm camera, capturing everything as it happened.

That, for me, is the single most telling piece of evidence that there was more than one shooter. The final head shot alone could not possibly have come from the book depository.... and no matter how the Warren Commission's theoretical physicists attempts to make the claim that it did, show that clip to a thousand ballistics experts, one at a time, for the first time ever, and a thousand of them will tell you that that shot came from a low position, in front of, and to the left of the car.

The Zapruder film is the one single thing that conspirators couldn't plan for and it is the basis of every challenge to the Warren Commission's findings.

Also, regarding Paddy's comments about the Vietnam War (I recommend Geoffrey C Ward and Ken Burns excellent history of the war, which was made into an HBO documentary series), a little reported fact about the day of the assassination is that later on that day, Kennedy was scheduled to meet with a high ranking general (can't remember the N.ame now) who he wanted to take advice from regarding the practicalities of removing American troops from Vietnam. Events meant that that meeting never took place and LBJ was inexorably sucked into committing America deeper and deeper into a war that, from the outset, and as the Pentagon Papers proved, successive Presidents knew America could never win.

Fascinating topic.


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# Definition:Ellipse/Eccentricity

## Definition

Let $K$ be an ellipse specified in terms of:

a given straight line $D$
a given point $F$
a given constant $e$ such that $0 < e < 1$

where $K$ is the locus of points $P$ such that the distance $p$ from $P$ to $D$ and the distance $q$ from $P$ to $F$ are related by the condition:

$q = e p$

The constant $e$ is known as the eccentricity of the ellipse.

## Also denoted as

Some sources use $\epsilon$ for the eccentricity of a conic section.


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# Dimensions and materials of a capacitor

• August 4th 2007, 10:23 AM
Dean
Dimensions and materials of a capacitor
The below question is coming up in a exam of mine soon, does anyone have the answer?

Q. Describe with the aid of diagrams how the dimensions and materials of a capacitor influence its operation.
• August 4th 2007, 10:38 AM
topsquark
Quote:

Originally Posted by Dean
The below question is coming up in a exam of mine soon, does anyone have the answer?

Q. Describe with the aid of diagrams how the dimensions and materials of a capacitor influence its operation.

There's no diagram for what the material does (unless you want to get into how the electron shells set up dipoles in the dielectric material...I don't imagine many people want to do that. ;) ) The reaction of a material to an applied electric field is summed up through the dielectric constant, $\varepsilon$. Generally the larger the dielectric constant of the material that is placed between the capacitor plates, the more charge (and hence energy) the capacitor can store.

As far as the dimensions of the capacitor is concerned if you look at the derivation of the capacitance for several types of capacitors (such as parallel plate, spherical, and cylindrical) you will see that there is an inverse relationship between the capacitance and the distance between the plates:
$C \propto \frac{1}{d}$
(I think the capacitance is actually inversely proportional to ln(d) for the spherical capacitor. I'd have to look that one up to be sure.)

Likewise the area of the capacitor plates (as you might expect) is directly proportional to the capacitance.
$C \propto A$

I'd advise learning at least one derivation of the capacitance to show for answering the question to provide an example of these statements.

Here's a bit of trivia that might or might not be useful to you in this: Most capacitors you buy on the market (the long thin ones anyway) are actually parallel plate capacitors that have been rolled into a cylindrical shape. I imagine the reason is that they are easier to build than a cylindrical capacitor, but there may be other reasons. It might be fruitful to look into this. (Or perhaps not.)

-Dan


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## Wednesday, March 14, 2018

### production scheduling: Minimum up-time

In [1] a minimum up-time question is posted:

• Assume we have $$T=12$$ periods. If we produce in period $$t$$ we have a profit of $$c_t$$. Some $$c_t$$'s are negative.
• If we turn production on, it should remain on for at least $$n=5$$ periods.
• We want to maximize total profit.
• How can we write a constraint that captures this minimum up-time condition?

We can recognize production is turned on in period $$t$$ by observing $$x_{t-1}=0$$ and $$x_t=1$$ where $$x_t$$ is a binary variable indicating whether our production process is turned on or off. So our constraint can look like:
$x_{t-1}=0,x_{t}=1 \Longrightarrow \sum_{k=t}^{t+n-1} x_k = n\>\>\>\forall t$
In a MIP model we can translate this into:
$\sum_{k=t}^{t+n-1} x_k \ge n(x_t-x_{t-1}) \>\>\>\forall t$
This formulation is not completely obvious. We note that $$x_t-x_{t-1}$$ is zero or negative for all cases except $$x_{t-1}=0,x_{t}=1$$.

Some notes:
• Behavior near the boundaries is always important. E.g. we could assume $$x_0=0$$.
• Let's also assume $$x_{T+1}=0$$ so we need to finish our production run in the time horizon.
• The MIP constraint can also be written as: $\sum_{k=t+1}^{t+n-1} x_k \ge (n-1)(x_t-x_{t-1}) \>\>\>\forall t$ as we know $$x_t=1$$ when this thing kicks in.
• So this gives us 12 constraints for our $$T=12, n=5$$ problem.
• We can disaggregate the summation into individual constraints $x_k \ge x_t-x_{t-1}\text{ for } k=t+1,\dots,t+n-1$ This is tighter and may solve faster. Advanced solvers may use an "implied bound" cut to do this automatically (and smarter) [2].
A complete model can look like:
\begin{align} \max \>&\sum_t c_t x_t\\ &\sum_{k=t}^{t+n-1} x_k \ge n(x_t-x_{t-1}) \\ & x_t \in \{0,1\}\end{align}
I implemented this in GAMS. GAMS assumes that variables indexed outside their domain are zero. This means I don't have to do anything special for $$t=1$$ and for $$t\gt T-n$$.

A solution with random $$c_t$$ is:

 Optimal Solution
For this small case we could have enumerated all possible feasible production schedules and pick the best one. We have 42 possible solutions:

 All Feasible Solutions ordered by Total Profit

For $$T=24,n=5$$ we have 24 constraints, while enumeration of all feasible solutions would lead to 4316 solutions. NB: I used the Cplex solution pool to enumerate the feasible solutions.

