Change cell text color based on cell value in lightning:datatable
How do I get lightning:datatable to do some undocumented thing X?
Are proofs by contradiction really logical? Let's say that I prove statement $A$ by showing that the negation of $A$ leads to a contradiction.   My question is this: How does one go from "so there's a contradiction if we don't have $A$" to concluding that "we have $A$"?  That, to me, seems the exact opposite of logical. It sounds like we say "so, I'll have a really big problem if this thing isn't true, so out of convenience, I am just going to act like it's true". Optimizing $(X_{n}+c)^{2}$ to show that $P(\overline{X}_{n}\geq \lambda) \leq E(X_{n}^{2})/(EX_{n}^{2}+ \lambda^{2})$ Define $\overline{X}_{n}:=\max\limits_{1\leq m \leq n} X_{m}$ and let $(X_{n})_{n}$ be a martingale where $X_{0}:=0$ and $EX_{n}^{2}&lt; \infty$  Show that $P(\overline{X}_{n}\geq \lambda) \leq E(X_{n}^{2})/(EX_{n}^{2}+ \lambda^{2})$  As a hint: Consider $(X_{n}+c)^{2}$ and optimize over $c$.  It is clear that $((X_{n}+c)^{2})_{n}$ is a submartingale and when I optimize over $c$, I get:   $X_{n}^{2}+2X_{n}c +c^{2}\Rightarrow 0=2X_{n}+2c=0\Rightarrow -X_{n}=c$  It is also clear I need to use Doob's inequality but I am not sure how to go about this, and how the above optimization helps me. How do I stop program from skipping over getline? Natural Deduction - How to define literals? I'm currently working on the following question:  "At least one of Plato and Democritus believed in the theory of forms. Plato believed in the theory of forms only if he was not an atomist, and Democritus was an atomist only if he did not believe in the theory of forms. Democritus was an atomist. Prove, using Natural Deduction, that Plato was not an atomist"  I have been working for quite some time to take the information and turn it into a set of literals and statements I can work with.  So far, I have got $P \lor D$,  $P \Rightarrow \lnot a$,  $D \Rightarrow A$,  $D = A$  However, I cannot seem to make these prove the statement using natural deduction, any hints? Mean Value Theorem: $\frac{2}{\pi}<\frac{\sin x}{x}<1$ I need to show that $\dfrac{2}{\pi}&lt;\dfrac{\sin(x)}{x}&lt;1$ for $0&lt;x&lt;\dfrac{\pi}{2}$.  I know I need to use the mean value theorem, would I just say that since $f$ is continuous in the interval (call it I).  We know $\exists c\in I$ such that $f'(c) = \dfrac{f\left(\dfrac{\pi}{2}\right)-f(0)}{\dfrac{\pi}{2}}$. I don't know where this is going though.  Also, would I need to show $\lim_{x \to 0}\dfrac{\sin(x)}{x} = 1$? Is there a way to do this without L'H Rule? Select Input Texture file name as parameter/node Possible to click on an object in the viewport and the object list hierarchy automatically goes to that object also? What are good advanced books on the physics and science of photography? I am looking for books about the physics of DSLR, including modern photography optics and sensor electronics. If I already have some books on optics and electronics, I have found fairly hard to find good resource for these fields taking photography as a basis, with examples taken from photography and chapters dedicated to lenses optics for instance.  So far what I have found is either too generic, or, if dealing with photography, lacks the physical expertise I would like to get (I mean books with equations. Everybody loves them.)  Good books for physics of photography exist, but they are quite old, the last good I have found were written by Kingslake in the 70s and definitely miss the non-optical part, and the optical stuff is a bit old-fashioned now (but very nice books BTW).  To sum up, I would like:   Very technical references Dealing with physical issues specific to DSLRs and modern photography, such as diffraction limits, image stabilization, properties of coatings, noise correction - whatever you can think of actually...     EDIT: Based on the first results and a quick glimpse at the references given, I would recommend:   The  looks like a bible. Everything seems to be included. It could be a bit more technical, but it gives a lot of bibliography to go deeper if necessary. , for lighting  and  for sensor technology  and the somewhat easier  for optics   Not to forget the , wonderful resource. A PCI Express 3.0 Video Card into a PCI-E 1.0 x16 slot Perhaps I'm trying to push my mobo too hard, but I think I have read that PCI-e 3.0 is back compatible to previous PCI-e specifications. But 3.0 into a 1.0, is it possibly asking too much?  