Sunday, March 22, 2015

Awesome Nerd News: Meet John Urschel, Chess Player, Mathematician, and NFL Athlete

John Urschel, offensive lineman for the Baltimore Ravens, is one smart cookie.  He's just published a paper entitled "A Cascadic Multigrid Algorithm for Computing the Fiedler Vector" in the Journal of Computational Mathematics.  Sound mind in a sound body, indeed, mens sana in corpore sano.

Here's the abstract:
In this paper, we develop a cascadic multigrid algorithm for fast computation of the Fiedler vector of a graph Laplacian, namely, the eigenvector corresponding to the second smallest eigenvalue. This vector has been found to have applications in fields such as graph partitioning and graph drawing. The algorithm is a purely algebraic approach based on a heavy edge coarsening scheme and pointwise smoothing for refinement. To gain theoretical insight, we also consider the related cascadic multigrid method in the geometric setting for elliptic eigenvalue problems and show its uniform convergence under certain assumptions. Numerical tests are presented for computing the Fiedler vector of several practical graphs, and numerical results show the efficiency and optimality of our proposed cascadic multigrid algorithm.
I have no idea what that means, but I do know how hard it is to get published in a scholarly journal.   Congratulations, John!

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