Convert Fade In-out Transition to Crossfade with concating Video in FFMPEG
crossfade between 2 videos using ffmpeg
How do I pass a string into subprocess.Popen (using the stdin argument)? How was this answer posted after this question was closed? Question:   Answer:   The question was closed at 11:57:57 (according to the hover-over-"x-mins-ago" bar) and the answer was posted at 12:16:35. It's a fairly lengthy answer, so it's possible that it was started to be written before it was closed but I swear I've started to answer a question then I got a banner along the top saying "this question has been closed" and the answer was no longer post-able. Minimum of the Gamma Function $\Gamma (x)$ for $x>0$. How to find $x_{\min}$? Smart guides aren't smart TL:DR Smart guides aren't accurate - even though the snap, (end up causing more problems in the long run) is there a way to fix it?  Maybe there are some settings that I'm missing (need to be changed)    I use my smart guides all the time (and am overall pleased with them). I do have my issues with it, as explained here:  A lot of times, when I'm trying to make a bunch of triangles like this:    Done by making a triangle, cloning, flipping, rotating etc. Repeat until full  (Perfect) Snapping using Smart Guides    Ends up looking likebetween the triangles (Outline Mode)    Now I personally (with a strong attention to detail) will notice that there is something off after making just 1 or 2 triangles (Even before outline mode... strokes look oh so slightly thicker/off)   And then I check in outline mode... and sure enough:    Notice the line spaces (and this is in outline mode, so if I didn't notice it before, now it's sitting right in front of my nose)  The way I (seemingly) "fixed" the first image was by adding in a thick stroke outline so that masks out the difference, however, in a lot of my cases I don't want to have a stroke at all (and then you really notice the problems). How do we prove that something is unprovable? What are Unity's keyboard and mouse shortcuts? In Unity, are there any pre-defined shortcuts, e.g. to open the dash or unhide the launcher? WSOD after migrating to another site? Troubleshooting a site migration Multi-OS Portable TeX system Finding first and last index of some value in a list in Python Simulating data to fit a mediation model I am interested in finding a procedure to simulate data that are consistent with a specified mediation model.  According to the general linear structural equation model framework for testing mediation models first outlined by  and described elsewhere such as , mediation models for outcome $Y$, mediator $\newcommand{\med}{\rm med} \med$, and predictor $X$ and are governed by the following three regression equations: \begin{align} Y    &amp;= b_{11} + b_{12}X + e_1                \tag{1}  \\ \med &amp;= b_{21} + b_{22}X + e_2                \tag{2}  \\ Y    &amp;= b_{31} + b_{32}X + b_{32} \med + e_3  \tag{3} \end{align} The indirect effect or mediation effect of $X$ on $Y$ through $\med$ can either be defined as $b_{22}b_{32}$ or, equivalently, as $b_{12}-b_{32}$.  Under the old framework of testing for mediation, mediation was established by testing $b_{12}$ in equation 1, $b_{22}$ in equation 2, and $b_{32}$ in equation 3.  So far, I have attempted to simulate values of $\med$ and $Y$ that are consistent with values of the various regression coefficients using rnorm in R, such as the code below:  x   &lt;- rep(c(-.5, .5), 50) med &lt;- 4 + .7 * x + rnorm(100, sd = 1)   # Check the relationship between x and med mod &lt;- lm(med ~ x) summary(mod)  y &lt;- 2.5 + 0 * x + .4 * med + rnorm(100, sd = 1)  # Check the relationships between x, med, and y mod &lt;- lm(y ~ x + med) summary(mod)  # Check the relationship between x and y -- not present mod &lt;- lm(y ~ x) summary(mod)   However, it seems that sequentially generating $\med$ and $Y$ using equations 2 and 3 is not enough, since I am left with no relationship between $X$ and $Y$ in regression equation 1 (which models a simple bivariate relationship between $X$ and $Y$) using this approach.  This is important because one definition of the indirect (i.e., mediation) effect is $b_{12}-b_{32}$, as I describe above.  Can anyone help me find a procedure in R to generate variables $X$, $\med$, and $Y$ that satisfy constraints that I set using equations 1, 2, and 3? In the Linux system, we can use bellow command to enable packets forwarding:  ~ # sysctl net.ipv4.ip_forward=1 net.ipv4.ip_forward = 1   but how can I realize the same function in Windows?  I use Windows Server 2008 R2. Windows Active Directory naming best practices? This is a  about Active Directory domain naming.   