what exactly is a correlation of zero meant to be, does that mean that changes in x does not affect y, if that is the case, from the scatter plot  That is completely false, as sometimes as x increases, y decreases or increases
What is covariance in plain language and how is it linked to the terms dependence, correlation and variance-covariance structure with respect to repeated-measures designs?
Search favorite questions by tag Favorite questions on Stack Overflow I feel is highly unused feature of all the features provided on the site. (This again is my personal opinion)  I have favorited around 90 question till date and it gets very very very difficult if I want to search for a question which I remember I have favorited, which defeats the entire purpose of one favouriting a question, so here is my small suggestion.  Favorites by tags  Screen 1        Screen 2        Please share your opinions on this. Dynamic select list in the form (dependent dropdown) Compare two dates with JavaScript Can someone suggest a way to compare the values of two dates greater than, less than, and not in the past using JavaScript? The values will be coming from text boxes. How to install apk in 2nd user of android 5.0 without playstore So, android 5.0.2 doesn't allow side loading of apks for 2nd user (irrespective of whether it is guest or standard user). "Unknown Sources" is disabled and is uncheckable. And I use a pure Cyanogen Mod 12 (android 5.0.2) without any Google apps. So, there is no Play Store app.  But I have root access.  As shown in the pics, Unknown Sources is Uncheckable and installation is blocked.  (Click image to enlarge)     With this situation, how can i install apks on to the 2nd user account??  EDIT:   It seems Google intentionally (in the name of security) blocked sideloading apks for 2nd user in android 5.0.2. There is a bug report . And sideloading was reenabled in android 5.1.   I will post how to sideload apks on lolipop 2nd user using adb. If this can be done without adb please post. I want to change my thesis topic (to the extent that the ethos is still in tact) but my advisor does not agree. What can I do? I am doing a phd where my aim is to solve a problem A which is very interesting. My supervisor has got a lot of connections in a technology B and he claims to be an expert in B. I came to this group because of these accomplishments. But soon I realized that B is not really a great technology for A.   So in my phd proposal I proposed a method which encompasses B but is more general (say R). Now I realize that I do not want to use B at all because my preliminary results are not encouraging. In fact, I am inclined to use E as a base technique which does not have any impact on R.  But my supervisor, who is interested in only publishing in B  and frowns upon everything else (it was a nightmare to convince him to let me work on R) is dead against it. He says that he is an expert in B and his vision of the group is not inclined with me trying other things.  There are other professors in my university who have worked in E and could collaborate but my supervisor won't collaborate with people from outside his kingdom. I also know professors from outside my university who could help me if needed. I could knock the doors of school committee in order to  help me but that would create a lot of problems as my supervisor wields a lot of power and influence everywhere.    Another query is, is it ethical to collaborate with people outside the university (of course after letting my supervisor know) for my PhD work. My Masters supervisor would be happy to help me out.  Edit: After looking at comments, I am thinking that after all, it is MY PhD. Yes, I have spent 1.5 years, but 1.5 years is left. Why should I spend any moment of my life on something I find to be not exciting, particularly less exciting because it is forced on me. And in those 1.5 years I learnt to write well and also learnt 'A' which is important. Its not total waste. My supervisor has his agenda, and why should I give up mine to make him happy? His vision is fine, but he does not have the right to force his vision on me. Proof concerning Stirling numbers of the first kind How do I show that   $${ n\brack 2} = \frac{n!}{2} \sum_{m=1}^{n-1} \frac{1}{m(n-m)}$$  using a combinatorial argument?  My definition of ${n \brack 2}$ is "the number of elements of $S_n$ which can be decomposed as the product of exactly $2$ disjoint cycles". Should I disable google maps scroll wheel zoom? In most applications of google maps the scroll wheel will zoom the map instead of scrolling it.  Personally I find this confusing, and after years of using google maps, both on the google maps web site and embedded google maps, I still often make the mistake of trying to scroll the map with scroll wheel and end up zooming it instead.  The google maps API allows me to disable scrollwheel zoom when I embed a map in my page.  The question is should I disable it?  On the one hand scroll wheel zoom is unconventional in the context of the web as a whole - in the vast majority of cases the scroll wheel scrolls things.  On the other hand scroll wheel zoom is established convention for maps.  It definitely would be a better experience for me if scroll wheel zooming was disabled, but what about the web browsing population in general?  