Extremevalue statistics of brain networks: Importance of balanced condition
Abstract
Despite the key role played by inhibitoryexcitatory couplings in the functioning of brain networks, the impact of a balanced condition on the stability properties of underlying networks remains largely unknown. We investigate properties of the largest eigenvalues of networks having such couplings, and find that they follow completely different statistics when in the balanced situation. Based on numerical simulations, we demonstrate that the transition from Weibull to Fréchet via the Gumbel distribution can be controlled by the variance of the column sum of the adjacency matrix, which depends monotonically on the denseness of the underlying network. As a balanced condition is imposed, the largest real part of the eigenvalue emulates a transition to the generalized extremevalue statistics, independent of the inhibitory connection probability. Furthermore, the transition to the Weibull statistics and the smallworld transition occur at the same rewiring probability, reflecting a more stable system.
 Publication:

Physical Review E
 Pub Date:
 June 2014
 DOI:
 10.1103/PhysRevE.89.062718
 arXiv:
 arXiv:1311.6950
 Bibcode:
 2014PhRvE..89f2718J
 Keywords:

 87.18.Sn;
 02.50.r;
 02.10.Yn;
 89.75.k;
 Neural networks;
 Probability theory stochastic processes and statistics;
 Matrix theory;
 Complex systems;
 Quantitative Biology  Neurons and Cognition;
 Condensed Matter  Disordered Systems and Neural Networks;
 Nonlinear Sciences  Adaptation and SelfOrganizing Systems;
 Physics  Physics and Society
 EPrint:
 7 pages, 10 figures