 Optimal solution for T=24

There are a number of extensions one can encounter:

• There may be some initial state. We need more than just the state at $$t=0$$. Basically we need to know for how many periods we are in the 'on'-state.
• We may relax the assumption that $$x_{T+1}=0$$.
• A maximum up-time is also not too difficult using a similar construct. Say we limit up-time to $$m$$ periods. Then we can require:$\sum_{k=t}^{t+m} x_k \le m$ I.e. we don't want to see a series of $$m+1$$ ones. See the picture below for an example with $$T=24, n=3, m=4$$.
• A minimum down-time is sometimes encountered in power generation models. This is close to minimum up-time: make $$y_t=1-x_t$$ and apply our tools we described above on $$y_t$$.
• Limiting the number of start-ups or shut-downs is quite a standard requirement. E.g. to limit the number of times we start a production run: \begin{align} &s_t \ge x_t-x_{t-1}\\& \sum_t s_t \le K \\ & s_t \in \{0,1\} \end{align}
 Run-lengths between 3 and 5.

#### Nitty-Gritty Implementation Details

The basic constraints discussed above are: \begin{align}&\sum_{k=t}^{t+n-1} x_k \ge n(x_t-x_{t-1}) &\forall t &\text{ (minimum length)}\\ & \sum_{k=t}^{t+m} x_k \le m & \forall t & \text{ (maximum length)} \end{align}  In GAMS, the minimum and maximum run-length constraints can be stated straightforwardly as:

alias(t,k);

minlength(t)..

sum(k$(ord(k)>=ord(t) and ord(k)<=ord(t)+n-1), x(k)) =g= n*(x(t)-x(t-1)); maxlength(t).. sum(k$(ord(k)>=ord(t) and ord(k)<=ord(t)+m), x(k)) =l= m;

I often prefer to keep model equations as simple as possible. We can do this by precalculating a set tk(t,k):

set tk(t,k) 'for use in minlength';
tk(t,k) =
ord(k)>=ord(t) and ord(k)<=ord(t)+n-1;
display tk;

minlength(t)..

sum(tk(t,k), x(k)) =g= n*(x(t)-x(t-1));

 Structure of the set tk

This also allows us to debug things before the rest of the model is complete. We can simply use display statements or use the gdx viewer. Equations can only be meaningfully debugged by trying to solve the model they are part of.

A slightly different approach is to rely on leads:\begin{align}&\sum_{k=1}^{n} x_{t+k-1} \ge n(x_t-x_{t-1}) &\forall t &\text{ (minimum length)}\\ & \sum_{k=1}^{m+1} x_{t+k-1} \le m & \forall t & \text{ (maximum length)} \end{align}This is also easily transscribed into GAMS syntax:

minlength(t)..

sum(k$(ord(k)<=n), x[t+(ord(k)-1)]) =g= n*(x(t)-x(t-1)); maxlength(t).. sum(k$(ord(k)<=m+1), x[t+(ord(k)-1)] ) =l= m;

#### More details: disaggregated version

The disaggregated version$x_k \ge x_t-x_{t-1}\text{ for } k=t+1,\dots,t+n-1$ needs a little bit more attention.  If we just translate this to:

minlength2(tk(t,k))..
x(k) =g= x(t)-x(t-1);

then we allow partial runs near the end of the planning horizon.

 Partial runs are not allowed

To prevent this we need to forbid $$x_t \gt x_{t-1}$$ near the end.

minlength2a(tk(t,k))..
x(k) =g= x(t)-x(t-1);

minlength2b(t)$( ord(t)+n-1 > card(t)).. x(t) =l= x(t-1); Interestingly (at least to me), the "leads" formulation is easier. We just can use: minlength3(t,k)$(ord(k)<=n-1)..
x(t+
ord(k)) =g= x(t)-x(t-1);

This will automatically generate $$0 \le x_t-x_{t-1}$$ where needed.

To get a feeling about possible performance improvement when disaggregating the min-length constraint, we need a slightly larger problem. So I used $$T=1024$$ and used $$N=10$$ machines. So our decision variable is now $$x_{i,t}$$.

AggregatedDisaggregated
Size
SINGLE EQUATIONS       10,241
SINGLE VARIABLES       10,241
DISCRETE VARIABLES     10,240

SINGLE EQUATIONS       40,961
SINGLE VARIABLES       10,241
DISCRETE VARIABLES     10,240

Objective 17304.883540 17304.883540
Iterations, Nodes 10547 iterations, 13 nodes 6234 iterations, 0 nodes
Time Cplex Time: 7.39sec (det. 1900.93 ticks) Cplex Time: 5.13sec (det. 1728.88 ticks)

The disaggregated version does better: it can solve the problem during preprocessing.

#### The quest for zero nodes

After doing these experiments with disaggregation I was asking myself:

Is there an aggregated formulation that solves this problem in zero nodes?

It is standard wisdom in integer programming that one should disaggregate variable upper bound constraints on sums of variables. These are constraints of the form:$x_1+\dots+x_n \le (u_1+\dots+u_n) y, \> y \in \{0,1\}$where $$u_j$$ is a valid upper bound on $$x_j \ge 0, (j = 1,\dots,n)$$. This single constraint is equivalent, given the integrality of $$y$$, to the following collection of "disaggregated" constraints: $x_j \le u_j y_j \>(j = 1,\dots,n)$The reason the second, disaggregated formulation is preferred is that, while equivalent given integrality, its linear-programming relaxation is stronger. However, given the ability to automatically disaggregate the first constraint, these "implied bound" constraints can be stored in a pool and added to the LP only as needed. Where $$n$$ is large this latter approach will typically produce a much smaller, but equally effective LP.
Our constraint $\sum_{k=t}^{t+n-1} x_k \ge n(x_t-x_{t-1}) \> \forall t$ is not exactly this form. We can coerce this by:\begin{align} & \sum_{k=t}^{t+n-1} x_k \ge n y_t\\ & y_t \ge x_t-x_{t-1}\\ &y_t \in \{0,1\}\end{align} Here are the results:

AggregatedDisaggregatedAggregated v2
SINGLE EQUATIONS       10,241
SINGLE VARIABLES       10,241
DISCRETE VARIABLES     10,240

SINGLE EQUATIONS       40,961
SINGLE VARIABLES       10,241
DISCRETE VARIABLES     10,240

SINGLE EQUATIONS       20,481
SINGLE VARIABLES       20,481
DISCRETE VARIABLES     20,480

obj=17304.883540 obj=17304.883540 obj=17304.883540
10547 iterations, 13 nodes 6234 iterations, 0 nodes 12477 iterations, 0 nodes
Cplex Time: 7.39sec (det. 1900.93 ticks) Cplex Time: 5.13sec (det. 1728.88 ticks) Cplex Time: 20.61sec (det. 6098.72 ticks)

We achieved our zero nodes, but at a price that is too high. In any case the Cplex performance on this model (with any of these formulations) is fantastic.

