  Our mysterious brain is believed to operate near a non-equilibrium point and
generate critical self-organized avalanches in neuronal activity. Recent
experimental evidence has revealed significant heterogeneity in both synaptic
input and output connectivity, but whether the structural heterogeneity
participates in the regulation of neuronal avalanches remains poorly
understood. By computational modelling, we predict that different types of
structural heterogeneity contribute distinct effects on avalanche
neurodynamics. In particular, neuronal avalanches can be triggered at an
intermediate level of input heterogeneity, but heterogeneous output
connectivity cannot evoke avalanche dynamics. In the criticality region, the
co-emergence of multi-scale cortical activities is observed, and both the
avalanche dynamics and neuronal oscillations are modulated by the input
heterogeneity. Remarkably, we show similar results can be reproduced in
networks with various types of in- and out-degree distributions. Overall, these
findings not only provide details on the underlying circuitry mechanisms of
nonrandom synaptic connectivity in the regulation of neuronal avalanches, but
also inspire testable hypotheses for future experimental studies.
