  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.
