Maximal information transfer and behavior diversity in Random Threshold Networks

Random Threshold Networks (RTNs) are an idealized model of diluted, non-symmetric spin glasses, neural networks or gene regulatory networks. RTNs also serve as an interesting general example of any coordinated causal system. Here we study the conditions for maximal information transfer and behavior diversity in RTNs. These conditions are likely to play a major role in physical and biological systems, perhaps serving as important selective traits in biological systems. We show that the pairwise mutual information is maximized in dynamically critical networks. Also, we show that the correlated behavior diversity is maximized for slightly chaotic networks, close to the critical region. Importantly, critical networks maximize coordinated, diverse dynamical behavior across the network and across time: the information transmission between source and receiver nodes and the diversity of dynamical behaviors, when measured with a time delay between the source and receiver, are maximized for critical networks.