Unable to upload photos in question from the Stack Exchange Android app
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How to use `ybar interval` without skipping the last value I have the following code  \documentclass[tikz]{standalone} \usepackage{pgfplots} \usepackage{pgfplotstable} \usepackage{filecontents}  \begin{filecontents}{testdata.dat}   -3.316988309367815e-07 0.07000000000000001   -1.948815911147526e-08 0.13   7.15864175355987e-08 0   1.799432483450127e-07 0   0.0002850606647384129 0   0.0009429559686380238 0.08999999999999997   0.00157188462064142 0   0.005259918700865051 0   0.01739392641273605 0.18   0.06208364670743995 0.55   68.69485148165926 6.970000000000001   31.217611224923 79.12   0 12.89 \end{filecontents}  \pgfplotsset{compat=newest} \pgfplotstableread{testdata.dat}\datatable  \begin{document} \begin{tikzpicture} \begin{axis}[   ybar interval,   width=10cm,   height=5cm,   enlargelimits=false,    xtick=data,   ymin=0, ymax=100,   xticklabels={0 -- 0.063,0.063 -- 0.125,0.125 -- 0.25,0.25 -- 0.5,0.5 -- 1,                1 -- 2,2 -- 4,4 -- 5.6,5.6 -- 8,                8 -- 11.2,11.2 -- 16,16 -- 22.4,22.4 -- 31.5},   x tick label style={rotate=60,anchor=east}   ]   \addplot table[x expr=\coordindex,y=0]{\datatable};   \addplot table[x expr=\coordindex,y=1]{\datatable};  \end{axis} \end{tikzpicture} \end{document}   and the output looks like this:    But the command ybar interval does skip the last value. It should look like:    I prefer to have the last value to show up in the interval 22.4 -- 31.5. How do I achieve this without inserting a row of zeros to my table? 32-bit, 64-bit CPU op-mode on Linux I'm confused. Running Fedora Linux, lscpu yields:  Architecture:            i686 CPU op-mode(s):          32-bit, 64-bit ...   But when I try to install a 64-bit program (Chrome) I get error like:     Package /....x86_64.rpm has incompatible architecture x86_64. Valid architectures are ['i686', 'i586', 'i486', i386']   I'm less interested in being able to install Chrome and more interested in why lscpu says that my CPU can run in 64-bit mode; clearly this can't mean I can run 64-bit programs. Can anyone clarify? Black screen after suspend-after moving to the nvidia official drivers (not priority) Suppose that $5\leq q\leq p$ are both prime. Prove that $24|(p^2-q^2)$.   This is what I got so far. I figured that since $p,q$ are bigger than $5$, there are only odd primes for this conjecture. Then I can rename $p=2m+1,q=2n+1,m,n∈Z$.  We want to show $(p^2-q^2 )=24k,k∈Z$. By substituting $2m+1$ for $p$ and $2n+1$ for $q$, we get  $((2m+1)^2-(2n+1)^2)$. If we expand it, we get $4(m^2+n^2+m-n)$ Q. I think I can make $4(m^2+n^2+m-n)$ look like $24k$. How should I approach ?  And my prof. commented that "I would take this proof in small steps.  Rather than trying initially to prove that $24 | p^2-q^2$, look at the progress you already have.  You proved $4 | p^2-q^2$.  Can you prove 8 is a factor?  What about 3?  Then see if you can put together what you have to get 24 as a factor."  I am stuck here. Any helps? I don't do math a long time, so I completely don't remember how to prove that: $$ \sum_{i=1}^\infty \frac{i}{2^i} = 2 $$  Can anybody help me? If I want to print multiple figures in figure, I'm using subfigure in the figure environment. This work quit well and is looking smart, if all figures have the similar height. Now there is this figure which is more than two times higher than the other ones. I would like to order the subfigures like its shown in the following picture:     But I don’t know how to get this into Latex.   My regular code for four subfigures:  \begin{figure} \centering \begin{subfigure}{0.32\textwidth}    \centering    \includegraphics[width=\textwidth]{highone}    \caption{}    \label{fig:a} \end{subfigure} \begin{subfigure}{0.32\textwidth}     \centering     \includegraphics[width=\textwidth]{b}     \caption{}     \label{fig:b} \end{subfigure} \begin{subfigure}{0.32\textwidth}     \centering     \includegraphics[width=\textwidth]{c}     \caption{}     \label{c} \end{subfigure} \begin{subfigure}{0.32\textwidth}     \centering     \includegraphics[width=\textwidth]{d}     \caption{}     \label{fig:d} \end{subfigure} \caption{Blabla.} \label{fig:abcd} \end{figure}   Thank you for your help! Why does $(\frac{p-1}{2}!)^2 = (-1)^{\frac{p+1}{2}}$ mod $p$? Assume $p$ is prime and $p\ge 3$.  Through experimentation, I can see that it's probably true. Using Wilson's theorem and Fermat's little theorem, it's equivalent to saying $2^2 4^2 6^2 \cdots (p-1)^2 = (-1)^{\frac{p+1}{2}}$ mod $p$, but I can't figure out any more than that. Is it possible to cancel or clear a notification created by using notify-send? So I wrote a little script that makes sure a certain user plugs in a laptop when he logs on (it disables if he doesn't). The script uses notify-send to tell him to plug it in. If he plugs it in, the script quits. Is it possible to clear the notification automatically when he plugs it in? I'm thinking it might require somehow getting the process id spawned by notify-send and killing that PID, but I don't know how to do this.  Here's the current script:  #!/bin/bash   cat /sys/class/power_supply/BAT0/status OUTPUT="$(cat /sys/class/power_supply/BAT0/status)" echo "${OUTPUT}" if [ "${OUTPUT}" = "Charging" ] || [ "${OUTPUT}" = "Unknown" ]; then     echo charging or full elif [ "${OUTPUT}" = "Discharging" ]; then     notify-send -i /home/evamvid/Documents/Programming/OokiNoUse/power25.png "Hey there brother" "plug it in"     COUNTER=0 while [ "$COUNTER" -le 12 ] do     cat /sys/class/power_supply/BAT0/status     OUTPUT="$(cat /sys/class/power_supply/BAT0/status)"     echo "${OUTPUT}"     if [ "${OUTPUT}" = "Charging" ] || [ "${OUTPUT}" = "Unknown" ]; then         exit     elif [ "${OUTPUT}" = "Discharging" ]; then         COUNTER=$(($COUNTER+1))         echo $COUNTER         sleep 1     fi done fi Is it possible to set up and watch a game between just computer AI opponents? No human players, just AI and have the ability to scroll around and see what the AIs are doing with the turn management being also automated, so the AIs just end turn when they are done. Oh, and all of this hopefully without any sort of fog of war.  