I have a distance matrix that I want to cluster. What methods can I use to cluster the elements just based on the distance matrix (beside hierarchical clustering)?
I have a (symmetric) matrix M that represents the distance between each pair of nodes. For example,       A   B   C   D   E   F   G   H   I   J   K   L A   0  20  20  20  40  60  60  60 100 120 120 120 B  20   0  20  20  60  80  80  80 120 140 140 140 C  20  20   0  20  60  80  80  80 120 140 140 140 D  20  20  20   0  60  80  80  80 120 140 140 140 E  40  60  60  60   0  20  20  20  60  80  80  80 F  60  80  80  80  20   0  20  20  40  60  60  60 G  60  80  80  80  20  20   0  20  60  80  80  80 H  60  80  80  80  20  20  20   0  60  80  80  80 I 100 120 120 120  60  40  60  60   0  20  20  20 J 120 140 140 140  80  60  80  80  20   0  20  20 K 120 140 140 140  80  60  80  80  20  20   0  20 L 120 140 140 140  80  60  80  80  20  20  20   0   Is there any method to extract clusters from M (if needed, the number of clusters can be fixed), such that each cluster contains nodes with small distances between them. In the example, the clusters would be (A, B, C, D), (E, F, G, H) and (I, J, K, L).  I've already tried UPGMA and k-means but the resulting clusters are very bad.  The distances are the average steps a random walker would take to go from node A to node B (!= A) and go back to node A. It's guaranteed that M^1/2 is a metric. To run k-means, I don't use the centroid. I define the distance between node n cluster c as the average distance between n and all nodes in c.  Thanks a lot :)
This question led to a new package:      I'm giving my students an old exam and barely remembered to change the date at the top. A colleague and I joked about how long we could reuse the same exam, and it made me wonder if I could use LaTeX to create an exam that looked like it was written in 1963 on a typewriter.  Here's what I'd like to see:   Typewriter font even in math mode. (Several ways to accomplish this; is there a "best" way?) Slight inconsistencies in the printing of each letter. I attempt this below adapting code taken from . Each word has a random vertical shift, though I'd like to see it reduced to each letter having its own vertical shift. Other typewriter-like irregularities would be great. It would be great if math-mode delimeters \left(, \right}, etc., can be created in a piece-meal fashion as they did in days of old. Fraction bars, tops of square-root symbols -- any horizontal line, really -- is made up of a series of en-dashes that don't quite match up.   Here is what I've come up with so far:  \documentclass[10pt]{article}% This is a document class providing more font size options \usepackage{graphicx} \usepackage{ifthen} \usepackage[textwidth=7.5in,textheight=9.5in]{geometry} \pagestyle{empty}  % thanks to Bruno Le Floch: https://tex.stackexchange.com/q/9331/4012 % and in his comments to https://tex.stackexchange.com/a/29458/4012 \usepackage[first=-1,last=1]{lcg}% you can play around with these values \makeatletter \newcommand{\globalrand}{\rand\global\cr@nd\cr@nd} \makeatother  \newcommand{\randomvshift}[1]{\globalrand\raisebox{\value{rand}pt}{#1}}  %%% thanks to Martin Scharrer: https://tex.stackexchange.com/q/11598/4012 \makeatletter \def\typewriter#1{%     \@typewriter#1 \@empty } \def\@typewriter#1 #2{%    \randomvshift{#1}\space    \ifx #2\@empty\else     \expandafter\@typewriter    \fi    #2% } \makeatother \begin{document}\tt  \typewriter{Math 101 Fall 1963}  \begin{enumerate} \item   \typewriter{$\frac{\texttt{d}}{\texttt{dx}}\texttt{(x)}^2$}  \item \typewriter{State the Fundamental Theorem of Calculus.}  \end{enumerate}  \end{document} Determining members of local groups via C# I wondered whether anybody knows how to obtain membership of local groups on a remote server programmatically via C#. Would this require administrator permissions? And if so is there any way to confirm the currently logged in user's membership (or not) of these groups? Are electrons miniature black holes? I just noticed that I lost a bunch of points from my reputation score, and I used the "reputation" tab on my user profile page to try and track down the cause.  During my investigation, I noticed there was an unusual event of type "reversal". In the normal place of a question title, it says "voting corrected".     What does this mean, and what caused it?  Did I do something wrong? Why did I lose all of that reputation? Is the system punishing me for leaving too many good answers?  Is there any way to earn it back? My understanding is that light can not escape from within a black hole (within the event horizon).  I've also heard that information cannot propagate faster than the speed of light.  It would seem to me that the gravitational attraction caused by a black hole carries information about the amount of mass within the black hole.  So, how does this information escape?  Looking at it from a particle point of view: do the gravitons (should they exist) travel faster than the photons? Custom thumbnailers don’t work on Ubuntu 18.10 and 18.04 Recently I had a bunch of my own scripts for the thumbnails in Nautilus: , , office documents and so on.  