@article{AgarwalMaheswaranMarwanetal.2018,
  author    = {Agarwal, Ankit and Maheswaran, Rathinasamy and Marwan, Norbert and Caesar, Levke and Kurths, J{\"u}rgen},
  title     = {Wavelet-based multiscale similarity measure for complex networks},
  series = {The European physical journal : B, Condensed matter and complex systems},
  volume    = {91},
  journal   = {The European physical journal : B, Condensed matter and complex systems},
  number    = {11},
  publisher = {Springer},
  address   = {New York},
  issn      = {1434-6028},
  doi       = {10.1140/epjb/e2018-90460-6},
  pages     = {12},
  year      = {2018},
  abstract  = {In recent years, complex network analysis facilitated the identification of universal and unexpected patterns in complex climate systems. However, the analysis and representation of a multiscale complex relationship that exists in the global climate system are limited. A logical first step in addressing this issue is to construct multiple networks over different timescales. Therefore, we propose to apply the wavelet multiscale correlation (WMC) similarity measure, which is a combination of two state-of-the-art methods, viz. wavelet and Pearson's correlation, for investigating multiscale processes through complex networks. Firstly we decompose the data over different timescales using the wavelet approach and subsequently construct a corresponding network by Pearson's correlation. The proposed approach is illustrated and tested on two synthetics and one real-world example. The first synthetic case study shows the efficacy of the proposed approach to unravel scale-specific connections, which are often undiscovered at a single scale. The second synthetic case study illustrates that by dividing and constructing a separate network for each time window we can detect significant changes in the signal structure. The real-world example investigates the behavior of the global sea surface temperature (SST) network at different timescales. Intriguingly, we notice that spatial dependent structure in SST evolves temporally. Overall, the proposed measure has an immense potential to provide essential insights on understanding and extending complex multivariate process studies at multiple scales.},
  language  = {en}
}
@article{ZaikinKurths2006,
  author    = {Zaikin, Alexey and Kurths, J{\"u}rgen},
  title     = {Optimal length transportation hypothesis to model proteasome product size distribution},
  series = {Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences},
  volume    = {32},
  journal   = {Journal of biological physics : emphasizing physical principles in biological research ; an international journal for the formulation and application of mathematical models in the biological sciences},
  number    = {3-4},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0092-0606},
  doi       = {10.1007/s10867-006-9014-z},
  pages     = {231 -- 243},
  year      = {2006},
  abstract  = {This paper discusses translocation features of the 20S proteasome in order to explain typical proteasome length distributions. We assume that the protein transport depends significantly on the fragment length with some optimal length which is transported most efficiently. By means of a simple one-channel model, we show that this hypothesis can explain both the one- and the three-peak length distributions found in experiments. A possible mechanism of such translocation is provided by so-called fluctuation-driven transport.},
  language  = {en}
}
@article{GoswamiBoersRheinwaltetal.2018,
  author    = {Goswami, Bedartha and Boers, Niklas and Rheinwalt, Aljoscha and Marwan, Norbert and Heitzig, Jobst and Breitenbach, Sebastian Franz Martin and Kurths, J{\"u}rgen},
  title     = {Abrupt transitions in time series with uncertainties},
  series = {Nature Communications},
  volume    = {9},
  journal   = {Nature Communications},
  publisher = {Nature Publ. Group},
  address   = {London},
  issn      = {2041-1723},
  doi       = {10.1038/s41467-017-02456-6},
  pages     = {10},
  year      = {2018},
  abstract  = {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 Ni{\~n}o-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.},
  language  = {en}
}
@article{ThielRomanoKurthsetal.2008,
  author    = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen and Rolfs, Martin and Kliegl, Reinhold},
  title     = {Generating surrogates from recurrences},
  issn      = {1364-503X},
  year      = {2008},
  abstract  = {In this paper, we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be only one centre in the brain that produces the fixational movements in both eyes or a close link between the two centres.},
  language  = {en}
}
@article{WuZhouChenetal.2010,
  author    = {Wu, Ye and Zhou, Changsong and Chen, Maoyin and Xiao, Jinghua and Kurths, J{\"u}rgen},
  title     = {Human comment dynamics in on-line social systems},
  issn      = {0378-4371},
  doi       = {10.1016/j.physa.2010.08.049},
  year      = {2010},
