@article{PortaDiRienzoWesseletal.2009, author = {Porta, Alberto and Di Rienzo, Marco and Wessel, Niels and Kurths, J{\"u}rgen}, title = {Addressing the complexity of cardiovascular regulation}, issn = {1364-503X}, doi = {10.1098/rsta.2008.0292}, year = {2009}, language = {en} } @article{PavlovAnisimovSemyachkinaGlushkovskayaetal.2009, author = {Pavlov, Alexey N. and Anisimov, A. A. and Semyachkina-Glushkovskaya, Oxana V. and Matasova, E. G. and Kurths, J{\"u}rgen}, title = {Analysis of blood pressure dynamics in male and female rats using the continuous wavelet transform}, issn = {0967-3334}, doi = {10.1088/0967-3334/30/7/013}, year = {2009}, abstract = {We study gender-related particularities in cardiovascular responses to stress and nitric oxide (NO) deficiency in rats using HR, mean arterial pressure (MAP) and a proposed wavelet-based approach. Blood pressure dynamics is analyzed: (1) under control conditions, (2) during immobilization stress and recovery and (3) during nitric oxide blockade by N-G-nitro-L-arginine-methyl ester (L-NAME). We show that cardiovascular sensitivity to stress and NO deficiency depends upon gender. Actually, in females the chronotropic effect of stress is more pronounced, while the pressor effect is weakened compared with males. We conclude that females demonstrate more favorable patterns of cardiovascular responses to stress and more effective NO control of cardiovascular activity than males.}, language = {en} } @article{SchwarzBenzKurthsetal.1993, author = {Schwarz, udo and Benz, Arnold O. and Kurths, J{\"u}rgen and Witt, Annette}, title = {Analysis of solar spike events by means of symbolic dynamics methods}, issn = {004-6361}, year = {1993}, abstract = {Using quantities of symbolic dynamics, such as mutual information, Shannon information and algorithmic complexity, we have searched for interrelations of spikes emitted simultaneously at different frequencies during the impulsive phase of a flare event. As the spikes are related to the flare energy release and are interpreted as emissions originating at different sites having different magnetic field strengths, any relation in frequency is interpretated as a relation in space. This approach is appropriate to characterize such spatio-temporal patterns, whereas the popular estimate of fractal dimensions can be applied to low-dimensional systems only. Depending on the energy release and emission processes, two types of fragmentation are possible: a scenario of global organization (spikes are emitted in a succession of similar events by the same system) or a scenario of local organization (many systems triggered by an initial event). Mutual information which is a generalization of correlation indicates a relation in frequency beyond the bandwidth of individual spikes. The scans in the spectrograms with large mutual information also show a low level of Shannon information and algorithmic complexity, indicating that the simultaneous appearance of spikes at other frequencies is not a completely stochastic phenomenon (white noise). It may be caused by a nonlinear deterministic system or by a Markov process. By means of mutual information we find a memory over frequency intervals up to 60 MHz. Shannon information and algorithmic complexity concern the mbox{whole} frequency region, i.e. the global source region. A global organization is also apparent in quasi-periodic changes of the Shannon information and algorithmic complexity in the range of 2 - 8 seconds. The finding is compatible with a scenario of local organization in which the information of one event spreads spatially and triggers further events at different places. The region is not an ensemble of independently flashing sources, each representing a system that cascades in energy after an initial trigger. On the contrary, there is a causal connection between the sources at any time. The analysis of the four spike events suggests that the structure in frequency is not stochastic but a process in which spikes at nearby locations are simultaneously triggered by a common exciter.