Seems like either I’m doing something wrong (thumbnail generation behavior changed), or custom thumbnailes don’t work in latest GNOME at all, even my previous scripts, which worked smoothly on previous versions of Ubuntu.  I’ve done some research, tried to run a simple script (see below) and it didn’t work out.  My test thumbnailer in /usr/share/thumbnailers/z.thumbnailer:  [Thumbnailer Entry] Exec=/home/maximal/thumb.sh %s %i %u %o MimeType=image/webp;image/x-webp   Where /home/maximal/thumb.sh is:  #!/bin/bash echo $0 &gt;&gt; /home/maximal/thumb.log echo $1 &gt;&gt; /home/maximal/thumb.log echo $2 &gt;&gt; /home/maximal/thumb.log echo $3 &gt;&gt; /home/maximal/thumb.log echo $4 &gt;&gt; /home/maximal/thumb.log   Then, when I remove thumbnail cache rm -rf ~/.cache/thumbnails and restart Nautilus nautilus -q, my log file doesn’t contain anything and ~/.cache/thumbnails/fail/gnome-thumbnail-factory contains all the failed thumbs (looks like corrupted/empty PNGs):    So, apparently, Nautilus even didn’t try to execute my thumbnailer script. When I try to run thumb command itself, it works perfectly. For example convert through cwebp|dwebp package:  convert -thumbnail 256x256 file.webp png:file.webp.png   When I wrap this command to a thumbnailer, it looks like it wasn’t even requested to run by Nautilus.  [Thumbnailer Entry] Exec=convert -thumbnail %sx%s %i png:%o MimeType=image/webp;image/x-webp;   Exactly the same situation occurs with other my thumbnailers: audio waveforms, office documents, photoshop files and so on.  Could anyone help? Recently my audio input, from USB headset and USB guitar cable have stopped working. Going into Windows 'Sounds' and enabling 'Listen to this device' outputs the audio as expected; the problem is not with the devices. However, as soon as I try to use them with any other program, discord, for example, no audio input is detected by discord.  I have tried everything I can think of and some suggestions from Googling around;   Updating everything - windows, drivers, all related software Rolling windows back to the last build Trying different USB ports Reinstalling drivers and software Running Windows troubleshooters Playing with device properties settings   But nothing seems to work, any suggestions? How to determine function name from inside a function I am trying to compute this integral/limit, I don't feel like I have any good insight...   $$\lim_{n \to \infty} \int_0^{n^2} e^{-x^2}n\sin\frac{x}{n} \, dx.$$  I have tried to make a change of variable to get rid of the $n^2$, I changed to $X=\frac{x}{n^2}$ but got something even worse, I've tried to reach a situation where I could use a convergence theorem for Lebesgue Integrals,... I'm not sure I'm even on the right track!  Could you give me a hint on how to start this?  Thank you very much! What is a 'rollback'? What is a 'rollback' on Stack Exchange sites? I have seen this mentioned but I do not understand the term. Please note: This post is not a sandbox for performing rollbacks. Please do not perform rollbacks on this post without valid reason. If you want to try out a few rollbacks, do it  instead.   See also   in the Help Center Badge "multiplier" a little bit misaligned on the profile page Well, you can see it for yourself. The badge multiplier is a bit misaligned. Can you fix this please? (I know it's kinda a minor issue but it's bugging me and it's somehow off)    If it helps, I'm using Chrome version 44.0.2403.125 m. (Also repro'ed on FireFox 39.0 and )    For no good reason, that's a screenie from 's profile page. Microsoft Edge missing in Start menu and pins Lighting in a Minecraftian World Minecraft is a game that is largely based on a heightmap and uses that heigtmap information to flood the world with light.  From my understanding the highest point in the heightmap is the end of the sunlight influenced area.  Everything above that is lit by sunlight, everything below that just is influenced by light nearby in a radius of 8 blocks.  Thus if you have a floating island on the top of your world everything below that will be seen essentially as a cave.  When two lights influence the same point the brighter light wins (unsure about that).  Either way there are a couple of problems with minecrafts lighting model: first of all, if your world does not have a heightmap it becomes trickier to figure out what exactly is supposed to emit sunlight and what not.  A simple way would be to assume that the world is (in my case) a floating rock and then traverse each axis from both directions and figure out where the rock starts and ends.  But this does not fully eliminate the problem as dents in the rock are not supposed to be in darkness.  Minecraft itself will cache the light information in its chunks together with the information about the material of a block.  Thus only if the world is modified the lighting has to update.  Unfortunately that process is still pretty slow on updates and on quick light changes one can see the lighting lag behind.  That's especially true if a lot of blocks change (TNT, sunset etc.) and you're not running the fastest computer (Or Java on Mac).  