I'm thinking about buying an AMD . My mobo is an Asus p5g41-m le Options to hide reputation information on Stack Overflow? I'm running macOS Catalina 10.15.4 on a 2018 MacBook Pro 15", which has the T2 chip (if anything else is relevant, let me know and I'll update the question.)  I'm a developer and I'm in the process of writing and debugging a C command-line utility that's supposed to take a few miliseconds to run and exit.  My internet connection went down while I was coding (WiFi was still connected, but my ISP was down), and afterwards I noticed that, after compiling the app, the first time I ran it, it took a few seconds to run rather than the expected fraction of a second.  I turned off WiFi (so there was no active network connection), compiled my app again, and ran it -- this time it ran as quick as I would expect.  Turn on WiFi, compile and run again, first run of the app takes longer than expected.  Maybe I'm paranoid, but it sure sounds like macOS is trying to ask Apple's servers for blessing to run my app. Is this the case, or could there be another explanation? If it's indeed the case, can anyone link to an article explaining what's going on under the hood?  UPDATE: as requested, here are timings for an average of three runs of the following command, under different conditions:  touch file.c &amp;&amp; make &amp;&amp; time ./file &amp;&amp; time ./file  The first measurement is the average time for running file for the first time after compilation (the third command in the chain). The second measurement is the average time for running file for the second time after compilation (the fourth command in the chain).  WiFi on, with internet: 347 ms/3 ms.  WiFi on, without internet: 5024 ms/3 ms.  All network connections offline: 24 ms/2 ms. Given a command that changes its behaviour when its output is going to a terminal (e.g. produce coloured output), how can that output be redirected in a pipeline while preserving the changed behaviour?  There must be a utility for that, which I am not aware of.  Some commands, like grep --color=always, have option flags to force the behaviour, but the question is how to work around programs that rely solely on testing their output file descriptor.  If it matters, my shell is bash on Linux. Is it unethical to cite a paper or book that you have never looked at? Suppose I see that Book X is cited by several papers with reference to some particular Fact Y. I wish to cite Fact Y. As far as I know, Book X is the only reference for Fact Y.   I have never looked at Book X. Nonetheless, I cite it like this:  'Fact Y' (see Book X)  My question is: Is this ethical, given that I've never looked at Book X?  More context for my question. I am NOT asking whether this is good scientific practice. I am NOT asking how a good scientist should actually go about citing Fact Y. I am NOT asking if this could undermine your credibility as a scientist.  Instead, I am asking this question because it seems to be a somewhat-common practice. And moreover, as far as I know, no scientist has ever been issued even an official rebuke (much less fired) for engaging in such practice. This would suggest to me that this practice is not considered to be unethical.   Of course, it is not binary as to whether a practice is unethical. But I would simply like to know whether the academic community in general considers this to be even a mildly unethical practice. Or if it is perhaps very slightly unethical, but not a big deal. Or if it is not in the least bit unethical. Find $\min(\operatorname{trace}(AA^T))$ for invertible $A_{n\times n}$ For invertible $A_{n\times n}$ find $\min(\operatorname{trace}(AA^T))$  (a) $0$ (b) $1$ (c) $n$ (d) $n^2$  Clearly for $A=I$, it is $n$, and I am unable to get any lower values, but how do I prove it. As much as I have tried, it doesn't seem possible to use separate labels when using a casesconstruction (from the amsmath package).  Ideally, I would like to be able to write something like  \documentclass{article} \usepackage{amsmath} \begin{document} \begin{equation} f(x)=\begin{cases}   1&amp;x\geq0\label{positive}\\   0&amp;x&lt;0\label{negative} \end{cases} \end{equation} \end{document}   and later refer to both cases at different places. What would be the best way to achieve this result? Apparently ;-) the standard containers provide some form of guarantees.  What type of guarantees and what exactly are the differences between the different types of container?  