Robustness of Griffiths effects in homeostatic connectome models.

I provide numerical evidence for the robustness of the Griffiths phase (GP) reported previously in dynamical threshold model simulations on a large human brain network with N=836733 connected nodes. The model, with equalized network sensitivity, is extended in two ways: introduction of refractory states or by randomized time-dependent thresholds. The nonuniversal power-law dynamics in an extended control parameter region survives these modifications for a short refractory state and weak disorder.

Heterogeneity effects in power grid network models.

We have compared the phase synchronization transition of the second-order Kuramoto model on two-dimensional (2D) lattices and on large, synthetic power grid networks, generated from real data. The latter are weighted, hierarchical modular networks. Due to the inertia the synchronization transitions are of first-order type, characterized by fast relaxation and hysteresis by varying the global coupling parameter K.

Griffiths phases in infinite-dimensional, non-hierarchical modular networks.

Griffiths phases (GPs), generated by the heterogeneities on modular networks, have recently been suggested to provide a mechanism, rid of fine parameter tuning, to explain the critical behavior of complex systems. One conjectured requirement for systems with modular structures was that the network of modules must be hierarchically organized and possess finite dimension. We investigate the dynamical behavior of an activity spreading model, evolving on heterogeneous random networks with highly modular structure and organized non-hierarchically.

Critical dynamics on a large human Open Connectome network.

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. While in the case of simple threshold models 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.

Universality of (2+1)-dimensional restricted solid-on-solid models.

Extensive dynamical simulations of restricted solid-on-solid models in D=2+1 dimensions have been done using parallel multisurface algorithms implemented on graphics cards. Numerical evidence is presented that these models exhibit Kardar-Parisi-Zhang surface growth scaling, irrespective of the step heights N. We show that by increasing N the corrections to scaling increase, thus smaller step-sized models describe better the asymptotic, long-wave-scaling behavior.