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End date: 2024 × Start date: 2020 × DDC: 510 × Publisher: Dordrecht [u.a.] : Springer Science + Business Media B.V × WGL Institute: PIK ×

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    Causal coupling inference from multivariate time series based on ordinal partition transition networks
    (Dordrecht [u.a.] : Springer Science + Business Media B.V, 2021) Subramaniyam, Narayan Puthanmadam; Donner, Reik V.; Caron, Davide; Panuccio, Gabriella; Hyttinen, Jari
    Identifying causal relationships is a challenging yet crucial problem in many fields of science like epidemiology, climatology, ecology, genomics, economics and neuroscience, to mention only a few. Recent studies have demonstrated that ordinal partition transition networks (OPTNs) allow inferring the coupling direction between two dynamical systems. In this work, we generalize this concept to the study of the interactions among multiple dynamical systems and we propose a new method to detect causality in multivariate observational data. By applying this method to numerical simulations of coupled linear stochastic processes as well as two examples of interacting nonlinear dynamical systems (coupled Lorenz systems and a network of neural mass models), we demonstrate that our approach can reliably identify the direction of interactions and the associated coupling delays. Finally, we study real-world observational microelectrode array electrophysiology data from rodent brain slices to identify the causal coupling structures underlying epileptiform activity. Our results, both from simulations and real-world data, suggest that OPTNs can provide a complementary and robust approach to infer causal effect networks from multivariate observational data.
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    Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure
    (Dordrecht [u.a.] : Springer Science + Business Media B.V, 2021) Braun, Tobias; Unni, Vishnu R.; Sujith, R.I.; Kurths, Juergen; Marwan, Norbert
    We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot-based analysis for different paradigmatic systems and nonlinear empirical data in order to demonstrate the ability of our method to detect dynamical transitions ranging across different temporal scales. It succeeds to distinguish states of varying dynamical complexity in the presence of noise and non-stationarity, even when the time series is of short length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and geometric features beyond linear structures in the recurrence plot can be accounted for. This makes lacunarity more broadly applicable as a recurrence quantification measure. Lacunarity is usually interpreted as a measure of heterogeneity or translational invariance of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogeneity in the temporal recurrence patterns at all relevant time scales. We demonstrate the potential of the proposed method when applied to empirical data, namely time series of acoustic pressure fluctuations from a turbulent combustor. Recurrence lacunarity captures both the rich variability in dynamical complexity of acoustic pressure fluctuations and shifting time scales encoded in the recurrence plots. Furthermore, it contributes to a better distinction between stable operation and near blowout states of combustors.