Detect wether machine is 32 or 64 bits
How to find out if my system is i386 or x86_64 before installing Ubuntu?
What is wrong with this query? (Unknown error parsing query) Equivalence between least squares and MLE in Gaussian model I am new to Machine Learning, and am trying to learn it on my own. Recently I was reading through  and had a basic question.   Slide 13 says that "Least Square Estimate is same as Maximum Likelihood Estimate under a Gaussian model". It seems like it is something simple, but I am unable to see this. Can someone please explain what is going on here? I am interested in seeing the Math.   I will later try to see the probabilistic viewpoint of Ridge and Lasso regression also, so if there are any suggestions that will help me, that will be much appreciated also. How do you allocate more RAM to Minecraft? There is a lot of lag when I play Minecraft. I think this is due to the low amount of RAM I've allocated to Minecraft. (495MB)  How do you allocate more RAM to Minecraft?  I checked my other computer (Intel i5 Core) and it had the same amount of RAM allocated to Minecraft. However, Minecraft did not lag on that computer.  After I installed Optifine on this computer, the lag stopped (I don't know why cause I read that Optifine splits the load onto 2 cores, but I have only one core (At least I think so, a sticker on the laptop says Intel CORE i7)). Are there any series whose convergence is unknown? Are there any infinite series about which we don't know whether it converges or not? Or are the convergence tests exhaustive, so that in the hands of a competent mathematician any series will eventually be shown to converge or diverge? EDIT: People were kind enough to point out that without imposing restrictions on the terms it's trivial to find such &quot;open problem&quot; sequences. So, to clarify, what I had in mind were sequences whose terms are composed of &quot;simple&quot; functions, the kind you would find in an introductory calculus text: exponential, factorial, etc. Fully charged MacBook Air turns off when power cord removed I have a MacBook Air, 2009, with a recently replaced Apple battery in December 2012. Recently, when power cord comes off, the computer shuts down. Also, it usually will not restart unless power cord is attached. The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition A function $f: M\rightarrow N$ is defined to be continuous iff $\forall$ open set $U\subseteq N$, the preimage of $U$ is also open.  I was trying to prove that such a definition would be equivalent to the $\epsilon -\delta$ definition in a metric space, and I could only do so if I assume $f$ is surjective, or otherwise a counterexample would be $g: \mathbb{R}\rightarrow\mathbb{R}$ where $g(x)=x^2$. As if I take $U=(-1,1)$, then its preimage is $[0,1)$, which is neither open or closed. In fact, any $U$ containing elements that cannot be achieved by $g$ would face the same problem.  So I was wondering that have I remembered the definition of preimage wrong, or do I need to make sure that $U$ must be chosen from the image set of $f$? 90s (or earlier) Japanese anime movie: two planets at war, young man is in love with princess from the other planet, and floods his own village I would like to find out the title of a Japanese anime feature film (not a series) that I saw on Romanian TV in the early 90s.   It was about a feud between the peoples of two planets (one very technologically advanced, the other not). The two planets go to war against each other, and a young man from one of the planets falls in love with a princess from the other planet.  I recall a scene where the army of the second planet take off in hot air balloons when they go to war.  The only other thing I recall is that there is a dam next to the village where the young man lives, and for some reason he opens the dam gates and floods his own village.   I do not recall there being robots in the movie, however I remember very vaguely that the technology level was probably at the level of late 19th century Europe on one planet and pre-industrial on the other one.  What it's not:   Nobunaga the Fool Aldnoah Zero Queen Millennia Uchuu Senkan Yamato (movie) Infinite group with only two conjugacy classes Detailed Bathymetric/Bathymetry contour data (0-200M) I'd like to see if somebody has been trying to log-in by brute-force into my Ubuntu 12.04 server over SSH. How can I see if such activities have been taking place? What is wrong with this proof?    Is $\pi=4?$ What's the difference between "speak" and "talk", grammatically speaking? There are a number of questions e.g.  and  that deal with the slightly different connotations of the words "speak" and "talk". However, there also seem to be some grammatical differences between the two words. This question is about whether there's a way to formally pin down these differences, or whether they're just contingent features of the two words having different histories.  Some examples of grammatical differences are as follows:   be talkative ... be speakative speak French ... talk French give a talk ... give a speech (as opposed to a speak) speak up ... talk up (the meanings of the two phrases being completely different, with "up" being a preposition only in the latter case) speaking of which ... talking of which grammatically speaking ... grammatically talking   On the other hand, many other constructions work just as well with either (though they might have subtly different meanings), for example   speak to ... talk to speak with ... talk with speak about ... talk about   I'm interested in whether there's a way to pin down these differences (e.g. are the two words classified as different types of verb in some way?), or whether they're essentially just arbitrary. I'm also interested in why we have these two different words with subtly different meanings. Is the distinction between “speak” and “talk” a feature of many languages, or is it just a peculiarity of English?  