dorsal/arxiv
View SchemaBrain, Music and non-Poisson Renewal Processes
| Authors | Simone Bianco, Massimiliano Ignaccolo, Mark S. Rider, Mary J. Ross, Phil Winsor, Paolo Grigolini |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0610037 |
| URL | https://arxiv.org/abs/q-bio/0610037 |
| DOI | 10.1103/PhysRevE.75.061911 |
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.
{
"annotation_id": "e517581c-b10f-4931-8b30-0aa2b1280512",
"date_created": "2026-03-02T18:01:35.009000Z",
"date_modified": "2026-03-02T18:01:35.009000Z",
"file_hash": "4bc6548d7b229be187ae76d4f1a0213fac33640b160df99897491675f99887ec",
"private": false,
"record": {
"abstract": "In this paper we show that both music composition and brain function, as\nrevealed by the Electroencephalogram (EEG) analysis, are renewal non-Poisson\nprocesses living in the non-ergodic dominion. To reach this important\nconclusion we process the data with the minimum spanning tree method, so as to\ndetect significant events, thereby building a sequence of times, which is the\ntime series to analyze. Then we show that in both cases, EEG and music\ncomposition, these significant events are the signature of a non-Poisson\nrenewal process. This conclusion is reached using a techniques of statistical\nanalysis recently developed by our group, the Aging Experiment (AE). First, we\nfind that in both cases the distances between two consecutive events are\ndescribed by non-exponential histograms, thereby proving the non-Poisson nature\nof these processes. The corresponding survival probabilities $\\Psi(t)$ are well\nfitted by stretched exponentials ($\\Psi(t) \\propto exp(-(\\gamma t)^\\alpha$),\nwith $0.5 \u003c\\alpha \u003c1$.) The second step rests on the adoption of the AE, which\nshows that these are renewal processes. We show that the renewal stretched\nexponential is the emerging tip of an iceberg, whose underwater part has slow\ntails with an inverse power law structure with power index $\\mu = 1 + \\alpha$.\nWe find that both EEG and music composition yield $\\mu \u003c 2$. On the basis of\nthe recently discovered complexity matching effect, according to which a\ncomplex system $S$ with $\\mu_S \u003c 2$ responds only to a complex driving signal\n$P$ with $\\mu_P = \\mu_S$, we conclude that the results of our analysis may\nexplain the influence of music on human brain.",
"arxiv_id": "q-bio/0610037",
"authors": [
"Simone Bianco",
"Massimiliano Ignaccolo",
"Mark S. Rider",
"Mary J. Ross",
"Phil Winsor",
"Paolo Grigolini"
],
"categories": [
"q-bio.NC"
],
"doi": "10.1103/PhysRevE.75.061911",
"title": "Brain, Music and non-Poisson Renewal Processes",
"url": "https://arxiv.org/abs/q-bio/0610037"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "52c99804-ce94-4e56-8d37-225985839e40",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}