Positional parameters question
how to loop through arguments in a bash script
A gerund or use a regular noun? Which of these is correct or more natural?        One of my greatest strengths is critically analyzing.      One of my greatest strengths is critical analyzing.     One of my greatest strengths is critical analysis. So from what I understand transistors are one of the most important electronic elements for computers because of TTL (Transistors-Transistors Logic).  Is this true? If so, how exactly does this work? I have heard the terms "logic gate" and "logic block" tossed around. As the title says. How do I get from  $\frac{n}{\varphi(n)}$ to $\sum\limits_{d \mid n} \frac{\mu^2(d)}{\varphi(d)}$?  I know that $$\frac{n}{\varphi(n)}=\frac{\sum\limits_{d \mid n} \varphi(d)}{\sum\limits_{d \mid n} \mu(d)\frac{n}{d}},$$ and I suspect it is down this road I should go. But I get totally confused by the sums and I have no clue on how to divide them and "combine" them into one again. Any hints or advice would be much appreciated. evaluate the limit as $x$ approaches $0$ of $(\cos x-1)/x$ without l'Hopital's rule I know with l'Hopital's rule it becomes $-\sin(x)$ which has the limit $0$. However, I have been wondering how to evaluate this limit without l'Hopital's rule. Could Tom Bombadil have defeated Sauron? Why does the loss/accuracy fluctuate during the training? (Keras, LSTM) Incorrect bookmarks and page number in table of contents I have problem with table of contents and with bookmarks. In pdf file   table of contents shows wrong page number of Introduction and Bibliography, Bookmarks: introduction and bibliography don't bring me to the correct page.   Part of my code  \documentclass[12pt,a4paper]{book}  \usepackage[polish]{babel} \usepackage{polski} \usepackage[cp1250]{inputenc} \usepackage[pdftex,pagebackref=false,draft=false,pdfpagelabels=false,pdfstartview=FitH,pdfstartpage=1,bookmarks=true,pdfauthor={LiN},pdftitle={PD},pdfsubject={Titlei},pdfkeywords={words},unicode=true]{hyperref}  \usepackage{tocloft}  \begin{document} \tableofcontents \addcontentsline{toc}{chapter}{Introduction} \chapter*{Introduction} \chapter{Chapter1} \section{Section} \addcontentsline{toc}{chapter}{Bibliography} \begin{thebibliography}{9999999}% \bibitem{1}Author, \emph{Title of book}, Publisher. \end{thebibliography} \end{document}   How can I change that? How can I remove a suggestion from the Chrome address bar? I've got a couple of URL autocomplete suggestions where Chrome suggests the wrong URL consistently.   How can I delete the incorrect entry from the address bar's suggestion list? The page I want shows up too but it's never the first result. Why do I not see evidence of discrete energy in the spectrum? The electromagnet spectrum looks to be continuous, yet energy is discrete. Shouldn't one see evidence of the electron's "quantum leap"? What's going on?     Moderator, please size my photo. Thank you. "Access denied" when trying to end a process on Windows 8 Most common method for deciding when to stop training a neural net on a batch I have created my own neural net which is using batch gradient descent. In other words, it trains on batches of examples all at once.  My issue is trying to figure out when to stop the training of the batch. I'll try to make things as understandable as possible since there are so many options, but please comment if you need clarification.  Each batch allows me to compute a list of output errors that correspond to the error the computer has on each example. Each error is a vector with elements equal to the number of output neurons.  Let each error vector be notated by e1, e2, e3, ... so the list of output errors is [e1, e2, ...]. Let an error vector in general be notated by e.  Now there are 2 things we can do to a vector or a list:   Average: average all of the elements in a vector or list. This will be notated by the function a(). For example to find the average error of an example we would do a(e) Check: make sure that each element in the vector or list is below a certain value. If any of the elements are too high, we continue to train on the entire batch. (This function can also be applied to a single value.) This will be notated by the function c(). For example, if we wanted to make sure the average error in e was low enough, we would do c(a(e)) Sum: add up all of the elements in the vector or list. This will be notated by the function s(). For example, s(e) would be totaling the error found in error vector e.   Here are the methods I have determined for deciding when to stop gradient descent:   Iterative: just run the training a certain number of times Average of averages: Find the average error of each example, then find the average of those and make sure it's below a certain amount. This is given by the formula c(a([a(e1), a(e2), ...])) Specific error: Check to make sure the error in each output neuron is below a certain amount. This is given by the formula c(e1), c(e2), ... Specific averages: Check to make sure the average error in each example is below a certain amount. This is given by the formula c([a(e1), a(e2), ...]) Sum of sums: Total up all the error in the entire batch and then make sure it's low enough. This is given by the formula c(s([s(e1), s(e2), ...]) Sum of averages: Find the average error of each example, then add up all those and make sure it's below a certain amount. This is given by the formula c(s([a(e1), a(e2), ...])) Average of sums: Compute the average total error in each example, and then make sure it's below a certain amount. This is given by the formula c(a([s(e1), s(e2), ...])) Specific sums: Check to make sure the total of the error in each example is below a certain amount. This is given by the formula c([s(e1), s(e2), ...])   So my question is this:  Which one of these options is most commonly used when training neural nets? Why? (Is there another option that I've missed?)  (Edit: I have found a very general version of this question , where the answers seem to say there is no specifically good way. If that is still true, please say so in your answer. Note that this is not a duplicate, as I explain the specific methods I would like to use.)  