Did Palpatine have the very same powers as Darth Plagueis?
Did Sidious know the secret of cheating death?
It would be helpful if we could see the number of upvotes cast for our comments, or other people's comments in response to us directly in the user profile in either the activity tab or the response tab respectively. It should be quite easy to implement (e.g. sharing a single partial view for displaying comments).  It could be useful, since we can evaluate the legitimacy of the comment and address horrible mistakes sooner. Are security.ubuntu.com updates eventually merged into normal updates? Upon my observation, seems new packages will first appear in security.ubuntu.com, but if you upgrade later, they will appear in XX.archive.ubuntu.com (depends on your config),  Was that true ? I want to determine whether a multi-line string ends with a line containing specified pattern.  These code failed, it doesn't match.  s=`echo hello &amp;&amp; echo world &amp;&amp; echo OK` [[ "$s" =~ 'OK$' ]] &amp;&amp; echo match Summation of series $\sum_{n=1}^\infty \frac{n^a}{b^n}$? Can I choose to delay my turn in combat? Capitalize fields of study? Iridescence In Cycles? Is it possible to create an  shader in Cycles? Specifically for something like , , , etc.. So I know the basic gist is that fusion power's main issue is sustaining the fusion. I also know that there are two methods. The Torus method and the laser method. The torus magnetically contains plasma and heats it with radiation and accelerates the plasma around to make strong enough collisions that protons fuse. The laser method uses 192 lasers and focuses it on tiny frozen hydrogen pellets and aims to initiate fusion each time pellets are dropped.  The though struck me when we could sorta combine the two designs together. The torus doesn't have to worry about making fusion happen at a specific location but it has issues in that the plasma is unevenly heated and leaks. On the other hand, the laser design is extremely complicated in the level of precision needed and would have to repeat this for every pellet. This lead me to think to make something precise and contained at the same time.  I see that particle colliders are able to direct two beams of protons and have them collide at a specific spot with a very precise energy. Couldn't we tune the energy of the two beams of protons to the energy required for them to fuse? We have the ability to smash them into bits, surely we have the ability to have them fuse. (I'm thinking about the type of collider that circles two beams in opposite directions)  It would be at much lower energies than normal colliders and would be very precise and it would be possible to fuse at a specific location that has greater leeway because for protons that missed collision, they'd just circle around again! Thus protons would efficiently be used and very little would be wasted. There wouldn't be problems of plasma leakage because we are focusing them in a thin tight beam.   It seems that this idea has girth, or I feel this way at least, can someone back me up by offering some calculations on how to calculate the efficiency? How would I go about calculating the two circling beams of protons and at what specific velocity would be needed? etc. What exactly does Perl's "bless" do? I understand one uses the "bless" keyword in Perl inside a class's "new" method:  sub new {     my $self = bless { };     return $self; }       But what exactly is "bless" doing to that hash reference ? How to start a background process in Python? Markdown source:  `http://google.com`  - `http://google.com`     - `http://google.com`   Rendered result:  http://google.com   http://google.com   http://google.com    Note that the third code span is a link. Adding a newline before the list item makes the link disappear. Area 51 reputation changes do not show up in the new Top Bar Contraction mapping in the context of $f(x_n)=x_{n+1}$. I'm interested in convergence of $f(x_n)=x_{n+1}$ and often hear this term referenced.  What does it mean to be a contraction mapping in the context of the sequence of real numbers given by $f(x_n)=x_{n+1}$? And what does it tell us about such sequence?  A search online gives the answer given by Wikipedia, that it is a function $f$ defined on a metric space $(M,d)$ from $M$ to itself with the property that for some real number $k \in [0,1)$,  $$d(f(x),f(y)) \leq k d(x,y)$$  This definition is quite unhelpful because I barely know what a metric space is. I feel like this definition is to generalized, and I'm interested in in the specific case of recursively defined real sequences $f(x_n)=x_{n+1}$ that there should be a more specific answer to my question. Apt-get 403 Forbidden, but accessible in the browser How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$ ? zsh I/O redirection: redirecting and then piping; what is going on? Validity of maximising log-likelihood for maximum likelihood estimation For reasons owing to mathematical convenience, when finding MLEs (maximum likelihood estimates), it is often the log-likelihood function---as opposed to the standard likelihood function---which is maximised.  