Plotting a list of complex numbers on an argand diagram
Plotting complex numbers as an Argand Diagram
This community wiki explains the current restrictions by the United States of America on the entry of individuals who may pose a risk of transmission of the SARS-Cov2, the virus which causes the Covid-19 disease. Dictionary definitions  often seem to use the terms sentience, awareness, and consciousness as if they are synonymous with each other. Is this really the case? If not, how do they differ? Some books suggest that sentience and awareness are simply facets of the larger concept of consciousness. $ax\equiv b\pmod{\! n}$ has a unique solution if $\gcd(a,n) = 1$ How can I prove that $\,ax\equiv b\pmod{\! n}\,$ has a unique solution if $\,\gcd(a,n) = 1$?  I suspect that the Bezout identity for $\,\gcd(a,b) = 1$ is the key but I don't see how to proceed. My  objective is to classify sensor signals.  The concept of my solution so far is : i) Engineering features from raw signal ii) Selecting relevant features with ReliefF and a clustering approach iii) Apply N.N, Random Forest and SVM  However I am trapped in a dilemma. In ii) and iii), there are hyperparameters like k-Nearest Neigbours for ReliefF or the window length, for which the sensor signal is evaluated, or the number of hidden units in each layer of N.N.  There are 3 Problems I see here : 1) Tuning feature selection parameters will influence the classifier performance 2) Optimizing hyperparameters of classifier will influence the choice of features. 3) Evaluating each possible combination of configuration is intractable.  So my questions are : a) Can I make a simplifying assumption, s.t. tuning feature selection parameters can be decoupled from tuning classifier parameters ? b) Are there any other possible solutions ? Why isn't $V= V_1 + V_2$? $V=V_a - V_c = V_a - V_b + V_b - V_c$, $V_a - V_b= V_1$ and $V_b - V_c = V_2$ Doesn't that prove that $V = V_1 + V_2$? Regardless of $V_3$, If i'm wrong , is there a way to obtain $V$ in terms of $V_1$, $V_2$ and $V_3$ Where do I find the current C or C++ standard documents? For many questions the answer seems to be found in "the standard". However, where do we find that? Preferably online.  Googling can sometimes feel futile, again especially for the C standards, since they are drowned in the flood of discussions on programming forums.  To get this started, since these are the ones I am searching for right now, where are there good online resources for:   C89 C99 C11 C++98 C++03 C++11 C++14 C++17 Remove Actions/Filters added via Anonymous Functions That's a freaking bad practice I must say. Spent last two hours finding a solution to remove actions and filters added via Anonymous functions.    This is the code used on a Parent Theme, and I need to remove it.  /**  * Add custom columns to admin comments grid  *  * Rate that user set.  */ add_filter( 'manage_edit-comments_columns', function( $default ) {     $columns['smr_comment_rate']  = __( 'Rate', 'txtdmn' );      return array_slice( $default, 0, 3, true ) + $columns + array_slice( $default, 2, NULL, true ); });   Got , played with it heavily, but no help. So, is there any other alternative that will remove actions/filters added via anonymous functions?  Thanks There are a lot of legendaries available in ORAS, however a lot of them will only show up/be available if certain prerequisites are met.  I know Groudon/Kyogre are available through the Story, and      Rayquaza &amp; Deoxys   through the postgame Delta episode, but what about the other available legendaries? What do I need to do to catch them? How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)? pgfpages and section I'm making a Beamer presentation. I need to show some notes on a second screen, so I'm using pgfpages.  Whereas, when I put a section, it appears 2 times :/ Here, it's a minimal code with the problem. Have you any idea ?  \documentclass{beamer} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} \usepackage[francais]{babel}  \usepackage{pgfpages} \setbeameroption{show notes on second screen=right}    \begin{document} \begin{frame} \tableofcontents \end{frame}  \begin{frame} \section{test} toto \end{frame}  \end{document}   Thanks ! I need help with this exercise.  I need to prove $$\int_{0}^{1}x^{-x}\ dx=\sum_{n=1}^{\infty}n^{-n}$$  I think I should use some convergence theorem, but I'm stuck.  Thanks a lot! how to get the string-lengths stored in array (C) $2$ out of $3$ property of the unitary group How could the human race be saved in Interstellar? In  (2014) the human race seemed to be facing pretty poor odds until they discovered a convenient wormhole placed by an unknown entity expressed as "they". Later in the movie, we discover that       "they" are actually the human race in the future, reaching back in  time to save itself.   