Who cooked and served food for the prisoners of Azkaban?
How does Azkaban's management work?
In MLE for continuous rv, why is it ok to evaluate a pdf at a point? Why is a vector space equal to its tangent space for any point? I'm self-studying Guillemin and Pollack, but I'm stuck on Problem 3 of section 2. It says that if $V$ is a vector subspace of $\mathbb{R}^N$, then $T_x(V)=V$ if $x\in V$.  If $x\in V$, then since $V$ is a manifold, there is a local parametrization $\phi: U\to V$ where $U$ is open in $\mathbb{R}^k$. Without loss of generality, we can require $\phi(0)=x$. Then $T_x(V)$ is defined to be the image of $d\phi_0$ on $\mathbb{R}^k$.   An arbitrary element of $T_x(V)$ looks like $$ d\phi_0(v)=\lim_{t\to 0}\frac{\phi(0+tv)-\phi(0)}{t}=\lim_{t\to 0}\frac{\phi(tv)-x}{t} $$  but this doesn't seem very useful to show $T_x(V)=V$. What is the right approach? How to determine exact contrast ratio Because of the recent Web accessibility Law in my region, I need to ensure I'm designing with an appropriate contrast ratio.  WCAG says the value of this ratio is 4.5:1    How do I figure this out in in Photoshop and Illustrator? Minion Pro, TL2016 and LuaLaTeX Which of the following sets are compact in $\mathbb{M}_n(\mathbb{R})$[NBHM_PhD Screening Test-2013, Topology] Which of the following sets are compact in $\mathbb{M}_n(\mathbb{R})$ (a) The set of all upper triangular matrices all of whose eigenvalues satisfy $|\lambda|≤2 $. (b) The set of all real symmetric matrices all of whose eigenvalues satisfy $|\lambda|≤2 $. (c) The set of all diagonalizable matrices all of whose eigenvalues satisfy $|\lambda|≤2 $.  (a) &amp; (c) are not true. But I am not sure about (b).can anybody help me please. Preamble: I know that 'give a reason when downvoting' is a very common request, and I assure you that I have read these posts and the discussions in them and my request is very different. This isn't about encouraging people to comment and is more about gathering metrics.  I'd like to see a feature whereby people who are downvoted get some better feedback on why they were downvoted, especially given that people rarely leave comments in practice.  So my suggestion is that when user clicks on the downvote, they are prompted to pick from a short list (No more than 5) of common reasons. It would be a popup that replaces the existing "Please consider adding a comment" box.  The user receiving the downvote would see how many people downvoted them for each reason, but not who did it. It would significantly address the issue of people being too lazy to comment or not wanting to comment (for fear of retaliation or any other reason) while helping to ensure the user gets useful feedback.  Perhaps the downvote could also be weighted based on whether or not a reason is picked.  For questions the list might look something like:   Not a question Not relevant to the subject area Trivial question with no research effort Poorly asked question Other   And for answers, this might be:   Nonconstructive or not an answer Incorrect or dangerous answer Poor explanation Doesn't answer the original question Other How do I install a fingerprint reader on Lenovo ThinkPad? Does a single photon's energy depend on frequency? (photoelectric effect) What do I need to know about temperature and food safety? What general rules do I need to follow to keep my food safe? How do I know what temperature to cook something to, or whether my food is safe at room temperature? Can I use lens brand X on interchangeable lens camera brand Y? What exactly are censored data? I have read different descriptions of censored data:  A) As explained in  thread, unquantified data below or above a certain threshold is censored. Unquantified means data is above or below a certain threshold but we do not know the exact value. Data is then marked at the low or high threshold value in the regression model. It matches the description in this , which I've found very clear (2nd slide on first page). In other words $Y$ is capped to either a minimum, a maximum value or both because we do not know the true value outside of that range.   B) A friend told me that we can apply a censored data model to partially unknown $Y$ observations, provided we have at least some limit information about the unknown $Y_i$ outcomes. For example, we want to estimate the final price for a mix of silent and open auctions based on some qualitative criteria (type of goods, country, bidders wealth, etc.). While for the open auctions we know all final prices $Y_i$, for the silent auctions we only know the first bid (say, $1,000) but not the final price. I was told that in this case data is censored from above and a censored regression model should be applied.  