#### References

1. Linear programming - optimizing profit with tricky constraints, https://stackoverflow.com/questions/49261669/linear-programming-optimizing-profit-with-tricky-constraints
2. Bixby E.R., Fenelon M., Gu Z., Rothberg E., Wunderling R. (2000) MIP: Theory and Practice — Closing the Gap. In: Powell M.J.D., Scholtes S. (eds) System Modelling and Optimization. CSMO 1999. IFIP — The International Federation for Information Processing, vol 46. Springer, Boston, MA


text:
Warning

This documents an unmaintained version of NetworkX. Please upgrade to a maintained version and see the current NetworkX documentation.

# networkx.generators.random_clustered.random_clustered_graph¶

random_clustered_graph(joint_degree_sequence, create_using=None, seed=None)[source]

Generate a random graph with the given joint independent edge degree and triangle degree sequence.

This uses a configuration model-like approach to generate a random graph (with parallel edges and self-loops) by randomly assigning edges to match the given joint degree sequence.

The joint degree sequence is a list of pairs of integers of the form $$[(d_{1,i}, d_{1,t}), \dotsc, (d_{n,i}, d_{n,t})]$$. According to this list, vertex $$u$$ is a member of $$d_{u,t}$$ triangles and has $$d_{u, i}$$ other edges. The number $$d_{u,t}$$ is the triangle degree of $$u$$ and the number $$d_{u,i}$$ is the independent edge degree.

Parameters: joint_degree_sequence (list of integer pairs) – Each list entry corresponds to the independent edge degree and triangle degree of a node. create_using (NetworkX graph constructor, optional (default MultiGraph)) – Graph type to create. If graph instance, then cleared before populated. seed (integer, random_state, or None (default)) – Indicator of random number generation state. See Randomness. G – A graph with the specified degree sequence. Nodes are labeled starting at 0 with an index corresponding to the position in deg_sequence. MultiGraph NetworkXError – If the independent edge degree sequence sum is not even or the triangle degree sequence sum is not divisible by 3.

Notes

As described by Miller [1] (see also Newman [2] for an equivalent description).

A non-graphical degree sequence (not realizable by some simple graph) is allowed since this function returns graphs with self loops and parallel edges. An exception is raised if the independent degree sequence does not have an even sum or the triangle degree sequence sum is not divisible by 3.

This configuration model-like construction process can lead to duplicate edges and loops. You can remove the self-loops and parallel edges (see below) which will likely result in a graph that doesn’t have the exact degree sequence specified. This “finite-size effect” decreases as the size of the graph increases.

References

 [1] Joel C. Miller. “Percolation and epidemics in random clustered networks”. In: Physical review. E, Statistical, nonlinear, and soft matter physics 80 (2 Part 1 August 2009).
 [2] M. E. J. Newman. “Random Graphs with Clustering”. In: Physical Review Letters 103 (5 July 2009)

Examples

>>> deg = [(1, 0), (1, 0), (1, 0), (2, 0), (1, 0), (2, 1), (0, 1), (0, 1)]
>>> G = nx.random_clustered_graph(deg)

To remove parallel edges:

>>> G = nx.Graph(G)

To remove self loops:

>>> G.remove_edges_from(nx.selfloop_edges(G))


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# Angels We Have Heard On High

on PTXmas

## Lyrics

Angels we have heard on high
Sweetly singing o'er the plains
Echoing their joyous strains
full lyrics
Angels we have heard on high
Sweetly singing o'er the plains
Echoing their joyous strains
full lyrics

## Features of This Track

hip hop influences
jazz vocals
improvisational approach
r&b roots

## Similar Tracks

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Love all your songs.....st a y cute smomich
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Adcanizales, w h o were they.
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highwaters02 4
That is a cute song
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I watched the season with my husband and I just happen to runt into two of them at a rest stop between SD and LA. They were so nice and allowed me to take a picture with them.
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I love them too!
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I love you vary much pentatonix but
I don't know all about you
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I am alwas listen to to your misic And by alwas i mean every day ... Haha!!!!!!!! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !!!!!!!!!!!! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !!!!!!!!!!!!
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I don't know about u guys but i listen to Christmas music all year...haha
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Love this holiday ptx
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kt.phillips
I LOVE PENTATONIX HOLIDAY HITS! FOLLOW ME IF YOU PEEPS AGREE!! GO PENTATONIX!! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !
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*sighs* listening to Christmas music on 10/6/15, my favorite thing to do.
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And they only use there voices!!!!
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love it
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Work it PTX!<3 :)
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I am set for life
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Pentatonix is the best
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I love them!!!!!!!! ! ! !
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Such a pretty song saw it on channel one!!!!

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# Need Help

#### GMAN679

##### New member
Hi, I just need a confirmation on the equation Y=Cosechx from -4 is less than and equal to X, which is less than and equal 4 is the same as
Y=e^4+e^-4 And that the value generated if equation was processed, supposed to generate the y value of 27.3?
2

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi, I just need a confirmation on the equation Y=Cosechx from -4 is less than and equal to X, which is less than and equal 4 is the same as
Y=e^4+e^-4 And that the value generated if equation was processed, supposed to generate the y value of 27.3?
2
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

#### topsquark

##### Senior Member
Let' me supplement Subhostosh's comment with a

What??

That problem statement makes no sense. You seem to be asking how to define csch(x) in terms of exponentials but what are you doing with $$\displaystyle -4 \leq x \leq 4$$ and x = 4? And where did 27.3 come from?

