Network algorithmics and the emergence of information integration in cortical models.

An information-theoretic framework known as integrated information theory (IIT) has been introduced recently for the study of the emergence of consciousness in the brain [D. Balduzzi and G. Tononi, PLoS Comput. Biol. 4, e1000091 (2008)]. IIT purports that this phenomenon is to be equated with the generation of information by the brain surpassing the information that the brain's constituents already generate independently of one another. IIT is not fully plausible in its modeling assumptions nor is it testable due to severe combinatorial growth embedded in its key definitions. Here we introduce an alternative to IIT which, while inspired in similar information-theoretic principles, seeks to address some of IIT's shortcomings to some extent. Our alternative framework uses the same network-algorithmic cortical model we introduced earlier [A. Nathan and V. C. Barbosa, Phys. Rev. E 81, 021916 (2010)] and, to allow for somewhat improved testability relative to IIT, adopts the well-known notions of information gain and total correlation applied to a set of variables representing the reachability of neurons by messages in the model's dynamics. We argue that these two quantities relate to each other in such a way that can be used to quantify the system's efficiency in generating information beyond that which does not depend on integration. We give computational results on our cortical model and on variants thereof that are either structurally random in the sense of an Erdős-Rényi random directed graph or structurally deterministic. We have found that our cortical model stands out with respect to the others in the sense that many of its instances are capable of integrating information more efficiently than most of those others' instances.