Unveiling the topological structure of chaotic flows from data

Sciamarella, Denisse; Mindlin, Gabriel B.

doi:10.1103/physreve.64.036209

Cited by 19 publications

(20 citation statements)

References 11 publications

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“…The approach adopted in this work is built upon the algorithm described in [24]. BraMAH builds non simplicial complexes, i.e.…”

Section: Computational Stepsmentioning

confidence: 99%

“…The price to pay is that such a cell has a non simplicial nature, but nothing prevents the computation of the homology groups of a non simplicial complex. This approach, called Branched Manifold analysis through Homologies (BraMAH), was first reported in [23], and described in detail in [24]. BraMAH calculates homologies keeping track of the information that is required to identify the mutual organization of the branches in a branched manifold, as well as the localization of twists or torsions, thanks to the supplementary computation of orientability chains.…”

Section: Introductionmentioning

confidence: 99%

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Topology of dynamical reconstructions from Lagrangian data

Charó

Artana

Sciamarella

2020

Physica D: Nonlinear Phenomena

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Branched Manifold analysis through Homologies (BraMAH) is a technique that computes the state-space topology of a dynamical reconstruction from scalar data. This work introduces the application of this technique to Lagrangian time series. The approach unveils the topological structure underlying the behavior of a fluid particle. When applied to a set of sparse particles, the results of the analysis can be used to classify them according to the dynamics they deploy during a given time window. Topological grids can be constructed to portray the spatial organization of the topological classes. The connection between the topological grids and the transport properties of the flow is examined using streaklines. Even if demonstrated here in the context of kinematic flow models, the generality of the method allows for its potential application to experimental or observational Lagrangian data satisfying the technical requirements for the analysis.

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“…The approach adopted in this work is built upon the algorithm described in [24]. BraMAH builds non simplicial complexes, i.e.…”

Section: Computational Stepsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Topology of dynamical reconstructions from Lagrangian data

Charó

Artana

Sciamarella

2020

Physica D: Nonlinear Phenomena

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“…7 Density estimation techniques are typically histogram 10,11 or GMM 12 based. Topological analysis techniques include templates 13 and global vector field reconstruction. 14 Dynamical systems methods have been used in many applications.…”

Section: Previous Workmentioning

confidence: 99%

“…Without large sample sizes and the use of nonlinear filtering techniques, their estimations are suspect. 19 Topological analysis techniques such as templates 13 have been applied to simulated chaotic systems, 20 voltage, 20 and laser 21 …”

Section: Previous Workmentioning

confidence: 99%

Statistical models of reconstructed phase spaces for signal classification

Povinelli

Johnson

Lindgren

et al. 2006

IEEE Trans. Signal Process.

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This paper introduces a novel approach to the analysis and classification of time series signals using statistical models of reconstructed phase spaces. With sufficient dimension, such reconstructed phase spaces are, with probability one, guaranteed to be topologically equivalent to the state dynamics of the generating system, and, therefore, may contain information that is absent in analysis and classification methods rooted in linear assumptions. Parametric and nonparametric distributions are introduced as statistical representations over the multidimensional reconstructed phase space, with classification accomplished through methods such as Bayes maximum likelihood and artificial neural networks (ANNs). The technique is demonstrated on heart arrhythmia classification and speech recognition. This new approach is shown to be a viable and effective alternative to traditional signal classification approaches, particularly for signals with strong nonlinear characteristics.

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“…Yet, systematic work in that direction is needed. The use of homologies for the branched manifold (instead of knot theoretical quantities for the orbits) allows us to qualitatively extend the range of applicability of the existing topological techniques to higher dimensional cases [12].…”

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confidence: 99%