Figure 3
From: The recovery of parabolic avalanches in spatially subsampled neuronal networks at criticality
Temporal coarse graining at critical value of g: Rescue of scaling exponent, equivalence between threshold and fractional sampling, and increased mean pairwise neuron correlation. (a) The maximum scaling exponent across different temporal binning values as a function of the balance parameter, g, for a subsampled model (f = 0.1%) employing a 1-spike threshold. Notably, the retrieval of χ = 2 is exclusively observed in critical models (gc = 3.5), but promptly diminishes in slightly subcritical or supercritical models. In supercritical models, we obtain ceaseless activity (shaded gray region), precluding the identification of avalanches at the specified threshold. Yellow circles mark g values used in (c). (b) Collapsed scaling exponent curves for different values of the sampling fraction, f, ranging from 100 to 0.1% for a threshold that is scaled by the sampling fraction as θ = 3000*f (i.e., a threshold of 3000 spikes for the fully sampled model translates to a threshold of 3 spikes for the 0.1% sampled model). Inset: The total collapse error as a function of collapse exponent, ξ. The error is taken over multiple different curves with θ ranging from 100 to 100,000. The error shows a clear minimum at ξ = 1, indicating the threshold can be scaled proportionally with the sampling fraction to obtain the best collapse. (c) The rescue of χ = 2 correlates with an increase of the mean delayed pair-wise correlation among neurons, which is independent of the fraction of neurons sampled. However, the temporal coarse graining regime of k for which χ = 2 (green area) is not predicted by this pair-wise correlation. For a supercritical (g = 3.475) network, the mean pairwise correlation is lower, but still increases with temporal coarse graining. For a subcritical network (g = 3.6), the mean delayed pair-wise correlation is close to 0.