}, language = {en} } @article{KurthsSchwarz1993, author = {Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Application of techniques of nonlinear dynamics to SS Cyg}, isbn = {0-7503-0282-8}, year = {1993}, abstract = {We look for structural properties in the light curve of the dwarf nova SS Cyg by means of techniques from nonlinear dynamics. Applying the popular Grassberger-Procaccia procedure, Cannizzo and Goddings (1988) showed that there is no evidence for a low-dimensional attractor underlying this record. Because there are some hints for order in the light curve, we search for other signatures of deterministic systems. Therefore, we use other methods recently developed in this theory, such as local linear prediction and recurrence maps. Our main findings are: i] the prediction error grows exponentially during outburst phases, but via a power law in the quiescent states, ii] there are some rather regular patterns in this light curve which sometimes recur, but the recurrence is not regular. This leads to the following conclusions: i] The outburst dynamics shows a higher degree of order than the quiescent one. There are some hints for deterministic chaos in the outburst behavior. ii] The light curve is a complex mixture of deterministic and stochastic structures. The analysis presented in this paper shows that methods of nonlinear dynamics can be an efficient tool for the study of complex processes, even if there is no evidence for a low-dimensional attractor.}, language = {en} } @article{SchinkelMarwanKurths2009, author = {Schinkel, Stefan and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Brain signal analysis based on recurrences}, issn = {0928-4257}, doi = {10.1016/j.jphysparis.2009.05.007}, year = {2009}, abstract = {The EEG is one of the most commonly used tools in brain research. Though of high relevance in research, the data obtained is very noisy and nonstationary. In the present article we investigate the applicability of a nonlinear data analysis method, the recurrence quantification analysis (RQA), to Such data. The method solely rests on the natural property of recurrence which is a phenomenon inherent to complex systems, such as the brain. We show that this method is indeed suitable for the analysis of EEG data and that it might improve contemporary EEG analysis.}, language = {en} } @article{ItohKurths2010, author = {Itoh, Naoki and Kurths, J{\"u}rgen}, title = {Change-point detection of climate time series by nonparametric method}, issn = {2078-0958}, year = {2010}, abstract = {In one of the data mining techniques, change-point detection is of importance in evaluating time series measured in real world. For decades this technique has been developed as a nonlinear dynamics. We apply the method for detecting the change points, Singular Spectrum Transformation (SST), to the climate time series. To know where the structures of climate data sets change can reveal a climate background. In this paper we discuss the structures of precipitation data in Kenya and Wrangel Island (Arctic land) by using the SST.}, language = {en} } @article{KurthsSchwarz1994, author = {Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Chaos theory and radio emission}, year = {1994}, abstract = {The application of chaos theory has become popular to understand the nature of various features of solar activity because most of them are far from regular. The usual approach, however, that is basing on finding low- dimensional structures of the underlying processes seems to be successful only in a few exceptional cases, such as in rather coherent phenomena as coronal pulsations. It is important to note that most phenomena in solar radio emission are more complex. We present two kinds of techniques from nonlinear dynamics which can be useful to analyse such phenomena: i] Fragmentation processes observed in solar spike events are studied by means of symbolic dynamics methods. Different measures of complexity calculated from such observations reveal that there is some order in this fragmentation. ii] Bursts are a typical transient phenomenon. To study energization processes causing impulsive microwave bursts, the wavelet analysis is applied. It exhibits structural differences of the pre- and post-impulsive phase in cases where the power spectra of both are not distinct.}, language = {en} } @article{MarwanKurths2009, author = {Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Comment on "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" by Rohde et al. : [Physica D 237 (2008) 619-629]}, issn = {0167-2789}, doi = {10.1016/j.physd.2009.04.018}, year = {2009}, abstract = {In the recent article "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" (Physica D 237 (2008) 619-629), Rohde et al. stated that the performance of RQA in order to detect deterministic signals would be below traditional and well-known detectors. However, we have concerns about such a general statement. Based on our own studies we cannot confirm their conclusions. Our findings suggest that the measures of complexity provided by RQA are useful detectors outperforming well-known traditional detectors, in particular for the detection of signals of complex systems, with phase differences or signals modified due to the measurement process.}, language = {en} } @article{RomanoThielSchwarzetal.2001, author = {Romano, Maria Carmen and Thiel, Marco and Schwarz, Udo and Kurths, J{\"u}rgen and Lange, Holger and Hauhs, M.