Why not have the icons to the left of each of the 'Hot Network Questions' go to that community's front page? Seems logical.
I would like to see the icons in the 'Hot Network Questions' right panel clickable, leading to the homepage of the site where the question comes from.  It would make it more comfortable to switch to the site when you want rather to visit it than to see that specific "hot" question.
Why doesn't backpropagation work when you initialize all the weight the same value (say 0.5), but works fine when given random numbers?   Shouldn't the algorithm calculate the error and work from there, despite the fact that the weights are initially the same? EM algorithm gaussian mixtures- derivation I'm trying to make sense of a derivation I'm following from the lecture notes of Stanford's ML course.  Specifically the notes are here:   I'm particular I'm interested in the step where they are optimizing the lower bound of the log-likelihood by finding the derivative of that function w.r.t the mean (top of page 7). I'm a bit stuck on going from line 1 to line 2 in that sequence.  To copy here (using abbreviated notation for space):  $$ \nabla \mu_s \sum_{i=1}^{m}\sum_{j=1}^{k} w_j^{(i)}\log\frac{\alpha_j \exp\psi_{j}^{(i)}\phi_j}{w_j^{(i)}}  \qquad(1) $$ $$ \nabla \mu_s \sum_{i=1}^{m}\sum_{j=1}^{k} w_j^{(i)}\psi_{j}^{(i)}\qquad(2) $$ where $\psi_{j}^{(i)} =-\frac{1}{2}(x^{(i)}-\mu_j)^T\Sigma^{-1}_{j}(x^{(i)}-\mu_j)$ and $\alpha_j=\frac{1}{(2\pi)^{n/2}|\Sigma_j|^{1/2}}$.  The quantity $\mu_s$ is the mean (of a multivariate gaussian distribution) for class $s$.    In short, I'm not sure how they get from (1) to (2).  From just changing the log of (1) I see:  $$ \nabla \mu_s \sum_{i=1}^{m}\sum_{j=1}^{k} w_j^{(i)}\log \left(\alpha_j \exp\psi_{j}^{(i)}\phi_j\right) - w_j^{(i)}\log w_j^{(i)} \qquad(1) $$  To get to their form (2) my impression is that they take pre-emptively discard terms that would contain derivatives of $w_j^{(i)}$ (w.r.t. $\mu_s$).  At least if you assume that much, you get to (2).  However, as they show earlier in that PDF,  $$ w_j^{(i)} = p(z^{(i)}=j | x^{(i)}) =\frac{p(x^{(i)}|z^{(i)}=j)p(z^{(i)}=j) }{\sum_j p(x^{(i)},z^{(i)}=j) } $$ i.e. this quantity is the posterior distribution of the class labels.  Intuitively, it seems like $\partial w_j^{(i)}/ \partial \mu_s$ should be non-zero.  After all, changing the location of the mean $\mu_s$ would change your posterior probability for a particular class given the same data.  (Right?).  Just from a mechanical point of view, $\partial w_j^{(i)}/\partial \mu_j$ would seemingly have some non-zero terms since $p(x^{(i)}|z^{(i)}=j) \sim \mathcal{N}(\mu_j, \Sigma_j)$.  If I work through the algebra, I get  $$ \frac{\partial w_j^{(i)}}{\partial \mu_j} = w_j^{(i)}(1-w_j^{(i)})\frac{\partial \psi^{(i)}_{j}}{\partial \mu_j} $$  What am I missing here?  If I take the log-likelihood (without even thinking about EM algorithm),    $$ \ell = \sum_{i=1}^{m}\log \sum_{j=1}^{k}p(x^{(i)}|z^{(i)}=j)p(z^{(i)}=j) $$ and differentiate w.r.t $\mu_s$, I correctly get  $$ \mu_s^* = \frac{\sum_{i=1}^{m}w_s^{(i)}x^{(i)}}{\sum_{i=1}^{m}w_s^{(i)}} $$  so I'm comfortable with the eventual result, just not the intermediate steps. I upgraded my Mega Ring and have been looking for Mega Stones, and I found . However, the Mega Stone isn't in the place it's supposed to be, and I'm sure the location is right. Why isn't my Mega Stone here? Can the graph of a bounded function ever have an unbounded derivative? I've got this situation:  ./ ./myscript.sh ./arguments.txt ./test.sh   Inside myscript.sh, I have to run the file test.sh, passing to it the arguments contained inside arguments.txt.  myscript.sh is:  arguments=$(cat arguments.txt) source test.sh $arguments   This works well if if arguments.txt