Events for 04/17/2025 from all calendars

Mathematical Biology Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Jiaxin Jin, University of Louisiana at Lafayette

Title: Infinitesimal Homeostasis in Mass-Action Systems

Abstract: Homeostasis occurs in a biological system when a chosen output variable remains approximately constant despite changes in an input variable. In this work we specifically focus on biological systems which may be represented as chemical reaction networks and consider their infinitesimal homeostasis, where the derivative of the input-output function is zero. The specific challenge of chemical reaction networks is that they often obey various conservation laws complicating the standard input-output analysis. We derive several results that allow to verify the existence of infinitesimal homeostasis points both in the absence of conservation and under conservation laws where conserved quantities serve as input parameters. In particular, we introduce the notion of infinitesimal concentration robustness, where the output variable remains nearly constant despite fluctuations in the conserved quantities. We provide several examples of chemical networks which illustrate our results both in deterministic and stochastic settings.

The Foias Lectures

Time: 4:00PM - 00:00AM

Location: Blocker 117

Speaker: Igor Kukavica, University of Southern California

Title: Free boundary problems - Foias Lecture III

Abstract: We will address the local existence of solutions to the water wave problem, modeled by the incompressible Euler equations in a domain with an evolving boundary. Our focus will be on the local existence of solutions for initial velocities that are rotational and belong to low-regularity Sobolev spaces.