TY - JOUR A1 - Assmann, Birte A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Niemitz, Carsten T1 - Recurrence plot analyses suggest a novel reference system involved in newborn spontaneous movements JF - Behavior research methods : a journal of the Psychonomic Society N2 - The movements of newborns have been thoroughly studied in terms of reflexes, muscle synergies, leg coordination, and target-directed arm/hand movements. Since these approaches have concentrated mainly on separate accomplishments, there has remained a clear need for more integrated investigations. Here, we report an inquiry in which we explicitly concentrated on taking such a perspective and, additionally, were guided by the methodological concept of home base behavior, which Ilan Golard developed for studies of exploratory behavior in animals. Methods from nonlinear dynamics, such as symbolic dynamics and recurrence plot analyses of kinematic data received from audiovisual newborn recordings, yielded new insights into the spatial and temporal organization of limb movements. In the framework of home base behavior, our approach uncovered a novel reference system of spontaneous newborn movements. Y1 - 2006 U6 - https://doi.org/10.3758/BF03192793 SN - 1554-351X SN - 1554-3528 VL - 38 IS - 3 SP - 400 EP - 406 PB - Springer CY - New York ER - TY - JOUR A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Kurths, Jürgen A1 - Rolfs, Martin A1 - Kliegl, Reinhold T1 - Generating surrogates from recurrences N2 - 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. Y1 - 2008 UR - http://rsta.royalsocietypublishing.org/ SN - 1364-503X ER - TY - JOUR A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Kurths, Jürgen T1 - Spurious structures in recurrence plots induced by embedding N2 - In this paper we show that delay embedding produces spurious structures in a recurrence plot (RP) that are not present in the real attractor. We analyze typical sets of simulated data, such as white noise and data from the chaotic Rossler system to show the relevance of this effect. In the second part of the paper we show that the second order Renyi entropy and the correlation dimension are dynamical invariants that can be estimated from Recurrence Plots with arbitrary embedding dimension and delay Y1 - 2006 U6 - https://doi.org/10.1007/s11071-006-2010-9 ER - TY - JOUR A1 - von Bloh, Werner A1 - Romano, Maria Carmen A1 - Thiel, Marco T1 - Long-term predictability of mean daily temperature data N2 - We quantify the long-term predictability of global mean daily temperature data by means of the Renyi entropy of second order K-2. We are interested in the yearly amplitude fluctuations of the temperature. Hence, the data are low- pass filtered. The obtained oscillatory signal has a more or less constant frequency, depending on the geographical coordinates, but its amplitude fluctuates irregularly. Our estimate of K-2 quantifies the complexity of these amplitude fluctuations. We compare the results obtained for the CRU data set (interpolated measured temperature in the years 1901- 2003 with 0.5 degrees resolution, Mitchell et al., 2005(1)) with the ones obtained for the temperature data from a coupled ocean-atmosphere global circulation model (AOGCM, calculated at DKRZ). Furthermore, we compare the results obtained by means of K-2 with the linear variance of the temperature data Y1 - 2005 SN - 1023-5809 ER - TY - JOUR A1 - Romano, Maria Carmen A1 - Thiel, Marco A1 - Kurths, Jürgen A1 - von Bloh, Werner T1 - Multivariate recurrence plots N2 - We propose a new approach to calculate recurrence plots of multivariate time series, based on joint recurrences in phase space. This new method allows to estimate dynamical invariants of the whole system, like the joint Renyi entropy of second order. We use this entropy measure to quantitatively study in detail the phase synchronization of two bidirectionally coupled chaotic systems and identify different types of transitions to chaotic phase synchronization in dependence on the coupling strength and the frequency mismatch. By means of this analysis we find several new phenomena, such a chaos-period-chaos transition to phase synchronization for rather large coupling strengths. (C) 2004 Elsevier B.V. All rights reserved Y1 - 2004 SN - 0375-9601 ER - TY - JOUR A1 - Thiel, M. A1 - Romano, Maria Carmen A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Timmer, Jens T1 - Surrogate-based hypothesis test without surrogates N2 - Fourier surrogate data are artificially generated time series, that - based on a resampling scheme - share the linear properties with an observed time series. In this paper we study a statistical surrogate hypothesis test to detect deviations from a linear Gaussian process with respect to asymmetry in time (Q-statistic). We apply this test to a Fourier representable function