It is well known that independence of random variables implies zero correlation but zero correlation need not imply independence.  I came across plenty of mathematical examples demonstrating dependence despite zero correlation. Are there any real life examples to support this fact?
Any hard-working student is a counterexample to "all students are lazy".  What are some simple counterexamples to "if random variables $X$ and $Y$ are uncorrelated then they are independent"?
Creating compressed GeoTIFF with QGIS Clipper tool? I have a geo-tiff created by Pix4D which is about 375 Mb in file size.   I have clipped it to a smaller area using Qgis 2.8(using Raster ‣ Extraction ‣ Clipper), and the output file is about 900 MB in size.  Why did the clipping process generate such a large file, when the source file was smaller?   How do I run the clipper tool so that it produces a smaller size? Evaluating $\zeta(0)$ using the functional equation of Riemann-Zeta function. $$\zeta(it)=2it\pi it−1\sin(i\pi t/2)\Gamma(1−it)\zeta(1−it).$$ Everything on the RHS is never zero,  Does that means LHS has no zeros, since $\sin(s)$ has a simple zero at $s=0$ while $\zeta(1−s)$ has a simple pole at $s=0$  (the Laurent expansion), so the product $\sin(i\pi t/2)\zeta(1−it)$ is finite and nonzero at $t=0$.  My question is that from functional equation one can't get direct answer $\zeta(0)=−1/2$ unless using alternate infinite series ! Catching poisoned arrows When catching an arrow tipped with poison (like the ones used by yuan-ti) with an ability like the one the monk has or the one given by arrow catching gloves: does the ability reduce the poison damage? If so, is the total damage or the piercing one caused by the arrow only the damage that must be downed to 0 to catch the missile? Cruising the old questions I came across juantheron asking for $\int \frac {\sec x\tan x}{3x+5}\,dx$ He tried using $(3x+5)^{-1}$ for $U$ and $\sec x \tan x$ for $dv$while integrating by parts.  below is his work.  How can I calculate $$ \int {\sec\left(x\right)\tan\left(x\right)  \over 3x + 5}\,{\rm d}x $$  My Try:: $\displaystyle \int \frac{1}{3x+5}\left(\sec x\tan x \right)\,\mathrm dx$  Now Using Integration by Parts::  We get  $$= \frac{1}{3x+5}\sec x +\int  \frac{3}{(3x+5)^2}\sec x\,\mathrm  dx$$  Here he hit his road block.   I tried the opposite tactic   Taking the other approach by parts.   let $$U= \sec x \tan x$$ then$$ du= \tan^2 x \sec x +\sec^3 x$$ and $$dv=(3x+5)^{-1}$$ then $$v=\frac 1 3 \ln(3x+5)$$ Thus $$\int \frac {\sec x \tan x}{3x+5}\,dx= \frac {\ln(3x+5)\sec x \tan x}{3} - \int \frac {\ln(3x+5) [\tan^2 x \sec x +\sec^3 x]}{3} \,dx$$    As you can see I got no further than he did.   So how many times do you have to complete integration by parts to get the integral of the original $\frac {\sec x \tan x}{3x+5} \, dx$ or is there a better way? I was able to post in chat with less than 20 rep by joining 20 sites I joined 20 other sites (out of the many) and even with 1 rep was able to post in any of the chatrooms. For example: In ELL, I have just 1 rep and have posted messages in its chat.  ell.stackexchange.com/users/18923/lamart This seems like a bug because I should have needed 20 rep to post. . EDIT: From , I got the idea to make this edit. To reproduce this bug/error:  Create a new SE account. Use it to make an account here. You will get 1 default rep. Choose a random SE site and use this account to get 1 rep on that random site. Repeat the above step 20 times. Now you have 1 rep on 20 network sites but the net SE rep is 20. Go to the ELL chat and ping me. (important step)  From my comment: I have now got 40 rep since people voted this question up. Initially I had net 20 rep gained by creating 20 accounts on 20 different SE sites. Those default 1rep added up to get me to 20rep and I was able to chat. The link says one needs 20 rep in any of the SE site to chat in &quot;all the other&quot; category chatrooms..... but I did not have 20 rep on ELL at that moment. A question about long exact sequence of finite dim vector spaces Q) Prove that if $0\rightarrow V_1\rightarrow V_2\rightarrow...\rightarrow V_k\rightarrow 0$ is an exact sequence of finite dimensional vector spaces, then $\sum_{i=1}^{k}(-1)^idim (V_i) = 0$.  For $k=3$, I see that the statement is true. For $k&gt;3$, am I correct in understanding that $V_2 = V_1\oplus V_3 (\implies dim(V_2)=dim(V_1)+dim(V_3))$ and $V_3 = V_2\oplus V_4(\implies dim(V_3)=dim(V_2)+dim(V_4))$ and so on?   If it is true, then for $k=4$, $\sum_{i=1}^{4}(-1)^idim (V_i) = -m_1+m_1+m_3-m_2-m_4+m_4$ and am not sure why $m_2=m_3$ for the sum to be $0$? where $m_i = dim(V_i)$. Thanks. How can I search for one label but not another? What search query will return conversations that have the label Reading but not the label Ignore?  