-Dan

#### Jomo

##### Elite Member
Just for the record,−4≤x≤4, is read as x is between -4 and 4 inclusive


text:
# On which physical cpu/core does a process run?

## Recommended Posts

Is there a way to find that out? I need this for performance evaluation. I found out that it might be task_struct->oncpu, which unfortunately is only accessible inside the kernel :(

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Quote:
 Original post by hydrooIs there a way to find that out?I need this for performance evaluation.I found out that it might be task_struct->oncpu, which unfortunately is only accessible inside the kernel :(

A process may run on any or all cores, at the same time. There is no way to find out outside of the kernel because it requires a context switch to the kernel, so (a) the process may not even be running when the query is made and (2) the answer is just as likely not correct by the time the kernel call returns.

##### Share on other sites
It's not totally important to be 100% in timing correct by the way.
I'd give it a try. And watch how accurate it'd be.

Or can I get an info when a process is rescheduled to another queue?

##### Share on other sites
On windows you can request a thread runs on a particular processor/core (something like SetThreadAffinity() I believe). I assume you can do something similar on the major operating systems. However, in general it is a bad idea as the OS knows a lot better than you how to schedule threads/processes.

##### Share on other sites
I don't want to pin them down. I want to find out where they are at the moment.

thanks for the input guys

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Its kind of like trying to pin the exact location and momentum of an electron..

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I am pretty sure that you can find out where it is. Because even when a process is not running it's still in the queue of it's cpu.
And as I said its not the goal to be 1ms-correct.

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Quote:
 Original post by hydrooI am pretty sure that you can find out where it is. Because even when a process is not running it's still in the queue of it's cpu.

Is it? or is it in the ready queue, not assigned to a CPU until it's running? If that's the case, no matter how often you look, your process will never appear to be getting any CPU at all on a single-processor system, and chances are it's not running on a multiprocessor system.

Your best bet is to read the Linux kernel code to understand how the scheduler works.

##### Share on other sites
Quote:
Original post by Bregma
Quote:
 Original post by hydrooI am pretty sure that you can find out where it is. Because even when a process is not running it's still in the queue of it's cpu.

Is it? or is it in the ready queue, not assigned to a CPU until it's running? If that's the case, no matter how often you look, your process will never appear to be getting any CPU at all on a single-processor system, and chances are it's not running on a multiprocessor system.

Your best bet is to read the Linux kernel code to understand how the scheduler works.

I am pretty sure that there is no central queue (I read about the O(1)-Scheduler. Don't know how CFS handles things). Processes will most likely be scheduled to the cpu they were scheduled to before, to for example exploit locality. Only under certain circumstances it will be moved to another cpu.
This wouldn't be possible without indication where a process has been, would it.

So I guess there is no easy way to do it.

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Probably one the best questions on this forum in a while.

I don't know of any easy way to do this. You could try and modify the kernel to log the information (which is going to be tremendous BTW and slow everything down).

Doing this from user space in your app would get messy.

How often does a process (thread is a process on linux) switch CPUs. My guess is that it happens more often that you would expect.

You could keep track of the gettimeofday() time of common thread entry/blocking points (after IO blocking or mutex, etc). Won't give you an idea of what CPU you are on, but will give you an idea of what really matters, ie how the threads are interacting and blocking.

Also gettimeofday() is a syscall, so you might want to use RDTSC in x86 chips to simply read the CPU clock cycle counter instead (but keep in mind it wraps around quickly...),

// for 32bit machinestypedef signed long long is8;static inline is8 VCycle(void) { is8 x; asm volatile("rdtsc\n\tmov %%edx, %%ecx\n\t" :"=A" (x)); return x; }// or for when running in 64bit modetypedef unsigned int iu4;typedef signed long is8;static inline is8 VCycle(void) { iu4 aa,dd; asm volatile("rdtsc" : "=a" (aa), "=d" (dd)); return ((is8)aa)|(((is8)dd)<<32); }

BTW, I know the 64bit one works, because I use it all the time, forget if I tested the 32bit version!

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Oh, if you go the modify the kernel route, this will help if you intend to add a syscall to return CPU info to a userspace process,

http://tldp.org/HOWTO/html_single/Implement-Sys-Call-Linux-2.6-i386/

BTW, looks like a getcpu() vsyscall has been proposed and tested before on x86-64

http://sourceware.org/ml/libc-alpha/2006-06/msg00024.html

[Edited by - TimothyFarrar on January 17, 2008 4:47:20 PM]

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Regarding that this proposal has been made 1.5 years ago and it hasn't been implemented yet, it will not be implemented, right.

Timing is not the issue. We already have a measurement environment. By contract we have to record the process location "somehow". Making a kernel patch/module would be the worst case.

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Yeah, a getcpu() syscall will probably never happen in the main branch.

Still your own personal kernel patch might be the best option. I've done it before (custom modified http server running kernel side), and it's not bad if you are using it for testing only.

If you do go the kernel modification route, I think on more recent kernels there is a common vdso page which is mapped into every process. This page is read/execute only and supplies the entry/exit for the vsyscall. I'm not sure if this has been done yet, but one kernel optimization effort was to get a vgettimeofday area into vdso page such that you could simply read the area to gettimeofday() instead of doing an actual syscall. Since the vdso page is always virtually mapped to the same physical page in the kernel, you might be able to write the pids in there as well (from inside the scheduler) for the current pid running on each processor. Then just poll in userspace land to find which processor your current pid is on.

Also I'm not 100% up to date on glibc2 pthreads anymore, so you might have to check that each thread gets its own pid still. I believe there is a way to create threads (processes on linux) which share pids. So you might need a second number for identification...

In theory it should work...

BTW, if you do find/implement a good way of getting current cpu id from userland, please post what you did :)

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Thanks so far.
To lower your enthusiasm a bit:
I actually never done kernel-hacking. And my priorities at work are totally different (I am working on the visualization part). So I won't be the one to implement it. Chances are that a student will take this task.
I will keep you updated, but don't expect anything soon.

It's a bit sad, since ordinary (non kernel patching) linux users won't be able to use this feature.

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Quote:
 Original post by hydrooIt's a bit sad, since ordinary (non kernel patching) linux users won't be able to use this feature.