From my still limited understanding of 3D graphics lighting a world like minecraft shouldn't be the biggest issue.  How would you tackle the problem?  I think the basic requirements for lighting in a voxel world would be   update fast enough that it could happen in a single frame.  One might be able to do the lighting in the graphics device and download the changed light information to the main RAM. light information must be quickly available for the main game logic so not entirely based on the graphics device: reasoning: light affects the growth of grass, spawning of monsters etc. light updates would have to be local to a chunk or have some other limit so that one does not have to relight the whole world which might be very large in size.   The main idea would be to make the light updates fast, not necessarily more beautiful. For general light rendering performance improvements one could easily add SSAO on top of that which should result in much nicer worlds. Countability of disjoint intervals According this problem/solution set from an MIT class (http://ocw.mit.edu/courses/mathematics/18-100c-analysis-i-spring-2006/exams/exam1_sol.pdf), the assertion:  "Every collection of disjoint intervals in R is countable."  is True, because "every interval contains a rational number", and the rationals are countable.  It seems to me this should be False, with possible counterexample:  { [x,x] | x is an element of R}  ie the set of all singelton intervals on R. Why isn't this a valid counterexample? Counting files in leaves of directory tree If a series converges, then the sequence of terms converges to $0$. Capacitor Voltage Rating How to find the voltage rating of a capacitor after knowing the capacitance value.  Example, For a power supply, If the input voltage is 60V and output is 5V. The input capacitor(C1) value is 100uf and output capacitor value is 1000uf.  What is the voltage rating for both the capacitors and how to find them. I have run into an issue with WPF and Commands that are bound to a Button inside the DataTemplate of an ItemsControl. The scenario is quite straight forward. The ItemsControl is bound to a list of objects, and I want to be able to remove each object in the list by clicking a Button. The Button executes a Command, and the Command takes care of the deletion. The CommandParameter is bound to the Object I want to delete. That way I know what the user clicked. A user should only be able to delete their "own" objects - so I need to do some checks in the "CanExecute" call of the Command to verify that the user has the right permissions.  The problem is that the parameter passed to CanExecute is NULL the first time it's called - so I can't run the logic to enable/disable the command. However, if I make it allways enabled, and then click the button to execute the command, the CommandParameter is passed in correctly. So that means that the binding against the CommandParameter is working.  The XAML for the ItemsControl and the DataTemplate looks like this:  &lt;ItemsControl      x:Name="commentsList"     ItemsSource="{Binding Path=SharedDataItemPM.Comments}"     Width="Auto" Height="Auto"&gt;     &lt;ItemsControl.ItemTemplate&gt;         &lt;DataTemplate&gt;             &lt;StackPanel Orientation="Horizontal"&gt;                 &lt;Button                                                  Content="Delete"                     FontSize="10"                     Command="{Binding Path=DataContext.DeleteCommentCommand, ElementName=commentsList}"                      CommandParameter="{Binding}" /&gt;             &lt;/StackPanel&gt;                                 &lt;/DataTemplate&gt;     &lt;/ItemsControl.ItemTemplate&gt; &lt;/ItemsControl&gt;   So as you can see I have a list of Comments objects. I want the CommandParameter of the DeleteCommentCommand to be bound to the Command object.  So I guess my question is: have anyone experienced this problem before? CanExecute gets called on my Command, but the parameter is always NULL the first time - why is that?  Update: I was able to narrow the problem down a little. I added an empty Debug ValueConverter so that I could output a message when the CommandParameter is data bound. Turns out the problem is that the CanExecute method is executed before the CommandParameter is bound to the button. I have tried to set the CommandParameter before the Command (like suggested) - but it still doesn't work. Any tips on how to control it.  Update2: Is there any way to detect when the binding is "done", so that I can force re-evaluation of the command? Also - is it a problem that I have multiple Buttons (one for each item in the ItemsControl) that bind to the same instance of a Command-object?  Update3: I have uploaded a reproduction of the bug to my SkyDrive: Why did Itachi say that he needs to get someone's MS to get EMS while Sasuke only had a normal Sharingan? How do I troubleshoot the "Error, press shutter release button again" message on my Nikon? The LCD on my Nikon D3000 is displaying the following error message:     Error. Press shutter release button again.   I have pressed the shutter release button but the camera still does not work.