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Advantages of ROC curves When are "if" and "whether" equivalent? How to take the gradient of the quadratic form? It's stated that the gradient of:  $$\frac{1}{2}x^TAx - b^Tx +c$$  is   $$\frac{1}{2}A^Tx + \frac{1}{2}Ax - b$$  How do you grind out this equation? Or specifically, how do you get from $x^TAx$ to $A^Tx + Ax$? How to access java-classes in the default-package? I'm working now together with others in a grails project. I have to write some Java-classes. But I need access to an searchable object created with groovy. It seems, that this object has to be placed in the default-package.   My question is: Is there a way to access this object in the default-package from a Java-class in a named package? I have the following code for a Figure with 4 subfigures:  \documentclass{article} \usepackage{graphicx} \usepackage{caption} \usepackage{subcaption}  \begin{document}  \begin{figure}[b]     \centering     \begin{subfigure}[b]{\textwidth}         \includegraphics[width=\textwidth]{./plots/arm1.pdf}         \subcaption{$Q^{*}$ values for arm 1}         \label{fig:arm1}     \end{subfigure}     ~     \begin{subfigure}[b]{\textwidth}         \includegraphics[width=\textwidth]{./plots/arm2.pdf}         \subcaption{$Q^{*}$ values for arm 2}         \label{fig:arm2}     \end{subfigure}      ~     \begin{subfigure}[b]{\textwidth}         \includegraphics[width=\textwidth]{./plots/arm3.pdf}         \subcaption{$Q^{*}$ values for arm 3}         \label{fig:arm3}     \end{subfigure}      ~     \begin{subfigure}[b]{\textwidth}         \includegraphics[width=\textwidth]{./plots/arm4.pdf}         \subcaption{$Q^{*}$ values for arm 4}         \label{fig:arm4}     \end{subfigure}      \caption{$Q^{*}$ values for different arms}     \label{fig:arms} \end{figure}  \end{document}   This results in   But this way, the 4 subfigures are too large to fit on 1 page. I would like to split this over 2 pages, keeping the subcaptions a, b, ... How can I do this? When are stopovers permitted on Japan Railways (JR) trains? Regarding : in general, what are the rules governing stopovers for JR trains if one does not use a rail pass? A stopover means you have a ticket from stations A to B (say, Tokyo to Hiroshima) and you disembark and exit the ticket gates at an intermediate station (say, Kyoto).  (Spoiler alert: it's complicated.) Why are Flash applications so sluggish/crashy? I've noticed that Flash applications tend to be more sluggish under Ubuntu than they do under Windows on the same machine. This is particularly noticeable when watching HD video or playing graphics/physics-heavy games. Are there any ways of improving the performance of Flash under Ubuntu, or is this just an issue with the Linux version that I will have to live with?  Currently I'm just cutting down on the number of tabs open, blocking flash ads, and closing other programs, but I'm looking for ways to affect Flash itself.  Other things I have already been doing include using Youtube's HTML5 feature and playing videos straight from /tmp in VLC. I was wondering if there was some way of streamlining Flash itself though. Perhaps not.  More Specific Question: Is there anything I can do in mms.cfg to boost performance? Any way to open windows from the windows bar using a shortcut? for example to open the first window on the left Ctrl+1, to open the second window on the left Ctrl+2.  Im using xfce4 at this moment, but if under xfce4 is not possible, is there any other desktop environment that permits this?  Since I have several windows open for the same application, I not searching for sortcuts related to the application but as I say below, to the window. Schrödinger Equation for Two Electrons? I'm having trouble finding a simple answer to this question (maybe because there isn't one), but I'm just confused about how the Schrödinger Equation would look for two electrons. I understand that it would exist in 6 dimensional configuration space, but how does the potential look? It's confusing that the potential would be different for each electron depending on where the other one is. How to implement "confirmation" dialog in Jquery UI dialog? This is problem 31b) from Dummit and Foote chapter 14.2. I am looking for a hint on how to attack the problem, since I have been thinking about it for a couple of hours but I don't even know where to start. The problem says:  Let $K$ be a finite extension of $F$ of degree $n$. Let $\alpha$ be an element of $K$. Prove that the minimal polynomial for $\alpha$ over $F$ is the same as the minimal polynomial for the linear transformation $T_{\alpha}$. In this problem, $T_{\alpha}$ is an $F$-linear transformation of $K$ that arises from $\alpha$ acting by left multiplication on $K$.  