I understand the principle of image convolution. Maybe. I think it is this:  You use a small matrix with numbers in it,  Then take a sample of an image with as many pixels as you have numbers in your matrix,  Then do a dot product, then add up all the terms and   then use the result as the new value for the pixel located in the center of your image sample.  Now, my question is this:  Does it make sense to think about an image kernel for convolution whose values actually depend on the image? For example, consider a 'sharpen' kernel:   0  1  0  1  4  1 0  1  0   I want to change the value in the center to be a number between 1 and 5 depending on the brightness of the pixel which is two places to the left.  The reason I ask this is because I've noticed that when I look at an image, I actually look at 'neighborhoods'. not just individual pixels. While bright spots might catch my attention. I recognize parts of an image before it 'clicks'. So if I am using some parts of an image to inform me about the 'neighborhood' that part lives in, I am wondering if this sort of 'dynamic kernel' could produce a matrix that informs us more meaningfully about the image. Obviously I am naive and know very little about image processing but a lot of papers on image convolution get technical very fast and then I'm lost. I am afraid to ask this on stack overflow because there is no specific code I am asking about..  EDIT: The link you posted does not have any mention of the signal processing site. As the question has no specific coding it is therefore not a question for stack overflow. Whether it belongs in math, signal processing or other section is not immediately obvious to a neophyte. I appreciate the recommendation to post on signal processing.
There seems to be more than a few computer science/programming Stack Exchange networks (is that the correct term?). Stack Overflow, being the first, has by far the most users, questions, and answers.  What is the reasoning for creating the others, and are there clear guidelines for which kinds of questions should be posted? I can see a large amount of potential overflow, many cases of people not getting a good answer to their question, because the person who has the answer isn't browsing that particular network at the moment.  I understand that they were probably created for organizational purposes, but wouldn't it almost make more sense to just have them as categories under Stack Overflow, keep them separated but still connected, instead of making people have to create multiple 'account's, one for each network?  I am sure there was a very good reason to break them up, but as someone that is new to SE, it can be somewhat intimidating to decide which one to post in to ensure you get a good answer. For example, if I am a computer science student, my first instinct might to be to post in the computer science network, until I see that it literally has 1% of the users as the Stack Overflow network, which still seems to be for programming/computer science related questions.  So my second instinct would then to be to post it into the Stack&nbsp;Overflow site on the basis that I have a significantly higher chance of my question being seen and getting a good answer. Then I notice that there is also a 'programmers' network, and I don't even begin to know where that fits in. I, and I am assuming most people, will probably just post on Stack&nbsp;Overflow to be safe.  My question is, other than the short little description blurb of each one, is there a clear cut set of guidelines which what each network is intended for, what kinds of questions should go to each one, and is anything being done to encourage people to post in these newer, smaller (more specialized?) networks as opposed to just posting in big daddy Stack Overflow?  Now again, this is for computer science/programming/"why isn't this code doing what I want?" related questions, I am not saying that if I had a question about Linux or WordPress or something I would have the same confusion.
