extracting part of a vector
Best way to extract a subvector from a vector?
When is it appropriate to end a sentence in a preposition? Like many others, I commonly find myself ending a sentence with a preposition.  Yes, it makes me cringe.  I usually rewrite the sentence, but sometimes (in emails) I just live with it.  To, with... you know who you are.  Should I keep fighting myself on this one, or is it okay in some circumstances? A switch that is only ON if the reference voltage is matched -+ 0.1 volts Im a beginnerish will electronic and im looking for a switch that is only ON if the reference voltage is matched -+ 0.25 volts. So if i have a reference of 2.7v to match and i feed the switch a 2.75v the switch would be ON. But if i feed it  2.5v or 2.85v the switch would is OFF.   This might be a simple google search, but i am lacking the correct terminology. I'm using a PIN code to log on my computer. However, Num ⇩ is always turned off, even if on before shutting down my computer. This is quite annoying as I always have to retype my PIN.  I've tried the suggestions  (same as ). But with no result. If I don't enable num lock on log in screen and use the numbers above the normal keys, num lock turns on after log on. Then it's too late, unfortunately.  So, how can I make num lock enabled by default when logging in? Thanks.  Edit: While I still want to solve this, I've figured it is not such a big problem. I will need to press some key for the "enter PIN screen" to show, and using Num ⇩ works and enables num lock. But then, still annoying if the computer was only locked (with num lock on) and I turn it off, hehe. How is Selenium RC different from Selenium Web driver and some good pointers for a naive beginner to learn to scripting please? Thanks! I want to implement the EM algorithm manually and then compare it to the results of the normalmixEM of mixtools package. Of course, I would be happy if they both lead to the same results. The main reference is Geoffrey McLachlan (2000), .  I have a mixture density of two Gaussians, in general form, the log-likelihood is given by (McLachlan page 48):      $$ \log L_c(\Psi) = \sum_{i=1}^g \sum_{j=1}^n z_{ij}\{\log \pi_i + \log f_i(y_i;\theta_i)\}. $$ The $z_{ij}$ are $1$, if the observation was from the $i$th component density, otherwise $0$. The $f_i$ is the density of the normal distribution. The $\pi$ is the mixture proportion, so $\pi_1$ is the probability, that an observation is from the first Gaussian distribution and $\pi_2$ is the probability, that an observation is from the second Gaussian distribution.   The E step is now, calculation of the conditional expectation:      $$ Q(\Psi;\Psi^{(0)}) = E_{\Psi(0)}\{\log L_c(|\Psi)|y\}. $$ which leads, after a few derivations to the result (page 49):      \begin{align} \tau_i(y_j;\Psi^{(k)}) &amp;= \frac{\pi_i^{(k)}f_i(y_j;\theta_i^{(k)}}{f(y_j;\Psi^{(k)}}  \\[8pt]                        &amp;= \frac{\pi_i^{(k)}f_i(y_j;\theta_i^{(k)}}{\sum_{h=1}^g \pi_h^{(k)}f_h(y_j;\theta_h^{(k)})} \end{align} in the case of two Gaussians (page 82):      $$ \tau_i(y_j;\Psi) = \frac{\pi_i \phi(y_j;\mu_i,\Sigma_i)}{\sum_{h=1}^g \pi_h\phi(y_j; \mu_h,\Sigma_h)} $$ The M step is now the maximization of Q (page 49):      $$ Q(\Psi;\Psi^{(k)}) = \sum_{i=1}^g\sum_{j=1}^n\tau_i(y_j;\Psi^{(k)})\{\log \pi_i + \log f_i(y_j;\theta_i)\}. $$ This leads to (in the case of two Gaussians) (page 82):      \begin{align} \mu_i^{(k+1)} &amp;= \frac{\sum_{j=1}^n \tau_{ij}^{(k)}y_j}{\sum_{j=1}^n \tau_{ij}^{(k)}}  \\[8pt] \Sigma_i^{(k+1)} &amp;= \frac{\sum_{j=1}^n \tau_{ij}^{(k)}(y_j - \mu_i^{(k+1)})(y_j - \mu_i^{(k+1)})^T}{\sum_{j=1}^n \tau_{ij}^{(k)}} \end{align} and we know that (p. 50)      $$ \pi_i^{(k+1)} = \frac{\sum_{j=1}^n \tau_i(y_j;\Psi^{(k)})}{n}\qquad (i = 1, \ldots, g). $$ We repeat the E, M steps until $L(\Psi^{(k+1)})-L(\Psi^{(k)})$ is small.        I tried to write a R code (data can be found ).    # EM algorithm manually # dat is the data  # initial values pi1       &lt;-  0.5 pi2       &lt;-  0.5 mu1       &lt;- -0.01 mu2       &lt;-  0.01 sigma1    &lt;-  0.01 sigma2    &lt;-  0.02 loglik[1] &lt;-  0 loglik[2] &lt;- sum(pi1*(log(pi1) + log(dnorm(dat,mu1,sigma1)))) +               sum(pi2*(log(pi2) + log(dnorm(dat,mu2,sigma2))))  tau1 &lt;- 0 tau2 &lt;- 0 k    &lt;- 1  # loop while(abs(loglik[k+1]-loglik[k]) &gt;= 0.00001) {    # E step   tau1 &lt;- pi1*dnorm(dat,mean=mu1,sd=sigma1)/(pi1*dnorm(x,mean=mu1,sd=sigma1) +            pi2*dnorm(dat,mean=mu2,sd=sigma2))   tau2 &lt;- pi2*dnorm(dat,mean=mu2,sd=sigma2)/(pi1*dnorm(x,mean=mu1,sd=sigma1) +            pi2*dnorm(dat,mean=mu2,sd=sigma2))    # M step   pi1 &lt;- sum(tau1)/length(dat)   pi2 &lt;- sum(tau2)/length(dat)    mu1 &lt;- sum(tau1*x)/sum(tau1)   mu2 &lt;- sum(tau2*x)/sum(tau2)    sigma1 &lt;- sum(tau1*(x-mu1)^2)/sum(tau1)   sigma2 &lt;- sum(tau2*(x-mu2)^2)/sum(tau2)    loglik[k] &lt;- sum(tau1*(log(pi1) + log(dnorm(x,mu1,sigma1)))) +                 sum(tau2*(log(pi2) + log(dnorm(x,mu2,sigma2))))   k         &lt;- k+1 }   # compare library(mixtools) gm &lt;- normalmixEM(x, k=2, lambda=c(0.5,0.5), mu=c(-0.01,0.01), sigma=c(0.01,0.02)) gm$lambda gm$mu gm$sigma  gm$loglik   The algorithm is not working, since some observations have the likelihood of zero and the log of this is -Inf. Where is my mistake? YA dystopia novel of battle school with unusual military control scheme Expected Value of a Hypergeometric Random Variable I have been running Ubuntu 18.04 for a couple of weeks. I upgraded from 16.04 and all went smoothly.   I am not sure what I changed, but this morning I noticed that the "Settings" Icon that launches gnome-control-center is missing from "Show Applications" and the applications menu as well. When I searched from "Show Applications" for gnome-control-center or just settings, nothing showed up.   So, I figured I must have accidentally removed it and figured a reinstall of the package would resolve the issue. I have searched and found several postings where this worked. I tried:  sudo apt install gnome-control-center   And then rebooted - which reinstalled the gnome-control-center and I could then launch it from the command line. However, there was still no Settings Icon in any of the menus.   I also tried many other suggestions including:  sudo apt-get install --reinstall gnome-control-center sudo apt-get install ubuntu-desktop sudo apt install ubuntu-desktop --reinstall sudo apt-get install unity-control-center   However, none of these has been successful in restoring the icon into "Show Applications" or any applications menu.   Anyone have any suggestions on something I haven't tried? Would be much appreciated.  Or, is there a way to just manually recreate the icon?   Output of locate gnome-control-center.desktop:  /usr/share/applications/gnome-control-center.desktop  /home/dccrens/.local/share/applications/gnome-control-center.desktop /home/dccrens/.gnome/apps/gnome-control-center.desktop   I am running Ubuntu 18.04 desktop on kernel 4.15.0-45-generic. Can NDSolve handle discontinuous data? Following an earlier question ,  I would love to implement the  as suggested by Russell McMahon.   That way I could switch between 4AA batteries (1.2V*4 or 1.5V*4) and USB power. The battery voltage would nicely be regulated to 5V too. And the idea was to use the shutdown pin of the chip IF USB power is detected. The device also has to work when no batteries are present.  I am not too experienced with this, but I thought to connect the 5V from the USB to the SHUTDOWN pin from the LDO chip. Pitywise, the pin function is inverted, if SHUTDOWN is low, Vout from the LDO chip is low.  I am now considering using an XOR gate to make the thing work:         &ndash; Schematic created using   I would love to limit the amount of components, but the number of diodes is already high, and the whole thing feels a bit crafted   My questions:    Is there a better suitable chip (with an inverted shutdown pin) is there a better circuit (without voltage drop) to get this (I would prefer to get rid of D1, but then, the XOR has no desired operation) How to throttle callback of jQuery event? I have seen a "Universal Laptop Adapter" sold in a computer shop before. I am thinking of getting one for a laptop. Is it safe to use? What differences are there between one of these and a typical laptop adapter? This is a trivial problem, but it annoys me that I can't get to the bottom of it:  I'm running Windows 8, Powershell version 3.0. By right-clicking on the title bar I can go into the Properties and change the font, size, background colour etc without any problems.  