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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.
- 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.
- ItemExploring brain function from anatomical connectivity(Lausanne : Frontiers Media, 2011) Zamora-López, Gorka; Zhou, Changsong; Kurths, JürgenThe intrinsic relationship between the architecture of the brain and the range of sensory and behavioral phenomena it produces is a relevant question in neuroscience. Here, we review recent knowledge gained on the architecture of the anatomical connectivity by means of complex network analysis. It has been found that cortico-cortical networks display a few prominent characteristics: (i) modular organization, (ii) abundant alternative processing paths, and (iii) the presence of highly connected hubs. Additionally, we present a novel classification of cortical areas of the cat according to the role they play in multisensory connectivity. All these properties represent an ideal anatomical substrate supporting rich dynamical behaviors, facilitating the capacity of the brain to process sensory information of different modalities segregated and to integrate them toward a comprehensive perception of the real world. The results here exposed are mainly based on anatomical data of cats’ brain, but further observations suggest that, from worms to humans, the nervous system of all animals might share these fundamental principles of organization.
- ItemCortical hubs form a module for multisensory integration on top of the hierarchy of cortical networks(Lausanne : Frontiers Media, 2010) Zamora-López, Gorka; Zhou, Changsong; Kurths, JürgenSensory stimuli entering the nervous system follow particular paths of processing, typically separated (segregated) from the paths of other modal information. However, sensory perception, awareness and cognition emerge from the combination of information (integration). The corticocortical networks of cats and macaque monkeys display three prominent characteristics: (i) modular organisation (facilitating the segregation), (ii) abundant alternative processing paths and (iii) the presence of highly connected hubs. Here, we study in detail the organisation and potential function of the cortical hubs by graph analysis and information theoretical methods. We find that the cortical hubs form a spatially delocalised, but topologically central module with the capacity to integrate multisensory information in a collaborative manner. With this, we resolve the underlying anatomical substrate that supports the simultaneous capacity of the cortex to segregate and to integrate multisensory information.
- ItemDiminished heart beat non-stationarities in congestive heart failure(Lausanne : Frontiers Media, 2013) Camargo, Sabrina; Riedl, Maik; Anteneodo, Celia; Kurths, Jürgen; Wessel, NielsStudies on heart rate variability (HRV) have become popular and the possibility of diagnosis based on non-invasive techniques compels us to overcome the difficulties originated on the environmental changes that can affect the signal. We perform a non-parametric segmentation which consists of locating the points where the signal can be split into stationary segments. By finding stationary segments we are able to analyze the size of these segments and evaluate how the signal changes from one segment to another, looking at the statistical moments given in each patch, for example, mean and variance. We analyze HRV data for 15 patients with congestive heart failure (CHF; 11 males, 4 females, age 56±11 years), 18 elderly healthy subjects (EH; 11 males, 7 females, age 50±7 years), and 15 young healthy subjects (YH; 11 females, 4 males, age 31±6 years). Our results confirm higher variance for YH, and EH, while CHF displays diminished variance with p-values <0.01, when compared to the healthy groups, presenting higher HRV in healthy subjects. Moreover, it is possible to distinguish between YH and EH with p < 0.05 through the segmentation outcomes. We found high correlations between the results of segmentation and standard measures of HRV analysis and a connection to results of detrended fluctuation analysis (DFA). The segmentation applied to HRV studies detects aging and pathological conditions effects on the non-stationary behavior of the analyzed groups, promising to contribute in complexity analysis and providing risk stratification measures.
- ItemFully solvable lower dimensional dynamics of Cartesian product of Kuramoto models([London] : IOP, 2019) Chen, Zewen; Zou, Yong; Guan, Shuguang; Liu, Zonghua; Kurths, JürgenImplementing a positive correlation between the natural frequencies of nodes and their connectivity on a single star graph leads to a pronounced explosive transition to synchronization, additionally presenting hysteresis behavior. From the viewpoint of network connectivity, a star has been considered as a building motif to generate a big graph by graph operations. On the other hand, we propose to construct complex synchronization dynamics by applying the Cartesian product of two Kuramoto models on two star networks. On the product model, the lower dimensional equations describing the ensemble dynamics in terms of collective order parameters are fully solved by the Watanabe-Strogatz method. Different graph parameter choices lead to three different interacting scenarios of the hysteresis areas of two individual factor graphs, which further change the basins of attraction of multiple fixed points. Furthermore, we obtain coupling regimes where cluster synchronization states are often present on the product graph and the number of clusters is fully controlled. More specifically, oscillators on one star graph are synchronized while those on the other star are not synchronized, which induces clustered state on the product model. The numerical results agree perfectly with the theoretic predictions. © 2019 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.
- ItemExplosive death induced by mean–field diffusion in identical oscillators([London] : Macmillan Publishers Limited, part of Springer Nature, 2017) Verma, Umesh Kumar; Sharma, Amit; Kamal, Neeraj Kumar; Kurths, Jürgen; Shrimali, Manish DevWe report the occurrence of an explosive death transition for the first time in an ensemble of identical limit cycle and chaotic oscillators coupled via mean–field diffusion. In both systems, the variation of the normalized amplitude with the coupling strength exhibits an abrupt and irreversible transition to death state from an oscillatory state and this first order phase transition to death state is independent of the size of the system. This transition is quite general and has been found in all the coupled systems where in–phase oscillations co–exist with a coupling dependent homogeneous steady state. The backward transition point for this phase transition has been calculated using linear stability analysis which is in complete agreement with the numerics.