Why is L2 regression good for handling multicollinearity?
Why is ridge regression called "ridge", why is it needed, and what happens when $\lambda$ goes to infinity?
How to approximate the student-t CDF at a point without the hypergeometric function? Is there a way to closely approximate the CDF of a student-t distribution at a point $x$ without involving the hypergeometric function? For example, by using a series expansion, or expressing the CDF in terms of simpler functions?  The t-distribution can   $$t = \frac{X\sqrt{n}}{Y}$$  where $X$ is normally distributed with mean 0 and variance $\sigma^2$; $\frac{Y^2}{\sigma^2}$ has a chi-squared distribution. Maybe this expression can help simplify the t CDF?  I am trying to write an algorithm to compute the student-t CDF for any real number, so using the hypergeometric function will be extremely difficult. I am also trying to avoid integrating the PDF to get the CDF. A is similar to $A^k$, then each eigenvalue of $A$ is a root of unity Let $A \in \mathbb{C}(n,n)$ and $k \geq 2$ be an integer such that $$A \sim A^k$$. Show that if $A$ is non-singular then each eigenvalue of $A$ is a root of unity.   Attempt: Since $A \sim A^k$, $$PA = A^kP$$ where $P$ is an invertible matrix. Since $A$ is invertible, $0$ cannot be an eigenvalue of $A$. Suppose $$Av = \lambda v \quad v \neq 0$$ then $$PAv = \lambda Pv$$ $$\therefore A^k(Pv) = \lambda (Pv) $$ but this implies that $Pv$ is an eigenvector of $A$. But the eigenvalues of $A^k$ are $\lambda^k$ $$\therefore \lambda^k=\lambda$$ which gives the conclusion required.   My questions is: Is the logic correct? If so, Am I missing any details? If not, then how could I approach this?   Thanks! Does anyone know of a nice (and preferably free) way to integrate Prolog and C#?  Im looking to create a Prolog dll or similar to call from my managed code, and retrieve an answer once all the processing has been complete. Im looking for it to be predominantly one sided (c# calls Prolog).  I have seen  which talks about Prologs real world usage but I was wondering if anyone had either any experience with c# &amp; Prolog? or a nice tutorial/article? jQuery appended table adds closing tag at the end of the text automatically. Why? Does the VBA "And" operator evaluate the second argument when the first is false? E: Problem executing scripts APT Update::Post-Invoke-Success error during apt-get update I cannot install any package. It seems the command apt-get update must be run but it throws some errors:  $ sudo apt-get update Get:1 http://security.ubuntu.com/ubuntu xenial-security InRelease [102 kB]      Hit:2 http://ve.archive.ubuntu.com/ubuntu xenial InRelease                      Hit:3 http://ve.archive.ubuntu.com/ubuntu xenial-updates InRelease              Hit:4 http://ve.archive.ubuntu.com/ubuntu xenial-backports InRelease            Fetched 102 kB in 23s (4337 B/s)                                                *** Error in `appstreamcli': double free or corruption (fasttop): 0x000000000210f4b0 *** ======= Backtrace: ========= /lib/x86_64-linux-gnu/libc.so.6(+0x777e5)[0x7fac8d8317e5] [...] Aborted (core dumped) Reading package lists... Done E: Problem executing scripts APT::Update::Post-Invoke-Success   'if /usr/bin/test -w /var/cache/app-info -a -e /usr/bin/appstreamcli;   then appstreamcli refresh &gt; /dev/null; fi' E: Sub-process returned an error code I'm trying to connect to another computer in my house via ssh. Both computers have ubuntu and openssh installed. When I run the command "ssh username@ip" on terminal I'm asked for the user's password I'm trying to connect to. I type it but I get this error "Permission denied, please try again." I'm sure the password is correct, then why can't I access? Escaping regex string I want to use input from a user as a regex pattern for a search over some text.  It works, but how I can handle cases where user puts characters that have meaning in regex? For example, the user wants to search for Word (s): regex engine will take the (s) as a group.  I want it to treat it like a string &quot;(s)&quot; .  I can run replace on user input and replace the ( with \( and the ) with \) but the problem is I will need to do replace for every possible regex symbol. Do you know some better way ? Can we raise the bar for reputation for late answers to bypass the review queue? I would like to raise the bar for late answers to enter the Late Answers Review Queue to 50 rep, which is the threshold after which users gain the ability to comment. Here are some answers that were posted by users with between 10 to 50 rep (yes, there's a little selection bias to be sure. I suspect most/all of these will be 10k links only by the time you're reading this. Note, all of these are from the last 5 hours.  These are all from Stack Overflow, where I have the most experience, but since Late Answers have a much higher probability to be bad across all stacks, I think this applies generally. Also, I have bolded all the users references to the inability to comment, that were not in their original answers:    (23 rep)     Solution provide by @brandonyang works for me too! (I can't add comments in a response 'cause my low reputation, sorry).   (47 rep)     I tried your answer but it doesn't work in office 365 outlook online. Do you have any suggestions?   (26 rep)     My question is somehow related to the same issue. I am fairly new to C# and have been doing JAVA for quite a long time. When I am coding in C# with .Net framework 4.5.1 using visual studio 2013, I get errors for using certain libraries but I donot know which dll should I reference in my project How do C# people figure that out? For example I wanted to code to draw an ellipse and needed system.Windows.Media and System.Windows.Controls both of which were giving me errors, after googling for quite sometime I got to know that we need to reference PresentationFramework.dll, is this the only way to figure it out?      