Trying to find a true condition for an empty record
How do I compare strings in Java?
Prove that if $ f\mathrm{(}z\mathrm{)} $ is analytic at the infinity  ,then :  $ {\lim}_{{z}\mathrm{\rightarrow}\mathrm{\infty}}{f}\prime{\mathrm{(}}{z}{\mathrm{)}}\mathrm{{=}}{0} $ How do I document a module in Python? That's it. If you want to document a function or a class, you put a string just after the definition. For instance:  def foo():     """This function does nothing."""     pass   But what about a module? How can I document what a file.py does? Resetting crontab file to default How to restore original size and unboot my bootable USB pendrive I recently made my pen-drive bootable with Ubuntu 14.04. But I need to unboot my pen-drive now. I formatted my pen-drive once,But the size of the pen-drive still shows 2.25 MB. Whereas,this is an 8GB pen-drive. How can I get rid of this problem. I'm still using Windows 7. "The following packages have been kept back:" Why and how do I solve it? When to choose checked and unchecked exceptions In Java (or any other language with checked exceptions), when creating your own exception class, how do you decide whether it should be checked or unchecked?  My instinct is to say that a checked exception would be called for in cases where the caller might be able to recover in some productive way, where as an unchecked exception would be more for unrecoverable cases, but I'd be interested in other's thoughts. Imagine a situation in which the whole place is on fire, a bomb is about to explode, everyone is running for their lives and someone is checking his looks on the mirror... pretty inappropriate for the situation, don't you think? I'm looking for an idiom or colloquial/slang/informal expression to describe such an indifferent stance. Counting and rasterizing polygon overlaps in ArcGIS Desktop? How do you take a vector layer with overlapping polygons and turn it into a raster where each cell counts the number of polygons containing that cell?    We are looking at polygons of fire burn areas between 1976 to 2000 and want to see how many fires would be contained in each raster cell. Did not receive site association bonus (+100 rep) Why does demand for stock rise when a company appears to have high future value? So a company decides to raise money by selling shares of its stock. The stock is offered at an initial price of their determination. The stock is then traded in a market where forces of supply and demand, as well as speculation, affect its price.  When a company performs well (or makes decisions that will likely increase the company's earnings in the future), more people want to buy that stock than do people wanting to sell it. This creates demand for that stock which causes its sell/bid prices rise. When a company performs poorly, the opposite occurs; more people want to sell the stock than want to buy. This creates a surplus that causes sell/bid prices to fall.  Understanding this, people speculate over company performance to determine the future behavior of a stock, and attempt to "buy low, sell high" or "borrow high, return low" in order to make a profit.  But my question is regarding the first part of that process. What is it about company performance that causes the perceived value of its stock to rise? This is especially perplexing since I would guess that most people don't exercise their voting rights, and many stocks don't pay dividends.  It's not like a shareholder has any direct financial gains from increased company earnings (speculative stock pricing notwithstanding).  What is the intrinsic value of the stock?  It seems to me that all participants in a stock market tacitly agree that stock price will have a direct correlation with company performance. So another way of asking the question is, would an opposite agreement hold? What financially (this isn't a question about logistics, communication, or feasibility) stops all participants in a market from agreeing to value a particular company's stock inversely with respect to the company's performance?  Since I feel like I can't quite nail down my question, another form of it would be, why is stock market behavior driven by company performance? 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 am developing a game with a Minecraft-like terrain made out of blocks. Since basic rendering and chunk loading is done now, I want to implement block selecting.  