Academic
Publications
Wasserstein distances in the analysis of time series and dynamical systems

Wasserstein distances in the analysis of time series and dynamical systems,10.1016/j.physd.2010.08.005,Physica D-nonlinear Phenomena,Michael Muskulus,

Wasserstein distances in the analysis of time series and dynamical systems   (Citations: 1)
BibTex | RIS | RefWorks Download
A new approach based on Wasserstein distances, which are numerical costs of an optimal transportation problem, allows us to analyze nonlinear phenomena in a robust manner. The long-term behavior is reconstructed from time series, resulting in a probability distribution over phase space. Each pair of probability distributions is then assigned a numerical distance that quantifies the differences in their dynamical properties. From the totality of all these distances a low-dimensional representation in a Euclidean space is derived, in which the time series can be classified and statistically analyzed. This representation shows the functional relationships between the dynamical systems under study. It allows us to assess synchronization properties and also offers a new way of numerical bifurcation analysis.The statistical techniques for this distance-based analysis of dynamical systems are presented, filling a gap in the literature, and their application is discussed in a few examples of datasets arising in physiology and neuroscience, and in the well-known Hénon system.
Journal: Physica D-nonlinear Phenomena - PHYSICA D , vol. 240, no. 1, pp. 45-58, 2011
Cumulative Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
    • ...of variability within the system calculated as the power of RRI oscillations in various frequency ranges. The overall amount of variability in these ranges of the RRI PSD is an obviously essential dimension of neurocardiac dynamics, but unlikely the only dimension, especially if one considers the possibility that RRI PSD dynamics can change qualitatively and non-linearly in response to perturbation ...

    Marsha E. Bateset al. The Redistribution of Power: Neurocardiac Signaling, Alcohol and Gende...

Sort by: