With data.table, is SD[which.max(Var1)] the fastest way to find the max of a group?
finding the index of a max value in R
Block IPs if they access a resource Assume that $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$ and $f$ is positive on the interval $(0,1)$ and $0$ at the endpoints.    I want to prove that $$\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx &gt;4. $$  I could not make any progress. Since the unit interval is compact, we know that the continuity of $f, f'$ and $f''$ are uniform and they attain their maximum and minimum values. Moreover, I tried to apply the Mean Value Theorem but I failed. I don't really get why these hyperbolic functions are named after trig functions. Can someone enlighten me? How to install ibus-avro in Ubuntu 16.04 LTS? I tried to install ibus-avro, using the procedure that applied in Ubuntu 14.04 LTS. This procedure does not work in Ubuntu 16.04 LTS. Is there any other procedure to install avro in my new version of Ubuntu? Edits on closed posts Should questions or answers on questions that are closed be edited, even if the question is closed and the edit does not change anything about the reason it's closed? Example:  was just edited, which I saw in the review queue. It certainly improves the answer, but since the answer doesn't really have to exist on SE at all (because the question is off-topic), should this edit be made? In my understanding, the only reason that the edit option for a closed question is not greyed out is so that it can be edited to make it comply with the SE rules. I can clearly see that $\dfrac{n!}{n^n}\to 0$ when $n\to\infty$. But how do I know if the sum $$\sum_{n=1}^{\infty}\frac{n!}{n^n}$$ is convergent or not? I know this might be basic, but thank you if anyone can help me. How do I export the code documentation in C# / VisualStudio 2008? I have always made a point of writing nice code comments for classes and methods with the C# xml syntax. I always expected to easily be able to export them later on.  Today I actually have to do so, but am having trouble finding out how. Is there something I'm missing? I want to go Menu->Build->Build Code Documentation, but there is no option to do that, there. This problem is from Romanian G.M. and although it is very short, it is also (I think) very hard. Let $x, y, z$ real non-negative numbers such that $x+y+z=3$. Prove that   $$27 \leq (x^2+2)(y^2+2)(z^2+2) \leq 44 $$  I didn't succeed in any of the inequalities, I only managed to find the equality cases ($x=y=z=1$ for the first one and one of them $3$ and the others $0$). Any hint/idea/solution is welcome. I am going to install Ubuntu to dual boot with Windows 8 soon, but one of my friends warned me that partitioning my hard drive will slow my computer down. I run on a 500GB HDD and 8GB of ram if that helps at all. Is that true if I do it? Any way to change my review of suggested edit? I goofed and rejected a suggested edit, a vote that was actually directed at the previous edit that I was reviewing. As this is unfair to the user who posted the suggested edit in question, is there any way in which to change/cancel my reject? How to enable MySQL client auto re-connect with MySQLdb? I came across PHP way of doing the trick:  my_bool reconnect = 1; mysql_options(&amp;mysql, MYSQL_OPT_RECONNECT, &amp;reconnect);   but no luck with MySQLdb (python-mysql).  Can anybody please give a clue? Thanks. Class imbalance strategies When dealing with the class imbalance problem in a binary classifier, there are three ways I know of to address it: over-sampling, under-sampling and using cost-sensitive methods.   Are there any guidelines, rules of thumb or general strategies to choose among these methods? A possible answer would be: over-sample when the positive class has more than 100 instances (I just made it up). I am trying to compile a list of the different ways to come up with the closed form for the sum in the title. So far I have the famous Gauss story, the argument by counting doubletons, and using generating functions. Is there any other (significantly) different way to discover the closed form?  To clarify, Gauss's method was to take $1+2+3+\dots+n$, write it backwards, and add it up. Kolmogorov proved, that, as one considers independent (not necessary equally distributed) Random Variables: $\{X_n\}_{n\ge0}\subseteq \mathcal L^2$   With $\mathrm{Var} (X_n)=\sigma^2_n$ and without loss of generality $E[X_n]=0$.  If $\sum_{n=0}^\infty \frac{\sigma^2_n}{n^2} \lt \infty$ then SLLN holds, that is:  $$\frac1n\sum_{k=0}^n X_k \rightarrow 0 \,\,\,\,\,\,\,\,\,\,\,\,\,\text{a.s.}$$  Something different:  Also it is known, that if $\sup_{n\ge0}\sigma^2_n =: v \lt \infty$ pairwise uncorrelated $(X_n)_{n\ge0}$ will suffice for SLLN to hold.  My question in view of this situation: Is it possible to weaken the condition of $(X_n)_{n\ge0}$ beeing independent and instead merely consider pairwise uncorrelated $(X_n)_{n\ge0}$? How do I change the hostname without a restart? I want to change the OS hostname but I do not want to restart.  I have edited /etc/hostname but it requires a restart to get implemented. How to avoid this? Proof of properties of injective and surjective functions. I'd like to see if these proofs are correct/have them critiqued.     Let $g: A \to B$ and $f: B \to C$ be functions.  Then:   (a) If $g$ and $f$ are one-to-one, then $f \circ g$ is one-to-one.   (b) If $g$ and $f$ are onto, then $f \circ g$ is onto.   (c) If $f \circ g$ is one-to-one, then $f$ is one-to-one?   (d) If $f \circ g$ is one-to-one, then $g$ is one-to-one?   (e) If $f \circ g$ is onto, then $f$ is onto?   (f) If $f \circ g$ is onto, then $g$ is onto?     (a)  Let $a,b \in A$.  If $(f \circ g)(a)=(f \circ g)(b)$, then $f(g(a))=f(g(b))$.  Since $f$ is one-to-one, we know that $g(a)=g(b)$.  And, since $g$ is one-to-one is must be that $a=b$.  Hence $f \circ g$ is one-to-one.    (b) Since $f$ is surjective we know that for all $c \in C$ there is a $b\in B$ such that $f(b)=c$.  Since $g$ is surjective, there is a $a \in A$ such that $g(a)=b$.  Hence, for all $c \in C$ there is an $a \in A$ such that $(f \circ g)(a)=f(g(a))=f(b)=c$.    (c)  This is false.  Let $A=\{1\}$, $B=\{1,2\}$, and $C=\{1\}$. Define $g(1)=1$ and $f(1)=f(2)=1$. Then $f \circ g$ is injective, but $f$ is not injective.    (d)  This is true.  Let $a,b \in A$ where $a \neq b$.  If $(f\circ g)(a)\neq(f\circ g)(b)$, then $f(g(a))\neq f(g(b))$.  Hence $g(a) \neq g(b)$.  (e)  Since $f \circ g$ is surjective, then for every $ c \in C$ there is an $a \in A$ such that $f(g(a))=c$.   Let $b = g(a)$.  Then $b \in B$ and $f(b)=g(f(a))=c$.  Thus $f(b)=c$.  Hence $f$ is surjective.  (f)  Using the same set up as part (c), we have that $g$ is not surjective since there is nothing in $A$ such that $g$ will go to 1. How was the Cloak of Invisibility Created? Guaranteed lifetime of temporary in C++? I found several plugins (like  and ) to get the ability to attach a picture to a WP user. But these plugins are not maintained any more.  Since there's apparently no plugin that does it today, is there an easy way to do it manually? Word for "scary thing that's about to occur"? I have the feeling I'm forgetting a very simple word. But anyway, is there a word for that? Example:     The [...] that haven't occurred yet are the most scary ones.