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- ItemNovel fixed-time stabilization of quaternion-valued BAMNNs with disturbances and time-varying coefficients(Springfield, MO : AIMS Press, 2020) Wei, Ruoyu; Cao, Jinde; Kurths, JürgenIn this paper, with the quaternion number and time-varying coefficients introduced into traditional BAMNNs, the model of quaternion-valued BAMNNs are formulated. For the first time, fixed-time stabilization of time-varying quaternion-valued BAMNNs is investigated. A novel fixed-time control method is adopted, in which the choice of the Lyapunov function is more general than in most previous results. To cope with the noncommutativity of the quaternion multiplication, two different fixed-time control methods are provided, a decomposition method and a non-decomposition method. Furthermore, to reduce the control strength and improve control efficiency, an adaptive fixed-time control strategy is proposed. Lastly, numerical examples are presented to demonstrate the effectiveness of the theoretical results. © 2020 the Author(s), licensee AIMS Press.
- ItemComplex networks for climate model evaluation with application to statistical versus dynamical modeling of South American climate(Heidelberg : Springer, 2014) Feldhoff, Jan H.; Lange, Stefan; Volkholz, Jan; Donges, Jonathan F.; Kurths, Jürgen; Gerstengarbe, Friedrich-WilhelmIn this study we introduce two new node-weighted difference measures on complex networks as a tool for climate model evaluation. The approach facilitates the quantification of a model’s ability to reproduce the spatial covariability structure of climatological time series. We apply our methodology to compare the performance of a statistical and a dynamical regional climate model simulating the South American climate, as represented by the variables 2 m temperature, precipitation, sea level pressure, and geopotential height field at 500 hPa. For each variable, networks are constructed from the model outputs and evaluated against a reference network, derived from the ERA-Interim reanalysis, which also drives the models. We compare two network characteristics, the (linear) adjacency structure and the (nonlinear) clustering structure, and relate our findings to conventional methods of model evaluation. To set a benchmark, we construct different types of random networks and compare them alongside the climate model networks. Our main findings are: (1) The linear network structure is better reproduced by the statistical model statistical analogue resampling scheme (STARS) in summer and winter for all variables except the geopotential height field, where the dynamical model CCLM prevails. (2) For the nonlinear comparison, the seasonal differences are more pronounced and CCLM performs almost as well as STARS in summer (except for sea level pressure), while STARS performs better in winter for all variables.
- ItemUnraveling gene regulatory networks from time-resolved gene expression data - a measures comparison study(London : BioMed Central, 2011) Hempel, Sabrina; Koseska, Aneta; Nikoloski, Zoran; Kurths, Jürgen; Walther, DirkBackground Inferring regulatory interactions between genes from transcriptomics time-resolved data, yielding reverse engineered gene regulatory networks, is of paramount importance to systems biology and bioinformatics studies. Accurate methods to address this problem can ultimately provide a deeper insight into the complexity, behavior, and functions of the underlying biological systems. However, the large number of interacting genes coupled with short and often noisy time-resolved read-outs of the system renders the reverse engineering a challenging task. Therefore, the development and assessment of methods which are computationally efficient, robust against noise, applicable to short time series data, and preferably capable of reconstructing the directionality of the regulatory interactions remains a pressing research problem with valuable applications. Results Here we perform the largest systematic analysis of a set of similarity measures and scoring schemes within the scope of the relevance network approach which are commonly used for gene regulatory network reconstruction from time series data. In addition, we define and analyze several novel measures and schemes which are particularly suitable for short transcriptomics time series. We also compare the considered 21 measures and 6 scoring schemes according to their ability to correctly reconstruct such networks from short time series data by calculating summary statistics based on the corresponding specificity and sensitivity. Our results demonstrate that rank and symbol based measures have the highest performance in inferring regulatory interactions. In addition, the proposed scoring scheme by asymmetric weighting has shown to be valuable in reducing the number of false positive interactions. On the other hand, Granger causality as well as information-theoretic measures, frequently used in inference of regulatory networks, show low performance on the short time series analyzed in this study. Conclusions Our study is intended to serve as a guide for choosing a particular combination of similarity measures and scoring schemes suitable for reconstruction of gene regulatory networks from short time series data. We show that further improvement of algorithms for reverse engineering can be obtained if one considers measures that are rooted in the study of symbolic dynamics or ranks, in contrast to the application of common similarity measures which do not consider the temporal character of the employed data. Moreover, we establish that the asymmetric weighting scoring scheme together with symbol based measures (for low noise level) and rank based measures (for high noise level) are the most suitable choices.
