Various people have advocated centering independent variables in regression, on the grounds that the intercept then refers to a sensible point (the mean of each IV) rather than the often impossible case that all the IVs are 0.  But does this really help?  First, the intercept is often not of interest.  Second, the mean of the variables depends on the particular data set.  Third, that means that, if you want to interpret the intercept, you need to know the mean of each IV.  So, I'd say that this reason for centering is not a good one. (There are some other reasons for centering which I am not discussing here).  Am I missing something?
In some literature, I have read that a regression with multiple explanatory variables, if in different units, needed to be standardized.  (Standardizing consists in subtracting the mean and dividing by the standard deviation.)  In which other cases do I need to standardize my data?  Are there cases in which I should only center my data (i.e., without dividing by standard deviation)?
Maximal ideals of polynomial rings in infinitely many variables Let $k$ be an algebraically closed field. Nullstellensatz states that the maximal ideals of the polynomial ring $R=k[X_1,\dots,X_n]$ are precisely those of the form $\langle X_1-a_1,\dots,X_n-a_n\rangle$, with $(a_1,\dots,a_n)\in k^n$.     What if we are working with infinitely many variables, say $\{X_i\}_{i\in I}$, being $I$ an infinite set? Again, the ideals of the form $\bigl\langle\{X_i-a_i: i\in I\}\bigr\rangle$, with $(a_i)_{i\in I}\subseteq k$ are maximal (even if $k$ is not algebraically closed), but what about the converse? Does an Echo Knight fighter's echo provoke an opportunity attack when it moves? trying to install libgraph Annoying FrontEnd bugs in Mathematica 10 Hyperref "enquotes" metadata EDIT: As Bill B. and Caramdir point out in their comments after Bill B. produced his results posted below, more information is needed in order to make a better call. To remedy, my output was produced using MiKTeX 2.8 pdflatex with no special command line flags or switches. My pdf viewer is Adobe Acrobat Pro 9.0. The platform is Windows 7. All software including hyperref is fully up to date against the latest rev levels and patches.  As I'm guessing that this is a pretty normal setup, at least in the Windows world, I'd be very interested (and grateful) in learning whether this problem affects other people or whether it's just some kind of rather weird one-off. My gut feel after seeing Bill B's results (and also after having traversed hyperref's code) is that the culprit is Adobe Acrobat or possibly MiKTeX pdflatex.    Can anyone corroborate? I'd be very grateful to know.    Original question:  I have a problem with hyperref; it "enquotes" Author and Keywords (but not Title or Subject) metadata if the data sent to these contain a comma or semi-colon (but not, say, a full stop or a colon).    I've included some figures and code that show this below.         \documentclass{article}  \newcommand*\metadata{% % uncomment all but one line below %  a  b  c%     &lt;-- no problem    a, b, c%     &lt;-- problem %  a; b; c%     &lt;-- problem %  a: b: c%     &lt;-- no problem %  a* b* c%     &lt;-- no problem }  \usepackage[   pdftitle={\metadata},    % never enquoted   pdfauthor={\metadata},   % enquoted if , or ; is present   pdfsubject={\metadata},  % never enquoted   pdfkeywords={\metadata}, % enquoted if , or ; is present ]{hyperref}  \begin{document}   Press ctl-d (in Acrobat Reader) to see pdf file metadata. \end{document}   Not only is this quite ugly but, more importantly, it interferes with metadata extracting programs used by certain document repositories.   I've worked my way through hyperref's code without much success. Would anyone have a solution for this problem?  Or advice about what I might be doing wrong? The keyboard on my laptop seems to be typing by itself:   It sometimes types characters like 134, whether by itself or when I hit certain keys. Repeating characters may appear unexpectedly. The system volume may change by itself, or windows like the Print dialog or Web browser may appear.   This can happen without any input or as I type, and may occur more often when certain keys are pressed. Sometimes, the keyboard fails to respond altogether. This is happening regardless of the software involved.  