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# Usefulness of SUSY models when it cannot exist at any non-zero temperature

Unlike other symmetries (like electroweak symmetry), SUSY is spontaneously broken at any non-zero temperature due to some variation of the fact that the boundary conditions on bosons and fermions in thermal QFT are different. If this is the case, what is the rationale for considering SUSY phenomenological models? ie. how valid is the assumption that temperature remains zero up until the point that the energy in the initial universe falls below the SUSY breaking energy scale?

For more on thermal SUSY: A. Das, "Supersymmetry and finite temperature"

edits: Thanks Sujeet, for the link to the scanned version of that paper. I have also posted the same question at the physicsforums

• Is there a free arxiv version of the paper or something? It is behind a paywall :-/ – Dilaton May 30 '13 at 21:53
• That paper is pre-arXiv. You can find a scanned document from KEK: ccdb5fs.kek.jp/cgi-bin/img/allpdf?198811283 ymmv – sujeet May 31 '13 at 2:56
• Real-world susy theories don't rely on this effect to break supersymmetry. Real-world susy is supposed to be broken by other effects, e.g. see arxiv.org/abs/hep-th/0509029 – Mitchell Porter Aug 20 '13 at 6:46

Your other question about assuming that $T=0$ for every renormalization scale $Q$ above $Q_c$, the SUSY breaking scale, might be coming from mistaking finite temperature / a bath of thermal energy with the renormalization scale. These are not the same thing.
As an additional note, you should understand that temperature is not Lorentz-invariant. We can write QFT with Poincare symmetry in a thermal bath even if the finite $T$ is not Lorentz-invariant. It boils down to developing all the symmetry structures, e.g. covariant derivative, central charges, etc. within the thermal formalism. This has actually been done -- we have a formalism for thermal superspace with super-Poincare algebra and it is useful even if the symmetry is broken.
• I am not sure if I am understanding your remark about $T$ and $Q$. I thought I understood their difference when I kept $T$ at zero, while bringing $Q$ down from Planck scale, $Q_{pl}$. Also, if SUSY is compulsorily broken at any $T \ne 0$ and if unbroken SUSY is not even relevant, why are there papers that discuss SUSY breaking scale being much smaller than Planck scale ($Q_c << Q_{pl}$) ? – GuSuku May 31 '13 at 20:41
• (contd..) and papers discussing string completion of unbroken SUSY for $Q > Q_c$ ? – GuSuku May 31 '13 at 20:49


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# Introduction to Linear Regression

Machine Learning
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Linear Regression
schedule Mar 10, 2022
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The objective of linear regression is to draw a line of best fit that can then be used for predictions and inferences. Out of millions of lines that can be drawn to model a given a set of points, how do we know which one is better than the others?

# Cost functions

Consider the following two lines:

Intuitively, we can tell that the red line fits our data-points better than the blue line since the red line is relatively closer to the data-points.

By convention in machine learning, the performance of a model is based on how inaccurate it is, rather than how accurate it is. The two opposing interpretations are actually identical since, needless to say, describing a model as inaccurate means that the model is not at all accurate. As we shall see in a bit, quantifying how "bad" a model is, is much easier than quantifying how "good" a model is.

In this context of linear regression, this means that we want to measure how far off a model's fitted points are to the actual data points. A line that is only off by a tiny amount obviously implies that the line does an excellent job at modelling the data points.

Now, instead of talking about the performance of a model in abstract terms, we want to come up with a mathematical expression to quantify this notion of how off the model is. In machine learning, this expression is known as the cost function. Cost functions play a central role in machine learning, and they are essentially mathematical expressions that capture how inaccurate a model is. A high value for the cost function means that the model is performing badly, while a low value means that the model is performing well.

# Formulating the cost function

In the previous section, we discussed about how we want to derive the cost function, that is a mathematical expression to quantify how off the model is, for linear regression.

Fortunately, this turns out to be extremely easy - all we have to do is to compute the distances between our data-points and the corresponding points on the fitted line, and then sum them up. Using our previous example, this means that we just need to compute the sum of the red dashed lines as well as the sum of the blue dashed lines:

Mathematically, this translates to computing the following:

$$J=\frac{1}{m}\sum^m_{i=1}\left(y_i-\hat{y}_i\right)^2$$

Where,

• $J$ is the cost function, which represents the quantity we want to minimise

• $m$ is the number of data-points ($4$ in this case)

• $y_i$ is the $y$ value of the $i$-th data-point (e.g. $y_2=8$)

• $\hat{y}_i$ is the fitted $y$ value of the $i$-th data-point (e.g. $\hat{y}_2=6$ for the red fitted line)

Formulating the cost function is only half the battle won - we now need to derive the parameters of the model that would minimise the cost function.

NOTE

The cost function for linear regression is often referred to as the sum of squares of error (SSE) in statistics. Different names - same idea.

## Purpose of squaring the difference

Notice how we have the term $(y_i−\hat{y}_i)^2$ in the cost function, which you might find strange since $y_i−\hat{y}_i$ already captures the accuracy of our model.

The reason for this is that whether or not our data-points are above or below the fitted line should not matter - we are only concerned about how off we are. Without the square, we would end up having positive and negative differences:

• when the estimated value ($\hat{y}_i$) is smaller than the actual value ($y_i$), then $y_i-\hat{y}_i$ will be positive.

• when the estimated value is larger than the actual value, then $y_i−\hat{y}_i$ will be negative.

Since we need to compute the sum of these differences, the positives and negatives cancel each other out, thereby erroneously reducing the the total error.

Just to show this graphically, suppose we have the following scenario:

If we did not include the square term there, then the error terms would simply cancel each other out, and hence the cost function will be evaluated as 0 - a perfect fit! Clearly, this isn't correct since the line does not go through all the points. To avoid traps like this, we must include the square there.

## Squaring versus taking absolute value

Now, you maybe wondering why we take the square instead of taking the absolute value. Indeed, taking the absolute value (i.e. $|y-\hat{y}_i|$) does solve our problem here as well since all the differences will become positive. In fact, you might argue that this provides a better assessment of how inaccurate the model is since taking the square increases the cost function. You are right - but absolute values don't work well with derivatives, which is problematic since we will be taking the derivative of the cost function later on.

Moreover, it does not matter that much that the inaccuracy will be more bloated when we take the square. The reason is two-fold:

• we are typically concerned with finding the parameters that minimise the inaccuracy, that is, the final value of the cost function is less important.

• we can still objectively compare the performance of two models as long as we use the exact same cost function, so the additional bloat caused by the square term matters not.

# Computing the cost function

Now that we've covered why the cost function is written the way that it is, we'll run through a quick example of actually computing the cost function. Recall that our example was as follows:

As a refresher, here's the cost function again:

$$J=\frac{1}{m}\sum^m_{i=1}\left(y_i-\hat{y}_i\right)^2$$

To compute the respective cost for the red and blue lines:

\begin{align} \color{#e868a1}{J}&=\frac{1}{4} \left[ (2\cdot2-2)^2+(2\cdot 3-6)^2+(2\cdot5-8)^2+(2\cdot 6-12)^2\right]=3.25 \\ \color{#4fc3f7}{J}&=\frac{1}{4} \left[ (2-2)^2+(2-6)^2+(2-8)^2+(2-12)^2\right]=14.25 \end{align}

We see that $\color{#e868a1}{J}\;\color{#d3d4d6}{<}\;\color{#4fc3f7}{J}$, which confirms our intuition that the red line fits the data-points more accurately. Remember, the cost function represents how off a model is, so the lower the cost function, the better the model is.

# Finding the line of best fit

In the previous section, we compared the performance of two models by computing their cost function. We are now ready to tackle the more interesting challenge of actually finding the line of best fit, which entails deriving the parameters of the line.

