I have multiple plots (about 15 different figures) that have the same axes (i.e., same ymin and ymax values and same xticks). One of the plots has very large values. I don't want to either increase ymax nor use log scale for the y-axis. I want to display the y values greater than ymax by adding a discontinuity on the y-axis.  Here is an MWE:  \documentclass[preview=true]{standalone} \usepackage{pgfplots} \begin{document} \begin{preview} \begin{tikzpicture} \begin{axis}[ymin=0,ymax=100, log ticks with fixed point, ] \addplot table { 1 10 2 20 4 25 }; \end{axis} \end{tikzpicture}% \begin{tikzpicture} \begin{axis}[ymin=0,ymax=100, log ticks with fixed point, ] \addplot table { 1 50 2 100 4 200 }; \end{axis} \end{tikzpicture} \end{preview} \end{document}   What I need:    I have added the short lines on the axes and the plot are to denote the discontinuity. The numbers 100 and 200 on the y-axis may not be a good idea; this kind of presentation may be a source of misunderstanding. It may be better to display y values as labels near data points as follows:    The input data of plots comes from a pgfplotstable.
Is there an easy way to 'break' the axis in a pgfplots environment? What I'm talking about is something like     Any minimal plot will do as an example...for example  \documentclass{minimal}   \usepackage{tikz} \usepackage{pgfplots}  \begin{document} \begin{tikzpicture} \begin{axis}[ymin=0, ymax=80] \addplot {x*0};  \addplot {x^2+50}; \end{axis} \end{tikzpicture}  \end{document}   For example, in the below plot,    I want to break the axis from around y = 10 to y = 40.   Any ideas? Does PGF have this functionality? A search for `break' in the manual doesn't yield anything.
I need to find all group homomorphisms of $S_n\to\mathbb{C}^*$ (for $n\ge2$), and also all group homomorphisms of $A_n\to\mathbb{C}^*$ (for $n\ge2$).  Someone on this site, two years ago, seems to have already asked the same question (). I understand what the questioner says there, but I don't understand it when he says:     Therefore there is exactly one $g:\mathbb{Z}/2\mathbb{Z}\to\mathbb{C}^*$, so all elements of $a\in\mathbb{C}^*$ give us $\operatorname{ord}(a)\mid g[\mathbb{Z}/2\mathbb{Z}]$, so $a$ can only be $-1$ or $1$. Now we know that $f:S_n\to\{-1,1\}$ &hellip;   What is he saying there? And how to go on from there? (I do not understand the answer given either &hellip;)  I hope that someone here can help me further. (And if I'm not allowed to ask this question because is has already been asked two years ago, please tell me what to do instead).  Thank you in advance! Use of .apply() with 'new' operator. Is this possible? Why does an integral change signs when flipping the boundaries? Let us define a very simple integral:   $f(x) = \int_{a}^{b}{x}$    for $a,b\ge 0$.  Why do we have the identity $\int_{a}^{b}{x} = -\int_{b}^{a}{x}$?  I drew the graphs and thought about it but to me integration, at least in two-dimensions, is just taking the area underneath a curve so why does it matter which direction you take the sum? I am wondering the following question: Let $X$ be a separable Banach space which is linearly isomorphic to a dual Banach space $Y^*$. Is there a Banach space $Z$ such that $X$ is lineraly isometric to the dual of $Z$: $X=Z^*$.  I think that the answer is no, but I do not have a counterexample. Since $L_1$ is not isometric to any dual Banach space, maybe one can find a dual Banach space which is isomorphic to $L_1$...  To finish, do that change anythink if I suppose $X$ to be almost linearly isometric to $Y^*$ ? By almost linearly isometric I mean that for every $\varepsilon &gt;0$ there exist $T$: $X \to Y$ a linear isomorphism satisfying $\|T\|  \|T^{-1}\| \leq 1+\varepsilon$. Remove extra header lines from file, except for the first line I have a file that looks like this toy example.  My actual file has 4 million lines, about 10 of which I need to delete.  ID  Data1  Data2 1    100    100 2    100    200 3    200    100 ID  Data1  Data2 4    100    100 ID  Data1  Data2 5    200    200   I want to delete the lines that look like the header, except for the first line.  