Why is there only one discriminant axis when doing Linear Discriminant Analysis on two classes?
Why with two classes, LDA gives only one dimension?
Are there any guarantees in JLS about order of execution static initialization blocks? Why did Palpatine wait so long before giving Order 66? Print programs with its proper syntax I have defined my own language whose syntax is very close to the one of Pascal. I would like to type the following program for instance. Many people use the packages algorithmicx or algorithm2e to print programs, but it seems that we have to use their specific keywords of its syntax like procedure, end while.  I just want to indent spaces when needed, and bold some words when I want (sorry that I could not bold letters in the following figure). Do I have to use  texttt for each line? Also, with verbatim, I could not bold words...  Also, as the program is not large, I would need to put it on the left side of the page, and leave space for some explanasion text on its right hand side. So I  guss I need to get them all together, and use multicols.  Could anyone help?  program test                                      some text here var   i : integer;                                    ...    b : boolean; begin    i := 1;                                        ...    b := true;    while i &lt; 15 do       i := i  + 1;       b := not b                                  some text here    od end   Edit1: Following @Werner's tabbing solution, I have made the code a minipage:  \begin{minipage}[t]{0.48\linewidth}% \begin{tabbing} Werner's solution \end{tabbing} \end{minipage}\hfill \begin{minipage}[t]{0.48\linewidth} a paragraph \end{minipage}   Actually as the code shows, I want the texts to be another separated minipage on the right hand side of the code. I have then 2 questions:   is it reasonable to make 0.48\linewidth instead of 0.5\linewidth? 0.48\linewidth is a conventional choice? is it possible to make a frame around the code, and use \caption and \label to make it a reference (I prefer figures)? How do I list the default installed packages? I am developing an offline installer for all versions of Ubuntu, and I need Ubuntu's default installed packages list. Is there a way to get this information from any server (web server)? Any script to fetch any Ubuntu version's default installed packages list.  I will give the Ubuntu version, and the script will fetch the packages list.  Note: I need at least a server address. I can write a script for this. urlEvent is undefined Color gradient for bars in pgfplots I want that each bar in my diagram has a color gradient from black to white (from left to the right). However, for the following code, the gradient exists for the entire diagram such that the left bar is black, the middle one is gray, and the right one is white.   \documentclass{report}  \usepackage{pgfplots}   \begin{document}  \begin{tikzpicture}      \begin{axis}[ybar]          \addplot[left color=black,right color=white] coordinates {(1,2) (2,3) (3,4)};      \end{axis}  \end{tikzpicture}  \end{document} When to use \par and when \\, \newline, or blank lines Is it possible to get back your deleted Terraria character? How can I add an application to the GNOME window manager? The GNOME on-board documentation covers only the things anyone can easily guess. I have an application for that I can only start from the command line. Not that I mind using a terminal but ...  