Griffiths phases on a large human Open Connectome network

Sep 5, 2017, 3:15 PM


oral Session 6


Geza Odor (MTA-EK-MFA, Research Center for Energy, Hungarian Academy of Sciences)


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 Griffiths effects, 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 effects without network fragmentation. Thus, connectomes with high graph dimensions can be subject to rare-region effects and can show measurable Griffiths effects. Another important observation is that power-laws may occur in a single network, without sample averaging, due to the modular topological structure. 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 Griffths effects qualitatively. $ $ [1] M.T. Gastner and G. Ódor, Sci. Rep. 5 , 14451 (2015). [2] G. Ódor PRE 94, 062411 (2016).

Primary author

Geza Odor (MTA-EK-MFA, Research Center for Energy, Hungarian Academy of Sciences)


Michael Gastner (Yale-NUS College, 16 College Avenue West, 01-220 Singapore 138527)

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