Unless you try to land your patch in the mainline kernel. I don't know what application you're working on exactly, but if knowing the CPU something runs on is required for some kind of QA or certification or something, it might make it in :-)

##### Share on other sites
Can you explain why you need to know this? I really think you are on the wrong path in trying to find this information out, because it's simply not useful to know in isolation. So, please, explain why you think you need to know.

Quote:
 Original post by TimothyFarrarHow often does a process (thread is a process on linux) switch CPUs. My guess is that it happens more often that you would expect.

For switching, it's actually probably less often. A good task scheduler aims for good task/CPU affinity. That is, it tries very hard to retain execution locality, because running a task on the same CPU it ran last time is always going to be more efficient than running it on another CPU.

Quote:
 Original post by TimothyFarrarAlso gettimeofday() is a syscall, so you might want to use RDTSC in x86 chips to simply read the CPU clock cycle counter instead (but keep in mind it wraps around quickly...)

It's kinda tricky to use RDTSC properly. For example, on many multicore AMD CPUs and almost all multiprocessor systems, the RDTSC is not synchronized between CPUs, so the results can be all over the place. If you're measuring very small things you're probably safe thanks to task affinity, but otherwise you need to force the task to run only on a single CPU for the duration of the time between two RDTSC instructions or use some other timing method.

Quote:
 Original post by TimothyFarrar// for 32bit machinestypedef signed long long is8;static inline is8 VCycle(void) { is8 x; asm volatile("rdtsc\n\tmov %%edx, %%ecx\n\t" :"=A" (x)); return x; }// or for when running in 64bit modetypedef unsigned int iu4;typedef signed long is8;static inline is8 VCycle(void) { iu4 aa,dd; asm volatile("rdtsc" : "=a" (aa), "=d" (dd)); return ((is8)aa)|(((is8)dd)<<32); }

This is super, super wrong. Let me count the ways:

1. RDTSC does not provide accurate measurements without a serializing instruction beforehand. CPUID is usually a good choice for this.
2. If the code was written properly you wouldn't need separate implementations for x86 and x86_64.
3. The "32-bit" version silently clobbers ECX, which will cause very subtle bugs. You need to tell the compiler that you are clobbering registers.
4. The EDX->ECX move would be unnecessary if the appropriate asm contraints had been used. See also #2.
5. The typedefs are unnecessary.
6. The result of RDTSC is totally not a signed value.
7. The return in the "64-bit" version appears to be the result of an explosion at the parens factory.

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Quote:
 Original post by truthsayerCan you explain why you need to know this? I really think you are on the wrong path in trying to find this information out, because it's simply not useful to know in isolation. So, please, explain why you think you need to know.

just in case you are still reading:
"It might be interesting for the user." - plain

You can analyze the connection between topology of your system and the your software topology (mpi+threading/possibly nested), especially on clustered smp-machines this kind of information is valuable.

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text:
# Chapter 8 Initialize with genomic data

circlize is quite flexible to initialize the circular plot not only by chromosomes, but also by any type of general genomic categories.

## 8.1 Initialize with cytoband data

Cytoband data is an ideal data source to initialize genomic plots. It contains length of chromosomes as well as so called “chromosome band” annotation to help to identify positions on chromosomes.

### 8.1.1 Basic usage

If you work on human genome, the most straightforward way is to directly use circos.initializeWithIdeogram() (Figure 8.1). By default, the function creates a track with chromosome name and axes, and a track of ideograms.

Although chromosome names added to the plot are pure numeric, actually the internally names have the “chr” index. When you adding more tracks, the chromosome names should also have “chr” index.

circos.initializeWithIdeogram()
text(0, 0, "default", cex = 1)
circos.info()
## All your sectors:
##  [1] "chr1"  "chr2"  "chr3"  "chr4"  "chr5"  "chr6"  "chr7"  "chr8"
##  [9] "chr9"  "chr10" "chr11" "chr12" "chr13" "chr14" "chr15" "chr16"
## [17] "chr17" "chr18" "chr19" "chr20" "chr21" "chr22" "chrX"  "chrY"
##
## [1] 1 2
##
## Your current sector.index is chrY
## Your current track.index is 2
circos.clear()

By default, circos.initializeWithIdeogram() initializes the plot with cytoband data of human genome hg19. Users can also initialize with other species by specifying species argument and it will automatically download cytoband files for corresponding species.

circos.initializeWithIdeogram(species = "hg18")
circos.initializeWithIdeogram(species = "mm10")

When you are dealing rare species and there is no cytoband data available yet, circos.initializeWithIdeogram() will try to continue to download the “chromInfo” file form UCSC, which also contains lengths of chromosomes, but of course, there is no ideogram track on the plot.

In some cases, when there is no internet connection for downloading or there is no corresponding data avaiable on UCSC yet. You can manually construct a data frame which contains ranges of chromosomes or a file path if it is stored in a file, and sent to circos.initializeWithIdeogram().

cytoband.file = system.file(package = "circlize", "extdata", "cytoBand.txt")
circos.initializeWithIdeogram(cytoband.file)

cytoband.df = read.table(cytoband.file, colClasses = c("character", "numeric",
"numeric", "character", "character"), sep = "\t")
circos.initializeWithIdeogram(cytoband.df)

If you read cytoband data directly from file, please explicitly specify colClasses arguments and set the class of position columns as numeric. The reason is since positions are represented as integers, read.table would treat those numbers as integer by default. In initialization of circular plot, circlize needs to calculate the summation of all chromosome lengths. The summation of such large integers would throw error of integer overflow.

By default, circos.intializeWithIdeogram() uses all chromosomes which are available in cytoband data to initialize the circular plot. Users can choose a subset of chromosomes by specifying chromosome.index. This argument is also for ordering chromosomes (Figure 8.2).

circos.initializeWithIdeogram(chromosome.index = paste0("chr", c(3,5,2,8)))
text(0, 0, "subset of chromosomes", cex = 1)
circos.clear()

When there is no cytoband data for the specified species, and when chromInfo data is used instead, there may be many many extra short contigs. chromosome.index can also be useful to remove unnecessary contigs.

