Brain, Music and non-Poisson Renewal Processes

Abstract

In this paper we show that both music composition and brain function, as revealed by the Electroencephalogram (EEG) analysis, are renewal non-Poisson processes living in the non-ergodic dominion. To reach this important conclusion we process the data with the minimum spanning tree method, so as to detect significant events, thereby building a sequence of times, which is the time series to analyze. Then we show that in both cases, EEG and music composition, these significant events are the signature of a non-Poisson renewal process. This conclusion is reached using a techniques of statistical analysis recently developed by our group, the Aging Experiment (AE). First, we find that in both cases the distances between two consecutive events are described by non-exponential histograms, thereby proving the non-Poisson nature of these processes. The corresponding survival probabilities $\Psi (t)$ are well fitted by stretched exponentials ($\Psi (t)\propto exp(-(\gamma t{)}^{\alpha }$), with $0.5<\alpha <1$.) The second step rests on the adoption of the AE, which shows that these are renewal processes. We show that the renewal stretched exponential is the emerging tip of an iceberg, whose underwater part has slow tails with an inverse power law structure with power index $\mu =1+\alpha$. We find that both EEG and music composition yield $\mu <2$. On the basis of the recently discovered complexity matching effect, according to which a complex system $S$ with ${\mu }_S<2$ responds only to a complex driving signal $P$ with ${\mu }_P={\mu }_S$, we conclude that the results of our analysis may explain the influence of music on human brain.

14 pages, 4 figures. Updated content. Updated figures

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