Final file:  ID  Data1  Data2 1    100    100 2    100    200 3    200    100 4    100    100 5    200    200   How can I do this? Why Lasso or ElasticNet perform better than Ridge when the features are correlated I have a set of 150 features, and many of them are highly correlated with each other. My goal is to predict the value of a discrete variable, whose range is 1-8. My sample size is 550, and I am using 10-fold cross-validation.   AFAIK, among the regularization methods (Lasso, ElasticNet, and Ridge), Ridge is more rigorous to correlation among the features.  That is why I expected that with Ridge, I should obtain a more accurate prediction.  However, my results show that the mean absolute error of Lasso or Elastic is around 0.61 whereas this score is 0.97 for the ridge regression. I wonder what would be an explanation for this.  Is this because I have many features, and Lasso performs better because it makes a sort of feature selection, getting rid of the redundant features? I've been learning C#, and I'm trying to understand lambdas.  In this sample below, it prints out 10 ten times.  class Program {     delegate void Action();     static void Main(string[] args)     {         List&lt;Action&gt; actions = new List&lt;Action&gt;();          for (int i = 0; i &lt; 10; ++i )             actions.Add(()=&gt;Console.WriteLine(i));          foreach (Action a in actions)             a();     } }   Obviously, the generated class behind the lambda is storing a reference or pointer to the int i variable, and is assigning a new value to the same reference every time the loop iterates.  Is there a way to force the lamda to grab a copy instead, like the C++0x syntax  [&amp;](){ ... } // Capture by reference   vs.  [=](){ ... } // Capture copies Are software titles italicized? The titles of freestanding works (books, movies, plays, albums, etc.) are italicized; smaller parts within these works (chapters in a book, articles in a magazine, songs within an album) are not (they are put in quotes, instead).  How are software titles treated?  My understanding is that if a particular program resembles a book or a dramatic work (like a video game), its title is italicized -- otherwise, it is treated as a proper noun, just like any other product.     I played Grand Theft Auto, instead of reading "Democracy in Ancient Greece" in Microsoft Encarta and preparing my presentation in PowerPoint.   Is this approach correct? I have a module with a page callback handler for the path "products". So if the user navigates to products/apples then the module presents a page about our apples, and if they go to products/oranges then etc. These pages include detail about the various products.  I would like XML Sitemap to be populated from my module. After all, it's my module that knows what products exist, their descriptions etc.  Any hook or anything I can use for that? When is a gerund supposed to be preceded by a possessive adjective/determiner? I assume that the following sentences are grammatically correct:   He resents your being more popular than he is. Most of the members paid their dues without my asking them. They objected to the youngest girl's being given the command position. What do you think about his buying such an expensive car? We were all sorry about Jane's losing her parents like that.   I'm still getting used to this possessive gerund structure. It sounded so weird to me at first. Is the structure used in both formal and informal contexts? Are there any alternative structures that result in the same meaning and are more frequently used? (Examples taken from ) How to define servlet filter order of execution using annotations in WAR I have a cron job that runs every minute on an Ubuntu 12.04 box  $sudo crontab -e * * * * * mylogin /pathto/file.sh &gt; /log/filelog   If I run file.sh, the bash script does some stuff and echos out runs:  $ ./file.sh  runs   If I check the log of cron tab it shows that the job is running:  Jul 10 12:41:01 localhost CRON[1811]: (root) CMD (mylogin /pathto/file.sh &gt; /log/filelog) Jul 10 12:41:01 localhost CRON[1810]: (CRON) info (No MTA installed, discarding output) Jul 10 12:42:01 localhost CRON[1813]: (root) CMD (mylogin /pathto/file.sh &gt; /log/filelog)   However, the script is not running. It is not doing it's work and not echoing runs to /log/filelog.  $cat /log/filelog  #shows nothing   What other steps can I take to debug this problem? Prove the equality: $\det\left[\begin{smallmatrix} -2a &a+b &a+c \\ b+a&-2b &b+c \\ c+a&c+b &-2c \end{smallmatrix}\right] = 4(a+b)(b+c)(c+a)$ i have to prove:   $$\begin{vmatrix} -2a &amp;a+b  &amp;a+c \\   b+a&amp;-2b  &amp;b+c \\   c+a&amp;c+b  &amp;-2c  \end{vmatrix} = 4(a+b)(b+c)(c+a)$$   I have tried many calculations between the rows and columns of the determinant to get to the answer i want to solve the exercise however none of them gave me something right. Can someone help? What to do with meta questions referring to currently non-existing features? I sometimes come across such questions like that:    The "Not a real question" close reason doesn't exist for long time. It doesn't make sense to answer, comment, or even up/downvote (since there's nothing more to vote for/against it).   Shouldn't such questions be locked as historical ones? Should I flag them for moderator attention or just ignore them? Install a single specific package from future distribution I'm currently using precise. I need to upgrade a certain package (namely  and it's dependencies) to a newer version, which is currently found in raring (alfa at the time of writing this). How to do it ?  What will happen if I just add to my sources.list:  deb http://archive.ubuntu.com/ubuntu raring main   Will the next apt-get update / apt-get upgrade, upgrade most of my system to raring then ? How do I read the history of my reputation? Estimator for $\theta$ using the method of moments Exercise :     Using the method of moments, find the estimator for $\theta$ for a random sample $X_1, \dots, X_n$ that follows the distribution with pdf $f(x) = \theta x^{-2}, \; 0 &lt; \theta \leq x &lt; \infty$, where $\theta$ is the unknown parameter.   Attempt :  $$m_1' = \bar{X}$$  $$μ_1' = \int_\theta^xu\theta u^{-2}\mathrm{d}u=\int_\theta^x\theta u^{-1}\mathrm{d}u=\big[\theta \ln u\big]_\theta^x =\theta\ln x - \theta\ln\theta$$  Thus, the estimator is given by :  $$m_1' = μ_1' \Rightarrow \theta\ln x - \theta\ln\theta = \bar{X}$$  But we cannot solve that equation with respect to $\theta$, so we'll take the moments of bigger order :  $$m_2' = \frac{1}{n}\sum_{i=1}^nX_i^2$$ $$μ_2' = \int_\theta^x u^2 \theta u^{-2} \mathrm{d}u = \int_\theta^x \theta \mathrm{d}u = \big[\theta u\big]_\theta^x =\theta x - \theta ^2 $$  Thus the solution of the following quadratic equation for $\theta &gt;0$, gives as the estimator of $\theta$ :  $$\theta^2-x\theta +\frac{1}{n}\sum_{i=1}^nX_i^2$$  Question : Is my solution correct ? Shall the upper bound be $x$ or $\infty$ ? mysqldump, preserve update_time and modify_time attributes as listed by show table status from Does mysqldump preserve the create_time and update_time attributes that are output by show table status from?  If not, is there an option that does this?   it looks like mysqldump preserves this data if you export to XML. EDIT: Well the data is included in the export. Whether it's read in at the other end I'm not sure.  Is there a way to do this with a normal .sql dump? Can we modify "Ask question" to automatically suggests tags based on your question content.   So instead that user needs to type "team-foundation-server" or "TFS" or "TeamFoundationServer" he will see list of tags auto-populated with ajax which he (or she) can then select and it will be associated with the question. So basically only thing we need is code which will cross-match question content with list of known tags while user is typing and display results in some nice ajax-enabled list/cloud/whatever UI control. This should be separate control for tags suggestions so user still has option to use standard tag list input to type-in tags.  In this case, instead of three (or more) tag variations we would have only one tag for Team-Foundation-Server. Is there a way to recover deleted data from a SSD / USB Flash drive?  All I could find were recovery for damaged drives, but I want to recover deleted data.  So how do I do this?