Sum or average of gradients in (mini) batch gradient decent?
Mean or sum of gradients for weight updates in SGD
How can I capitalize the first letter of each word in a string in Perl? polynomial converges uniformily to analytic function How to render world position pass I am trying to learn how to find the product of non-disjoint cycles, as you may have guessed from the title. I have the basic idea, but I do not understand it entirely.  I am trying to find $(1352)(256)$ and $(1634)(1352)$, multiplying from right to left.  Please give me some hints/suggestions.  Thank you. Schengen Visa Expiration I have a multiple entry 90 days Schengen visa (category C) from 15 March 2014 till 21 Dec 2014.    With this visa I entered The Netherlands on 4 April 2014 and left there on 13 April 2014.    I am planning to re-enter The Netherlands on 19 Dec 2014 and leave there for London (I have a valid UK visa as well) on 21 Dec 2014, at 7 am from Amsterdam.    Am I permitted to stay in The Netherlands on 21 Dec 2014 or should I leave the country on 20 Dec evening itself? Why is the Java plugin (JRE) disabled in Chrome? In some cases, questions and answers that have been deleted are still showing up on /review pages. They do not have "Improve" buttons, but they can still be approved or rejected. I'm not sure what causes a post to end up in this limbo state instead of being removed from the queue entirely, which I think is what's supposed to happen.  The suggested edit I noticed this on was , but it just leads to a "Page Not Found" message now.  Tim Stone provided the following screenshot of another instance : Why doesn't backpropagation work when you initialize all the weight the same value (say 0.5), but works fine when given random numbers?   Shouldn't the algorithm calculate the error and work from there, despite the fact that the weights are initially the same? I know that if the moment generating function of two distribution converges to the same function then the two distribution converges in CDF. But how can we prove this thing explicitly ? I'm Swedish, but living in Switzerland at the moment. Can I open a US bank account? Either when in the US on vacation or through the internet/phone?  There are lots of situations when I find myself in need of an american credit card or just a bank account. When ordering things online (most retailers refuse to accept my orders if I try to pay with my Swedish or Swiss credit card, even if I ship it to an US address... ) etc etc. Add source to figure caption How can I add a source to a figure? I need to add \ref, \cite or just free text. Something like that: \begin{figure} [ht]   \centering   \includegraphics[width=0.95\textwidth]{res/figure.pdf}     \caption{Caption}     \source{\ref{},\cite{} or free Text}   \label{fig:gliederung} \end{figure}  Should give me:  The source shouldn't appear in \listoffigures. If $f:U\to V$ is holomorphic and $f'(z)\neq 0$ for all $z\in U$, then$f$ is locally bijective. I am trying to solve the following problem:     Let $f:U\to V$ be a holomorphic function such that $f'(z)\neq 0$ for all $z\in U$. Show that for all $z_0\in U$, there exists a disc $D_\varepsilon(z_0)\subseteq U$ such that $f:D_\varepsilon(z_0)\to f(D_\varepsilon(z_0))$ is bijective.   Atempt:  I am trying to use Rouche's Theorem, but I am stuck on a particular step. Let $z_0\in U$. Since $f'(z_0)\neq 0$, there is a disc $D_r(z_0)\subseteq U$ such that $$f(z)=f(z_0)+(z-z_0)h(z),\quad\forall z\in D_r(z_0)$$ where $h$ is holomorphic on $D_r(z_0)$ and $h(z)\neq 0$ for all $z\in D_r(z_0)$.   Let $0&lt;\varepsilon&lt;r$ to be defined later and fix $w\in D_\varepsilon(z_0)$. To show that $f$ is injective in $D_\varepsilon(z_0)$ is to show that the function $f(z)-f(w)$ has exactly one zero in $D_\varepsilon(z_0)$. But $$F(z):=(z-z_0)h(z)$$ has exactly one zero in $D_\varepsilon(z_0)$, so we might want to apply Rouche's Theorem with $F$ and $$G(z):=f(z)-f(w)-(z-z_0)h(z)=f(z_0)-f(w)=-(w-z_0)h(w)$$ to conclude that $F$ and $F+G$ have the same number of zeros and hence $f$ is injective. But that means that we need to find $0&lt;\varepsilon&lt;r$ such that $|G(z)|&lt;|F(z)|$ on $\partial D_\varepsilon(z_0)$. That is, $$|w-z_0||h(w)|&lt;|z-z_0||h(z)|$$ for all $w\in D_\varepsilon(z_0)$ and $z\in\partial D_\varepsilon(z_0)$.  Can we find such $\varepsilon&gt;0$?  It seems intuitive since if we expand $h$ in a power series at $z_0$, $h(z)=\sum_{n=0}^\infty a_n(z-z_0)^n$, then $$|w-z_0||h(w)| = |w-z_0|\sum_{n=0}^\infty a_n|w-z_0|^n &lt; |z-z_0|\sum_{n=0}^\infty a_n|z-z_0|^n.$$ for $w\in D_\varepsilon(z_0)$ and $z\in\partial D_\varepsilon(z_0)$. But this is of course not a proof. Can someone please explain this weird Pygame importing convention? Must an ideal contain the kernel for its image to be an ideal? Trying to install ubuntu on a laptop. The "bios/uefi" has no uefi boot options &amp; the windows boot manager just kicks in. The only "option" is "boot from hard disk". So we tried to use efibootmgr to put grub to boot first.  When we run an efibootmgr -o xxxx,xxxx,xxxx command it seems like the order gets fixed but on reboot the windows boot manager still has control, then when we re-opened the live usb &amp; checked the boot order it remains unaffected.  What are other ways to change the efi boot order? Maybe by mounting the efi partition (in mnt) and doing what? How to Hide sections of InfoPath form based on Group membership I need to Hide "Sections" of InfoPath form using SharePoint or AD group membership (either is fine). How can I achieve this?  InfoPath 2010 in SharePoint 2010 Prove that the derivative of $x^w$ is $w x^{w-1}$ for real $w$ Can anyone give a proof of the derivative of this type of function? Specifically showing that  $\dfrac{d(x^w)}{dx} = wx^{w-1}$ for a real $w$?  I tried to use the Taylor series expansion for $(x+dx)^w$ and got the correct result. However, the proof of the Taylor series requires knowledge of the derivative of these functions. So this is essentially circular reasoning. I know that the same series is also given by the binomial expansion, but that's not entirely satisfactory either, because where's the proof that the binomial expansion works for all reals (isn't it only apparent for integers)? So far all of the arguments I've come across involve circular reasoning. I was thinking of showing that the binomial expansion is true for all reals using some form of proof by induction e.g. something like this.  I'm really not sure. Video grid with vstack and hstack Prove that equation has exactly 2 solutions I am a n00b to physics. What physics I know comes from high school and popular science books.  At school we were taught about atoms and what make up atoms, but we weren't actually told what the particles were!  So sure an atom has electrons orbiting around a nucleus made of protons and neutrons, but what exactly is an ?  And if we don't know, how can we fire them from guns, like they do in experiments ... etc  Any clarification on this would be great.