}, title = {Conceptual model of runoff from a forested catchment}, year = {2001}, abstract = {We investigate the relationship between precipitation and runoff data from a small forested catchment in the Harz mountains (Germany). For this purpose, we develop a conceptual model including memory effects to predict the runoff signal using the precipitation data as input. An enhanced variant of the model also includes air temperature as input variable. We show in terms of correlation functions that this model describes main dynamical properties of the runoff, especially the delay between rain event and runoff response as the annual persistence in the runoff data.}, language = {en} } @article{SchinkelMarwanDimigenetal.2009, author = {Schinkel, Stefan and Marwan, Norbert and Dimigen, Olaf and Kurths, J{\"u}rgen}, title = {Confidence bounds of recurrence-based complexity measures}, issn = {0375-9601}, doi = {10.1016/j.physleta.2009.04.045}, year = {2009}, abstract = {In the recent past, recurrence quantification analysis (RQA) has gained an increasing interest in various research areas. The complexity measures the RQA provides have been useful in describing and analysing a broad range of data. It is known to be rather robust to noise and nonstationarities. Yet, one key question in empirical research concerns the confidence bounds of measured data. In the present Letter we suggest a method for estimating the confidence bounds of recurrence-based complexity measures. We study the applicability of the suggested method with model and real- life data.}, language = {en} } @article{RetzlaffBauernschmittMalbergetal.2009, author = {Retzlaff, Beatrice and Bauernschmitt, Robert and Malberg, Hagen and Brockmann, Gernot and Uhl, Christian and Lange, Ruediger and Kurths, J{\"u}rgen and Bretthauer, Georg and Wessel, Niels}, title = {Depression of cardiovascular autonomic function is more pronounced after mitral valve surgery : evidence for direct trauma}, issn = {1364-503X}, doi = {10.1098/rsta.2008.0272}, year = {2009}, abstract = {The analysis of baroreflex sensitivity (BRS) and heart rate variability (HRV) leads to additional insights into patients' prognosis after cardiovascular events. The following study was performed to assess the differences in the post-operative recovery of autonomic regulation after mitral valve (MV) and aortic valve (AV) surgery with a heart lung machine. Among the 43 consecutive male patients enrolled in a prospective study, 26 underwent isolated AV surgery and 17 isolated MV surgery. Blood pressure as well as ECG signals were recorded the day before, 24 hours after and one week after surgery. BRS was calculated according to the dual sequence method, and HRV was calculated using standard linear as well as nonlinear parameters. There were no major differences between the two groups in the pre-operative values. At 24 hours a comparable depression of HRV and BRS in both groups was observed, while at 7 days there was partial recovery in AV patients, which was absent in MV patients: p(AV versus MV) < 0.001. While the response of the autonomic system to surgery is similar in AV and MV patients, there is obviously a decreased ability to recover in MV patients, probably attributed to traumatic lesions of the autonomic nervous system by opening the atria. Ongoing research is required for further clarification of the pathophysiology of this phenomenon and to establish strategies to restore autonomic function.}, language = {en} } @article{EbelingMolgedeyKurthsetal.2002, author = {Ebeling, Werner and Molgedey, Lutz and Kurths, J{\"u}rgen and Schwarz, Udo}, title = {Entropy, complexity, predictability, and data analysis of time series and letter sequences}, isbn = {3-540-41324-3}, year = {2002}, abstract = {The structure of time series and letter sequences is investigated using the concepts of entropy and complexity. First conditional entropy and transinformation are introduced and several generalizations are discussed. Further several measures of complexity are introduced and discussed. The capability of these concepts to describe the structure of time series and letter sequences generated by nonlinear maps, data series from meteorology, astrophysics, cardiology, cognitive psychology and finance is investigated. The relation between the complexity and the predictability of informational strings is discussed. The relation between local order and the predictability of time series is investigated.