Can the derivative of a $C^1$ function vanish at the infinity imply it has a limit at the infinity?
Limit of derivative is zero. Does it imply a limit for f(x)?
I recently read a lot about neural networks using GRU or LSTM units. There are many easy to use frameworks like tensorflow that do not even require high knowledge about programming. Unfortunately, I never really found good information on how the training of those networks work. Simple backpropagation might probably not work for gated recurrent networks or is just too inefficient for networks with such a high number of variables to learn.  So my question is:  What are the state-of-the-art algorithms used for the initialization and training of neural networks with GRU or LSTM units? I am not looking for frameworks to use, but for initialization and update equations for the internal parameters. When I include a  \usepackage{forest} all colored text title, section headings disappears with IEEE Access journal template How can I tackle this problem? I seem to be having issues when I try and save the output file as a .png, or .jpeg for that matter. I've set up my user preferences, File, Render Output to my desktop as well as render output in the editor window. What am I missing here? I'm obviously very new to this program and your help would be appreciated. Thanks for your time How to extract and install .deb without the command dpkg? I am running Debian jessie stable in order to understand how the .deb package interacts with the system. What is the correct way to extract and install a packge_name.deb without the command dpkg? How would you cut a shape out of an object using another object? Coming from SketchUp one of the tools I miss most is the circle draw tool which lets you draw a circle on any face and then you could extrude it in/out. The only tool that I know of that comes close to this is the knife tool but this would be very impractical to cut out with the knife  Example:    Is there any tool in blender that can match this function? also how could you do this with squares? I'm stuck with the proof of the following:  Suppose that $(s_n)$ converges to $s$, $(t_n)$ converges to $t$, and $s_n \leq t_n \: \forall \: n$. Prove that $s \leq t$.   I've tried starting with $s_n \leq t_n \: \forall : n$ and the definitions of each limit (i.e. $|s_n - s| \leq \epsilon \: \forall \: n &gt; N_1$), but I'm not really getting very far. Any help is appreciated! How to remove white space before reference? Recently, my answers are showing at the bottom of the page, even though I got good scores on those answers.       How do I change this back? Prediction based on bayesian model I have created a bayesian model that estimates 6 parameters using rjags from R. Now i want to do some predictions based on new data in R. Can anyone help me with an example.  model {    B.m[1] &lt;- Kb # mean B[1]    B[1] ~ dnorm( B.m[1], tau_B)    for(t in 2 : 10) { # Process model       B.m[t]&lt;- max( B[t-1] + rB[t-1](1 -B[t-1]/K) - C[t-1] , 0.0)       B[t] ~ dnorm(B.m[t], tau_B) } # Observation mode       for (t in 1: 10) {          LogC_mean[t] &lt;- log( max(qsegB[t]Eff[t], 0.000001))          C[t] ~ dlnorm(LogC_mean[t], tau_c) } # Prior          b~dbeta(1, 1)          cv &lt;- 1          K.mean &lt;- 500000          K.v &lt;- pow(cvK.mean, 2)          K.tau &lt;- 1/K.v          K ~ dnorm(K.mean, K.tau)          r ~ dlnorm(0.0, 1.4)          qseg ~ dlnorm(-15.4, 1.44)          tau_c ~ dgamma(0.001,0.001)          tau_B ~ dgamma(0.01,0.01)        }     } How can I convert my Java program to an .exe file? If I have a Java source file (*.java) or a class file (*.class), how can I convert it to a .exe file?  I also need an installer for my program. In natural language parsing, what is the feature function? I'm working in the area of natural language processing, to be specific I'm reviewing the parsers that take advantage of data-mining techniques.   I've read an introduction to natural language processing, specifically the  by Della Pietra and others. In that paper, the authors explain that features are indicator functions that take into account certain aspects of the text. The problem is that this aspects affect the maximum entropy function.  In the case of parsing, I have problems understanding the concept of features. For parsing one must have:   Two sets, $X$ for the sentences and $Y$ for the parses For each sentence $x \in X$, one must have the N-best list of candidate parses; denoted $GEN(x) \subset Y$. Training samples $(x_j,y_j)$. The $x_j$ are sentences and the $y_j$ are parses. And a feature mapping $\Phi(X,Y)$ that maps each pair (x,y) to a vector of feature values.   The problem of parsing will consist of finding the weight vector such that the following expression is minimized  $$ -\sum log P(y_j|x_j,w) + \lambda ||w||_1 $$  where   $$ P(y_j|x_j,w) = \frac{exp \{w^T \Phi(x_j,y_j)\}   }{ \sum_{u \in GEN(x)} exp\{ w^T\Phi(x_j,u) \}  } $$  My question is, what are the features in this case? Some codified version of the parsing tree? Are the features a statistical concept?  I will also appreciate any bibliography that can be useful in tackling this issue.  UPDATE: I've talked to a professor and he had just told me that the features are obtained after doing a classification algorithm based on the parse-tree. Do you know what kind of classification is done with the parse tree? Meaning: To This Day Pass the output of previous command to next as an argument How does "curved space" explain gravitational attraction? They say that gravity is technically not a real force and that it's caused by objects traveling a straight path through curved space, and that space becomes curved by mass, giving the illusion of a force of gravity.  That makes perfect sense for planetary orbits, but a lot less sense for the expression of gravity that we are the most familiar with in our day-to-day lives: "what goes up must come down."  Imagine that I hold a ball in my hand, several feet off the ground, with my fingers curled around it, and my hand is above the ball.  Then I open my fingers, releasing my grip on it, being very careful to not impart any momentum to the ball from my hand as I do so.  An object at rest remains at rest unless acted upon by an outside force.  If the ball is not moving (relative to my inertial reference frame), it has no path to travel that's any different from the Earth's path through space.  It should remain at rest, hanging there in the air.  And yet it falls, demonstrating that an outside force (gravity) did indeed act upon it.  How does curved space explain this? What are the norms in Ito isometry? Itō isometry from :     Let $W : [0, T] \times \Omega \to \mathbb{R}$ denote the canonical   real-valued Wiener process defined up to time $T &gt; 0$, and let $X :  [0, T] \times \Omega \to \mathbb{R}$ be a stochastic process that is   adapted to the natural filtration $\mathcal{F}_{*}^{W}$ of the Wiener   process. Then $$      \mathbb{E} \left[ \left( \int_{0}^{T} X_{t} \, \mathrm{d} W_{t} \right)^{2} \right] = \mathbb{E} \left[ \int_{0}^{T} X_{t}^{2} \,  \mathrm{d} t \right], $$ where $\mathbb{E}$ denotes expectation with   respect to  $\gamma$. In other words, the Itō   stochastic integral, as a function, is an isometry of normed vector   spaces with respect to the norms induced by the inner products $$      ( X, Y )_{L^{2} (W)} := \mathbb{E} \left( \int_{0}^{T} X_{t} \, \mathrm{d} W_{t} \int_{0}^{T} Y_{t} \, \mathrm{d} W_{t} \right) =  \int_{\Omega} \left( \int_{0}^{T} X_{t} \, \mathrm{d} W_{t}  \int_{0}^{T} Y_{t} \, \mathrm{d} W_{t} \right) \, \mathrm{d} \gamma  (\omega) $$ and $$      ( A, B )_{L^{2} (\Omega)} := \mathbb{E} ( A B ) = \int_{\Omega} A(\omega) B(\omega) \, \mathrm{d} \gamma (\omega). $$   I was wondering what the two normed spaces are and what their norms are, so that the two normed spaces are isometric wrt their norms?  Thanks and regards! Can a wizard choose where to place their soul piece when creating a horcrux? Batch renaming files with pattern I have some files named like these:  63018933.mp4?token=1325697436_b0c3e70c6e339380b4a484c576a8c287  63808488.mp4?token=1325697401_4ae5f7a68d93873c8881b303e7655e14  How do I rename all them to, for example 63018933.mp4(remove characters after mp4)? I know that $S_n$ is generated by a number of things, like all transpositions, all transpositions of the form $(1\,a)$, the transpositions $(1\,2),(2\,3),\dots,(n-1\, n)$, and  just the two elements $(123\dots n),(1\,2)$.      Suppose $n$ is prime. If you just have $(123\dots n)$ and some arbitrary transposition $(a\, b)$, how does this also generate $S_n$?    Can you somehow get to $(1\,2)$ or reduce it to some other previous case? Moving SQL Server to different domain Let $A$ be a $m \times n$ matrix with entries from some field $F$. Define the determinant rank of $A$ to be the largest possible size of a nonzero minor, i.e. the size of the largest invertible square submatrix of $A$. It is true that the determinant rank is equal to the rank of a matrix, which we define to be the dimension of the row/column space.  It's not difficult to see that $\text{rank} \geq \text{determinant rank}$. If some submatrix of $A$ is invertible, then its columns/rows are linearly indepedent, which implies that the corresponding rows/columns of $A$ are also linearly indepedent.  Is there a nice proof for the converse?