C) Finally there is the definition given by the  where $Y$ is missing altogether but the predictors are available. I'm not sure how this example is different from truncated data.  So what exactly are censored data? What are the differences between struct and class in C++? This question was .  Now I'd like to learn the differences between a struct and a class in C++. Please discuss the technical differences as well as reasons for choosing one or the other in OO design.  I'll start with an obvious difference:   If you don't specify public: or private:, members of a struct are public by default; members of a class are private by default.   I'm sure there are other differences to be found in the obscure corners of the C++ specification. What happens when the Runner stack is empty? When the corporation R&amp;D is empty the corporation loses.  What happens when the Runner's stack is empty?    I think that: He must finish the game with only the cards on the table.  or  I doubt that: He reshuffles the heap into a new stack. Examples and further results about the order of the product of two elements in a group Let $G$ be a group and let $a,b$ be two elements of $G$. What can we say about the order of their product $ab$?   says "not much":     There is no general formula relating the order of a product $ab$ to the orders of $a$ and $b$. In fact, it is possible that both $a$ and $b$ have finite order while $ab$ has infinite order, or that both $a$ and $b$ have infinite order while $ab$ has finite order.   On the other hand no examples are provided. $(\mathbb{Z},+), 1$ and $-1$ give an example of elements of infinite order with product of finite order. I can't think of any example of the other kind! So:   What's an example of a group $G$ and two elements $a,b$ both of finite order such that their product has infinite order?     Wikipedia then states:     If $ab = ba$, we can at least say that $\mathrm{ord}(ab)$ divides $\mathrm{lcm}(\mathrm{ord}(a), \mathrm{ord}(b))$   which is easy to prove, but not very effective. So:   What are some similar results about the order of a product, perhaps with some additional hypotheses? Why does the degree of freedom of SSR equals 1 in simple linear regression Name tikz pic as if it was a node I'm confused about tikz pics. I can freely define them without issue, and even add coordinates inside that will be available by name inheritance like (-A) as for example in \pic (S) at (0,0) {myPic}; \draw (S-A) -- ++(0,0);. This is all documented around p. 255 of the pgf manual.  However I don' understand why it is not possible to give a name to a pic like the one above if no coordinate is defined inside it. By default it would be great if it could behave like a normal node.  MWE:  \documentclass{minimal} \usepackage{tikz}  \tikzset{     myBlock/.pic = {         \node[draw,minimum width=1cm,minimum height=0.5cm] at (0,0) {};     },     myBlockNamed/.pic = {         \node[draw,minimum height=1cm,minimum width=0.5cm] (-m) at (0,0) {};     }, }  \begin{document} \begin{tikzpicture}     \pic () at (0,0) {myBock}; % can't give it a name     \pic (S) at (3,0) {myBlockNamed}; % can give it a name     \draw (S-A) -- ++(2,0); \end{tikzpicture} \end{document}   The underlying point is I'm working on a control blocs library (so that we can stop the chat below with @Alenanno). For example here is the definition of a math operator  \tikzset{     mySum background/.style = {         circle, minimum size=1.5em, fill=white,     },     mySum edge/.style = {         draw=black, circle, minimum size=1.5em, line width=.5pt,     },     pics/bOp/.style = {     code = {       \node [mySum background] {};       \foreach \t [count=\i] in {#1}{         \pgfmathsetmacro{\angle}{\i*90}         \node[anchor=center, font=\tiny] at (\angle:0.45em) {$\t$};       }       \node [mySum edge] {};     },   }, } Can ASP.NET MVC generate elements with lower case name and id attributes Let $f(z)=\sum\limits_{n=0}^{\infty}a_n z^n$ be an analytic function in $|z|\leq R$ such that $|f(z)|\leq M$. Prove an inequality about $f$'s zero I have recently installed lubuntu 11.10 on my old laptop (acer aspire 5315 celeron) and observed that fan is not working properly on lubuntu side.I find it strange that it is working perfectly under window vista.   How could I solve this problem? 301 redirect blogspot to an existing domain? Is it possible to redirect a blogspot site to an existing URL?  Note that I don't want to buy a new domain and tell blogspot to use that, eg as per this question: .    Instead I am trying to 301 redirect to an existing website in order to combine the website and the blog in one place.  So it needs to be:  301 example.blogspot.com/post to example.com/blog/post