Figure 3. Temporal organization of neuronal avalanches. A, Correlation of the power-law exponent β of the duration distribution between stimulus-evoked and resting state. Each point represents a single subject. B, A three-dimensional phase plot of the power-law exponents β and α versus the branching parameter σ for both stimulus-evoked and rest. Stars indicate across subjects mean and two-dimensional projections of the mean. Each violet and green point corresponds to a single subject at stimulus-evoked and rest, respectively. C, A grand (across subjects) cascade duration distributions for stimulus-evoked and rest data (solid violet and green line, respectively). Dashed black line represents a power law with an exponent of −2. Inset, From a single subject. Cascade duration distributions follow power laws, as expected for neuronal avalanches. D, Top, Histogram of number of avalanches from discrete durations for both stimulus-evoked and rest. Each bar represent a bin of duration Δt = 3.932 ms. The histogram was cut at 20 × Δt = 78.64 ms for better visualization (longest avalanche collected 56 × Δt = 220.19 ms). Bottom, A difference between stimulus-evoked and rest normalized duration histograms (i.e., after division by the corresponding sum of all avalanches collected at each cognitive state separately; inset, same for size histograms, histograms were cut at an avalanche size of 100 for better visualization). Although there are more avalanches collected during stimulus-evoked than in rest (>5.42%), the avalanches collected during stimulus-evoked tend to be lengthier (and larger) than in rest. E, F, Avalanche shape collapse analysis. E, The mean avalanche size for each duration 〈S〉(T) as a function of duration, T in log–log scales. The extracted power-law exponent b + 1 is equal to 1.48 and 1.50 for stimulus-evoked and rest, respectively. F, The estimated scaling function χ̂(T) [which collapses the temporal profile for each duration, S(t, T) to the universal shape F(t/T)] as a function of duration T. The extracted power-law exponent b is equal to 0.37 and 0.40 for stimulus-evoked and rest, respectively. Insets, Mean avalanche shape for each duration, before and after collapse, for both stimulus-evoked (left) and rest (right). G, H, A correlation between σlast, a new estimate based on calculating the ratio between the last two bins of each avalanche in the reverse direction, and σ, which relies on the first two bins, for both stimulus-evoked and rest. We found that these two estimates are highly correlated and provide similar estimates (σlast = 1.15 ± 0.17 and 1.14 ± 0.23 for stimulus-evoked and rest, respectively), reflecting a symmetry between avalanche initiation and termination. Insets, Excluding avalanches of size 1 and 2, for which the definitions of σ and σlast are identical, still preserves a high correlation between the two estimates.