If I were to keep increasing the mass of particles I throw at a double slit, at what point would it stop creating an interference pattern?
How to prove wave nature of large object?
(Built-in) way in JavaScript to check if a string is a valid number I'm hoping there's something in the same conceptual space as the old VB6 IsNumeric() function? Jutifying: irrational + rational = irrational Group of even order contains an element of order 2 I am working on the following problem from group theory:     If $G$ is a group of order $2n$, show that the number of elements of $G$ of order $2$ is odd.   That is, for some integer $k$, there are $2k+1$ elements $a$ such that $a \in G,\;\; a*a = e$, where $e$ is the identity element of $G$. How to access the grub boot menu in order to generate bootchart? I am running Ubuntu Gnome 15.04, and I want to generate a bootchart to help me diagnose some system problems. However in  it says:    So how do I access the grub boot menu in order to append this text? And just to be clear, how should the line look once I have appended the necessary text? Also, is grub already installed for I don't appear to have either or these packages: grub or grub2?    OS Information:  No LSB modules are available. Distributor ID: Ubuntu Description:    Ubuntu 15.04 Release:    15.04 Codename:   vivid Mis-aligned shapefiles in QGIS? Why did sampling boost the performance of my model? I have an imbalanced dataset with 88 positive samples and 128575 negative samples. I was reluctant to over/undersample the data since it's a biological dataset and I didn't want to introduce synthetic data. I built a Random Forest Classifier with this original dataset. I got an F1 score of 0 for the positive class. Zero precision. Zero recall. I cross-checked the predictions and test data. The model predicts some positives none of which are actually positive. Worst performance.  So, I tried to oversample the positive class. I upsampled the positives to 1000 samples. To my surprise, the F1 score for this dataset was 0.97, for the positive class. Then I tried lesser samples. I was able to achieve an F1 score of 0.83 with 200 positive samples, which is just 2.25 times of the original positive samples.  I would like to know why this occurs. For 88 samples, F1 score is 0.00 (rounded off to two digits). For 200 samples it's 0.83. There is no data leakage. All the features are engineered. I used imbalanced-learn module for oversampling. Can someone explain why is this difference in performance? In this movie there are scientists who (spoilers ahead)       ...are creating a simulation. One scientist starts seeing odd looking characters but no one else sees them. He asks around and more and more characters are missing or don't know about the characters in the story he knows about.  He finds out that he is part of a simulation. He finds out that the characters only he remembers have been deleted. He also finds out that there are characters from his own simulation that have broken free of his simulation and are in his world.    Hints: I remember this being an older film (70's?); it might have been foreign film possibly with subtitles (not Hollywood); it might have been part of the Criterion collection; I'm pretty sure I streamed it from Hulu. Sorry, I can't remember more details. Multiple one to many relationships in series I am making a DB for storing reports that have following fields:  Ad_system, Ad_Campaing, Ad_Group, Keyword, Date, Impressions, Clicks, Conversions   Logic is that, Ad_system can have multiple Ad_Campaings, Ad_Campaing can have multiple Ad_Groups and Ad_Groups can have multiple Keywords, and for every Keyword there is a report. Should It be like this? Because it kind of makes sense to me, but it doesn't look correct. Primary key can also be:  ad.system.name for first table  ad.system.name ad.campaing.name for second table  ad.system.name ad.campaing.name ad.group.name for third table  ad.system.name ad.campaing.name ad.group.name keyword for fourth table  They will always be unique, but then Report will always have all DB columns in it, so it's kind of redundant.  Is the approach that I have in the diagram below correct? Or is a better one what I just described? If I am not mistaken both should satisfy 3rd NF. If $G$ is a compact topological group, how to show that a finite index subgroup of $G$ is open ? I really don't know where/how to start...  PS : I precise that by "compact" I mean that it is hausdorff and that any recovering of $G$ by open sets has a finite sub-recovering (sorry if I wasn't unclear) Application of Kirchhoff's laws in circuits with inductors As we know, the  are applicable for conservative electric fields. Now it is applicable for circuits where inductors are present but the field there is not .  So how are the  Kirchhoff's laws  applicable there? What happens if you are refused entry between two countries? Last month, I was travelling on a backpacking trip across Russia and the Baltic states (Schengen zone). I'm an Indian by nationality. So I had to get the respective single entry visa for Russia and Schengen Europe.  At the border crossing into Estonia by road (at Ivangorod-Narva), I exited the Russian border with an exit stamp (so now I can't go back to Russia since I had a single entry visa). When I was at the immigration checkpoint of Estonia, I was heavily questioned on the intent of my travel to Europe while entering Estonia by road.   Though I finally got into Europe, It got me wondering - what happens if a foreign national is denied entry into a country not at the airport but by land between 2 countries he cannot go into ?  Generally, if you are denied entry at the airport the airline has the obligation to fly you back to your country. But what happens when you are stuck between two countries and you cant get into either ? What happens to you then ? How to expand primary partition when WUBI is used to install? I have installed Ubunut 12.04 using WUBI. The "Installation size" options I chosen was 18GB i.e the amount of space you want to "give up" for WUBI. That is the space wubi's Ubuntu install is able to use. Wubi creates a disk image (loopmounted device) on your host system in/on which Ubuntu is installed. Now, I am running out of memory in primary partition.   