I'm trying to use a framework implemented in python to use GA (Genetic algorithms) and other related algorithms . But I'm not sure about what framework to use, I've found two interesting options Pymoo and JmetalPy, the former it seems well documented it and the latter isn't looks like it (it's under construction), but the version in Java is very popular and well know. I need choose a framework to make a comparation with an algorithm made by me. For this reason a reliable framework is needed and with small learning curve. Do you have any good or  bad experience using it?, Do you know another framework? Pymoo:   JmetalPy:
I need to use a metaheuristic algorithm to solve an optimization problem on a Python codebase.  Metaheuristics usually need to be written in C++ or Java as they involve a lot of iterations, while Python is weak from this point of view.  Questions:   do any Python metaheuristic packages which wrap faster languages as C++/Java exist? do any Python metaheuristic packages based on maybe cython on numba exist? other solutions?
$\max(\{n: n+5 | n^5 + 5\})$ What is the maximum value of $n$ if $n + 5$ divides $n^5 + 5$, $n$ being a natural number? I tried to solve by binomial theorem but it failed. Can someone please verify my proof?     Is the collection $\tau_\infty = \{U:X-U$ is infinite or empty or all of $X\}$ a topology on $X$?   No. Let $X = \mathbb{R}$.  Clearly, $\{x\} \in \tau_\infty$ for all $x \in X$.  Set $\displaystyle{B = \cup_{x \neq 0} \{x\}}$. Clearly, $X - B = \{0\}$, but $\{0\} \notin \tau_\infty$. Since $\tau_\infty$ is not closed under arbitrary unions, it does not define a topology on $X$. How to determine if .NET code is running in an ASP.NET process? I have an instance of a general purpose class that will be executed both under ASP.NET and a stand alone program. This code is sensative to the process where it is being run - that is, there are certin methods that should not called if running under ASP.NET. How do you determine if the code is executing in an ASP.NET process?  The solution I am currently using is answered below.    I wish someone would add a comment as to why this question has gotten downvoted and/or propose a better way to ask it! I can only assume at least some folks have looked at the question and said "what an idiot, ASP.NET code is .NET code". Compound possessives and yours Scroll to bottom of div? I am creating a chat using Ajax requests and I'm trying to get messages div to scroll to the bottom without much luck. I am wrapping everything in this div: #scroll {     height:400px;     overflow:scroll; }  Is there a way to keep it scrolled to the bottom by default using JS? Is there a way to keep it scrolled to the bottom after an ajax request? Goal: I have a function $f(x,y)=z$ (two variables for illustration only) which I know almost nothing about--it has a compact domain which I can determine, it is non-negative, and bounded above.  My goal is to find the maximum value $f(x,y)$ takes on its domain.  I can query the function and I know the values at a few points: $f(x_1, y_1)=z_1, f(x_2, y_2)=z_2,..., f(x_n, y_n)=z_n$.  Optimization via Linear Regression:  I have used linear regression (and related methods like the lasso) to model functions like this in the past; this is the method that I am very comfortable with.  Typically, I might try to find a polynomial (of degree $k$) which relatively accurately models the data. The end result would be to say that:   $$f(x,y)\approx \beta_1 + \beta_2 x + \beta_3 y + \beta_4 x^2 + \beta_5 xy + \beta_6 y^2 + ... + \beta_{m}y^{k}.$$  Determining the coefficients is done by solving the .  The "best degree" for the polynomial might be determined using $k$-fold cross validation.  Once the "best" polynomial has been determined, one can choose any of a number of methods to optimize it (Newton's method, gradient descent, hill climbing, etc).  Then, if all goes well, the optimal value on the polynomial corresponds to an optimal value of $f(x,y)$.  Bayesian Optimization:  Recently, I was describing this technique (linear regression) to a colleague who asked: "What is the difference between that and Bayesian Optimization?"  I've been attempting to answer this question for the last couple days, and so far I don't have anything really conclusive.  After reading , trying to read  and getting stuck reading  I think I understand the following about BO:   Start with a prior (a guess as to what family of functions the black box belongs to... or at least some family of functions which you believe might be able to describe $f$ well).  It looks using a  as a prior is popular. Specify whatever is needed to build your prior (for GP this is a covariance function). As you go along, you maintain two evolving functions, a "mean" function $m(x,y)$ and a "confidence interval" function $c(x,y)$.  