Dynamics of timescales on complex lattices

A popular idea in biology is that the intrinsic timescale of an individual “unit” plays a crucial role in the information processed by the system as whole. For example, it has been proposed that the intrinsic timescales of single neurons in different brain areas are related to functional differences between these areas. However, disentangling between intrinsic and collective timescales remains a highly nontrivial task, and could benefit by drawing intuition from simple physical toy models. To this end, we consider the prototypical model of collective temporal behavior: kinetic Ising models, where identical units are connected with a given topology, and neighboring units stochastically interact with one another. We analyze how the behavior of such models is altered when considering many aspects relevant to their computational implementation, namely, finite temporal resolution, topological connectivity, and finite system size. Not coincidentally, these considerations have biological analogues. For example, the clock speed of processor is functionally similar to an “inverse refractory period” of a neuron. While locality of interactions can be exploited for parallel simulation of physical systems, the diversity of topologies in biological systems is key to their expressive power.