I appreciate any helpful suggestions on how to start attacking the problem or any possible hint. Thanks! How to display special German characters "ÄÜÖß" in a map? Interpreting Granger causality test's results I'm trying to educate myself on Granger Causality. I've read the posts on this site and several good articles online.  I also came across a very helpful tool, the , that allows you to enter your time series and calculate the Granger Stats.  Below, is the output from the sample data included on the site. I have also taken a crack at interpreting the results.   My Questions:     Is my interpretation directionally correct?   What key insights have I overlooked?   Also what is the meaning and interpretation of the CCF charts?  (I'm assuming CCF is cross correlation.)     Here are the results and plots that I have interpreted:  Summary of computational transaction Raw Input   view raw input (R code) Raw Output  view raw output of R engine Computing time  2 seconds R Server    'Herman Ole Andreas Wold' @ wold.wessa.net  Granger Causality Test: Y = f(X) Model   Res.DF  Diff. DF    F   p-value Complete model  356          Reduced model   357 -1  17.9144959720894    2.94360540545316e-05  Granger Causality Test: X = f(Y) Model   Res.DF  Diff. DF    F   p-value Complete model  356          Reduced model   357 -1  0.0929541667364279  0.760632773377753       My interpretation:    Test was based upon 357 data points and was performed with a lag value of 1 The p-value of 0.0000294 means I can reject the null hypothesis that x does not cause y for the Y = f(x). The p-value of .76 allows me to accept the null for X = f(Y) The fact that first hypothesis was rejected and second accepted is a good thing  I'm a little rusty on my F-test so I don't really have anything to say on this for now. I'm also not sure how to interpret the CCF graph.   I really appreciate it if any of you who are well versed with Granger-causality could let me know if I'm interpeting this correctly and also fill in some of the blanks.   Thanks for your help. Can I see images and watch movies inside the terminal emulator What is color temperature and how does it affect my photography? Regular Expression Uppercase Replacement in C# I have the following C# which simply replaces parts of the input string that look like EQUIP:19d005 into URLs, like this:  input = Regex.Replace(input, @"(EQUIP:)(\S+)", @"&lt;a title=""View equipment item $2"" href=""/EquipmentDisplay.asp?eqnum=$2""&gt;$1$2&lt;/a&gt;", RegexOptions.IgnoreCase);   The HTML ends up looking like this.  &lt;a title="View equipment item 19d005" href="/EquipmentDisplay.asp?eqnum=19d005"&gt;EQUIP:19d005&lt;/a&gt;   The only trouble is that the destination page expects the eqnum querystring to be all UPPERCASE so it returns the correct equipment when eqnum=19D005 but fails if it receives eqnum=19d005.  I guess I can modify and correct EquipmentDisplay.asp's errant requirement of uppercase values however, if possible I'd like to make the C# code comply with the existing classic ASP page by uppercasing the $2 in the Regex.Replace statement above.  Ideally, I'd like the HTML returned to look like this:  &lt;a title="View equipment item 19d005" href="/EquipmentDisplay.asp?eqnum=19D005"&gt;EQUIP:19d005&lt;/a&gt;   Notice although the original string was EQUIP:19d005 (lowercase), only the eqnum= value is uppercased.  Can it be done and if so, what's the tidiest way to do it? What's the action of banging two beers together called? Undergraduate/High-School-Olympiad Level Introductory Number Theory Books For Self-Learning Quick question: what is the compiler flag to allow g++ to spawn multiple instances of itself in order to compile large projects quicker (for example 4 source files at a time for a multi-core CPU)? How to get autofocus to work with D5100 and AF-P DX Nikkor I just bought Nikon 18 - 55 mm f/3.5 - 5.6G VR AF-P DX Nikkor from .  When I connected it to my Nikon D5100, the autofocus didn't work. There was nothing about this from the original seller's website.  Is there anything I can do short of returning?