I wanted to ask if there are any free render farms. I tried to find one but I couldn’t. If anyone finds a “free” render farms pls tell me.
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I have attempted a proof of this, but upon looking at my notes, I feel it might be incorrect: it is noticeably simpler than the one in my notes.  Proposition: any permutation in $S_n$ can be written as a product of disjoint cycles.  Proof (attempt): $s\in S_n$. Let $\langle s\rangle$ act on $X=\{1,\cdots,n\}$. Define $x\sim x'\iff x'\in\text{Orb}(x)$ for $x,x'\in X:$ this is clearly an equivalent relation, hence the orbits partition $X$. Each orbit corresponds a cycle in $s$, so we are done.  Does this hold, or have I missed something vital? Roll a 6-sided die until the total $\geq M$. Mean amount by which $M$ is exceeded? Here is the question:  You roll a fair 6-sided dice iteratively until the sum of the dice rolls is greater than or equal to M. What is the mean and standard deviation of the sum minus M when M=300?  Should I write a code to answer these kind of questions?  Please give me some hints on that. thanks! Is the product of two non-holomorphic function always non-holomorphic? Suppose $h(z)$ is a complex function. I have noticed that $h(z) = f(z)\cdot g(z)$, where $f(z)$ and $g(z)$ are non-holomorphic. Can $h(z)$ be holomorphic?   Can a similar statement be made, if $f(z)$ is holomorphic, but $g(z)$ is not? Cycles not rendering with background image What's the main difference between Intel processor generations? What are the main differences between each processor generation of Intel processors/chipsets? Is there a performance difference?  I've already seen processors from first to sixth generation, however I don't know/understand the exact differences. How to find out why "context is incorrect"? I have been trying to write my first addon for Blender over the last couple of days. One error I came across quite often is the context is incorrect error for an operation of bpy.ops.  I learned that one can ask the poll function of an operator if the context is correct, but this does not tell why the context is correct/incorrect. What would be the best way to figure that out? Only way I could think of is to look into the code of the poll function. If that is the best way, what is the fastest way to find the appropriate piece of code? How to render from Eevee in Blender 2.8? I have the Blender 2.8 version from the 21st Sep 2018 I was looking forward to render a test sequence but cannot find a render button anywhere? Does anyone know where to find it? There is an option to filter only one color (R,G,B,Y) in my camera. What I want to know is can this effect be achieved in photoshop? And what is this called? I tried googling monochrome and came up with nothing. My camera calls it part color. Err http://archive.canonical.com natty InRelease     Err http://security.ubuntu.com oneiric-security InRelease                Err http://extras.ubuntu.com natty InRelease                             Err http://security.ubuntu.com oneiric-security Release.gpg   Temporary failure resolving ‘security.ubuntu.com’ Err http://archive.canonical.com natty Release.gpg   Temporary failure resolving ‘archive.canonical.com’ Err http://extras.ubuntu.com natty Release.gpg   Temporary failure resolving ‘extras.ubuntu.com’ Err http://gb.archive.ubuntu.com oneiric InRelease Err http://gb.archive.ubuntu.com oneiric-updates InRelease Err http://gb.archive.ubuntu.com natty-backports InRelease Err http://gb.archive.ubuntu.com oneiric Release.gpg   Temporary failure resolving ‘gb.archive.ubuntu.com’ Err http://gb.archive.ubuntu.com oneiric-updates Release.gpg   Temporary failure resolving ‘gb.archive.ubuntu.com’ Err http://gb.archive.ubuntu.com natty-backports Release.gpg   Temporary failure resolving ‘gb.archive.ubuntu.com’  Reading package lists... Done W: Failed to fetch http://gb.archive.ubuntu.com/ubuntu/dists/oneiric/InRelease       W: Failed to fetch http://gb.archive.ubuntu.com/ubuntu/dists/oneiric-updates/InRelease   W: Failed to fetch http://gb.archive.ubuntu.com/ubuntu/dists/natty-backports/InRelease   W: Failed to fetch http://security.ubuntu.com/ubuntu/dists/oneiric-security/InRelease   W: Failed to fetch http://archive.canonical.com/ubuntu/dists/natty/InRelease   W: Failed to fetch http://extras.ubuntu.com/ubuntu/dists/natty/InRelease   W: Failed to fetch http://archive.canonical.com/ubuntu/dists/natty/Release.gpg  Temporary failure resolving ‘archive.canonical.com’ W: Failed to fetch http://security.ubuntu.com/ubuntu/dists/oneiric-security/Release.gpg  Temporary failure resolving ‘security.ubuntu.com’ W: Failed to fetch http://extras.ubuntu.com/ubuntu/dists/natty/Release.gpg  Temporary failure resolving ‘extras.ubuntu.com’ W: Failed to fetch http://gb.archive.ubuntu.com/ubuntu/dists/oneiric/Release.gpg  Temporary failure resolving ‘gb.archive.ubuntu.com’ W: Failed to fetch http://gb.archive.ubuntu.com/ubuntu/dists/oneiric-updates/Release.gpg  Temporary failure resolving ‘gb.archive.ubuntu.com’ W: Failed to fetch http://gb.archive.ubuntu.com/ubuntu/dists/natty-backports/Release.gpg  Temporary failure resolving ‘gb.archive.ubuntu.com’ W: Some index files failed to download. They have been ignored, or old ones used instead.   