Basically, you can predict the value at any point by evaluating $m(x,y)$ and you are confident that $f(x,y)\in [m(x,y)-c(x,y), m(x,y)+c(x,y)]$. Bayesian optimization provides a systematic way of updating/exploiting the model by alternatively selecting points where the confidence interval is wide (you are very uncertain about the value) or at optimal points on the model $m(x,y)$.   My Question: Is it fair/correct to say that the major difference between Bayesian Optimization and simply optimizing the linear regression model is that Bayesian Optimization provides the systematic way of sampling with the goal of optimizing the model and reducing uncertainty whereas the linear regression model ignores the idea of uncertainty and doesn't explicitly provide a means of updating the model?  Said another way, is the linear regression model an example of what might be a "mean" function $m(x,y)$ in Bayesian Optimization?  If I stick with linear regression, specify how to compute the uncertainty, and provide a means of updating/improving the model (exploit/explore) am I just doing Bayesian Optimization (without calling it that)?  Background: My background is in pure mathematics (graph theory) but my new job has me working with a lot of data (so I'm self learning statistics).  With that in mind, my statistics vocabulary is somewhat limited (so I appreciate answers that either avoid technical terminology or briefly explain any technical terminology used)--for example, Monday was the first time I heard/read the word "prior" used in a stats sense and I'm still not 100% sure I understand that correctly. How do I prove that in every commuting family there is a common eigenvector? The proof given by my textbook is highly non-satisfying. The author adopted some magic-like "reductio ad absurdum" and the proof (although is correct) didn't reveal the nature of this problem. I made my own effort into it and tried a different approach. Yet I can't finish it.  Let $\mathscr{F}$ be a commuting family in $M_n(\mathbb{C}^n)$, and $A\in\mathscr{F}$, then $A$ has $n$ eigenvalues. We pick one, say $\lambda$. Let $x$ be one of its eigenvector.  We can easily prove that, if $A$ has no other eigenvector with eigenvalue $\lambda$ that linearly independent with $x$, which means that $\{cx|c\in\mathbb{C}\}$ are the only vectors satisfying $Ax=\lambda x$, then $x$ is a common eigenvector. Because $\forall B\in\mathscr{F}$ and $\forall y\in \{cx|c\in\mathbb{C}\}$, $$A(Bx)=ABx=BAx=B(Ax)=B(\lambda x)=\lambda (Bx)$$, so that $Bx$ has to be in $\{cx|c\in\mathbb{C}\}$, that is, $Bx=c_0x$ for some $c_0\in\mathbb{C}$, which means $x$ is a eigenvector of $B$ too.  But what if there are vectors satisfying $Ax=\lambda x$ that's not in  $\{cx|c\in\mathbb{C}\}$? Well, then we should have a set of linearly independent eigenvectors $\{x_1,x_2,...,x_k\}$, that $\{c_1x_1+c_2x_2+...+c_kx_k|c_i\in\mathbb{C}\}$ are the only vectors satisfying $Ax=\lambda x$.  Now, I have a reasonable hypothesis that there exists some $x=c_1x_1+c_2x_2+...+c_kx_k$, that can be proven to be a common eigenvector of $\mathscr{F}$. I've tried some approaches to prove it but all failed.  Do you guys believe it's true? And if it is true then how do I prove it? When using QuickLook to quickly look through multiple images (pressing space and then using the arrow keys to navigate), some images will not get displayed by QuickLook when hitting them up a second time (going back for example).   A GIF does a much better job than me showcasing the issue. So here's me previewing a few random images:    I have tried deleting   ~/Library/Preferences/com.apple.QuickLookDaemon.plist ~/Library/Caches/com.apple.QuickLookDaemon/Cache.db ~/Library/Caches/com.apple.QuickLookDaemon32/Cache.db ~/Library/Containers/com.apple.quicklook.ui.helper  and restarting, unfortunately to no avail.  Repairing permissions and restarting the Finder in 32-bit mode, as suggested  by others, don't appear to have any effect on this issue either.  This happens with all kinds of images, no matter their source or format. PHP Session data not being saved I have one of those "I swear I didn't touch the server" situations. I honestly didn't touch any of the php scripts. The problem I am having is that php data is not being saved across different pages or page refreshes. I know a new session is being created correctly because I can set a session variable (e.g. $_SESSION['foo'] = "foo" and print it back out on the same page just fine. But when I try to use that same variable on another page it is not set! Is there any php functions or information I can use on my hosts server to see what is going on?  Here is an example script that does not work on my hosts' server as of right now:  &lt;?php session_start(); if(isset($_SESSION['views']))     $_SESSION['views'] = $_SESSION['views']+ 1; else     $_SESSION['views'] = 1;  echo "views = ". $_SESSION['views']; echo '&lt;p&gt;&lt;a href="page1.php"&gt;Refresh&lt;/a&gt;&lt;/p&gt;'; ?