contains at most one argument:  firstargument    The substitution is:  ++ source test.sh 'firstargument'   But the problem is with two or more arguments. It does this:  ++ source test.sh 'firstargument secondargument'   Also, I don't know in advance the number of arguments inside arguments.txt. There can be zero or more. This code is part of a larger code that generates an Arithmetic Quiz, although the code I have show below just saves the score that the user got on the test and their name. When saving the code it checks if the user has taken the quiz before. If the user has taken the quiz before it saves it as 'Older Score' or 'Oldest Score', however if the user has not taken the quiz before it generates a new row for them. Additionally it works out the average score and highest score for all users it has the data for. For my task I'm supposed to make the code as short as possible.  name = ""+first_name+" "+last_name rows_data = [] class_file_names = ['Class 1.csv', 'Class 2.csv', 'Class 3.csv'] scan = open(class_file_names[int(math_class)-1], 'r+') rows = csv.reader(scan) for row in rows:     rows_data.append(row) scan.close() class_file_names=['Class 1.csv', 'Class 2.csv', 'Class 3.csv'] csvfile=open(class_file_names[int(math_class)-1], 'w', newline="") fieldnames = ['Student Name', 'Oldest Score', 'Older Score', 'Latest Score', 'Average', 'Highest'] writer = csv.DictWriter(csvfile, fieldnames=fieldnames) writer.writeheader() nameFound=False for x in rows_data[1:]:     if x[0] == name:         x[3]=x[2]         x[2]=x[1]         x[1]=str(score)         x[4]=(int(x[1])+int(x[2])+int(x[3]))/3         x[5]=max(x[1],x[2],x[3])         nameFound=True     writer.writerow({'Student Name': x[0], 'Oldest Score': x[3], 'Older Score': x[2], 'Latest Score': x[1], 'Average': x[4], 'Highest' : x[5]})  if nameFound==False:     writer.writerow({'Student Name': name, 'Latest Score': score, 'Older Score': '0', 'Oldest Score': '0', 'Average': score, 'Highest': score}) csvfile.close() input("Test complete! Press anything to close.") CPU Emulation and locking to a specific clock speed If you had read my other , you'll know I've spent this weekend putting together a 6502 CPU emulator as a programming exercise.  The CPU emulator is mostly complete, and seems to be fairly accurate from my limited testing, however it is running incredibly fast, and I want to throttle it down to the actual clock speed of the machine.  My current test loop is this:      // Just loop infinitely.     while (1 == 1)     {                         CPU.ClockCyclesBeforeNext--;          if (CPU.ClockCyclesBeforeNext &lt;= 0)         {             // Find out how many clock cycles this instruction will take             CPU.ClockCyclesBeforeNext = CPU.OpcodeMapper.Map[CPU.Memory[CPU.PC]].CpuCycles;              // Run the instruction             CPU.ExecuteInstruction(CPU.Memory[CPU.PC]);              // Debugging Info             CPU.DumpDebug();             Console.WriteLine(CPU.OpcodeMapper.Map[CPU.Memory[CPU.PC]].ArgumentLength);              // Move to next instruction             CPU.PC += 1 + CPU.OpcodeMapper.Map[CPU.Memory[CPU.PC]].ArgumentLength;                                                 }     }   As you can tell, each opcode takes a specific amount of time to complete, so I do not run the next instruction until I count down the CPU Cycle clock. This provides proper timing between opcodes, its just that the entire thing runs way to fast.  The targeted CPU speed is 1.79mhz, however I'd like whatever solution to the clock issue to keep the speed at 1.79mhz even as I add complexity, so I don't have to adjust it up.  