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- ItemLimitations of red noise in analysing Dansgaard-Oeschger events(München : European Geopyhsical Union, 2010) Braun, H.; Ditlevsen, P.; Kurths, J.; Mudelsee, M.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.
- ItemSimilarity estimators for irregular and age-uncertain time series(München : European Geopyhsical Union, 2014) Rehfeld, K.; Kurths, J.Paleoclimate time series are often irregularly sampled and age uncertain, which is an important technical challenge to overcome for successful reconstruction of past climate variability and dynamics. Visual comparison and interpolation-based linear correlation approaches have been used to infer dependencies from such proxy time series. While the first is subjective, not measurable and not suitable for the comparison of many data sets at a time, the latter introduces interpolation bias, and both face difficulties if the underlying dependencies are nonlinear. In this paper we investigate similarity estimators that could be suitable for the quantitative investigation of dependencies in irregular and age-uncertain time series. We compare the Gaussian-kernel-based cross-correlation (gXCF, Rehfeld et al., 2011) and mutual information (gMI, Rehfeld et al., 2013) against their interpolation-based counterparts and the new event synchronization function (ESF). We test the efficiency of the methods in estimating coupling strength and coupling lag numerically, using ensembles of synthetic stalagmites with short, autocorrelated, linear and nonlinearly coupled proxy time series, and in the application to real stalagmite time series. In the linear test case, coupling strength increases are identified consistently for all estimators, while in the nonlinear test case the correlation-based approaches fail. The lag at which the time series are coupled is identified correctly as the maximum of the similarity functions in around 60–55% (in the linear case) to 53–42% (for the nonlinear processes) of the cases when the dating of the synthetic stalagmite is perfectly precise. If the age uncertainty increases beyond 5% of the time series length, however, the true coupling lag is not identified more often than the others for which the similarity function was estimated. Age uncertainty contributes up to half of the uncertainty in the similarity estimation process. Time series irregularity contributes less, particularly for the adapted Gaussian-kernel-based estimators and the event synchronization function. The introduced link strength concept summarizes the hypothesis test results and balances the individual strengths of the estimators: while gXCF is particularly suitable for short and irregular time series, gMI and the ESF can identify nonlinear dependencies. ESF could, in particular, be suitable to study extreme event dynamics in paleoclimate records. Programs to analyze paleoclimatic time series for significant dependencies are included in a freely available software toolbox.
- ItemPrevention and trust evaluation scheme based on interpersonal relationships for large-scale peer-to-peer networks(New York, NY : Hindawi Publishing Corporation, 2014) Li, L.; Kurths, J.; Yang, Y.; Liu, G.In recent years, the complex network as the frontier of complex system has received more and more attention. Peer-to-peer (P2P) networks with openness, anonymity, and dynamic nature are vulnerable and are easily attacked by peers with malicious behaviors. Building trusted relationships among peers in a large-scale distributed P2P system is a fundamental and challenging research topic. Based on interpersonal relationships among peers of large-scale P2P networks, we present prevention and trust evaluation scheme, called IRTrust. The framework incorporates a strategy of identity authentication and a global trust of peers to improve the ability of resisting the malicious behaviors. It uses the quality of service (QoS), quality of recommendation (QoR), and comprehensive risk factor to evaluate the trustworthiness of a peer, which is applicable for large-scale unstructured P2P networks. The proposed IRTrust can defend against several kinds of malicious attacks, such as simple malicious attacks, collusive attacks, strategic attacks, and sybil attacks. Our simulation results show that the proposed scheme provides greater accuracy and stronger resistance compared with existing global trust schemes. The proposed scheme has potential application in secure P2P network coding.
- ItemChallenges in network science: Applications to infrastructures, climate, social systems and economics(Heidelberg : Springer, 2012) Havlin, S.; Kenett, D.Y.; Ben-Jacob, E.; Bunde, A.; Cohen, R.; Hermann, H.; Kantelhardt, J.W.; Kertész, J.; Kirkpatrick, S.; Kurths, J.; Portugali, J.; Solomon, S.Network theory has become one of the most visible theoretical frameworks that can be applied to the description, analysis, understanding, design and repair of multi-level complex systems. Complex networks occur everywhere, in man-made and human social systems, in organic and inorganic matter, from nano to macro scales, and in natural and anthropogenic structures. New applications are developed at an ever-increasing rate and the promise for future growth is high, since increasingly we interact with one another within these vital and complex environments. Despite all the great successes of this field, crucial aspects of multi-level complex systems have been largely ignored. Important challenges of network science are to take into account many of these missing realistic features such as strong coupling between networks (networks are not isolated), the dynamics of networks (networks are not static), interrelationships between structure, dynamics and function of networks, interdependencies in given networks (and other classes of links, including different signs of interactions), and spatial properties (including geographical aspects) of networks. This aim of this paper is to introduce and discuss the challenges that future network science needs to address, and how different disciplines will be accordingly affected.
