Numeric example of the Expectation Maximization Algorithm
What is an intuitive explanation of the Expectation Maximization technique?
It seems Microsoft has tried to solve this problem .  In Windows 7, there is no boundary between monitors and the mouse can move freely across the top of the screen between my 3 monitors, provided I had set their heights equal in display settings. Windows 8 introduced sticky corners. See .  Windows 10 got sticky corners as well. There are a few pixels at the top corners of each display where the mouse cannot cross over onto the other display. One must move the cursor down to avoid this region in order to get to the next display.  The image shows roughly the region where mouse movement is not permitted in Windows 10, but is allowed in Windows 7.    Personally, I had no problem with unrestricted mouse movement across the top of my screens - I got used to "aiming" for the x, and the convenience of unrestricted cursor movement. Like all the people who wanted to disable it in W8, I'm wondering if there is a way to disable it in W10.  Edit to address possible duplicate:  Although the problem is identical to the one in , solutions to solve the problem in W8 involving editing the registry key MouseCornerClipLength do not work in W10, since that registry key is not present in W10. Also adding that key and setting the value doesn't work. I searched the entire registry and couldn't find it in another location. No other W10 keys in the node referenced in the W8 solution are obvious replacements.  Edit to address possible solutions in comments  harrymc's  and  that worked for for Windows 8.1 do not work in Windows 10. PHP: Return all dates between two dates in an array Can you grammatically end a sentence with "with"? Do you want to come with? Can I come with?  I seem to hear this construction more often in recent years, but it still grates on my ear. I know it's often said that one shouldn't , but I class that rule along with  (i.e. — pedantic tosh). Is it always informal/casual speech to end a sentence with &quot;with&quot;? Was it ever thus? Visual Studio Solutions Folder as real Folders I have a Visual Studio Solution. Currently, it is an empty solution (=no projects) and I have added a few solution folders.  Solution Folders only seem to be "virtual folders", because they are not really created in the Filesystem and files inside solution folders are just sitting in the same folder as the .sln file.  Is there a setting that i've overlooked that tells Visual Studio to treat Solution Folders as "real" folders, that is to create them in the file system and move files into it when I move them inside the solution into one of those folders?  Edit: Thanks. Going to make a suggestion for VS2010 then :) How to change Status Bar text color in iOS I am writing pseudo code in the algorithmic environment. It is quite long and doesn't fit on one single page. Instead of it continuing on the next page, it is cut off. I tried inserting it into a figure environment, but the problem persists. Is there a solution to have the code continue on the next page? Is the possessive of "one" spelled "ones" or "one's"? I've been confused about this as long as I can remember. Should it be:     One should do ones duty.   or     One should do one's duty.   I'm guessing it should be the latter. But that doesn't sit well with the possessive pronoun 'its'. For example:     It is its own purpose.   vs.     It is it's own purpose.   Here, the former seems clearly correct. A graph $G$ is bipartite if and only if $G$ can be coloured with 2 colours Java inner class and static nested class What is the main difference between an inner class and a static nested class in Java? Does design / implementation play a role in choosing one of these? ConTeXt: Flush right formula numbers in cases environment I would like to have the formula numbers of the cases environment flush right like regular formulas (not at a fixed distant from the cases like it is by default with the default setting numberdistance=2.5\emwidth). How can I do that?  \starttext  \startplaceformula     \startformula         \startcases             \NC x = 1 \NR[+]             \NC y = 1 \NR[+]         \stopcases     \stopformula \stopplaceformula  \stoptext     What I want (but with the left bracket):  \starttext  \startplaceformula     \startformula         \startalignment[n=1]             \NC x = 1 \NR[+]             \NC y = 1 \NR[+]         \stopalignment     \stopformula \stopplaceformula  \stoptext If $\lambda_{max} = n$, then $n\times n$ positive, reciprocal matrix A is consistent At the end of . the author states that  Suppose we have $n \times n$ matrix $A$ having only positive elements and satisfying the property $a_{ij}=1/a_{ji}$ (a matrix satisfying this property is called a reciprocal matrix).  