Any ideas? I'm using Python, and would like to insert a string into a text file without deleting or copying the file. How can I do that? If virtual particles sometimes add more mass/energy to a system then was inputed or comes out in the output, how do they not violate conservation of mass/energy. How to fix "404 Not Found" crawl errors reported by Google in Search Console I was checking on Google webmaster tools for my blog site to see if there's any indication on why my blog traffic decreased to half in one day and i saw 43 Not Found crawl errors and 5 in Sitemap Not Found errors.   The 5 Not Found errors in Sitemap were the links to categories. I guess I renamed categories that's why Google can't find the links.   As for the 43 other Not Found errors, I see blog post titles that contain ' or . For example "McDonald's" or "O.N.E."  They weren't found by Google crawler.   There is also a blog post with /CachedYou at the end and a blog post with /www.example.com attached at the end.  They weren't found by Google crawlers either.   How do I correct those Not Found Errors? Show that $S = \sqrt{S^2}$ is a biased estimator of $\sigma$ given a random sample from a normal distribution ... Suppose $Y_1, \ldots, Y_n$ is a random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. Let $S^2$ be the sample variance, which is unbiased for $\sigma^2$.  GOAL: Show that $S = \sqrt{S^2}$ is a biased estimator of $\sigma$.  I realize that $(n-1)S^2/ \sigma ^2$ is chi-square with $(n-1)$ degrees of freedom.  I am given that $$E(S) = E\left[\frac{\sigma}{\sqrt{n-1}} \left[\frac{(n-1)S^2}{\sigma^2}\right]^{1/2}\right] = \frac{\sigma}{\sqrt{n-1}} \int_0^\infty v^{1/2} \frac{1}{\Gamma[(n-1)/2] 2^{(n-1)/2}} v^{(n-1)/2} e^{-v/2} \, dv$$  Can anyone help me understand why they have $v^{1/2}$ and $v^{(n-1)/2}$ (combining them $v^{n/2}$ as I think it should be $v^{1/2}$ and $v^{\frac{(n-1)}{2}-1}$ (combining both terms give $v^{(n-2)/2}$ since the pdf for chi-square distribution is $$ f(v) = \frac{v^{(x/2)-1} e^{-v/2}}{2^{x/2}\Gamma(x/2)},$$ where $x$ is degree of freedom?  Could anyone please tell me which one is the correct answer with explanation?  Thank you Need hint: Determine whether the series $\sum_{n=1}^{\infty}(\frac{n}{n+1})^{n^2}$ is convergent or divergent. Ability to retract reopen/delete votes It seems that now we can retract close votes but we cannot retract reopen votes or delete votes.  I am trying to retract my reopen vote  but it does not allow me to.  Can we have that ability? Number of zero digits in factorials Here is a riddle someone has been asked in a job interview: How many zero digits are there in $100!$?  Well, I found the first $24$ quite fast by counting how many times five divides $100!$ ($5$ divides $20$ times and $25$ divides it $4$ times).   However, there are more zero digits in the middle of the number (these can be found by hand, by typing factorial(100) in sage).  My question is whether there is a smart way to determine the number of zero digits in $100!$, and more generally in $n!$.  By the way, this will not affect the job interview as it was finished some time ago. Why did Bilbo physically age faster than Gollum? Without using Axiom of Choice, prove that $$\forall\alpha\geq\omega,~~|L_\alpha|=|\alpha|,$$  in which $\alpha$ is an ordinals, $\omega$ is the set of natural numbers, $L_\alpha$ is the $\alpha$-th constructiable set, $|x|$ is the cardinals of $x$.  I am learning a set theory, and I have read a proof by using AC. The AC is used only when $\alpha$ is a limit ordinals during the transfinite inductive method for $\alpha$ . I wonder if there is a proof without AC. 　THANKS! How to measure capacitance without LC meter? I would like to use capacitors salvaged from old electronics, but I currently don't have an LC meter.    