xcode4 doesn't support Perforce? Microbot Alpha says "All of your minions are considered Microbots."  Does this mean while this card is in play, every single minion in play and in discard and in my hand are considered Microbots?   For every Microbot Fixer in play, does every single minion I have in play now get +1 because they are all microbots? If Microbot Archive is in play, does every single minion I have now cause me to draw a card when destroyed? If I play Microbot Reclaimer, can I shuffle any minions from my discard pile into my deck (by considering them all microbots)?   It looks like this link addresses the first item above:   And it looks like this link addresses the 3rd item, implying that minions in the discard are not minions because they are out of play: Is it the case that for all sets $A, B, C,$ and $D$, $(A \times B) \cup (C \times D) = (A \cup B) \times (C \cup D)$? I think I have managed to work this out, however there is no solution provided with the question so I thought it best to check.   My working:  Let $(x,y) \in (A \times B) \cup (C \times D)$  $\Rightarrow x \in (A$ or $C)$ and $y \in (B$ or $D)$  $\Rightarrow (x, y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow (A \times B) \cup (C \times D) \subseteq (A \cup C) \times (B \cup D)$  Now let $(x,y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow x \in (A$ or $C) $ and $y \in (B$ or $D)$  $\Rightarrow (x, y ) \in (A \times B) \cup (A \times D) \cup (C \times B) \cup (C \times D)$  $\Rightarrow (A \cup C) \times (B \cup D) \nsubseteq (A \times B) \cup (C \times D)$  $\Rightarrow (A \times B) \cup (C \times D) \not= (A \cup C) \times (B \cup D)$  Is this correct?  Thank you. Is there an official rule that the minimum damage can't be negative? A slightly humorous thought occurred to me (a recovering rules lawyer) after reading .     "None of the answers actually specify that 0 is the minimum damage."   Logically it wouldn't make sense for an attack to apply negative damage or healing, except in specific cases like hitting a flame elemental with a fire attack. Ruling that you could do negative damage would lead to an exploit to avoid costs of healing. As such I highly doubt any DM would make such a ruling. I definitely wouldn't except for the most absurd and humorous of games were failure is the expected result not success.  Another possibility (as suggested by Secespitus) is that negative damage would reflect back on the attacker. This could be seen as punching a strongman so hard (or in just the wrong way) as to injure your own hand.  This would also play well in a failure is the only option game, and if there is a rule suggesting that it would be an appropriate answer to this question as well.  Take the case of a person with less than 8 Strength, no levels in monk, and does not have a tavern brawler.  Would they do -1(1 - 2) damage on unarmed strikes? If so what would the result of the negative damage be?   "Healing" the target because such a puny hit actually raises their fighting spirits and makes them more capable of fighting Reflective Damage, the attacker actually takes 1 point of damage, representing injury to his hand or other damage   I am curious to know if there is an official rule stating that the minimum damage an attack can do is 0 or is there something in the damage calculation that I am missing that would otherwise prevent negative damage? Puzzle: Find largest rectangle (maximal rectangle problem) Is there an equivalent of MATLAB's Workspace window in Mathematica? Workflow for developing add-on/script I'm trying to figure out a good workflow for developing scripts and add-ons in Blender. Here's what I'm currently doing as I try my luck with a PyNode add-on:   Open blender Create a text editor panel Open my script (external text file) Edit my script in a nice external editor Reload the script Save the .blend file Run the script   Now that I can see what my code does, this Blender instance has been modified, so I can't (make changes to my script and) run my script again. So I do this:   Close blender Open blender with the .blend from step 6 and repeat steps 4-7, over and over and over..   Is there a better workflow for this sort of thing? What do you call someone who is supported? Synonym for a supportee (Which doesn't seem to be a word)?  I created products that retail and we sell them and give the proceeds to charities. Trying to figure out a single word to use as a page title for those that we support were we can list the charities (With their permission of course).  Thanks I believe there are several ways to prove that $\sum\limits^{\infty}_{n=1}\left(1-\frac{1}{\sqrt{n}}\right)^n$ converges. Can you, please, post yours so that we can learn from you?  HERE IS ONE   Let $n\in\Bbb{N}$ be fixed such that $a_n=\left(1-\frac{1}{\sqrt{n}}\right)^n.$ Then, \begin{align} a_n&amp;=\left(1-\frac{1}{\sqrt{n}}\right)^n \\&amp;=\exp\ln\left(1-\frac{1}{\sqrt{n}}\right)^n\\&amp;=\exp \left[n\ln\left(1-\frac{1}{\sqrt{n}}\right)\right] \\&amp;=\exp\left[ -n\sum^{\infty}_{k=1}\frac{1}{k}\left(\frac{1}{\sqrt{n}}\right)^k\right]\\&amp;=\exp\left[ -n\left(\frac{1}{\sqrt{n}}+\frac{1}{2n}+\sum^{\infty}_{k=3}\frac{1}{k}\left(\frac{1}{\sqrt{n}}\right)^k\right)\right]\\&amp;=\exp \left[-\sqrt{n}-\frac{1}{2}-\sum^{\infty}_{k=3}\frac{n}{k}\left(\frac{1}{\sqrt{n}}\right)^k\right]\\&amp;\equiv\exp \left(-\sqrt{n}\right)\exp \left(-\frac{1}{2}\right)\end{align} Choose $b_n=\exp \left(-\sqrt{n}\right)$, so that  \begin{align} \dfrac{a_n}{b_n}\to\exp \left(-\frac{1}{2}\right).