This is what I'm seeing when I try to run sudo apt-get update. I did an update on my instance yesterday and am now experiencing this. Can a Half-Elf have Drow Ancestry? Why I cannot unpin some directories from file explorer in windows 10 Consecutively Adding Sines One thing, I'm not a mathematician so please be patient. I am still in Algebra II Trig. Leading with that, why does  $$ x_0 = \sin 1, \space  x_1 = x_0 + \sin x_0, \space x_2 = x_1 + \sin x_1 ... $$ and after a while, $$ x = \pi $$  I know this to be true because I have evaluated this on my TI-84 and more deeply evaluated it with this program I made:   To $100000$ Iterations (which I believe is enough)   So what's the math behind it? Why does adding $\sin 1$ in this manner produce $\pi$? Why doesn't doing the same thing using $100$ produce $\pi$? For example,  $$\sin(1) = 0.841470...,\space \sin(1) + \sin(0.8414...), \sin(1) + \sin(0.841470...) + \sin(1.587095126...),\space ... $$ $$ = \pi$$  My question is different from the mentioned because my function is not taking the sin of a sin consecutively, but is this following function: $f(x) = x + \sin x$ and is not $f(x) = \sin x$ and therefore can exhibit different properties I need explained. How should I use quotation marks in sections of multiline dialogue? If I want to introduce a “pause” between lines of dialogue from the same person by inserting a spacing line, how should I use the quotation marks correctly to indicate continued dialogue? I really don’t want to write it in a gossipy “he said, she said” way!  I have noticed that closing quotations aren’t always placed on the end of a line.  What are the rules? i install ubuntu and followed a guide to put 20gb in '/' and the rest (150gb) in '/home'. Now i just found out that a lot of the things installed in ubuntu usually goes to '/' instead of '/home'. I have a lot more things to install.  So what is the point of '/home' ? How do I fix this ? Should I transfer 150gb from '/home' to / ?  Filesystem      Size  Used Avail Use% Mounted on udev            7.8G     0  7.8G   0% /dev tmpfs           1.6G  9.5M  1.6G   1% /run /dev/sda6        19G   16G  1.8G  91% / tmpfs           7.8G  676K  7.8G   1% /dev/shm tmpfs           5.0M  4.0K  5.0M   1% /run/lock tmpfs           7.8G     0  7.8G   0% /sys/fs/cgroup /dev/sda2        96M   29M   68M  31% /boot/efi /dev/sda8       159G  1.1G  150G   1% /home tmpfs           1.6G   56K  1.6G   1% /run/user/1000   what is /boot ? Its not '/' or '/home' How do I get attention for one of my own questions without a good answer? XGBoost Loss function Approximation With Taylor Expansion As an example, take the objective function of the XGBoost model on the $t$'th iteration:  $$\mathcal{L}^{(t)}=\sum_{i=1}^n\ell(y_i,\hat{y}_i^{(t-1)}+f_t(\mathbf{x}_i))+\Omega(f_t)$$  where $\ell$ is the loss function, $f_t$ is the $t$'th tree output and $\Omega$ is the regularization. One of the (many) key steps for fast calculation is the approximation:  $$\mathcal{L}^{(t)}\approx \sum_{i=1}^n\ell(y_i,\hat{y}_i^{(t-1)})+g_tf_t(\mathbf{x}_i)+\frac{1}{2}h_if_t^2(\mathbf{x}_i)+\Omega(f_t),$$  where $g_i$ and $h_i$ are the first and second derivatives of the loss function.   What I'm asking for is convincing arguments to demystify why the above approximation works:  1) How does XGBoost with the above approximation compare to XGBoost with the full objective function? What potentially interesting, higher-order behavior is lost in the approximation?  2) It's a bit hard to visualize (and depends on the loss function) but, if the loss function has a large cubic component, then the approximation will likely fail. How is it that this doesn't cause problems for XGBoost? How to intuitively understand eigenvalue and eigenvector? I want to derive a closed formula for the integral $$I_n= \int \frac {dx}{\prod_{r=0}^n (x+r)}$$  On writing out first few terms we get   For $n=0$, $$I_0=\ln \vert x\vert+C$$ For $n=1$, $$I_1=\ln \vert x\vert-\ln \vert x+1\vert+C$$ For $n=2$ $$I_2=\frac {1}{2!}\left(\sum_{r=0}^2 (-1)^r\binom {2}{r} \ln \vert x+r\vert\right)+C$$ For $n=3$ $$I_3=\frac {1}{3!}\left(\sum_{r=0}^3 (-1)^r\binom {3}{r} \ln \vert x+r\vert\right)+C$$  Hence for generalized $n$ we have $$I_n=\frac {1}{n!}\left(\sum_{r=0}^n (-1)^r\binom {n}{r} (\ln \vert x+r\vert)\right)+C$$  Now this is just an observation but I want to prove that it is correct. I have tried lot of methods but not useful. Partial fractions would have been most useful but would go out on tedious task which is nearly impossible.  Also integration by parts won't help nor any trig substitution. So any ideas are welcome.  And ya,  this is not a homework question,  it's a question which I just saw in a integral challenge paper. I have a simple one line command which works perfectly in terminal, but does not work in the "Startup Applications" app thing.  The line of code is : xmodmap /home/seph/Code/Ubuntu\ Scripts/Xmodmap  It's not that much of a hassle to copy it from "Startup Applications" and paste it into terminal, but I don't really get why it isn't working.  I followed someone else's instructions to do it in the first place, so maybe I did something wrong?  In any case, wouldn't it be the obvious and logical assumption that it just types whatever you put in it into Terminal? There are a few "automatically protect questions" requests out there, but I'd like to add another twist.  I'd like to request that questions that have three or more deleted answers by users with &lt;50 rep be automatically protected.  The reasoning behind this is that we have lots and lots of "not an answer" flags in the mod queue.  But we cannot protect a question from the mod queue, so we have to open each answer, evaluate if the question needs protecting, then protect it.    This process takes a long time, and can definitely be automated, as the only thing you really need to check is how many new users are posting non-answers or are spamming their awful products.