Fontawesome with LaTeX I'm trying to use the package fontawesome with LaTeX, since the documentation says "This package works both with XƎ(LA)TEX and Lua(LA)TEX (using fontspec to load the included original otf font), as well as (pdf)(LA)TEX (using an included type1 conversion and character mapping of the font)."  The point is that, after installing the package, I get an error when I try to compile:   ! Fatal fontspec error: "cannot-use-pdftex" ! ! The fontspec package requires either XeTeX or LuaTeX to function. ! ! You must change your typesetting engine to, e.g., "xelatex" or "lualatex" ! instead of plain "latex" or "pdflatex". ! ! See the fontspec documentation for further information. ! ! For immediate help type H &lt;return&gt;.   What should I do to be able to use the symbols the package gives?  Thanks in advance.  Minimal example: This is enough to get the error.  \documentclass[a4paper,openright,10pt]{article} \usepackage{fontawesome}  \begin{document} Hi \faMale  \end{document}   In addition, I got the package from texlive-fonts-extra.  Using TexMaker 4.1 and TeX Live 2013.20140215-1
fontawesome and pdflatex When using pdflatex and the fontawesome package the below error shows up.   !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! Fatal fontspec error: "cannot-use-pdftex" !  ! The fontspec package requires either XeTeX or LuaTeX to function. !  ! You must change your typesetting engine to, e.g., "xelatex" or "lualatex" ! instead of plain "latex" or "pdflatex". !  ! See the fontspec documentation for further information. !  ! For immediate help type H &lt;return&gt;. !...............................................     Wish to keep on using "pdflatex" instead of "xelatex" or "lualatex".   In fontawesome Version 4.4.0 manual it says "When using the (pdf)(LA)TEX engine, the fontawesome package doesn’t require any external package".  Tried solutions proposed for this question () without success.   MWE:  \documentclass{article} \usepackage{fontawesome} \begin{document} {\faAdjust} \end{document}
Why are PCA eigenvectors orthogonal and what is the relation to the PCA scores being uncorrelated? I'm reading up on PCA, and I'm understanding most of what's going on in terms of the derivation apart from the assumption that eigenvectors need to be orthogonal and how it relates to the projections (PCA scores) being uncorrelated? I have two explanations provided below which use a link between orthogonality and correlation but fail to really explain it: , .  In the second picture it says that the condition $a_{2}^{T}a_{1}=0$  is imposed to ensure that the projection $y_{2}=Xa_2$ will be uncorrelated with $y_{1}=Xa_1$. Can someone provide an example to show why orthogonal vectors ensure uncorrelated variables?  What would happen in PCA if I chose vectors which are not orthogonal; is this even possible? I have read elsewhere that orthogonality is just a by-product of the covariance matrix being symmetric which would suggest that it's not possible to have non pairwise orthogonal eigenvectors. However in the first picture in search of the most 'suitable' matrix it almost seems as we are choosing $p_{1},\ldots,p_{m}$ to be orthogonal to give us a more convenient matrix $\textbf{P}$ one which has nice properties.  I've read other posts on this topic but have been unsatisfied with incorporation of the intuition with uncorrelated variables. I really appreciate any help in understanding this confusion!! I've just installed a new SSD replacing an HDD in my old (late 2008) iMac. When I switched it on all I got on screen was a question mark.   On the advice of my son I tried cmdR during switch on with no result.   I then tried alt which at least got me a cursor on the screen, but nothing else. Any suggestions? I've got everything backed up on an external Hard Drive, by the way. Do Stack Exchange sites allow editing of comments and posts from other users? I understand there has been so much on this topic but I am still confused. I get that if the person is the subject it is who and anything else is whom. However, I'm really struggling to work out this rule for the following sentence:     The scope of which his account of morality applies to is therefore restricted to those whom/who the ‘notion of justification to a being of that kind makes sense.’   Should it be who or whom? I can't work out the subject and object. Running two MySQL servers that use the same data directory Is there a way in Java to determine if a path is valid without attempting to create a file? Is Checksum to file back decoding possible? So, I was having this weird thought. If the checksums(MD5 or SHA...) are unique to any file and are modified if any part of the file is edited, why cant the checksums be decoded back to get the original file? That is if I want to send a large(say 700MB) video, instead I could send just the hash and the file be decoded locally in my friend's computer. I know the thought is stupid, but is it possible by any chance? Or am I missing some thing here? And forgive me if I'm wrong, I ain't a professional. I have a variable, x, and I want to know whether it is pointing to a function or not.  