We understand from the books that there are multiple parts of the Ministry of Magic and its counterparts devoted to deceiving Muggles, including concocting explanations for Muggle head of states in the event of magical catastrophes. We also know that Obliviators will wipe any Muggle's memory of such an accident.  But what happens when a Muggle takes a video or photo of a magical incident, which their phone then uploads to cloud storage? Even if you wiped the Muggle's memory and broke their phone, they'd still be able to access their cloud storage later, and upload the media to a sharing site.  Stopping a disaster like this has three parts:     Wizards have to know and understand how cloud storage works, including the idea of redundant backups among different servers. If the media is uploaded, they also have to understand how to find that media within every server that stores it. Wizards have to be able to interface with computers via magic to correct the problem. Wizards have to be able to find every Muggle that ever saw the media and obliviate them. If the media was uploaded to a sharing site, this could potentially be anything from a handful of people to hundreds of millions!    Alternately, wizards have to convince all Muggles that ever saw the media that it was fake. But if wizards can't solve parts 1-3, the problem will keep happening.  It seems to me there's no way wizards can avoid getting detected by Muggles once cloud storage becomes common, but am I missing something?
In the Harry Potter universe, wizards and witches have managed to keep Muggles unaware of their existence, across the planet and over many centuries. Up to the timeframe that the novels take place in (the 1990s), I can see how this can be achieved through a combination of discretion and magic, with discretion being the preferred method on occasion (e.g., you don't need magic to slip into Platform 9 3/4 unnoticed, you just need to check that nobody is looking).   Our current world of 2016, however, its a very different place. The UK is (in)famously heavily camera-monitored (). Even more poignantly, a very large (and growing) segment of the population carries an internet-enabled HD camera with them at all times and are willing to use it at a moment's notice (, but it is comedy in part because a more realistic version could happen). It looks like, the moment something magical happens in public, a video of it would be on Youtube/Facebook/Twitter and within minutes.   How does the Ministry of Magic deal with this development? Do they need to create a dedicated corps to monitor social media services and alter records as necessary?
Why uniform closure $\mathscr{B}$ of an algebra $\mathscr{A}$ of bounded complex functions is uniformly closed? Let $\mathscr{A}$ be an algebra of bounded complex functions. (Or if necessary, continuous and domain of functions is compact)  Definition:  $\mathscr{B}$ is uniformly closed iff $f\in\mathscr{B}$ whenever $f_n\in \mathscr{B} (n=1,2,\cdot)$ and $f_n\rightarrow f$ uniformly.  $\mathscr{B}$ is the uniform closure of $\mathscr{A}$ iff $\mathscr{B}$ is the set of all functions which are limits of uniformly convergent sequences of members of $\mathscr{A}$.  ============  Let $\mathscr{B}$ be a uniform closure of $\mathscr{A}$.  How do i prove that $\mathscr{B}$ is uniformly closed in ZF?  Does Stone-Weierstrass theorem require choice since it is critical to prove Stone-Weierstrass Theorem? Beryllium Vacuum Sphere Boat/Aircraft Does there exist a magical shell piping which would allow easily to grep through bunch of .gz log files without needing to extract them somewhere?  .gz files are Apache logs, result of log rotation. I'd like to quickly check how often certain URIs are accessed in the past. Prove the following in $S_n$:  Let $\alpha = (a_1,a_2,\ldots,a_s)$ be a cycle and let $\pi$ be a permutation in $S_n$. Then $\pi\alpha\pi^{-1}$ is the cycle $(\pi(a_1),\ldots,\pi(a_s)).$     I'm not sure where to even start. What is the equation for the tension on the ends of a cable suspended at different heights? I'm looking for an equation to find the tension on the ends of a cable suspended between two poles (one higher than the other) with no load but the cable itself.    I determined that the tension would be different on each end, that the shape of the suspended cable would be a  truncated at one end, and that the following would be the variables necessary in the equation:   cable weight cable length vertical distance between ends horizontal distance between ends   Some links that could be helpful: How to prove $\vdash\neg P\to (P\to Q)$? I am trying to prove,  $$\vdash\neg P\to (P\to Q)$$  where $P$ and $Q$ are arbitrary but otherwise fixed formulas. The only axioms and rule of inference that I can use are,  $\color{crimson}{\text{Axiom 1.}}\  P\to (Q\to P)$ $\color{crimson}{\text{Axiom 2.}}\  (S\to (P\to Q))\to((S\to P)\to (S\to Q))$ $\color{crimson}{\text{Axiom 3.}}\  (\neg Q\to\neg P)\to(P\to Q)$ $\color{crimson}{\text{Rule of Inference.}}$ .  I know that in Angelo Margaris's book First Order Mathematical Logic there is a proof (page 53) but as I have mentioned , the dot notation seems very confusing and translating them to the nested parentheses notation seems very difficult to me. So, I am trying on my own to prove the result. Can anyone help? Find $\lim_{n \to \infty} \left[\frac{(n+1)^{n + 1}}{n^n} - \frac{n^{n}}{(n-1)^{n-1}} \right]$ (a question asked at trivia) How do I show the current node title in page.html.twig OR in node.html.twig? If I want to show the current node title in page.html.twig (by default it seems to only be available in node.html.twig) I have to create a preprocess function like so:  function theme_preprocess_page(&amp;$variables, $hook) {   // Set our page title so we can access it in page.html.twig   if ($node = \Drupal::routeMatch()-&gt;getParameter('node')) {     $variables['my_node_title'] = $node-&gt;title-&gt;value;   } }   And then I have to overwrite page-title.html.twig by copying it into my current theme folder and commenting out everything.  This doesn't seem "right".  