Adaptive, locally linear models of complex dynamics

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

The dynamics of complex systems generally include high-dimensional, nonstationary, and nonlinear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties, we detail an approach based on local linear models within windows determined adaptively from data. While the dynamics within each window are simple, consisting of exponential decay, growth, and oscillations, the collection of local parameters across all windows provides a principled characterization of the full time series. To explore the resulting model space, we develop a likelihood-based hierarchical clustering, and we examine the eigenvalues of the linear dynamics. We demonstrate our analysis with the Lorenz system undergoing stable spiral dynamics and in the standard chaotic regime. Applied to the posture dynamics of the nematode Caenorhabditis elegans, our approach identifies fine-grained behavioral states and model dynamics which fluctuate about an instability boundary, and we detail a bifurcation in a transition from forward to backward crawling. We analyze whole-brain imaging in C. elegans and show that global brain dynamics is damped away from the instability boundary by a decrease in oxygen concentration. We provide additional evidence for such near-critical dynamics from the analysis of electrocorticography in monkey and the imaging of a neural population from mouse visual cortex at single-cell resolution.
Original languageEnglish
Pages (from-to)1501-1510
Number of pages10
JournalProceedings of the National Academy of Sciences of the United States of America
Volume116
Issue number5
Early online date17 Jan 2019
DOIs
Publication statusPublished - 29 Jan 2019

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Caenorhabditis elegans
Linear Models
Space Simulation
Visual Cortex
Posture
Neuroimaging
Haplorhini
Cluster Analysis
Oxygen
Brain
Growth
Population
Electrocorticography

Keywords

  • Animal behavior
  • Clustering
  • Dynamical criticality
  • Neural dynamics
  • Time-series segmentation

Cite this

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title = "Adaptive, locally linear models of complex dynamics",
abstract = "The dynamics of complex systems generally include high-dimensional, nonstationary, and nonlinear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties, we detail an approach based on local linear models within windows determined adaptively from data. While the dynamics within each window are simple, consisting of exponential decay, growth, and oscillations, the collection of local parameters across all windows provides a principled characterization of the full time series. To explore the resulting model space, we develop a likelihood-based hierarchical clustering, and we examine the eigenvalues of the linear dynamics. We demonstrate our analysis with the Lorenz system undergoing stable spiral dynamics and in the standard chaotic regime. Applied to the posture dynamics of the nematode Caenorhabditis elegans, our approach identifies fine-grained behavioral states and model dynamics which fluctuate about an instability boundary, and we detail a bifurcation in a transition from forward to backward crawling. We analyze whole-brain imaging in C. elegans and show that global brain dynamics is damped away from the instability boundary by a decrease in oxygen concentration. We provide additional evidence for such near-critical dynamics from the analysis of electrocorticography in monkey and the imaging of a neural population from mouse visual cortex at single-cell resolution.",
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Adaptive, locally linear models of complex dynamics. / Costa, Antonio C.; Ahamed, Tosif; Stephens, Greg J.

In: Proceedings of the National Academy of Sciences of the United States of America, Vol. 116, No. 5, 29.01.2019, p. 1501-1510.

Research output: Contribution to JournalArticleAcademicpeer-review

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