Starting from the definition of 2-Wasserstein distance \begin{align*} \text{D}^2_{\text{W}} (\mu, \nu) = \inf \limits_{\gamma \in \Gamma(\mu, \nu)} \int_{M\times M} \| x - y \|^2 \text{d}\gamma(x,y), \end{align*} how to prove this reduces to $$ \text{D}^2_{\text{W}} (P, Q) = \sum \limits_{i=1}^...

As far as I know, any tag that is only used once every 6 months is pruned automatically. If that tag was the only one left on a question, the question becomes untagged and history of the previous tag, for good or evil, is lost. Can we get a list of questions about to be orphaned, so that we can ...

I wrote a SEDE query to determine which single-use tags will be deleted and when, and it also shows the only question using it and which tags it has. You could check this list once in a while and retag when necessary. (You originally requested this for Arqade, and tag pruning has been switched o...

Let $M$ be a (tracial) von Neumann algebra acting on a Hilbert space $\mathcal{H}$. A cocycle action of a discrete group $G$ on $M$ is a pair $(\sigma, v)$ with $\sigma : G \to Aut(N)$ and $v : G \times G \to \mathcal{U}(M)$ satisfying the following three conditions for all $k,l,m \in G$: (1) $\s...

I am trying to approximate the derivative of $f(x)=\frac{1-e^x}{x}$ at $x=0$ using the Richardson extrapolation with the $x_k=2^{-k}$ for $k=0,1,2$. It is mentioned to use $a(x)=\frac{f(x)-f(-x)}{2x}$ Questions: What is this $\color{red}{q}$ in the formula of the $a_{k,n}$ given below. In the lec...