}, language = {en} } @article{ZamoraLopezZhouKurths2009, author = {Zamora-Lopez, Gorka and Zhou, Changsong and Kurths, J{\"u}rgen}, title = {Graph analysis of cortical networks reveals complex anatomical communication substrate}, issn = {1054-1500}, doi = {10.1063/1.3089559}, year = {2009}, abstract = {Sensory information entering the nervous system follows independent paths of processing such that specific features are individually detected. However, sensory perception, awareness, and cognition emerge from the combination of information. Here we have analyzed the corticocortical network of the cat, looking for the anatomical substrate which permits the simultaneous segregation and integration of information in the brain. We find that cortical communications are mainly governed by three topological factors of the underlying network: (i) a large density of connections, (ii) segregation of cortical areas into clusters, and (iii) the presence of highly connected hubs aiding the multisensory processing and integration. Statistical analysis of the shortest paths reveals that, while information is highly accessible to all cortical areas, the complexity of cortical information processing may arise from the rich and intricate alternative paths in which areas can influence each other.}, language = {en} } @article{HellandGapelyukSuhrbieretal.2010, author = {Helland, Vanessa Carolina Figuera and Gapelyuk, Andrej and Suhrbier, Alexander and Riedl, Maik and Penzel, Thomas and Kurths, J{\"u}rgen and Wessel, Niels}, title = {Investigation of an automatic sleep stage classification by means of multiscorer hypnogram}, issn = {0026-1270}, doi = {10.3414/Me09-02-0052}, year = {2010}, abstract = {Objectives: Scoring sleep visually based on polysomnography is an important but time-consuming element of sleep medicine. Where-as computer software assists human experts in the assignment of sleep stages to polysomnogram epochs, their performance is usually insufficient. This study evaluates the possibility to fully automatize sleep staging considering the reliability of the sleep stages available from human expert sleep scorers. Methods: We obtain features from EEG, ECG and respiratory signals of polysomnograms from ten healthy subjects. Using the sleep stages provided by three human experts, we evaluate the performance of linear discriminant analysis on the entire polysomnogram and:only on epochs where the three experts agree in their-sleep stage scoring. Results: We show that in polysomnogram intervals, to which all three scorers assign the same sleep stage, our algorithm achieves 90\% accuracy. This high rate of agreement with the human experts is accomplished with only a small set of three frequency features from the EEG. We increase-the performance to 93\% by including ECG and respiration features. In contrast, on intervals of ambiguous sleep stage, the sleep stage classification obtained from our algorithm, agrees with the human consensus scorer in approximately 61\%. Conclusions: These findings suggest that machine classification is highly consistent with human sleep staging and that error in the algorithm's assignments is rather a problem of lack of well-defined criteria for human experts to judge certain polysomnogram epochs than an insufficiency of computational procedures}, language = {en} } @article{WesselRiedlKurths2009, author = {Wessel, Niels and Riedl, Maik and Kurths, J{\"u}rgen}, title = {Is the normal heart rate "chaotic" due to respiration?}, issn = {1054-1500}, doi = {10.1063/1.3133128}, year = {2009}, abstract = {The incidence of cardiovascular diseases increases with the growth of the human population and an aging society, leading to very high expenses in the public health system. Therefore, it is challenging to develop sophisticated methods in order to improve medical diagnostics. The question whether the normal heart rate is chaotic or not is an attempt to elucidate the underlying mechanisms of cardiovascular dynamics and therefore a highly controversial topical challenge. In this contribution we demonstrate that linear and nonlinear parameters allow us to separate completely the data sets of the three groups provided for this controversial topic in nonlinear dynamics. The question whether these time series are chaotic or not cannot be answered satisfactorily without investigating the underlying mechanisms leading to them. We give an example of the dominant influence of respiration on heart beat dynamics, which shows that observed fluctuations can be mostly explained by respiratory modulations of heart rate and blood pressure (coefficient of determination: 96\%). Therefore, we recommend reformulating the following initial question: "Is the normal heart rate chaotic?" We rather ask the following: " Is the normal heart rate 'chaotic' due to respiration?"}, language = {en} } @article{PalusKurthsSchwarzetal.2001, author = {Palus, Milan and Kurths, J{\"u}rgen and Schwarz, Udo and Novotn{\´a}, Dagmar and Charv{\´a}tov{\´a}, Ivanka}, title = {Is the solar activity cycle synchronized with the solar inertial motion?