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Adaptive, locally linear models of complex dynamics.

Antonio C Costa1, Tosif Ahamed2, Greg J Stephens3,2

  • 1Department of Physics and Astronomy, Vrije Universiteit Amsterdam, 1081HV Amsterdam, The Netherlands.

Proceedings of the National Academy of Sciences of the United States of America
|January 19, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a novel data-driven method using local linear models to analyze complex system dynamics. The approach reveals fine-grained behavioral states and near-critical dynamics in biological systems, aiding in understanding complex behaviors.

Keywords:
animal behaviorclusteringdynamical criticalityneural dynamicstime-series segmentation

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Area of Science:

  • Complex Systems Analysis
  • Nonlinear Dynamics
  • Computational Neuroscience

Background:

  • Complex systems exhibit high-dimensional, nonstationary, and nonlinear behaviors, challenging quantitative analysis.
  • Understanding these dynamics is crucial for fields ranging from physics to neuroscience.
  • Existing methods often struggle to capture the full complexity of such systems.

Purpose of the Study:

  • To develop a principled approach for characterizing complex time series dynamics.
  • To identify and analyze fine-grained behavioral states and transitions in biological systems.
  • To investigate the role of environmental factors and near-critical dynamics in neural activity.

Main Methods:

  • Adaptive local linear modeling within data-determined windows.
  • Likelihood-based hierarchical clustering to explore model space.
  • Eigenvalue analysis of local linear dynamics.
  • Application to Lorenz system, nematode posture, C. elegans whole-brain imaging, monkey ECoG, and mouse V1 neural populations.

Main Results:

  • The approach successfully characterizes complex dynamics, revealing exponential decay, growth, and oscillations.
  • Identified fine-grained behavioral states and a bifurcation in C. elegans crawling.
  • Demonstrated damping of global brain dynamics by decreased oxygen concentration in C. elegans.
  • Observed near-critical dynamics across diverse biological systems, including neural activity.

Conclusions:

  • The local linear modeling approach provides a powerful tool for dissecting complex system dynamics.
  • The findings suggest that biological systems, particularly neural networks, may operate near critical points.
  • Environmental factors like oxygen concentration can significantly influence neural dynamics and stability.