Speaker: Kevin Bassler (University of Houston)

Title: Symmetry in critical random Boolean networks dynamics

Abstract: Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems will be explored. I will show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used to both greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. Classes of functions occur at the same frequency. These classes are orbits of the controlling symmetry group. I will show the nature of the symmetry that controls the dynamics of critical random Boolean networks by determining the frequency of output functions utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. I will also compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. These results demonstrate the usefulness and power of using symmetry to characterize complex network dynamics, and introduce a novel approach to the analysis of heterogeneous complex systems.