Mathematical Biology

Registration Problems and Applications to Biomathematics I will discuss some mathematical approaches to various registration problems, where one seeks to align points from different spaces. These include matching points between different metric spaces or registering graphs or hypergraphs with different node sets. Along the way, I'll talk about motivating problems that come from biology, such …

Stochastic switching of delayed feedback suppresses oscillations in genetic regulatory systems Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates the effect of delayed feedback. To do so, we consider a hybrid model …

Deconstructing the Integrated Oscillator Model for Pancreatic Beta-Cells Electrical bursting oscillations in the beta-cells of pancreatic islets have been a focus of investigation for more than fifty years. This has been aided by mathematical models, which are descendants of the pioneering Chay-Keizer model that was published 40 years ago. This presentation describes the key biophysical …

Trait-shift induced interaction modification and unusual consequences onecosystem dynamics Ecosystems are traditionally modeled by networks of species with constant interaction strengths between them. However, it has been increasingly recognized that there is substantial intraspecific variation in ecologically important traits. The distribution of such traits within a species can shift in response to environmental change or …

Controlling Pattern Formation in Active-Ordered Fluids Active fluids comprised of reconstituted biopolymers and motor proteins are self-driven materials that exhibit rich spatiotemporal dynamics. These dynamics are characterized by buckling instabilities and the proliferation of topological defects in orientational order. These defects drive material flows and give the system its striking, characteristic texture and dynamics. One …