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 is put to test in detecting transitions in real data from an experiment of rhythmic coordination in ensembles of interacting humans. The recurrence plots of topological portraits highlight collective transitions in coordination patterns that were elusive to more traditional methods. This sensitivity to collective transitions would be lost if the behavioral dynamics of individuals were treated as separate degrees of freedom instead of constituents of the topology that they collectively forge. Such multiscale topological portraits highlight collective aspects of coordination patterns that are irreducible to properties of individual parts. The present work demonstrates how the analysis of multiscale coordination dynamics can benefit from topological methods, thereby paving the way for further systematic quantification of complex, high-dimensional dynamics in living systems.
Topological portraits of multiscale coordination dynamics
Mengsen Zhang, William D. Kalies, J. A. Scott Kelso, Emmanuelle Tognoli
The UvA’s Faculty of Science is launching a major recruitment campaign called ‘Connecting Science’ in the areas of Physics, Chemistry, Mathematics, and Computer Science. Our ambition is to attract top talent from all over the world to a large number of newly created faculty positions in a wide range of exciting scientific directions. We offer a stimulating environment and excellent conditions for research, tightly connected to challenging educational programmes. We are looking for ambitious and motivated scientists to connect different scientific disciplines. Our goal is to have a maximal impact on science and society.
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The Northeast Journal of Complex Systems (NEJCS) is launched by the community of Complex Systems researchers in the US Northeast region to provide a solution to the above challenge. As the official journal of the Complex Systems Society US Northeast Chapter, NEJCS serves as an open-access publication venue that is completely free for everyone, including authors, readers, libraries, and the public. Editors and reviewers also work “for free” as this journal is run by many volunteers. This is made possible by the editorial management and support provided by the Center for Collective Dynamics of Complex Systems and the Open Repository @ Binghamton (ORB) initiative at Binghamton University, State University of New York. Even though its name carries the word “Northeast”, this journal is open to everyone regardless of geographical locations. International contributions are more than welcome as well.
Sayama, Hiroki and Georgiev, Georgi (2019) "Editorial Introduction to the Northeast Journal of Complex Systems (NEJCS)," Northeast Journal of Complex Systems (NEJCS): Vol. 1 : No. 1 , Article 1.