  abstract  = {Human comment is studied using data from 'tianya' which is one of the most popular on-line social systems in China. We found that the time interval between two consecutive comments on the same topic, called inter-event time, follows a power-law distribution. This result shows that there is no characteristic decay time on a topic. It allows for very long periods without comments that separate bursts of intensive comments. Furthermore, the frequency of a different ID commenting on a topic also follows a power-law distribution. It indicates that there are some "hubs" in the topic who lead the direction of the public opinion. Based on the personal comments habit, a model is introduced to explain these phenomena. The numerical simulations of the model fit well with the empirical results. Our findings are helpful for discovering regular patterns of human behavior in on-line society and the evolution of the public opinion on the virtual as well as real society.},
  language  = {en}
}
@article{WinterhalderSchelterKurthsetal.2006,
  author    = {Winterhalder, Matthias and Schelter, B and Kurths, J{\"u}rgen and Schulze-Borthage, A and Timmer, Jens},
  title     = {Sensitivity and specificity of coherence and phase synchronization analysis},
  doi       = {10.1016/j.physleta.2006.03.018},
  year      = {2006},
  abstract  = {In this Letter, we show that coherence and phase synchronization analysis are sensitive but not specific in detecting the correct class of underlying dynamics. We propose procedures to increase specificity and demonstrate the power of the approach by application to paradigmatic dynamic model systems. (c) 2006 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{DanaBlasiusKurths2006,
  author    = {Dana, Syamal Kumar and Blasius, Bernd and Kurths, J{\"u}rgen},
  title     = {Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators},
  issn      = {1054-1500},
  doi       = {10.1063/1.2197168},
  year      = {2006},
  abstract  = {We study the transition to phase synchronization in two diffusively coupled, nonidentical Chua oscillators. In the experiments, depending on the used parameterization, we observe several distinct routes to phase synchronization, including states of either in-phase, out-of-phase, or antiphase synchronization, which may be intersected by an intermediate desynchronization regime with large fluctuations of the frequency difference. Furthermore, we report the first experimental evidence of an anomalous transition to phase synchronization, which is characterized by an initial enlargement of the natural frequency difference with coupling strength. This results in a maximal frequency disorder at intermediate coupling levels, whereas usual phase synchronization via monotonic decrease in frequency difference sets in only for larger coupling values. All experimental results are supported by numerical simulations of two coupled Chua models},
  language  = {en}
}
@article{VasconcelosLopesVianaetal.2006,
  author    = {Vasconcelos, D. B. and Lopes, S. R. and Viana, R. L. and Kurths, J{\"u}rgen},
  title     = {Spatial recurrence plots},
  doi       = {10.1103/Physreve.73.056207},
  year      = {2006},
  abstract  = {We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is applied to the study of complex patterns generated by coupled map lattices, which are characterized by measures of complexity based on SRPs. We show that the complexity measures we propose for SRPs provide a systematic way of investigating the distribution of spatially coherent structures, such as synchronization domains, in lattice profiles. This approach has potential for many more applications, e.g., in surface roughness analyzes},
  language  = {en}
}
@article{BaptistaPereiraKurths2006,
  author    = {Baptista, Murilo da Silva and Pereira, Tiago and Kurths, J{\"u}rgen},
  title     = {Upper bounds in phase synchronous weak coherent chaotic attractors},
  issn      = {0167-2789},
  doi       = {10.1016/j.physd.2006.02.007},
  year      = {2006},
  abstract  = {An approach is presented for coupled chaotic systems with weak coherent motion, from which we estimate the upper bound value for the absolute phase difference in phase synchronous states. This approach shows that synchronicity in phase implies synchronicity in the time of events, a characteristic explored to derive an equation to detect phase synchronization, based on the absolute difference between the time of these events. We demonstrate the potential use of this approach for the phase coherent and the funnel attractor of the Rossler system, as well as for the spiking/bursting Rulkov map.},
  language  = {en}
}
@article{BaptistaPereiraSartorellietal.2005,
  author    = {Baptista, Murilo da Silva and Pereira, Tiago and Sartorelli, J. C. and Caldas, Ibere Luiz and Kurths, J{\"u}rgen},
  title     = {Non-transitive maps in phase synchronization},
  year      = {2005},
  abstract  = {Concepts from Ergodic Theory are used to describe the existence of special non-transitive maps in attractors of phase synchronous chaotic oscillators. In particular, it is shown that, for a class of phase-coherent oscillators, these special maps imply phase synchronization. We illustrate these ideas in the sinusoidally forced Chua's circuit and two coupled Rossler oscillators. Furthermore, these results are extended to other coupled chaotic systems. In addition, a phase for a chaotic attractor is defined from the tangent vector of the flow. Finally, it is discussed how these maps can be used for the real-time detection of phase synchronization in experimental systems. (c) 2005 Elsevier B.V. All rights reserved},
  language  = {en}
}
@article{KitajimaKurths2005,
  author    = {Kitajima, H. and Kurths, J{\"u}rgen},
  title     = {Synchronized firing of FitzHugh-Nagumo neurons by noise},
  issn      = {1054-1500},
