Is there a gravitational force between antiparticles? For example,  between two antiprotons. Do the antiprotons repluse each other?
I know that the gravitational interaction of antimatter is expected to be the same as normal matter.  But my question is, has it ever been experimentally validated?  I think it would not be a trivial experiment, because electromagnetic effects have to be eliminated, so neutral particles would be needed. Maybe diamagnetically trapped antihidrogen atoms could be examined as to which direction they fall?
To consume REST services there is a lot of boilerplate code needed:   Build Apex Objects to model the responses Code to deserialize REST responses to those classes Handling of HTTP requests, responses and errors ...   Did anyone come up with patterns or best practices codified into an open source library or framework that one could just reuse in a similar project without reinventing the callout-wheel over an over again?  Like the zillions of trigger-frameworks that exist as repos on Github... Usage of "as if" as interjection My question concerns the usage of "as if" as an idiomatic interjection. The references I have consulted (etymonline, online dictionaries, etc.) seem to agree that "as if" is used in this context to convey incredulity or doubt. This is how I have always thought of it.  The other day, I was with friends who used "as if" to express their surprise and joy about a wedding proposal. They weren't being sarcastic or incredulous; they were genuinely happy about the proposal. Here is a loosely paraphrased version of what they said:  "As if they're getting married!"  Is my friends' usage of "as if" standard? Is it a primarily regional distinction? (I am in Ontario, Canada right now.) The closest example we could come up with is someone says "I can't believe that you won first prize!" Of course, the person can and does believe it, so their words ought not to be taken literally. Is it the same idea with "as if"? Find the number of ways in distributing $8$ distinct balls into $6$ distinct boxes such that there is at least $1$ ball in each box.  We are well acquainted with the traditional Inclusion-Exclusion principle in solving this and it will come up as $191520$ ways.  I tried in this way:  When we distribute $8$ balls into $6$ boxes we have two possible cases  Case $1.$ There are exactly $2$ boxes with $2$ balls each  Case $2.$ There is exactly $1$ Box with $3$ balls in it.  For Case $1$, the distribution is done by choosing $2$ boxes from $6$ boxes and $2$ balls from $8$ balls and those two balls can be arranged in $2!$ ways. But I require another two balls from remaining $6$ balls to be placed in each of these two boxes which can be done in $\binom{6}{2} \times 2!$ ways. Finally remaining $4$ balls can be distributed in remaining $4$ boxes in $4!$ ways. So total number of ways for Case $1.$ is  $$\binom{6}{2} \times \binom{8}{2} \times 2! \times \binom{6}{2} \times 2! \times 4!=604800$$  For Case $2$, the number of ways is  $$\binom{6}{1} \times \binom{8}{3} \times 5!=40320$$  I am pretty sure the value obtained for Case $2.$ is correct. but I could not find where I went wrong in Case $1.$ Why does main method in Java always need arguments? How do I delete all empty directories in a directory from the command line? Say I have a directory named foo/. This folder includes subdirectories. How can I delete all the empty directories in one command? After reinstalling TeXLive distribution (install-tl-20160318, Ubuntu 14.04), a issue occurs with the updated version of the titlesec package: the section numbering is lost.  What could it be missing? Is there a modification I have not seen?  Below is a MWE comparison of the two versions. The prevtitlesec package is a reinstall of the previous version (2011/12/15).  \documentclass{book} \usepackage[margin=2cm,a4paper]{geometry} %\usepackage{prevtitlesec}% 2011/12/15 version \usepackage{titlesec}% 2016/03/15 version \usepackage{lipsum}  \begin{document}  \chapter{Title of the first chapter} \lipsum[1] \section{A test section} \lipsum[4] \subsection{A test subsection} \lipsum[4] \subsection{A test subsection} \lipsum[4]  \end{document}   titlesec package 2011/12/15:    titlesec package 2016/03/15: I am supposed to integrate $f(z)=$$\frac{5}{z}$ from -3 t0 3 but I am having trouble understanding how to do this. I've done the integration the "hard" way by using parametrizations but now I need to use the fact that $f(z)$ is analytic everywhere except at $z=0$ and a different method to perform the integration but I am stumped. How does Linux know where its swap partition is? I've read that you need to put the swap partition on HDD rather than SSD.   My questions are the following:    When and how is the "checking" done by the distribution (or something else) to find its Swap partition?  Does it happen during boot?  It just checks all available disks and searches for a partition with 'swap' flag?  What happens if there are several partitions like that?  