\end{align} Since $b_n \to 0$, there exists $N$ such that for all $n\geq N,$ \begin{align} \exp \left(-\sqrt{n}\right)&lt;\dfrac{1}{n^2}.\end{align} Hence, \begin{align}\sum^{\infty}_{n=N}b_n= \sum^{\infty}_{n=N}\exp \left(-\sqrt{n}\right)\leq \sum^{\infty}_{n=N}\dfrac{1}{n^2}&lt;\infty,\end{align} and so, $\sum^{\infty}_{n=1}b_n&lt;\infty\implies \sum^{\infty}_{n=1}a_n&lt;\infty$ by Limit comparison test. Integral $\int\csc^3{x} \ dx$ I found these step which explain how to integrate $\csc^3{x} \ dx$. I understand everything, except the step I highlighted below.  How did we go from: $$\int\frac{\csc^2 x - \csc x \cot x}{\csc x - \cot x}\,dx%$$ to  $$\int \frac{d(-\cot x + \csc x)}{-\cot x + \csc x} \quad?$$  Thank you for your time! $$ \int \csc^3 x\,dx = \int\csc^2x \csc x\,dx$$ To integrate by parts, let $dv = \csc^2x$ and $u=\csc x$. Then $v=-\cot x$ and $du = -\cot x \csc x \,dx$. Integrating by parts, we have: $$\begin{align*} \int\csc^2 x \csc x \,dx &amp;= -\cot x \csc x - \int(-\cot x)(-\cot x\csc x\,dx)\\ &amp;= -\cot x \csc x - \int \cot^2 x \csc x\,dx\\ &amp;= -\cot x\csc x - \int(\csc^2x - 1)\csc x\,dx &amp;\text{(since }\cot^2 x = \csc^2-1\text{)}\\ &amp;= -\cot x \csc x - \int(\csc^3 x - \csc x)\,dx\\ &amp;= -\cot x\csc x - \int\csc^3 x\,dx + \int \csc x\,dx \end{align*}$$ From $$\int \csc^3 x\,dx = -\cot x\csc x - \int\csc^3 x\,dx + \int \csc x\,dx$$ we obtain $$\begin{align*} \int\csc^3x\,dx + \int\csc^3 x\,dx &amp;= -\cot x \csc x + \int\csc x\,dx\\ 2\int\csc^3 x\,dx &amp;= -\cot x\csc x + \int\csc x\,dx\\ \int\csc^3x\,dx &amp;= -\frac{1}{2}\cot x\csc x + \frac{1}{2}\int\csc x\,dx\\ &amp;=-\frac{1}{2}\cot x\csc x + \frac{1}{2}\int\frac{\csc x(\csc x - \cot x)}{\csc x - \cot x}\,dx\\ &amp;= -\frac{1}{2}\cot x \csc x + \frac{1}{2}\int\frac{\csc^2 x - \csc x\cot x}{\csc x - \cot x}\,dx\\ &amp;= -\frac{1}{2}\cot x \csc x + \frac{1}{2}\int\frac{d(-\cot x+\csc x)}{-\cot x +\csc x}\\ &amp;= -\frac{1}{2}\cot x\csc x + \frac{1}{2}\ln|\csc x - \cot x|+ C \end{align*}$$ How to use an alpha map in Blender Render? Choosing variables to include in a multiple linear regression model How to Execute ShortCut From Command line in Windows 7 We came with a scenario where we have to use Shortcut file (.lnk), which is on the desktop, to execute an application for a headless device (i.e, without manual intervention).  Is there any way to execute it from Command prompt? Earlier today I posted  which yielded a .  I'd like to attract attention to this answer in the hope that the answer will get upvoted, as a kind of reward for the quality of the answer.  Is there anything that I can do to achieve this? I have tried  \includegraphics{http://www.site.com/path/to/figure.png}   But this returns the error   ERROR: Package pdftex.def Error: File `http://www.website.com/path/to/figure.png' not found.    Are there other options? velocity of an object after leaving a ramp This issue came up when I got different records counts for what I thought were identical queries one using a not in where constraint and the other a left join. The table in the not in constraint had one null value (bad data) which caused that query to return a count of 0 records. I sort of understand why but I could use some help fully grasping the concept.  To state it simply, why does query A return a result but B doesn't?  A: select 'true' where 3 in (1, 2, 3, null) B: select 'true' where 3 not in (1, 2, null)   This was on SQL Server 2005. I also found that calling set ansi_nulls off causes B to return a result. Intuitively, $\lim\limits_{t\to -\infty}te^t=0$, since $e^t\to 0$ much faster than $t\to -\infty$.   Is there a way to more rigorously compute this? Writing it as $e^t/(1/t)$ seems resistant to l'Hopital's rule. Class is not key value coding-compliant I already searched the internet but could not find a solution to this. Maybe it is the same question as  but there was no answer.  I want to render a video with tracking, but the output "loses" color information and gets kind of greyish. I first thought that it is related to the renderer, but it happens in Cycles and Eevee. Therefore i made a sample image, added it to the image sequence editor and rendered it as 1 frame. Resulting in the same problem.  I placed the original image beside blenders output so that you can see the difference. The only idea I came up with is that something with the lighting is not correct but I can't find a setting for that.  I am using Blender 2.80 with the default settings. Only set the output resolution to match the input resolution.