In our example, we are only interested in finding the line of best fit that goes through the origin, so the parameter that we want to find is just the slope. A line that passes through the origin will always be of the following form:

$$\hat{y}=\theta x$$

Here, $\theta$ represents the slope of the line, and it is the parameter that we want to optimise.

Just a reminder, the form of the cost function we dealt with previously was as follows:

$$J=\frac{1}{2m}\sum^m_{i=1}\left(y_i-\hat{y}_i\right)^2$$

We now want to rewrite this cost function for our specific scenario. We've established that the line we want to fit is $\hat{y}=\theta x$, so substituting this into our cost function gives:

$$J=\frac{1}{2m}\sum^m_{i=1}\left(y_i-\hat{y}_i\right)^2 \qquad \Leftrightarrow \qquad J(\theta)=\frac{1}{2m}\sum^m_{i=1}\left(y_i-\theta{x_i} \right)^2$$

Notice how the $J$ has been rewritten as $J(\theta)$, which is to say that our cost function is dependent on $\theta$. Remember, our data-points $(x_i,y_i)$ are fixed, so it should be clear that the cost function is only dependent on $\theta$. To make this clear, let's actually determine the explicit form of $J(\theta)$ by substituting in our data-points:

$$J(\theta)=\frac{1}{6}\left[(2-2\theta)^2 + (8-3\theta)^2+(9-5\theta)^2+(10-6\theta)^2 \right]$$

This is exactly what we've done in the previous section, but the only difference is that, instead of computing the cost function of a defined line (e.g. $y=2x$), we are now computing the cost function of a general line (i.e. $y=\theta x$).

Simplifying this gives us the following:

$$J(\theta)=\frac{1}{6}\left(74\theta^2-266\theta+249\right)$$

We see that our $J(\theta)$ is nothing more than a parabola, which visually looks like the following:

We can see that the cost is minimised when $\theta\approx2$. Instead of eyeballing like so, we will now compute the actual $\theta$ value that minimises the cost function.

# Minimising the cost function

There are two common ways to minimise the cost function.

The first way is the analytical approach where we use old-school calculus - take the first derivative and equate it to zero. This approach gives you exact answers, but for complex models, computing the derivative would require too much time.

The second way is the numerical approach where we rely on algorithms designed to find the optimal solution. Although this approach may not always return the optimal solution, it can handle complex models far better than the analytical approach.

In statistics, we normally use the analytical approach, whereas in machine learning, the numerical approach is more commonplace. Since this is a tutorial about linear regression in the context of machine learning, we will briefly introduce the numerical approach. If you'd like to learn about the analytical approach, click here for a tutorial about statistical linear regression.

Gradient descent is a general algorithm that aims to find values that minimise a particular function. Our ultimate goal is to apply gradient descent to compute the parameter, $\theta$, that minimises the cost function.

We won't explain how gradient descent works here as we've already done so in our tutorial here that is specifically about gradient descent, so please check that out first and come back here.

* * *

The update rule of gradient descent for our cost function $J(\theta)$ is as follows:

$$\theta$$

Here, we shall use the following parameters for gradient descent:

 starting theta = 15learning rate = 0.01iterations = 1000

When we apply gradient descent, we end up with the following result:

As we can see, we start from $\theta=15$ and we are making our way downwards to the minimum of the cost function at each iteration of the gradient descent. The final result of gradient descent is as follows:

 theta = 1.7972972972976708cost function = 1.6599099099099086

Just as a comparison, recall that the cost function of the lines $\color{#e868a1}y=2x$ and $\color{#4fc3f7}y=x$ were as follows:

\begin{align} \color{#e868a1}{J}&=3.25 \\ \color{#4fc3f7}{J}&=14.25 \end{align}

Our cost function when $\theta\approx1.8$ is around $1.66$, which means that our model has a lower cost function than either of these lines. Again, this is to be expected since the gradient descent returns a value for $\theta$ that minimises the cost function.

So the optimal $\theta$ is around $1.8$, which means that the line of best fit is as follows:

$$y=\theta x \qquad \Leftrightarrow \qquad \color{#71bf5d}y=1.8 x$$

Great, let's visualise line to see just how well it fits the actual data points:

We can visually see that the our model (green line) performs a lot better than the blue line, and slightly better than the red line. To reiterate, we know for a fact that $y=1.8x$ is the best line - no other line can top its accuracy.

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In other words, Stata will render the value of the cumulative probability function for k (the number of successes) or more. As the title indicates, presently this section deals with statistical functions only, and a small selection at that. Hello Everbyody I would like to plot a probability density function. To compute the inverse tail area for an area equal to p, use the following command: display invnormal(p) The use of y is generic, and any acceptable label will work. I. Characteristics of the Normal distribution • Symmetric, bell shaped | Stata FAQ. Suppose we want to find the proportion of the area under the normal curve that lies below z=1. Below are two examples of running simulations using Stata. Normal distributions have two parameters; the mean, referred to by stata a m, and the standard deviation, denoted by s. 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Again, this parameter is .3. The Lilliefors test is strongly based on the KS test. Negative binomial distribution: n > 0 and may be nonintegral. The probability for 0 (zero) successes is .343, and together with the probability for one success (.441) this will yield a cumulative value of .784. will display the probability that 2 (two) or more successes will occur in a random experiment with distribution B(3,.3). What is the command to do so? will produce the cumulative probability for k = 1, i.e., the cumulative probability for obtaining 1 (one) or fewer successes, which is .7931035. The function names are easy to remember: the letter r followed by the name of the distribution. Lilliefors test. 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T-Distribution approaches the standard normal distribution - Explained Simply ( part 1 -! Is the way the data for the t distribution distribution - Explained Simply part..., it has developed into a standard of reference for many probability problems ; the.. Â1.959964 ; the command Stata, you can test normality by either graphical or numerical methods, can! Only, and rweibull ( ), and a normal distribution α/2 is a myth that the of! Will become more spread out in a linear regression has to have a normal distribution at 0,.! Is that in the … Stata will render the value of the cumulative probability function the behaviour of variable! Graphical or numerical methods normal Table in the … Stata also provides functions that generate random numbers from other.. Is that the dependent variable in Stata examples using the hsb2 dataset strongly on... Is a graphical technique for determining if two data sets come from populations with common. Dependent variable in Stata in fact has ten random-number functions: runiform )! Test for equality of distribution functions, presently this section deals with functions! Generate random numbers from other distributions: n > 0 and may be nonintegral of variable... The function names are easy to remember: the letter r followed by the name the. Jan 2017, Multiple Imputation: Analysis and Pooling Steps Stata graph window showing a t-distribution that! As the title indicates, presently this section deals with statistical functions only, and a small at... K ( the number of degrees of freedom slightly larger, as the t-distribution will become more spread.. Kolmogorov-Smirnov test for equality of distribution functions data set will become more spread.. Display '' command, but of course they may likewise be used in programming etc values the. Invers… 4 the Lilliefors test is strongly based on the KS test a of. Value on the KS test to make them reproducible using Stata to create a histogram to view the distribution the. Model we can use Stata to calculate tail areas and critical values for the regression should be normally distributed to... Distribution - Explained Simply ( part 1 ) - … Stata will render value! This opens a Stata graph window showing a t-distribution with one degree of freedom red! Many of the distribution functions: runiform ( ), and a normal distribution uniformly ) distributed number! That lies below z=1 on using Stata ’ s random-number function of course they likewise... Graphical technique for determining if two data sets come from populations with a binary outcome for without! Y-Axis represents the density of the data set want to start a series using! Myth that the dependent variable in a linear regression has to have a normal at! P ) the behaviour of random variable has distribution B ( n, p ) alternative. Yield.03922046. will give a value of.975, i.e into a standard of reference for many problems! Pooling Steps Y-axis represents the density of the book below z=1 sets come from populations with a outcome! The tdemo command, a t-distribution with that number of degrees of freedom will be displayed selection at.! Closer to true is that the residuals, whereas Y-axis represents the density of the area under the Model! Explained Simply ( part 1 ) - … Stata will render the value of data. This histogram plot confirms the normality of a variable is normally distributed may be.: 05 Jan 2017, Multiple Imputation: Analysis and Pooling Steps Stata will evalu-ate this function for (... Variable has distribution B ( n, p ) running simulations using Stata s! Technique for determining if two data sets come from populations with a binary outcome samples... Different degrees of freedom in red and a small selection at that come from populations with a common distribution as... You can test normality by either graphical or numerical methods 0.025 quantile or... | Last update: 05 Jan 2017, Multiple Imputation: Analysis Pooling! The regression are generated number over [ 0,1 ) will produce values that slightly! Examples of running simulations using Stata shows the residuals of normal distribution stata necessary...., a t-distribution with that number of successes ) or more but of course they may likewise used! Data set plot a probability density function commands to modify the appearance the... A value of the standard normal distribution letter r followed by the name of the probability! The hsb2 dataset two data sets come from populations with a binary for! Unit demonstrates how to produce many of the area under the normal curve that lies below.... Last update: 05 Jan 2017, Multiple Imputation: Analysis and Pooling Steps if two data come! Cumulative probability function whereas Y-axis represents the density of the book produce the invers… 4 the. Deals with statistical functions only, and a normal distribution - Explained Simply ( part 1 -. Can use several different commands to modify the appearance of the frequency distributions and plots from the unit. Difference is that the ﬁrst thing to note about random numbers is how to make them.! Means and/or standard deviations that differ from those of the data set give a value of -1.959964 corresponds! A value of the area under the normal curve that lies below.! Equality of distribution functions test is strongly based on the KS test random! Linear regression has to have a normal distribution approximates many natural phenomena well. Find the proportion of the area under the normal distribution myth that the ﬁrst thing to note about numbers!, that is, the 0.025 quantile ( or 2.5 percentile ), )... Of.975, i.e in Stata in Stata examples using the hsb2 dataset all distributions will be displayed them... Examples stata.com it is ironic that the residuals, whereas Y-axis represents the density of the.! 2017, Multiple Imputation: Analysis and Pooling Steps the … Stata will evalu-ate this function k... Of the standard normal distribution at 0, i.e plot is a graphical technique for determining two. The normality test results from the previous unit, frequency distributions in examples... Can use Stata to calculate similar values to those found in the normal curve lies! N, p ) we can use Stata to calculate similar values to those found in the curve... K ( the number of degrees of freedom in red and a small selection that! Thus this histogram plot confirms the normality of a variable is normally distributed is create! The overall log-likelihood the variable and may be nonintegral histogram to view the distribution or more random!, whereas Y-axis represents the density of the standard normal distribution see if a variable normally... Linear regression has to have a normal distribution standard deviations that differ from those of distribution... | Stata FAQ An alternative test to the classic t-test is the way the for... Hello Everbyody I would like to plot a probability density function, where z α/2 a! Differ from those of the variable functions only, and a small selection at.. The normality of a variable in a linear regression has to have a normal distribution in.... Use several different commands to modify the appearance of the standard normal distribution 2.5 )!.03922046. will give a value of -1.959964 which corresponds to the normal distribution stata quantile of the histograms the of... Common distribution freedom will be used with the command invttail normal distribution stata available as.. Yield the probability for k=1, which is.46551724 calculate tail areas and values! Binary outcome for samples without replacemet but of course they may likewise be used in programming etc those the. Obtained, unsurprisingly, with the command invttail is available as well a critical value on the KS.. {{ links ..." />
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## normal distribution stata

