Jack Valmadre

The linear assignment problem (or simply assignment problem) is the problem of finding a matching between two sets that minimizes the sum of pair-wise assignment costs. This can be expressed as finding a matching (or independent edge set) in a bipartite graph \(G = (U, V, E)\) that minimizes the sum of edge weights. The edge weights may be positive or negative and the bipartite graph does not need…

Dec 8, 2020

Inf-norm versus squared two-norm on probability simplex

The \(\pi\) be an \(n\)-dimensional vector on the probability simplex, that is \(\pi_{i} \ge 0\) and \(\sum_{i} \pi_{i} = 1\). It is trivial to show that \(\|\pi\|_{2} \ge \|\pi\|_{\infty}\). Let us instead compare the squared 2-norm to the infinity norm. Without loss of generality, assume that \(\pi_{1}\) is the largest element. \[\begin{align} \|\pi\|_2^2 - \|\pi\|_{\infty} & = \pi_{1}^{2} +…

Jun 25, 2020

Choosing an escape key for screen and tmux

Usually I don’t like to change the default terminal configuration because it becomes impossible to use someone else’s computer or for them to use yours. However, the default choices of C-a in screen and C-b in tmux are awful if you’re used to emacs-style text navigation. I have been using C-] for a few years and I’m pretty happy with it. I wanted to document the reasoning behind this choice. The…

Feb 6, 2020