cmds.cpp has this:  namespace TestNamespace {     template&lt;typename... Args&gt;     void tprint(Args const&amp; ... args)     {         std::ostringstream message;         using List= int[];         (void)List{0, ((void)(message &lt;&lt; args), 0) ... };          std::cout &lt;&lt; message.str();     } }   cmds.h has this:  namespace TestNamespace {     template&lt;typename... Args&gt; void tprint(Args const&amp; ... args); }   main.cpp has this:  #include "cmds.h"  using namespace TestNamespace;  void func() {     tprint("test\n"); }   Compiler happily compiles. Linker, however, says:  main.cpp: undefined reference to `void TestNamespace::tprint&lt;char [6]&gt;(char const (&amp;) [6])' collect2: error: ld returned 1 exit status   Makefile flags:  CPPFLAGS=-std=c++11 -m32 -Wall -g -I./ -Wno-trigraphs LDFLAGS=-std=c++11 -m32 -L./ -lm   What is going on?
Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)
How to start/stop/restart a thread in Java? Why is log-of-sum-of-exponentials $f(x)=\log\left(\sum_{i=1}^n e^ {x_i}\right)$ a convex function for $x \in\mathbb R^n$? How to prove $f(x)=\log\left(\displaystyle\sum_{i=1}^n e^{x_i}\right)$ is a convex function?  EDIT1: for above function $f(x)$, following inequalities hold:  $$\max\{x_1,x_2,\ldots,x_n\}\leqslant f(x)\leqslant\max\{x_1,x_2,\ldots,x_n\}+\log n$$  and I have tried proving its convexity via definition of a convex function with above inequalities, but that didn't work.  EDIT2: I have posted my answers below. Is there an optimal loss function for dealing with imbalanced classes? I'm aware that there are many ways of dealing with datasets where there is a strong class imbalance in the target variable: downsampling the more prevalent and less important class, over-weighting the valuable minority class, etc. Are there any loss functions that are ideally suited for these types of problems? I've heard of AUC, but AUC sounds like a means of evaluating a model once its training is complete (correct me if I'm wrong). Log loss and squared loss penalize a model's over confidence, but overconfidence and class imbalance seem unrelated. Is that true? I have my local.machine, the proxy.machine and target.machine. local.machine doesn't have direct contact with target.machine, but needs to go through proxy.machine.   I want to scp a file from target.machine to local.machine. Is this possible to do with just one command from local.machine? Can we model gravitation as a repulsive force? This question is actually related to my earlier question ("").  The fact that objects move a lot in the universe and that the universe is expanding, can imply that gravity is a repulsive force that increases with distance.. so the farthest objects repel us more.  This can still explain several existing observations, e.g., why does the apple fall?   Motion is the result of such repulsion. Two objects unlucky enough not to be moving relative to each other get squished due to the repulsion of the rest of the universe  around them. The earth repels the apple less than the stars so it is pushed towards the earth.   Furthermore, it can explain the expanding universe without the need for dark energy.  This could be demonstrated in a thought experiment. If we take a lot of same-charge particles (with small mass) such as electrons and lock them in a large box at a low enough temperature. The mutual repulsion of the particles may cause similar motion as if due to gravitational attraction.   Another experiment would be to measure the slight changes in our weight during day and night when the sun and earth align (if their masses are large enough to detect the feeble change in repulsion).   [EDIT: the question in the original form may not have been clear. It is "can we model".. with a yes/no answer and why (not). If downvoting, please justify. When should I use a List vs a LinkedList I tried the Chrome development version for a few days, didn't like it because my tabs became broken and wouldn't load properly. I changed back to the live version, but I forgot to uninstall the development version, which gave me 2 chrome icons on my task bar, but they would both load a broken version of Chrome. I then uninstalled Chrome through the control panel and reinstalled the live version, but I now have one of those broken links on my task bar (a blank page with a folded corner) that points to a version of Chrome that's no longer there. Is there a way to remove this icon? Regarding the sum $\sum_{p \ \text{prime}} \sin p$ I'm very confident that  $$\sum_{p \ \text{prime}} \sin p $$  diverges. Of course, it suffices to show that there are arbitrarily large primes which are not in the set $\bigcup_{n \geq 1} (\pi n - \epsilon, \pi n + \epsilon)$ for sufficiently small $\epsilon$. More strongly, it seems that $\sin p$ for prime $p$ is dense in $[-1,1]$.   This problem doesn't seem that hard though. Here's something that (to me) seems harder.      If $p_n$ is the nth prime, what is $$\limsup_{n \to +\infty} \sum_{p \ \text{prime} \leq p_n} \sin p?$$   What is $$\sup_{n \in \mathbb{N}} \sum_{p \ \text{prime} \leq p_n} \sin p? $$   Of course, we can ask analogous questions for $\inf$.   I'm happy with partial answers or ideas. For example, merely an upper bound. What would happen to a teaspoon of neutron star material if released on Earth? I've read on NASA's page on neutron star that one teaspoonful of that star would weigh over 20 billion tonnes on Earth. If it was somehow possible to bring it to earth would it:   Burn and disappear during Earth atmosphere entry? Assuming we have 20 billion tonnes of mass occupying the volume of a teaspoon here on Earth, would it fall through the ground under its own weight? I often find myself adding a lot of \textsl{} around inside \emph{} or \textit{} blocks because I find italicized digits to look too "showoffy" and "baroque" and to hinder legibility (I'm using $$ when the number has a mathematical sense, but this situation occurs in less technical texts like CVs, and such.).  