I had hoped I could do something like:  &gt;&gt;&gt; isinstance(x, function)   But that gives me:  Traceback (most recent call last):   File "&lt;stdin&gt;", line 1, in ? NameError: name 'function' is not defined   The reason I picked that is because  &gt;&gt;&gt; type(x) &lt;type 'function'&gt; Truncated 200GB table but disk space not released I have only 2GB left, so I need to remove this history table. This table now is empty but the database disk space not released. And the database file is 320GB. I have a webpage that implements a set of tabs each showing different content. The tab clicks do not refresh the page but hide/unhide contents at the client side.  Now there is a requirement to change the page title according to the tab selected on the page ( for SEO reasons ). Is this possible? Can someone suggest a solution to dynamically alter the page title via javascript without reloading the page? Can I downgrade to macOS Mojave if I buy the new 2019 MacBook Pro? During the last phase of layout I frequently get a single line or two on a separate page. Rather then pulling the whole paragraph on that last page I would like to "squeeze" the lines on the previous page a bit.  Is there a way to mark the current page to be squeezed a bit if necessary, but let LaTeX reset this marking automatically after the page is done? Is there any canon evidence that FN-2187 actually worked in sanitation? Finn tells Han that he worked in "Sanitation" on Starkiller.  FINN The flooding tunnels are over that ridge. We'll get in that way. HAN What was your job when you were based here? FINN Sanitation. HAN Sanitation? Then how do you know how to disable the shields? FINN I don't. I'm just here to get Rey   It just occurs to me - the "I was in sanitation" line given to Han seems to be the only actual canon evidence of "Sanitation" job.   But was it the truth"?!?!  Finn is always trying to create a positive impression of himself with the Resistance, from the get-go:   He tells Poe that he's rescuing him because that's the "Right thing to do" (with Poe quickly seeing through the fib: "You need a pilot!") He tells Rey that he's Resistance (she buys that because she's a romantic 19 year old still playing with X-Wing pilot helmet) He tells Han that he's Resistance (that one lasts about a minute - Han was not a romantic 19 year old even at 19 :)   In reality, we know that he was 1% of his class, model stormtrooper cadet, personally groomed for promotion by Captain Phasma (; ).  However, I am pretty sure telling Han "Hey, I was 1% of my class, model stormtrooper cadet, groomed for promotion by Captain Phasma"  isn't high on his list of brand management plans.  Far better to pretend to be a lowly "sanitation" worker than top-flight cadet that he really was.  So, my question is - do we have any direct canon evidence proving that the "sanitation" job was real and not a fib to make himself look better to Han/Resistance?  Knowing where trash compactor was isn't direct evidence, though it is circumstantial one. How do I get my Mac to boot from an Ubuntu USB key? If you select "USB" and "Mac" on , it gives a series of command line instructions to make a USB key which the MacBook will boot into Ubuntu from.  I've followed them to the letter two or three times on different USB keys, and it doesn't work. There's a very great deal of technical discussion about EFI etc. but this set of instructions seems to suggest it should just work, but it doesn't.  Help? I'm increasingly unhappy with the more locked-down approach Apple is taking, and I'd quite like to start using Linux with a view to transitioning over to using it as my main operating system, but booting from the CD takes forever, runs slowly and I'm really hoping to get it moving off USB.  Can anybody help me? What has Ramsay done to Theon torture-wise? My friend told me that Ramsay flayed Theon; this question is in two parts:   Is this correct? and What else has Ramsay possibly done?   I have not read the books, but don't mind spoilers from them. Trash icon and files have disappeared from the desktop after upgrade to Ubuntu 19.04 There is a common story that airline ticket prices rise significantly if you buy them less than two weeks before departure.  And that any time before that will yield standard prices.  Is that advice valid for flying during holiday seasons?  As an example: if I want to fly coast to coast USA on December 7th, must I buy my ticket ASAP, or would I get a similar price buying on November 21st? I've recently been learning about differential equations, and my teacher has been giving some particularly difficult examples out for those of us who finish early. He gave us the following differential equation: $$x=y\frac{dy}{dx}-\left(\frac{dy}{dx}\right)^{2}$$ With the hint "Differentiate with respect to $y$, then let $\frac{dy}{dx}=p$". I've solved it after the lesson and would like someone to check whether or not I've done so correctly.    