Avalanches in self-organized critical neural networks: A minimal model for the neural SOC universality class

The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting that this homeostasis of brain activity could occur even without a central regulator, via self-organization on the level of neurons and their interactions, alone. Such physical mechanisms from the class of self-organized criticality exhibit characteristic dynamical signatures, similar to seismic activity related to earthquakes. Measurements of cortex rest activity showed first signs of dynamical signatures potentially pointing to self-organized critical dynamics in the brain. Indeed, recent more accurate measurements allowed for a detailed comparison with scaling theory of non-equilibrium critical phenomena, proving the existence of criticality in cortex dynamics. We here compare this new evaluation of cortex activity data to the predictions of the earliest physics spin model of self-organized critical neural networks. We find that the model matches with the recent experimental data and its interpretation in terms of dynamical signatures for criticality in the brain. The combination of signatures for criticality, power law distributions of avalanche sizes and durations, as well as a specific scaling relationship between anomalous exponents, defines a universality class characteristic of the particular critical phenomenon observed in the neural experiments. The spin model is a candidate for a minimal model of a self-organized critical adaptive network for the universality class of neural criticality. As a prototype model, it provides the background for models that include more biological details, yet share the same universality class characteristic of the homeostasis of activity in the brain.Comment: 17 pages, 5 figure

Typical run of the network self-organization algorithm.

<p>Regardless of initial connectivity and dynamical regime, the network evolves to a critical configuration. Top: when starting with completely isolated nodes the “network” is obviously subcritical and links will be inserted. Thus, both the connectivity (red) and the branching parameter (blue) as an indicator of network criticality increase. The network approaches a critical state where the branching parameter stabilizes close to one. Bottom: with higher initial connectivity, the network is supercritical at first. Links are removed from the network while the branching parameter approaches the critical value of one. As the self-organization algorithm is constructed to maximize activity correlations between linked nodes, the ratio of activating links (green) slowly increases in both cases.</p

Typical run with higher activation thresholds .

<p>When activation thresholds are increased, a node needs more than one excitatory input to become active itself. Thus, higher overall connectivity is needed to allow signal propagation on a critical level. The adaptation process responds accordingly and maintains a connectivity around while the branching parameter shows larger fluctuations between sub- and supercritical states, but in general is kept on a moderate level and does not diverge with increasing connectivity.</p