MS07 - MFBM-09

Probability & stochastic processes in biology: models, methods, and community (Part 3)

Thursday, July 17 at 3:50pm

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Organizers:

Jinsu Kim (POSTECH), Eric Foxall (The University of British Columbia - Okanagan Campus), and Linh Huynh (Dartmouth College)

Description:

Mathematical biology has a long and rich history of physics-based models and methods. These include both explicitly physics-based models, such as mechanical models of cell wall geometry and molecular models of protein translation and folding, and those inspired by physics, such as interacting particle system models in ecology and epidemiology, to name just a few. In some cases, existing approaches are not optimal for the study of biochemical systems due to various issues including the curse of dimensionality, infinite state spaces, and uncertainty in model structure. Methods from probability theory, especially new methods developed specifically for the study of biological phenomena, can simplify and strengthen our analysis and understanding of these phenomena. In this minisymposium, which has two parts due to significant interest in the subject, we gather researchers from diverse backgrounds and fields of study to exchange ideas, models and methods. The intention is to foster communication and collaboration in the study of stochastic processes across all of biology, and especially to avail researchers of recent developments that could be fruitful in unexpected areas of application. Special requirement: Some of our speakers are only available on July 14th. Therefore, we kindly request that our minisymposium be scheduled on July 14th.



Hwai-Ray Tung

University of Utah
"Extreme first passage times with fast immigration"
Many scientific questions can be framed as asking for a first passage time (FPT), which generically describes the time it takes a random 'searcher' to find a 'target.' The important timescale in a variety of biophysical systems is the time it takes the fastest searcher(s) to find a target out of many searchers. Previous work on such fastest FPTs assumes that all searchers are initially present in the domain, which makes the problem amenable to extreme value theory. In this paper, we consider an alternative model in which searchers progressively enter the domain at some 'immigration' rate, which may be constant, time inhomogeneous, or proportional to the population size. In the fast immigration rate limit, we determine the probability distribution and moments of the k-th fastest FPT. Our rigorous theory applies to many models of stochastic motion, including random walks on discrete networks and diffusion on continuous state spaces. Mathematically, our analysis involves studying the extrema of an infinite sequence of random variables which are both not independent and not identically distributed. Our results constitute a rare instance in which extreme value statistics can be determined exactly for strongly correlated random variables.



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Annual Meeting for the Society for Mathematical Biology, 2025.