From what I've gathered, this approach is deemed valid as a result of the monotonically increasing nature of the (natural) logarithm function.  My understanding of a monotonically increasing function is: for all $x$ and $y$ (defined on a subset of the reals), if $x \leq y$ then $f(x) \leq f(y)$.  This, however, does not appear to be the case for all log-likelihood functions; for example: for the log-likelihood $\text{Gamma}(3, 5)$ function, if $x = 0.15$ and $y = 0.46$, then $f(x) = -0.59$ and $f(y) = -1.19$.  Clearly, I've misunderstood this concept. Fundamentally, I guess I'm asking can somebody (preferably mathematically) demonstrate why:  $$ \hat{\theta} = \text{argmax} \text{ } L(\theta) = \text{argmax} \text{ } \text{log} \text{ } L(\theta) $$  where $\hat{\theta}$ is the MLE for a given likelihood function. I am running logistic regression on a small dataset which looks like this:    After implementing gradient descent and the cost function, I am getting a 100% accuracy in the prediction stage, However I want to be sure that everything is in order so I am trying to plot the decision boundary line which separates the two datasets.  Below I present plots showing the cost function and theta parameters. As can be seen, currently I am printing the decision boundary line incorrectly.    Extracting data  clear all; close all; clc;  alpha = 0.01; num_iters = 1000;  %% Plotting data x1 = linspace(0,3,50); mqtrue = 5; cqtrue = 30; dat1 = mqtrue*x1+5*randn(1,50);  x2 = linspace(7,10,50); dat2 = mqtrue*x2 + (cqtrue + 5*randn(1,50));  x = [x1 x2]'; % X  subplot(2,2,1); dat = [dat1 dat2]'; % Y  scatter(x1, dat1); hold on; scatter(x2, dat2, '*'); hold on; classdata = (dat&gt;40);   Computing Cost, Gradient and plotting  %  Setup the data matrix appropriately, and add ones for the intercept term [m, n] = size(x);  % Add intercept term to x and X_test x = [ones(m, 1) x];  % Initialize fitting parameters theta = zeros(n + 1, 1); %initial_theta = [0.2; 0.2];  J_history = zeros(num_iters, 1);   plot_x = [min(x(:,2))-2,  max(x(:,2))+2]  for iter = 1:num_iters  % Compute and display initial cost and gradient     [cost, grad] = logistic_costFunction(theta, x, classdata);     theta = theta - alpha * grad;     J_history(iter) = cost;      fprintf('Iteration #%d - Cost = %d... \r\n',iter, cost);       subplot(2,2,2);     hold on; grid on;     plot(iter, J_history(iter), '.r');  title(sprintf('Plot of cost against number of iterations. Cost is %g',J_history(iter)));     xlabel('Iterations')     ylabel('MSE')     drawnow      subplot(2,2,3);     grid on;     plot3(theta(1), theta(2), J_history(iter),'o')     title(sprintf('Tita0 = %g, Tita1=%g', theta(1), theta(2)))     xlabel('Tita0')     ylabel('Tita1')     zlabel('Cost')     hold on;     drawnow      subplot(2,2,1);     grid on;         % Calculate the decision boundary line     plot_y = theta(2).*plot_x + theta(1);  % &lt;--- Boundary line      % Plot, and adjust axes for better viewing     plot(plot_x, plot_y)     hold on;     drawnow  end  fprintf('Cost at initial theta (zeros): %f\n', cost); fprintf('Gradient at initial theta (zeros): \n'); fprintf(' %f \n', grad);   The above code is implementing gradient descent correctly (I think) but I am still unable to show the boundary line plot. Any suggestions would be appreciated.    logistic_costFunction.m  function [J, grad] = logistic_costFunction(theta, X, y)      % Initialize some useful values     m = length(y); % number of training examples      grad = zeros(size(theta));      h = sigmoid(X * theta);     J = -(1 / m) * sum( (y .* log(h)) + ((1 - y) .* log(1 - h)) );      for i = 1 : size(theta, 1)         grad(i) = (1 / m) * sum( (h - y) .* X(:, i) );     end  end   EDIT:  As per the below answer by @Esmailian, now I have something like this:  [m, n] = size(x);  x1_class = [ones(m, 1) x1' dat1']; x2_class = [ones(m, 1) x2' dat2'];  x = [x1_class ; x2_class] What are the differences between a multidimensional array and an array of arrays in C#? What is the difference between OpenOffice and the newly created LibreOffice? What is the difference between OpenOffice and LibreOffice? I understand that LibreOffice is another fork that is going to be developed. I have used OpenOffice since v1 and am wondering if there is a definite advantage to uninstalling and trying LibreOffice.