Homological landscape of human brain functional sub-circuits

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.