Could someone help me write a renewcommand to automate this, or better, a single low level command that makes \emph, \itshape, \textit and friends choose slanted over italic for numbers? I'm not too familiar with the low level latex font selection system nor with a way to detect digits from regular letters.  Edit: MWE of what I need and what I want to avoid  \documentclass{article} \begin{document} He thought: '\emph{Why 1234567890 apples?}' then he realized '\emph{ah yes, he has \textsl{1234567890} childs}' \end{document}   gives:   I find the italicized version (first one) of 2,3,4 and 7 to look especially bad. I'm looking for the title of a Sci-Fi story (probably pre-1990) where a group is sent off into deep space and I believe unbeknownst to them it's a one-way journey.  In the course of the journey they all become very intelligent, they make psychoactive drugs from the plants on board, I recall that they discovered it's a one-way journey to test the affects of space travel, and they redesign/refit their engines and return to Earth.  Lame recall, sorry, that's all I got. Any help appreciated. I use the highlight mode in vim to copy a few characters.  I then want to paste more than once.  My current technique does not work well.  Sample text: Linux Solaris Irix HP-UX  Suppose I want to copy the word Linux, then paste over Solaris and Irix.   Place cursor at L in Linux Command v (for visual hilite), then e (for end-of-word), then y (for yank/copy) Now Linux is on my "vim clipboard" Move cursor to S in Solaris (first instance) Command v (for visual hilite), then e (for end-of-word), then p (for paste) Text is now: Linux Linux Irix HP-UX, but now Solaris is on my "vim clipboard" Move cursor to I in Irix (second instance) Command v (for visual hilite), then e (for end-of-word), then p (for paste) Text is now: Linux Linux Solaris HP-UX which is not what I expected.   I resort to using highlite/paste with the mouse (via X Terminal).  Surely, I can do this better.  How? It seems that through various related questions here, there is consensus that the "95%" part of what we call a "95% confidence interval" refers to the fact that if we were to exactly replicate our sampling and CI-computation procedures  many times, 95% of thusly computed CIs would contain the population mean. It also seems to be the consensus that this definition does not permit one to conclude from a single 95%CI that there is a 95% chance that the mean falls somewhere within the CI. However, I don't understand how the former doesn't imply the latter insofar as, having imagined many CIs 95% of which contain the population mean, shouldn't our uncertainty (with regards to whether our actually-computed CI contains the population mean or not) force us to use the base-rate of the imagined cases (95%) as our estimate of the probability that our actual case contains the CI?   I've seen posts argue along the lines of "the actually-computed CI either contains the population mean or it doesn't, so its probability is either 1 or 0", but this seems to imply a strange definition of probability that is dependent on unknown states (i.e. a friend flips fair coin, hides the result, and I am disallowed from saying there is a 50% chance that it's heads).  Surely I'm wrong, but I don't see where my logic has gone awry... Can you Start Skyrim 'silent' without the launcher showing up? I'm considering the ring $\mathbb{Z}[\sqrt{-n}]$, where $n\ge 3$ and square free. I want to see why it's not a UFD.   I defined a norm for the ring by $|a+b\sqrt{-n}|=a^2+nb^2$. Using this I was able to show that $2$, $\sqrt{-n}$ and $1+\sqrt{-n}$ are all irreducible. Is there someway to conclude that $\mathbb{Z}[\sqrt{-n}]$ is not a UFD based on this? Thanks. Is a business card necessary for a graduate student? I know some PhD students have their own business cards, but I don't know if it is a standard practice for PhD students to have their own business cards. I think a business card can be useful for networking in conference or collaborating with some industrial partners. So, is are business cards necessary for a PhD student or other graduate students attending conferences?   PS: in case it is field-specific, I would like to know the different practices in different fields How to assign the result of the previous expression to a variable? What are imaginary numbers? At school, I really struggled to understand the concept of imaginary numbers.  My teacher told us that an imaginary number is a number that has something to do with the square root of $-1$.  When I tried to calculate the square root of $-1$ on my calculator, it gave me an error.  To this day I still do not understand imaginary numbers.  It makes no sense to me at all.  Is there someone here who totally gets it and can explain it?  Why is the concept even useful? Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$ Let $a\ge 2$ be an integer. Show that for positive integers $m,n$, we have $a^n - 1$ divides $a^m - 1$ if and only if $n$ divides $m$.   I am having trouble showing this. I've seen a similar problem on here but it only shows one direction for the proof. I would like to see both directions.  This is what I have so far: Let $m = nq + r$, then $a^m - 1 = a^{nq + r}- 1 = a^{nq}a^r - 1 = a^{nq}a^r - a^r + a^r - 1 = a^r(a^{nq} - 1) + a^r - 1$. Since $0\le r\lt n$, $r = 0$ then $a^m - 1$ = $a^{nq} - 1$ so $a^m$ = $a^{nq}$ . Thus $m = nq$ hence $n\mid m$. keep duplicates out of $PATH on source I have the following code that's source-d by my .shellrc  PATH="${PATH}:${HOME}/perl5/bin" PATH="${PATH}:${HOME}/.bin" export PATH   but if I make changes to other code and then source this file, my path continues to get longer and longer with each source, each time appending these when they're already there. What can I do to prevent this?