After experimenting with Windows domains and domain controllers in a virtual environment, I've realized that having an active directory domain named identically to a DNS domain is bad idea (Meaning that having example.com as an Active Directory name is no good when we have the example.com domain name registered for use as our website).   , but I'm still not sure about what other rules there are around naming Active Directory domains.  Are there any best practices on what an Active Directory name should or shouldn't be? Minimize the sum of distances between two point and a circle Let's $A$,$B$ and $O$ be random point in a plane, such that they are not colinear. Let's $c$ be a circle centered on $O$, such that points $A$ and $B$ are outside of it. Find a point $X$ that lies on the circle $c$ and the sum $AX + BX$ is minimal.  First I tried to minimize the function:  $$f(x,y) = \sqrt{(A.x - x)^2 + (A.y - y)^2} + \sqrt{(B.x - x)^2 + (B.y - y)^2}$$ with  constraint $$g(x,y) = x^2 + y^2 - r^2 = 0$$  By moving $O$ to $(0,0)$ and do the same with $A$,$B$ so the relative distance will not change.  But these works when we know the coordinates of $A$,$B$ and the radius of the circle. Yet this isn't the right way because the problem is to construct that point.  Later I tried to approach using geometry.  The smallest distance from the point $A$ to the circle is the intersection of the circle $c$ and the ray $OA$, this is the same for $B$. Then we construct circles centered on $A$ and $B$ that are tangent to $c$. If the two circle intersect we'll get a common point for the both $A$ and $B$ and the distance will be minimal. Using computer I find the point X should be somewhere around the intercetion of the circle $c$ and the ray from $O$ to the new point.   Sometimes the optimal point differs just a bit and also this method fails when the two circles do not intersect each other Give each site a parallel site for polling, recommendations and subjective-ish stuff How to change the default fonts in Windows 10 I have read the entries for other OS versions.    Changing the MS Shell Dlg (2) entries in FontSubstitues registry key doesn't seem to work (in Windows 10), or it works in two minor places.  I don't have access to a Windows 95/98/etc. machine, the "earliest" I have is Windows 8.1, so I can't use the Plus directory trick either (directory doesn't exist). For the WindowMetrics registry entry, I seem to have all the *Font keys to be set to the font I want, but that doesn't seem to be doing the trick (on Windows 10). For Windows 8/8.1, there was a program called Windows 8 Font Changer, which worked like a charm, but doesn't seem to on Windows 10 (though it was probably that program run that changed the fonts in the WindowMetrics).   Thanks.   Update: One more method that came out that is perhaps still not the solution: Winaero Tweaker (winaero.com), as it has some issues, the biggest two of which seem to be:   If you have changed the size of text etc. from: "Settings –> Display –> Advanced display settings –> Advanced sizing of text and other items –> set a custom scaling level (not recommended)", the changes do not stick upon a logoff-login or restart. You need to have changed it, if at all, only through "Settings –> Display –> Change the size of text, etc." (which goes up to only a certain percentage, depending on the maximum resolution of your device – 125% on a tablet of mine, which I was able to set to 175% or even 200% with the other, older method that is now apparently listed as not recommended).  Even though it lists a number of items to change the font and size of, not everything gets changed. A typical example of this is the right click menu on the desktop, which still shows the View, Sort By, etc. items in the default font, however much it has a clear 'Change menu font' item. What is the difference between conditioning on regressors vs. treating them as fixed? I've seen animated GIF images of screen casts (like the one below) promoted a few times on this site as a way to improve answers.    What toolchain is being used to create these? Is there a program that does this automagically, or are people taking screencasts, converting them into a series of static frames, and then creating the GIF images? Let $f(x)\in C^2:[0,1]\rightarrow\mathbb{R}$ satisfy $f(0)=0,f(1)=1,f'(0)=f'(1)=0$, prove that: $$\max_{x\in[0,1]}|f''(x)|\ge4$$  By using Taylor series I can prove that $\max_{x\in[0,1]}|f''(x)|\ge2$, but I cannot go further. I was trying to prove following inequality:  $$|\sin n\theta| \leq n\sin \theta \ \text{for all n=1,2,3... and } \  0&lt;\theta&lt;π $$  I succeeded in proving this via induction but I didn't get "feel" over the proof. Are there other proof for this inequality? How to play a YouTube clip in background/minimised?