I have two displays running in my current setup: A 27" monitor (it's not 4k, but it's got a somewhat higher resolution than 1920x1080), and a 15" MacBook with the Retina display.   The minor inconvenience I'm running into is that the mouse sometimes gets stuck on the large monitor and won't cross the gap to the laptop display.  As far as I can tell, this is because the edges of the displays are not scaled/mapped to each other's edges. So if the mouse is in the top-right or bottom-right corners of the larger display it's can't cross to the laptop because no shared edge exists there:     I remember running into this issue on a Linux machine and being able to change the mapping/scaling of the display edges so that the mouse can always cross that gap.   So I'm wondering, on El Capitan or Sierra, is there a way to make both displays share a common edge? Either through a setting, config, or even a third-party app?
I use a Full HD 24" external display besides my 15" MacBook Pro Retina, on which I use the option for most screen estate regarding the Retina display. In the display arrangement screen, the MacBook Pro is therefore a bigger rectangle than the external display. Is there a way to size these rectangles regarding their "real world size" instead of resolution? I'm annoyed by my cursor teleporting vertically whenever I move from one display to another.
Is an integer a sum of two rational squares iff it is a sum of two integer squares? Let $a\in \mathbb Z$. Is it true that $a$ is a sum of two squares of rational numbers if and only if it is a sum of two squares of integers?  I came to face this problem while dealing with quaternion algebras. Forward/Inverse Search Does Not work on certain tex files The probability of two dice summing to k is simple enough, make a diagram of the throws,  $$ \begin{array}{c}  &amp;|&amp;1&amp;2&amp;3&amp;4&amp;5&amp;6\\\hline 1&amp;|&amp;2&amp;3&amp;4&amp;5&amp;6&amp;7\\ 2&amp;|&amp;3&amp;4&amp;5&amp;6&amp;7&amp;8\\ 3&amp;|&amp;4&amp;5&amp;6&amp;7&amp;8&amp;9\\ 4&amp;|&amp;5&amp;6&amp;7&amp;8&amp;9&amp;\color{green}{10}\\ 5&amp;|&amp;6&amp;7&amp;8&amp;9&amp;\color{green}{10}&amp;11\\ 6&amp;|&amp;7&amp;8&amp;9&amp;\color{green}{10}&amp;11&amp;12\\ \end{array} $$  and the probability of a sum is just the length of the corresponding diagonal divided by $36$. For instance, $\mathrm{P}(\mathrm{sum} = 10) = \frac{3}{36} = \frac{1}{12}$. However, it's not as easy to draw a diagram for three dice or more, so how would a general formula look? If someone is my proxy, I am their _____? Bonus question: If I am a proxy for multiple people, what's the collective noun for that group? Can you find shadow orbs in terraria demo? I have the PS vita demo, and was wondering if you could find any shadow orbs in that tutorial world. Thanks. Was Grand Moff Tarkin under Darth Vader's control? In A New Hope, we see Grand Moff Tarkin ordering Darth Vader around. Also, it was . It's uncertain whether he knew .  But considering that Darth Vader was a Sith Lord, and a Jedi before that, are we entirely sure he wasn't secretly controlling Tarkin through a Jedi Sith mind trick? Reviewing suggested edit of own post after completing 20 reviews I've completed 20 suggested edits reviews today. Then, I came across a  and I approved it.   Then, I had a doubt that whether the review count has incremented or not, oh! it's not incrementing. System works fine.  But, take a look at review page,     The edit was already reviewed by one reviewer and then I reviewed it. As I'm the Owner of the post it's enough to approve the edit. But, the review history doesn't show the detail that I had approved it. It's misleading that only one vote of a reviewer who is neither the community user nor the OP nor the moderator, is enough.  So, what should we do in this type of situation?  Is it correct to make OP to review the suggested edit after completing daily limit?  Should we need to display/hide the OP has approved the edit in the review history? is the Turkish version of mancala, with its own set of rules.  I am planning on doing a project in it. Are there any game engines that either specifically play it, or universal Mancala players that plays it after supplying the options?  EDIT:  I am not looking for an app, but for a game engine. For example in chess,  is a playing app, while  is an open-source engine. Return a value when using jQuery.each()? Do greenhouse gasses make the world habitable? An ageing gent says he does not accept this statement:  It's a fact that greenhouse gases, predominantly water vapour, keep the Earth  from being hostile and cold; that CO2 albeit in trace quantities is also a  greenhouse gas and therefore helps keep the planet warm...   I know no more about why he rejects this statement - maybe it is that water vapour alone would do the job. The gent in question has a first class degree and a doctorate in physics.    Is there a debate within the physics community over this or am I misunderstanding? What are the integer solutions to $a^{b^2} = b^a$ with $a, b \ge 2$ I saw this in quora.  What are all the integer solutions to $a^{b^2} = b^a$ with $a, b \ge 2$?  