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Topological phase transitions in functional brain networks.

Fernando A N Santos1, Ernesto P Raposo2, Maurício D Coutinho-Filho2

  • 1Departamento de Matemática, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil and Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife, PE, Brazil.

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Researchers discovered topological phase transitions in functional brain networks by merging topology and physics concepts. These transitions, linked to Euler entropy singularities, reveal multidimensional topological holes, offering new brain network analysis markers.

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Area of Science:

  • Neuroscience
  • Network Science
  • Topology

Background:

  • Functional brain networks are modeled using correlations in brain region activity time series.
  • Network topology, including higher-dimensional structures, is crucial for understanding complex systems.
  • Topological Data Analysis (TDA) provides a framework for analyzing such complex data.

Purpose of the Study:

  • To discover topological phase transitions in functional brain networks.
  • To integrate concepts from TDA, topology, geometry, physics, and network theory.
  • To identify potential markers for brain network organization.

Main Methods:

  • Utilizing Topological Data Analysis (TDA) to process functional brain network data.
  • Investigating the relationship between Euler entropy singularities and network topology.
  • Applying concepts from statistical physics, specifically phase transitions and percolation theory.

Main Results:

  • Discovery of topological phase transitions in functional brain networks.
  • Demonstration that these transitions coincide with Euler entropy singularities.
  • Observation of the emergence of multidimensional topological holes in brain networks during these transitions.

Conclusions:

  • Topological phase transitions in brain networks are linked to the emergence of topological holes.
  • These findings suggest a high-dimensional extension of percolation theory in brain networks.
  • The study opens avenues for developing robust topological and geometrical markers for brain network organization.