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Identification of criticality in neuronal avalanches: I. A theoretical investigation of the non-driven case

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posted on 2023-06-08, 14:45 authored by Timothy J Taylor, Caroline Hartley, Péter L Simon, Istvan Kiss, Luc BerthouzeLuc Berthouze
In this paper, we study a simple model of a purely excitatory neural network that, by construction, operates at a critical point. This model allows us to consider various markers of criticality and illustrate how they should perform in a finite-size system. By calculating the exact distribution of avalanche sizes, we are able to show that, over a limited range of avalanche sizes which we precisely identify, the distribution has scale free properties but is not a power law. This suggests that it would be inappropriate to dismiss a system as not being critical purely based on an inability to rigorously fit a power law distribution as has been recently advocated. In assessing whether a system, especially a finite-size one, is critical it is thus important to consider other possible markers. We illustrate one of these by showing the divergence of susceptibility as the critical point of the system is approached. Finally, we provide evidence that power laws may underlie other observables of the system that may be more amenable to robust experimental assessment.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Journal of Mathematical Neuroscience

ISSN

2190-8567

Publisher

BioMed Central

Issue

5

Volume

3

Page range

1-26

Department affiliated with

  • Informatics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2013-04-24

First Open Access (FOA) Date

2013-04-24

First Compliant Deposit (FCD) Date

2013-04-23

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