PS >> I am unable to post this as a comment hence putting it as answer.      Thanks.   (19 rep)     i like  video. It explains the differences between int and Integer and cautions of using Integer   (21 rep)     I have a question, i am actually trying to copy the database from Prod server to test server ( SQL server 2008R2). I am wondering would it copy the users logins, roles and permission as well ?      I know I suggested 50 rep above, but while I was compiling that, I . Perhaps it should be 100 rep, not 50. I am less confident about this, but I thought I'd add it as an addendum for discussion.     The answer posted  is the simplest solution that you are looking for to solve your problem, so take a look ;) I've installed emacsformacosx on my OSX box.  I'd like to shove my macmini in a data center and run it headless.  I've gotten x-windows working.  If I run xeyes, it displays on my Windows 7 client.  Emacs works from the command line on the osx box.  However, if I start up emacs from the windows client, it pops it up on the server instead of the client.  What am I doing wrong? PUA.Phishing.Bank Found Manual/automatic line breaks and text alignment in TikZ nodes How can I automatically forward Facebook messages to my email or phone? I can create email addresses that forward to other email addresses.  Likewise, can I automatically forward Facebook messages to either my email or phone? Where does the extra kinetic energy come from in a gravitational slingshot? On a systems level, I understand that as electrons are pushed into a wire, there is a net field and a net electron velocity.  And I've read that the net electron drift is slow.  But electricity travels through the wire, essentially at c, and I want to understand that mechanism.  My apologies if my question is poorly stated, I know bare bones undergraduate quantum theory circa 1990s but it doesn't explain the motion of electricity in detail.  Here's my conception, I'm hoping someone will fill in the holes, ha ha.  An electron moves into the wire.  It's got a kinetic energy.  After travelling a short distance, it spontaneously emits a photon, which hits another electron in a valence shell.  That electron then presumably does the same.  If this conception is simply wrong, please enlighten me.  The questions that arise:   Presumably at this level, electrons are acting more like waves and less like particles, but is there any classical component in the picture, ie are electrons coming in imparting other electrons with kinetic energy through repulsion, or does it not work that way? If electrons momentarily have energy, then pass it on by a photon, what determines when that photon is emitted, and what frequency it will be?  I assume that electrons in this cloud are not limited by any kind of exclusion principal, and that any frequencies are possible? Why should a photon emitted by an electron be in the direction of travel?  Conservation of momentum tells me that if an electron is moving, the photon should be emitted in that direction, slowing the electron, but could an electron emit a photon in the opposite direction?  If it did, I assume it would somehow have had to absorb energy from elsewhere? That sounds possible by analogy with quantum tunneling. What is the mechanism by which electrons propagating increase the temperature of the material?  Are they transmitting energy to the electrons in the valence shell, which tug at the nucleus, do some photons hit the nuclei directly, or is there some other way?  Presumably, electricity travels slower than light, because there is some time in each exchange, and some time when electrons are moving at sublight speeds before emitting a photon.  By how much is this slower than light, and what is the speed of each interaction? Can a ring without a unit element have a subring with a unit element? How can I speed up data transfer between local computers on a WiFi network? I have a router with ADSL Pentagram Cerberus 6331-42. Is it normal to have transfer speeds between two computers of max 1MB/s (not 1 Mbit)? How can I set my router up to make it faster at transferring data in my local WiFi network?  I have a PC and a laptop. Both are running Windows 7. I don't use a firewall. I've set the network area up correctly; I can see other computers.  Is it possible to make the router faster by changing its values? I don't use secure encryption such as WPA or WEP; only MAC filtering.  My values in Interface Setup > Wireless are:       Here are my thoughts after few years I've published this topic:    use 5Ghz bandwidth if possible  use range extender if Your router is too far  try wifi analyzer app for mobile phone to check what channel is the less used Pre-1972 sci-fi short story or novel: alien(?) tunnel where people try new moves and get destroyed if they're not the correct ones I have the two PGF nodes foo and bar positioned in a row.  \documentclass{article} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document}   \begin{tikzpicture}[node distance=0.2cm,mynode/.style={rectangle,draw}]     \node[mynode] (foo)                {foo};     \node[mynode] (bar) [right=of foo] {bar};   \end{tikzpicture} \end{document}   How can I create a third node below those two nodes with the width of foo, bar and the node distance between them? Is there a way to do this with the fit library or is this the wrong approach? Primitive of holomorphic Function $\frac{1}{z}$ on an Annulus. Given an Annulus with $A(0,r,R)$ show by considering Cauchy's Theorem for primitives that there is no holomorphic function with $f'(z)=\dfrac{1}{z}$.   I am struggling to picture this since but it seems like there are issues because $f(z)=\log z$ isn't well defined in the same range as $\dfrac{1}{z}$.  Am I looking to show that $\int_Ag(z)dz = 0$ where $g(z) = \dfrac{1}{z}$?