Measuring Mutual Information in Random Boolean Networks
Bartolo Luque
Antonio Ferrera
Centro de Astrobiología (CAB),
Ciencias del Espacio, INTA,
Carretera de Ajalvir km. 4,
28850 Torrejón de Ardoz, Madrid, Spain
Abstract
During the past few years an area of active research in the field of complex systems is that of their information storing and processing abilities. Common opinion has it that the most interesting behavior of these systems is found "at the edge of chaos," which would seem to suggest that complex systems may have inherently nontrivial information processing abilities in the vicinity of sharp phase transitions. A comprehensive, quantitative understanding of why this is the case is however still lacking. Indeed, even "experimental" (i.e., often numerical) evidence that this is so has been questioned for a number of systems. In this paper we will investigate, both numerically and analytically, the behavior of random boolean networks (RBNs) as they undergo their order-disorder phase transition. We will use a simple mean field approximation to treat the problem, and without lack of generality we will concentrate on a particular value for the connectivity of the system. In spite of the simplicity of our arguments, we will be able to reproduce analytically the amount of mutual information contained in the system as measured from numerical simulations.
