Complexity matching in neural networks

In the wide literature on the brain and neural network dynamics the notion of criticality is being adopted by an increasing number of researchers, with no general agreement on its theoretical definition, but with consensus that criticality makes the brain very sensitive to external stimuli. We adopt...

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Bibliographic Details
Published in:New journal of physics 2015-01, Vol.17 (1), p.15003-17
Main Authors: Mafahim, Javad Usefie, Lambert, David, Zare, Marzieh, Grigolini, Paolo
Format: Article
Language:English
Subjects:
Avalanches
Brain
Complexity
Firing
information transfer
integrate-and-fire
Links
Matching
Mittag-Leffler
neural network
Neural networks
Periodic variations
phase transition
Physics
power law
Strength
temporal complexity
Temporal logic
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Summary:In the wide literature on the brain and neural network dynamics the notion of criticality is being adopted by an increasing number of researchers, with no general agreement on its theoretical definition, but with consensus that criticality makes the brain very sensitive to external stimuli. We adopt the complexity matching principle that the maximal efficiency of communication between two complex networks is realized when both of them are at criticality. We use this principle to establish the value of the neuronal interaction strength at which criticality occurs, yielding a perfect agreement with the adoption of temporal complexity as criticality indicator. The emergence of a scale-free distribution of avalanche size is proved to occur in a supercritical regime. We use an integrate-and-fire model where the randomness of each neuron is only due to the random choice of a new initial condition after firing. The new model shares with that proposed by Izikevich the property of generating excessive periodicity, and with it the annihilation of temporal complexity at supercritical values of the interaction strength. We find that the concentration of inhibitory links can be used as a control parameter and that for a sufficiently large concentration of inhibitory links criticality is recovered again. Finally, we show that the response of a neural network at criticality to a harmonic stimulus is very weak, in accordance with the complexity matching principle.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/17/1/015003