### 8.1.2 Pre-defined tracks

After the initialization of the circular plot, circos.initializeWithIdeogram() additionally creates a track where there are genomic axes and chromosome names, and create another track where there is an ideogram (depends on whether cytoband data is available). plotType argument is used to control which type of tracks to add. (figure Figure 8.3).

circos.initializeWithIdeogram(plotType = c("axis", "labels"))
text(0, 0, "plotType = c('axis', 'labels')", cex = 1)
circos.clear()

circos.initializeWithIdeogram(plotType = NULL)
text(0, 0, "plotType = NULL", cex = 1)
circos.clear()

### 8.1.3 Other general settings

Similar as general circular plot, the parameters for the layout can be controlled by circos.par() (Figure 8.4). Do remember when you explicitly set circos.par(), you need to call circos.clear() to finish the plotting.

circos.par("start.degree" = 90)
circos.initializeWithIdeogram()
circos.clear()
text(0, 0, "'start.degree' = 90", cex = 1)

circos.par("gap.degree" = rep(c(2, 4), 12))
circos.initializeWithIdeogram()
circos.clear()
text(0, 0, "'gap.degree' = rep(c(2, 4), 12)", cex = 1)

## 8.2 Customize chromosome track

By default circos.initializeWithIdeogram() initializes the layout and adds two tracks. When plotType argument is set to NULL, the circular layout is only initialized but nothing is added. This makes it possible for users to completely design their own style of chromosome track.

In the following example, we use different colors to represent chromosomes and put chromosome names in the center of each cell (Figure 8.5).

set.seed(123)
circos.initializeWithIdeogram(plotType = NULL)
circos.track(ylim = c(0, 1), panel.fun = function(x, y) {
chr = CELL_META$sector.index xlim = CELL_META$xlim
ylim = CELL_META$ylim circos.rect(xlim[1], 0, xlim[2], 1, col = rand_color(1)) circos.text(mean(xlim), mean(ylim), chr, cex = 0.7, col = "white", facing = "inside", niceFacing = TRUE) }, track.height = 0.15, bg.border = NA) circos.clear() ## 8.3 Initialize with general genomic category Chromosome is just a special case of genomic category. circos.genomicInitialize() can initialize circular layout with any type of genomic categories. In fact, circos.initializeWithIdeogram() is implemented by circos.genomicInitialize(). The input data for circos.genomicInitialize() is also a data frame with at least three columns. The first column is genomic category (for cytoband data, it is chromosome name), and the next two columns are positions in each genomic category. The range in each category will be inferred as the minimum position and the maximum position in corresponding category. In the following example, a circular plot is initialized with three genes. df = data.frame( name = c("TP53", "TP63", "TP73"), start = c(7565097, 189349205, 3569084), end = c(7590856, 189615068, 3652765)) circos.genomicInitialize(df) Note it is not necessary that the record for each gene is only one row. In following example, we plot the transcripts for TP53, TP63 and TP73 in a circular layout (Figure 8.6). tp_family = readRDS(system.file(package = "circlize", "extdata", "tp_family_df.rds")) head(tp_family) ## gene start end transcript exon ## 1 TP53 7565097 7565332 ENST00000413465.2 7 ## 2 TP53 7577499 7577608 ENST00000413465.2 6 ## 3 TP53 7578177 7578289 ENST00000413465.2 5 ## 4 TP53 7578371 7578554 ENST00000413465.2 4 ## 5 TP53 7579312 7579590 ENST00000413465.2 3 ## 6 TP53 7579700 7579721 ENST00000413465.2 2 In the following code, we first create a track which identifies three genes. circos.genomicInitialize(tp_family) circos.track(ylim = c(0, 1), bg.col = c("#FF000040", "#00FF0040", "#0000FF40"), bg.border = NA, track.height = 0.05) Next, we put transcripts one after the other for each gene. It is simply to add lines and rectangles. The usage of circos.genomicTrack() and circos.genomicRect() will be discussed in Chapter 9. n = max(tapply(tp_family$transcript, tp_family$gene, function(x) length(unique(x)))) circos.genomicTrack(tp_family, ylim = c(0.5, n + 0.5), panel.fun = function(region, value, ...) { all_tx = unique(value$transcript)
for(i in seq_along(all_tx)) {
l = value$transcript == all_tx[i] # for each transcript current_tx_start = min(region[l, 1]) current_tx_end = max(region[l, 2]) circos.lines(c(current_tx_start, current_tx_end), c(n - i + 1, n - i + 1), col = "#CCCCCC") circos.genomicRect(region[l, , drop = FALSE], ytop = n - i + 1 + 0.4, ybottom = n - i + 1 - 0.4, col = "orange", border = NA) } }, bg.border = NA, track.height = 0.4) circos.clear() In Figure 8.6, you may notice the start of axes becomes “0KB” while not the original values. It is just an adjustment of the axes labels to reflect the relative distance to the start of each gene, while the coordinate in the cells are still using the original values. Set tickLabelsStartFromZero to FALSE to recover axes labels to the original values. ## 8.4 Zooming chromosomes The strategy is the same as introduced in Section 6.1. We first define a function extend_chromosomes() which copy data in subset of chromosomes into the original data frame. extend_chromosomes = function(bed, chromosome, prefix = "zoom_") { zoom_bed = bed[bed[[1]] %in% chromosome, , drop = FALSE] zoom_bed[[1]] = paste0(prefix, zoom_bed[[1]]) rbind(bed, zoom_bed) } We use read.cytoband() to download and read cytoband data from UCSC. In following, x ranges for normal chromosomes and zoomed chromosomes are normalized separetely. cytoband = read.cytoband() cytoband_df = cytoband$df
chromosome = cytoband$chromosome xrange = c(cytoband$chr.len, cytoband\$chr.len[c("chr1", "chr2")])
normal_chr_index = 1:24
zoomed_chr_index = 25:26

# normalize in normal chromsomes and zoomed chromosomes separately
sector.width = c(xrange[normal_chr_index] / sum(xrange[normal_chr_index]),
xrange[zoomed_chr_index] / sum(xrange[zoomed_chr_index]))

The extended cytoband data which is in form of a data frame is sent to circos.initializeWithIdeogram(). You can see the ideograms for chromosome 1 and 2 are zoomed (Figure 8.7).

circos.par(start.degree = 90)
circos.initializeWithIdeogram(extend_chromosomes(cytoband_df, c("chr1", "chr2")),
sector.width = sector.width)

bed = generateRandomBed(500)
circos.genomicTrack(extend_chromosomes(bed, c("chr1", "chr2")),
panel.fun = function(region, value, ...) {
circos.genomicPoints(region, value, pch = 16, cex = 0.3)
})

Add a link from original chromosome to the zoomed chromosome (Figure 8.7).

circos.link("chr1", get.cell.meta.data("cell.xlim", sector.index = "chr1"),
"zoom_chr1", get.cell.meta.data("cell.xlim", sector.index = "zoom_chr1"),
col = "#00000020", border = NA)
circos.clear()


text:
# Closed Elements Uniquely Determine Closure Operator

Jump to navigation Jump to search

## Theorem

Let $\left({S, \preceq}\right)$ be an ordered set.

