DEFICIENCY ZERO FOR RANDOM REACTION NETWORKS UNDER ERDOS-RENYI AND STOCHASTIC BLOCK MODEL FRAMEWORKS - TUNG NGUYEN -UNIVERSITY OF WISCONSIN-MADISON

Reaction networks are commonly used to model a variety of physical systems from the microscopic world like cell biology and chemistry, to the macroscopic world like epidemiology and evolution biology. At its core, a reaction network model consists of two components: the network (or graph) component, and the dynamics under such a graph. Not surprisingly, there is a strong connection between the network structure and the qualitative behavior of the dynamical system. Certain network structures such as deficiency zero ensure many desirable behaviors of the dynamical systems including existence and stability of equilibrium.
In this talk, Mr Nguyen will attempt to address a natural question: how prevalent these structures (in particular deficiency zero) are among random reaction networks. To answer this question, it is important to have a framework to generate random reaction networks. He will present two such frameworks: an Erdos-Renyi framework, and a stochastic block model framework-which is essentially a more generalized version of Erdos-Renyi. Next, he will discuss deficiency zero structure and its importance in the theory of reaction networks, and examine its prevalence under the two random networks frameworks above.

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