2019
DOI: 10.1103/physreve.100.032414
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Topological phase transitions in functional brain networks

Abstract: Functional brain networks are often constructed by quantifying correlations among brain regions.Their topological structure includes nodes, edges, triangles and even higher-dimensional objects.Topological data analysis (TDA) is the emerging framework to process datasets 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, topo… Show more

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Cited by 63 publications
(88 citation statements)
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“…Recently, topological data analysis (TDA), has been adopted in neuroimaging as a tool to quantify and visualize the evolution of the brain network at different thresholds (Lee et al, 2011(Lee et al, , 2017Stolz et al, 2018;Sizemore et al, 2018Sizemore et al, , 2019Expert et al, 2019;Santos et al, 2019). The main objective of this method is to model the network as a topological space instead of a graph (Edelsbrunner et al, 2000;Zomorodian and Carlsson, 2005), allowing the assessment of the functional connectivity matrix as a topological process instead of a static threshold-dependent representation of the network.…”
Section: Introductionmentioning
confidence: 99%
“…Recently, topological data analysis (TDA), has been adopted in neuroimaging as a tool to quantify and visualize the evolution of the brain network at different thresholds (Lee et al, 2011(Lee et al, , 2017Stolz et al, 2018;Sizemore et al, 2018Sizemore et al, , 2019Expert et al, 2019;Santos et al, 2019). The main objective of this method is to model the network as a topological space instead of a graph (Edelsbrunner et al, 2000;Zomorodian and Carlsson, 2005), allowing the assessment of the functional connectivity matrix as a topological process instead of a static threshold-dependent representation of the network.…”
Section: Introductionmentioning
confidence: 99%
“…When χ = 0 for a given value of the density of the network, the Euler entropy is singular, χ → ∞. Under specific hypotheses, a topological phase transition in a complex network occurs when the Euler characteristic is null [64]. This statement finds support in the behaviour of χ at the thermodynamic phase transitions across various physical systems [73].…”
Section: Topological Phase Transitionsmentioning
confidence: 85%
“…Further studies contrasting different neuroscientific techniques with TDA must be done to explain in neurobiological level what a topological metrics represent and how they correlate with brain functioning. However, it is already possible to use these metrics to differentiate groups [26,64], and plausible to assume that the interpretation of some classical metrics could be extrapolated to higher orders interactions. For example, the concept of the centralities using pair-wise interactions is used to understand node importance and hubs, the same, in theory, could be applied to the relationships between 3 or more vertices by extending the definition of centrality from networks to simplicial complexes, as done in [88,89].…”
Section: Discussionmentioning
confidence: 99%
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