The recovery of parabolic avalanches in spatially subsampled neuronal networks at criticality

Scaling relationships are key in characterizing complex systems at criticality. In the brain, they are evident in neuronal avalanches-scale-invariant cascades of neuronal activity quantified by power laws. Avalanches manifest at the cellular level as cascades of neuronal groups that fire action potentials simultaneously. Such spatiotemporal synchronization is vital to theories on brain function yet avalanche synchronization is often underestimated when only a fraction of neurons is observed. Here, we investigate biases from fractional sampling within a balanced network of excitatory and inhibitory neurons with all-to-all connectivity and critical branching process dynamics. We focus on how mean avalanche size scales with avalanche duration. For parabolic avalanches, this scaling is quadratic, quantified by the scaling exponent,