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 …
A stochastic first-order reaction gene translation and nuclear-to-cell ratio homeostasis model Cell size varies between different cell types, and between different growth and osmotic conditions. However, the nuclear-to-cell volume ratio (N/C ratio) is largely maintained. In this presentation, I will first introduce an osmotic pressure balance model of N/C ratio determination, which relates the N/C …
Understanding the effect of white matter delays on large scale brain dynamics The presence of myelin is a powerful structural factor that controls the conduction velocity of mammalian axons. It is the combination of local synaptic activity and non-local delayed axonal interactions within the cortex that is believed to be the major source of large-scale …
High-Order Accuracy Computation of Coupling Functions for Strongly Coupled Oscillators We develop a general framework for identifying phase reduced equations for finite populations of coupled oscillators that is valid far beyond the weak coupling approximation. This strategy represents a general extension of the theory from and yields coupling functions that are valid to higher-order accuracy …
Modelling intermediate filaments – from filament elongation to network organization Intermediate filaments (IFs) constitute a crucial component of the cytoskeleton, playing vital roles in maintaining cell shape, mechanical integrity, and providing support for cell migration and signalling. Unlike microtubules and actin filaments, intermediate filaments form a diverse family of proteins, including keratins, vimentin, desmin, and …
Mathematical Optimization of Drug Regimens Improvements in drug regimens can make a difference in both clinical trial success and patient outcomes. Optimal control can be used to mathematically optimize regimens, which can then be tested experimentally and clinically. I will show examples of optimization of regimens for math models of various diseases, and discuss some …
