Colloquium on July 28th, 2008

Kevin E. Bassler
Department of Physics, University of Houston

The evolution of networks of competing Boolean nodes

Boolean networks were originally proposed as simple models of genetic regulatory networks and have since been applied to of a variety of other physical, social, and economic systems.
They consist of a directed graph with nodes that have binary output states that are heterogeneous functions of the binary input they receive from the nodes connected to them by the in-links of the graph. Depending on the functions of the nodes, Boolean networks have two phases of dynamical behavior, fixed and "chaotic", and a continuous transition between the two phases. The talk will discuss the evolution of Boolean networks that occurs when the nodes compete against each other in a fustrated use of a limited resource. This dynamics causes the network to evolve to a critical state at the boundary of the two dynamical phases. Using computer simulations and group theoretic arguments, it will be shown that, for large networks, the dynamics is highly symmetrical and results in the evolution of canalized networks. Canalization is a form of network robustness thought to be important for developmental biological systems. While for finite size networks, it will be shown that the symmetry of the evolutionary dynamics is broken and the network evolves to be input inverting rather than canalized.