If its largest eigenvalue $\lambda_{max}$ is equal to $n$, then the matrix $A$ satisfies the property (consistency property) $a_{ij} a_{jk} = a_{ik}$ where $i,j,k=1,2,...,n$.  I'm not convinced this theorem is true. Could anyone help? iCloud has sucked up all my laptop's files - can you transfer files directly from iCloud to Google Drive? I'm trying to disconnect my macbook from iCloud, as it's been creating some problems.  I was told by an Apple Support employee that doing so is only recommended once you've backed up everything from your Mac somewhere, to ensure you don't lose any files - so my goal is to upload everything to Google Drive before messing with my laptop's iCloud settings. The problem is, almost none of the projects that I want to back up to Google Drive are truly on my laptop - instead I mostly just have folders full of file names, which are placeholders for the real files that have been sucked into iCloud. This means I have to re-download everything to my computer before uploading it all to Google Drive. Another crucial piece of information is that I only have 1 GB of storage left on my macbook, which prevents me from re-downloading any complete projects/folders at a time. So unfortunately my current method is this: downloading 1-5 files at a time, uploading these few things to Google Drive, deleting the copies from my laptop and trash, repeat (thousands of times). So, I was wondering if anyone could offer any alternative methods for uploading stuff to Google Drive in this situation - for example, is there a way to transfer files directly from iCloud to Google Drive without having to download them to my laptop first? I should probably mention that I've scoured my laptop for duplicated files and applications I no longer use, make sure to empty my trash regularly, etc (I also asked Apple Support to help me make sure I wasn't missing out on any other ways to maximize storage space). The most obvious culprit of my lack of space is the massive 150 GB iCloud folder on my laptop, which appears to contain duplicates of everything on my computer. I can't seem to do anything about it until I've disconnected from iCloud itself (its reasons for existence are unclear to me in the first place...but that's beside the point lol). For all $x,y\in\mathbb{R}$   define that $x\equiv y$   if $x^{2}=y^{2}$  . Then $\equiv$  is an equivalence relation on $\mathbb{R}$  , there are infinitely many equivalence classes, one of them consists of one element and the rest consist of two elements.  Solution  True. To show that \equiv  is reflexive we need to show that \forall x\in\mathbb{R}  :x=x.  Let x\in\mathbb{R}  , x\equiv\mbox{\ensuremath{x}}  if x^{2}=x^{2},   which is obvious.  [x]  ={y\in\mathbb{R}  |x\equiv y}  =[0]={y\in\mathbb{R}|0\equiv y}={0}  . Hence y^{2}  =0^{2}   =0   which implies that y=0  . How do I change my username? Some time ago, when I installed Ubuntu, I chose a rather stupid username for my account that I do not want to use anymore. How do I change this (including the name of my home directory, and the name in the terminal) without losing settings for applications? How do I keep permissions and my keys for various authentification (e.g. email, SSH, GPG and more)? What settings could possibly get lost if I changed my username? Suppose, I want to refer multiple equations (1), (2), (3), (4), (5) and (7) so that they appear as (1-5, 7):  \documentclass[fleqn,preprint,10pt]{article} \usepackage{amsmath} \usepackage{amssymb} \usepackage{amsfonts} \begin{document} \begin{align} \label{1}\psi([e_1,e_2]) = \psi(e_2) = e_2 = (e_2,2e_3) = (-2e_3,e_2) = (\psi(e_1), \psi(e_2))\\ \label{2}\psi([e_1,e_3]) = \psi(2e_3) = 2e_1 = (e_1,2e_3) = (-2e_3,e_1) = (\psi(e_1),\psi(e_3))\\ \label{3}\psi([e_2,e_3]) = 0 = (e_2,e_1) = (\psi(e_2),\psi(e_3)),\\ \label{4}\left\{e_4, e_1\right\},\,\,\,\left\{e_4, e_2\right\},\,\,\,\left\{e_4, e_3\right\},\,\,\,\left\{e_4, e_1+\epsilon\,e_2\right\},\\ \label{5}\left\{e_1, e_2\right\},\,\,\,\left\{e_3, e_1\right\},\,\,\,\left\{e_3, e_2\right\},\\ \label{6}\left\{e_4, e_1\right\},\,\,\,\left\{e_4, e_2\right\},\,\,\,\left\{e_4, e_3\right\},\,\,\,\left\{e_4, e_1+\epsilon\,e_2\right\},\\ \label{7}\text{Nor}_{L_4\oplus L_3}\left(\{e_2\}\right)/\{e_2\}=\,\{e_1, e_3, e_4\} \end{align} \end{document} Determine the exact value of equations involving more two trig variables $2\cos^2x=1+\sin x$.  Determine the exact values of $x$ such that $0 \leq x \leq 2\pi$.    I am experiencing problems with factoring this question.  First I started by getting everything on to the left side so: $2\cos^2x-\sin x-1=0$.  Then seeing as there are two trig variable here ($\cos$ and $\sin$), I used the pythagorean identity and replaced $2\cos^2x$ with $1-2\sin^2x$ to make it into a one variable question: $1-1-2\sin^2x-\sin x-1=0$.   