All Questions

Given a function $f$ from a finite set $X$ to itself, it seems natural to consider $\kappa_f := (\sum_{x \in X} |f^{-1}(x)|^2)/|X|$ as a measure of the non-invertibility of $f$: it equals 1 if $f$ is ...

Fix some positive integers $N$ and $d_k$, $k=1,2,\dots$ with $N=\sum_{k=1}^\infty d_k$. Suppose you have a graph $G$ taken randomly uniformly among the set of all (unoriented) graphs with $N$ ...

Say we have a joint distribution on a finite alphabet $\mathcal{X}\times \mathcal{Y}$. It could be a communication link where we want to send a random message $X$ over a channel, but it gets garbled ...

Given is a chain factor graph as presented in the image below with the following properties: Each node can take values 0 or 1 All unary potentials are equal (e.g. $U(a)=0$) for every node $a$ All ...