Baltimore Ravens offensive lineman John Urschel, 23, isn't giving up football anytime soon even though one of his passions, mathematics, largely depends on the health of his brain. Urschel recently co-wrote a paper in the Journal of Computational Mathematics. The essay is called "A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians.”
Urschel published the paper with three colleagues and then tweeted about it Tuesday. Urschel's academic accomplishment came the same week Chris Borland retired from the NFL as a precaution for his future neurological health.
My paper, A Cascadic Multigrid Algorithm for Computing the Fiedler Vector..., has been published in the Journal of Computational Mathematics â€” John Urschel (@MathMeetsFball) March 18, 2015
Borland gave up the last three years of his $2.9 million contract and retired after just one season with the NFL due to concerns about potentially facing a long-term neurological injury.
The two are hardly strangers. Urschel called Borland "one of the toughest football players I've ever had the pleasure of playing against," and admitted he was jealous of Borland, against whom he first played in college, for giving up his pro football career. "Playing a hitting position in the NFL can’t possibly help your long-term mental health," Urschel wrote in the Players Tribune Wednesday, acknowledging that his mental health would play a vital role in a "bright career ahead of me in mathematics."
But he added: "I play because I love the game. I love hitting people. There’s a rush you get when you go out on the field, lay everything on the line and physically dominate the player across from you."
Borland suffered three concussions while playing football in high school, and an investigation by the NFL found former players are up to 35 times more likely to suffer from Alzheimer's disease and dementia than the average person. One in three NFL players will develop neurocognitive problems.
Urschel, who was born in Canada and attended Penn State University, was drafted in 2014 by the Baltimore Ravens to block for quarterback Joe Flacco. In addition to his math prowess, he is also an accomplished chess player. The 6-foot-3, 301-pounder signed his rookie contract with the Ravens for $2.36 million over four years, with a $144,560 signing bonus.
“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,” the description read on the Cornell University Library website. “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.”