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Looking at the questions and answer to these two questions.  &amp;  and neither mentions the longevity of magic. I recall several instances of magic failing to last; the money that was spread at the  and the broken  on.  If I recall correctly when Voldemort died, the curses on several people were lifted.  I don't recall if any other spells fell apart with his death.  Is there any canon evidence on the the length of time a spell will live? Reverse / invert a dictionary mapping Given a dictionary like so:  my_map = {'a': 1, 'b': 2}   How can one invert this map to get:  inv_map = {1: 'a', 2: 'b'} Understanding the parameters inside the Negative Binomial Distribution I was trying to fit my data into various models and figured out that the fitdistr function from library MASS of R gives me Negative Binomial as the best-fit. Now from the  page, the definition is given as:     NegBin(r,p) distribution describes the probability of k failures and r   successes in k+r Bernoulli(p) trials   with success on the last trial.   Using R to perform model fitting gives me two parameters mean and dispersion parameter. I am not understanding how to interpret these because I cannot see these parameters on the wiki page. All I can see is the following formula:    where k is the number of observations and r=0...n. Now how do I relate these with the parameters given by R? The help file does not provide much information either.   Also, just to say a few words about my experiment: In a social experiment that I was conducting, I was trying to count the number of people each user contacted in a period of 10 days. The population size was 100 for the experiment.   Now, if the model fits the Negative Binomial, I can blindly say that it follows that distribution but I really want to understand the intuitive meaning behind this. What does it mean to say that the number of people contacted by my test subjects follows a negative binomial distribution? Can someone please help clarify this? Passing a formatted NSDate Redirect 301 with hash part (anchor) # How will Ubuntu automatically allocate the disk partition sizes when we select Erase disk and install Ubuntu during installation?    Can the settings for automatic space allocation be changed? Does personified Death really exist in Harry Potter? I went through the last book, Harry Potter and the Deathly Hallows, yesterday and a question popped in my mind: Does Death, the supposed creator of the Deathly Hallows, really exist in the Harry Potter universe? Dumbledore thought otherwise and I am with the same school of thought.  By the way who created the deathly Hallows actually?  Update:  1) Why were the brothers so sure that the hooded figure was death(couldn't it be a more powerful wizard playing with them)  2) Couldn't, Beedle and the brothers create this story? Could someone please explain the differences between the 3 fitting methods, method = c("CSS-ML", "ML", "CSS"), in Arima?  If I run the code below I get an error message, but if I specify method="ML" in Arima it runs fine.  So I was curious what the difference was between the 3 fitting methods.  Code with error:  library("fpp")  tsTrain &lt;- window(hsales,end=1989.99)  pvar&lt;-1:10 dvar&lt;-1:2 qvar&lt;-1:7  OrderGrid&lt;-expand.grid(pvar,dvar,qvar)  n &lt;- function(a,b,c) {Arima(tsTrain, order=c(a,b,c))} ModFit &lt;- do.call(Vectorize(n, SIMPLIFY=FALSE), unname(OrderGrid))   Fixed Code:  library("fpp")  tsTrain &lt;- window(hsales,end=1989.99)  pvar&lt;-1:10 dvar&lt;-1:2 qvar&lt;-1:7  OrderGrid&lt;-expand.grid(pvar,dvar,qvar)  n &lt;- function(a,b,c) {Arima(tsTrain, order=c(a,b,c),method="ML")} ModFit &lt;- do.call(Vectorize(n, SIMPLIFY=FALSE), unname(OrderGrid)) How do I get my Mac to boot from an Ubuntu USB key? If you select "USB" and "Mac" on , it gives a series of command line instructions to make a USB key which the MacBook will boot into Ubuntu from.  I've followed them to the letter two or three times on different USB keys, and it doesn't work. There's a very great deal of technical discussion about EFI etc. but this set of instructions seems to suggest it should just work, but it doesn't.  Help? I'm increasingly unhappy with the more locked-down approach Apple is taking, and I'd quite like to start using Linux with a view to transitioning over to using it as my main operating system, but booting from the CD takes forever, runs slowly and I'm really hoping to get it moving off USB.  