Topological portraits of multiscale coordination dynamics

Complexity Digest

Zhang, M., Kalies, W., Kelso, J., Tognoli, E. (2020). Topological portraits of multiscale coordination dynamics. Journal of Neuroscience Methods https://dx.doi.org/10.1016/j.jneumeth.2020.108672

 

Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a challenge in both theoretical and empirical realms. The present work shows how integrating approaches from computational algebraic topology and dynamical systems may help us meet this challenge. In particular, we focus on the application of multiscale topological analysis to coordinated rhythmic processes. First, theoretical arguments are introduced as to why certain topological features and their scale-dependency are highly relevant to understanding complex collective dynamics. Second, we propose a method to capture such dynamically relevant topological information using persistent homology, which allows us to effectively construct a multiscale topological portrait of rhythmic coordination. Finally, the method…

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