I want to establish causality between two variables/attributes of some time series data.   Is there any method to prove and establish the causality mathematically?
In his 1984 paper , Paul Holland raised one of the most fundamental questions in statistics:     What can a statistical model say about   causation?   This led to his motto:     NO CAUSATION WITHOUT MANIPULATION   which emphasized the importance of restrictions around experiments that consider causation.  Andrew Gelman makes :     "To find out what happens when you change something, it is necessary to change it."...There are things you learn from perturbing a system that you'll never find out from any amount of passive observation.   His ideas are summarized in .  What considerations should be made when making a causal inference from a statistical model?
Is it possible for an American to get a Chinese visa in Hong Kong? Is it possible to construct a multi-colored double-bladed lightsaber? I was just watching  video of some SW dueling at the 2015 World Fencing Championship, and wondered if it's actually possible in the SW universe to construct a multi-colored double-bladed lightsaber?   Are there any accounts of such a thing? If not, would it at least be theoretically possible to make one, or, are there obvious limitations? Do there exist an infinite number of 'rational' points in the equilateral triangle $ABC$? Let's call a point $P$ which satisfies the following condition 'a rational point'.  Condition: Each distance $PA, PB, PC$ from a point $P$ to three vertices $A, B, C$ of an equilateral triangle $ABC$ which has edge-length $1$ is rational number.  I'm interested in this point because I found the following three:  1. There exist an infinite number of rational points on an edge of the equilateral triangle $ABC$.  2. There exist an infinite number of rational points on the circumference of the circumscribed circle of the equilateral triangle $ABC$.  3. There exists a rational point in the equilateral triangle $ABC$.  Supposing that $A(0,\frac{\sqrt3}{2}), B(-\frac12,0), C(\frac12,0)$, one example for the above 3 is the following: $$P\left(\frac{61}{2058},\frac{220}{1029}\sqrt3\right), \left(PA, PB, PC\right)=\left(\frac{73}{147}, \frac{95}{147}, \frac{88}{147}\right).$$  I found this example by using computer. I found the other examples, but I don't know there exist an infinite number of rational points in the equilateral triangle $ABC$. Then, here are my questions.  Question 1: Do there exist an infinite number of rational points in the equilateral triangle $ABC$ ?  Question 2: Can we find all rational points in the equilateral triangle $ABC$ ? Repeat command n times? Is it possible to define a command, which repeats the following command n-times? Call it for example \Repeat, then   \Repeat[4] \command{...}    should be equivalent to   \command{...} \command{...} \command{...} \command{...} The sum of powers of two and two's complement – is there a deeper meaning behind this? Is everything greater than None? The successive difference of powers of integers leads to factorial of that power. Here's the formula:     $$\sum_{r=0}^{n}\binom{n}{r}(-1)^r(n-r)^n=n!$$   Can anyone give a proof of this result?  Note: The original question was to prove the more general     $$\sum_{r=0}^{n}\binom{n}{r}(-1)^r(l-r)^n=n!$$   for an integer $l$, which some of the answers address. Bug? LaTeX misparses nested optional arguments LaTeX seems to be having problems handling nested optional arguments. I've included a minimal code example that generates the error:  \documentclass[12pt,oneside]{book} \begin{document}  \newcommand{\termbad}[2][]{#2#1} \newcommand{\termgood}[2][]{#2#1}  \newcommand{\up}[1]{#1} \newcommand{\dd}[1][]{#1}  \termgood{\up{Tart}}{Pop} \termbad[\up{Tart}]{Pop}      \termgood{\dd[Tart]}{Pop} \termbad[{\dd[Tart]}]{Pop} %\termbad[\dd[Tart]]{Pop}   \end{document}   If you run this code, it works. If you remove the % in the second to last line, it fails with:  Runaway argument?  Tart{Pop} \par \par \end {document}  !File ended while scanning use of \dd.   After further tinkering, I have discovered the problem: LaTeX is reading the ] for the inner optional argument as the end of the outer optional argument and then passing a malformed argument in. So it is passing in \dd[Tart as the optional argument to \termbad instead of \dd[Tart].  This still feels like a bug to me. Nesting braces in arguments works, brackets should as well. The following are workarounds:   Enclose the inner optional argument in braces (as in the line before %). Redefine your inner function to require its argument instead of using optional arguments. Redefine your outer function to require its argument instead of using optional arguments.   Any one of the three works around the issue.  (Reposted here; question was originally posted to stackexchange and then closed instead of being migrated.) How do you performance test JavaScript code? CPU Cycles, Memory Usage, Execution Time, etc.?  Added: Is there a quantitative way of testing performance in JavaScript besides just perception of how fast the code runs? I have a problem with a virus in windows 7, I don't know what kind of virus is infected my OS, I installed kasersky antivirus, and clear all detected viruses. After that I can't open any antivirus sites, can't ping any antivirus sites. example:  C:\Windows\system32&gt;ping kaspersky.com Pinging kaspersky.com [38.117.98.231] with 32 bytes of data: General failure. General failure. General failure. General failure.  