I've read different places that talk about bias terms in neural nets like this    But I still have trouble understanding what it is used for and how it affects the neural network.  In a neural network, where would you place it? There can be hundreds of neurons, how do you know which one to link it to? And how many bias terms do you need? How do you know you need one?  Can anyone explain?
Why are bias nodes used in neural networks?  How many you should use?  In which layers you should use them: all hidden layers and the output layer?
List of functions not integrable in elementary terms When teaching integration to beginning calculus students I always tell them that some integrals are "impossible" (with a bit of expansion on what that actually means).  However I must admit that the examples I give mostly come from "folklore" or guesswork.  Can anyone point me to a list (not a complete list of course!) of fairly simple elementary functions whose antiderivatives are not elementary?  I'm thinking of things like $\exp(x^2)$ which is the standard example, $\sin(\exp(-x))$ perhaps, things like this, not hugely complicated formulae. After installing Windows 10 on my  it took my user name 'Jeremy' and created a user folder named C:\Users\jerem.  I want to rename the folder C:\Users\Jeremy.  does not work. There are a couple of reasons.   OneDrive is now a fully integrated part of the OS, and it completely breaks.  A find/replace in the registry seems to work, but it's hard to be confident in that approach. When the computer is rebooted, the TabletInputService writes a TextHarvester.dat file to the old user profile location (creating it if needed). This makes it impossible to keep the folder deleted. An old  doesn't work. This issue also causes an error message to pop up every time the computer boots. Problems installing xpatch I need to install the xpatch package to make changes to my biblatex setup. The readme file in the install package simply says to run “latex xpatch.ins.” I've moved the xpatch folder (including xpatch.ins and xpatch.dtx files) to the /usr/local/texlive/2011/../texmf-local/ folder. When I run the command above, I get the output Generating file(s) ./xpatch.sty  ! Cannot find file xpatch.dtx. \readsource ...ot find file \uptospace #1 \qStop }                                                   \else \processedLines \z@ ... l.34 ...xpatch.sty} {\from{xpatch.dtx} {package}}}   I've checked, and the .dtx file is in the folder. Any ideas what the problem is? How do I get the subscribers of an event? I need to copy the subscribers of one event to another event. Can I get the subscribers of an event (like MyEvent[0] returning a delegate)?  If this is not possible I would use the add accessor to add the delegates to a list. Would that be the best solution? "Is the same" or "are the same"? Which is the correct one?     On average, the polyunsaturated fat content in one teaspoon of the olive oil and canola oil is the same        On average, the polyunsaturated fat content in one teaspoon of the olive oil and canola oil are the same How to handle repeated references in footnotes? Do parts of a hash carry the properties of the entire hash? When I need to generate unique id's based on some information hashing is typical choice. However, sometimes that id needs to be of a particular size.  I've seen a lot of schemes (HMAC-MD5-96 in SSH, CGA in SeND for IPv6) that use a portion of a hash, so I'm thinking it might be alright to use it that way.    Which properties of a hash are preserved and which do not apply anymore?  Obviously, with less bits, the chance of collision goes up, but can I still rely on the partial hash for uniform character distribution?  What about the ?  I'm guessing that if a hash modifies the entire hash upon the smallest change to the input, that would imply that a portion of that hash would be equally well changed.  Am I thinking about this correctly?  Also, would these behaviors be different for different hashing algorithms? SEO preference: does a site with WWW rank better than without WWW? After having read various articles on this site about WWW or Non-WWW website setup, ,  and , and after having setup a correct redirection rule in .Htaccess to at least eliminate duplicate contents (currently the non-www solution (e.g. http://example.com) I have a feeling that my site rank less since I changed this.   My confusion was strengthened by these two opponents:     &amp;     Could the change of www.example.com >> http://example.com have a factual impact on ranking?  