- ItemLocal difference measures between complex networks for dynamical system model evaluation(San Francisco, CA : Public Library of Science (PLoS), 2015) Lange, S.; Donges, J.F.; Volkholz, J.; Kurths, J.
- ItemRecurrence networks-a novel paradigm for nonlinear time series analysis(College Park, MD : Institute of Physics Publishing, 2010) Donner, R.V.; Zou, Y.; Donges, J.F.; Marwan, N.; Kurths, J.This paper presents a new approach for analysing the structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network, which links different points in time if the considered states are closely neighboured in phase space. In comparison with similar network-based techniques the new approach has important conceptual advantages, and can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases. It has been demonstrated here that there are fundamental relationships between many topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related to the dynamical complexity of a time series, most of which are not yet provided by other existing methods of nonlinear time series analysis. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
- ItemAn electronic analog of synthetic genetic networks(San Francisco, CA : Public Library of Science (PLoS), 2011) Hellen, E.H.; Volkov, E.; Kurths, J.; Dana, S.K.An electronic analog of a synthetic genetic network known as the repressilator is proposed. The repressilator is a synthetic biological clock consisting of a cyclic inhibitory network of three negative regulatory genes which produces oscillations in the expressed protein concentrations. Compared to previous circuit analogs of the repressilator, the circuit here takes into account more accurately the kinetics of gene expression, inhibition, and protein degradation. A good agreement between circuit measurements and numerical prediction is observed. The circuit allows for easy control of the kinetic parameters thereby aiding investigations of large varieties of potential dynamics.
- ItemCardio-respiratory coordination increases during sleep apnea(San Francisco, CA : Public Library of Science (PLoS), 2014) Riedl, M.; Müller, A.; Kraemer, J.F.; Penzel, T.; Kurths, J.; Wessel, N.Cardiovascular diseases are the main source of morbidity and mortality in the United States with costs of more than $170 billion. Repetitive respiratory disorders during sleep are assumed to be a major cause of these diseases. Therefore, the understanding of the cardio-respiratory regulation during these events is of high public interest. One of the governing mechanisms is the mutual influence of the cardiac and respiratory oscillations on their respective onsets, the cardiorespiratory coordination (CRC). We analyze this mechanism based on nocturnal measurements of 27 males suffering from obstructive sleep apnea syndrome. Here we find, by using an advanced analysis technique, the coordigram, not only that the occurrence of CRC is significantly more frequent during respiratory sleep disturbances than in normal respiration (p-value<10-51) but also more frequent after these events (p-value<10-15). Especially, the latter finding contradicts the common assumption that spontaneous CRC can only be observed in epochs of relaxed conditions, while our newly discovered epochs of CRC after disturbances are characterized by high autonomic stress. Our findings on the connection between CRC and the appearance of sleep-disordered events require a substantial extension of the current understanding of obstructive sleep apneas and hypopneas.
- ItemAnalysing dynamical behavior of cellular networks via stochastic bifurcations(San Francisco, CA : Public Library of Science (PLoS), 2011) Zakharova, A.; Kurths, J.; Vadivasova, T.; Koseska, A.The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.
- ItemNoise-Aided Logic in an Electronic Analog of Synthetic Genetic Networks(San Francisco, CA : Public Library of Science (PLoS), 2013) Hellen, E.H.; Dana, S.K.; Kurths, J.; Kehler, E.; Sinha, S.We report the experimental verification of noise-enhanced logic behaviour in an electronic analog of a synthetic genetic network, composed of two repressors and two constitutive promoters. We observe good agreement between circuit measurements and numerical prediction, with the circuit allowing for robust logic operations in an optimal window of noise. Namely, the input-output characteristics of a logic gate is reproduced faithfully under moderate noise, which is a manifestation of the phenomenon known as Logical Stochastic Resonance. The two dynamical variables in the system yield complementary logic behaviour simultaneously. The system is easily morphed from AND/NAND to OR/NOR logic.