We are probably all familiar with this one: How come Fred and George don't realize the long-dead Peter Pettigrew is alive? They had the map for many years while Wormtail was at Hogwarts (he was Percy's rat first).
Fred and George stumbled upon the Marauder's map in their first year. They passed it on to Harry while in their fifth year. Also note that, while talking to Harry on the train, Ron described Scabbers as being "Percy's old rat".   Hence, we can safely assume that the twins had the Marauder's Map for about five years. How could they not see Peter Pettigrew on the map, with Percy for first two years and with Ron for the next three years?  How come Harry didn't see Peter? How was Lupin the only one able to see Peter on the map?
I am lost in normalizing, could anyone guide me please.  I have a minimum and maximum values, say -23.89 and 7.54990767, respectively.  If I get a value of 5.6878 how can I scale this value on a scale of 0 to 1. In my rebuilding project I have counted 18 outlets and lights on one bedroom circuit that travels through 3 rooms. Is that ok? Clean install Windows 8.1 or Windows 8 from OEM key Browse an UNC path using Windows CMD without mapping it to a network drive C:\&gt; cd \\somewhere '\\somewhere' CMD does not support UNC paths as current directories.   What I usually do to get around this is to map that directory to a network drive and then I could easily access it from the command prompt.  But is there an easier way on how to get around this? Trigonometric Uncertainty Propagation subequations and array in braces I need something like this:  \left\{ first line  (1a) second line (1b) third line  (1c) \right.   all lines should be aligned to left Multiple AES Key Derivation from a master key Does C# have extension properties? What does Pokémon Appraisal actually tell you in Pokémon Go? Where to insert the exclamation mark Where would I insert an exclamation mark and a comma in the below sentence?     "Look at that boy" he exclaimed. My dev team is getting ready to start a new project. The shop has been a "VB shop" since the days of VB3, but the prevailing opinion now is that we're a ".NET shop" and since C# was created specifically for .NET, whereas VB.NET was a retrofit, we've decided to move forward writing C# only. The controversy revolves around the question of whether the Microsoft.VisualBasic namespace has a legitimate place in new development or if it is only for backward compatibility for VB6 (and older) code. A further, and more interesting question is whether the code "under" the Microsoft.VisualBasic namespace is even .NET code of if it is really the old VB runtime carefully packaged in a .NET wrapper, making it in fact a COM interop control (similar to how WinForms wraps the non-.NET Win32 windowing API but exposes only .NET APIs for consumption).  To make this even more confusing, our dev team has a Microsoft Consulting Services consultant telling us Microsoft no longer supports Visual Basic, including the VB runtime underlying the Microsoft.VisualBasic namespace.  What I'm looking for are links -- preferably to unimpeachable Microsoft sources -- to documentation that definitively answers this question one way or the other. I've already tried several search permutations on Google and not gotten any closer to getting to the bottom of this question.  EDIT: Apparently I didn't make my question clear. I'm not asking if VB.NET is true .NET code. I'm trying to determine if whatever is "under" the Microsoft.VisualBasic namespace is .NET code or if it's the old VB6 runtime carefully packaged and exposed as .NET code. Someone already said that 9/10 of the namespace simply wraps code from elsewhere in .NET; what about that other 1/10? How can I automatically log out the guest account after a period of inactivity? As part of a kiosk system, I have set up a Guest account on a Mac OS X Snow Leopard computer. This account is cleared every time someone logs off the computer. However, plenty of people don't. Is there any way that I can automatically log out this guest account after a period of inactivity?  I tried using the security preferences pane, but that just causes the confirm logout dialog to show up.  I have hacked around the /System/Library/User Templates/ folder, so I can set the screensaver, desktop background, &amp;c. If something like ScriptSaver can solve my problem, I will gladly use it. A while back, I read a story in a collection, but I don't remember very much. I know that it was about some missionaries on Mars. Eventually they found a bunch of spheres that apparently have escaped sin by leaving the material world. I don't remember anything else about it. Someone told me that it was in "The Martian Chronicles" by Ray Bradbury, but I checked my copy and couldn't find. I'm pretty sure that it was by Ray Bradbury though. Help would be greatly appreciated. "You've earned (badge)" panel layouts are broken When I visit  I see this:     The "Congratulations! You've earned (badge)" section has dropped down completely beneath the tabs under it. The "You've earned a new privilege!" section has a gap at the bottom:     Shog9 says in comments how to reproduce this:     Gotta have earned a badge, not dismissed the notification, and be looking at your own profile. Show that if $g \circ f$ is injective, then so is $f$. The Problem:  Let $X, Y, Z$ be sets and $f: X \to Y, g:Y \to Z$ be functions.  (a) Show that if $g \circ f$ is injective, then so is $f$.  (b) If $g \circ f$ is surjective, must $g$ be surjective?  Where I Am:  So, I really have trouble with these, for some reason. I can draw pictures and make sense of the problems, but writing down proofs is very difficult for me.   Basically, for (a), I ended up with some complicated statement involving an implication implying another implication and then tried to derive a contradiction. It just got so convoluted that I couldn't make sense of it anymore, and I know there's a quick, elegant way to show it.  For (b), I know that $g$ need not be surjective. Once again, though, proving it directly from definitions has given me a bit of a headache.  Any help here would be appreciated. Thanks in advance.  The Proofs!  Ok, I did it. Thanks for the help, everyone! Let me know if there's anything wrong with these proofs, or if they could bet any better.  (a) Suppose $f$ is not injective. Then $$ f(x_1)=f(x_2) \implies x_1 \ne x_2 \text{        }(*).$$ Let $f(x_1)=y_0=f(x_2)$ and let $g(y_0)=z_0$. Then $$ (g \circ f)(x_1) = (g \circ f)(x_2) = g(y_0) = z_0. $$ Since $g \circ f$ is injective, $$ (g \circ f)(x_1) = (g \circ f_2) \implies x_1 = x_2. $$ However, this contradicts $(*)$. Therefore, $f$ must be injective.  (b) Suppose $g$ is not surjective. Then  $$ \forall y \in Y, \exists z \in Z \text{ such that } g(y) \ne z \text{         }(**).$$  Since, $g \circ f$ is surjective,  $$ \forall z \in Z, \exists x \in X \text{ such that } g(f(x)) = z \text{       } (***). $$  Let $f(x) = y$. Then,  $$ g(f(x)) = g(y) = z. $$  Because of $(***)$, this is true for all $z \in Z$, which contradicts $(**)$. Therefore, $g$ must be surjective. Problem with Refsection Examples and Counterexamples of Relations which Satisfy Certain Properties A set with a finite integral of measure zero? Decoupling caps, PCB layout I guess I've been somewhat ignorant when it comes to the finer details of pcb layout. Lately I've read a couple of books that try their best to lead me on the straight and narrow. Here is a couple of examples of a recent board of mine, and I have highlighted three of the decoupling caps. The MCU is a LQFP100 package and the caps are 100nF in 0402 packages. The vias connect to ground and power plane.     The top cap (C19) is placed according to best practices (as I understand them). The other two are not. I haven't noticed any problems. But then again the board has never been outside the lab.  I guess my question is: How big a deal is this? As long as the tracks are short, does it matter?  The Vref pins (reference voltage for the ADC) also have a 100nF cap across them. Vref+ comes from an onboard TL431 shunt regulator. Vref- goes to ground. Do they require special treatment like shielding or local ground?    EDIT    Thanks for great suggestions! My approach has always been to rely on an unbroken ground plane. A ground plane will have the lowest possible impedance, but this approach may be too simplistic for higher frequency signals. I've made a quick stab at adding local ground and local power under the MCU (The part is an NXP LPC1768 running at 100MHz). The yellow bits are the decoupling caps. I'll look into paralleling caps. The local ground and power are connected to the GND layer and the 3V3 layer where indicated.  The local ground and power are made with polygons (pour). It's going to be a major rerouting job to minimize the length of the "tracks". This technique will limit how many signal tracks can be routed under and across the package.  Is this an acceptable approach? ARIMA equation interpretation I'm trying to replicate ARIMA (1,0,1)(1,0,1) equation in excel as a formula but I am not able to understand the interpretation of white noise residual e(t) or u(t).If could help me understand the interpretation and how to derive it from raw data it'll be really great.  Thanks