Download APPLIED MATHEMATICS SEMINAR - Arlington

Colloquium
University of Texas at Arlington - Department of Mathematics
Proudly Presents:
Dr. Jonathan Rubin
Professor
Department of Mathematics
University of Pittsburgh
Friday, April 1, 2016
3:00 p.m.
PKH 311
“Every breath you take: Some mathematics inspired by
respiration”
Abstract:
Without conscious thought, we breath over and over again reliably throughout most of our lives,
adjusting automatically to changes in metabolic and environmental demands. This remarkable capability
requires the generation of a robust, tunable rhythm by a network of neurons in the brain stem, as well as
a range of feedback mechanisms. Understanding these systems leads to a range of interesting
mathematics problems. I will review the basic dynamics of generation of rhythmic activity in a single
respiratory neuron, which involves a two-timescale system of ordinary differential equations. I will then
progress to considering a pair of coupled neurons and finally to a network of N neurons for N
significantly larger than two. In doing so, I will diverge into some recent mathematical findings on
multiple-timescale dynamics and on directed graphs, including some rigorous new results on (1) bounds
on degrees that ensure graphicality of a bidegree sequence and (2) enumeration of digraphs that satisfy a
given graphic bidegree sequence.
Refreshments before the talk and socializing following the talk
http://www.uta.edu/math/seminars/