Is there a better way? Is past simple ever justified with 'by'? Can anyone shed some light on the following aspect?  By 5 PM I gave him the book.  By 5 PM I had given him the book.  In both the sentences the book was given before 5 PM and no later than 5 PM. But I can't understand then what the difference between them is. a Also is it right to use simple past with 'by' at all? If yes, then why and if not, then why is it incorrect to use simple past with 'by'? Is it possible to reference an excel cell in a comment? I have an Excel balance sheet with a total at the bottom. On that cell I have a comment that says that the reason the total is X is because of what happens in J2. What happens if I insert another row before that, now my comment is wrong because all the rows jumped up a value.  Is there any way to reference a cell dynamically in an Excel commment? What JavaScript keywords (function names, variables, etc) are reserved? Flag dialogs for grayed-out posts are also grayed-out Fade in each element - one after another I am trying to find a way to load a JSON page to display my content, which I currently have. But I am trying to fade in each element one after another? Is anyone familiar with a way to do that?  Fade in each element with a slight delay?  Here is an example of my code, I am using the jquery framework.  CODE: R's randomForest can not handle more than 32 levels. What is workaround? R's randomForest package can not handle factor with more than 32 levels. When it is given more than 32 levels, it emits an error message:     Can not handle categorical predictors with more than 32 categories.   But the data I have has several factors. Some of them have 1000+ levels and some of them have 100+. It even has 'state' of united states which is 52.   So, here's my question.   Why is there such limitation? randomForest refuse to run even for the simple case.  &gt; d &lt;- data.frame(x=factor(1:50), y=1:50) &gt; randomForest(y ~ x, data=d)   Error in randomForest.default(m, y, ...) :    Can not handle categorical predictors with more than 32 categories.   If it is simply due to memory limitation, how can scikit learn's randomForeestRegressor run with more than 32 levels? What is the best way to handle this problem? Suppose that I have X1, X2, ..., X50 independent variables and Y is dependent variable. And suppose that X1, X2 and X3 has more than 32 levels. What should I do?  What I'm thinking of is running clustering algorithm for each of X1, X2 and X3 where distance is defined as difference in Y. I'll run three clusterings as there are three problematic variables. And in each clustering, I wish I can find similar levels. And I'll merge them.  How does this sound? Adding Table to Layout View using ArcPy? I am using ArcGIS 10.1 and I have a non-spatial table and some layers in a Data Frame.   When I switch to Layout View I want to be able to show the map in a data frame element and the table in another element (something that one could do with "Add Table To Layout" from Table Options, but I want to do this in one step without having to go to Table Options).   Is there a way to do this using ArcPy?   I couldn't find any function in the ArcPy library that would create a new Layout Element ... and then I also don't know how to add the contents of the table to the Layout Element. I'm a bit confused on how extra damage works for critical hits. Let's take the following example: A thief with sneak attack rolls a crit. I'm under the impression he rolls double his normal attack damage dice AND double his Sneak Attack damage dice. Is this accurate? Another example, I finished DM-ing my first campaign recently. The Giant Spider enemy monster has an melee attack that causes a constitution saving throw. If the player fails, the enemy rolls an additional 2D8 of damage. In this situation, if there was a critical hit, and the player failed their saving throw, would I also roll double dice on the additional damage? Or is that considered a separate attack? An awful lot of people seem to use the phrase "substitute X for Y" to mean "replace X with Y", while I've always used and understood it as "replace Y with X". This makes sense to me, given that a substitute is the replacement, not the thing which has been replaced.  I thought I might be able to figure things out from a dictionary, but now after seeing two sorts of definitions, I'm even more confused:   to put or use in the place of another to take the place of; replace   The first one suggests that the object will be the substitute (replacement), the thing put into place, while the second suggests that the object will be the thing which has been replaced.  Is one of these usages more correct in any sense? (I know this is probably a pointless question, since people will continue to speak the way they speak.) Is there perhaps a difference between American and British English?   And most importantly, is there any reliable way to tell what someone means when they ask how to substitute honey for sugar, or is the verb simply guaranteed to cause confusion? How to create a folder in HOME Folder with ModelBuilder in ArcGis 10? I really tried hard to do this on my own, but I keep failing ... Using multi-column and multi-row commands confused me. I know some of you might frown upon such a request but I really need help getting this table implemented .. So I'm sorry if I upset anyone.  My preamble has :   \documentclass[12pt,a4paper]{report} \usepackage[lmargin=3.81cm,tmargin=2.54cm,rmargin=2.54cm,bmargin=2.52cm]{geometry} \linespread{1.5}     Is there a way I can convert this from excel to LaTeX form ? I tried an add-in before but it didn't work for me. Also online generators cannot combine cells the way I want them (unless I didn't find a better table generator ? ) Can I visit other Schengen countries on a long-term Schengen visa or residency permit? I have requested for a French long term (Type D) student visa from a consulate in India. It's a national Type D visa and not a Schengen visa. My question is that can we still go to other Schengen countries on this visa? If not then can we get a Schengen visa from a consulate in France?