Has anyone tried any quantum computing programming code that shows or demonstrates the advantage of a quantum computer over classical computers? Thanks a lot.
It is generally believed and claimed that quantum computers can outperform classical devices in at least some tasks.  One of the most commonly cited examples of a problem in which quantum computers would outperform classical devices is $\text{Factoring}$, but then again, it is also not known whether $\text{Factoring}$ is also efficiently solvable with a classical computer (that is, whether $\text{Factoring}\in \text{P}$).  For other commonly cited problems in which quantum computers are known to provide an advantage, such as database search, the speedup is only polynomial.  Are there known instances of problems in which it can be shown (either proved or proved under strong computational complexity assumptions) that quantum computers would provide an exponential advantage?
Align cell height of the tabularx rows The following latex code prints rows one at a time. However all the cells of the rows don't come out aligned. How can I fix it.   \documentclass{beamer}     \usepackage{tabularx}    \begin{document}  \begin{frame}{}  \begin{tabularx}{3.50in}{lXX}           \hline           &amp; Observation &amp; Conclusion \\           \hline             \uncover&lt;2-&gt;{1.} &amp; \uncover&lt;2-&gt;{Observation 1 } &amp; \uncover&lt;2-&gt;{Conclusion 1} \\   \uncover&lt;3-&gt;{2.} &amp; \uncover&lt;3-&gt;{Observation 2} &amp; \uncover&lt;3-&gt;{Conclusion 2} \\           \end{tabularx}      \end{frame}   \end{document}   The output looks as follows :    As we can see cells in first column do not align with the rest of the rows. Will appreciate any input as to how to fix this. Novel about a teleportation device and a con artist alien I read two (maybe three) books about a protagonist who communicates with an alien who provides the instructions on how to create a device to teleport. The device is flawed in that it purposefully uses more energy (much more) by taking it from the rotation of the Earth.  The main character and two others continue to fight, commit intrigue, etc. The alien then uses them to recruit other races to do the same thing. What does it mean when Git says 'rewrite' or 'rename' in a commit message? show that $x$ is in $\ell^1$ if $\sum x_ny_n$ is convergent for all $y=(y_n)\in{c_0}$ If $x=(x_n)$ is a sequence of complex numbers such that the series $\sum  x_ny_n$ is convergent for all $y=(y_n)\in{c_0}$. Then prove that $x\in{\ell^1}$. Can anyone tell me what is the meaning of $c_0$  in this question and how to proceed on proving it. After migration to MacOSX 10.11 "El Capitan", how to run simple utilities such as "texdoc" and "kpsewhich"? Last night, I migrated my MacBook's operating system from 10.10 "Yosemite" to 10.11 "El Capitan". Everything seemed to go smoothly. Happily, regarding my TeX-related work, I am able to use the GUI front ends "TeXworks" and "TeXshop" just fine since completing the OS upgrade. I use MacTeX2015, with all the latest updates installed.  Oddly, though, since completing the upgrade I can no longer run any MacTeX command-line utilities such as texdoc and kpsewhich. (Actually, as I just discovered, I can no longer run pdflatex either from a command line. However, I never do run pdflatex from a command line prompt, so that's not an urgent problem for me -- at least not for now.)  The suggestions given in the posting  do not seem to be applicable to this case, as they all seem to revolve around setting up /usr/texbin correctly -- /usr/texbin is no longer allowed under MacOSX 10.11. The document  by Herb Schulz deals in depth with adjusting settings in the GUI front ends, but it appears not to touch on what to do about /usr/texbin, which appears to be the now-missing link to TeX's command line utilities.   Pointers and solutions most welcome! A priori power analysis for generalized linear mixed-effects model Let's say I have a data set (with a binary DV) which I used a generalized linear mixed-effects model on. I am currently trying to run a simulation-based power analysis to determine the sample size I should try to collect for a replication attempt.   I know about the  function for fitted lme4 model objects, which will create simulated responses that follow the size and structure of the actual dataset.  My question is, how can I use this fitted model object to run an a-priori power analysis for my replication?. In other words, is there an easy way to extract the necessary information from the simulate function, vary the sample size, then to simulate responses?  EDIT:  Here is a simple example with ten subjects that should give me a good starting place. The data here are totally fake so the effects are not close to what I have in the pilot data.  