"These findings are critical [to inform/for informing] future research"
How does one know when to use a gerund or an infinitive?
How to partition an encrypted disk In the inline math mode ($...$), if the formula is too long, LaTeX will try to break it on operators, e.g.  very long text followed by a very long equation like $a+b+c+d+e+f+g+h+i+j+k+l$ etc   may be rendered as  very long text followed by a very long equation like a+b+c+d+e+f+g+h+i+ j+k+l etc   However, the break won't happen if they are separated by commas, e.g.  very long text followed by a very long equation like $a,b,c,d,e,f,g,h,i,j,k,l$ etc   will overflow the page like  very long text followed by a very long equation like a,b,c,d,e,f,g,h,i,j,k,l etc   How to make LaTeX able to insert line breaks after a comma too? Can the Universe be deterministic and still allow free will? Possible Duplicate:             As asked in the title, can a Universe which is deterministic at its fundamental level still allow free will? Proving that if $V$ is an inner product space and $U_1, U_2$ are subsets, then $U_1 \subset U_2$ if and only if $U^{\perp}_2 \subset U^{\perp}_1$ Alright Ubuntu wizards, I jacked up my system a bit unnecessarily, which is now giving me the chance to learn more about how to fix it...a vicious cycle. Anyway, I have it mostly up and running again to my liking, though I am receiving this (photo attached) prompt when my system boots:  libkmod: ERROR ../libkmod/libkmod-config.c:686 kmod_config_parse: /etc/modprobe.d/blacklist.conf line 56: ignoring bad line starting with 'rt2800usb'   Other users had success with just deleting the bad line from their blacklist.conf file, which I have done. Line 56 no longer exists, but I'm still receiving the same error. So am I missing something? Is there some follow-up command I need to give Ubuntu after saving the conf file? Some document elements (e.g., figures in the book class) are numbered per chapter (figure 1.1, 1.2, 2.1, ...). How can I achieve continuous numbering (figure 1, 2, 3, ...)?  And vice versa: Some document elements (e.g., figures in the article class) are numbered continuously. How can I achieve per-section numbering?  \documentclass{book}% for "vice versa" variant, replace `book` with `article`  \begin{document}  \chapter{foo}% for "vice versa" variant, replace `\chapter` with `\section`  \begin{figure} \centering \rule{1cm}{1cm}% placeholder for graphic \caption{A figure} \end{figure}  \end{document}   Bonus question: Is it possible to adjust the numbering of the sectioning headings themselves? Can I, e.g., switch from per-chapter to continuous numbering of sections in the book class? What is $\mathbb{E}[W(s)\mathrm{e}^{W(S)}]$ where W(S) is a standard Brownian Motion? I know that since it is a Brownian motion that $W(s)\sim{N(0,s)}$. One approach I tried, was to see that $W(s)-W(0)\sim N(0,1)$ and to let $X = W(s)$ and then solve $\mathbb{E}[X\mathrm{e}^X]$ but I end up with some awful integral. I was wondering whether there was an easier way? Or perhaps a simple way to solve this integral: $\int_{-\infty}^{\infty} \frac{1}{\sqrt{2{\pi}s}}x\mathbb{e}^{x}\mathbb{e}^{-\frac{x^2}{2s}}$ Prove $[0, 1]$ and $(0, 1]$ are equinumerous by use of bijection What my thought was that the bijection was a piecewise function:  $f(x) = 1/n+1$ if $x = 1/n$ for some $n \in \Bbb N$ and $x=1/n$ if $x \neq1/n$ for some $n \in \Bbb N$.  However, the textbook says this is incorrect. I don't actually see why. Was it a matter of brackets or the open variable $(0,1]$, which is what I tend to think. Grid search vs. random search for hyperparameter tuning I am interested in comparing the computational cost of grid search vs. random search algorithm for hyperparameter tuning. Is random search computationally less expensive then grid search? Is there an article/paper that talks about this topic? Thank you, What is Deviance? (specifically in CART/rpart) What is "Deviance," how is it calculated, and what are its uses in different fields in statistics?  In particular, I'm personally interested in its uses in CART (and its implementation in rpart in R).   I'm asking this since the  seems somewhat lacking and your insights will be most welcomed. Sum of two squares modulo p Fourier series of Log sine and Log cos Is there evidence of dark matter in our galaxy? Is there evidence of dark matter in our galaxy?  How can we measure this, say, how many percent of the center of our galaxy is dark matter?  I did not find the answer in the question $ \int_{-2}^{0} \frac{x}{\sqrt{e^x+(x+2)^2}} dx $ = -$  2.887270... $  The function has no antiderivate and there's no symmetry here to help, if you solve this I would be thankful if you would for a highschooler ^^ Is “ ’s ” ever correct for pluralization? I want to prove:  $$\int_{0}^{2\pi}\frac{1}{a^{2}\cos^2t+b^{2}\sin^{2}t}dt=\frac{2\pi}{ab}$$  by the deformation theorem of complex variable.  Then I consider a parameterization $\gamma:[0,2\pi]\rightarrow A$, traveled in the opposite direction of the clock hand, of the ellipse (in $\mathbb{C}$):  $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$  I thought of searching for a function $f:A\rightarrow \mathbb{C}$ (analytic in $A$) and a curve $\lambda:[0,2\pi]\rightarrow A$ (homotopic to $\gamma$) and use the deformation theorem:  $$\int_{\gamma}f = \int_{\lambda}f$$  But I can not find a function $f(z)$ that meets what I need, can you help me to find the f?   P.D: Necessarily I have to use the theorem of deformation Imagine your college buddy is now running a multi-billion dollar company, while you're still stuck at the same white-collar day job 5 years after graduation. You chat with him and want to express the idea that you're happy for him and fancy having his lifestyle--something like "I wish I could buy a yacht and cruise around the world like you do; I'm glad you're doing really well!"  Basically, it's the feeling of envy when you take out the resentment from it. Is there a word for it?   (I thought about "admire", but found it too strong and broad) Japan is a volcanically active country which means it has a plethora of onsen (hot springs) all around the country.  Visiting these onsen is supposed to be a popular vacation destination for the work-weary Japanese.    I've been told that, as with other things in Japan, there is a rather strict etiquette surrounding the use of the onsen.  In particular, the two things I've read about so far are   Swimming Suits are not allowed. It is very important that one bathe immediately before entering the onsen.   Are these true?  Are there any other taboos that a naive American should be aware of? Postgres : Relation does not exist error A short story about finding an inhabitable planet and meeting aliens So the story goes, humans in a spaceship search for an inhabitable planet, being surprised they found none in the vicinity of Earth. They find one, and it seems uninhabited. At the same time are observed by the aliens, who go down on the planet to meet them. The aliens sit them down and tell them a story about war and conflict that ruled the galaxy, and how all the sentient races in the galaxy got together and got rid of the race that tried to conquer all by blowing up their planets.  In the end you realise man is this terrible conqueror the aliens are talking about.