Can anybody help me? Changing console font on Ubuntu 10.04 Server How can I change local console font on Ubuntu 10.04 Server to Inconsolata? How do I boot my PC from GRUB? A  is formed when a raindrop refracts light, but why then does the whole sky not become a huge rainbow when it rains? Would the light not be dispersed into ordinary white light? What causes it to look as if each end is nearly touching the ground? How to get city name from latitude and longitude coordinates in Google Maps? How to save an alias of an eval $(other_comand) command I've been using docker for a while and there's a command I write each time I boot up my docker:  eval $(docker-machine env)   I know eval shouldn't be used unless necessary, but it's mentioned by the following:  docker-machine env outputs environment variables like this:  docker-machine env export DOCKER_TLS_VERIFY="1" export DOCKER_HOST="tcp://&lt;some_ip&gt;:&lt;some_port&gt;" export DOCKER_CERT_PATH="/home/gableroux/.docker/machine/machines/default" export DOCKER_MACHINE_NAME="default" # Run this command to configure your shell:  # eval $(docker-machine env)   eval grabs these and load them in my current session.  Now what if I'd like to have an alias like this:  alias dockereval="eval $(docker-machine env)"   Syntax is good, but the problem is when a dotfile (let's say .zshrc as an example), well the content of the $() is evaluated when registering the alias when you source that file.  which dockereval   Results in  dockerenv: aliased to eval   I tried a few things like:  alias dockereval="docker-machine env | eval" alias dockereval="docker-machine env | /bin/bash" alias dockereval="eval `docker-machine env`"   but none did work. 2nd one is probably because it's running in a different session, 3rd does the same as $() I guess  Is there an other way to load these environment variables with an alias? Do I need a UK visa? How and where to apply? I live in Germany since May 2013 as a spouse of German citizen. In Nov 2015 we divorced and I have German residence permit till Jan 2018. We have a son in this marriage and legally I have the right to live in Germany indefinitely. I would like to visit my brother and sister who are British citizens living in UK. What is the visa procedure for me to travel to UK for a week.  Do I need a visa to enter UK ? My questions is very simple. How can I set security setting for a PDF file created with PDFLatex?  I should set some password or print permissions, etc. How do I fix the GPG error "NO_PUBKEY"? Integer $x$ for which $x^4+x^3+x^2+x+1$ is perfect square. Integer values of $x$ for which $\bf{x^4+x^3+x^2+x+1}$ is a Perfect Square.  $\underline{\bf{My\; Try}}$:: Let $\bf{x^4+x^3+x^2+x+1 = k^2}$, where $k\in \mathbb{Z}$  $4x^4+4x^3+4x^2+4x+1 = 4k^2 = (2k)^2$  Now How can I proceed after that  Help Required,  Thanks I am trying to solve the following two problems:  1) Prove that the functions $\cos(z)$, $\sin(z)$ are surjective over the complex numbers.  2) Find all $z \in \mathbb C$: $cos(z) \in \mathbb R$ and find all $z \in \mathbb C$: $\sin(z) \in \mathbb R$.  For 1),I've tried to prove it for the function $\cos(z)$ (I suppose the other one is analogue)  so I've used the fact that $\cos(z)=\dfrac{e^{iz}+e^{-iz}}{2}$.  Let $w \in \mathbb C$, I want to show there exists $z \in \mathbb C : f(z)=w$, i.e., $\dfrac{e^{iz}+e^{-iz}}{2}=w$, multiplying by $2$ and then by $e^{iz}$ yields $e^{2iz}+1=2we^{iz}$ iff $e^{2iz}-2we^{iz}+1=0$.   I don't know if this approach is the correct one but here I've replaced $e^{iz}$ by $x$, so the solutions of the equation would be the roots of the polynomial $p(x)=x^2-2wx+1$, by the quadratic formula, I get that $x \in \{\dfrac{2w+w_0}{2},\dfrac{2w-w_0}{2}\}$, where $w_0^2=4w^2-4$.  Then, $e^{iz} \in \{\dfrac{2w+w_0}{2},\dfrac{2w-w_0}{2}\}$. At this point I got lost, I would like to explicitly show that $z$ exists and I can't see existence directly from the fact that $e^{iz}=\dfrac{2w+w_0}{2}$ or $e^{iz}=\dfrac{2w-w_0}{2}$.  First I thought of taking logarithm of both sides of the equation ir order to solve for $z$, but this is not a legitimate operation unless $e^{iz} \in \mathbb R$.   I couldn't go any farther.  For point 2) I have no idea what to do, should I use the identity $\cos(z)=\dfrac{e^{iz}+e^{-iz}}{2}$?  I would appreciate some help with the two points (specially with point 2), at least in 1) I could do something).   Btw, Happy new year! Is it possible to change the linkage of Nether portals?