Get a process number with MPI_Allreduce
MPI Get Processor with Minimum value
Inconsistency in display of animated avatars It has been discussed previously that animated avatars are disliked because they cause a distraction from the content. However, currently animated avatars are not treated consistently.   On desktop, animated avatars are displayed as a still image, both in posts and on the profile page. On mobile, animated avatars are displayed as a still image in posts, but animated on the profile page.   I'm tagging this  because I'm guessing one of these two is unintended. Either avatars should animate on the profile page on both desktop and mobile, or on neither. (I sincerely hope that we are all agreed there should be no animation of avatars in posts.)  Example animated profile    This appears to animate on mobile, and show a still image on desktop (for myself and for other users who have tried).    I'd also like to hear arguments for and against animating only on the profile page, but the main purpose of this post is to clear up the inconsistency. How to find application's path from command line? For example, I have git installed on my system. But I don't remember where I installed it, so which command is fit to find this out? Problem 20-9 in Lee's Introduction to Smooth Manifolds (2nd Ed.) asks to prove that for a Lie group $G$, and for $X, Y\in \text{Lie}(G)=\mathfrak g$, there is $\epsilon&gt;0$ and a smooth map $Z:(-\epsilon, \epsilon)\to \mathfrak g$ such that   $$(\exp tX)(\exp tY) = \exp\left(t(X+Y) + \frac{1}{2}t^2[X, Y] + t^3 Z(t)\right)$$   What we want to show is that the first and second term in the Taylor expansion of $\exp^{-1}\left((\exp tX)(\exp tY)\right)$ are $t(X+Y)$ and $\frac{1}{2}t^2[X, Y]$ respectively.  Calculating the first term is easy since we just need to differentiate $\exp^{-1}((\exp tX)(\exp tY))$ with respect to $t$ at $t=0$ once, and this gives the desired result.  But for the second term we need to take the second derivative at which I am stuck. How much set theory and logic should typical algebraists/analysts/geometers know? (soft-question) I know enough amount of set theory and logic to study grad-level math. However, I don't know more advanced set theory and logic, such as the ones on Kunen's or Shoenfield's texts. Although it's good to learn such advanced topics, I may not have enough time to do so, since I will probably put my emphasis on algebra, analysis or geometry as well as mathematical physics.   Although how much set theory and logic I should learn is totally up to what sort of analysis, algebra or geometry I will study, I want to know how much of them typical competitive algebraists/analysts/geometers know. If you are one of them, how much do you know? Transforming positively skewed data with positive and negative values My data (see image below) is positively skewed and contains both positive and negative values. I'd like to transform it to achieve normality so I can apply a repeated measures ANOVA, but can't find a technique that works.  I've considered the following options:   Square-rooting: doesn't keep the sign Square-rooting then making the original negative values negative: makes my data bimodal Natural log transform: can't do this with negative values Add a constant then log transform: this arbitrarily leaves my lowest value as an outlier '' transform (Cox, 2005; also Whittaker et al. 2005): makes my data bimodal Outlier removal (2.5 SD): doesn't fix normality, but an ANOVA on this data has similar results to an ANOVA on the raw data (for better or worse). Perform the non-parametric equivalent (Friedman test) and compare the results: will do this today   My supervisor suggests I should stick with the outlier removal though the data is still visibly skewed, and 'see what the reviewers suggest' but I just wanted to check here in case there was anything I was missing.  Original data:    With outliers (2.5 SD) replaced with the value at that criterion. I later decided to just exclude the outliers, so imagine the highlight data points in each condition removed. What kind of ship was flying away from Rey in her flashback? The ship flying away from Rey in her flashback of being left on Jakku looks like one of the ships in the group that takes her away when she is captured.  If so, and it is a First Order ship that dropped her off, this is an interesting Easter egg. How to pass Unicode characters as JSP/Servlet request.getParameter? Is it true that a dihedral group is nonabelian? Is it true that a dihedral group is nonabelian?  I'm not sure if the result is true. I checked it for some lower order and I think the result may correct.   But I failed to prove/disprove the result. Separability over intersection of intermediate fields Let $E\mathop{/}F$ be a finite-degree normal extension of fields. Let $K$ and $L$ be intermediate fields (that is, $F\subseteq K\subseteq E$ and $F\subseteq L\subseteq E$) such that $E$ is separable over both $K$ and $L$. Show that $E$ is separable over $K\cap L$.   So I was thinking that if $f=\min_{K\cap L}(\alpha)$. Then $\min_{K}(\alpha)$ divides $f$. But if $f$ has repeated roots then I don't see what goes wrong.   Thanks! Indefinite integral $\int(\sin x)^2/(x\cdot\cos x-\sin x)^2\,dx$ How to find the antiderivative of $\dfrac{(\sin x)^2}{(x\cdot\cos x-\sin x)^2}$? I know that series theory can solve the problem. But I wish to solve the problem by the antiderivative way. The numerator and denominator divide the $x^2$ at the same time, don't they? Finding center and radius of circumcircle Find the center and radius of the circle which circumscribes the triangle with (complex) vertices $a_1,a_2,a_3$. Express the result in symmetric form.   