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A topological classification of population bursts in spiking neural network

Sergey А. Lobov, Lobachevsky State University, Innopolis University, Russia
Alexey I. Zharinov, Lobachevsky State University, Russia
Olga Semenova, Lobachevsky State University, Russia
Victor B. Kazantsev, Lobachevsky State University, Innopolis University, Russia

Abstract

The question of the functional unit of information processing in the brain is still open. In recent decades, a fairly large amount of experimental data has appeared, indicating the important role of waves of neuronal activity in networks of the cerebral cortex. Studies on dissociated hippocampal and cortical neuronal cultures in vitro demonstrate the presence of various topological types of population bursts of spikes: in the form of a propagating wave and in the form of “instantaneous” activation of a network. In the latter case, excitation can be transmitted first to distant and then to nearby neurons. In a model study on a spiking neural network (SNN), we showed that the topological type of neural activity depends on the average length of connections between neurons - the connectivity radius. At a small radius (the predominance of local connections), the activity spreads in the form of travelling waves with a pronounced leading and trailing edge. With an increase in the radius of connectivity, blurring of the leading and trailing edges is observed up to the "instant" activation of the network. In this case, excitation is first transferred through neurons that are distant from each other, and then neurons are activated between such points of rapid transmission of activity. We analysed the velocity of propagation of activity depending on the connectivity radius and demonstrated that in the “instant” type of transmission, it is limited by axonal delays, and in the “wave” type, by synaptic delays. In addition, we have shown that with an increase in the connectivity radius, the SNN's ability to STDP-driven synchronization is lost. Based on the results of the work, we propose a new topological classification of network activity.

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Sergey A. Lobov
Lobachevsky State University, Innopolis University
Russia

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