  year      = {2005},
  abstract  = {We investigate the influence of noise on synchronization between the spiking activities of neurons with external impulsive forces. We first analyze the dependence of the synchronized firing on the amplitude and the angular frequency of the impulsive force in the noise-free system. Three cases (regular spiking, traveling wave, and chaotic spiking) with low synchronized firing are chosen to study effects due to noise. In each case we find that small noise can be a promoter of synchronization phenomena in neural activities, by choosing an appropriate noise intensity acting on some of the neurons. (C) 2005 American Institute of Physics},
  language  = {en}
}
@article{BeimGrabenFrischFinketal.2005,
  author    = {Beim Graben, Peter and Frisch, Stefan and Fink, A. and Saddy, Douglas and Kurths, J{\"u}rgen},
  title     = {Topographic voltage and coherence mapping of brain potentials by means of the symbolic resonance analysis},
  issn      = {1539-3755},
  year      = {2005},
  abstract  = {We apply the recently developed symbolic resonance analysis to electroencephalographic measurements of event- related brain potentials (ERPs) in a language processing experiment by using a three-symbol static encoding with varying thresholds for analyzing the ERP epochs, followed by a spin-flip transformation as a nonlinear filter. We compute an estimator of the signal-to-noise ratio (SNR) for the symbolic dynamics measuring the coherence of threshold-crossing events. Hence, we utilize the inherent noise of the EEG for sweeping the underlying ERP components beyond the encoding thresholds. Plotting the SNR computed within the time window of a particular ERP component (the N400) against the encoding thresholds, we find different resonance curves for the experimental conditions. The maximal differences of the SNR lead to the estimation of optimal encoding thresholds. We show that topographic brain maps of the optimal threshold voltages and of their associated coherence differences are able to dissociate the underlying physiological processes, while corresponding maps gained from the customary voltage averaging technique are unable to do so},
  language  = {en}
}
@article{MeineckeZieheKurthsetal.2005,
  author    = {Meinecke, Frank C. and Ziehe, Andreas and Kurths, J{\"u}rgen and M{\"u}ller, Klaus-Robert},
  title     = {Measuring phase synchronization of superimposed signals},
  issn      = {0031-9007},
  year      = {2005},
  abstract  = {Phase synchronization is an important phenomenon that occurs in a wide variety of complex oscillatory processes. Measuring phase synchronization can therefore help to gain fundamental insight into nature. In this Letter we point out that synchronization analysis techniques can detect spurious synchronization, if they are fed with a superposition of signals such as in electroencephalography or magnetoencephalography data. We show how techniques from blind source separation can help to nevertheless measure the true synchronization and avoid such pitfalls},
  language  = {en}
}
@article{SurovyatkinaKravtsovKurths2005,
  author    = {Surovyatkina, E. D. and Kravtsov, Y. A. and Kurths, J{\"u}rgen},
  title     = {Fluctuation growth and saturation in nonlinear oscillators on the threshold of bifurcation of spontaneous symmetry breaking},
  issn      = {1539-3755},
  year      = {2005},
  abstract  = {We study prebifurcation fluctuation amplification in nonlinear oscillators subject to bifurcations of spontaneous symmetry breaking which are manifest in the doubling of stable equilibrium states. Our theoretical estimates of both the linear growth and the nonlinear saturation of the fluctuations are in good agreement with our results from numerical simulations. We show that in the saturation mode, the fluctuation variance is proportional to the standard deviation of the external noise, whereas in the linear mode, the fluctuation variance is proportional to the noise variance. It is demonstrated that the phenomenon of prebifurcation noise amplification is more pronounced in the case of a slow transition through the bifurcation point. The amplification of fluctuations in this case makes it easier to form a symmetric probability of the final equilibrium states. In contrast, for a fast transition through the bifurcation point, the effect of amplification is much less pronounced. Under backward and forward passages through the bifurcation point, a loop of noise-dependent hysteresis emerges here. We find that for a fast transition of the nonlinear oscillator through the bifurcation point, the probability symmetry of the final equilibrium states is destroyed},
  language  = {en}
}
@article{ShabuninAstakhovKurths2005,
  author    = {Shabunin, A. and Astakhov, Vladimir V. and Kurths, J{\"u}rgen},
  title     = {Quantitative analysis of chaotic synchronization by means of coherence},
  issn      = {1539-3755},
  year      = {2005},
  abstract  = {We use an index of chaotic synchronization based on the averaged coherence function for the quantitative analysis of the process of the complete synchronization loss in unidirectionally coupled oscillators and maps. We demonstrate that this value manifests different stages of the synchronization breaking. It is invariant to time delay and insensitive to small noise and distortions, which can influence the accessible signals at measurements. Peculiarities of the synchronization destruction in maps and oscillators are investigated},
