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Author: Kurths, J. × Subject: probability ×

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Now showing 1 - 5 of 5
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    Local 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.
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    Analysing 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.
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    Estimation of sedimentary proxy records together with associated uncertainty
    (Göttingen : Copernicus GmbH, 2015) Goswami, B.; Heitzig, J.; Rehfeld, K.; Marwan, N.; Anoop, A.; Prasad, S.; Kurths, J.
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    Long-term changes in the north-south asymmetry of solar activity: A nonlinear dynamics characterization using visibility graphs
    (Göttingen : Copernicus GmbH, 2014) Zou, Y.; Donner, R.V.; Marwan, N.; Small, M.; Kurths, J.
    Solar activity is characterized by complex dynamics superimposed onto an almost periodic, approximately 11-year cycle. One of its main features is the presence of a marked, time-varying hemispheric asymmetry, the deeper reasons for which have not yet been completely uncovered. Traditionally, this asymmetry has been studied by considering amplitude and phase differences. Here, we use visibility graphs, a novel tool of nonlinear time series analysis, to obtain complementary information on hemispheric asymmetries in dynamical properties. Our analysis provides deep insights into the potential and limitations of this method, revealing a complex interplay between factors relating to statistical and dynamical properties, i.e., effects due to the probability distribution and the regularity of observed fluctuations. We demonstrate that temporal changes in the hemispheric predominance of the graph properties lag those directly associated with the total hemispheric sunspot areas. Our findings open a new dynamical perspective on studying the north-south sunspot asymmetry, which is to be further explored in future work.
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    The Switch in a Genetic Toggle System with Lévy Noise
    (London : Nature Publishing Group, 2016) Xu, Y.; Li, Y.; Zhang, H.; Li, X.; Kurths, J.