say either is better or worse. Are they holding information back?  I am confused fellow folks...  As much as I would like to separate facts from fiction, I am aware that not all the good valid information is written. Not on google webmaster site and perhaps not elsewhere. If so it seems out of date!  Does or does not a WWW domain impact SEO/rank better than its NON-WWW version? (Given that you have setup a proper redirect to avoid duplicates and go with one) Blender Cycles Bake Not Looking Like Object in Rendered View I have a couch in Blender that looks like this in rendered view.    I baked it with a combined texture and this is what it came out to be.    This is what it looks like added to the mesh.    Why does the view with the baked image not look exactly like the rendered view?  Does it have something to do with my mesh and faces?  This is my mesh.    This has never happened to me before as I baked a couple things before this which came out perfectly. I want to add a comma in the thousands place for a number.     String.Format()? TikZ: Named nodes in nested `pic`s I am using the new TikZ/PGF 3.0 pic feature.  I use them heavily, including using a pic inside another pic.  The problem is that Tikz sometimes cannot find the node names of nested pics.  I expect the following to work:  \documentclass{standalone} \usepackage{tikz} \usetikzlibrary{positioning} \begin{document} \begin{tikzpicture} \tikzset{complex/.pic={   \node(re) {re};   \node[right=0mm of re](im) {im}; }} \tikzset{su3v/.pic={   \path pic(c0) {complex};   \path pic[right=1mm of c0im](c1) {complex};   \path pic[right=1mm of c1im](c2) {complex}; }} \tikzset{spinor/.pic={   \path pic(v0) {su3v};   \path pic[below=2mm of v0c2re](v1) {su3v};   \path pic[below=2mm of v1c2re](v2) {su3v};   \path pic[below=2mm of v2c2re](v3) {su3v}; }}  \path pic {su3v};       % Works \path pic(name) {su3v}; % ! Package pgf Error: No shape named namec0im is known. \path pic {spinor};     % ! Package pgf Error: No shape named v0c1im is known. \end{tikzpicture} \end{document}   What is wrong here? Find a formula for a sequence $\{\sqrt{3},\sqrt{3\sqrt{3}},\sqrt{3\sqrt{3\sqrt{3}}},...\}$ There are some sections of tracks that allow you to deploy your hang glider or parachute.  This allows you to glide in relative safety until you hit the track again.  But you can also hit forward or back on the control stick to tilt down or up, respectively.  Is there an advantage to staying in the air?  Or does heading back down towards the track give you more speed than just gliding along? Google Chrome is my favorite browser, and I can't imagine going on without it. Suddenly (without closing and re-opening) the browser; chrome has been reading characters upside down, very weird:    Chrome version:    I tried restarting my browser and my MAC (running OS X Yosemite 10.10), but the error keeps on coming. We've never had an explicit policy around downvoting -- users are free to, if they like, cast all their votes as downvotes. Whether this behavior is desirable or not is another matter.   Now, we do discourage downvoting by making downvotes cost -1 rep to the casting voter. But, there's nothing in our policy that says continual downvoting is bad or wrong or inappropriate.  However, my thoughts on this are changing. I no longer think it is community friendly behavior to cast an extreme number of downvotes, and I am considering an explicit policy forbidding it.  Some data points (as of today):  Total SO upvotes cast: 45,555,530  Total downvotes cast: 365,192  users with more than 100 downvotes cast: 596  users with > 100 downvotes and the lowest ratio of upvotes to downvotes:           |           |         | up:down user id | downvotes | upvotes |  ratio --------+-----------+---------+---------  187712 |       201 |      37 |    0.18    2525 |       580 |     149 |    0.25  136829 |       137 |      43 |    0.31   55943 |       438 |     140 |    0.31   19405 |       236 |      94 |    0.39    5640 |      3299 |    1337 |    0.40  180659 |       126 |      66 |    0.52   78613 |       348 |     198 |    0.56   39892 |       181 |     109 |    0.60     432 |       310 |     197 |    0.63  238704 |       198 |     132 |    0.66   12643 |       170 |     116 |    0.68   18256 |       219 |     152 |    0.69  122428 |       167 |     118 |    0.70  118854 |       120 |      86 |    0.71  105662 |       273 |     201 |    0.73  187690 |       135 |     101 |    0.74    1782 |       573 |     430 |    0.75   (this is a complete list, there are no more below this threshold.)  