TY - JOUR

T1 - Topological phase transitions in functional brain networks

AU - Santos, Fernando A. N.

AU - Raposo, Ernesto P.

AU - Coutinho-Filho, Maurício D.

AU - Copelli, Mauro

AU - Stam, Cornelis J.

AU - Douw, Linda

PY - 2019/9/30

Y1 - 2019/9/30

N2 - 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.

AB - 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.

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85072960901&origin=inward

U2 - 10.1103/PhysRevE.100.032414

DO - 10.1103/PhysRevE.100.032414

M3 - Article

C2 - 31640025

VL - 100

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 3

M1 - 032414

ER -