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Search Results: 1 - 10 of 2156 matches for " Norbert Marwan "
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How to avoid potential pitfalls in recurrence plot based data analysis
Norbert Marwan
Physics , 2010, DOI: 10.1142/S0218127411029008
Abstract: Recurrence plots and recurrence quantification analysis have become popular in the last two decades. Recurrence based methods have on the one hand a deep foundation in the theory of dynamical systems and are on the other hand powerful tools for the investigation of a variety of problems. The increasing interest encompasses the growing risk of misuse and uncritical application of these methods. Therefore, we point out potential problems and pitfalls related to different aspects of the application of recurrence plots and recurrence quantification analysis.
Line Structures in Recurrence Plots
Norbert Marwan,Juergen Kurths
Physics , 2004, DOI: 10.1016/j.physleta.2004.12.056
Abstract: Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the phase-space trajectory. This provides us a better understanding of the structures occuring in recurrence plots. The relationship between the time-scales and line structures are of practical importance in cross recurrence plots. Using this relationship within cross recurrence plots, the time-scales of differently sampled or time-transformed measurements can be adjusted. An application to geophysical measurements illustrates the capability of this method for the adjustment of time-scales in different measurements.
Extended Recurrence Plot Analysis and its Application to ERP Data
Norbert Marwan,Anja Meinke
Physics , 2002, DOI: 10.1142/S0218127404009454
Abstract: We present new measures of complexity and their application to event related potential data. The new measures base on structures of recurrence plots and makes the identification of chaos-chaos transitions possible. The application of these measures to data from single-trials of the Oddball experiment can identify laminar states therein. This offers a new way of analyzing event-related activity on a single-trial basis.
Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems
Norbert Marwan,Jürgen Kurths
Physics , 2015, DOI: 10.1063/1.4916924
Abstract: We present here two promising techniques for the application of the complex network approach to continuous spatio-temporal systems that have been developed in the last decade and show large potential for future application and development of complex systems analysis. First, we discuss the transforming of a time series from such systems to a complex network. The natural approach is to calculate the recurrence matrix and interpret such as the adjacency matrix of an associated complex network, called recurrence network. Using complex network measures, such as transitivity coefficient, we demonstrate that this approach is very efficient for identifying qualitative transitions in observational data, e.g., when analyzing paleoclimate regime transitions. Second, we demonstrate the use of directed spatial networks constructed from spatio-temporal measurements of such systems that can be derived from the synchronized-in-time occurrence of extreme events in different spatial regions. Although there are many possibilities to investigate such spatial networks, we present here the new measure of network divergence and how it can be used to develop a prediction scheme of extreme rainfall events.
Change in the Embedding Dimension as an Indicator of an Approaching Transition
Yair Neuman, Norbert Marwan, Yohai Cohen
PLOS ONE , 2014, DOI: 10.1371/journal.pone.0101014
Abstract: 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.
Generalised Recurrence Plot Analysis for Spatial Data
Norbert Marwan,Juergen Kurths,Peter Saparin
Physics , 2006, DOI: 10.1016/j.physleta.2006.08.058
Abstract: Recurrence plot based methods are highly efficient and widely accepted tools for the investigation of time series or one-dimensional data. We present an extension of the recurrence plots and their quantifications in order to study recurrent structures in higher-dimensional spatial data. The capability of this extension is illustrated on prototypical 2D models. Next, the tested and proved approach is applied to assess the bone structure from CT images of human proximal tibia. We find that the spatial structures in trabecular bone become more self-similar during the bone loss in osteoporosis.
Recurrence Plots 25 years later -- gaining confidence in dynamical transitions
Norbert Marwan,Stefan Schinkel,Jürgen Kurths
Physics , 2013, DOI: 10.1209/0295-5075/101/20007
Abstract: Recurrence plot based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantification analysis. We show how this approach can be used to study significant changes in dynamical systems due to a change in control parameters, chaos-order as well as chaos-chaos transitions. Finally we study and discuss climate transitions by analysing a marine proxy record for past sea surface temperature. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots.
Analysing spatially extended high-dimensional dynamics by recurrence plots
Norbert Marwan,Jürgen Kurths,Saskia Foerster
Physics , 2014, DOI: 10.1016/j.physleta.2015.01.013
Abstract: Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply this method on spatially extended chaos, such as derived from the Lorenz96 model and show that the recurrence plot based measures can qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analyzing satellite image time series of vegetation cover with contrasting dynamics as a spatially extended and potentially high-dimensional example from the real world.
The backbone of the climate network
Jonathan F. Donges,Yong Zou,Norbert Marwan,Juergen Kurths
Physics , 2010, DOI: 10.1209/0295-5075/87/48007
Abstract: We propose a method to reconstruct and analyze a complex network from data generated by a spatio-temporal dynamical system, relying on the nonlinear mutual information of time series analysis and betweenness centrality of complex network theory. We show, that this approach reveals a rich internal structure in complex climate networks constructed from reanalysis and model surface air temperature data. Our novel method uncovers peculiar wave-like structures of high energy flow, that we relate to global surface ocean currents. This points to a major role of the oceanic surface circulation in coupling and stabilizing the global temperature field in the long term mean (140 years for the model run and 60 years for reanalysis data). We find that these results cannot be obtained using classical linear methods of multivariate data analysis, and have ensured their robustness by intensive significance testing.
Complex networks in climate dynamics - Comparing linear and nonlinear network construction methods
Jonathan F. Donges,Yong Zou,Norbert Marwan,Jürgen Kurths
Physics , 2009, DOI: 10.1140/epjst/e2009-01098-2
Abstract: Complex network theory provides a powerful framework to statistically investigate the topology of local and non-local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system.
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