Applied Mathematics Seminar

The Applied Mathematics Seminar has talks on a wide range of topics, including but not limited to approximation theory and practice, numerical linear algebra, numerical optimization, numerical aspects of computer science, theoretical and applied partial differential equations and their numerical solutions, and mathematical biological models.

Spring 2025

For the Spring 2025 semester we will meet in Maxim Doucet Hall 202 at 9:30 am on Thursdays for in-person talks. For more information contact Xiang-Sheng Wang.

1. 13 March 2025
   Infinitesimal Homeostasis in Mass-Action Systems, Part 2
   Jiaxin Jin
   University of Louisiana at Lafayette
   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.
2. 27 February 2025
   Infinitesimal Homeostasis in Mass-Action Systems, Part 1
   Jiaxin Jin
   University of Louisiana at Lafayette
   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.