Network dynamics in cultured networks are characterized by a critical branching parameter of σ = 1, suggesting a state of optimal information transmission. A, Estimate of branching parameter σ from individual avalanches. σ = the ratio of descendant electrodes to ancestor electrodes. B, Sketch depicting the critical behavior of a branching process over time. If σ > 1, the size of the avalanche will grow over time, taking over the network (epilepsy), whereas at σ < 1, the avalanche will diminish quickly in size. Only at σ = 1 (critical) can avalanches persist at all scales. C, Values of σ for individual cultures (circles) based on single ancestor (left) or multiple ancestor (right) calculations. Boxes, Means ± SD. D, Phase plot of (σ, α) as a function of Δt. Note that the trajectory passes through critical point (1,-1.5) at the average population IEI of 4.2 msec. σ calculated from single ancestor avalanches. Circles, LFPs; squares, number of electrodes; ± SE.