The end of the movie gets a little wild on the physics end, and I'm happy to take that ending as is - no need for it to make sense - but one very basic detail does bother me:  How could the human race have gone back in time to save itself from circumstances that would have caused us to go extinct without our own help (the convenient wormhole)? Atomic Physics: stimulated emission I'm studying a chapter about atomic physics right now but there's thing I just don't seem to understand. When stimulated emission occurs, there's an incoming photon which stimulates the atom to go an energy level lower with the result that a new photon gets emitted.  Can someone explain the reason why the incoming photon stimulates the atom to emit a second one? To me it seemed more logic for the atom to absorb the photon and go an energy level up. There seems to be a phenomenon which I don't know about. Problem:  Ajax suggest-search on [n] ingredients in recipes. That is: match recipes against multiple ingredients.  For instance: SELECT Recipes using "flower", "salt" would produce: "Pizza", "Bread", "Saltwater" and so forth.  Tables:  Ingredients [     IngredientsID INT [PK],     IngredientsName VARCHAR ]  Recipes [     RecipesID INT [PK],     RecipesName VARCHAR ]  IngredientsRecipes [     IngredientsRecipesID INT [PK],     IngredientsID INT,     RecipesID INT ]   Query:  SELECT     Recipes.RecipesID,     Recipes.RecipesName,     Ingredients.IngredientsID,     Ingredients.IngredientsName FROM     IngredientsRecipes      INNER JOIN Ingredients     ON IngredientsRecipes.IngredientsID = Ingredients.IngredientsID      INNER JOIN Recipes     ON IngredientsRecipes.RecipesID = Recipes.RecipesID WHERE     Ingredients.IngredientsName IN ('salt', 'water', 'flower')   I am currently constructing my query using ASP.NET C# because of the dynamic nature of the WHERE clause.  I bites that I have to construct the query in my code-layer instead of using a stored procedure/pure SQL, which in theory should be much faster.  Have you guys got any thoughts on how I would move all of the logic from my code-layer to pure SQL, or at least how I can optimize the performance of what I'm doing?  I am thinking along the lines of temporary tables:  Step one: SELECT IngredientsID FROM Ingredients and INSERT INTO temp-table  Step two: SELECT RecipesName FROM Recipes joined with IngredientsRecipes joined with temp-table.IngredientsID How can I test the quality of a RNG? On electronics.stackexchange we had  about constructing a True Random Number Generator. Since the method relies on noise, which isn't deterministic, the only way to test the quality of the RNG seems to be empirical. Not being a statistician I suggested to test a long bit sequence for normality, but I have no idea what outcome is acceptable and what isn't. For instance counting single bits I guess we have a thumbs-up for a 499500/500500 distribution, but when is the ratio too much skewed to be acceptable? Same for 2-bit and longer sequences. Of course, if testing for normality is a Bad Idea™, I'd like to hear it, including better alternatives.    edit Diehard was mentioned a few times, but I'm not sure this answers my question. The normality test should give a normal distribution, with better bell curve approximations for longer sequences. Diehard seems also to have tests which either should result in normal or exponential distributions. But my question remains: how do I judge the results? Just by looking at the curve and discern a bell curve in it? To get back at my first example, a 499500/500500 distribution is definitely OK, and a 950000/50000 distribution definitely is a no-no, so where does the switch-over happen? Evaluate $\lim_{x \to 0} (x\lfloor\frac{1}{x}\rfloor)$ What are the best JVM settings you have found for running Eclipse? Why aren't variables declared in "try" in scope in "catch" or "finally"? In C# and in Java (and possibly other languages as well), variables declared in a "try" block are not in scope in the corresponding "catch" or "finally" blocks.  For example, the following code does not compile:  try {   String s = "test";   // (more code...) } catch {   Console.Out.WriteLine(s);  //Java fans: think "System.out.println" here instead }   In this code, a compile-time error occurs on the reference to s in the catch block, because s is only in scope in the try block.  (In Java, the compile error is "s cannot be resolved"; in C#, it's "The name 's' does not exist in the current context".)  The general solution to this issue seems to be to instead declare variables just before the try block, instead of within the try block:  String s; try {   s = "test";   // (more code...) } catch {   Console.Out.WriteLine(s);  //Java fans: think "System.out.println" here instead }   However, at least to me, (1) this feels like a clunky solution, and (2) it results in the variables having a larger scope than the programmer intended (the entire remainder of the method, instead of only in the context of the try-catch-finally).  My question is, what were/are the rationale(s) behind this language design decision (in Java, in C#, and/or in any other applicable languages)?