I'm not sure where to start in this question. The circumcenter is the intersection of the perpendicular bisectors, but I don't know how to calculate the line equation of the perpendicular bisectors yet. As for the radius, after we find the circumcenter $c$ we can calculate it using $|c-a_1|$ (or $|c-a_2|$ or $|c-a_3|$; all three should be equal.) So how can I calculate the circumcenter? Is it a wise-decision to buy full-frame lenses for use on an APS-C body? I have a Canon 550D which I've been using for around a year now. I really love it and have learned a great deal with this and the 18 - 135mm kit lens. But now with experience I feel the need to get some better glass. I won't be buying a new body any time soon because I figure investing in some good glass is more important.   As I have looked around, I see quite a few good used L lenses I can get in ebay for good bargain prices. But I know that the EF lenses don't have the same focal length in the cropped sensors. Is it a wise decision to buy these EF lenses or buy the cropped sensor alternatives?  I have the following lenses in mind that I am looking to buy down the line from the canon range over the next several months.  16-35mm f/2.8L, 24-70mm f/2.8L, 70-200 f/4L.  Are these apt choices for cropped sensors? I know most pros with FFs use these but I am a bit skeptic that they will serve the same purpose for me. If so what are the alternatives for this that have almost as good image quality? "Actually" vs "really" When I am faced with a simple linear congruence such as  $$9x \equiv 7 \pmod{13}$$ and I am working without any calculating aid handy, I tend to do something like the following:  "Notice" that adding $13$ on the right and subtracting $13x$ on the left gives: $$-4x \equiv 20 \pmod{13}$$  so that $$x \equiv -5 \equiv 8 \pmod{13}.$$  Clearly this process works and is easy to justify (apart from not having an algorithm for "noticing"), but my question is this: I have a vague recollection of reading somewhere this sort of process was the preferred method of C. F. Gauss, but I cannot find any evidence for this now, so does anyone know anything about this, or could provide a reference? (Or have I just imagined it all?)  I would also be interested to hear if anyone else does anything similar. I know that Wubi is slower in disk IO, but I can't find anything about it online other than vague statements such as "slightly slower disk seeks".  Has anyone done any benchmarks to quantify the speed difference? How can I communicate with a Unix domain socket via the shell on Debian Squeeze? I’m running a Debian Squeeze web server. I’ve installed memcached on it, and configured memcached to listen on a Unix domain socket (at /tmp/memcached.sock), as it only needs to receive messages from the website, which lives on the same server.  It seems to be working fine, but I’d also like to communicate with memcached via the shell, to check that it’s doing what I think it’s doing.  memcached accepts messages via a simple ASCII protocol (if I understand correctly). If it was listening on TCP/IP, I could send messages to it via e.g. nc:  $ echo "stats settings" | nc localhost 11211   But I can’t figure out how to send that text to the domain socket instead.  On my laptop (which runs OS X Lion), both nc and telnet have options (-U and -u respectively) to use domain sockets. However, on my Debian Squeeze web server, these options aren’t present. How can I make a more realistic glass shader? Here's a sample scene:  A room with a window, a point light to project light into the room, an HDR environment outside the room and a nice Image by Rembrandt that should be somewhat reflected on the glass:    Using a standard glass shader on the window, the direct light from the lamp does not shine into the room, regardless of how bright that light is. So I can't recreate the impression of hard day light, with clearly defined areas of light and shadow.    Adding a transparent shader to the glass shader I get a very pleasing result. The light from the lamp illuminates into the room creating defined shadows, transparency seems unaffected, to see the HDR in the background, the refection seem correct to me (I also like how I get double reflections from the thick glass).    Even though I am quite happy with this solution, I've gotten a few comments on making a setup with light path nodes controlling the mix of transparent and glass. The biggest issue is that the reflections on the glass are brighter than what they should be.  So the question is: By using this approach am I messing up any of the qualities of glass? And if so, what would make a proper glass shader that is realistic, in terms of letting direct light through, while keeping reflections, refraction and transparency?  A file to play with:    The HDR image used was created by Influence of charged particle's own electric field on itself I read this in my textbook: A charged particle or object is not affected by its own electric field.  Since I find this completely unintuitive and my mind is yelling "wrong! wrong! how could a particle even distinguish between its own field and the external fields?" I would really like to hear an explanation about why this is true, if it is.  (A corollary question that comes to my mind after thinking about this is... What about gravity and mass considering the analogous situation? And the other two forces?) What is the Mediator in this Feynman Diagram $q\bar{q} \rightarrow gg$? Let's consider the t-channel version of the process $q\bar{q} \rightarrow gg$. What is the mediator in this case, a $q$ or a $\bar{q}$? Naively, I would have thought a $q$ (as to have one fermion line), but I am not $100 \%$ sure. Why is there a big delay after entering a wrong password? I notice a weird (well, according to me) thing about passwords. For example, if I type an incorrect password during login, there will be a few seconds' delay before the system tells me so. When I try to sudo with a wrong password I would also have to wait before the shell says "Sorry, try again".  I wonder why it takes so long to "recognize" an incorrect password? This has been seen on several distributions I use (and even OSX), so I think it's not a distribution specific thing.