Lafayette, USA
Title: Homeostasis Patterns
Abstract: Homeostasis is a regulatory mechanism that keeps a specific variable close to a set value as other variables fluctuate. The notion of homeostasis can be rigorously formulated when the model of interest is represented as an input-output network, with distinguished input and output nodes, and the dynamics of the network determines the corresponding input-output function of the system. In this context, homeostasis can be defined as an “infinitesimal” notion, namely, the derivative of the input-output function is zero at an isolated point. We introduce the notion of a homeostasis pattern, defined as a set of nodes, in addition to the output node, that are simultaneously infinitesimally homeostatic. We prove that each homeostasis type leads to a distinct homeostasis pattern. Moreover, we describe all homeostasis patterns supported by a given input-output network in terms of a combinatorial structure associated to the input-output network. We call this structure the homeostasis pattern network.
Bio: I joined the Department of Mathematics as an assistant professor in August 2024. I received my B.S. in Mathematics from Shanghai Jiao Tong University in 2014, my M.S. in Mathematics from the University of Wisconsin-Madison in 2015, and my Ph.D. in Mathematics from the University of Wisconsin-Madison in 2021. Prior to joining UL Lafayette, I served as a Zassenhaus Assistant Professor in the Department of Mathematics at The Ohio State University.
My research focuses on applying dynamical systems to mathematical biology or biochemistry and applied partial differential equations in mathematical physics, with three distinct areas of emphasis: (i) investigation of the dynamical equivalence between reaction models and the relationship between reaction rates and graph structures with complex-balanced realizations, (ii) analysis of the network structure in input-output networks to characterize homeostasis points in the input-output function, (iii) exploration of the existence and regularity of solutions for the kinetic equations and the stability of the equilibrium of some kinetic models.