Also, how many swap partitions do I need to have if I run, for example, two different distributions on the same disk, let's say Fedora and Ubuntu? Forward/Inverse Search Does Not work on certain tex files Do film industries outside India use intervals/Intermission? Deriving the conditional distributions of a multivariate normal distribution We have a multivariate normal vector ${\boldsymbol Y} \sim \mathcal{N}(\boldsymbol\mu, \Sigma)$. Consider partitioning $\boldsymbol\mu$ and ${\boldsymbol Y}$ into  $$\boldsymbol\mu = \begin{bmatrix}  \boldsymbol\mu_1 \\  \boldsymbol\mu_2 \end{bmatrix} $$ $${\boldsymbol Y}=\begin{bmatrix}{\boldsymbol y}_1 \\  {\boldsymbol y}_2 \end{bmatrix}$$  with a similar partition of $\Sigma$ into $$  \begin{bmatrix} \Sigma_{11} &amp; \Sigma_{12}\\ \Sigma_{21} &amp; \Sigma_{22} \end{bmatrix} $$ Then, $({\boldsymbol y}_1|{\boldsymbol y}_2={\boldsymbol a})$, the conditional distribution of the first partition given the second, is  $\mathcal{N}(\overline{\boldsymbol\mu},\overline{\Sigma})$, with mean $$ \overline{\boldsymbol\mu}=\boldsymbol\mu_1+\Sigma_{12}{\Sigma_{22}}^{-1}({\boldsymbol a}-\boldsymbol\mu_2) $$ and covariance matrix $$ \overline{\Sigma}=\Sigma_{11}-\Sigma_{12}{\Sigma_{22}}^{-1}\Sigma_{21}$$  Actually these results are provided in Wikipedia too, but I have no idea how the $\overline{\boldsymbol\mu}$ and $\overline{\Sigma}$ is derived. These results are crucial, since they are important statistical formula for deriving Kalman filters. Would anyone provide me a derivation steps of deriving $\overline{\boldsymbol\mu}$ and $\overline{\Sigma}$ ? Thank you very much! If I remove Minecraft sound files from .minecraft/assets/objects, will Minecraft be unable to play them? In Minecraft, there are a lot of cool sounds. I decided to find there location and move them to my desktop. I have Ubuntu, and if when I remove them from that folder will Minecraft be unable to play them or is it smart enough to figure out that they are gone and download them again. Before minecraft was installed, it had to download the files. I even moved my favorite song (creative 6) from the sounds. The sounds are not labeled and have seemingly random names like b0b12118a97ddd733a50e9382e91a21652568641 and how will I know what to call them that will be recognized without digging through the index if Minecraft fails to download them? Or do I not have to worry because it will download them again upon launch?  Note: Why does it not label them and call them random names? Is there any way to index my Github account to google search. I see that many people's account show up as soon as I type their name, but mine doesn't show up even after I type my name followed by github n search. Given any uncountable subset $S$ of the unit interval. Then $S$ clearly has an accumulation point and indeed uncountably many (which might also be a nice exercise). So my question is: Is there an accumulation point, that again lies in $S$? How may I reference the script tag that loaded the currently-executing script? cron Vs. sleep - which is the better one in terms of efficient cpu/memory utilization? How do I resize partitions using command line without using a GUI on a server? I only have access to the server via a terminal and I can't use graphical tools such as GParted! I want to create a new partition from a part of the root (about 768mb) for swap.  # df -h Filesystem      Size  Used Avail Use% Mounted on /dev/vda         20G  1.3G   18G   7% / udev             10M     0   10M   0% /dev tmpfs           199M  4.9M  194M   3% /run tmpfs           100M   12K  100M   1% /run/user tmpfs           5.0M  4.0K  5.0M   1% /run/lock I am currently facing a "performance problem" while using grep. I am trying to locate the occurrences of many (10,000+) keywords in many (think Linux kernel repository size) files. The objective is to generate a kind of index for each keyword:   keyword: my_keyword filepath 1 filepath 2 ------ keyword: my_keyword2 ...   Being fairly new to shell scripting, I have tried a few naive approaches:  while read LINE; do     echo "keyword: "$LINE &gt;&gt; $OUTPUT_FILE     grep -E -r --include='Makefile*' "($LINE)" . &gt;&gt; "$OUTPUT_FILE"     echo "-----" done &lt; $KEYWORD_FILE   This takes about 45 minutes to complete, with the expected results.  Note: all they keywords I search for are located in a file ("KEYWORD_FILE", so fixed before anything starts), and the files in which to search can be determined before the search starts. I tried to stored the list of files to search in before the search like that:  file_set=( $(find . -name "Kbuild*" -o -name "Makefile*") )   and then replace the grep call by  echo {$file_set[*]} | parallel -k -j+0 -n 1000 -m grep -H -l -w "\($LINE\)" &gt;&gt; "$OUTPUT_FILE"   It takes about an hour to complete&hellip;  Question: considering I can use whatever technique I want, provided it's sh compliant, how can this be done "faster" and/or more efficiently ?  Perhaps grep is not the tool to use, and my use of parallel is wrong&hellip; any ideas are welcome! Can a familiar attune and wear or use a magic item? Is it possible for a familiar to attune to and then wear or wield a magic item? Survey database design: associate an answer to a user I'm doing the conceptual model for a survey database.  The goal is store the answers given by users (it's going to be an Android app).  I have three entities: user, question and option.  A question will have one or more options (for example: How many employees do you have? 1-40, 40-1000, +1000).  Options will have a text (1-40) and a value (the value selected by user).  User will select one (or more) of these options.  My conceptual design is:    I don't know how to associate an answer with an user.  How can I represent that relation? Do I have another entity to represent option value?  This model will store questions and pre-made answers (offered answers) and allows them to be re-used in different surveys.  I have to represent question like this one:    This question is related to this one: