remove indent when bolding the beginning of paragraph
What is the use of percent signs (%) at the end of lines? (Why is my macro creating extra space?)
How can I recursively delete all files of a specific extension in the current directory? How do I safely delete all files with a specific extension (e.g. .bak) from current directory and all subfolders using one command-line? Simply, I'm afraid to use rm since I used it wrong once and now I need advice. Diminishing returns / non-linear reputation from “great” answers Over time I realized a very annoying property of the Stack Overflow reputation system: Easy answers to popular question are rewarded with a lot more reputation points than actually great answers. In case anybody actually needs examples for this, here are two examples from :   gained me 420 rep, I invested 2 minutes writing it, and it only was a wild guess.   took me about an hour for the research and the math and gained me 40 rep.  Now I know that you are bound to get more rep for answers that are useful to more people, and I'd say that's fine. But the current situation is quite extreme: 30% of my reputation is from 5 of my 330 answers, and they are definitely far from being my best ones.  A final example that is not from my profile, but more extreme: Do you really think  is worth 40000 reputation?  My proposition to improve that situation would be to make the reputation gain from a single answer non-linear, maybe even have it capped at a certain point. I'm not sure on how that non-linear function should look exactly, and would leave good proposals for that to users with more experience than me. Why can't a single ReLU learn a ReLU? As a follow-up to  I simplified even more and tried to train a single ReLU (with random weight) to a single ReLU.  This is the simplest network there is, and yet half the time it fails to converge.  If the initial guess is in the same orientation as the target, it learns quickly and converges to the correct weight of 1:      If the initial guess is "backwards", it gets stuck at a weight of zero and never goes through it to the region of lower loss:        I don't understand why.  Shouldn't gradient descent easily follow the loss curve to the global minima?  Example code:  from tensorflow.keras.models import Sequential from tensorflow.keras.layers import Dense, ReLU from tensorflow import keras import numpy as np import matplotlib.pyplot as plt  batch = 1000   def tests():     while True:         test = np.random.randn(batch)          # Generate ReLU test case         X = test         Y = test.copy()         Y[Y &lt; 0] = 0          yield X, Y   model = Sequential([Dense(1, input_dim=1, activation=None, use_bias=False)]) model.add(ReLU()) model.set_weights([[[-10]]])  model.compile(loss='mean_squared_error', optimizer='sgd')   class LossHistory(keras.callbacks.Callback):     def on_train_begin(self, logs={}):         self.losses = []         self.weights = []         self.n = 0         self.n += 1      def on_epoch_end(self, batch, logs={}):         self.losses.append(logs.get('loss'))         w = model.get_weights()         self.weights.append([x.flatten()[0] for x in w])         self.n += 1   history = LossHistory()  model.fit_generator(tests(), steps_per_epoch=100, epochs=20,                     callbacks=[history])  fig, (ax1, ax2) = plt.subplots(2, 1, True, num='Learning')  ax1.set_title('ReLU learning ReLU') ax1.semilogy(history.losses) ax1.set_ylabel('Loss') ax1.grid(True, which="both") ax1.margins(0, 0.05)  ax2.plot(history.weights) ax2.set_ylabel('Weight') ax2.set_xlabel('Epoch') ax2.grid(True, which="both") ax2.margins(0, 0.05)  plt.tight_layout() plt.show()     Similar things happen if I add bias: 2D loss function is smooth and simple, but if the relu starts upside down, it circles around and gets stuck (red starting points), and doesn't follow the gradient down to the minimum (like it does for blue starting points):    Similar things happen if I add output weight and bias, too.  (It will flip left-to-right, or down-to-up, but not both.) I have been racking my brains over how in bloody hell can you have a different header for the title (or first) page of a document.   I am not asking here how I can not have a header by clearing the page style for this page using \thispagestyle{plain} or something of the sort but how can I have a different header just for the very first page.   Please help as I have a deadline to meet.   So far, I have not been able to find anything useful on TeX.SE.   Here is some of my code to give you some idea of what I want to achieve:  \documentclass[12pt]{article} \usepackage{amsmath} \usepackage[margin=2.5cm]{geometry} \usepackage[utf8]{inputenc} \usepackage{amsfonts} \usepackage{fancyhdr} \usepackage{hyperref} \usepackage{graphicx} \usepackage{csc} \pagestyle{fancy} \fancyhead[L]{**Left Header for all pages**}\fancyhead[R]{**Right Header for all pages**} \lhead{**Left Header for just the first page**} \rhead{**Right Header for just the first page**} \title{Problem Set 1}         \author{MyBloodyName} \date{January 31, 2017} \begin{document}     \maketitle     \newpage     Easier? \end{document} Exact probability of random graph being connected The problem: I'm trying to find the probability of a random undirected graph being connected. I'm using the model $G(n,p)$, where there are at most $n(n-1) \over 2$ edges (no self-loops or duplicate edges) and each edge has a probability $p$ of existing. I found a simple formula online  where $f(n)$ is the probability of $G(n,p)$ being connected. But apparently it's too trivial for the writer to explain the formula (it was just stated briefly).  