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Topological phase transitions in functional brain networks

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Autor(es):
Santos, Fernando A. N. [1, 2] ; Raposo, Ernesto P. [1] ; Coutinho-Filho, Mauricio D. [1] ; Copelli, Mauro [1] ; Stam, Cornelis J. [3, 4] ; Douw, Linda [5]
Número total de Autores: 6
Afiliação do(s) autor(es):
[1] Univ Fed Pernambuco, Dept Fis, Lab Fis Teor & Computac, BR-50670901 Recife, PE - Brazil
[2] Univ Fed Pernambuco, Dept Matemat, BR-50670901 Recife, PE - Brazil
[3] Vrije Univ Amsterdam, Dept Clin Neurophysiol, Amsterdam Neurosci, Amsterdam UMC, NL-1081 HV Amsterdam - Netherlands
[4] Vrije Univ Amsterdam, MEG Ctr, Amsterdam Neurosci, Amsterdam UMC, NL-1081 HV Amsterdam - Netherlands
[5] Vrije Univ Amsterdam, Dept Anat & Neurosci, Amsterdam Neurosci, Amsterdam UMC, NL-1081 HZ Amsterdam - Netherlands
Número total de Afiliações: 5
Tipo de documento: Artigo Científico
Fonte: Physical Review E; v. 100, n. 3 SEP 30 2019.
Citações Web of Science: 0
Resumo

Functional brain networks are often constructed by quantifying correlations between time series of activity of brain regions. Their topological structure includes nodes, edges, triangles, and even higher-dimensional objects. Topological data analysis (TDA) is the emerging framework to process data sets under this perspective. In parallel, topology has proven essential for understanding fundamental questions in physics. Here we report the discovery of topological phase transitions in functional brain networks by merging concepts from TDA, topology, geometry, physics, and network theory. We show that topological phase transitions occur when the Euler entropy has a singularity, which remarkably coincides with the emergence of multidimensional topological holes in the brain network. The geometric nature of the transitions can be interpreted, under certain hypotheses, as an extension of percolation to high-dimensional objects. Due to the universal character of phase transitions and noise robustness of TDA, our findings open perspectives toward establishing reliable topological and geometrical markers for group and possibly individual differences in functional brain network organization. (AU)

Processo FAPESP: 13/07699-0 - Centro de Pesquisa, Inovação e Difusão em Neuromatemática - NeuroMat
Beneficiário:Jefferson Antonio Galves
Linha de fomento: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs