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Summary

This study introduces novel decomposition methods to analyze complex collective motion in material and life sciences. The approach effectively classifies group dynamics and predicts outcomes, even with intricate interactions.

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Area of Science:

  • Complex Systems Science
  • Nonlinear Dynamics
  • Collective Behavior Analysis

Background:

  • Modeling complex collective behavior in material and life sciences is challenging.
  • Existing models struggle to bridge micro-level interactions with macro-level group functions.
  • Global statistics often fail to capture the nuances of complex interactions in collective motion.

Purpose of the Study:

  • To introduce equation-free decomposition methods for extracting and classifying latent global dynamics.
  • To analyze complex interactions in nonlinear dynamical systems using limited data dimensions.
  • To apply these methods to real-world systems, such as group sports, for predicting group success.

Main Methods:

  • Developed basic decomposition methods to extract and discriminate dynamics in rule-based models (e.g., fish schooling).
  • Verified the method's ability to identify distinct temporal frequency modes and spatial coherence.
  • Extended methods to map high-dimensional feature spaces for analyzing complex, changing interaction rules in small-dimensional systems.

Main Results:

  • Successfully extracted and discriminated dynamics in a fish-schooling model, revealing distinct emergent motions.
  • Identified different temporal frequency modes and spatial interaction coherence across multiple spatiotemporal scales.
  • Classified dynamics in human group sports data and predicted group objective achievement.

Conclusions:

  • The decomposition methods offer a powerful, equation-free approach to understanding complex collective motion.
  • The techniques can classify dynamics in diverse systems, including active matter exhibiting non-trivial dominance laws.
  • This work bridges the gap between interaction rules and emergent group functions in complex systems.