Replication Data for: Temporal correlations in neuronal avalanche occurrence

Intermittent dynamics is ubiquitous in nature and often associated with long-range spatio-temporal correlations. Generally, it can be described as a slow accumulation-fast relaxation process, where quiescent periods are followed by bursts of activity. Recently, in vitro and in vivo studies have shown that ongoing cortical activity in the brain consists of sequences of synchronized bursts, named neuronal avalanches, whose size and duration are power law distributed. This finding positions ongoing activity among those processes which are far from equilibrium but nevertheless characterized by correlations similar to those observed in equilibrium critical phenomena. The statistics of quiet times plays a central role in the understanding of their temporal organization and has enlightened the presence of correlations between avalanche sizes and quiet times. Here, by means of conditional probabilities detrended of statistical noise, we investigate the relationship between these two quantities, as well as between sizes of consecutive avalanches recorded in cortex slice cultures. We show that the time one has to wait until the next avalanche occurs correlates with the size of the previous avalanche: The larger the current avalanche, the longer one has to wait for the next avalanche. Similarly, the time elapsed since the last avalanche correlates with the size of the next one, namely, shorter quiet times tend to be followed by smaller avalanches and viceversa. Finally we demonstrate that sizes of consecutive avalanches are correlated. In particular we show that, for close-in-time avalanches, the preceding avalanches tend to be larger. Our analysis represents the first attempt to provide a quantitative estimate of correlations between activity and quiescence in the framework of neuronal avalanches. By explicitly taking into account statistical fluctuations, we demonstrate significant correlations between synchronized bursts and the following quiescent periods. These correlations need to be considered when identifying mechanisms governing spontaneous activity.