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- 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.
- 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.
- 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.
- ItemFinding recurrence networks' threshold adaptively for a specific time series(Göttingen : Copernicus GmbH, 2014) Eroglu, D.; Marwan, N.; Prasad, S.; Kurths, J.Recurrence-plot-based recurrence networks are an approach used to analyze time series using a complex networks theory. In both approaches-recurrence plots and recurrence networks-, a threshold to identify recurrent states is required. The selection of the threshold is important in order to avoid bias of the recurrence network results. In this paper, we propose a novel method to choose a recurrence threshold adaptively. We show a comparison between the constant threshold and adaptive threshold cases to study period-chaos and even period-period transitions in the dynamics of a prototypical model system. This novel method is then used to identify climate transitions from a lake sediment record.
- ItemReview: Visual analytics of climate networks(Göttingen : Copernicus GmbH, 2015) Nocke, T.; Buschmann, S.; Donges, J.F.; Marwan, N.; Schulz, H.-J.; Tominski, C.
- ItemCorrelation networks from flows. The case of forced and time-dependent advection-diffusion dynamics(San Francisco, CA : Public Library of Science (PLoS), 2016) Tupikina, L.; Molkenthin, N.; López, C.; Hernández-GarcÃa, E.; Marwan, N.; Kurths, J.
- ItemCorrelating the ancient Maya and modern european calendars with high-precision AMS 14C dating(London : Nature Publishing Group, 2013) Kennett, D.J.; Hajdas, I.; Culleton, B.J.; Belmecheri, S.; Martin, S.; Neff, H.; Awe, J.; Graham, H.V.; Freeman, K.H.; Newsom, L.; Lentz, D.L.; Anselmetti, F.S.; Robinson, M.; Marwan, N.; Southon, J.; Hodell, D.A.; Haug, G.H.The reasons for the development and collapse of Maya civilization remain controversial and historical events carved on stone monuments throughout this region provide a remarkable source of data about the rise and fall of these complex polities. Use of these records depends on correlating the Maya and European calendars so that they can be compared with climate and environmental datasets. Correlation constants can vary up to 1000 years and remain controversial.Wereport a series of high-resolution AMS14C dates on a wooden lintel collected from the Classic Period city of Tikal bearing Maya calendar dates. The radiocarbon dates were calibrated using a Bayesian statistical model and indicate that the dates were carved on the lintel betweenAD 658-696. This strongly supports the Goodman-Mart?nez-Thompson (GMT) correlation and the hypothesis that climate change played an important role in the development and demise of this complex civilization.
- ItemNetworks from Flows - From Dynamics to Topology(London : Nature Publishing Group, 2014) Molkenthin, N.; Rehfeld, K.; Marwan, N.; Kurths, J.Complex network approaches have recently been applied to continuous spatial dynamical systems, like climate, successfully uncovering the system's interaction structure. However the relationship between the underlying atmospheric or oceanic flow's dynamics and the estimated network measures have remained largely unclear. We bridge this crucial gap in a bottom-up approach and define a continuous analytical analogue of Pearson correlation networks for advection-diffusion dynamics on a background flow. Analysing complex networks of prototypical flows and from time series data of the equatorial Pacific, we find that our analytical model reproduces the most salient features of these networks and thus provides a general foundation of climate networks. The relationships we obtain between velocity field and network measures show that line-like structures of high betweenness mark transition zones in the flow rather than, as previously thought, the propagation of dynamical information.