New questions in stochastics prompted by physiology and medicine
January 27, 2021
3:00 pm ONLINE
Abstract
The life sciences are pushing the boundaries of stochastic processes
theory. In this talk, I will illustrate this point through three
diverse problems. The first problem comes from pharmacology. What
should you do if you accidentally miss a dose of medication? Skip the
dose? Double your next dose? I will formulate a mathematical model to
answer this question and show that it requires generalizing an exotic
random variable studied by Erdos and others in the 1930s. The results
of this analysis challenge current medical recommendations on this
question. Second, in a very different biological and mathematical
problem, I will show how a longstanding question about insect
respiration leads to a new class of stochastic PDEs that provides
significant physiological insight. Finally, in another disparate
problem, I will address a question from human fertilization. Why do
300 million sperm cells search for the egg when only a single sperm
cell is necessary? I will show how the apparent redundancy in this and
other systems in cell biology can be understood in terms of recent
results in extreme statistics that modify traditional timescale
calculations.
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