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

Taylor, Timothy J, Hartley, Caroline, Simon, Péter L, Kiss, Istvan Z and Berthouze, Luc (2013) Identification of criticality in neuronal avalanches: I. A theoretical investigation of the non-driven case. Journal of Mathematical Neuroscience, 3 (5). pp. 1-26. ISSN 2190-8567

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Abstract

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.

Item Type: Article
Schools and Departments: School of Engineering and Informatics > Informatics
School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Q Science > QP Physiology > QP0351 Neurophysiology and neuropsychology
R Medicine > RC Internal medicine > RC0321 Neurosciences. Biological psychiatry. Neuropsychiatry
Depositing User: Luc Berthouze
Date Deposited: 24 Apr 2013 08:06
Last Modified: 24 Jun 2017 17:22
URI: http://sro.sussex.ac.uk/id/eprint/44422

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