Therefore I need to find out what block the first person camera is facing. I already heard of unprojecting the whole scene but I decided against that because it sounds hacky and isn't accurate. Maybe I could somehow cast a ray in view direction but I do not know how to check the collision with a block in my voxel data. Of course this calculations must be done on the CPU since I need the results to perform game logic operations.  So how could I find out which block is in front of the camera? If it is preferable, how could I cast a ray and check collisions? Suppose $Y_1, \ldots, Y_n$ is a random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. Let $S^2$ be the sample variance, which is unbiased for $\sigma^2$.  GOAL: Show that $S = \sqrt{S^2}$ is a biased estimator of $\sigma$.  I realize that $(n-1)S^2/ \sigma ^2$ is chi-square with $(n-1)$ degrees of freedom.  I am given that $$E(S) = E\left[\frac{\sigma}{\sqrt{n-1}} \left[\frac{(n-1)S^2}{\sigma^2}\right]^{1/2}\right] = \frac{\sigma}{\sqrt{n-1}} \int_0^\infty v^{1/2} \frac{1}{\Gamma[(n-1)/2] 2^{(n-1)/2}} v^{(n-1)/2} e^{-v/2} \, dv$$  Can anyone help me understand why they have $v^{1/2}$ and $v^{(n-1)/2}$ (combining them $v^{n/2}$ as I think it should be $v^{1/2}$ and $v^{\frac{(n-1)}{2}-1}$ (combining both terms give $v^{(n-2)/2}$ since the pdf for chi-square distribution is $$ f(v) = \frac{v^{(x/2)-1} e^{-v/2}}{2^{x/2}\Gamma(x/2)},$$ where $x$ is degree of freedom?  Could anyone please tell me which one is the correct answer with explanation?  Thank you Zoom in/out on click in OpenLayers 3? How to prevent iMessage syncing without access to device I foolishly logged into someone's iPad with my Apple ID. This person is now receiving my full communications on iMessage. I know I can remove my account from that iPad but I don't have access to it. How can I stop the device from getting my iMessages without physical access? Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$? How does dark matter halo outside a galaxy help to explain galaxy rotation curve? How does a   outside a galaxy help to explain a ?  Suppose for simplicity we use a model of a star rotating about a more massive star in a fixed circular orbit. For another star at larger radius, the velocity should be smaller but observationally for spiral galaxies, the opposite happens (moves at even more speed or at least at the same speed as the closer star).  People hypothesize that dark matter halo may be present “surrounding” the system (i.e., halo exists outside the system) to account for such observation. I feel that exactly the opposite should be the case that is, dark matter halo should be inside the galaxy rather than outside. Reason being, if dark matter is outside the galaxy then the effective gravitational pull on the rotating star towards the center will be reduced due to outward attraction on the star exerted by dark matter existing outside. Thus, its speed of rotation should be reduced; but we observe the opposite. So how does dark matter halo "surrounding" a galaxy help to explain galaxy rotation curve? Where am I making mistake in argument? Dealing with multiple private DNS servers Generating samples from singular Gaussian distribution Let random vector $x = (x_1,...,x_n)$ follow multivariate normal distribution with mean $m$ and covariance matrix $S$. If $S$ is symmetric and positive definite (which is the usual case) then one can generate random samples from $x$ by first sampling indepently $r_1,...,r_n$ from standard normal and then using formula $m + Lr$, where $L$ is the Cholesky lower factor so that $S=LL^T$ and $r = (r_1,...,r_n)^T$.  What about if one wants samples from singular Gaussian i.e. $S$ is still symmetric but not more positive definite (only positive semi-definite). We can assume also that the variances (diagonal elements of $S$) are strictly positive. Then some elements of $x$ must have linear relationship and the distribution actually lies in lower dimensional space with dimension $&lt;n$, right?  It is obvious that if e.g. $n=2, m = \begin{bmatrix} 0 \\ 0 \end{bmatrix}, S = \begin{bmatrix} 1 &amp; 1 \\ 1 &amp; 1\end{bmatrix}$ then one can generate $x_1 \sim N(0,1)$ and set $x_2=x_1$ since they are fully correlated. However, is there any good methods for generating samples for general case $n&gt;2$? I guess one needs first to be able identify the lower dimensional subspace, then move to that space where one will have valid covariance matrix, then sample from it and finally deduce the values for the linearly dependent variables from this lower-dimensional sample. But what is the best way to that in practice? Can someone point me to books or articles that deal with the topic; I could not find one. Does a correlation matrix of two variables always have the same eigenvectors?