and obtain a representation of the asymmetry in time of the sample data, a characteristic for nonlinear processes, and the significance in terms of the Fourier coefficients. The main outcome is that we calculate the expected value of the mean and the standard deviation of the asymmetries of the surrogate data analytically and hence, no surrogates have to be generated. To illustrate the results we apply our method to the saw tooth function, the Lorenz system and to measured X-ray data of Cygnus X-1 Y1 - 2004 SN - 0218-1274 ER - TY - JOUR A1 - Thiel, M. A1 - Romano, Maria Carmen A1 - Kurths, Jürgen T1 - How much information is contained in a recurrence plot? N2 - Recurrence plots have recently been recognized as a powerful tool for the analysis of data. Not only the visualization of structures of the time series but also the possibility to estimate invariants from them and the possibility to analyze non-stationary data sets are remarkable. However, the question of how much information is encoded in such a two-dimensional and binary representation has not been discussed so far. In this Letter we show that-under some conditions-it is possible to reconstruct an attractor from the recurrence plot, at least topologically. This means that all relevant dynamical information is contained in the plot. (C) 2004 Elsevier B.V. All rights reserved Y1 - 2004 SN - 0375-9601 ER - TY - JOUR A1 - Thiel, M. A1 - Romano, Maria Carmen A1 - Read, P. L. A1 - Kurths, Jürgen T1 - Estimation of dynamical invariants without embedding by recurrence plots N2 - In this paper we show that two dynamical invariants, the second order Renyi entropy and the correlation dimension, can be estimated from recurrence plots (RPs) with arbitrary embedding dimension and delay. This fact is interesting as these quantities are even invariant if no embedding is used. This is an important advantage of RPs compared to other techniques of nonlinear data analysis. These estimates for the correlation dimension and entropy are robust and, moreover, can be obtained at a low numerical cost. We exemplify our results for the Rossler system, the funnel attractor and the Mackey-Glass system. In the last part of the paper we estimate dynamical invariants for data from some fluid dynamical experiments and confirm previous evidence for low dimensional chaos in this experimental system. (C) 2004 American Institute of Physics Y1 - 2004 SN - 1054-1500 ER - TY - JOUR A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Kurths, Jürgen A1 - Rolfs, Martin A1 - Kliegl, Reinhold T1 - Twin surrogates to test for complex synchronisation N2 - We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of Rossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems Y1 - 2006 UR - http://www.mendeley.com/research/twin-surrogates-to-test-for-complex-synchronisation/#page-1 U6 - https://doi.org/10.1209/epl/i2006-10147-0 ER - TY - JOUR A1 - Romano, Maria Carmen A1 - Thiel, Marco A1 - Kurths, Jürgen A1 - Mergenthaler, Konstantin A1 - Engbert, Ralf T1 - Hypothesis test for synchronization : twin surrogates revisited N2 - The method of twin surrogates has been introduced to test for phase synchronization of complex systems in the case of passive experiments. In this paper we derive new analytical expressions for the number of twins depending on the size of the neighborhood, as well as on the length of the trajectory. This allows us to determine the optimal parameters for the generation of twin surrogates. Furthermore, we determine the quality of the twin surrogates with respect to several linear and nonlinear statistics depending on the parameters of the method. In the second part of the paper we perform a hypothesis test for phase synchronization in the case of experimental data from fixational eye movements. These miniature eye movements have been shown to play a central role in neural information processing underlying the perception of static visual scenes. The high number of data sets (21 subjects and 30 trials per person) allows us to compare the generated twin surrogates with the "natural" surrogates that correspond to the different trials. We show that the generated twin surrogates reproduce very well all linear and nonlinear characteristics of the underlying experimental system. The synchronization analysis of fixational eye movements by means of twin surrogates reveals that the synchronization between the left and right eye is significant, indicating that either the centers in the brain stem generating fixational eye movements are closely linked, or, alternatively that there is only one center controlling both eyes. Y1 - 2009 UR - http://ojps.aip.org/chaos/ U6 - https://doi.org/10.1063/1.3072784 SN - 1054-1500 ER - TY - JOUR A1 - Zou, Yong A1 - Thiel, M. A1 - Romano, Maria Carmen A1 - Kurths, Jürgen A1 - Bi, Q. T1 - Shrimp structure and associated