Logistic regression with unbalanced sampling
Does an unbalanced sample matter when doing logistic regression?
What should my Objective-C singleton look like? Integration of $\frac {1}{1+\sin x}$ For $\int \frac {1}{1+\sin x} \mathrm{d}x$, my calculus textbook told me to multiply the integrand by $\frac {1- \sin x}{1- \sin x}$ to obtain: $$ \int \frac{1-\sin x}{1-\sin^2 x} \mathrm{d}x= \int \frac{1-\sin x}{\cos^2 x} \mathrm{d}x$$  From here, it is a matter of breaking up the integral to two very trivial integrals, $\int \sec^2x \mathrm{d}x$ and $\int \sec x \tan x \mathrm{d}x$, which are easily found via commonly known rules.  My question is whether there exists a way of finding $\int \frac {1}{1+\sin x} \mathrm{d}x$ without having to perform the multiplication by $1- \sin x$ in the numerator and denominator. I have an iPhone 5 running iOS 9.1 and a Macbook Pro running Yosemite.  Both devices are set up to sync photos to and from iCloud.  When I take a photo on the iPhone (for further processing on the Macbook), it takes an inordinate amount of time until the photo shows up in the Macbook's photos library - sometimes up to 10-20 minutes. Sometimes it seems to work faster if I quit the Photos app on both devices, and start it again.  I often end up sending myself photos through E-Mail because it's quicker. That seems ridiculous!  Is there a way to force a sync on the iPhone, or to speed up the process some other way? Indirectly access environment variable Given I have in a bash script  ev=USER   How can I get the environment variable value for $USER using ev?  Tried naively doing:  echo ${"$"$ev}   which results in bad substitution.  I'd expect to get back whatever the value of $USER is. I was told that the following does not work:     Employees having children will be granted a day off.   However, this sounds better:     Having children, those employees will be granted a day off.   What is wrong with the first clause? PHP: Return all dates between two dates in an array If photons have no mass, how can they have momentum? Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.  Can someone help me with this? Does gravity affects on electrons in a noticeable way? Is there a way to force a free electron move in a low speed in order to observe it actually hitting 'on the floor'? How to prove that the sum and product of two algebraic numbers is algebraic? Suppose $E/F$ is a field extension and $\alpha, \beta \in E$ are algebraic over $F$. Then it is not too hard to see that when $\alpha$ is nonzero, $1/\alpha$ is also algebraic. If $a_0 + a_1\alpha + \cdots + a_n \alpha^n = 0$, then dividing by $\alpha^{n}$ gives $$a_0\frac{1}{\alpha^n} + a_1\frac{1}{\alpha^{n-1}} + \cdots + a_n = 0.$$     Is there a similar elementary way to show that $\alpha + \beta$ and $\alpha \beta$ are also algebraic (i.e. finding an explicit formula for a polynomial that has $\alpha + \beta$ or $\alpha\beta$ as its root)?    The only proof I know for this fact is the one where you show that $F(\alpha, \beta) / F$ is a finite field extension and thus an algebraic extension. Is there any way to hide your Steam status from others? Is there any way to prevent others from seeing your Steam status without removing them as a friend?   Let's say I want to play Borderlands 2 without letting some friends know. Is there any way to hide my status to prevent them from knowing I'm playing it?  Basically, what I'm asking if Steam has an "Appear Offline" option. Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$ In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? Am I looking for a better behaved distribution for the independent variable in question, or to reduce the effect of outliers, or something else? Java socket/serialization, object won't update Can bosons that are composed of several fermions occupy the same state? It is generally assumed that there is no limit on how many bosons are allowed to occupy the same quantum mechanical state. However, almost every boson encountered in every-day physics is not a fundamental particle (with the photon being the most prominent exception). They are instead composed of a number of fermions, which can not occupy the same state.  Is it possible for more than one of these composite bosons to be in the same state even though their constituents are not allowed to be in the same state? If the answer is "yes", how does this not contradict the more fundamental viewpoint considering fermions? Let $(X, d(x,y))$ be a complete metric space. Prove that if $A\subseteq X$ is a closed set, then $A$ is also complete.  My attempt: I tried to prove that every Cauchy sequence $(b_n)$ of points of $A$ converges to a point $b\in A$. However could not figure out the exit way. Maybe I am on the wrong track. Could you please help me?  edit: More from my attempt:  Suppose $A$ is a closed set and let $(x_n)$ be a sequence of points $A$ such that $\lim_n x_n\to b$.  Suppose now that $A$ has the property that $b\in A$, whenever $x_n$ converges to $b$. We know that every element of $x_n$ which is convergent in $X$ also converges to a point in $A$. Since $x_n$ is a Cauchy sequence in $A$, it must converge to a point $y\in A$. But the limit of a convergent sequence is unique.   Take $x\in A$ and select an appropriate $n$, which enables $x_n$ to converge to a point $x$ in $X$. Since the limit is unique, it must follow that $x=y$. Thus $x\in A$ and $A$ is closed.   If $A$ is a closed subset of $X$, then any Cauchy sequence of a point in $A$ is convergent in $X$ and hence converges to a point in $A$. Thus $A$ is complete. What is the difference between read() and fread()? What is the best symbol to use for the d'Alembertian? Normally, most people use the symbol $\Box$ to represent the  (including the linked to Wikipedia page).  Recently I wanted to use \hat\Box and \tilde\Box, but they do not render very well.    What is the "best" way to create such symbols?    Aside: The above image is rendered using my local install of pdflatex: pdfTeX 3.1415926-1.40.10-2.2 (TeX Live 2009/Debian). The symbols seem to render fine on some online services: e.g. "" produces    from   \begin{align*} \Box &amp;= \sum_a \partial^a\partial_a \,, &amp; \hat\Box &amp;= \sum_a \mathcal{D}^a\mathcal{D}_a \end{align*} How to partition a list in a specific way Install ffmpeg in Ubuntu 12.04 LTS Background :  I used ffmpeg to merge two videos side by side. First I install ffmpeg by following command as it suggest by Ubuntu itself.  sudo apt-get install libav-tools   or   sudo apt-get install ffmpeg   But then I realize it is not the correct version since it doesn't support for -filter_complex and few other functions.   After a few hours researcher I found  and I succeed with video conversion as well. As per that article, it is suggesting we need to build it our own.        Question :  What is easiest way to install that ffmpeg version (which is support for -filter_complex ) without following all those steps ?