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- ItemDynamic patterns of expertise: The case of orthopedic medical diagnosis(San Francisco, CA : Public Library of Science (PLoS), 2016) Assaf, D.; Amar, E.; Marwan, N.; Neuman, Y.; Salai, M.; Rath, E.
- ItemAbrupt transitions in time series with uncertainties(London : Nature Publishing Group, 2018) Goswami, B.; Boers, N.; Rheinwalt, A.; Marwan, N.; Heitzig, J.; Breitenbach, S.F.M.; Kurths, J.Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Niño-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an 'uncertainty-aware' framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon.
- ItemRecurrence networks-a novel paradigm for nonlinear time series analysis(College Park, MD : Institute of Physics Publishing, 2010) Donner, R.V.; Zou, Y.; Donges, J.F.; Marwan, N.; Kurths, J.This paper presents a new approach for analysing the structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network, which links different points in time if the considered states are closely neighboured in phase space. In comparison with similar network-based techniques the new approach has important conceptual advantages, and can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases. It has been demonstrated here that there are fundamental relationships between many topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related to the dynamical complexity of a time series, most of which are not yet provided by other existing methods of nonlinear time series analysis. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
- ItemChange in the embedding dimension as an indicator of an approaching transition(San Francisco, CA : Public Library of Science (PLoS), 2014) Neuman, Y.; Marwan, N.; Cohen, Y.Predicting a transition point in behavioral data should take into account the complexity of the signal being influenced by contextual factors. In this paper, we propose to analyze changes in the embedding dimension as contextual information indicating a proceeding transitive point, called OPtimal Embedding tRANsition Detection (OPERAND). Three texts were processed and translated to time-series of emotional polarity. It was found that changes in the embedding dimension proceeded transition points in the data. These preliminary results encourage further research into changes in the embedding dimension as generic markers of an approaching transition point.
- ItemIdentifying causal gateways and mediators in complex spatio-temporal systems(London : Nature Publishing Group, 2015) Runge, J.; Petoukhov, V.; Donges, J.F.; Hlinka, J.; Jajcay, N.; Vejmelka, M.; Hartman, D.; Marwan, N.; Paluš, M.; Kurths, J.
- ItemA unified and automated approach to attractor reconstruction(London : IOP, 2021) Kraemer, K. H.; Datseris, G.; Kurths, J.; Kiss, I. Z.; Ocampo-Espindola, J. L.; Marwan, N.We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful reconstruction of systems inheriting different time scales. In contrast to the established methods, the minimization of an appropriate cost function determines the embedding dimension without using a threshold parameter. Moreover, the method is capable of detecting stochastic time series and, thus, can handle noise contaminated input without adjusting parameters. The superiority of the proposed method is shown on some paradigmatic models and experimental data from chaotic chemical oscillators.
- ItemIdentification of dynamical transitions in marine palaeoclimate records by recurrence network analysis(Göttingen : Copernicus GmbH, 2011) Donges, J.F.; Donner, R.V.; Rehfeld, K.; Marwan, N.; Trauth, M.H.; Kurths, J.The analysis of palaeoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, in this paper we argue that the statistical properties of recurrence networks - a recently developed approach - are promising candidates for characterising the system's nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. In a first order approximation, the results of recurrence network analysis are invariant to changes in the age model and are not directly affected by non-equidistant sampling of the data. Specifically, we investigate the behaviour of recurrence network measures for both paradigmatic model systems with non-stationary parameters and four marine records of long-term palaeoclimate variations. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. We demonstrate that recurrence network analysis is able to detect relevant regime shifts in synthetic data as well as in problematic geoscientific time series. This suggests its application as a general exploratory tool of time series analysis complementing existing methods.
- ItemEstimation of sedimentary proxy records together with associated uncertainty(Göttingen : Copernicus GmbH, 2015) Goswami, B.; Heitzig, J.; Rehfeld, K.; Marwan, N.; Anoop, A.; Prasad, S.; Kurths, J.
- ItemSpatial structures and directionalities in Monsoonal precipitation over South Asia(Göttingen : Copernicus GmbH, 2010) Malik, N.; Marwan, N.; Kurths, J.Precipitation during the monsoon season over the Indian subcontinent occurs in form of enormously complex spatiotemporal patterns due to the underlying dynamics of atmospheric circulation and varying topography. Employing methods from nonlinear time series analysis, we study spatial structures of the rainfall field during the summer monsoon and identify principle regions where the dynamics of monsoonal rainfall is more coherent or homogenous. Moreover, we estimate the time delay patterns of rain events. Here we present an analysis of two separate high resolution gridded data sets of daily rainfall covering the Indian subcontinent. Using the method of event synchronization (ES), we estimate regions where heavy rain events during monsoon happen in some lag synchronised form. Further using the delay behaviour of rainfall events, we estimate the directionalities related to the progress of such type of rainfall events. The Active (break) phase of a monsoon is characterised by an increase(decrease) of rainfall over certain regions of the Indian subcontinent. We show that our method is able to identify regions of such coherent rainfall activity.
- ItemComparison of correlation analysis techniques for irregularly sampled time series(Göttingen : Copernicus GmbH, 2011) Rehfeld, K.; Marwan, N.; Heitzig, J.; Kurths, J.Geoscientific measurements often provide time series with irregular time sampling, requiring either data reconstruction (interpolation) or sophisticated methods to handle irregular sampling. We compare the linear interpolation technique and different approaches for analyzing the correlation functions and persistence of irregularly sampled time series, as Lomb-Scargle Fourier transformation and kernel-based methods. In a thorough benchmark test we investigate the performance of these techniques. All methods have comparable root mean square errors (RMSEs) for low skewness of the inter-observation time distribution. For high skewness, very irregular data, interpolation bias and RMSE increase strongly. We find a 40 % lower RMSE for the lag-1 autocorrelation function (ACF) for the Gaussian kernel method vs. the linear interpolation scheme,in the analysis of highly irregular time series. For the cross correlation function (CCF) the RMSE is then lower by 60 %. The application of the Lomb-Scargle technique gave results comparable to the kernel methods for the univariate, but poorer results in the bivariate case. Especially the high-frequency components of the signal, where classical methods show a strong bias in ACF and CCF magnitude, are preserved when using the kernel methods. We illustrate the performances of interpolation vs. Gaussian kernel method by applying both to paleo-data from four locations, reflecting late Holocene Asian monsoon variability as derived from speleothem δ18O measurements. Cross correlation results are similar for both methods, which we attribute to the long time scales of the common variability. The persistence time (memory) is strongly overestimated when using the standard, interpolation-based, approach. Hence, the Gaussian kernel is a reliable and more robust estimator with significant advantages compared to other techniques and suitable for large scale application to paleo-data.