Following the hint, $$\frac{dx}{dy}=\frac{1}{p}=p+y\frac{dp}{dy}-2p\frac{dp}{dy}$$ Which rearranges to $$p-\frac{1}{p}+y\frac{dp}{dy}=2p\frac{dp}{dy}$$ Multiplying through by $\frac{dy}{dp}$, $$\left(p-\frac{1}{p}\right)\frac{dy}{dp}+y=2p$$ Rearranging into the form $\frac{dy}{dp}+f(p)y=g(p)$, and writing $p-\frac{1}{p}=\frac{p^{2}-1}{p}$ $$\frac{dy}{dp}+\frac{p}{p^{2}-1}y=\frac{2p^{2}}{p^{2}-1}$$ Our integrating factor is $$e^{\int\frac{p}{p^{2}-1}dp}=e^{\frac{1}{2}\ln(p^{2}-1)}=\sqrt{p^{2}-1}$$ So we have $$\sqrt{p^{2}-1}\frac{dy}{dp}+\frac{p}{\sqrt{p^{2}-1}}y=\frac{2p^{2}}{\sqrt{p^{2}-1}}$$ The left hand side is, by design, $\frac{d}{dp}(y\sqrt{p^{2}-1})$, and the right hand side can be integrated as follows: $$\int \frac{2p^{2}}{\sqrt{p^{2}-1}}dp=\int\frac{2(p^{2}-1)+2}{\sqrt{p^{2}-1}}dp=\int 2\sqrt{p^{2}-1}dp+\int \frac{2}{\sqrt{p^{2}-1}} dp$$ These can both be solved using the substitution $p=\cosh(u)$, and gives $$y\sqrt{p^{2}-1}=p\sqrt{p^{2}+1}-\cosh^{-1}(p)+\alpha$$ Where $\alpha$ is an arbitrary constant. Dividing, we finally have $$y=p+\frac{\cosh^{-1}(p)+\alpha}{\sqrt{p^{2}-1}}$$  Here I was stuck for a long time, until I realised that we also have the equation we began with: $x=py-p^{2}$, which we can solve as a quadratic in $p$ to also get $$p=\frac{y\pm \sqrt{y^{2}-4x}}{2} \implies p^{2}=\frac{y^{2}+y^{2}-4x \pm 2y\sqrt{y^{2}-4x}}{4}$$  Thus, $$y=\frac{y\pm \sqrt{y^{2}-4x}}{2}+\frac{\cosh^{-1}\left(\frac{y\pm \sqrt{y^{2}-4x}}{2}\right)+\alpha}{\sqrt{\frac{y^{2}-2x \pm y\sqrt{y^{2}-4x}}{2}-1}}$$  This is as good as I can do - we have a relation between $y$ and $x$ - am I done? Is this the correct answer? Is there an easier way?     Thank you for your time.    Following the suggestion by @Valentin $$\frac{dy}{dp}=1+\frac{\frac{1}{\sqrt{p^{2}-1}}\sqrt{p^{2}-1}-p\frac{\cosh^{-1}(p)+\alpha}{\sqrt{p^{2}-1}}}{p^{2}-1}=1+p\frac{1-\frac{\cosh^{-1}(p)+\alpha}{\sqrt{p^{2}-1}}}{p^{2}-1}$$ Hence, $$dx=\frac{dy}{p}=dp\left(\frac{1}{p}+\frac{1-\frac{\cosh^{-1}(p)+\alpha}{\sqrt{p^{2}-1}}}{p^{2}-1}\right)$$ While accepting an offer to grad school, one is basically entering into a lasting relationship with one's adviser - most likely, someone whom the applicant has never met before, and the only exposure has been through the potential adviser's website/publications. It is in the interest of both parties to ensure (to the greatest possible extent) that there are no personal/professional traits of either that hamper the formation of a pleasant working relationship - no-one would want to go through the ordeal of having to change advisers midway!  While the faculty has a chance to have a good look at the applicant's profile as well as his motivations (through his grades and SOP), the applicant doesn't have a similar opportunity. So, I'm interested to know what parameters can be used to gauge a potential fit. I've thought of the following:   Past students:  Did anyone ever drop out/change advisers midway, and if so, for what reasons? These would be a bit hard to find though, as I don't expect the faculty concerned would list them on their website. It would be great if anyone could let me know how to find out the list of incoming students to a department for any year. Publication rate, taking into account the venues where they were accepted. Time taken to graduate - though I accept this is more dependent on the student, a median figure should be telling ... What they did post Ph.D. - did anyone get tenure if they went into academia, or is almost everyone unable to break out of being a post-doc?  Tenure status: I'm a bit unsure about this, so wanted the community's opinions about it. Just so that I'm clear, I'm only trying to calibrate the applicant's expectations about the working style of his potential adviser - and hence need to know to what extent are the following "typical" assumptions valid.  Tenured professor  A full professor is more likely to get grant funding, hence less time spent on TAship - but could also mean less time/effort spent on interactions with students (either being busy with other projects/talks, or due to more commitments to family at that age).  Tenure-track faculty (Assistant profs)  More likely to be young and energetic, and could translate to more time spent on one-to-one discussions with grad students - but funding may prove to be an issue, and may have to be on TA for a longer period.   What other factors would be relevant in this matter, and to what extent am I correct/incorrect in either the factors considered, or for undertaking this exercise at all? What is the difference between sourcing ('.' or 'source') and executing a file in bash?