I am starting to step into the field of Topological Quantum Information and Computation and am in search of tools which I can use to directly simulate or realize these transformations in a textual or graphical manner.
Does something like  exist for topological (eg. braided) circuits?   Alternatively, any ideas on how @ is getting  (or something similar)?
The ground was ice-cold, no hint of anyone having lay/laid/lain there   at all.   Which one is the correct option? The assumptions are:    Alice and Bob have perfectly synchronized clocks Alice and Bob have successfully exchanged a pair of entangled photons   The idea is simply to have Alice and Bob perform the Quantum Eraser Experiment (doesn't need to be the delayed choice).   Alice and Bob agree on a specific time when Bob's photon will be between the "path marker" (which is usually just after the slits) and the detector.  If Alice acts collpasing the wave-function on her photon, the interference pattern will disappear. If not it won't.  Alice and Bob can be spatially separated...  What am I misunderstanding?   The only meaningful difference from this spatially separated quantum eraser experiment to one done on tabletop is that you won't be able to use a coincidence detector, but that is not impeditive to identifying the interference pattern, just will make errors more probable. Which we should be able to deal with a appropriate protocol...  There is a experimental paper with a small amount of citations pointing out to the breaking of complementarity in a very similar setup: What is the remainder when $24^{1202}$ is divided by $1446$? I tried remainder theorem but that does not simplify it.   I tried factorizing $1446$ as $2\cdot3\cdot241$ and got remainders when numerator is divided by $2,3$ and $241$ individually but then I did not know what to do next? Stuck! Is there a way to input particular sections of source code using \lstinputlisting (from the listings package) in a flexible way?  It's possible to use the firstline and lastline options to input particular line ranges, but this isn't robust to changes to the source file.  For example, suppose that the input source file is:  int square(int x) {   return x * x; }  int cube(int x) {   return x * x * x; }   In my LaTeX document, I can include the cube procedure using the command \lstinputlisting[firstline=5,lastline=7]{source.c}.  But suppose I later decide to rewrite the cube procedure.  The input source file becomes:  int square(int x) {   return x * x; }  int cube(int x) {   int x2;   x2 = square(x);   return x * x2; }   Now my LaTeX document will not show the final two lines of cube because the listing uses only lines 5-7.  I could manually update the line range, but this is tedious and error-prone.  Is there a way to mark sections of source code with some kind of label so that the listing will be robust to these sorts of changes?  For instance, perhaps the input source file would be something like  int square(int x) {   return x * x; }  /**\beginlabel{lst:cube} **/ int cube(int x) {   int x2;   x2 = square(x);   return x * x2; } /**\endlabel{lst:cube} **/   so that I could use something like \lstinputlisting[lines=lst:cube]{source.c} to include the section that I want and remain robust to changes.  I am open to using other packages for source code listings (e.g., minted) if helpful. Acne underneath skin Introduction  Okay, I've almost won my war. The battle, its almost won... However, I must still claim victory in my final battle. The battle against the little enemies, the ones that have fought with my blade of benzoyl peroxide every single day.  Problem  Through spot treatments I have been able to fell every single one of these spots, but only the ones on my face. I've been using a spot treatment with benzoyl peroxide in, which has worked really well for me. However, my issue comes here:     There are spots underneath my skin, I think. The areas where they come through are a bit red.   So, because there is still slightly red skin on my face, and I think this is causing my acne to constantly return. I need to stop this, and end my war once and for all.  What I've tried   Washing my face with a rag and sponge every day, three times a day Changing my pillow case every day Using a benzoyl peroxide spot treatment Minimizing how much I touch my face Not interfering with the spots with my fingers, not picking at them, not playing with them. Just letting spot creams eradicate them.   Conclusion  Seriously, this driving me up the wall. I spot cream in the evening, by the time tomorrow has ended and its time for a shower, they've all come back. Its like they're coming in waves, damn waves! I must put an end to this.  So, how can I prevent acne from coming back within the space of a single school day? How can I get rid of these once and for all? What types of measures could I try? I have no reason to visit my doctor, its only acne, but I have no idea what I can try now.  Is there even a point in me trying? I acknowledge that I am a teenager, but no others that I know seem to have acne/spots like I do. Find a value anywhere in a database how to remove frost free outdoor faucet drain valve assembly I've tried unscrewing the part outlined in red below. No dice. Do I just need to remove the whole rod (above the red outline) and replace it?) If so, can anyone point me to instructions for them.  