Critical dynamics on a large human Open Connectome network
Géza Ódor
MTA-EK-MFA, Research Center for Energy, Hungarian Academy of Sciences, P. O. Box 49, H-1525 Budapest,
Hungary
Michael Gastner
Yale-NUS College, 16 College Avenue West, 01-220 Singapore 138527
Extended numerical simulations of threshold models have been performed on a human brain network with
N=836733 connected nodes available from the Open Connectome Project [1].  While in the case of simple
spreading models like contact process, SIS or threshold model a sharp discontinuous phase transition, without
any critical dynamics arises, variable threshold models exhibit extended power-law scaling regions.  This is
attributed to fact that Griths eects, stemming from the topological or interaction heterogeneity of the
network, can become relevant if the input sensitivity of nodes is equalized. Nonuniversal power-law avalanche
size and time distributions have been found with exponents agreeing with the values obtained in electrode
experiments of the human brain [2]. Power-law activity time dependences occur sub-critically in an extended
control parameter space region without the assumption of self-organization.  Probably the most important
result of this study is that negative weights enable local sustained activity and promote strong rare-region
eects without network fragmentation. Thus, connectomes with high graph dimensions can be subject to rare-
region eects and can show measurable Griths eects. Another important observation is that power-laws may
occur in a single network, without sample averaging, due to the modular topological structure. Eects of link
directness, as well as the consequence of inhibitory connections is studied. Robustness with respect of random
removal of links suggest that connectome generation errors do not modify the Griths eects qualitatively.
[1] M.T. Gastner and G. Ódor, Sci. Rep. 5 , 14451 (2015).
[2] G. Ódor PRE 94, 062411 (2016).