By collecting like terms it then becomes $-\sin^2x-\sin x=0$.  Now you could factor these with $0$ and $-1$, but then it creates uneven brackets so this musn't work.  I don't think the quadratic formula is necessary, but I am wondering if this could be treated as a difference of squares question.    If you replace the $\sin x$ and make the question into $-x^2-x=0$ it is a little easier to look at, however I am not sure if this is the right approach.  If someone could please clarify my answer, that would be appreciated! I only ask questions. Am I unwanted? Possible Duplicate:          I've been  for maybe a year to get answers to questions I couldn't find on my own.  I always make an attempt first to find the answer on my own.  As of this posting, I've asked 14 questions.  I only once gave an answer, and it was to a non-technical question, and only because I was really bored and had too much coffee to drink.  I wasn't intending to answer any other questions in the future, because on on my best days I'm only a mediocre programmer, and there are some real geniuses here on StackOverflow who can answer other peoples' questions faster and more accurately than I can.  It actually is my nature.  I am an Aquarian.  We are asker-listeners.  Today I discovered Meta Stack Overflow and started browsing around.  I became familiar with the concept of the "Help Vampire".  I seem to qualify.  I continued reading more posts on the topic and got the distinct impression that people who only ask, and never answer, are less than welcome here, rather despised.  So, should I just go away?  Or should I start contributing answers just to have a answer-to-question ratio of 3-to-1 (I read somewhere that's the average) even though I am less than one eighth as knowledgeable as the 10K+ guys and gals?    Or should I continue as I have begun?  I mean, doesn't a 0-questions-asked user like Jon Skeet need a Blankman?  Yin and yang, you know? How does gravity escape a black hole? 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? If "clearly evident" is redundant, what word or phrase suggests being indisputable but not readily apparent? A  asks whether the modifier "clearly" changes the meaning of "evident". I would have said, prior to examining a few dictionaries, that evident did not necessarily mean readily apparent, but to my surprise it does.  This brings me to ask what word or expression would mean something can be taken as a true fact, but not through an easily constructed (not obvious or readily apparent) rationale?   For example, if Sherlock Holmes says something is true while everyone else is still sitting on their hands, then it is evident to Holmes, but not to the rest of the world. So, from everyone else's point of view, it is not readily apparent, and (by definition) apparently it is not evident, clear, or clearly evident at all, based on the dictionary definitions. But (let's stipulate) it is true and deducible from the observable evidence. What would we call this?  Update  An update is highlighted above. I can see from some of the answers and comments that I may have gone off my mark with the phrase "not through an easy-to-follow rationale”, and I have modified the question to correct this. I understand that there can be rationales, arguments, or proofs that, once explained, may or may not be easy to follow. What I intend is that the rationale to support the indisputable conclusion is not (initially) easy to recognize or construct (not readily apparent) in the first place. I apologize for the confusion. (The original can be seen in the change history.)  Update 2  Shortly after offering a bounty to this request, I recalled a single word that I now believe is a very good match to the parameters specified in this inquiry as it is stated above. That word has not yet been suggested (or approached) by any answer or comment (active or deleted) at the time of this edit. This request is changed to a single word request. (However, if you feel a single word fits well but not without some additional supporting words, please offer your thoughts in an answer.) While my curiosity for the term has already been met, the request and bounty remain as an open challenge. I will post my own answer once the bounty has expired and been awarded. Minimal $ab$ for Rational Number $a/b$ in an Interval Given rational numbers $L$ and $U$, $0&lt;L&lt;U&lt;1$, find rational number $M=a/b$ such that $L \le M&lt;U$ and $(a\times b)$ is as small as possible---$a$ and $b$ are integers. For example,    If $L=66/101$ and $U=19/29$ then $M=17/26$. If $L=66/101$ and $U=19/28$ then $M=2/3$.   Right now I'm using a naive search that is exponential in complexity. Is there a better method?  If it is of any help, it can be assumed the prime factorization of numerator and denominator of $U$ and $L$ are known.