I've tried using label:reading -label:ignore but Gmail still returns conversations that have the label Ignore:    The query label:(reading -ignore) gives me the same results. Understanding Clip Warning 000117 for Polygons? This error makes little sense because 95% of the time this works without any problem, but here is the situation:  I am clipping polygon A by polygons B-H.  While most of the time this works perfectly, occasionally this happens:   All layers are from the same coordinate system, and the processing extent is the same as polygon A when I setup the clip. Polygons C-H clip just fine without any errors, so it is usually polygon B that has the issue; however, most of the time there are no issues whatsoever. The polygons do overlap each other. I have repaired the geometry, but the results are the same.  Given that it isn't a coordinate problem, a processing extent problem, or even a geometry problem, what else could it be causing this error, and what would I have to do to resolve this problem?  UPDATE:  The error happened again with my largest set of Polygon A; however, I then deleted 75% of the Polygon A set and it worked just fine. So my question now is: how limited is the Clip feature when it comes to large areas, and is there a way around this without having to divide the Polygon A shapefile into several segments? Is there any way to kill a Thread? Why is my profile image different? When I first signed up on a Stack Exchange site and got a profile image, it was this one (see my current user card I'm actually not sure what I look like any more):     Later, I got  and SEDE profiles, and my user image there was a different identicon. Because . I would have a picture of it, but that's the problem. ... Thanks to , I have a picture:     On those two sites, it changed from that purple one to this new one recently:   I don't know when the change happened exactly, but I KNOW I didn't change it (I don't know how to change it, otherwise I would have changed it to my main pink one).  Why did this change? Can I get my other icon back or will I be stuck with this new one?   Also, are the gravatars at Area 51 and SEDE securely generated?    After looking in my profile settings, I really confused (I am seeing my wrong avatar in more and more places since I first posted this.):        Seriously.......    What...?    (I'm using this , but be warned that they will try to IP block you after a certain number of requests to force you to pay... May look for a better alternative later.) Trying to attach a file from SD Card to email I am trying to launch an Intent to send an email. All of that works, but when I try to actually send the email a couple 'weird' things happen.  here is code   Intent sendIntent = new Intent(Intent.ACTION_SEND); sendIntent.setType("image/jpeg"); sendIntent.putExtra(Intent.EXTRA_SUBJECT, "Photo"); sendIntent.putExtra(Intent.EXTRA_STREAM, Uri.parse("file://sdcard/dcim/Camera/filename.jpg")); sendIntent.putExtra(Intent.EXTRA_TEXT, "Enjoy the photo"); startActivity(Intent.createChooser(sendIntent, "Email:"));   So if I launch using the Gmail menu context It shows the attachment, lets me type who the email is to, and edit the body &amp; subject. No big deal. I hit send, and it sends. The only thing is the attachment does NOT get sent.  So. I figured, why not try it w/ the Email menu context (for my backup email account on my phone). It shows the attachment, but no text at all in the body or subject. When I send it, the attachment sends correctly. That would lead me to believe something is quite wrong. Do I need a new permission in the Manifest launch an intent to send email w/ attachment? What am I doing wrong? I can think of three general ways of explaining why the universe contains more matter than antimatter:  (1) Near the Planck time, the universe had zero baryon asymmetry, but at some later time, determined by some GUT energy scale, the  were satisfied, and the baryon asymmetry became nonzero.  (2) Nonconservation of baryon number occurs only at Planckian energies. Near the Planck time, the baryon asymmetry evolved from zero to some nonzero value.  (3) The Sakharov conditions have never been satisfied. The baryon asymmetry has always been nonzero, and has simply scaled as expected. (Apparently one  $\Delta n=n_B-n_\bar{B}\propto s$, where $n$ is number density and $s$ is entropy density).  It seems like most theorists are interested in #1, but is there any reason why 2 and 3 aren't possible?  2 seems pretty reasonable, since for the reasons given in , we have good reasons to think that baryon number is not conserved under Planckian conditions.  