Figure 3. Impact of binning on avalanche size distributions P_sub(s) and scaling.

(a,d) Sampling N=2⁷ units at different bin sizes from sparse (a) and fully connected network (d). For small bin sizes (<16 steps), P_sub(s) deviates from a power law with slope 1.5 (dashed line). For larger bin sizes (≥ 32 steps), P_sub(s) is bin size invariant and shows the expected power law with cutoff. (b,e) Same as Fig. 2; for sufficiently large bin sizes P_sub(s) collapsed under subsampling scaling. (c,f) When applying a small bin size, here one step, P_sub(s) does not collapse. Parameters: Critical branching model (BM) with size M=2¹⁴ and sparse connectivity (k=4), except for d that has all-to-all connectivity (k=M).