Is there a ghost in my keyboard—is my keyboard broken?  A sample of text from the keyboard might look like this (normal QWERTY...ASDF...ZXC... sequence is expected):   QWERTYUIOPASDF)(G@*HKLZXCVBN QWERTYIOPASDFGL!#ZXCVB13 QWERTYUIOPASDFGHJKLZXCVB!#N qwertyu41iopasdf19g13h28j113k4113zxcvb4n qwerty4u1iopasdf0g7h1jklzxcvb13m qwert13uuuuuuuuuuuuuuuiopasdf87091134ghhhhhhhhhhhhhhhhhhhhhhh13jk13zxcvb14      This question comes up often and the answers are usually the same. This post is meant to provide a definitive, canonical answer for this problem. Feel free to edit the answer to add additional details. I have Java 8 and Ubuntu 18.04. I'm using NetBeans and when tried to make some program, it couldn't be done because JavaFX is missing.  I installed Java JDK with NetBeans from Oracle's site and thought everything is included but obviously I didn't check it well.   What should I do, what should I install? I'm not so good at this and don't know if problem is with Ubuntu or Java. :( Can a particle be physically observed inside a quantum barrier? I understand that if a particle approaches a finite potential barrier of height $V_0$ with energy $E &lt; V_0$, there is still a finite probability of finding the particle on the other side of the barrier due to quantum tunneling.  My question is, since the wavefunction is nonzero inside the barrier region, is it possible to actually make a position measurement and locate a particle inside the barrier?  I mean, if we can say that "there is a nonzero probability that the particle is inside the barrier", surely this would suggest we can do so?  If not, why not? Am I understanding the whole wavefunction/probability distribution thing right? How can I determine how much bleed to use? My wife wants a 4th baby, but I don't I have a notebook with no Scroll Lock key (or any shortcut using the 'Fn' key).  Somehow Excel 2010 got the Scroll Lock on. I see it left down in the status bar and now I can't navigate through cells using the arrow keys, which is pretty annoying. It wasn't turned on some hours ago, so I think I must have hit some Scroll Lock toggle shortcut in Excel 2010 by mistake.  Anyone knows what hot to turn off Scroll Lock in Excel (shortcut or menu option)? If $R_{1}$ and $R_{2}$ are relations on a set S with $R_{1};R_{2}=R_{2};R_{1}$. Then $R_{1}$ and $R_{2}$ are bijective maps For the surjectivity part, I showed that if $(a,b)\in I$ then $(a,c)\in R_{1}$ and $(c,b)\in R_{1}$ and $(a,c)\in R_{2}$ and $(c,b)\in R_{2}$ for some $c\in S$. Now for arbituary $(x,y)\in R_{1}$ we have $(x,z)\in I$ which implies that $(y,z)\in R_{2}$. But also $(y,z)\in R_{1}$, so $R_{1}$ is surjective. Similar argument for $R_{2}$  And for Injectivity, I've tried to show that if $aR_{1};R_{2}c$ and $bR_{2};R_{1}c$, then $a=b$ but I am not entirely sure what $a=b$ means in this context. Do I have to show that there is an equivalence relation containing (a,b)?  edit: $R_{1};R_{2}$ is a composition of two relations and $I=R_{1};R_{2}$ Can't install wine on Ubuntu 14.04 I cannot install Wine on Ubuntu 14.04.  When I try to install it on the Ubuntu Software Center I always get a message that says I have unmet dependencies. I tried installing Wine through the terminal and I get this:  Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  wine : Depends: wine1.6 but it is not going to be installed E: Unable to correct problems, you have held broken packages. How to evaluate the limit of this expression?  $$\lim_{x\to\infty} \frac{\sin^2\left( \sqrt{x+1}-\sqrt{x}\right)}{1-\cos^2\frac{1}{x}}$$  I managed to simplify the denominator into a sinus form by the Pythagorean formula, and also modified the argument of the sinus in the numerator by dividing with a conjugate which I think is necessary, into this final form:  $$\lim_{x\to\infty} \frac{\sin^2\left(\frac{1}{\sqrt{x+1}+\sqrt{x}}\right)}{\sin^2\frac{1}{x}}$$  And that's where I got stuck. So far I've tried to come up with some solution to eliminate the sinus from the denominator, without success. I'm sure the solution is pretty obvious but I don't quite know how to modify the trigonometric functions in this fashion, so any help would be most appreciated. What did Bill do to make Hanzo mad? During kill Bill, we learn that all the black mamba had to do to get Hanzo to build her a sword, was to mention Bill's name.  