Could anyone help me out to extend/stretch the partition size? How can light be called electromagnetic if it doesn't appear to be electric nor magnetic?  If I go out to the sunlight, magnets aren't affected (or don't seem to be).  And there is no transfer of electric charge/electrons (as there is in AC/DC current in space).   In particular, the  (which light is supposed to be composed of) have no electric charge (nor do they have ).   I'm looking for an explanation that can be appreciated by the average non-physicist Joe. What does Minecraft's scary music mean? Apparently it means there is a dungeon around but I can never find any?  If it does mean dungeons how far away will it trigger? Can I transfer trophies and data to a new account? Okay I have created a sub account on my ps3 as a new user. I wanted to change my psn online id. So I have copied all game data from the old account to my new account, but when I go to play the game it still says the trophies and data belong to the old account. I don't want to delete the old one and lose all my saved games and trophies, is there a way to either unlock and allow my new user to own the data and trophies or transfer the trophies and data so that my new account may own it? Why does the multi-paragraph quotation rule exist? It was suggested to me recently that Annihilator sacrifices (such as 's) are only chosen during resolution, rather than while they're going on the stack.  Do I choose those sacrifices during resolution? What part of the comprehensive rules backs that up?  I can't find any clarity on the internet, in the rules, on the MTG Salvation wiki for Annihilator, or in the ability's rulings. It seems reasonable, but I'd like to know what's behind it. Plus, if I can choose and then later  some stuff, all the better. Incompatibility between TikZ and babel In my preamble, you'll find:  \renewcommand{\baselinestretch}{1} \renewcommand{\familydefault}{\sfdefault} \usepackage[sfmath]{kpfonts} \usepackage[mathrmOrig]{sfmath} \usepackage{amsmath} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{animate} \usepackage{anysize} \usepackage{arcs} \usepackage{array} \usepackage[scale=0]{background} \usepackage{blindtext} \usepackage{calc} \usepackage{cancel} \usepackage{chngcntr} \usepackage{CJK} \usepackage{CJKspace} \usepackage{CJKpunct} \usepackage{colortbl} \usepackage{enumitem} \usepackage{epstopdf} \usepackage{etoolbox} \usepackage{fancybox} \usepackage{fancyhdr} \usepackage{float} \usepackage{framed} \usepackage{graphicx} \usepackage{hyphenat} \usepackage{ifthen} \usepackage{latexsym} \usepackage{lmodern} \usepackage{multicol} \usepackage{multirow} \usepackage{mwe} \usepackage{pgffor} \usepackage{rotating} \usepackage{tabularx} \usepackage{textcomp} \usepackage{tgheros,tgtermes,tgcursor} \usepackage{tikz} \usepackage{times} \usepackage{tipa} \usepackage{varwidth} \usepackage{wasysym} \usepackage{wboiboites} \usepackage[abs]{overpic} \usepackage[breaklinks,colorlinks=true,linkcolor=red,citecolor=red, urlcolor=blue]{hyperref} \usepackage[framemethod=TikZ]{mdframed} \usepackage[breakable, theorems, skins]{tcolorbox,empheq} \usepackage[default]{gillius} \usepackage[document]{ragged2e} \usepackage[latin1]{inputenc} \usepackage[spanish]{babel} \usepackage[T1]{fontenc} \usepackage[total={18.59cm,26.5cm},left=1.5cm,top=2.5cm]{geometry} \usetikzlibrary{matrix,arrows, positioning,shadows,shadings,backgrounds,calc, shapes, tikzmark} \usetikzlibrary{shadows.blur} \usetikzlibrary{shapes.symbols} \usetikzlibrary{patterns,fadings} \tcbuselibrary{skins,breakable,listings,theorems}    I'm trying to draw an arrow for X axis and Y axis.   \begin{tikzpicture} \draw[yellow!10, fill=blue!5](-1, -1) rectangle (7, 5); \draw[dotted] (-0.75,-0.75) grid (6.75,4.75); \node[below] at (-0.25,0){$O$}; \draw[-&gt;,black, thick] (-0.75,0)--(6.75,0); \end{tikzpicture}   But I get this error:    Additionally, if I remove -> from the options of \draw the tikz picture compiles normally. I'm trying to install  on my Ubuntu box (11.04). The website has a Ubuntu .deb available for download (for 10.10 and 10.04 so I chose 10.10).   However,   sudo dpkg -i mysql-workbench-gpl-5.2.34-1ubu1010-amd64.deb   yields:  (Reading database ... 194069 files and directories currently installed.) Preparing to replace mysql-workbench-gpl 5.2.34-1ubu1010 (using mysql-workbench-gpl-5.2.34-1ubu1010-amd64.deb) ... Unpacking replacement mysql-workbench-gpl ... dpkg: dependency problems prevent configuration of mysql-workbench-gpl:  mysql-workbench-gpl depends on libctemplate0; however:   Package libctemplate0 is not installed.  mysql-workbench-gpl depends on libpython2.6 (&gt;= 2.6); however:   Package libpython2.6 is not installed.  mysql-workbench-gpl depends on libzip1 (&gt;= 0.8); however:   Package libzip1 is not installed.  mysql-workbench-gpl depends on python-paramiko; however:   Package python-paramiko is not installed.  mysql-workbench-gpl depends on python-pysqlite2; however:   Package python-pysqlite2 is not installed. dpkg: error processing mysql-workbench-gpl (--install):  dependency problems - leaving unconfigured Processing triggers for bamfdaemon ... Rebuilding /usr/share/applications/bamf.index... Processing triggers for desktop-file-utils ... Processing triggers for python-gmenu ... Rebuilding /usr/share/applications/desktop.en_US.utf8.cache... Processing triggers for python-support ... Errors were encountered while processing:  mysql-workbench-gpl   My question is, is there a way to tell dpkg to automatically fetch missing dependencies, or do I need to manually apt-get install missing packages like libctemplate0 and  libpython2.6?   (Or alternatively, is there some other way to get MySQL Workbench easily up &amp; running?) Redirect parent window from an iframe action What JavaScript do I need to use to redirect a parent window from an iframe?  I want them to click a hyperlink which, using JavaScript or any other method, would redirect the parent window to a new URL.