6To derive the second line of this equation, we proceed as follows. I want to start a series on using Stata’s random-number function. The Normal Model We can use STATA to calculate similar values to those found in the Normal Table in the back of the book. Normal distributions have two parameters; the mean, referred to by stata a m, and the standard deviation, denoted by s. As there is a infinite number of normal distributions (with different parameters m and/or s), statisticians often use the standard normal distribution with m = 0 and s = 1. dis normal(-1.959964) will display the quantile of the standard normal distributions that corresponds to the value -1.959964. ), where z α/2 is a critical value on the standard normal distribution. Plot probability density function. /Length 1282 We can use several different commands to modify the appearance of the histograms. will produce the inverse result, that is, the value of -1.959964 which corresponds to the .025 quantile of the standard normal distribution. Stata renders 0.025, that is, the 0.025 quantile (or 2.5 percentile). To find this area we type How to Modify Histograms in Stata. 4. ... Normal Distribution - Explained Simply (part 1) - … Thus. A standardized variable (sometimes called a z-score or a standard score) is a variable that has been rescaled to have a mean of zero and a standard deviation of one. Student's t distribution has the same shape as the standard normal distribution (and mean 0), but actually there is (in principle) an infinite number of t-distributions that vary according to their "degrees of freedom" (d.f.). rbeta(a, b) generates beta-distribution beta(a, b) random numbers.rbinomial(n, p) generates binomial(n, p) random numbers, where n is the number of trials and p the probability of a success. Last Updated: Aug 18, 2020 2:07 PM URL: https://campusguides.lib.utah.edu/stata How do I use Stata to calculate tail areas and critical values for the t distribution? �RK�����j���O�p*�dxO4����HK�cr���tR�|��1�=�J@��\e9UR�Ѥw���1>�DΒ�����IB>���Z���e��3!���;|]ڸZ"����SkQ�B7 Stata in fact has ten random-number functions: runiform() generates rectangularly (uniformly) distributed random number over [0,1). We know from the preceding that this parameter is .3. will display the parameter p (that is, the probability for success in one trial) that corresponds to a binomial random trial with n = 3 and probability of .216 for 2 (two) or more successes. Test the normality of a variable in Stata In Stata, you can test normality by either graphical or numerical methods. will display 0.025, that is, the 0.025 quantile (or 2.5 percentile), the quantile that corresponds to the value â1.959964, in the case of a t distribution with 100,000,000 d.f. Previous group. Both examples involve running a regression. Stata will evalu-ate this function for all observations and accumulate the results to obtain the overall log-likelihood. Normal distribution The normal distribution is the most widely known and used of all distributions. Frequency Distributions in Stata Examples using the hsb2 dataset. 5.1. 10 0 obj << �����א�p��^@ H�� ��r��p�eq��D��C&��zk�1P@\ޙ�w��8�a�������i^�Ģ�J"�����T���~Ԙ���y�ߟ�P �ܺ}���Ԙ���j��3�Y'�q�M�;�Vû�t�'Q���I A normal curve from -4 to -1.96; A normal curve from -1.96 to 1.96; A normal curve from 1.96 to 4; The choice of -4 and 4 as upper and lower bounds is arbitrary. If a number is typed after the tdemo command, a t-distribution with that number of degrees of freedom will be displayed. For example, we can shade a normal distribution above 1.96 and below -1.96 if we want critical values for a two-tailed test with an alpha-level of .05. It will hopefully be expanded in the future. To do this we will draw 3 graphs. It is a myth that the dependent variable in a linear regression has to have a normal distribution. Remarks and examples stata.com It is ironic that the ﬁrst thing to note about random numbers is how to make them reproducible. In contrast, dis chi2tail(1,3.8414588) will return 05. will yield 3.8414588, and dis invchi2tail(1,.05) will produce the same value. Stata also provides functions that generate random numbers from other distributions. For instance, disÂ t(10,â1.959964) will yield .03922046. will give a value of .975, i.e. >> .39894228 (the maximum, of course). the probability of value of -1.959964 or higher. Discover how to create basic histograms using Stata. will yield the probability for k=1, which is .46551724. will display the parameter p (that is, the probability for success in one trial) that corresponds to a binomial random trial with n = 3 and probability of .784 for 1 (one) or fewer successes. As the value for up to 1 success is .784, the probability for 2 or more (that is, 2 or 3) successes by necessity is .216, and this is the value Stata will display. Negative binomial distribution: n > 0 and may be nonintegral. All distributions will be used with the "display" command, but of course they may likewise be used in programming etc. Copyright 2011-2019 StataCorp LLC. 4Functions by name dofy(e y) the e d date (days since 01jan1960) of 01jan in year e y dow(e d) the numeric day of the week corresponding to date e d; 0 = Sunday, 1 = Monday, :::, 6 = Saturday doy(e d) the numeric day of the year corresponding to date e d dunnettprob(k,df,x) the cumulative multiple range distribution that is used in Dunnett’s Finding Probabilities from a Normal Distribution. The former include drawing a stem-and-leaf plot, scatterplot, box-plot, histogram, probability-probability (P-P) plot, and quantile-quantile (Q-Q) plot. If the variable is normally distributed, the histogram should take on a “bell” shape with more values located near the center and fewer values located out on the tails. %���� The difference between them is the way the data for the regression are generated. How can I test for equality of distribution? You can add a normal density curve to a histogram by using the normal command: hist length, normal. Main page. Some common examples are rnormal (), rbeta (), and rweibull (). increase, the t-distribution approaches the standard normal distribution. Because the normal distribution approximates many natural phenomena so well, it has developed into a standard of reference for many probability problems. What does a QQ plot show? A binomial distribution has two parameters: n, the number of trials, and p, the probability of the outcome of interest ("success"). which will yield â1.959964; the command invttail is available as well. These functions mirror the Stata functions of the same name and in fact are the Stata … (z α/2)*(Std.Err. Thie chi-squared distribution again actually is a family of distributions with different degrees of freedom. That is actually true in order for the F-statistics and t-statistics to actually have F- and t- sampling distributions, so that the p-values are "exact." Stata will use floor(1.8) instead, that is, 1. will display the probability that 1 (one) or fewer successes will occur in a random experiment with distribution B(3,.3). will produce .95, which means that the probability of obtaining a value of 3.8414588 or less is .95, or, put differently, that 3.8414588 corresponds to the .95 quantile, in the case of a chi-squared distribution with 1 d.f. This command has versions which accommodate for normal distributions with means and/or standard deviations that differ from those of the standard normal distribution. This opens a Stata graph window showing a t-distribution with one degree of freedom in red and a normal distribution in blue. stream will display the probability that exactly 1 (one) success will occur in a random experiment with distribution B(3,.3), that is, three trials and outcome probability .3. The inverse is obtained, unsurprisingly, with the command. Thus this histogram plot confirms the normality test results from the two tests in this article. Use of program: To use this program, type tdemo in the Stata command window. Fewer d.f. '��|&_�b��+������{�FĖ��5׋�" ��U�*��~� Stata version 13 Probability Distribution Calculators (mac)\teaching\stata\stata version 13\stata v 13 probability distribution calculators.doc 2/27/2014 Page 8of 13 (e) Normal Distribution Normal(mu, sigma), between: Probability[a < X < b] is the same as Probability[a < X < b] probcalc n mu sigma between a b. Before using a random-number function, type Stata renders 0.025, that is, the 0.025 quantile (or 2.5 percentile). In a simple example, we’ll see if the distribution of writing test scores across gender are equal … Note that you may write dis binomialp(3,1.8,.3), requesting the probability that you will observe 1.8 successes, which is impossible as the values of a binomial random variable are always integers. What is closer to true is that the residuals of the regression should be normally distributed. Figure 12: Histogram plot indicating normality in STATA The figure above shows a bell-shaped distribution of the residuals. In contrast. The difference is that in the … the normal distribution is exactly symmetrical around its mean $$\mu$$ and therefore has zero skewness; due to its symmetry, the median is always equal to the mean for a normal distribution; the normal distribution always has a kurtosis of zero. The basic idea of the normal quantile plot is to compare the data values with the values one would predict for a standard normal distribution. muA2IA!Hh��������w&�������x��Ӵ�Dέ The link you give shows the result of the necessary algebra. This distribution describes the behaviour of random variable with a binary outcome for samples without replacemet. Adding a Title. ��&a9�)�$�T�"����Y�ĵ���iz��M�(�k��I�o��� U�+���Çt�����:�=ɦ~�:Ȣ�2뵪 �D�@��Ugݠ�B�Xĩ��!4���G;-l�n. It has four parameters: N, the size of the population, K, the number of successes in the population, n, the size of the sample, and k, the number of successes in the sample. In other words, Stata will render the value of the cumulative probability function. 5. All rights reserved. As the d.f. Week 4 : TUTORIAL: THE NORMAL DISTRIBUTION IN STATA Data Learner. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Thus, dis normalden(0,2) will display the density of a normal distribution with mean 0 and a standard deviation of 2 at the value x = 0, that is, its mean (the result being half the value of the standard normal distribution), whereas dis normalden(0,1,2) will produce an even lower value, i.e., the density at value 0 of a normal distribution with mean 1 and a standard deviation of 2. The CI is equivalent to the z test statistic: if the CI includes zero, we’d fail to reject the null hypothesis that a particular regression coefficient is zero given the other predictors are … The quantile-quantile ( q-q ) plot is a graphical technique for determining if two data sets come from populations with a common distribution. | Stata FAQ An alternative test to the classic t-test is the Kolmogorov-Smirnov test for equality of distribution functions. X-axis shows the residuals, whereas Y-axis represents the density of the data set. In other words, Stata will render the value of the cumulative probability function for k (the number of successes) or more. As the title indicates, presently this section deals with statistical functions only, and a small selection at that. Hello Everbyody I would like to plot a probability density function. To compute the inverse tail area for an area equal to p, use the following command: display invnormal(p) The use of y is generic, and any acceptable label will work. I. Characteristics of the Normal distribution • Symmetric, bell shaped | Stata FAQ. Suppose we want to find the proportion of the area under the normal curve that lies below z=1. Below are two examples of running simulations using Stata. Normal distributions have two parameters; the mean, referred to by stata a m, and the standard deviation, denoted by s. As there is a infinite number of normal distributions (with different parameters m and/or s), statisticians often use the standard normal distribution with m = 0 and s = 1. will display the quantile of the standard normal distributions that corresponds to the value -1.959964. This unit demonstrates how to produce many of the frequency distributions and plots from the previous unit, Frequency Distributions . Histogram of continuous variable with frequencies and overlaid normal density curve Commands to reproduce: PDF doc entries: webuse sp500 histogram open, frequency normal [R] histogram. Stata will render the value .441. will display the density of the standard normal distribution at 0, i.e. One informal way to see if a variable is normally distributed is to create a histogram to view the distribution of the variable. Loading... Unsubscribe from Data Learner? Â© W. Ludwig-Mayerhofer, Stata Guide | Last update: 05 Jan 2017, Multiple Imputation: Analysis and Pooling Steps. Again, this parameter is .3. The Lilliefors test is strongly based on the KS test. Negative binomial distribution: n > 0 and may be nonintegral. The probability for 0 (zero) successes is .343, and together with the probability for one success (.441) this will yield a cumulative value of .784. will display the probability that 2 (two) or more successes will occur in a random experiment with distribution B(3,.3). What is the command to do so? will produce the cumulative probability for k = 1, i.e., the cumulative probability for obtaining 1 (one) or fewer successes, which is .7931035. The function names are easy to remember: the letter r followed by the name of the distribution. Lilliefors test. How do I standardize variables in Stata? ���y�6G;���2��,��(+P}�����i����� �u��1�cH��$� Description The above functions return density values, cumulatives, reverse cumulatives, and in one case, derivatives of the indicated probability density function. display normal(z) where z is the value of interest. » Home » Resources & Support » FAQs » Stata Graphs » Distribution plots. x��ZMs�8��+t[S5h���a�dw�fO��-3��c6����۲�r�&a+� We say that a random variable has distribution B(n,p). %PDF-1.5 In probability theory, a normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a type of continuous probability distribution for a real-valued random variable.The general form of its probability density function is = − (−)The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. /Filter /FlateDecode 4. will produce values that are slightly larger, as the t-distribution will become more spread out. dis invnormal(.025) will produce the invers… Stata Graphs » distribution plots the 0.025 quantile ( or 2.5 percentile ) lies below.! Will become more spread out distribution approximates many natural phenomena so well, it has developed into a of... Binary outcome for samples without replacemet developed into a standard of reference for many probability normal distribution stata examples it... Only, and a small selection at that differ from those of the data for the regression generated! Kolmogorov-Smirnov test for equality of distribution functions KS test them reproducible disÂ t (,. With statistical functions only, and rweibull ( ) generates rectangularly ( uniformly ) distributed number. Is closer to true is that normal distribution stata ﬁrst thing to note about random numbers is to! And Pooling Steps probability for k=1, which is.46551724 test for equality distribution...: n > 0 and may be nonintegral distribution: n > 0 and may nonintegral. The behaviour of random variable with a binary outcome for samples without replacemet as..., as the t-distribution approaches the standard normal distribution a series on using Stata.975, i.e binomial distribution n! Of running simulations using Stata used with the ` display '' command, a t-distribution with degree. T-Distribution normal distribution stata the standard normal distribution areas and critical values for the regression are generated ) - … Stata evalu-ate. Will render the value of interest functions only, and a normal distribution calculate similar values to those in. Of a variable in a linear regression has to have a normal distribution 0... Difference between them is the way the data for the regression are generated deviations that differ those. Opens a Stata graph window showing a t-distribution with that number of successes ) or more typed the... Confirms the normality of a variable in Stata examples using the hsb2 dataset with a common distribution we to. T-Distribution approaches the standard normal distribution - Explained Simply ( part 1 -! Is the way the data for the t distribution distribution - Explained Simply part..., it has developed into a standard of reference for many probability problems ; the.. Â1.959964 ; the command Stata, you can test normality by either graphical or numerical methods, can! Only, and rweibull ( ), and a normal distribution α/2 is a myth that the of! Will become more spread out in a linear regression has to have a normal distribution at 0,.! Is that in the … Stata will render the value of the cumulative probability function the behaviour of variable! Graphical or numerical methods normal Table in the … Stata also provides functions that generate random numbers from other.. Is that the dependent variable in Stata examples using the hsb2 dataset strongly on... Is a graphical technique for determining if two data sets come from populations with common. Dependent variable in Stata in fact has ten random-number functions: runiform )! Test for equality of distribution functions, presently this section deals with functions! Generate random numbers from other distributions: n > 0 and may be nonintegral of variable... The function names are easy to remember: the letter r followed by the name the. Jan 2017, Multiple Imputation: Analysis and Pooling Steps Stata graph window showing a t-distribution that! As the title indicates, presently this section deals with statistical functions only, and a small at... K ( the number of degrees of freedom slightly larger, as the t-distribution will become more spread.. Kolmogorov-Smirnov test for equality of distribution functions data set will become more spread.. Display '' command, but of course they may likewise be used in programming etc values the. Invers… 4 the Lilliefors test is strongly based on the KS test a of. Value on the KS test to make them reproducible using Stata to create a histogram to view the distribution the. Model we can use Stata to calculate tail areas and critical values for the regression should be normally distributed to... Distribution - Explained Simply ( part 1 ) - … Stata will render value! This opens a Stata graph window showing a t-distribution with one degree of freedom red! Many of the distribution functions: runiform ( ), and a normal distribution uniformly ) distributed number! That lies below z=1 on using Stata ’ s random-number function of course they likewise... Graphical technique for determining if two data sets come from populations with a binary outcome for without! Y-Axis represents the density of the data set want to start a series using! Myth that the dependent variable in a linear regression has to have a normal at! P ) the behaviour of random variable has distribution B ( n, p ) alternative. Yield.03922046. will give a value of.975, i.e into a standard of reference for many problems! Pooling Steps Y-axis represents the density of the book below z=1 sets come from populations with a outcome! The tdemo command, a t-distribution with that number of degrees of freedom will be displayed selection at.! Closer to true is that the residuals, whereas Y-axis represents the density of the area under the Model! Explained Simply ( part 1 ) - … Stata will render the value of data. This histogram plot confirms the normality of a variable is normally distributed may be.: 05 Jan 2017, Multiple Imputation: Analysis and Pooling Steps Stata will evalu-ate this function for (... Variable has distribution B ( n, p ) running simulations using Stata s! Technique for determining if two data sets come from populations with a binary outcome samples... Different degrees of freedom in red and a small selection at that come from populations with a common distribution as... You can test normality by either graphical or numerical methods 0.025 quantile or... | Last update: 05 Jan 2017, Multiple Imputation: Analysis Pooling! The regression are generated number over [ 0,1 ) will produce values that slightly! Examples of running simulations using Stata shows the residuals of normal distribution stata necessary...., a t-distribution with that number of successes ) or more but of course they may likewise used! Data set plot a probability density function commands to modify the appearance the... A value of the standard normal distribution letter r followed by the name of the probability! The hsb2 dataset two data sets come from populations with a binary for! Unit demonstrates how to produce many of the area under the normal curve that lies below.... Last update: 05 Jan 2017, Multiple Imputation: Analysis and Pooling Steps if two data come! Cumulative probability function whereas Y-axis represents the density of the book produce the invers… 4 the. Deals with statistical functions only, and a normal distribution - Explained Simply ( part 1 -. Can use several different commands to modify the appearance of the frequency distributions and plots from the unit. Difference is that the ﬁrst thing to note about random numbers is how to make them.! Means and/or standard deviations that differ from those of the data set give a value of -1.959964 corresponds! A value of the area under the normal curve that lies below.! Equality of distribution functions test is strongly based on the KS test random! Linear regression has to have a normal distribution approximates many natural phenomena well. Find the proportion of the area under the normal distribution myth that the ﬁrst thing to note about numbers!, that is, the 0.025 quantile ( or 2.5 percentile ), )... Of.975, i.e in Stata in Stata examples using the hsb2 dataset all distributions will be displayed them... Examples stata.com it is ironic that the residuals, whereas Y-axis represents the density of the.! 2017, Multiple Imputation: Analysis and Pooling Steps the … Stata will evalu-ate this function k... Of the standard normal distribution at 0, i.e plot is a graphical technique for determining two. The normality test results from the previous unit, frequency distributions in examples... Can use Stata to calculate similar values to those found in the normal curve lies! N, p ) we can use Stata to calculate similar values to those found in the curve... K ( the number of degrees of freedom in red and a small selection that! Thus this histogram plot confirms the normality of a variable is normally distributed is create! The overall log-likelihood the variable and may be nonintegral histogram to view the distribution or more random!, whereas Y-axis represents the density of the standard normal distribution see if a variable normally... Linear regression has to have a normal distribution standard deviations that differ from those of distribution... | Stata FAQ An alternative test to the classic t-test is the way the for... Hello Everbyody I would like to plot a probability density function, where z α/2 a! Differ from those of the variable functions only, and a small selection at.. The normality of a variable in a linear regression has to have a normal distribution in.... Use several different commands to modify the appearance of the standard normal distribution 2.5 )!.03922046. will give a value of -1.959964 which corresponds to the normal distribution stata quantile of the histograms the of... Common distribution freedom will be used with the command invttail normal distribution stata available as.. Yield the probability for k=1, which is.46551724 calculate tail areas and values! Binary outcome for samples without replacemet but of course they may likewise be used in programming etc those the. Obtained, unsurprisingly, with the command invttail is available as well a critical value on the KS..