Ping statistics for 38.117.98.231:     Packets: Sent = 4, Received = 0, Lost = 4 (100% loss),   When I ping to other sites, I get reply normally: example woth pinging to google.com  C:\Windows\system32&gt;ping google.com  Pinging google.com [31.7.160.224] with 32 bytes of data: Reply from 31.7.160.224: bytes=32 time=2ms TTL=61 Reply from 31.7.160.224: bytes=32 time=2ms TTL=61 Reply from 31.7.160.224: bytes=32 time=1ms TTL=61 Reply from 31.7.160.224: bytes=32 time=1ms TTL=61  Ping statistics for 31.7.160.224:     Packets: Sent = 4, Received = 4, Lost = 0 (0% loss), Approximate round trip times in milli-seconds:     Minimum = 1ms, Maximum = 2ms, Average = 1ms   I tryed any antispyware/antimalware softwares, but null results.  Anyone else encountered this problem? "To be subject to" vs. "to be subjected to" I have a population of phone calls - 200,000.  There are different reasons for each call, but lets assume the number of reasons is known. i.e. 7 different call reasons: 1) Check on order 2) Cancel order 3) Billing information 4) Account information etc...  My question is, I want to get a statistically significant sample size so the number of calls I listen to in my sample are representative of the distribution of the reasons in the overall population of 200,000 calls.  What should the sample size be? Which methods to use to calculate the sample size? Under the U.S.'s Copyright Law, is it an act of copyright infringement if we changed the color of another artist's image to black and white? Find the limit if it exists of $S_{n+1} = \frac{1}{2}(S_n +\frac{A}{S_n})$ I've got a custom loop that I'm using to display some Real Estate listings that will be available within 60 days. I'm calling it with the following function:   &lt;?php  $sixtydays = date('Y/m/d', strtotime('+60 days')); $paged = (get_query_var('paged')) ? get_query_var('paged') : 1; $query = new PostsOrderedByMetaQuery(array(   'post_type' =&gt; array('post', 'real-estate'),   'meta_key' =&gt; 'Time Available',   'meta_compare' =&gt; '&lt;=',   'meta_value' =&gt; $sixtydays,   'paged' =&gt; $paged,   'orderby_meta_key' =&gt; 'Price',   'orderby_order'    =&gt; 'ASC' )); ?&gt; &lt;?php while ($query-&gt;have_posts()) : $query-&gt;the_post(); ?&gt;   While the loop works great, I can't get it to paginate. It shows the first 10 (my default) posts but doesn't show the pagination. The only way to display all posts is to show them on one page by adding 'posts_per_page' =&gt; -1, I have similar loops on other pages that have no problem paginating. The only difference with this one is that there are two meta keys that are filtering the posts.   I'm using WP Page Navi for this and the rest of my pages. I'm closing the loop and adding the pagination using the following code:   &lt;?php endwhile; // End the loop. Whew. ?&gt; &lt;?php wp_pagenavi(); ?&gt; &lt;?php wp_reset_query(); ?&gt;   How can I go about fixing this? Mount ext4 partition with >4KiB block size I'm attempting to mount a partition from a NAS and the block size is 65536 bytes, this is above my distribution's precompiled kernel memory paging size of 4KiB, so I cannot mount it normally.  Which kernel compilation parameters would I need to change to get a memory paging size large enough?  Would it be possible under the x86-64 architecture?  EDIT: There doesn't seem to be an option for it in make xconfig unless I'm just missing it.  From page_types.h under arch\x86\include\asm  /* PAGE_SHIFT determines the page size */ #define PAGE_SHIFT  12 #define PAGE_SIZE   (_AC(1,UL) &lt;&lt; PAGE_SHIFT) #define PAGE_MASK   (~(PAGE_SIZE-1))`   It doesn't look to be configurable.  I could change this number directly to 16 and it would probably make pretty explosions and destroy Tokyo.  I shall probably try it later this evening. List files sorted by the number of lines they contain How can I list the number of lines in the files in /group/book/four/word, sorted by the number of lines they contain?   ls -l command lists them down but does not sort them Biometric information for a UK visitor visa for the second time I submitted my biometric information when I applied for (and successfully received) the UK visitor visa.  Now, the visa has expired and I would like to apply for it again.   Do I need to submit my biometric information again?  Will the process be the exact same as before? Windows 10 100% Disk Usage after Startup After startup for 5 minutes my system is very slow. The Task Manager shows that the disk usage is at 100%. (Later this number is around 2-4 %, but sometimes for 1-2 minutes go up again at 100%.)  I searched a lot on Google. For example I read , and also other pages. I opened two topic on Microsoft answer.  and one in Hungarian.  But I didn't found the solution yet. So I would like to ask Community's help. :)  Here the steps I already done:   I disabled everything at startups (including services) and the issue is the same.  I disabled Prefetch and Superfetch, the Baground Intellingent Transmission, Windows Search and Windows Defender but the issue is still persists. I made a health check on HDD, I made defrag and file system error check, but there are no errors. Also I tried to reinstall the HDD's driver. I made a full hardware check up, with no errors. The Windows and all the drivers are up-to-date. I tried a clean start. The issue is the same. I deleted Dropbox and all antivirus. I turned of the MSI mode.      I using also Linux, where this error is not occurs. Good to know, that Windows had 4 partitions, but I deleted 2 of them for the Linux. I don't know what partitions was these but both was only 10 - 20 MB.  I using a Dell Inspiron 15R SE 7520 with Windows 10 Home.  Personally I think it can be the Intel Rapid Store Technology "driver", because the problem started around when I installed it. (However I'm not sure.) And my hardware not supported yet by Intel, so I have no the newest driver. However I deleted Intel's software and driver and the issue is the same.    Thank you in advance for your assistance! Why don't std::algorithms work directly on containers as well?