Functional scale-free networks in the two-dimensional Abelian sandpile model

Robustness of functional networks at criticality against structural defects

The robustness of dynamical properties of neuronal networks against structural damages is a central problem in computational and experimental neuroscience. Research has shown that the cortical network of a healthy brain works near a critical state and, moreover, that functional neuronal networks often have scale-free and small-world properties. In this work, we study how the robustness of simple functional networks at criticality is affected by structural defects. In particular, we consider a two-dimensional Ising model at the critical temperature and investigate how its functional network changes with the increasing degree of structural defects. We show that the scale-free and small-world properties of the functional network at criticality are robust against large degrees of structural lesions while the system remains below the percolation limit. Although the Ising model is only a conceptual description of a two-state neuron, our research reveals fundamental robustness properties of functional networks derived from classical statistical mechanics models.

Coexistence of Stochastic Oscillations and Self-Organized Criticality in a Neuronal Network: Sandpile Model Application

Self-organized criticality (SOC) and stochastic oscillations (SOs) are two theoretically contradictory phenomena that are suggested to coexist in the brain. Recently it has been shown that an accumulation-release process like sandpile dynamics can generate SOC and SOs simultaneously. We considered the effect of the network structure on this coexistence and showed that the sandpile dynamics on a small-world network can produce two power law regimes along with two groups of SOs-two peaks in the power spectrum of the generated signal simultaneously. We also showed that external stimuli in the sandpile dynamics do not affect the coexistence of SOC and SOs but increase the frequency of SOs, which is consistent with our knowledge of the brain.