Our results recover power-law distributions of neuronal avalanches, with critical scaling exponents close to 3/2. The resulting rewired network also exhibits the log-normal distributions of node degrees, and the power-law distributions of edge weights with exponents close to 3.

In our model, the sandpile model of self-organized criticality is imposed on hierarchical modular networks. Hebbian learning is imposed during avalanche events, as toppled sites are rewired to have stronger connections. Random prunings are also introduced during stasis times.

Empirical studies of brain networks, or connectomes, of various species reveal log-normal degree distributions and power-law edge weight distributions between functional elements. We attribute these statistical signatures to the brain criticality hypothesis.

We also observe the hierarchical scaling of Philippine cities based on population, which is a consequence of the Zipfian statistics. On the other hand, Gibrat's law is not observed, as the growth rates of the cities are found to be not independent of their populations.

Census data from the last 20 years manifest power-law statistics for the top 30% of cities/municipalities that hold 70% of the population. Population distributions follow the Pareto law with exponents close to 2.5, and rank-size trends follow Zipf's law with exponents of 0.7.