Working from  (about ) I have come up with this:  Container Types: ================ Container:     Forward Container         Reverse Container             Random Access Container     Sequence         Front Insert Sequence         Back  Insert Sequence     Associative Container         Simple   Associative Container         Pair     Associative Container         Sorted   Associative Container         Multiple Associative Container  Container Types mapped to Standard Containers =============================================  std::vector:    Sequence    Back        Sequence                    Forward/Reverse/Random Container std::deque:     Sequence    Front/Back  Sequence                    Forward/Reverse/Random Container std::list:      Sequence    Front/Back  Sequence                    Forward/Reverse Container std::set:       Sorted/Simple/Unique    Associative Container       Forward Container std::map:       Sorted/Pair/Unique      Associative Container       Forward Container std::multiset:  Sorted/Simple/Multiple  Associative Container       Forward Container std::multimap:  Sorted/Pair/Multiple    Associative Container       Forward Container   Container Guarantees: =====================                                                                                    Simp                                                                                   or                           For   Rev  Rand        Front  Back  Assoc        Sort   Mult                     Cont: Cont: Cont Cont: Sequ: Sequ:  Sequ: Cont:        Cont:  Cont: Copy    Const:      O(n) Fill    Const:                             O(n) begin()             O(1) end()               O(1) rbegin()                        O(1) rend()                          O(1) front()                                    O(1) push_front()                                     O(1) pop_front()                                      O(1) push_back()                                             O(1) pop_back()                                              O(1) Insert()                                                                          O(ln(n)) Insert: fill                               O(n) Insert: range                              O(n)                                   O(kln(n)+n) size()              O(n) swap()              O(1) erase key                                                     O(ln(n)) erase element                                                 O(1) erase range                                                   O(ln(n)+S) count()                                                       O(log(n)+k) find()                                                        O(ln(n)) equal range                                                   O(ln(n)) Lower Bound/Upper Bound                                                    O(ln(n)) Equality                  O(n) InEquality                O(n) Element Access                       O(1) In Russian roulette, is it best to go first? Assume that we are playing a game of Russian roulette (6 chambers) and that there is no shuffling after the shot is fired.  I was wondering if you have an advantage in going first?  If so, how big of an advantage?  I was just debating this with friends, and I wouldn't know what probability to use to prove it. I'm thinking binomial distribution or something like that.  If $n=2$, then there's no advantage. Just $50/50$ if the person survives or dies.   If $n=3$, then maybe the other guy has an advantage. The person who goes second should have an advantage.   Or maybe I'm wrong. Would Gravitational Time Dilation still apply between two gravitational sources? As explained on , when an object is experiencing strong gravitational forces, time passes slower for it. If, in theory, you had two objects exerting the same amount of gravitational pressure on an object in opposite directions, effectively cancelling each other out, would they cancel out the time dilation, or would they compound, making the time dilation more prevalant? How to make Gnome's "Activities" bar always visible? Travelling to Italy without my spouse who is a UK citizen I am India citizen married to a UK national who has been issued a Schengen Visa from the Italian consulate as a spouse of a UK national. My husband was supposed to travel with me but now can’t. We have decided that I should still pursue the trip without him as I will be joining our friends there. Please can someone let me know if I will still be allowed to travel to the Schengen region with a valid Schengen Visa issued as a spouse of a EEA national but without my husband joining me there in person ?