  language  = {en}
}
@article{SaparinThomsenProhaskaetal.2005,
  author    = {Saparin, P. I. and Thomsen, J. S. and Prohaska, Steffen and Zaikin, Alexei and Kurths, J{\"u}rgen and Hege, H. C. and Gowin, W.},
  title     = {Quantification of spatial structure of human proximal tibial bone biopsies using 3D measures of complexity},
  issn      = {0094-5765},
  year      = {2005},
  abstract  = {Changes in trabecular bone composition during development of osteoporosis are used as a model for bone loss in microgravity conditions during a space flight. Symbolic dynamics and measures of complexity are proposed and applied to assess quantitatively the structural composition of bone tissue from 3D data sets of human tibia bone biopsies acquired by a micro-CT scanner. In order to justify the newly proposed approach, the measures of complexity of the bone architecture were compared with the results of traditional 2D bone histomorphometry. The proposed technique is able to quantify the structural loss of the bone tissue and may help to diagnose and to monitor changes in bone structure of patients on Earth as well as of the space-flying personnel. © 2005 Elsevier Ltd. All rights reserved},
  language  = {en}
}
@article{SitzSchwarzKurths2004,
  author    = {Sitz, Andre and Schwarz, Udo and Kurths, J{\"u}rgen},
  title     = {The unscented Kalman filter : a powerful tool for data analysis},
  year      = {2004},
  language  = {en}
}
@article{OrgisBrandSchwarzetal.2009,
  author    = {Orgis, Thomas and Brand, Sascha and Schwarz, Udo and Handorf, D{\"o}rthe and Dethloff, Klaus and Kurths, J{\"u}rgen},
  title     = {Influence of interactive stratospheric chemistry on large-scale air mass exchange in a global circulation model},
  issn      = {1951-6355},
  doi       = {10.1140/epjst/e2009-01105-8},
  year      = {2009},
  abstract  = {A new globally uniform Lagrangian transport scheme for large ensembles of passive tracer particles is presented and applied to wind data from a coupled atmosphere-ocean climate model that includes interactive dynamical feedback with stratospheric chemistry. This feedback from the chemistry is found to enhance large-scale meridional air mass exchange in the northern winter stratosphere as well as intrusion of stratospheric air into the troposphere, where both effects are due to a weakened polar vortex.},
  language  = {en}
}
@article{RaabWesselSchirdewanetal.2006,
  author    = {Raab, Corinna and Wessel, Niels and Schirdewan, Alexander and Kurths, J{\"u}rgen},
  title     = {Large-scale dimension densities for heart rate variability analysis},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.73.041907},
  year      = {2006},
  abstract  = {In this work, we reanalyze the heart rate variability (HRV) data from the 2002 Computers in Cardiology (CiC) Challenge using the concept of large-scale dimension densities and additionally apply this technique to data of healthy persons and of patients with cardiac diseases. The large-scale dimension density (LASDID) is estimated from the time series using a normalized Grassberger-Procaccia algorithm, which leads to a suitable correction of systematic errors produced by boundary effects in the rather large scales of a system. This way, it is possible to analyze rather short, nonstationary, and unfiltered data, such as HRV. Moreover, this method allows us to analyze short parts of the data and to look for differences between day and night. The circadian changes in the dimension density enable us to distinguish almost completely between real data and computer-generated data from the CiC 2002 challenge using only one parameter. In the second part we analyzed the data of 15 patients with atrial fibrillation (AF), 15 patients with congestive heart failure (CHF), 15 elderly healthy subjects (EH), as well as 18 young and healthy persons (YH). With our method we are able to separate completely the AF (rho(mu)(ls)=0.97 +/- 0.02) group from the others and, especially during daytime, the CHF patients show significant differences from the young and elderly healthy volunteers (CHF, 0.65 +/- 0.13; EH, 0.54 +/- 0.05; YH, 0.57 +/- 0.05; p < 0.05 for both comparisons). Moreover, for the CHF patients we find no circadian changes in rho(mu)(ls) (day, 0.65 +/- 0.13; night, 0.66 +/- 0.12; n.s.) in contrast to healthy controls (day, 0.54 +/- 0.05; night, 0.61 +/- 0.05; p=0.002). Correlation analysis showed no statistical significant relation between standard HRV and circadian LASDID, demonstrating a possibly independent application of our method for clinical risk stratification},
  language  = {en}
}
@article{AnishchenkoNikolaevKurths2006,
  author    = {Anishchenko, Vadim S. and Nikolaev, S and Kurths, J{\"u}rgen},
  title     = {Winding number locking on a two-dimensional torus : synchronization of quasiperiodic motions},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.73.056202},
  year      = {2006},
  abstract  = {We propose a new autonomous dynamical system of dimension N=4 that demonstrates the regime of stable two- frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The interaction of two generators is also analyzed. The phenomenon of external and mutual synchronization of two-frequency oscillations is observed, for which winding number locking on a two- dimensional torus takes place},
  language  = {en}
}