}, year = {2001}, abstract = {The 300 year record of the yearly sunspot numbers and numerically generated trajectory of the solar inertial motion (SIM) were subjects of a synchronization analysis. Phase synchronization of the sunspot cycle and a fast component of the SIM have been found and confirmed with statistical significance in three epochs (1727-1757, 1802-1832 and 1863-1922) of the entire 1700-1997 record. This result can be considered as a quantitative support for the hypothesis that there is a weak interaction of gravity and solar activity.}, language = {en} } @article{BraunDitlevsenKurthsetal.2010, author = {Braun, Holger and Ditlevsen, Peter D. and Kurths, J{\"u}rgen and Mudelsee, Manfred}, title = {Limitations of red noise in analysing Dansgaard-Oeschger events}, issn = {1814-9324}, doi = {10.5194/cp-6-85-2010}, year = {2010}, abstract = {During the last glacial period, climate records from the North Atlantic region exhibit a pronounced spectral component corresponding to a period of about 1470 years, which has attracted much attention. This spectral peak is closely related to the recurrence pattern of Dansgaard-Oeschger (DO) events. In previous studies a red noise random process, more precisely a first-order autoregressive (AR1) process, was used to evaluate the statistical significance of this peak, with a reported significance of more than 99\%. Here we use a simple mechanistic two-state model of DO events, which itself was derived from a much more sophisticated ocean-atmosphere model of intermediate complexity, to numerically evaluate the spectral properties of random (i.e., solely noise-driven) events. This way we find that the power spectral density of random DO events differs fundamentally from a simple red noise random process. These results question the applicability of linear spectral analysis for estimating the statistical significance of highly non-linear processes such as DO events. More precisely, to enhance our scientific understanding about the trigger of DO events, we must not consider simple "straw men" as, for example, the AR1 random process, but rather test against realistic alternative descriptions.}, language = {en} } @article{TimmerSchwarzVossetal.2000, author = {Timmer, Jens and Schwarz, Udo and Voss, Henning U. and Wardinski, Ingo and Belloni, Tomaso and Hasinger, G{\"u}nther and VanDerKlis, Michael and Kurths, J{\"u}rgen}, title = {Linear and Nonlinear Time Series Analysis of the Black Hole Candidate Cygnus X-1}, year = {2000}, abstract = {We analyze the variability in the x-ray lightcurves of the black hole candidate Cygnus X-1 by linear and nonlinear time series analysis methods. While a linear model describes the overall second order properties of the observed data well, surrogate data analysis reveals a significant deviation from linearity. We discuss the relation between shot noise models usually applied to analyze these data and linear stochastic autoregressive models. We debate statistical and interpretational issues of surrogate data testing for the present context. Finally, we suggest a combination of tools from linear and nonlinear time series analysis methods as a procedure to test the predictions of astrophysical models on observed data.}, language = {en} } @article{ZolotovaPonyavinMarwanetal.2009, author = {Zolotova, Nadezhda V. and Ponyavin, Dmitri I. and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Long-term asymmetry in the wings of the butterfly diagram}, issn = {0004-6361}, doi = {10.1051/0004-6361/200811430}, year = {2009}, abstract = {Aims. Sunspot distribution in the northern and southern solar hemispheres exibit striking synchronous behaviour on the scale of a Schwabe cycle. However, sometimes the bilateral symmetry of the Butterfly diagram relative to the solar equatorial plane breaks down. The investigation of this phenomenon is important to explaining the almost-periodic behaviour of solar cycles. Methods. We use cross-recurrence plots for the study of the time-varying phase asymmetry of the northern and southern hemisphere and compare our results with the latitudinal distribution of the sunspots. Results. We observe a long-term persistence of phase leading in one of the hemispheres, which lasts almost 4 solar cycles and probably corresponds to the Gleissberg cycle. Long-term variations in the hemispheric-leading do not demonstrate clear periodicity but are strongly anti-correlated with the long-term variations in the magnetic equator.}, language = {en} } @article{VossTimmerKurths2004, author = {Voss, Henning U. and Timmer, Jens and Kurths, J{\"u}rgen}, title = {Modeling and identification of nonlinear systems}, issn = {0218-1274}, year = {2004}, language = {en} }