Etymologically, both words are from Germanic origins. “Talk” seems to have been formed from the Middle English tale, even though “speak” already existed in the English language by then (as far as I can tell). This makes it even more mysterious: Why did we form a new word as a synonym of one that was already established? Or were the meanings different at that time? Maximal Ideals in Ring of Continuous Functions Dummit and Foote, 7.4.33(a): Let $R$ be the ring of all continuous functions $[0,1] \to \mathbb{R}$ and let $M_c$ be the kernel of evaluation at $c \in [0,1]$, i.e. all $f$ such that $f(c) = 0$. Show that if $M$ is a maximal ideal in $R$ then $M = M_c$ for some $c$.    I am aware of proofs that use the compactness of $[0,1]$; however I have been told that a simpler proof exists using only the isomorphism theorems for rings along with basic facts about ideals. I have tried on my own to prove it this way but still have no success; is it possible?  (My attempts go something like: since $M$ is maximal, the quotient ring $R/M$ is a field. Then it would be nice to use the fact that $R/M$ has no zero divisors, but I can't quite make it work. Alternatively, consider $M \cap M_c$.) Finding probability of other child also being a boy A man visits a couple who have two children.One of them, a boy, comes in to the room. Find the probability p that other is also a boy  a) 1/3 b) 2/3 c) 1/2 d) 3/4  Correct Ans: a) 1/3  However I am getting answer as 1/2.My solution is as follows.  The couple has two children, hence the sample space is as follows.  B- Boy G - Girl  BB BG GG ( BG and GB mean the same thing as Girl,Boy), but it is already known that one is boy.So the sample space reduces to  BB BG  So now p is 1/2  Is there some mistake is my approach ? Windows 7 / 8 tool for amplifying sound / equivalent to pavucontrol? I'm watching live streamed videos, but the volume sometimes is barely loud enough.  With Windows, I can only turn the system volume and the flash volume up to maximum, and then bad luck if that's still not loud enough.  On Linux, on the same notebook, I have the same problem, but I can use pavucontrol (pulseaudio volume control) to amplify the sound volume beyond 100%.  Unfortunately, I can't always work on Linux, since Visual Studio and SQL-Server only run on Windows.  Is there any tool or way to amplify volume on Windows 7 / 8 , without having to resort to run Linux in a virtual machine? Class not found loading JDBC org.postgresql.Driver Metapost label based on variable value I want to label a scale based on a variable value and I wrote a metapost code like this.  $ := 1; for i = -.3cm step .6cm until 3.6cm:     label.bot(str$,(i,-3.7cm));     $ := incr($); endfor;   It just labels "$" instead of its value. How to output the variables value? Solving the diophantine equation $y^{2}=x^{3}-2$ It is known that the diophantine equation $y^{2}=x^{3}-2$ has only one positive integer solution $(x,y)=(3,5)$. The proof of it can be read from the book "About Indeterminate Equation" (in Chinese, by Ke Zhao and Sun Qi). But the method I have known of solving this problem is algebraic number theory.  My question:      Does there exists an elementary method for solving the diophantine equation $y^{2}=x^{3}-2$?   I have gotten an elementary method by the assumption that "$x$" is a prime. That is, we can get a conclusion from the equation that $3\mid x$. Since $x$ is a prime we get the only solution $(x,y)=(3,5)$. But if $x$ is not a prime, the answer seems to be difficult.  Thank you for your help. Understanding shape and calculation of confidence bands in linear regression I am trying to understand the origin of the curved shaped of confidence bands associated with an OLS linear regression and how it relates to the confidence intervals of the regression parameters (slope and intercept), for example (using R):  require(visreg) fit &lt;- lm(Ozone ~ Solar.R,data=airquality) visreg(fit)     It appears that the band is related to the limits of the lines calculated with the 2.5% intercept, and the 97.5% slope, as well as with the 97.5% intercept, and the 2.5% slope (although not quite):  xnew &lt;- seq(0,400) int &lt;- confint(fit) lines(xnew, (int[1,2]+int[2,1]*xnew)) lines(xnew, (int[1,1]+int[2,2]*xnew))     What I don't understand are two things:   What about the combination of 2.5% slope &amp; 2.5% intercept as well as 97.5% slope and 97.5% intercept? These give lines that are clearly outside the band plotted above. Maybe I don't understand the meaning of a confidence interval, but if in 95%  of the cases my estimates are within the confidence interval, these seem like a possible outcome? What determines the minimum distance between the upper and lower limit (i.e. close to the point where the two lines added above intercept)?    I guess both questions arise because I don't know/understand how these bands are actually calculated.   How can I calculate the upper and lower limits using the confidence intervals of the regression parameters (without relying on predict() or a similar function, i.e. by hand)? I tried to decipher the predict.lm function in R, but the coding is beyond me. I'd appreciate any pointers towards relevant literature or explanations suitable for stats beginners.  Thanks. How come gas molecules don't settle down? If the earth's gravity exerts a net downward gravitational force on all air molecules, how come the molecules don't eventually lose their momentum and all settle down? How is the atmosphere is still miles thick after billions of years?