Activation Confinement Inside Complex Networks Communities

TL;DR

This paper enhances an equivalent model for integrate-and-fire neuronal dynamics to better predict and analyze activation confinement within complex modular networks, revealing insights into transient spiking behavior and network wave phenomena.

Contribution

It generalizes the equivalent model to handle any complex network with modular structure, improving prediction accuracy and understanding of activation confinement mechanisms.

Findings

The modular equivalent model accurately predicts non-linear dynamics.

Activation confinement causes long activation times between communities.

Waves are induced by integrate-and-fire dynamics in steady state.

Abstract

In this work it is described how to enhance and generalize the equivalent model (arXiv:0802.0421) of integrate-and-fire dynamics in order to treat any complex neuronal networks, especially those exibiting modular structure. It has been shown that, though involving only a handful of equivalent neurons, the modular equivalent model was capable of providing impressive predictions about the non-linear integrate-and-fire dynamics in two hybrid modular networks. The reported approach has also allowed the identification of the causes of transient spiking confinement within the network communities, which correspond to the fact that the little activation sent from the source community to the others implies in long times for reaching the nearly-simultaneous activation of the concentric levels at the other communities and respective avalanches. Several other insights are reported in this work, including the smoothing of the spiking functions, the consideration of intra-ring connections and its effects, as well as the identification of how the weights in the equivalent model change for different source nodes. This work has paved the way for a number of promising developments, which are identified and discussed. Preliminary results are also described which reveal waves induced by the integrate-and-fire dynamics along the steady-state regime.