Figure 3

Exponent analysis for control cultures. (a)–(c) show the probability density function (PDF) of avalanche sizes, avalanche durations, as well as the joint PDF for size and duration, respectively, for a characteristic control culture. For this recording, the overall average inter-spike interval (ISI) is 32 ms and, thus, comparable to our temporal resolution/frame rate (30 ms). Throughout the whole article, we keep the convention that the temporal bin size of 1 corresponds to 30 ms and that the normalized duration corresponds to the duration of an avalanche measured in units of the chosen bin size (multiples of 30 ms). The two subpanels in (a) and (b) are the rescaled PDFs (i.e. multiplied by S^τ, or T^α for size and duration, respectively). Maximum likelihood estimation for the size distribution and the duration distribution and least squares fitting for the joint PDF give τ _control = 1.65 ± 0.1, α _control = 2.15 ± 0.2 and γ _control = 0.5 ± 0.1 for bin size 1. These exponents are within range of what is expected in the mean-field limit and are consistent with the scaling relation (4). See Materials and Methods for an extended analysis.