Figure 5

Parabolic avalanches in ongoing activity of frontal cortex exhibit threshold and temporal coarse-graining rescue of scaling exponent χ = 2 in line with critical model dynamics. (a) Lognormal distribution of avalanche number as a function of threshold for 17 different recordings (n = 5 mice; 2-photon imaging of ongoing activity in frontal cortex) at the original temporal resolution (k = 1, black) and after temporal coarse graining (k = 10, purple). Note the experimental variability at a given k, as well as the systematic shift in the distribution with change in k. A sample threshold (θ, grey dotted) shows how a given fixed threshold relates to these distributions. (b) Scaling exponent, χ, and (c) crackling noise deviation, DCC, as a function of temporal coarse grain factor, k and the spike density thresholds. The subregion in which χ ≅ 2 (broken line) is similar to the one identified in the critically balanced E-I model. At low thresholds, the scaling is rescued at smaller values of temporal coarse graining factor, k and at high thresholds, it is rescued at a larger value of k. Over this large range of parameters, the DCC is very noisy even a small change in the parameters can cause a large change in the DCC. (d) Z-scoring procedure for the lognormal distributions corrects for experimental variability as well as temporal coarse graining. A sample z-scored threshold (θ_z,k, grey dotted) shows how a given z-scored threshold relates to these distributions. (e) Scaling exponent, χ, and (f) crackling noise deviation, DCC, as a function of temporal coarse grain factor, k, and the z-scored threshold at the given k, θ_z,k. Figure D shows a robust rescue of χ ≅ 2 (broken line) for a large range of z-scored threshold values (− 1.5 to 1.5). The range of k values over which χ ≅ 2 becomes smaller with an increase in the z-scored threshold. Like B, Figure E shows that the DCC remains unreliable and noisy even when the thresholds are z-scored and tuned for each k.