In the derivation of the support vector machine solution, one has to differentiate the term $||w||^2$ with respect to $w$ at some point, where $w$ is the normal vector to the hyperplane. The result of this differentiation is $2w$.  Can anyone show me how it comes to $2w$? I am not so clear on how to differentiate a norm with respect to a vector-- I cant see how the result comes to be $2w$.
My problem is we want to minimize $1/2 \cdot \text{Norm}(w)^2$ under suitable constraints $y(i){[w^Tx_i+b]-1}$.  We write the Lagrangian and get the above equations.  I have a problem in differentiating with respect to $w$ can somebody elaborate on that? How do we get first equation?
I'm trying to crack a cypher that I believe is Vigenère encrypted and I'm currently stuck.  I calculated the key length by finding repeated sequences in the cypher and calculating the the common factors.  Word    distance factors agzd    16       2,4,8,16        zna     92       2,4,23,46,92 zdc     54       2,3,6,9,18,27,54 csio    44       2,4,11,22,44 omy     46       2,23,46 zab     5        5   I assume the key-length is 4 as these are the once that are common factors, but from here on trying to map the correct caesar shiffre for each position I'm stuck.  Can somebody confirm that my key-length calculation has no errors which would explain why I can't solve the cypher.  Here is the cypher:  jD 2GSA 7HNA ZNA w.m. V7KXA 36HBM MKE5 /H SGP9 +R GKKJ 2I A4OTC KDBCUR. 19+R 8Y TKJ JG4 IGO6 6U4T OJ hH/BIK. 196 qFKT+9 BNJK ZD6+Q AGZD. kJ'R EaOP6 4NCR ZK 36 / AGZD6C/HOIE2D. x0ZNAC2S8IO8DI HB xX8D4D 0XK O66M 0Y MN62S 8TZABBD2Za8BI. lBJ HA+DF 6UU/ 2J /FOZDC6S8I OJ kDC8G OO 2BLCYZ O66M 0Y G 925F4 UL J2JHCTGH FHH3K How could Argus Filch clean up the whole castle by himself without magic? Whenever I try to do a fluid simulation, the fluid domain remains visible.  I have tried:ctrl+a-scale, turn on/off visibility for render/viewport  Here's a video demonstrating my problem:   Here's the blend file in case I have messed up some settings:   Thank you for any help! In a linear program, I have a variable $y$ that must obey $y=\max(x-a,0)$ where $x$ is a linear combination of the other variables and $a$ is a constant. $x$ and $y$ and $a$ are always non-negative. If the objective function decreases w.r.t. $y$, then adding the constraint $y\geq x-a$ makes it work. Are there any way to add dummy varibles and contraints such that $y=\max(x-a,0)$ when the objective function increases w.r.t. $y$? I can't say $y\leq x-a$ because if $x-a&lt;0$ it contradicts the non-negativity of $y$ whereby the solution might no longer be in the feasible region or the problem might even be infeasible. CSS Margin Collapsing So essentially does margin collapsing occur when you don't set any margin or padding or border to a given div element? Mixing and Distributing Qualifiers ($\forall x$, $\exists x$) My overall upgrade went well, but I am left with a critically lingering issue of mysql-server not being able to install itself, and nothing I am trying gets it to work.  This is the error I see when trying to install/reinstall it:  Setting up mysql-server-5.7 (5.7.11-0ubuntu6) ... Job for mysql.service failed because the control process exited with error code. See "systemctl status mysql.service" and "journalctl -xe" for details. invoke-rc.d: initscript mysql, action "start" failed. dpkg: error processing package mysql-server-5.7 (--configure):  subprocess installed post-installation script returned error exit status 1 dpkg: dependency problems prevent configuration of mysql-server:  mysql-server depends on mysql-server-5.7; however:   Package mysql-server-5.7 is not configured yet.  dpkg: error processing package mysql-server (--configure):  dependency problems - leaving unconfigured No apport report written because the error message indicates its a followup error from a previous failure.                    Processing triggers for systemd (229-4ubuntu4) ... Processing triggers for ureadahead (0.100.0-19) ... Errors were encountered while processing:  mysql-server-5.7  mysql-server E: Sub-process /usr/bin/dpkg returned an error code (1)   I've tried completely removing it, though doing so attempts to install MariaDB because of dependencies (?). Any suggestions on what I can do to fix this would be most welcome.  EDIT: Looks like I'm not the only one: Existence of minimal $\sigma$-algebra and transfinite induction Find the value of $\sin\frac{2\pi}{7}+\sin\frac{4\pi}{7}+\sin\frac{8\pi}{7}$ Why does locking the rear tires on a vehicle cause it to spin? are often used in motor-sports and stunt driving to turn around tight corners.  Essentially, the driver applies the handbrake as he enters the turn, in order to "kick out" the back end and slide the vehicle around the corner.  However, applying the handbrake hard enough to lock the rear wheels while traveling straight will cause the rear of the vehicle to "kick out".  Given enough speed, the vehicle will spin 180 degrees.  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I'm simply bad at writing proofs. Please help? Is there any way to hide taskbar labels and not combine taskbar buttons? There are three options for customizing taskbar buttons in Windows 7:   Always combine, hide labels Combine when taskbar is full Never combine   Is there any way to hide labels and not combine taskbar buttons? Or even better, to exclude only certain applications from combining?  My main problem is that I switch a lot between two instances of a single application, and having to hover over combined icon and then choosing the correct one. Alt-Tabbing is not a good alternative when I'm switching between more than three applications; clicking on taskbar only once is what I'm looking for. Show that $\arctan\frac{1}{2}+\arctan\frac{1}{3}=\frac{\pi}{4}$ Show that $\arctan\frac{1}{2}+\arctan\frac{1}{3}=\frac{\pi}{4}$.   Attempt:  I've tried proving it but it's not equating to $\frac{\pi}{4}$. Please someone should help try to prove it. Is anything wrong with the equation? If there is, please let me know. Is there a way to assign a value to a variable, that value which we get in terminal by writing any command?  Example command: sensors  From that we get CPU temperature. How can I assign this value to a temp_cpu variable? Including Bitmap (.bmp) I can't include bitmaps with pdflatex. Here is my mwe:  \documentclass[12pt,a4paper]{article} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc} \usepackage[turkish]{babel} \addto\extrasturkish{\uccode`i=\string"9D \lccode`I=\string"19 } \addto\noextrasturkish{\uccode`i=`I \lccode`I=`i }   \usepackage{graphicx}  \begin{document}  \shorthandoff{=}  \includegraphics[width=5cm,height=5cm]{000.bmp} \end{document}   Gives the error Unknown graphics extension: .bmp. As you can see on this screenshot of 's Guake he has a startup message of ASCII art when he opens it, and that's what I'd like to do, can someone help me?