The desired formula: $f(n) = 1-\sum\limits_{i=1}^{n-1}f(i){n-1 \choose i-1}(1-p)^{i(n-i)}$  My method is: Consider any vertex $v$. Then there's a probability ${n-1 \choose i}p^i(1-p)^{n-1-i}$ that it will have $i$ neighbours. After connecting $v$ to these $i$ neighbours, we contract them ($v$ and its neighbours) into a single connected component, so we are left with the problem of $n-i$ vertices (the connected component plus $n-i-1$ other "normal" vertices.   Except that now the probability of the vertex representing connected component being connected to any other vertex is $1-(1-p)^i$. So I introduced another parameter $s$ into the formula, giving us:  $g(n,s)=\sum\limits_{i=1}^{n-1}g(n-i,i){n-1 \choose i}q^i(1-q)^{n-1-i}$,  where $q=1-(1-p)^s$. Then $f(n)=g(n,1)$. But this is nowhere as simple as the mentioned formula, as it has an additional parameter...  Can someone explain how the formula $f(n)$ is obtained? Thanks! Why are mathematical proofs that rely on computers controversial? There are many theorems in mathematics that have been proved with the assistance of computers, take the famous  for example. Such proofs are often controversial among some mathematicians. Why is it so?  I my opinion, shifting from manual proofs to computer-assisted proofs is a giant leap forward for mathematics. Other fields of science rely on it heavily. Physics experiments are simulated in computers. Chemical reactions are simulated in supercomputers. Even evolution can be simulated in an advanced enough computer. All of this can help us understand these phenomena better.   But why are mathematicians so reluctant? Why does mathematical convention deal so ineptly with multisets? Textbook recommendations for self-studying high school math? I'm a high school student who is trying to figure out a complete course of self-study for each year of high school. How can I self-learn grades of math without devoting too much time? This is a complex issue for me, as other students at my competitive high school have tutors and the like. Please recommend textbooks that have detailed explanations and progressive practice problems, for self-study for each area such as:  Algebra  Geometry  Trigonometry and Analytic Algebra  Pre-calculus  BC Calculus  Other people have skipped grades of math due to help from tutors and parents. Can I cover all of geometry and trigonometry in 8 months without going insane and be able to skip a grade? I don't understand the fact that let's say hypothetically I was pushing a block on a frictionless surface, and I kept applying the same force on the object how it would keep accelerating! Wouldn't there have to be a certain velocity where it would stop getting faster? If not then what is actually acting on the object to cause it to accelerate infinitely? I'm currently unable to access anything via the Stack Exchange app under iOS; is this a known issue? How to add shortcut keys for java code in eclipse I am fairly familiar with Unity and I know how to work most of the features within it. But I don't know what programing languages to use for my Unity game. I have heard that it might be C#, but I am unfamiliar with C-sharp so I was wondering if Unity can use any other languages. I would not like opinions on which one to use, I just want to know what Unity supports. How do I turn off some formats in GeoServer's WMS? Unable to solve equation for a variable by any method In Java, you can qualify local variables and method parameters with the final keyword.  public static void foo(final int x) {   final String qwerty = "bar";  }   Doing so results in not being able to reassign x and qwerty in the body of the method.  This practice nudges your code in the direction of immutability which is generally considered a plus. But, it also tends to clutter up code with "final" showing up everywhere. What is your opinion of the final keyword for local variables and method parameters in Java? How to stream a video with VLC in a LAN I don't want my users to change the system wallpaper. How do I the lock the wallpaper down? Update  Users are changing wallpaper by right clicking the picture and choosing set as wallpaper. How to restrict this behaviour?  Is it possible to remove Backgrounds Tab from Appearance Preferences? If yes how? End of File in C++ Why are the longer edges being beveled more? I'll preface this by saying I'm very new to Blender - I'm trying to put a bevel on an edge, looks something like this:    As you can see, the vertical side is much longer than the horizontal side.  When I apply to bevel to the edge there, the bevel stretches proportionally - so there's 'more' bevel on the longer side.  I want to bevel without any 'ratio' like that - just a 45-degree bevel, if that makes any sense.  Do I have to put in a loop cut to make the side lengths equal?  I tried using a sub-surf modifier, but it applies on a bunch of nearby edges, when I just want to round this one corner. How can one prove the Bohr-Sommerfeld quantization condition $$ \oint p~dq ~=~2\pi n \hbar $$ from the WKB ansatz solution $$\Psi(x)~=~e^{iS(x)/ \hbar}$$ for the Schroedinger equation? With $S$ the action of the particle defined by Hamilton-Jacobi equation $$ \frac{\partial S}{\partial t}+ \frac{(\nabla S)^{2} }{2m}+V(x)~=~0 .$$