dynamics in parametrically excited oscillators JF - International journal of bifurcation and chaos : in applied sciences and engineering N2 - We investigate the bifurcation structures in a two-dimensional parameter space (PS) of a parametrically excited system with two degrees of freedom both analytically and numerically. By means of the Renyi entropy of second order K-2, which is estimated from recurrence plots, we uncover that regions of chaotic behavior are intermingled with many complex periodic windows, such as shrimp structures in the PS. A detailed numerical analysis shows that, the stable solutions lose stability either via period doubling, or via intermittency when the parameters leave these shrimps in different directions, indicating different bifurcation properties of the boundaries. The shrimps of different sizes offer promising ways to control the dynamics of such a complex system. KW - bifurcation analysis KW - recurrence plot KW - period doubling KW - intermittency Y1 - 2006 U6 - https://doi.org/10.1142/S0218127406016987 SN - 0218-1274 VL - 16 IS - 12 SP - 3567 EP - 3579 PB - World Scientific Publ. Co CY - Singapore ER - TY - JOUR A1 - Romano, Maria Carmen A1 - Thiel, Marco A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Lange, Holger A1 - Hauhs, M. T1 - Conceptual model of runoff from a forested catchment N2 - 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. Y1 - 2001 UR - http://journals.worldscientific.com.sg/ijbc/11/1110/S0218127401003619.html ER - TY - JOUR A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Schwarz, Udo A1 - Kurths, Jürgen A1 - Hasinger, Günther A1 - Belloni, Tomaso T1 - Nonlinear Time series analysis of the X-ray flux of compact objects N2 - We analyse the X-ray light curves of compact objects using linear and nonlinear time series analysis methods. A Power Density Spectrum (PDS) describes the overall second order properties of the observed data well. To look beyond we propose the nonlinear Q-statistic to detect an asymmetry of the time series. This allows us to find relevant time scales. This method even grants a subclassification of the known states of X-ray sources. Y1 - 2001 SN - 0004-640x ER - TY - JOUR A1 - Romano, Maria Carmen A1 - Thiel, Marco A1 - Kurths, Jürgen A1 - Rolfs, Martin A1 - Engbert, Ralf A1 - Kliegl, Reinhold T1 - Synchronization Analysis and Recurrence in Complex Systems Y1 - 2006 SN - 978-3-527-40623-4 ER - TY - GEN A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Kurths, Jürgen A1 - Rolfs, Martin A1 - Kliegl, Reinhold T1 - Generating Surrogates from Recurrences N2 - 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 one centre only in the brain that produces the fixational movements in both eyes or a close link between two centres. T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - paper 238 KW - Æ Recurrence Plots KW - Surrogate Data KW - Hypothesis Test KW - Phase Synchronization Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-56906 ER - TY - GEN A1 - Thiel, Marco A1 - Romano, Maria Carmen A1 - Kurths, Jürgen A1 - Rolfs, Martin T1 - Twin Surrogates to Test for Complex Synchronisation N2 - We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of R¨ossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems. T3 - Zweitveröffentlichungen der Universität Potsdam : Humanwissenschaftliche Reihe - paper 264 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57231 ER - TY - JOUR A1 - Romano, Maria Carmen A1 - Thiel, M. A1 - Kurths, Jürgen A1 - Kiss, Istvan Z. A1 - Hudson, J. L. T1 - Detection of synchronization for non-phase-coherent and non-stationary data N2 - We present a new method to detect phase as well as generalized synchronization in a wide class of complex systems. It is based on the recurrences of the system's trajectory to the neighborhood of a former state in phase space. We illustrate the applicability of the algorithm for the paradigmatic chaotic Rossler system in the funnel regime and for noisy data, where other methods to detect phase synchronization fail. Furthermore, we demonstrate for electrochemical experiments that the method can easily detect phase and generalized synchronization in non-phase- coherent and even non-stationary time series Y1 - 2005 SN - 0295-5075 ER - TY - JOUR A1 - Kurths, Jürgen A1 - Romano, Maria Carmen A1 - Thiel, Marco A1 - Osipov, Grigory V. A1 - Ivanchenko, Mikhail V. A1 - Kiss, Istvan Z. A1 - Hudson, John L. T1 - Synchronization analysis of coupled noncoherent oscillators N2 - We present two different approaches to detect and quantify phase synchronization in the case of coupled non- phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the Rossler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators Y1 - 2006 UR - http://www.springerlink.com/content/102972 U6 - https://doi.org/10.1007/s11071-006-1957-x SN - 0924-090X ER -