Figure 2
From: The recovery of parabolic avalanches in spatially subsampled neuronal networks at criticality
Increasing the threshold in the fully sampled model underestimates the scaling exponent, χ, which can be rescued by temporal coarse graining. (a) Consolidated view of the avalanche size (α), duration (β), and scaling (χ) exponents as a function of threshold θ and temporal coarse-graining factor k (f = 100%, fully sampled model). Drive dominated: Low threshold regime (above the red broken line) dominated by external Poisson drive. White frames: Parameter regions displayed in (b) and (c). (b) At the highest temporal resolution (k = 1), high thresholds underestimate the scaling exponent, χ, as well as χcn, with DCC remaining low. Size exponent, α (left), duration exponent, β (middle), scaling exponent, χ, and expected crackling noise relation, χcn, (right) as a function of θ. (c) At high threshold (θ = 1000), temporal coarse graining recovers χ, but the χcn exhibits a singularity leading to high DCC. Size exponent, α (left), duration exponent, β (middle), as a function of coarse graining factor, k, (θ = 1000). α passes through 1 (red broken line; black triangle), which causes a singularity in χcn. (right). Note that the scaling exponent, χ, stabilizes to a value of 2 (right, black dashed line), whereas χcn grows until it passes through a singularity at the temporal coarse graining value of k = 17 (vertical broken line; triangle; see inset).