I did some searching on whether I should disable scroll zoom and couldn't find any guidelines. So, to scroll zoom or not to scroll zoom? I am a third year (starting fourth year in the fall) PhD student in mathematics. I've passed all qualifying exams and am currently doing research. As far as I can tell, I am not doing poorly. I have the good fortune of having a great advisor, being in a very supportive department, and having friends and family who genuinely care about my success.   The fact is research is hard. It appears to consist primarily of staring at a problem for days and days and days without getting anywhere. Sometimes, rarely, I do figure something out and that feels wonderful, but the overwhelming majority of my time appears to be spent banging my head against a mostly figurative wall. I am not complaining about the material being hard, and I am not averse to putting in hard work, but I get frequently discouraged when I realize the vast volumes of mathematics that I yet know nothing about (and probably never will). It's very hard to quantify progress - in particular, there are too few tangible returns after too many hours worked. I find myself thinking along the lines of "Oh, if only someone actually smart were thinking about this problem they would have solved it in moments" and so on.   I've talked about this to some number of people; here is some advice I have received:   Take a day off. Putting in hours upon hours of trying things doesn't magically lead to a solution, particularly if the brain is tired and just wants to sleep. Have a hobby. Since math research doesn't exactly provide instant gratification, a hobby might provide some instead.  Talk to other graduate students. Realize that many graduate students go through this.   I'm interested to know how other folks have dealt with being discouraged as a graduate student. Does it get better with time and experience? Is this a sign that research is not for me and that I should seriously consider a life outside academia? With the Taylor series representation of $\sin$ or $\cos$ as a starting point (and assuming no other knowledge about those functions), how can one:  a. prove they are periodic?  b. find the value of the period? series of young adult science fiction books from early 1980s about last of a race of martial experts that sees the destruction of his home planet Most of something is plural or singular? I am writing a literature review. My question is which sentence is correct?   Most of the existing work focus on... Most of the existing work focuses on ... Most of the existing studies focus on ...   Thanks I am given the information that $ \vec{u} = \langle 1, 1/2 \rangle$ and $\vec{v} = \langle 2,3 \rangle$.   There are a few pieces I am asked to find, and these are the one I am having trouble with:   $\left\Vert \large \frac{\vec{u}}{|| \vec{u}||}\right\Vert$  The magnitude of vector u is $ \sqrt{5}/2$, of which I correctly calculated; the unit vector is then $ \langle \large \frac{2 \sqrt{5}}{5}, \frac{ \sqrt{5}}{5} \rangle$. However, when I go to find the magnitude of the unit vector, I get $ \sqrt \frac{3}{5}$, which is clearly not one. What did I do wrong? How to apply for a UK standard visitor visa as a family? I am an Indian citizen residing in the United States. My wife and I are planning to travel to the UK for a week. We plan to apply for the UK standard visitor visa from the US. I was filling out the application and I have a few questions.   Travel History - The application asks for travel history to the United States, Canada, Australia and New Zealand. Considering that we're resident aliens in the United States, should we consider all the times we've traveled back to the US from India? Travel History - Should we also list out the times we've traveled to India from the US? Cost of the trip - Hypothetically if we plan to spend a total of ~4,000 USD on this trip, should I split up the cost and write down 2,000 USD on my application and 2,000 USD on my wife's application? Income - From what I've read on the forum, my wife must say that "someone else" i.e. me - is paying for her costs and mention my GWF number in the remarks on her application. Would that be sufficient considering that I'll be sending all income documents with my application? Savings - We have joint savings accounts. Should I mention the same amount on both our applications? Posting the documents - Is the up-to-date advice to send all documents in one packet? Or would sending them in separate packets at the same time be better? My thought was to annotate my wife's packet with my GWF number if we were to send them separately. Bank statements - We get e-statements. Would printing those out be enough? Serializing anonymous delegates in C# I am trying to determine what issues could be caused by using the following serialization surrogate to enable serialization of anonymous functions/delegate/lambdas.   // see http://msdn.microsoft.com/msdnmag/issues/02/09/net/#S3 class NonSerializableSurrogate : ISerializationSurrogate {     public void GetObjectData(object obj, SerializationInfo info, StreamingContext context)     {         foreach (FieldInfo f in obj.GetType().GetFields(BindingFlags.Instance | BindingFlags.Public | BindingFlags.NonPublic))             info.AddValue(f.Name, f.GetValue(obj));     }      public object SetObjectData(object obj, SerializationInfo info, StreamingContext context,                                 ISurrogateSelector selector)     {         foreach (FieldInfo f in obj.GetType().GetFields(BindingFlags.Instance | BindingFlags.Public | BindingFlags.NonPublic))             f.SetValue(obj, info.GetValue(f.Name, f.FieldType));         return obj;     } }     Listing 1 adapted from   The main issue I can think of that might be a problem is that the anonymous class is an internal compiler detail and it's structure is not guaranteed to remain constant between revisions to the .NET Framework. I'm fairly certain this is the case based on my research into the similar problem with iterators.  Background  I am investigating the serialization of anonymous functions. I was expecting this not to work, but found it did for some cases. As long as the lambda did *not&amp; force the compiler to generate an anonymous class everything works fine.   A SerializationException is thrown if the compiler requires a generated class to implement the anonymous function. This is because the compiler generated class is not marked as serializable.  Example  namespace Example {     [Serializable]     class Other     {         public int Value;     }      [Serializable]     class Program     {         static void Main(string[] args)         {             MemoryStream m = new MemoryStream();             BinaryFormatter f = new BinaryFormatter();              // Example 1             Func&lt;int&gt; succeeds = () =&gt; 5;             f.Serialize(m, succeeds);              // Example 2             Other o = new Other();             Func&lt;int&gt; fails = () =&gt; o.Value;             f.Serialize(m, fails); // throws SerializationException - Type 'Example.Program+&lt;&gt;c__DisplayClass3' in Assembly 'Example, Version=1.0.0.0, Culture=neutral, PublicKeyToken=null' is not marked as serializable.         }     }   Listing 2  This is similar to the issue of trying to serialize iterators and I had found the following code in a previous search (see ) Using the code from Listing 1 and an ISurrogateSelector I was able to successfully serialize and deserialize the second failing example.  Objective  I have a system that is exposed via a web service. The system has a complex but small state (many objects, not a lot of properties per object). The state is saved in the ASP.NET Cache, but is also serialized to a BLOB in SQL in case of cache expiration. Some objects need to execute arbitrary "events" upon reaching some condition. Hence they have properties accepting Action/Func objects. Contrived example:      class Command     {         public Command(Action action, Func&lt;bool&gt; condition);     }   Somewhere else      void DoSomethingWithThing(Thing thing)     {         state = Store.GetCurrentState();          Command cmd = new Command(() =&gt; thing.Foo(), () =&gt; thing.IsReady())         state.Add(cmd);          Store.Save(state);     } I am totally new to Linux, servers and websites. I recently set up Apache2, Python, PHP, and MySQL for setting up a LAMP server. I am using Xubuntu 16.04 and PHP 7.0.11. I followed a guide and placed a PHP file named testing.php in it with:  &lt;?php phpinfo(); ?&gt;    It doesn't show anything on localhost/testing.php All it shows is the code itself. What's the best and quickest way to detect whether you're running a 32 or 64-bit version of Windows Server from the command line?  (Cygwin is installed) Infinite group with only two conjugacy classes %AX = (%AH + %AL)  So why not %EAX = (%SOME_REGISTER + %AX) for some register %SOME_REGISTER? I have a file with the lines like below.  title1:A1 title2:A2 title3:A3 title4:A4 title5:A5  title1:B1 title2:B2 title3:B3 title4:B4 title5:B5  title1:C1 title2:C2 title3:C3 title4:C4 title5:C5  title1:D1 title2:D2 title3:D3 title4:D4 title5:D5  How can I achieve this?   title1    title2     title3    title4 A1         A2         A3         A4 B1         B2         B3         B4 C1         C2         C3         C4 D1         D2         D3         D4 The exchange of photons gives rise to the electromagnetic force Pardon me for my stubborn classical/semiclassical brain. But I bet I am not the only one finding such description confusing.  If EM force is caused by the exchange of photons, does that mean only when there are photons exchanged shall there be a force? To my knowledge, once charged particles are placed, the electromagnetic force is always there, uninterruptedly. According to such logic, there has to be a stream of infinite photons to build EM force, and there has to be no interval between one "exchange event" to another. A free light source from an EM field? The scenario is really hard to imagine.  For nuclei the scenario becomes even odder. The strong interaction between protons is caused by the exchange of massive pions. It sounds like the protons toss a stream of balls to one another to build an attractive force - and the balls should come from nothing.  Please correct me if I am wrong: the excitations of photons and pions all come from nothing. So there should be EM force and strong force everywhere, no matter what type of particles out there. Say, even electrical neutral, dipole-free particles can build EM force in-between. And I find no reason such exchanges of particles cannot happen in vacuum.   Hope there will be some decent firmware to refresh my classical brain with newer field language codes.