Topological portraits of multiscale coordination dynamics

Area of Science:

• Complex Systems Science
• Computational Topology
• Dynamical Systems Theory

Background:

• Living systems display organized behavior across multiple scales, posing challenges for quantifying complex dynamics.
• Existing methods struggle to systematically analyze multiscale coordination and emergent collective behaviors.

Purpose of the Study:

• To develop and apply a computational algebraic topology approach for quantifying multiscale coordination dynamics.
• To investigate the relevance of topological features and scale-dependency in collective dynamics.
• To detect subtle transitions in coordinated rhythmic processes using topological data analysis.

Main Methods:

• Integration of computational algebraic topology and dynamical systems.
• Application of persistent homology to construct multiscale topological portraits of rhythmic coordination.
• Analysis of recurrence plots derived from topological portraits of human coordination data.

Main Results:

• Multiscale topological portraits successfully identified collective transitions in human rhythmic coordination.
• These transitions were previously elusive to traditional analytical methods.
• Topological portraits revealed emergent collective properties irreducible to individual components.

Conclusions:

• Topological methods offer a powerful framework for systematically quantifying complex, high-dimensional dynamics in living systems.
• Multiscale topological analysis provides unique insights into collective coordination irreducible to individual behaviors.
• This approach enhances the understanding of emergent phenomena in biological and social systems.