Let $f, g: S \to S$ be closure operators on $S$.

Suppose that $f$ and $g$ have the same closed elements.

Then $f = g$.

## Proof

Let $x \in S$.

Let $C$ be the set of closed elements of $S$ (with respect to either $f$ or $g$) that succeed $x$.

By Closure is Smallest Closed Successor, $f \left({x}\right)$ and $g \left({x}\right)$ are smallest closed successors of $x$.

That is, $f \left({x}\right)$ and $g \left({x}\right)$ are smallest elements of $C \cap \bar\uparrow x$, where $\bar\uparrow x$ is the upper closure of $x$.

By Smallest Element is Unique, $f \left({x}\right) = g \left({x}\right)$.

Since this holds for all $x \in S$, $f = g$ by Equality of Mappings.

$\blacksquare$


text:
# What is the protocol for telling others you have found your mistake in your working?

I sometimes ask a question which is a problem that I can't solve because I have made a calculative error. Often, all it takes is for someone to point out the small error I have made (or for me to realise the error after reading the answers). How should I let the users know that I have found the source of my troubles? Should it be a comment on the question, or an edit inside the body of the question? One could also answer the question, but that is probably the worst option because it takes the credit away from other users. A comment may be overlooked, so I am leaning towards putting an edit into the question. Is this standard protocol?

As an example, I have found out the reason why I have calculated the order of $\tau\sigma$ and $\tau\sigma^2$ incorrectly (by assuming commutativity) in this question.

• My personal preference would be for a edit at the bottom of the question as it is easy to see for anyone first viewing the question. – Chris Nov 22 '15 at 1:17
• You could make it an answer but check the community wiki box so as not to gain reputation points. This is an especially good option is there are no existing answers, so it can be removed from the unanswered queue. – Cheerful Parsnip Nov 22 '15 at 15:00
• @Burn-Man: I agree, except that I would put the edit at the top of the question, so that nobody misses it. Something like: "Edited to add: Problem solved! My mistake was such-and-such." – TonyK Nov 22 '15 at 22:52


text:
# What is the period of f(t)=cos ( ( 4 t ) / 3 ) ?

$\frac{3 \pi}{2}$
Period of$f \left(t\right) = \cos \left(\frac{4 t}{3}\right)$ --> $\left(3\right) \frac{2 \pi}{4} = \frac{3 \pi}{2}$


text:
vst

vst -> Vim Startscreen

I got kinda bored of Vim's default start screen. So, I created a cool Vim start screen without using the VimStart plugin. See an image of it below:

Setup

The setup is pretty simple - all I do is open and modify a custom buffer whenever I run nvim without any arguments.

In init.vim, I execute the function Start() on VimEnter. To see more about how VimEnter works, see vim's helpscreen with :h VimEnter.

I set the function to return if there are command line arguments, the buffer isn't empty, vim isn't invoked by vim or gvim, or if I start in insert mode:

Then, I set a bunch of local options for the new buffer:

Then, I fill the content of the buffer with my ascii art:

I set some specific commands for this buffer:

To disable scrolling, I changed the scroll mappings on this buffer only:

And that's it! If you're curious, you can find my full init.vim file on Github.