Edit: as A.D pointed out, summing is pretty useless because it depends on how many values are in each list/array/batch. And if you know how many examples there are, you can just use averaging. So, the methods involving "summing" have been cut. Degree of Field Extensions and $F(\alpha)$ Suppose that $[F(\alpha):F]$ is odd. Show that $F(\alpha)=F(\alpha^{2})$. Generalize this statement if possible.    Clearly, we always have that $F(\alpha^{2}) \subset F(\alpha)$ by definition of the field generated by $F$ and $\alpha$ (assuming that we have a field extension $K/F$ where $\alpha \in K$). However, how can we show the other inclusion? If the degree is odd, then it follows that $\alpha$ will solve a polynomial of odd degree in $K[x]$ (for the coefficients in $F$). What would be a way to proceed from here? (and as well to generalize the statement?)  I was thinking of using the formula: $[F(\alpha):F]=[F(\alpha):F(\alpha^{2})][F(\alpha^{2}):F]$ and maybe proceed from there.   Thanks for the help. "put X down to" vs. "put down X to": subjects of verbs with two particles I expect I would have to put down many coats to do the job. ()   One factor to distinguish phrasal verbs from prepositional verbs is particle movement. Phrasal verbs can place the particle before or after direct object, whereas the preposition in prepositional verbs must precede the noun. (Biber et al. 1999)    So, I'm confused when analyzing the fragment "put down many coats to" because I'm not able to distinguish whether "put ... " is a phrasal verb or a prepositional verb. The confusion arises when I read in the Oxford Dictionary of English, under 'put' &rarr; 'phrasal verb', the form "put something down to" is correct.  So, the above sentence would be rewritten as follows :     I expect I would have to put many coats down to do the job.   Am I right? If not, how do I correctly distinguish phrasal verbs from prepositional verbs in the cases, like this one, where there are two particles (in this case 'down' and 'to')? There was a post this morning asking about how many people disable JavaScript. Then I began to wonder what techniques might be used to determine if the user has it disabled.   Does anyone know of some short/simple ways to detect if JavaScript is disabled? My intention is to give a warning that the site is not able to function properly without the browser having JS enabled.   Eventually I would want to redirect them to content that is able to work in the absence of JS, but I need this detection as a placeholder to start. I find myself needing to draw lots of elegantly curved paths in TikZ. Ideally, I'd just specify a series of points, and TikZ would calculate the extra data itself to draw a nice series of curves passing smoothly through these points, perhaps with an optional "looseness" parameter that I could specify. But the only way I can find to draw nice curves is by explicitly giving control points, or by manually specifying in and out angles.  I can think up a simple algorithm to do this, which would certainly be within TikZ's power to perform: just choose the in and out angles in a simple fashion based on the relative angles between each adjacent pair of line segments.  Is something like this already built-in? Or can someone cook something up that does the job?  Edit: Jake has provided an answer using the plot [smooth] functionality. This is almost perfect! But it can't do what I need, because it doesn't let me specify tangent angles manually where needed, which is especially important at the beginning and end of the curve. I would have thought this would be a natural and straightforward addition to the existing plot [smooth] algorithm: for every coordinate, an optional angle should be able to be specified as an argument, which if supplied is treated as the tangent angle for the curve at that point. And while we're at it, it wouldn't hurt to also allow the tension to be modified along the path.  A minimal extension to the algorithm would just accept two optional parameters, for the curve tangent at the beginning and end. Why doesn't PHP DOM include slash on self closing tags? Pretty printing XML with javascript What limits a motherboard from supporting more memory? My specific question is with the ASUS M3N78-VM motherboard that my home server uses. I currently have 4x2GB installed for a total of 8GB but I was hoping to upgrade to say 16GB (4x4GB). The official specifications of that motherboard says it only supports up to 8GB but it was released back when only 2GB sticks were available. What, if any, would prevent it from working with 4GB sticks now that 4GB sticks are available?  My general question is with motherboards in general... what would prevent a motherboard from working with bigger sticks if its all just the same type (DDR2 for example and same speeds) of memory? Let $M$ be a smooth manifold and let $N$ be a manifold with boundary. If $dF_{p}$ is an isomorphism, then $F\left(p\right)\in\mbox{int}M $. Service not avaliable Unity3d error in Kubuntu I'm trying to use  in Kubuntu, but I'm getting this error:  Service not avaliable, please try again later.   I've found :  Certain systems may experience "Service unavailable" errors when trying to log in. WORKAROUND: Launch Unity with LD_PRELOAD=/usr/lib/libresolv.so.2 /path/to/Unity (check the path to your local libresolv)   I've checked the path of libresolv.so.2 in my computer. I found it under /lib32/libresolv.so.2 and under /libx32/libresolv.so.2. (Don't know what the difference is).  When I run:  LD_PRELOAD=/lib32/libresolv.so.2 /opt/Unity/Editor/Unity   I get:  ERROR: ld.so: object '/lib32/libresolv.so.2' from LD_PRELOAD cannot be preloaded (wrong ELF class: ELFCLASS32): ignored.   and when I run:   LD_PRELOAD=/libx32/libresolv.so.2 /opt/Unity/Editor/Unity   I get:   ERROR: ld.so: object '/libx32/libresolv.so.2' from LD_PRELOAD cannot be preloaded (cannot open shared object file): ignored.   With both commands I also get this:  /opt/Unity/Editor/Unity: /opt/Unity/Editor/Data/Tools/libgpg-error.so.0: no version information available (required by /lib/x86_64-linux-gnu/libgcrypt.so.20)   Any suggestion?