Solutions I have found so far:  $a = 2^4 = 16, b = 2, a^{b^2}  = 2^{4\cdot 4} =2^{16}, b^a = 2^{16} $.  $a = 3^3, b = 3, a^{b^2} = 3^{3\cdot 9} =3^{27}, b^a = 3^{3^3} =3^{27} $.  In the general case, $a$ and $b$ have the same set of prime divisors, so let $a =\prod_P p_i^{a_i}$, $b =\prod_P p_i^{b_i} $ with each $a_i \ge 1, b_i \ge 1$.  $b^a =b^{\prod p_i^{a_i}} =(\prod p_j^{b_j})^{\prod p_i^{a_i}} =\prod p_j^{b_j\prod p_i^{a_i}} $  $a^{b^2} =a^{\prod p_i^{2b_i}} =(\prod p_j^{a_j})^{\prod p_i^{2b_i}} =\prod p_j^{a_j\prod p_i^{2b_i}} $  Therefore, for each $p_j$, $b_j\prod p_i^{a_i} =a_j\prod p_i^{2b_i} $.  I haven't gotten any further than this.  I conjecture that there are no other solutions. Troubleshooting for biber I'm trying to switch from BibTeX to biber and ran into the problem that biber does not produce any output file. I noticed several questions about problems with biber e.g.,            ,                       But none of them helped me in my particular situation (which was actually just an old version of biber somewhere in the path of my OS). Since I also noticed that several questions regarding problems with biber were closed as too localized since the underlying problem was due to formatting of a bib resource or similar simple issues, I would rather like to ask for a general troubleshooting guideline for using biber (since I saw many hints like "check/delete the cache", "check versions of this and that" etc.).  What steps are to be taken and what things (in particular files) to be checked if biber does not produce an output file (and its output on the command line does not directly give you the advice what to do)? an example of a non-abelian group $G$ containing a proper normal subgroup $N$ such that $G/N$ is abelian. Exposing database IDs - security risk? I've heard that exposing database IDs (in URLs, for example) is a security risk, but I'm having trouble understanding why.  Any opinions or links on why it's a risk, or why it isn't?  EDIT: of course the access is scoped, e.g. if you can't see resource foo?id=123 you'll get an error page. Otherwise the URL itself should be secret.  EDIT: if the URL is secret, it will probably contain a generated token that has a limited lifetime, e.g. valid for 1 hour and can only be used once.  EDIT (months later): my current preferred practice for this is to use UUIDS for IDs and expose them. If I'm using sequential numbers (usually for performance on some DBs) as IDs I like generating a UUID token for each entry as an alternate key, and expose that. Using an NSString in a switch statement Can an electron be in two places at the same time? So I've been reading a bit and watching some videos about the double slit experiment, and therefore the wave particle duality; I've also read this "implies" that a particle can be in two places at the same time. Can you clarify this, and how could that be possible? Why does 1+++2 = 3? How does Python evaluate the expression 1+++2?  How many ever + I put in between, it is printing 3 as the answer. Please can anyone explain this behavior  And for 1--2 it is printing 3 and for 1---2 it is printing -1 Will installing Ubuntu using the "erase entire disk" option remove and erase all currently existing partitions? I'm considering ditching Windows 8 and doing a fully clean install of Ubuntu. However, I'm concerned because my computer came with a built-in 16 GB recovery partition that would need to be erased as well.   If I pick the "erase entire disk" option during installation, will it wipe out this recovery partition too? Why are symmetric positive definite (SPD) matrices so important? I know the definition of symmetric positive definite (SPD) matrix, but want to understand more.   Why are they so important, intuitively?  Here is what I know. What else?   For a given data, Co-variance matrix is SPD. Co-variance matrix is a important metric, see this  for intuitive explanation. The quadratic form $\frac 1 2 x^\top Ax-b^\top x +c$ is convex, if $A$ is SPD. Convexity is a nice property for a function that can make sure the local solution is global solution. For Convex problems, there are many good algorithms to solve, but not for non-covex problems. When $A$ is SPD, the optimization solution for the quadratic form $$\text{minimize}~~~ \frac 1 2 x^\top Ax-b^\top x +c$$ and the solution for linear system $$Ax=b$$ are the same. So we can run conversions between two classical problems. This is important because it enables us to use tricks discovered in one domain in the another. For example, we can use the conjugate gradient method to solve a linear system.  There are many good algorithms (fast, numerical stable) that work better for an SPD matrix, such as Cholesky decomposition.   EDIT: I am not trying ask the identities for SPD matrix, but the intuition behind the property to show the importance. For example, as mentioned by @Matthew Drury, if a matrix is SPD, Eigenvalues are all positive real numbers, but why all positive matters. @Matthew Drury had a great answer to flow and that is what I was looking for. How to get the key for a given object from an NSMutableDictionary?