After closing and restarting Powershell, all of the changes I've made stick except that if I've set the font to Lucida Console then on reopening I get the Raster font.  (Note that all of the above applies to when I run Powershell as Administrator.)  So:   If I set the font to Lucida, then it switches to Lucida for the remainder of the session. If I set the font to anything other than Lucida, then it stays as that after closing and reopening. If I alter the window sizes or text colours or anything else, the changes persist after reopening. The only thing that goes wrong is that if I set the font to Lucida, it switches to 'Raster fonts' when I reopen. But cmd and powershell ISE don't have this problem - only the powershell console.   Can anyone suggest what might be going wrong?  (One observation I've made is that upon re-opening Powershell after setting the font to Lucida, at first the width of the window is what it would be if the font were Lucida, but then after a second, it widens slightly to accommodate the raster font.) How has the age of the Universe been derived from the observations made by the Planck mission? Why is it dangerous use a coiled extension cord Recently I asked about the  pertaining to Voldemorts new face. However I was corrected by ...     Well, I think the confusion comes with mixing movie canon with book canon. In Philosopher's Stone, here's what Harry sees when Quirrell unwraps his turban:           Harry would have screamed, but he couldn’t make a sound. Where there should have been a back to Quirrell’s head, there was a face, the most terrible face Harry had ever seen. It was chalk white with glaring red eyes and slits for nostrils, like a snake.          Philosopher's Stone - page 212 - UK - chapter 17, The Man With Two Faces      So it seems at some point between leaving school, and sticking his face to the back of Quirrel's head possessing Quirrel he got a new face some how.   How did he manage that? Is it some dark magic he applies? Is it from possessing snakes in Albania? Comparison theorem for ODE Dynamically reformatting man pages on terminal dimension changes One common workflow of mine is to open a manual page in a terminal, then another terminal in which to test things. The man page is formatted to the initial dimensions of the first terminal. When I now resize my windows (or have my WM do that for me automatically), there is either a gap to the right of the preformatted page, or lines wrap. At this point I usually q(uit) and !! (run again), which loses my position in the page.  I assume the formatting process is quite CPU intensive, or maybe it stems from ancient times of fixed terminal sizes. The less pager dynamically reacts to terminal resize events, so it should be possible in theory.  I tried perusing man pages, searching the Web, asking on IRC -- the whole lot -- but couldn't come up with anything.   Can I trigger reformatting from within or outside of the man utility? Is there a version of the man utility that resizes the page dynamically?  Is there way to customize some part of the formatting/display process to make it update on SIGWINCH? It is much more convenient and cleaner to use a single statement like  import java.awt.*;   than to import a bunch of individual classes  import java.awt.Panel; import java.awt.Graphics; import java.awt.Canvas; ...   What is wrong with using a wildcard in the import statement? What does this pen notation in my UK entry stamp mean? I entered the UK from Paris once (riding the Eurostar train), and after the UK border control officer placed an entry stamp in my passport, he added a notation in pen (picture below).  What does it mean?  I suspect it is some sort of "warning" (the border control officer was not happy with me, though thankfully did not refuse entry).  I've always been curious about what it means more precisely or whether my prediction is even correct.  I've entered the UK only once again after getting this stamp.  I was admitted then too, but it took a while (the border control officer went away for about 10 minutes to do something before letting me in).