What would be some really simple circuits, that would convert capacitance to something I can measure (voltage, current, frequency)? MacTEX-2014, TeXShop 3.36.1 on Mac OS 10.9.5 -- when using hyperref I do not see the colored border that should appear around the hyperlinks in the pdf.  for example, when compiled with pdflatex, the code below should produce a pdf with a green border around the link on the right of "abc", but it does not. Any idea how to check where the problem is?  \documentclass{article} \usepackage{hyperref} \hypersetup{colorlinks=false,pdfborder=0 0 1,citebordercolor={0 1 0}} \begin{document}  abc \cite{123}  \begin{thebibliography}{99} \bibitem{123} efg \end{thebibliography} \end{document}    this is the list of files from the generated .log     File List   article.cls    2007/10/19 v1.4h Standard LaTeX document class   size10.clo    2007/10/19 v1.4h Standard LaTeX file (size option)   hyperref.sty    2012/11/06 v6.83m Hypertext links for LaTeX   hobsub-hyperref.sty    2012/05/28 v1.13 Bundle oberdiek, subset hyperref (HO)   hobsub-generic.sty    2012/05/28 v1.13 Bundle oberdiek, subset generic (HO)     hobsub.sty    2012/05/28 v1.13 Construct package bundles (HO)   infwarerr.sty    2010/04/08 v1.3 Providing info/warning/error messages (HO)    ltxcmds.sty    2011/11/09 v1.22 LaTeX kernel commands for general use (HO)   ifluatex.sty    2010/03/01 v1.3 Provides the ifluatex switch (HO)     ifvtex.sty    2010/03/01 v1.5 Detect VTeX and its facilities (HO)    intcalc.sty    2007/09/27 v1.1 Expandable calculations with integers (HO)      ifpdf.sty    2011/01/30 v2.3 Provides the ifpdf switch (HO)   etexcmds.sty    2011/02/16 v1.5 Avoid name clashes with e-TeX commands (HO)   kvsetkeys.sty    2012/04/25 v1.16 Key value parser (HO)   kvdefinekeys.sty    2011/04/07 v1.3 Define keys (HO)   pdftexcmds.sty    2011/11/29 v0.20 Utility functions of pdfTeX for LuaTeX (HO)   pdfescape.sty    2011/11/25 v1.13 Implements pdfTeX's escape features (HO)   bigintcalc.sty    2012/04/08 v1.3 Expandable calculations on big integers (HO)     bitset.sty    2011/01/30 v1.1 Handle bit-vector datatype (HO)   uniquecounter.sty    2011/01/30 v1.2 Provide unlimited unique counter (HO)   letltxmacro.sty    2010/09/02 v1.4 Let assignment for LaTeX macros (HO)    hopatch.sty    2012/05/28 v1.2 Wrapper for package hooks (HO)   xcolor-patch.sty    2011/01/30 xcolor patch   atveryend.sty    2011/06/30 v1.8 Hooks at the very end of document (HO)   atbegshi.sty    2011/10/05 v1.16 At begin shipout hook (HO)   refcount.sty    2011/10/16 v3.4 Data extraction from label references (HO)    hycolor.sty    2011/01/30 v1.7 Color options for hyperref/bookmark (HO)     keyval.sty    2014/05/08 v1.15 key=value parser (DPC)    ifxetex.sty    2010/09/12 v0.6 Provides ifxetex conditional    auxhook.sty    2011/03/04 v1.3 Hooks for auxiliary files (HO)   kvoptions.sty    2011/06/30 v3.11 Key value format for package options (HO)     pd1enc.def    2012/11/06 v6.83m Hyperref: PDFDocEncoding definition (HO)   hyperref.cfg    2002/06/06 v1.2 hyperref configuration of TeXLive        url.sty    2013/09/16  ver 3.4  Verb mode for urls, etc.    hpdftex.def    2012/11/06 v6.83m Hyperref driver for pdfTeX   rerunfilecheck.sty    2011/04/15 v1.7 Rerun checks for auxiliary files (HO)    nameref.sty    2012/10/27 v2.43 Cross-referencing by name of section   gettitlestring.sty    2010/12/03 v1.4 Cleanup title references (HO) I know that there exist some attack when using same modulus.      But with a little modification, $m$ is the plain-text $N$ is the RSA modulus $r_1, r_2$ is the random padding $e, s$ is the public exponent $C_e, C_s$ is the cipher-text  encrypt as follow $$С_e = (m + r_1)^e   \bmod N$$ $$С_s = (m + r_2)^s   \bmod N$$  If attacker only knows $C_e, C_s, r_1, r_2, e, s, N$. Is it possible to know $m$?  It seems the  does not work? There is a length limit to Windows file extensions?