Anyway, how do I add the command (and preferably a nice logo) to GNOME WM? I want to change my computer's password. Right now my password is abc123. I run this command:  sudo passwd   I entered my current password and then a new one but the change does not take effect. How can I resolve this problem ? The Canon L lenses are much more expensive and presumably much better quality than non-L lenses. What makes an "L" lens? How much better are they over a similar length/speed "ordinary" canon lenses? File issues after importing Drupal site I recently tried to move my Drupal site to a new server using this page: . But now the style doesn't seem be loaded and more importantly I get this error on every page in the site (even on the frontpage):  Warning: file_put_contents(temporary://filef76T9k): failed to open stream: &quot;DrupalTemporaryStreamWrapper::stream_open&quot; call failed in file_unmanaged_save_data() (line 1900 of /Library/Server/Web/Data/Sites/Default/drupal/includes/file.inc). The file could not be created.  Any ideas what this could be about? Determine which app is drawing on top of other apps? The limit of reciprocal is the reciprocal of the limit While I was reading the book Exploratory examples for real analysis, I came across this:     to show that : $$\lim_{x\rightarrow x_o}\frac{1}{h(x)} = \frac{1}{\lim_{x\rightarrow x_o}{h(x)}} = \frac{1}{M}$$      Discussion:Let $\epsilon \gt 0$.we want to find $\delta \gt 0$ such that       if  $0 \lt |x-x_0| \lt \delta $,then $\Big|\frac{1}{h(x)}-\frac{1}{M}\Big|\lt \epsilon$.      In order to get expression involving $|h(x)-M|$,we first find the common denominator:        $\Big|\frac{1}{h(x)}-\frac{1}{M}\Big|=\Big|\frac{M-h(x)}{M~h(x)}\Big|$      $~=\Big|\frac{h(x)-M}{|M|~|h(x)|}\Big|$.      As we have to deal with variable term $|h(x)|$ in denominator.We can construct bound .Let $\epsilon =\frac{|M|}{2}$ ,since lim$_{x\to x_o}h(x)=M$,there exists $\delta_1\gt 0~~$ s.t.       if $0 \lt |x-x_0| \lt \delta_1 $,then $|h(x)-{M}|\lt \frac{|M|}{2}$.      As you study steps below,identify that step where $h(x)\neq 0$ for all $0 \lt |x-x_0| \lt \delta_1 $ plays a critical role:      $|M|=|M-h(x)+h(x)|$      $~~~~~~\leq |M-h(x)|+|h(x)|$      $~~~~~~= |h(x)-M|+|h(x)|$      $~~~~~~\lt \frac{M}{2}+|h(x)| \implies$      $\frac{|M|}{2} \lt |h(x)| \implies$      $\frac{1}{h(x)}\lt \frac{2}{|M|}$,where $0 \lt |x-x_0| \lt \delta_1 $.      Now that we've bound for $1/h(x)$,we can apply the definition to term $|h(x)-M|$.      Since     lim$_{x\rightarrow x_o}h(x)=M$,we can find $\delta_2 \gt 0$ such that,       $~~~~~~~~~~~~~~~~~~~~~~~~~~~~$if  $0 \lt |x-x_0| \lt \delta_2$, then $|h(x)-M|\lt \frac{|M|^2 \epsilon }{2}$   The thing I can't understand is for what purpose did the author work with such complicated expression involving $\epsilon $ in the end of the discussion? What is a NullPointerException, and how do I fix it? What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely? Clicking on  doesn't connect me with the meta S.Ex.SE site.  EDIT: For some entry points, . Observation courtesy Gilles.  I consider it a pity that the devs have not paid attention to this issue nor have indicated that they noted the problem. While HTTPS is not yet official on this network, I refrain from using unencrypted connections. I can't participate in metas, oh well.  EDIT #2 (2015-11-07) - with the switch to CloudFlare SSL the problem looks finally resolved.  EDIT #3 (2015-11-17) - still getting 403 Forbidden from CloudFlare. D'rats!..  EDIT #4 (2016-01-11) - We're still there. It's 2016 already... Starting a bounty. Kubuntu - can not enter wifi credentials after adding external wifi card My ethernet connection is quite unreliable (It uses powerline adapters) so I bought an external wifi adapter. I have plugged it in and run the command sudo ip address add 192.168.0.39/24 brd + dev enp7s0, and KDE has detected it. Unfortunately, it doesn't seem to realise it is a wireless network and therefore needs credentials. Where I could normally find a place to enter credentials (the network widget, system settings) there are none. KDE reports that the device is connected in the UI. How do I make it work out that it is wireless and