The two variables of interest are age in months (between subjects) and whether the stimulus is "similar" or "dissimilar" (within subjects). Each individual is exposed to three items within each similarity group, for a total of six binary responses for each subject. As seen in the model, I am interested in a possible interaction between age and similarity and include a random slope of similarity to do this.   Let me know if I need to modify anything/provide more information to make things easier.   set.seed(28)  fakeData &lt;- data.frame(ID = rep(1:10, each = 6),                        months = rep(round(runif(10, min = 60, max = 80)), each = 18),                        similarity = rep(c("Sim", "Dissim"), each = 3),                        response = sample(c(0, 1), 60, replace = TRUE))  fakeModel &lt;- glmer(response ~ months * similarity + (similarity | ID), family = binomial, data = fakeData) summary(fakeModel) Allowing only one download per Apple ID Distance between points along polyline ArcGIS for Desktop? I'm using ArcGIS 10.3 (Desktop), and I'm trying to measure the distance between points following a path determined by a set of polylines.  Hand measurement is not a viable option-- there are ~7500 points, and my polyline set is the global coastline.  The ultimate goal is to get the spacing of these points along the polylines, so that I can analyze this with respect to a few other variables.   I can read python-- with a bit of effort-- but not write or edit it, so code-based solutions will not be particularly useful to me.  I have tried using the linear referencing tools-- I snapped the points to the lines, then transformed the polylines to routes and used 'locate features'-- but because my points are not (entirely) ordered along the path, using the difference between  linear reference locations of subsequent points yields some fairly unlikely answers.  In addition, spot checks of (hand-measured, using the built-in path length measuring tool) point-to-point along-polyline distance yield different answers than given by the corresponding linear references for the point pair. (Some of the answers were close enough that they could very well be measurement error on my part, but others were nearly 20%, despite my having zoomed in and snapped the measurement cursor to the polyline, proceeding vertex-to-vertex.)  Sorting first by linear distance seems to fix the first problem, but in light of the second one, I remain skeptical of this process.   I then tried simply splitting the polylines into segments ('split line at point') using the (snapped) points as the dividers, with the eventual goal of finding the segment length with the calculate geometry feature.  This produced gibberish. I'm not sure what criteria ArcGIS used to split the lines, but it wasn't the point set I provided.  Segments in the resulting shapefile ran right through tens of points, only to terminate at a place with no point. (Also, there were segments utterly empty of points...you get the gist.) I reiterate that the pointset was specifically snapped to the polylines, so this problem shouldn't be caused by excessive distance between the point and the polyline.  I'm at a bit of a loss, here: could someone point out where I might have gone astray and/or suggest a solution?  Or, failing that, a new method that I could try?  It seems like a fairly basic (not necessarily simple, but fundamental) analysis to do with geographic data, and I don't understand why it has presented so many difficulties. Is a URL with a query string better or worse for SEO then one without one? I want to know, is there a huge difference in terms of SEO between these URLs:  example.com/ontario/toronto/listings   or  example.com/listings.php?p=ontario&amp;c=toronto   Will one URL rank higher than the other? Is there a huge difference here? Ward model implementation: specular component too weak I'm trying to implement the Ward shading model, the anisotropic, computationally efficient version:       This is how I made it:    float alphaX=0.5, alphaY=0.5; // asinotropic roughness float minFloat= 1.e-6;   vec4 Ward(vec3 L, vec3 N, vec3 V) {     vec3 H= normalize(L+V);     float NdotL= max(dot(N,L),0.0);     float NdotV= max(dot(N,V),0.0);      vec3 e= vec3(1.0,0.0,0.0);     vec3 T= normalize(cross(N,e));     vec3 B= normalize(cross(N,T));     float HdotT= max(dot(H,T),0.0);     float HdotB= max(dot(H,B),0.0);     float HdotN= max(dot(H,N),0.0);      float beta= -2.0 * ( pow(HdotN/alphaX, 2.0) + pow(HdotB/alphaY,2.0) ) / (1.0 + HdotN);     float den= max(minFloat, 4.0 * pi * alphaX * alphaY * sqrt(NdotL * NdotV) );     vec4 specular= Ps * 1.0/den * exp(beta);     return (Pd + specular) * NdotL; }   But I get a result similar to a lambertian surface or Oren-Nayar model, where the specular component is absent: I have noticed that some users have taken it upon themselves to create  that allow you to see a user's rank (percentile) among SO developers.  I like this.  I was wondering if the owners of the website are planning something like this in the future?  If so, are you planning on making this by tag?  (I care less about where I rank when compared to developers of a different language).  