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Mentions: It has been reported that there are consistent sequential patterns of spikes after the transitions to the up state during slow wave sleep. The up states may be characterized by critical dynamics for which the avalanche sizes distribution is scale-invariant. In order to understand the mechanism of the sequential patterns, it may thus be necessary to study the fine structure of avalanche transmission between multiple neuronal ensembles at criticality. We have developed an analytical model of avalanche dynamics in modular networks. The univariate distribution of avalanche sizes can be extended to a joint probability distribution describing the probability that neurons are active in each sub-network during avalanches that start from the sub-network with and the number of sub-networks. The mean temporal profile of the avalanches in each sub-network can then be detailed (see Figure 1 (A1) and (B1)) and are reminiscent of the temporal patterns observed experimentally. The sequential patterns depend on the average connection strengths between the sub-networks. At criticality, the cumulated temporal profiles can be collapsed using standard rescaling of the axes and yield a single universal scaling function (see Figure 1 (A2) and (A3)). After rescaling, the mean spiking times in each sub-network are functions of the durations of the avalanches. In Figure 1 (B3), the intervals between successive mean spiking times are proportionally shorter for longer avalanches near criticality.
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