I can't see in there. Worried that I'll pull it out and not be able to put it back in.  (The deeper I go in the plumbing the more things I find that there is no modern fitting-part :)  My new assembly  replaces the parts outlined in red. the new assembly has a female thread. I am HOPING that the thicker part of the pipe (just above the black "collar" stopper)  is screwed onto the pipe above.  However, I cannot unscrew it. There is nothing to get a hold of. It's perfectly round. I've tried dw40, and let it sit for 20 minutes. No love.  I'll try wacking it with a board in the direction along which it moves in when it screws (perpendicular to the threads per [this answer][2]) Proving that a number with digits 1...9 in some order, ending in 5, is not a perfect square. If "x" is a 9 digit number , which contains digits from 1 to 9 which ends in 5 . Prove that it can't be a perfect square ( digits are not to be repeated).  Please suggest the solution of this question. How to download all files from Ubuntu One? How can I mitigate edge halo when darkening skies in post-processing? When exactly does tmpwatch clear out files I place in /tmp? Reputation widget crash I have an issue with crashing reputation widget when it's added to the home screen. When I add it for the first time, it says "Please login before using this widget" (even though the app itself is logged in already). So I open the app, go back to the home screen, add the widget again and it crashes (and it's not added to the home screen). When I'll try to add it again, it says "Please login before using this widget" again. And then it just repeats - "Please login...", execute the app, crash, "Please login...", etc.  Restart of the device didn't make any change.  I have found .  My set up:  Stack Exchange app version: 1.0.89 Android version: 5.0.1 Device: Samsung Galaxy S4 How do I disable "Link Preview" in Chrome? Why doesn't LaTeX hyphenate words containing accents, e.g. "développement"? In this MWE, Latex doesn't hyphen the word "développement" and prefer to create a HUGE hbox.   \documentclass[a4paper,12pt,dvipsnames]{report} \usepackage[utf8]{inputenc} \usepackage[french]{babel} \usepackage{lmodern} \usepackage[a4paper, showframe]{geometry}  % Title Page \title{} \author{}   \begin{document} \section{Section}  \subsection{Subsection} \begin{description}  \item [Marhalie Toucse : ]  ingénieure de la plate-forme SORTATZ. Elle réalise   le développement du projet des tex écrit pour lipsum lagae legarc sgsi text text text text text text text text text.  \end{description} \end{document} Of Half-elven and mortal life When half-elvens choose mortal life, how would their bodies behave?  Half-elven are always elves by nature. Ever since they're born, their physical body and behaviour would be elvish - they have keen senses, they don't get physically weary, no illness, and so on.  Half-elvens are then offered a choice - Immortal elvish lives or mortal fate of men. When they choose the latter, like Elros and Arwen did, what would happen to their elvish nature? Would they lose it? I don't think they would lose their pointy ears, but what about the other elvish features that I mentioned before?  Are there any canonical references? Leaving values blank if not passed in str.format Should I be worried about electro-static discharge? Doing mostly micro-controller work, I have never bothered with grounding myself with a wrist-strap or any other implementation. Should I be worried about this? How serious is ESD when working at my workbench on projects? How do I get permissions to edit system configuration files? ASP.NET: Is there a way that I can simply pass a model into a view and render it to a string? Let $a\ge1$ and define the sequence $(x_n)$ recursively by: $$x_1 = \sqrt{a}$$ $$x_{n+1}= \sqrt{a+x_n}$$  Here's what I did:  Plugging in some values makes it seem as if the sequence is increasing. I first solve the equation $t=\sqrt{a+t}$, equivalently $t^2 -t -a =0$, to get an idea what's going on. The roots are $$t_{1,2}= \frac{1 \pm \sqrt{1+4a} }{2}.$$ Therefore, between the roots, that is for $$t\in \left( \frac{1 - \sqrt{1+4a} }{2}, \frac{1 + \sqrt{1+4a} }{2}\right)$$  we have $t^2-t-a \le 0 \iff t \le \sqrt{a+t}$. Here's my attempt at showing inductively that $$\forall n\in \mathbb{N}, \ x_n \le \frac{1 + \sqrt{1+4a} }{2}$$  For $n=1$, the statement is true (simple arithmetic). Suppose it's true for $n$. Consider  $$x_{n+1}= \sqrt{a+x_n}\le \sqrt{a+\frac{1 + \sqrt{1+4a} }{2}}=\frac{1 + \sqrt{1+4a} }{2},$$  because $\frac{1 + \sqrt{1+4a} }{2}$ satisfies $x=\sqrt{x+a}$.  So this establishes the sequence $(x_n)$ is bounded. Now, by induction again, I try to show it's monotonically increasing. The base case $x_1\le x_2$ is obvious. Assume (strong induction) $x_{n-1}\le x_n$ for all $n&gt;1$. But since we have $$x_1\le x_n \le \frac{1 + \sqrt{1+4a} }{2}, $$   then $x_n$ lies in the appropriate interval, so $x_n \le \sqrt{a+x_n}=x_{n+1}.$  Is this proof correct? Can the condition on $a$ be relaxed to $a&gt;0$? Maybe even small negative $a$? And could someone provide me with another proof of convergence of $x_n$? I absolutely hate this one!