This way, I can see how the AI manages resources and units and maybe learn a thing or two as a civ newb. No hair theorem for black holes and the baryon number Create Java console inside a GUI panel How can I create an instance of the Java console inside of a GUI panel? Unbounded continuous function on non-compact metric space Suppose $(S,d)$ is a non-compact metric space. Is it possible to construct an unbounded continuous function from $S$ to $\mathbb{R}$? If it is possible, please show the construction method :)  Here's my attempt to solve this problem: Because $S$ is not compact, we can find a neighborhood assignment function $N(x)$ so that a finite cover is not possible. Then each time we can find an uncovered point from the union of neighborhoods before, and change the function by $f(x):=max\{f(x),\text{a function which equals to the indice of this point at that point and gradually vanishes at further points from the selected point}\}$. However I'm concerned that while this function is unbounded, there may be some invalid points for this function (goes to infinity)...  EDIT: As I found out there is a duplicate question, however the elementary solution is not presented in that question, so I still wish to know about this problem. :) Is there any way to verify a cashier cheque? There are plenty of warnings around about forged cashier's cheques, and that if you deposit a forged one your bank will "hold you responsible".   What does it mean that the bank will "hold you responsible"? Clearly the money won't be credited. Will you be charged a fee like an NSF cheque? Will they try to prosecute you? Is there any way to confirm whether a cashiers cheque is forged? Could you for example tell your bank that you were uncertain of the origin, and ask them to confirm it? Can you call the issuer and verify (from the serial number) that they did in fact issue a cheque for that amount with you as the payee? Java: how do I check if a Date is within a certain range? I need to end my visa waiver period when leaving States to Canada so that I don't exceed the period of 90 days. But form I-94 is no longer a physical card, it's only online.  How do I know or ensure that it will be terminated and will not continue counting the days once I leave to Canada? How do I prevent mouse movement from waking up a suspended computer? I'm trying to solve the well known Coupon Collector's Problem by explicitly finding the probability distribution (so far all the methods I read involve using some sort of trick). However, I'm not having much luck getting anywhere as combinatorics is not something I'm particularly good at.   The Coupon Collector's Problem is stated as:  There are $m$ different kinds of coupons to be collected from boxes. Assuming each type of coupon is equally likely to be found per box, what's the expected amount of boxes one has to buy to collect all types of coupons?  What I'm attempting:  Let $N$ be the random variable associated with the number of boxes one has to buy to find all coupons. Then $P(N=n)=\frac{|A_n|}{|\Omega _n|}$, where $A_n$ is the set of all outcomes such that all types of coupons are observed in $n$ buys, and $\Omega _n$ is the set of all the possible outcomes in $n$ buys. I think $|\Omega _n| = m^n$, but I'm not even sure about that anymore, as all my attempts so far led to garbage probabilities that either diverged or didn't sum up to 1. Do's and Don't's of Undergraduate Research I was fortunate enough to get a position as a researcher for the Mayo Clinic's SURF Program this year. My PI's lab focus is on the the immune system's role in CNS axonal and neuronal injury, specifically through the lens of how innate and adaptive immune effectors interact w/ infected neurons.  Although I do research under a professor at my college and I volunteered for a state university lab during the previous summer, this is my first REU/SURF opportunity, and I REALLY want to make a good impression. Here are my questions:  What are the do's and don't's in terms of being a skilled and efficient researcher?  Since I am still an undergrad, I know that I will be a less useful asset to the lab than a grad student or post-doc, but what can I do as an undergrad to not burden my colleagues and PI?  Thank you all for your help! Wishing you all the very best! Assumptions of linear models and what to do if the residuals are not normally distributed I am a little bit confused on what the assumptions of linear regression are. So far I checked whether:  all of the explanatory variables correlated linearly with the response variable. (This was the case) there was any collinearity among the explanatory variables. (there was little collinearity). the Cook's distances of the datapoints of my model are below 1 (this is the case, all distances are below 0.4, so no influence points). the residuals are normally distributed. (this may not be the case)  But I then read the following:  violations of normality often arise either because (a) the distributions of the dependent and/or independent variables are themselves significantly non-normal, and/or (b) the linearity assumption is violated.  Question 1 This makes it sound as if the independent and depend variables need to be normally distributed, but as far as I know this is not the case. My dependent variable as well as one of my independent variables are not normally distributed. Should they be? Question 2 My QQnormal plot of the residuals look like this:   That slightly differs from a normal distribution and the shapiro.test also rejects the null hypothesis that the residuals are from a normal distribution: &gt; shapiro.test(residuals(lmresult)) W = 0.9171, p-value = 3.618e-06  The residuals vs fitted values look like:   What can I do if my residuals are not normally distributed? Does it mean the linear model is entirely useless? How to calculate hash value of a file in Java?