therefore needs credentials? Edit: With ethernet plugged out, (USB) adapter plugged in: $ ip address show 1: lo: &lt;LOOPBACK,UP,LOWER_UP&gt; mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1000     link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00     inet 127.0.0.1/8 scope host lo        valid_lft forever preferred_lft forever     inet6 ::1/128 scope host         valid_lft forever preferred_lft forever 2: enp7s0: &lt;NO-CARRIER,BROADCAST,MULTICAST,UP&gt; mtu 1500 qdisc fq_codel state DOWN group default qlen 1000     link/ether 04:d9:f5:8a:f5:e0 brd ff:ff:ff:ff:ff:ff  With ethernet plugged in, adapter plugged in: 1: lo: &lt;LOOPBACK,UP,LOWER_UP&gt; mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1000     link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00     inet 127.0.0.1/8 scope host lo        valid_lft forever preferred_lft forever     inet6 ::1/128 scope host         valid_lft forever preferred_lft forever 2: enp7s0: &lt;BROADCAST,MULTICAST,UP,LOWER_UP&gt; mtu 1500 qdisc fq_codel state UP group default qlen 1000     link/ether 04:d9:f5:8a:f5:e0 brd ff:ff:ff:ff:ff:ff     inet 192.168.0.51/24 brd 192.168.0.255 scope global dynamic noprefixroute enp7s0        valid_lft 863988sec preferred_lft 863988sec     inet6 fe80::7eb1:eca2:96a0:fe5c/64 scope link noprefixroute         valid_lft forever preferred_lft forever  With just ethernet: 1: lo: &lt;LOOPBACK,UP,LOWER_UP&gt; mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1000     link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00     inet 127.0.0.1/8 scope host lo        valid_lft forever preferred_lft forever     inet6 ::1/128 scope host         valid_lft forever preferred_lft forever 2: enp7s0: &lt;BROADCAST,MULTICAST,UP,LOWER_UP&gt; mtu 1500 qdisc fq_codel state UP group default qlen 1000     link/ether 04:d9:f5:8a:f5:e0 brd ff:ff:ff:ff:ff:ff     inet 192.168.0.51/24 brd 192.168.0.255 scope global dynamic noprefixroute enp7s0        valid_lft 863960sec preferred_lft 863960sec     inet6 fe80::7eb1:eca2:96a0:fe5c/64 scope link noprefixroute         valid_lft forever preferred_lft forever  With nothing: 1: lo: &lt;LOOPBACK,UP,LOWER_UP&gt; mtu 65536 qdisc noqueue state UNKNOWN group default qlen 1000     link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00     inet 127.0.0.1/8 scope host lo        valid_lft forever preferred_lft forever     inet6 ::1/128 scope host         valid_lft forever preferred_lft forever 2: enp7s0: &lt;NO-CARRIER,BROADCAST,MULTICAST,UP&gt; mtu 1500 qdisc fq_codel state DOWN group default qlen 1000     link/ether 04:d9:f5:8a:f5:e0 brd ff:ff:ff:ff:ff:ff  lsusb, adapter plugged in: Bus 004 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 003 Device 002: ID 046d:c31c Logitech, Inc. Keyboard K120 Bus 003 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 001 Device 003: ID 1d57:32da Xenta 2.4GHz Receiver (Keyboard and Mouse) Bus 001 Device 004: ID 0bda:b812 Realtek Semiconductor Corp. 802.11ac NIC Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub  I'm not adding it with it plugged out because it's obviously the Bus 001 Device 004: ID 0bda:b812 Realtek Semiconductor Corp. 802.11ac NIC. There were no restarts between any of these changes. Comparing two byte arrays in .NET Evaluate : $1+\frac{2}{6}+\frac{2\cdot 5}{6\cdot 12}+\frac{2\cdot 5\cdot 8}{6\cdot12\cdot 18}+\ldots$ Evaluate : $$1+\frac{2}{6}+\frac{2\cdot 5}{6\cdot 12}+\frac{2\cdot 5\cdot 8}{6\cdot12\cdot 18}+\ldots$$  thought: I have tried to manipulate the series so that the sum upto n terms , can be simplified. But I can't figure out any profitable result. $$\int x^3\sqrt{4-x^2}dx$$ I tried changing the expression like this: $$\int x^3\sqrt{2^2-x^2}dx=\int x^3\sqrt{(2-x)(2+x)}dx$$ And that's where I got stuck. I tried integration by parts but it doesn't simplify the expression.