ArticleProceedings of the National Academy of Sciences of the United States of America2019
Adaptive, locally linear models of complex dynamics.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 34 papers.
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34 citing papers in PubMed.
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- Larval zebrafish swim bouts in three dimensions reveal both new and redundant behaviours.Journal of the Royal Society, Interface · 2025Article
- The Administration of Ketamine Is Associated with Dose-Dependent Stabilization of Cortical Dynamics in Humans.The Journal of neuroscience : the official journal of the Society for Neuroscience · 2025Article
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- Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems.ArXiv · 2025Article
- Nrf1 acts as a highly-conserved determinon for maintaining robust redox homeostasis in the eco-evo-devo process of life histories.Cell stress · 2025Review
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- Discovery of a novel piperazine derivative, cmp2: a selective TRPC6 activator suitable for treatment of synaptic deficiency in Alzheimer's disease hippocampal neurons.Scientific reports · 2024Article
- A Markovian dynamics forProceedings of the National Academy of Sciences of the United States of America · 2024Article
- Light evokes stereotyped global brain dynamics in Caenorhabditis elegans.Current biology : CB · 2024Article
- Rapid automated 3-D pose estimation of larval zebrafish using a physical model-trained neural network.PLoS computational biology · 2023Article
- Non-Stationary Dynamic Mode Decomposition.bioRxiv : the preprint server for biology · 2023Article
- Review
- Social behavioral profiling by unsupervised deep learning reveals a stimulative effect of dopamine D3 agonists on zebrafish sociality.Cell reports methods · 2023Article
- Non-Stationary Dynamic Mode Decomposition.IEEE access : practical innovations, open solutions · 2023Article
- A deep learning framework for inference of single-trial neural population dynamics from calcium imaging with subframe temporal resolution.Nature neuroscience · 2022Article
- Review
- Discovering sparse control strategies in neural activity.PLoS computational biology · 2022Article
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3 authors.
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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
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