&gt;   The 'views' variable never gets incremented after doing a page refresh. I'm thinking this is a  problem on their side, but I wanted to make sure I'm not a complete idiot first.  Here is the phpinfo() for my hosts' server (PHP Version 4.4.7): Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$ Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$.   My try:  Let $\mathbb Z^n\cong \mathbb Z^m $. To show that $m=n$.  Case 1: Let $m&gt;n$. Now that $\mathbb Z^m$ has $m$ generators whereas $\mathbb Z^n$ has $n$  generators and an isomorphism takes a generator to generator ; that is the contradiction.  Please correct me if I am wrong.  The case  $m&lt;n$ also follows similarly. If I use the starting wealth rolls of my class, do I keep any remaining money left over? If I use the starting wealth rolls of my class, do I keep any remaining money left over after I buy equipment?  In D&amp;D 5e you can roll the 4d4 &times; 10 to determine starting gold, forgoing any equipment your class and background  gets.  This is not up for question.  What is up for question is whether or not the PC keeps any remaining gold that they don't spend on equipment.   As far as I have been able to tell, this is not explicitly stated in the PHB nor in the Basic Rules documents. Get the coordinates from ContourPlot and RegionPlot I’ve had a good look and can’t seem to find out how to select all elements matching certain classes in one jQuery selector statement such as this:  $('.myClass', '.myOtherClass').removeClass('theclass');   Any ideas on how to achieve this? The only other option is to do  $('.myClass').removeClass('theclass'); $('.myOtherClass').removeClass('theclass');   But I’m doing this with quite a few classes, so it requires much code. How to print file content only if the first line matches a certain pattern? Sunlight Sensitivity looks pretty bad — Disadvantage to attack rolls and Perception checks whenever you, your target, or what you're trying to perceive are in direct sunlight. I hope I'm missing something, since no other PC race has a comparable hindrance.  Are there any ways you have used to mitigate this flaw to make players of this race not at a severe disadvantage (or, if it doesn't need mitigation, explain why it's already balanced without any action required)? Split List into Sublists with LINQ Is there any way I can separate a List&lt;SomeObject&gt; into several separate lists of SomeObject, using the item index as the delimiter of each split?  Let me exemplify:  I have a List&lt;SomeObject&gt; and I need a List&lt;List&lt;SomeObject&gt;&gt; or List&lt;SomeObject&gt;[], so that each of these resulting lists will contain a group of 3 items of the original list (sequentially).  eg.:   Original List: [a, g, e, w, p, s, q, f, x, y, i, m, c] Resulting lists: [a, g, e], [w, p, s], [q, f, x], [y, i, m], [c]   I'd also need the resulting lists size to be a parameter of this function. I am really confused.  Which preposition is correct?     She is in/at the park.   They are in/at the park.   I am in/at the park.   Should I use in or at in these sentences? Tikz won't plot the function properly I tried to plot the following function but it didn't work:  y = 300 + 1000/x + 2.5x.  This is the document, but instead of the plot it only shows the axis.  \documentclass{article}  \usepackage{pgfplots}% This uses tikz \pgfplotsset{compat=newest}% use newest version  \pgfmathdeclarefunction{Function}{1}{%   \pgfmathparse{300 + 1000/x + 2.5}% }  \tikzset{My Line Style/.style={smooth, thick, samples=400}}  \begin{document} \begin{tikzpicture} \begin{axis}[     xmin=0.0,     xmax=250,     ymin=0,     ymax=50,     axis x line=bottom,     axis y line=left,      xlabel= $y$,     ylabel=Cost,      xtick={250},     xticklabels={250},         restrict x to domain=0:250,     ]        \addplot+[My Line Style, color=black, samples at={1,2,3,4,...,249,250}] (\x,{Function(\x)});   \end{axis}  \end{tikzpicture} \end{document} \documentclass{article} How is canonicity of derivative works determined for Star Wars? For all types of derivative works, namely:   Movies Novels Comic books Other written works (including RPG materials) Cartoons Video games Derivative movies (such as the infamous Ewok movies and even more infamous )   According to what rules does something become "canon" and who is responsible for the evaluation of a published work? How to prove that if $\forall x \in (a,b)$ Lebesgue integral $\int_{(a,x)}fd\lambda=0$, then $f(x)=0$ $\lambda$-almost everywhere? Let $f:(a,b)\rightarrow\mathbb{R}$.  The statement to prove is that if $\forall x \in (a,b)$ Lebesgue integral $\int_{(a,x)}fd\lambda=0$, then $f(x)=0$ $\lambda$-almost everywhere.  So if it wouldn't be true then we would have $\forall x \in (a,b):\int_{(a,x)}f_+d\lambda=\int_{(a,x)}f_-d\lambda\neq0$, so every interval contains positive and negative values of the function. It is  such an $f$ so my guess would be that this function is not Lebesgue measurable and we can't take this integral.  Thanks in advance!