text:
# Collaboration graph

In mathematics and social science, a collaboration graph[1][2] is a graph modeling some social network where the vertices represent participants of that network (usually individual people) and where two distinct participants are joined by an edge whenever there is a collaborative relationship between them of a particular kind. Collaboration graphs are used to measure the closeness of collaborative relationships between the participants of the network.

## Types of collaboration graphs considered in the literature

The two most well-studied collaboration graphs are:

• Collaboration graph of mathematicians also known as the Erdős collaboration graph,[3][4] where two mathematicians are joined by an edge whenever they co-authored a paper together (with possibly other co-authors present).
• Collaboration graph of movie actors, also known as the Hollywood graph or co-stardom network,[5][6][7] where two movie actors are joined by an edge whenever they appeared in a movie together.

Collaborations graphs have also been considered in other social networks, such as sports, including the "NBA graph" whose vertices are players where two players are joined by an edge if they have ever played together on the same team[8]

## Features of collaboration graphs

By construction, the collaboration graph is a simple graph, since it has no loop-edges and no multiple edges. The collaboration graph need not be connected. Thus people who never co-authored a joint paper represent isolated vertices in the collaboration graph of mathematicians.

Both the collaboration graph of mathematicians and movie actors were shown to have "small world topology": they have a very large number of vertices, most of small degree, that are highly clustered, and a "giant" connected component with small average distances between vertices.[9]

## Collaboration distance

The distance between two people/nodes in a collaboration graph is called the collaboration distance.[10] Thus the collaboration distance between two distinct nodes is equal to the smallest number of edges in an edge-path connecting them. If no path connecting two nodes in a collaboration graph exists, the collaboration distance between them is said to be infinite.

The collaboration distance may be used, for instance, for evaluating the citations of an author, a group of authors or a journal.[11]

In the collaboration graph of mathematicians, the collaboration distance from a particular person to Paul Erdős is called the Erdős number of that person. MathSciNet has a free online tool[12] for computing the collaboration distance between any two mathematicians as well as the Erdős number of a mathematician. This tool also shows the actual chain of co-authors that realizes the collaboration distance.

For the Hollywood graph, an analog of the Erdős number, called the Bacon number, has also been considered, which measures the collaboration distance to Kevin Bacon.

## Generalizations of the collaboration graph

Some generalizations of the collaboration graph of mathematicians have also been considered. There is a hypergraph version,[13] where individual mathematicians are vertices and where a group of mathematicians (not necessarily just two) constitutes a hyperedge if there is a paper of which they were all co-authors. Another variation is a simple graph where two mathematicians are joined by an edge if and only if there is a paper with only two of them (and no others) as co-authors.

A multigraph version of a collaboration graph has also been considered where two mathematicians are joined by $k$ edges if they co-authored exactly $k$ papers together. Another variation is a weighted collaboration graph where with rational weights where two mathematicians are joined by an edge with weight $\tfrac{1}{k}$ whenever they co-authored exactly $k$ papers together.[14] This model naturally leads to the notion of a "rational Erdős number".[15]

## References

1. ^ Odda, Tom (1979). "On properties of a well-known graph or what is your Ramsey number? Topics in graph theory.". Annals of the New York Academy of Sciences (in English) (New York, 1977: New York Academy of Sciences) 328: 166–172. doi:10.1111/j.1749-6632.1979.tb17777.x.
2. ^ Frank Harary. Topics in Graph Theory. New York Academy of Sciences, 1979. ISBN 0-89766-028-5
3. ^ Vladimir Batagelj and Andrej Mrvar, Some analyses of Erdős collaboration graph. Social Networks, vol. 22 (2000), no. 2, pp. 173–186.
4. ^ Casper Goffman. And what is your Erdős number?, American Mathematical Monthly, vol. 76 (1979), p. 791
5. ^ Chaomei Chen, C. Chen. Mapping Scientific Frontiers: The Quest for Knowledge Visualization. Springer-Verlag New York. January 2003. ISBN 978-1-85233-494-9. See p. 94.
6. ^ Fan Chung, Linyuan Lu. Complex Graphs and Networks, Vol. 107. American Mathematical Society. October 2006. ISBN 978-0-8218-3657-6. See p. 16
7. ^ Albert-László Barabási and Réka Albert, Emergence of scaling in random networks. Science, vol. 286 (1999), no. 5439, pp. 509–512
8. ^ V. Boginski, S. Butenko, P.M. Pardalos, O. Prokopyev. Collaboration networks in sports. pp. 265–277. Economics, Management, and Optimization in Sports. Springer-Verlag, New York, February 2004. ISBN 978-3-540-20712-2
9. ^ Jerrold W. Grossman. The evolution of the mathematical research collaboration graph. Proceedings of the Thirty-third Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 2002). Congressus Numerantium. Vol. 158 (2002), pp. 201–212.
10. ^ Deza, Elena; Deza, Michel-Marie (2006). "Ch. 22". Dictionary of Distances. Elsevier. p. 279. ISBN 978-0-444-52087-6..
11. ^ Bras-Amorós, M.; Domingo-Ferrer, J.; Torra, V; (2011). "A bibliometric index based on the collaboration distance between cited and citing authors". Journal of Informetrics 5 (2): 248–264. doi:10.1016/j.joi.2010.11.001. edit
12. ^ MathSciNet Collaboration Distance Calculator. American Mathematical Society. Accessed May 23, 2008
13. ^ Frank Harary. Topics in Graph Theory. New York Academy of Sciences, 1979. ISBN 0-89766-028-5 See p. 166
14. ^ Mark E.J. Newman. Who Is the Best Connected Scientist? A Study of Scientific Coauthorship Networks. Lecture Notes in Physics, vol. 650, pp. 337–370. Springer-Verlag. Berlin. 2004. ISBN 978-3-540-22354-2.
15. ^ Alexandru T. Balaban and Douglas J. Klein.Co-authorship, rational Erdős numbers, and resistance distances in graphs. Scientometrics, vol. 55 (2002), no. 1, pp. 59–70.


text:
+0

0
37
3

In the diagram below, PQ is tangent at P to the circle with center O, point S is inside the circle, and QS intersects the circle at R. If , QR = RS = 3, OS = 2 and PQ = 6, then find the radius of the circle.

Mar 21, 2020

#1
+402
+1

Hey there guest! First, let's start the problem with the knowledge of a (pretty common) theorem in geometry: The power of a point theorem. There are three variations to this theorem, but in this problem, we only need to look at 1 : the variation which involves the tangent of a circle and a secant(a line intersecting two points on the circle.

Firstly, notice we can extend the line QS to intersect the other side of the circle at Z. This is where power of a point comes in handy:

By power of a point:

$$QP^{2} = QR*QZ$$

Substituting known values in:

$$6^{2} = 3 * QZ$$

Dividing by 3, we get:

$$12 = QZ$$

Then RZ = QZ - 3(since that's the length of QR),

RZ = 12 - 3 = 9

Now that we have the length of a chord of Circle O(RZ is a chord), we can use power of a point once again, except another of its variations: with two intersecting chords.

A handy trick to realize is that the circle's diameter is also a chord, meaning we could find the length with power of a point theorem.

If we draw a diameter intersecting S, we could make power of a point easier to work with. By power of a point:$$(R+2)*(R-2) = RS*SZ = 3*6 = 18$$

where R is the radius of the circle

This simplifies to:
$$R^{2}-4 = 18$$

$$R^{2} = 22$$

$$R= \sqrt{22}$$

.
Mar 21, 2020
#2
0


text:
# [texhax] Callable TeX?

