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- ItemDevelopment of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators(Woodbury, NY : American Institute of Physics, 2017) Papadopoulos, Lia; Kim, Jason Z.; Kurths, Jürgen; Bassett, Danielle S.Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior, and it is interesting to ask how the structural organization of network interactions influences this process. Several studies have explored and uncovered optimal topologies for synchronization by making purposeful alterations to a network. On the other hand, the connectivity patterns of many natural systems are often not static, but are rather modulated over time according to their dynamics. However, this co-evolution and the extent to which the dynamics of the individual units can shape the organization of the network itself are less well understood. Here, we study initially randomly connected but locally adaptive networks of Kuramoto oscillators. In particular, the system employs a co-evolutionary rewiring strategy that depends only on the instantaneous, pairwise phase differences of neighboring oscillators, and that conserves the total number of edges, allowing the effects of local reorganization to be isolated. We find that a simple rule-which preserves connections between more outof- phase oscillators while rewiring connections between more in-phase oscillators-can cause initially disordered networks to organize into more structured topologies that support enhanced synchronization dynamics. We examine how this process unfolds over time, finding a dependence on the intrinsic frequencies of the oscillators, the global coupling, and the network density, in terms of how the adaptive mechanism reorganizes the network and influences the dynamics. Importantly, for large enough coupling and after sufficient adaptation, the resulting networks exhibit interesting characteristics, including degree-frequency and frequency-neighbor frequency correlations. These properties have previously been associated with optimal synchronization or explosive transitions in which the networks were constructed using global information. On the contrary, by considering a time-dependent interplay between structure and dynamics, this work offers a mechanism through which emergent phenomena and organization can arise in complex systems utilizing local rules.
- 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.
- ItemDynamics and collapse in a power system model with voltage variation: The damping effect(San Francisco, CA : Public Library of Science (PLoS), 2016) Ma, J.; Sun, Y.; Yuan, X.; Kurths, J.; Zhan, M.
- 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.
- ItemApplication of optical coherence tomography for in vivo monitoring of the meningeal lymphatic vessels during opening of blood–brain barrier: mechanisms of brain clearing(Bellingham, Wash. : SPIE, 2017) Semyachkina-Glushkovskaya, Oxana; Abdurashitov, Arkady; Dubrovsky, Alexander; Bragin, Denis; Bragina, Olga; Shushunova, Natalia; Maslyakova, Galina; Navolokin, Nikita; Bucharskaya, Alla; Tuchind, Valery; Kurths, Jürgen; Shirokov, AlexanderThe meningeal lymphatic vessels were discovered 2 years ago as the drainage system involved in the mechanisms underlying the clearance of waste products from the brain. The blood–brain barrier (BBB) is a gatekeeper that strongly controls the movement of different molecules from the blood into the brain. We know the scenarios during the opening of the BBB, but there is extremely limited information on how the brain clears the substances that cross the BBB. Here, using the model of sound-induced opening of the BBB, we clearly show how the brain clears dextran after it crosses the BBB via the meningeal lymphatic vessels. We first demonstrate successful application of optical coherence tomography (OCT) for imaging of the lymphatic vessels in the meninges after opening of the BBB, which might be a new useful strategy for noninvasive analysis of lymphatic drainage in daily clinical practice. Also, we give information about the depth and size of the meningeal lymphatic vessels in mice. These new fundamental data with the applied focus on the OCT shed light on the mechanisms of brain clearance and the role of lymphatic drainage in these processes that could serve as an informative platform for a development of therapy and diagnostics of diseases associated with injuries of the BBB such as stroke, brain trauma, glioma, depression, or Alzheimer disease.
- 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.
- 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.
- ItemProbing the Statistical Properties of Unknown Texts: Application to the Voynich Manuscript(San Francisco, CA : Public Library of Science (PLoS), 2013) Amancio, D.R.; Altmann, E.G.; Rybski, D.; Oliveira Jr., O.N.; da Costa, L.F.While the use of statistical physics methods to analyze large corpora has been useful to unveil many patterns in texts, no comprehensive investigation has been performed on the interdependence between syntactic and semantic factors. In this study we propose a framework for determining whether a text (e.g., written in an unknown alphabet) is compatible with a natural language and to which language it could belong. The approach is based on three types of statistical measurements, i.e. obtained from first-order statistics of word properties in a text, from the topology of complex networks representing texts, and from intermittency concepts where text is treated as a time series. Comparative experiments were performed with the New Testament in 15 different languages and with distinct books in English and Portuguese in order to quantify the dependency of the different measurements on the language and on the story being told in the book. The metrics found to be informative in distinguishing real texts from their shuffled versions include assortativity, degree and selectivity of words. As an illustration, we analyze an undeciphered medieval manuscript known as the Voynich Manuscript. We show that it is mostly compatible with natural languages and incompatible with random texts. We also obtain candidates for keywords of the Voynich Manuscript which could be helpful in the effort of deciphering it. Because we were able to identify statistical measurements that are more dependent on the syntax than on the semantics, the framework may also serve for text analysis in language-dependent applications.