When black mamba meets Bill at the end, she tells him that all she did was mention his name. Bill responds with, "that'll do it!"  So what was it that Bill did to Hanzo to make him come out of retirement and make another weapon of death? Is the function differentiable at $0$? Let $$f(x) = \begin{cases}\begin{align*}&amp;\cos{\dfrac{1}{x}}, &amp;x \neq0 \\ &amp;0, &amp;x=0. \end{align*}\end{cases}$$ Is the function $F(x) = \displaystyle \int_{0}^x f dx$ differentiable at $0$?  We can see that the function $f(x)$ is continuous everywhere except $x=0$. In order to show differentiability we will need to show the derivatives from the left and right are equal. So we need to show that $$\lim_{h \to 0^+} \dfrac{F(x+h)-F(x)}{h} = \lim_{h \to 0^-} \dfrac{F(x+h)-F(x)}{h}.$$ The derivative from the right is $$\lim_{h \to 0^+} \dfrac{F(x+h)-F(x)}{h} = \lim_{h \to 0^+} \dfrac{\displaystyle \int_{0}^x\cos{\dfrac{1}{x+h}}-\int_{0}^x\cos{\dfrac{1}{x}}}{h}$$ and the derivative from the left is $$\lim_{h \to 0^-} \dfrac{F(x+h)-F(x)}{h} = \lim_{h \to 0^-} \dfrac{\displaystyle \int_{0}^x\cos{\dfrac{1}{x+h}}-\int_{0}^x\cos{\dfrac{1}{x}}}{h}.$$ I am not sure how to proceed. Clearing Recently used coordinate reference systems using QGIS? After using some non usual SRC for demonstration purpose, I wish to clear my  "Recently used coordinate reference systems" list for the sake of praticity.  Is it possible?   I am using QGIS 2.10.1. How to show that the spherical metric satisfies the triangle inequality? For $x,y\in \mathbb R^n$ define  $$d(x,y)={\|x-y\| \over \sqrt{1+\|x\|^2} \sqrt{1+\|y\|^2}}$$ Here $\|x\|$ is the euclidean norm of a vector. How to prove that $d$ (the spherical metric) is indeed a metric?     Progress so far:    $d(x,y)\ge 0$ is obvious. $d(x,y) =0 \iff \|x-y\|=0 \iff x=y$, so the positivity holds. $d(x,y) = d(y,x)$ is clear from the formula, so symmetry holds.    But I am having difficulties with the triangle inequality. Writing it out in coordinates leads to a complicated inequality with square roots all over the place in denominators. Is there a better way? Security Review - CRUD/FLS Checks for every SOQL Query I know this sounds like a standard question, so please bear with me.  Recently our Security Reviews fail due to CRUD/FLS violations. The highlighted codelines include almost every SOQL Query in the application.  Our approach is usually as follows:   In case of displaying data on VF pages we either use sObjects fields or use the platform methods to check the accessibility of the fields In case of domain logic triggered by the user (e.g. by clicking a button on a VF page) we have a helper class that checks every field to be updated before doing the DML operation.   Up until recently this approach has worked fine (and passed pervious Security Reviews). As mentioned above the latest Security Review results seem to require us to check every field in a SOQL query for accessibility even if it is never displayed back to the user.    Let's suppose the following program flow as an example:   Query an object with some fields Perform some modification on said fields Perform an update on the sObject to save the modification using a helper class which checks for the required CUD/FLS rights for the modified fields   As I see it there is no need for checking field accessibility in step 1 in that case (since nothing is displayed back to the user and the dml operation is already protected). Is that correct or am I missing something? So is it really required to do an accessibility check for every SOQL Query in the code?  Another question would be how to handle background operations in that case like data purging. These have either to be running in system mode (which causes issues during the Security Review) or require the job to be started by a user with the appropriate access rights (which can be error prone and is not that user friendly). Is there any best practice regarding that.  Unfortunately I could not find a question targeting exactly that issue. Most of the questions I have found are related to how to perform that check (like  or ). So please apologize in case the question was already answered (I would really appreciate a link to the answer then).    Thanks for your time and help.  Mathias Java multiline string