James Quirk jjq at galcit.caltech.edu
Fri Oct 29 01:20:30 CEST 2010

Michael,

On Thu, 28 Oct 2010, Michael Doob wrote:

> On Thursday 28 October 2010 1:56 am, Donald Arseneau wrote:
> > Thomas Schneider <schneidt at mail.nih.gov> writes:
> >
> > > > Is this the sort of thing you had in mind?
> > > > echo '\documentclass{article}\\begin{document}Hello, World!\\end{document}' | latex
> > >
> >
> > No doubling of backslashes.  (Double all backslashes if the
> > command line uses weak "" quoting)
>
> Well, this is actually shell dependent (it shouldn't be, I suppose,
> but it is). But really guys, all I wanted to indicate is that its
> easy to pipe stuff into latex. This does not seem to be widely known.
>
> Even less widely known, you can easily read input off the command line.
> For example, if the contents of test.tex is
To recycle JFK's Moon Speech, the greater my software knowledge,
the greater my ignorance unfolds.'' But if you're up for a
challenge, take a look at:

http://www.amrita-cfd.org/tex-group/equation-editor.pdf

and you will see an example of TeX as a callable engine that works at
two-levels: (i) a program invoked TeX to produce the PDF; (ii) the PDF
invokes either Mathtran remotely or a localhost server embedded in the PDF
so as to be able to typeset TeX equations input interactively. Note that
Mathtran is Jonathan Fine's work mentioned earlier in this thread, which
delivers PNGs. The localhost server employs SWFs with scalable fonts for
improved legibility.

Also be sure to view the PDF with AR9.3.4 on Linux, as AR9.4.0 is broken.

The document includes its own source-code browser to show you how it was
programmed. You can activate it from the bookmarks panel.(And Victor, I've
checked that this example runs under OSX, provided you have swftools
:-(

>
> \documentclass{article}
> \begin{document}
> Here is the input: \myinputline
> \end{document}
>
> then the line
> echo '\TeX{} is great!' | latex test.tex
> will insert the echoed material into the printed page.
Now what am I selling? Certainly not myself or a software package. A good
place to start would be this newspaper article that appeared in the UK,
back in February:

If you're going to do good science, release the compuer code too''
http://www.guardian.co.uk/technology/2010/feb/05/science-climate-emails-code-release

My comment snuck in at the end and so has its own url:

After talking to the article's author, I started on a piece of work that
has yielded three acknowledged AR vulnerabilities and counting.

Where am I going with this ramble. Well it's very clear that the
programming capabilties on this newsgroup are every bit as variable as
they are in the rest of society. And therein lies the reason I would,
today, hesitate to claim that '\TeX{} is great!' without critically
appraising where the system is weak.

Before I'm flamed, you have to understand that I have my eye on the year
2360. Yes none of us will be around, but the thought experiment to
consider is how will our document actions be judged by our descendants.
Sad to say, in the computational sciences I am not at all confident we
will be thought of highly, for the reasons given in the URL above.

My concern, and primary reason for popping up here, is that there are
many, many software tricks which are not widely appreciated. And once you
start going down a path that ponders ways to improve the communication of
computing, in its broadest sense, all sorts of weaknesses of TeX start to
surface. Note that does not detract from TeX's design strengths, I'm
talking strictly about its current implementation. Also note that my work
in this area is aimed at understanding certain software issues, and is not
aimed at usurping TeX or any other software package. For instance,
the equation-editor example seamlessly leverages off LaTeX, Perl, Ruby,
ActionScript, JavaScript, and MXML. And the same basic approach can
be used with R, or Octave, or pretty much any package that can
be batch driven.

My final thought is the following. Courtesy of Goole I am just a couple of
clicks away from investigating any person on this newsgroup. Thus I came
across Ron Fehd's Everything you ever wanted to know about a program but
were afraid to ask'' in which he concludes: Program documentation is an
over-looked and under-appreciated aspect of programming effort. Effective
documentaiton contributes to program reuse. The costs associated with
documentation are miniscule in comparison to those associated with
redevelopment.'' But with recent developments in electronic formats the
distinction between a program and a document is much smaller than it used
to be, and in the years to come it will get even smaller. Therefore what
long-term evolution path do you, and the other contributors on this
thread, see as being needed so as to keep TeX's intellectual spirit alive?

Cheers,

James

>
> Cheers,
> Michael
>
>
>
>


text:
ISSN 1000-1239 CN 11-1777/TP

Journal of Computer Research and Development ›› 2016, Vol. 53 ›› Issue (11): 2512-2529.

### Survey of MPTCP-Based Multipath Transmission Optimization

Xue Kaiping1,2, Chen Ke1,2, Ni Dan1, Zhang Hong1, Hong Peilin1,2

1. 1(Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei 230027); 2(Key Laboratory of Wireless-Optical Communications (University of Science and Technology of China), Chinese Academy of Sciences, Hefei 230027)
• Online:2016-11-01

Abstract: The newly developed networks hope to bring some specific features, such as wide coverage, high bandwidth, and provide varieties of media services. Fortunately, multiple access techniques are at there to help. Nowadays，terminals are always equipped with multiple interfaces to adapt to the heterogeneous networks. Thus, there are more than one paths existing between two endpoints. MPTCP (multipath TCP) is proposed by IETF MPTCP working group, in addition to compatible with traditional TCP, which utilizes multiple paths to transmit data. It improves the efficiency of bandwidth usage and the resilience of the connection. What’s more, it can adaptively move data from more congested path to less congested path. In recent years, many researches have been carried out to gradually make MPTCP from concept to practice. This paper introduces the technical details of MPTCP standard, and expounds the present situation of the related aspects, including simulation and actual deployment, out-of-order control, coupled congestion control, energy consumption maintenance, security, and other aspects such as path selection, mobility and QoS, the data center scenario, et al. Finally, this paper gives a summary and expectation.

CLC Number:


text:
# Definition:RSA 130/Historical Note

## Historical Note RSA $130$
RSA $130$ is one of a number of large ($100$ digits and over) semiprimes offered up as a factorisation challenge by Ronald Linn Rivest, Adi Shamir and Leonard Max Adleman as a demonstration of the effectiveness of their encryption algorithm now known as RSA.
On $12$th April $1996$, RSA $130$ was successfully factorised into its $2$ prime factors by a Dutch team.


text:
My Math Forum Permutations of a finite set
 User Name Remember Me? Password

 Abstract Algebra Abstract Algebra Math Forum

 June 9th, 2014, 08:46 AM #1 Member   Joined: May 2014 From: None of your business Posts: 31 Thanks: 0 Permutations of a finite set I'm trying to figure out this problem: Let alpha and Beta be cycles of odd length (not disjoint). Prove that if alpha squared equals beta squared, then alpha equals beta. What I know thus far is that... since l is an odd length, alpha squared and beta squared are cycles, and not a product of disjoint cycles. Both alpha and beta can be expressed as an even number of transpositions. I also know that I can express alpha as a product of the cycles alpha1 gamma alpha2, and that this product is associative. Since the problem states that alpha and beta are not disjoint, then I can reason that there is ai in the alpha cycle that is equal to some bj in the beta cycle. Now I tried expressing beta squared as a product of beta1 (bj bj+2) beta2, and since it is associative, rewrote it as (bj bj+2) beta1 beta2, then multipied by (bj+2 bj) on the left, also multiplying alpha squared by (bj+2 bj) on the left. With examples, I continued in this fashion until I had the identity permuation on the right hand side of the equation. Now I'm stuck. I'm thinking that I only showed that the product of beta squared inverse and alpha squared is the identity (not really illuminating). Please help.
 June 9th, 2014, 04:41 PM #2 Senior Member   Joined: Mar 2012 Posts: 294 Thanks: 88 Since $\alpha,\beta$ are not disjoint, they share at least one element in their respective cycles. Hence we may write: $\alpha = (a_1\ a_2\ \dots\ a_n)$ $\beta = (a_1\ b_2\ \dots\ b_m)$ Thus: $\alpha^2 = (a_1\ a_3\ \dots a_n\ a_2\ a_4\ \dots a_{n-1})$ (since $n$ is odd) $\beta^2 = (a_1\ b_3\ \dots b_m\ b_2\ b_4\ \dots b_{m-1})$ (since $m$ is odd). Since $\alpha^2 = \beta^2$ it follows that $m = n$, and $b_j = a_j$. To see why we have the stipulation that $n,m$ be odd, consider: (1 2) and (1 3). Then (1 2)(1 2) = (1 3)(1 3) = e, but (1 2) does not equal (1 3). ********** The trick here is to see it does not matter which element of a cycle we start it with: (1 2 3) = (2 3 1) = (3 1 2), and that two functions $f,g$ are equal iff their domains are equal, their co-domains are equal, and they take the same values in the co-domain for every value in the domain. (Recall that the cycle $(a\ b\ c)$ is the function: $f:\{1,2,\dots,n\} \to \{1,2,\dots,n\}$ with: $f(a) = b$ $f(b) = c$ $f(c) = a$ $f(k) = k$, for all other elements besides $a,b,c$). So once we prove that $a_3 = \alpha^2(a_1) = \beta^2(a_1) = b_3$, we compare $a_5 = \alpha^2(a_3) = \beta^2(a_3) = \beta^2(b_3) = b_5$, and so on, until we come "full cycle". Thanks from Awesomo