 λ vst lap


text:
zbMATH — the first resource for mathematics

Gaussian random functions, Gaussian random vectors. (Fonctions aléatoires gaussiennes, vecteurs aléatoires gaussiens.) (French) Zbl 0902.60030
Montréal: Les Publications CRM. 217 p. (1997).
This monograph collects and unifies a tremendous amount of pure-mathematical research on the path behavior of Gaussian processes, at the same time presenting extensions to processes with values in Fréchet or Banach spaces. These extensions are surprisingly natural and painless, and allow statements about processes with higher-dimensional time parameter to be proved along with results for times in $${\mathbb{R}}^+$$. A central technical theme of the book is that Gaussian processes with general time-parameter can be represented linearly in terms of an integer-indexed white-noise Gaussian sequence, after which general topological constructions and isoperimetric-type inequalities give qualitative information about path behavior.
The Gaussian process properties treated in the book include 0-1 laws (Chapter 1); the comparisons (Chapter 3) of tail-probabilities for process suprema $$\sup_t X_t$$ against corresponding tail probabilities of processes $$Y_t$$ such that $$E(X_s-X_t)^2\leq E(Y_s-Y_t)^2$$ $$\forall s,t$$; path-boundedness and continuity (Chapters 4, 5); and iterated-logarithm and Strassen-type asymptotic laws characterizing almost-sure functional limits of process trajectories (Chapter 6). Final chapters are devoted to the already mentioned extensions to processes with general time-parameter and to the regularity of random Fourier series with coefficient sequence invariant in law under sign-changes. The book is essentially definitive on the Gaussian-process topics it covers, which have been largely completed as research areas over the course of the past 30 years. The author has been a prime contributor to this development, especially in the 70’s, and the particular unifying approaches of this book have been foreshadowed in several of his later papers.
Other topics, involving Gaussian processes but requiring different mathematical tools, are not even touched on in the book under review: the fine structure of Brownian motion, ergodic theory of Gaussian processes, multiple Wiener-Itô stochastic integrals, and level- and curve-crossing behavior. In particular, no mention is made of non-mathematical applications of the material of the book, such as the extensive uses in engineering and statistical signal-processing of the special features of Gaussian processes. As a result, much of the underlying motivation and history have been abstracted away: for example, Slepian’s (1962) applied motivations (related to level-crossings by stationary processes) for studying comparison inequalities play no role in the book, and the elegant result (Theorem 3.2.5) which subsumes Slepian’s is not specialized to reproduce his famous lemma.
The primary tools used in the book are the theory of probability on metric spaces, isoperimetric inequalities, duality theory of Frechet and Banach spaces, reproducing kernel Hilbert spaces, metric entropy and majorizing measures. The author does a remarkably clear job of summarizing the background theory which he assumes the reader has seen elsewhere, so much so that this research monograph could successfully – if properly supplemented by classical references on these tools – be used for teaching an advanced graduate course, which would be nearly self-contained with respect to coverage of Gaussian processes. However, in a course there would need to be many more examples. Perhaps the most beautiful aspect of the book – which makes it unique, as far as the reviewer is aware – is its unified treatment of the deep and thoroughgoing connection between the reproducing kernel Hilbert space (RKHS) associated with a Gaussian process and its path behavior.
The background theory is given in Chapter 2, including a very modern (i.e., abstract) treatment of the representations by random series which were formerly called Karhunen-Loève expansions. There also is introduced the powerful isoperimetric-type inequality of Sudakov-Tsirelson-Borell, which is the primary vehicle through which the RKHS continues to reappear in the treatment of path-boundedness and continuity in later chapters. One of the technical features of Gaussian processes which makes them special among stochastic processes is the possibility of bounding $$E \sup_t X_t$$ (both above and below) simply in terms of underlying process characteristics. As the author says in Chapter 5, “in all estimates regarding Gaussian processes, one remarks the phenomena of decoupling … which lead to bounds on a quantity of the type $$E \sup_t X_t$$ in terms of another quantity of the type $$\int \varphi(\mu) \mu(du)$$” [where $$\mu$$ is the law of the process]. The theory of majorizing measures, expounded in Chapter 5, gives the highest development of this idea, providing detailed treatment of Talagrand’s (relatively recent) solution of the long-standing problem of characterizing those (nonstationary) Gaussian processes which have continuous sample paths.
The organization of the material in the book is impeccable, and the writing is very clear, but there are some (not many) flaws in exposition, mostly related to the omission of standard examples which would motivate certain key results and render them more understandable. For instance, after a beautiful presentation of a very general result (Theorem 6.7.2), a generalization of a theorem of T. L. Lai [Z. Wahrscheinlichkeitstheorie Verw. Geb. 29, 7-19 (1974; Zbl 0272.60024)] connecting Strassen-type laws on the set of almost-sure limit points of paths in function space of a sequence of identically distributed Gaussian processes to their RKHS, the author omits explaining to the reader why the result essentially contains (as a very special case!) Strassen’s celebrated functional form of the law of the iterated logarithm for Wiener process. The book generally has rather few, but very well-chosen, examples. There are some, but relatively few, misprints. Although the book has no index, the results are presented in such a way that the key theorems in each chapter are easy to refer to. In summary, this is a beautiful book, rewarding for all researchers and advanced students in abstract probability theory who read French.

MSC:
 60G15 Gaussian processes 60-02 Research exposition (monographs, survey articles) pertaining to probability theory 60G17 Sample path properties 60B11 Probability theory on linear topological spaces


text:
What's new

# Standard Deviation of Credit Losses

#### dtammerz

##### Member
Subscriber
Hello,

in the BT Notes VRM Ch.6 (Credit Risk) p.17, in both the common standard deviation of loss as well as the ratio of portfolio standard deviation to the size of the portfolio, why does L=1? Is it always 1?

#### emilioalzamora1

##### Well-Known Member
Hi @dtammerz,

"L" in this case denotes the principal amount of the loan. For simplicity it is assumed 1; L = 1 in this case. L = 1 Million.

Hope this helps!

#### dtammerz

##### Member
Subscriber
Hi @dtammerz,

"L" in this case denotes the principal amount of the loan. For simplicity it is assumed 1; L = 1 in this case. L = 1 Million.

Hope this helps!
Thanks so much. This is helpful indeed.


text:
# DC Motor - need replacement [closed]

Ok I’m am hoping someone can help me. THREE of my 4 door locks stopped working. Dealer quotes me $500 (parts, labor, tax) or$200 (parts, tax). Quote to myself to fix

FC-280ST-16200
KD603713

Internet searches are proving it difficult to get a match of the last five digits. of FC-280ST-XXXXX or if I do find a match I am unable to buy from the manufacturer who my guess designed specifically SUBARU. How important are these last five digits and how risky is it to install a part whose last digits are different?

I found a spec sheet for FFC-280ST and wonder is it ok to use those specs to aid in my search finding a similar replacement? Any DC motor experts out there who can help me locate a little DC motor which can replace my broken ones?

• Did you try searching by make and model of the car instead? For example: "toyota camry door lock motor." Just a suggestion. – mkeith Feb 1 at 18:45
• Yes. No luck. Returns the entire part since the DC Motor is not sold alone. 2014 SUBARU FORESTER. I essentially extracted the motor from the part and will put back together once I find a replacement – KrazyKat Feb 1 at 18:52
• If you are in the US I would be tempted to buy this part for 10 bucks and see if it works. amazon.com/Central-Actuator-FC-280PC-22125-Spindle-Locking/dp/… – mkeith Feb 1 at 19:02
• They will all differ in winding details : lower "no load" speed corresponds with higher torque, less current use, lower stall current. So if you pick the 10000 rpm one it'll stress the wiring a bit less, have more torque, and the lock may operate a little slower. That would be my choice unless I still had one working one - then I'd measure it. Edit : funnily enough it's number is -16200, matching your photo. – Brian Drummond Feb 1 at 19:07
• @KrazyKat I wouldn't think twice about replacing the motors. I'd just do it, with some personal testing. You have a fourth "working" door lock. So you can measure the current under load, etc. I'd do that, as well, to use in evaluating motors. They are cheap enough, so I'd just have fun with this. I had a motorized window on a car where the only "part" they could sell me was \$200, which included a lot of stuff that was still working just fine -- an entire assembly. I just tore it down and replaced the one part that had "worn out" (it was plastic -- so I created a 3D printer part to replace it.) – jonk Feb 1 at 19:14