Speaker: Reinhard Laubenbacher, University of Florida
A Boolean network in n variables is a function from the set of binary strings of length n to itself, defined through n Boolean rules. Boolean networks are used in several applications, from electrical engineering to systems biology. Aside from their usefulness, there are many interesting mathematical questions about their properties. Perhaps the most fundamental one is about the relationship between the structure of the Boolean rules in the network, its “genotype,” and the resulting dynamics, its “phenotype,” in the language of biology. Boolean rules can be viewed as polynomials over the field with two elements, making them amenable to analysis using computational algebra. As a result, research motivated by these questions leads to a rich interplay between combinatorics, computer algebra, and dynamical systems theory, motivated by concepts from biology. This talk will present some results in this field and discuss some open problems. This work was motivated in part by the concept of “modularity” of biological systems, postulating that systems such as gene regulatory networks are modular, in the sense that they consist of weakly connected compositions of highly connected subnetworks, the modules. This talk will explore the concept in the context of Boolean network models of gene regulatory networks.