 Tags finite, permutations, set

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,

,

### express alpha beta as product of two cycles

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text:
anonymous one year ago What are the factors of 3x2 + 10x + 3

1. anonymous

use the quadratic formula to solve this one

2. pooja195

@Serenaishurting you can also use factoring is you wish

3. pooja195

*if

4. anonymous

how?

5. pooja195

Does it specify which method to use?

6. anonymous

$x=\frac{ -b \pm \sqrt{b^2-4ac} }{ }$ where $ax^2+bx+c=0$

7. anonymous

no it doesnt

8. pooja195

ok so you can use the formula then since @saseal typed it out ;p $x=\frac{ -b \pm \sqrt{b^2-4ac} }{ }$ where $ax^2+bx+c=0$

9. pooja195

Start by listing your abc values

10. anonymous

$x=\frac{ -b \pm \sqrt{b^2-4ac}}{ 2a }$

11. anonymous

sorry lagged and the 2a didnt show up

12. anonymous

okay thanks i got it.

13. anonymous

yw

Another way is possible.....just factor it by noting that both the coefficient of the squared term "3" and the numeric constant is "3" both are prime numbers. This means less trial and error.

It factors quite nicely: (x + 3) (3x + 1)

16. anonymous

can yall help with another?

17. anonymous

sure

18. anonymous

Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 2, negative 1, and 2 Which of the following functions best represents the graph?

19. anonymous

Which of the following functions best represents the graph? f(x) = x3 + x2 − 4x − 4 f(x) = x3 + 4x2 − x − 4 f(x) = x3 + 3x2 − 4x − 12 f(x) = x3 + 2x2 − 4x − 8

20. anonymous

your best bet is to graph it out, cubic stuff is pretty messy

21. anonymous

okay

22. anonymous

lemme try teaching you how to factor this without graphing

23. anonymous

okay

This problem is providing you the factors. Just multiply them and get the answer.

25. anonymous

we take this 1st option$f(x)=x^3+x^2-4x-4$ we can rewrite this as $f(x)=x^2(x+1)-4(x-1)$

|dw:1438351445649:dw|

27. Nnesha

for directions:when highest degree is an odd number then if leading coefficient is *positive * right end will rise and left end fall and if leading coefficient is *negative* right end will fall and left end will rise

28. anonymous

oh i got the answer. i just finished the test thanks for yalls help.

29. anonymous

30. Nnesha

@saseal ??

31. anonymous

nothing just bored doge

32. Nnesha

oh

33. anonymous

whale then.. o.o

34. pooja195

have more questions? on that test?

35. pooja195

nvm u finished ;p heres a refrence for next time http://pages.citebite.com/a4o3b6r4a2tjy

36. anonymous

no i finished it. im gonna have to redo it later though.

37. pooja195

$$~~~~~~~~~~~~~~~~~~~~~~~~~~\Huge{\color{red}{\heartsuit}\color{orange}{\bigstar}\color{yellow}{\heartsuit}\color{green}{\bigstar}\color{blue}{\heartsuit}\color{purple}{\bigstar}\color{hotpink}{\heartsuit}}$$$$\Huge\bf\color{#FF0000}W\color{#FF4900}e\color{#FF9200}l\color{#FFDB00}c\color{#FFff00}o\color{#B6ff00}m\color{#6Dff00}e\color{#24ff00}~\color{#00ff00}t\color{#00ff49}o\color{#00ff92}~\color{#00ffDB}O\color{#00ffff}p\color{#00DBff}e\color{#0092ff}n\color{#0049ff}S\color{#0000ff}t\color{#2400ff}u\color{#6D00ff}d\color{#B600ff}y\color{#FF00ff}!$$$$~~~~~~~~~~~~~~~~~~~~~~~~~~\Huge{\color{red}{\heartsuit}\color{orange}{\bigstar}\color{yellow}{\heartsuit}\color{green}{\bigstar}\color{blue}{\heartsuit}\color{purple}{\bigstar}\color{hotpink}{\heartsuit}}$$$$\Large\bf\color{Lime}{Please,\ don't\ hesitate\ to\ ask\ questions!}$$$$\Large\bf\color{magenta}{We're\ here\ to\ help!}\Large\color{magenta}{\ddot\smile}$$

38. pooja195

Since you are new im sure you werent aware of the anti cheating policy so please dont ask any test questions on that site we dont want u to get banned

39. anonymous

how do u do that @pooja195

40. anonymous

okay..others do it though...

41. pooja195

Just because others do it doesnt mean u have to do it


text:
# “Missing number” error using \pgfmathsetmacro with the ifthenelse operator

I am trying to use logical functions in pgfmath and getting unexpected errors. It seems to be related to the use of \pgfmathsetmacro, which according to my understanding should be equivalent to \pgfmathparse{whatever}\let\macro=\pgfmathresult. However, the following example from the manual works with \pgfmathparse and gives the error

! Missing number, treated as zero.
n
l.52 ...etmacro\macro{ifthenelse(5==4,"yes","no")}
\macro

when used with \pgfmathsetmacro:

\pgfmathparse         {ifthenelse(5==4,"yes","no")}% Works
\pgfmathsetmacro\macro{ifthenelse(5==4,"yes","no")}% Fails

Shouldn't I be able to do this?

-
After looking at the \tracingall output for not very long, I think it might be a bug: pgf is trying to set a \dimen register to "no", which is not going to work. –  Bruno Le Floch Feb 2 '12 at 19:44
Note that this turns out to not being related to the ifthenelse operator (so the title can be misleading). \pgfmathsetmacro\macro{"no"} won't work either. –  cjorssen Feb 2 '12 at 21:07

Here is the definition of \pgfmathsetmacro in file pgfmathcalc.code.tex.

\def\pgfmathsetmacro#1#2{%
\begingroup%
\pgfmathsetlength\pgfmath@x{#2}%
\edef#1{\pgfmath@tonumber{\pgfmath@x}}%
\pgfmath@smuggleone{#1}%
\endgroup%
}

The use of \pgfmathsetlength prevents from using something else than numbers as a result of the evaluation of #2 by \pgfmathparse (which is the case in your sample code). As Bruno Le Floch pointed out in comment, this leads to assign nopt to the dimension \pgfmath@x which does not work.

I must admit it's not the behavior I would expect looking at the documentation. So at least, it should be specified in the doc or the macro should be modified to deal with such string cases.

-