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Duy Duong-Tran1,2, Ralph Kaufmann3, Jiong Chen1,4

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Summary

This study introduces a novel homological formalism to quantify higher-order properties of human brain functional sub-circuits. The method reveals unique network characteristics and task-specific functional differences, offering insights into brain connectivity.

Keywords:
Functional NetworksFunctional sub-circuitHomological kernelTopological data analysis

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Area of Science:

  • Neuroscience
  • Network Science
  • Computational Biology

Background:

  • Human brain functional connectivity exhibits local and non-local properties.
  • Non-local properties of topological strata within functional sub-circuits remain underexplored.

Purpose of the Study:

  • To propose a homological formalism for quantifying higher-order characteristics of human brain functional sub-circuits.
  • To investigate the non-local properties of topological strata induced by local functional sub-circuits.

Main Methods:

  • Development of a homological formalism to analyze human brain functional connectivity.
  • Application of the formalism to quantify higher-order characteristics at whole-brain and sub-circuit levels.
  • Analysis of functional differences between rest and various tasks (emotion, motor, working memory).

Main Results:

  • Each homological order uniquely reveals complementary properties of brain functional sub-circuits.
  • A significant H1 homological distance between rest and motor tasks suggests self-similarity in functional connectivity.
  • Rest-task differentiation is most prominent at specific homological orders (H0 for emotion, H1 for motor, H2 for working memory).
  • Default mode network shows prominent rest-task dichotomy at H1 and H2 levels.
  • The limbic network plays a key role in homological reconfiguration across task and subject domains.

Conclusions:

  • The proposed homological formalism effectively quantifies higher-order properties of brain functional sub-circuits.
  • The findings highlight the self-similarity and task-specific functional organization of the human brain.
  • The formalism has potential applications beyond brain connectomics for analyzing complex network structures.