Saturation Probabilities of Continuous-Time Sigmoidal Networks

Abstract: From genetic regulatory networks to nervous systems, the interactions between elements in biological networks often take a sigmoidal or S-shaped form. This paper develops a probabilistic characterization of the parameter space of continuous-time sigmoidal networks (CTSNs), a simple but dynamically-universal model of such interactions. We describe an efficient and accurate method for calculating the probability of observing effectively M-dimensional dynamics in an N-element CTSN, as well as a closed-form but approximate method. We then study the dependence of this probability on N, M, and the parameter ranges over which sampling occurs. This analysis provides insight into the overall structure of CTSN parameter space.