What I'm looking for is something like this:  C#:      User is ranked #XX (Top XX %) ASP.Net: User is ranked #YY (Top YY %) No newline after (sub)section? I want my text to appear right after the call to \subsection{Name} but  I can't find how to do it. I'm using the article class.  An example of command:  \subsection{a)} Blah blah bla...   produces:     a)      Blah blah bla...   instead of what I want:     a) Blah blah bla...   Anything I could do? How are the number of views in a question calculated? I saw it's not just a page views number, because, if I press F5 several times, it won't increase the number of views.  They could store my IP address in a table, but wouldn't that make it slow? They would need to query a database one more time for each request. How can I balance uniformity of style files against modularity? I'm using Windows/TeXworks/MiKTeX, and I would like to have one style file I can use anywhere in any document in my top-level folder. If I want to add a new command or renew an old one, I'd like that to be available in all documents recursively contained in my top-level folder. I have a very hierarchical structure to my top-level folder. So this would seem to point to having a single file that TeXworks knows about. Could I add a path in Preferences -> Typesetting -> Paths for TeX and related programs? I've tried that, possibly superficially, without any success. Adding the correct folder to the Windows PATH variable doesn't seem to do the trick, either.   On the other hand, suppose I want to send someone a TeX file? It would be nice in such circumstances to be able to have the style file in the same folder as the TeX file. If I do that, how could I ensure that it's always up-to-date? Is there a script available somewhere that could take my master style file and push it down to all pre-existing lower-level locations?   Just to reiterate: I want uniformity of my style files in my very hierarchical folder structure. However, I would also like modularity, in that each folder is self-contained. How can I achieve that?  Also, out of curiosity, since I may acquire a Linux computer soon, how would I do this in, say, *ubuntu with TeXlive? I would like to create a XeLaTeX layout where  multicol's columns (two in this case, no figures, text only) are tilted where they meet. The lines still should be ordinary lines below each other, but the start/end points of each line should glide a bit each line for it to look something like this:  xxxxxxxxxx  xxxx xxxxxxxxxx  xxxx xxxxxxxxx  xxxxx xxxxxxxxx  xxxxx SECTION   xxxxxx xxxxxxxx  xxxxxx xxxxxxx  xxxxxxx xxxxxxx  xxxxxxx xxxxxx  xxxxxxxx xxxxxx  xxxxxxxx xxxxx  xxxxxxxxx xxxxx  xxxxxxxxx xxxx  SUBSECTION xxxx  xxxxxxxxxx   So not the whole column is tilted, but one gets narrower while the other one gets wider.  I've seen examples using \parshape, but those I found are based that one counts lines and more or less manually defines the shape. I also would need that LaTeX keeps the multicol functionality (page breaks, text flow, ...) and does this automatically on each page for a longer chapter.  How do I create such a layout? If multicol is not easy to mix with this layout, what would be an alternative? Why does the QGIS Server WMS layer not load in QGIS Desktop? Technique for finding the nth term I'm a trainee teacher and I need to pass a skills test in maths, but I'm having trouble in this particular area of algebra in finding the nth term of any sequence. I've been given a series of questions to answer one of them is:  Find the nth term of the sequence 3, 8, 15, 24.  I not only need to know the answer but more importantly the technique. This is GCSE level. Proving any number of the form $2^n$ can't be written as the sum of k consecutive numbers. Is it safe to replace a 4400mAh laptop battery with a 8800mAh battery? I have an Acer Aspire 5536G. My battery is having problems so I am thinking of replacing it. I have searched online through many sites and I found some good deals. However, currently my laptop has a 4400mAh lithium ion battery so I was thinking of replacing it with 8800mAh 12-cell battery that lasts more hours than 4400mAh without power plug. "define:" oneboxing selects completely bogus data I found this weird word, "burke", and decided to check it out. It turned out it was an alternative spelling of "berk". This is what define: berk in chat expanded to:    So, according to that, "berk" as a noun can mean "a fool, prat, twit", or "berk", or "berk", or "berk". Wow, who would have thought "berk" might mean berk. Three times, just to be sure.  That got me really curious so I checked the wiktionary page directly. It shows three meanings for "berk": the same as meaning #1 that was oneboxed, plus two others that are not at all simply stated as "berk".  Further down from there we can find the other three "berks". Number three, for instance, is easy to trace since "indefinite plural berkë" seems quite greppable. And it turns out that it's Albanian.