3 also seems reasonable to me, since even if baryon number is nonconserved at Planckian energies, that's only one of the three Sakharov conditions. I don't see any obvious fine-tuning objections to #3, since the scaling of baryon asymmetry with cosmological expansion isn't particularly drastic (not an exponential decay or anything). Is there something unphysical about maintaining $\Delta n\propto s$ all the way back to the Planckian era?   Some people might object to #3 on aesthetic grounds, since we "expect" the initial conditions of the universe to be symmetric, but that seems weak to me. After all, we don't object aesthetically to the fact that homogeneity was an imperfect symmetry of the early universe, and we even accept that the early universe was in a thermodynamically unlikely state. Ubuntu 14.04 System Logging I've set up an Ubuntu 14.04 Server (from an Ubuntu 12.04 Server) but today I wanted to look in the auth.log but this file is not used. It seems that ´syslog´ was deleted.  How does Ubuntu 14.04 log? I need this for a server.  Thank you. Reference Text that develops Linear Algebra with Knowledge of Abstract Algebra Background: Due to some unfortunate sequencing, I have developed my abstract algebra skills before most of my linear algebra skills. I've worked through Topics in Algebra by Herstein and generally liked his approach to vector spaces and modules. Besides a very elementary course in linear algebra (where most of the time went towards matrix multiplication), I have not developed any other linear algebra skills.  But it seems that it is now necessary for me to do so. Most of the topics that I am looking at now require some background of linear algebra and I still lack understanding of ideas like: bilinear forms, invariant subspaces, eigenvalues, requirements for diagonalization of a matrix and so forth.  This brings me to my question (provided there are any)     Question: What are some good texts that develop the theory of linear algebra from a perspective of general algebra?   Are there any texts that develop the key (elementary) ideas of linear algebra in an abstract setting? Thank you for the help! Time Dilation inside a hollow shell Assuming I have a hollow shell with total mass $M$ and radius $r$. On the surface, the gravitational time dilation would be  $$\tau=t \cdot \sqrt{1-\frac{v_{esc}^2}{c^2}}$$  where  $$v_{esc} = \sqrt{\frac{2 \cdot G \cdot M}{r}}$$  but inside the shell there would be no gravitational field (Newton's shell theorem and Birkhoff's theorem).  But still, the escape velocity required to escape to infinity would be the same as on the surface, since inside the shell you could move without any accelerating or decelerating forces acting on you until you reach the surface, from where you would get pulled backwards.  So is the time dilation inside the hollow shell relative to a field free observer at infinity    zero (I assume it's not) or  the same as on the surface (my best guess), or something completely different?   I found some not really duplicate but related threads on the interior of black holes which did not really focus on the math, but I am more behind the calculations in terms of $M$ and $r$. Does an uncountable discrete subspace of the reals exist? Does an uncountable and discrete subspace of the reals exist? Did English ever have a formal version of "you"? From the top of my head, Danish "De" (practically never used), German "Sie", Chinese "您", French "vous", Spanish "usted" are a formal way of addressing someone, especially if one isn't familiar with the addressee. Did English ever have this? It sounds as though Proto-Indo-European might have had this (based on my 4 examples), but perhaps someone can enlighten me? Can an abstract class have a constructor? Can an abstract class have a constructor?  If so, how can it be used and for what purposes? How to make \left, \right pairs of delimiter work over multiple lines? I have a very long equation that must be separated into two lines, and it has several pairs of nesting \left \right delimiters. Unfortunately, it seems that they need to be on the same line in order for them to work.  Also I'm using the align environment because I need the aligning functionality. Is there a way to have the size of delimiters automatically adjusted over multiple lines? How can I reject all changes in a Linq to SQL's DataContext? On Linq to SQL's DataContext I am able to call SubmitChanges() to submit all changes.  What I want is to somehow reject all changes in the datacontext and rollback all changes (preferable without going to the database).  Is this possible?