Based on this data I am leaning towards enforcing a "no more downvotes may be cast" if    You have at least (n) votes cast total Your upvote to downvote ratio is lower than ~ 0.5 I have a SQL script that creates a package with a comment containing an ampersand (&amp;). When I run the script from SQL Plus, I am prompted to enter a substitute value for the string starting with &amp;. How do I disable this feature so that SQL Plus ignores the ampersand? Why are neural networks becoming deeper, but not wider? In recent years, convolutional neural networks (or perhaps deep neural networks in general) have become deeper and deeper, with state-of-the-art networks going from 7 layers () to 1000 layers ( in the space of 4 years. The reason behind the boost in performance from a deeper network, is that a more complex, non-linear function can be learned. Given sufficient training data, this enables the networks to more easily discriminate between different classes.  However, the trend seems to not have followed with the number of parameters in each layer. For example, the number of feature maps in the convolutional layers, or the number of nodes in the fully-connected layers, has remained roughly the same and is still relatively small in magnitude, despite the large increase in the number of layers. From my intuition though, it would seem that increasing the number of parameters per layer would give each layer a richer source of data from which to learn its non-linear function; but this idea seems to have been overlooked in favour of simply adding more layers, each with a small number of parameters.  So whilst networks have become "deeper", they have not become "wider". Why is this? How do I update Custom Label's value using apex? Which one would be a better option metadata api or tooling api? Please provide example I'am working on post deployment automation process in salesforce. I am stuck on how should I update values in custom labels which needs tobe updated manually after a sandbox refresh. Lisp Executable I've just started learning Lisp and I can't figure out how to compile and link lisp code to an executable.  I'm using clisp and clisp -c produces two files:   .fas .lib   What do I do next to get an executable? I have too many sections in my presentation such that the left-hand-side navigation bar is full and only shows the first sections in Fig. 2, initial situation in Fig. 1.  Pseudocode    clean the left-hand-hand side navigation bar when exceed the threshold and start a new one there when on sufficient page  this feature occurs with Beamer Berkeley appendix so it is possible also with the main document   Code which problem shown in Fig. 2   \documentclass{beamer} \usetheme{Berkeley}  \logo{\includegraphics{logo.png}} \usepackage{hyperref} % https://tex.stackexchange.com/a/346486/13173 \newenvironment{slide}[1] {\begin{frame}[environment=slide,allowframebreaks] \frametitle{\insertsection-#1} } {\end{frame}} % fragile only if code % allowframebreaks not by default   \begin{document}  \title{Sensory system. Primary sensory modalities. Cortical modalities. Kinds of sensory disturbances. Spinal cord disorders. Spinal cord transverse and partial lesion. Cauda equina damage.} \author{Leo}  \section{Cortical modalities} \begin{slide}{basics}      More refined aspects of sensation ... \end{slide}  \section{Cortical modalities} \begin{slide}{basics}      More refined aspects of sensation ... \end{slide}  \section{Cortical modalities 2} \begin{slide}{basics}      More refined aspects of sensation ... \end{slide}  \section{Cortical modalities 3} \begin{slide}{basics}      More refined aspects of sensation ... \end{slide}  \section{Cortical modalities 4} \begin{slide}{basics}      More refined aspects of sensation ... \end{slide}  \end{document}   Fig. 1 Situation at the first page,  Fig. 2 Situation at Section 6 wheere the navbar has not changed,  Fig. 3 Samcarter's answer output + one slide addition but without \part{} - fails on sufficient page count       Output: the left-hand-side navigation bar is not refreshed when the amount of sections exceed its capacity on suffcient enough page     Testing Samcarter's proposal  I include one slide before Samcarter's body so I get the wrong output in Fig. 3.  Solution: Eventually correct output by just adding \part{} in the place where the new navbar is wanted.   TeXLive: 2016 OS: Debian 8.7