- 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.
- ItemImproving the LPJmL4-SPITFIRE vegetation–fire model for South America using satellite data(Katlenburg-Lindau : Copernicus, 2019) Drüke, Markus; Forkel, Matthias; von Bloh, Werner; Sakschewski, Boris; Cardoso, Manoel; Bustamante, Mercedes; Kurths, Jürgen; Thonicke, KirstenVegetation fires influence global vegetation distribution, ecosystem functioning, and global carbon cycling. Specifically in South America, changes in fire occurrence together with land-use change accelerate ecosystem fragmentation and increase the vulnerability of tropical forests and savannas to climate change. Dynamic global vegetation models (DGVMs) are valuable tools to estimate the effects of fire on ecosystem functioning and carbon cycling under future climate changes. However, most fire-enabled DGVMs have problems in capturing the magnitude, spatial patterns, and temporal dynamics of burned area as observed by satellites. As fire is controlled by the interplay of weather conditions, vegetation properties, and human activities, fire modules in DGVMs can be improved in various aspects. In this study we focus on improving the controls of climate and hence fuel moisture content on fire danger in the LPJmL4-SPITFIRE DGVM in South America, especially for the Brazilian fire-prone biomes of Caatinga and Cerrado. We therefore test two alternative model formulations (standard Nesterov Index and a newly implemented water vapor pressure deficit) for climate effects on fire danger within a formal model–data integration setup where we estimate model parameters against satellite datasets of burned area (GFED4) and aboveground biomass of trees. Our results show that the optimized model improves the representation of spatial patterns and the seasonal to interannual dynamics of burned area especially in the Cerrado and Caatinga regions. In addition, the model improves the simulation of aboveground biomass and the spatial distribution of plant functional types (PFTs). We obtained the best results by using the water vapor pressure deficit (VPD) for the calculation of fire danger. The VPD includes, in comparison to the Nesterov Index, a representation of the air humidity and the vegetation density. This work shows the successful application of a systematic model–data integration setup, as well as the integration of a new fire danger formulation, in order to optimize a process-based fire-enabled DGVM. It further highlights the potential of this approach to achieve a new level of accuracy in comprehensive global fire modeling and prediction.
- ItemBlood–Brain Barrier, Lymphatic Clearance, and Recovery: Ariadne’s Thread in Labyrinths of Hypotheses(Basel : Molecular Diversity Preservation International, 2018) Semyachkina-Glushkovskaya, Oxana; Postnov, Dmitry; Kurths, JürgenThe peripheral lymphatic system plays a crucial role in the recovery mechanisms after many pathological changes, such as infection, trauma, vascular, or metabolic diseases. The lymphatic clearance of different tissues from waste products, viruses, bacteria, and toxic proteins significantly contributes to the correspondent recovery processes. However, understanding of the cerebral lymphatic functions is a challenging problem. The exploration of mechanisms of lymphatic communication with brain fluids as well as the role of the lymphatic system in brain drainage, clearance, and recovery is still in its infancy. Here we review novel concepts on the anatomy and physiology of the lymphatics in the brain, which warrant a substantial revision of our knowledge about the role of lymphatics in the rehabilitation of the brain functions after neural pathologies. We discuss a new vision on the connective bridge between the opening of a blood–brain barrier and activation of the meningeal lymphatic clearance. The ability to stimulate the lymph flow in the brain, is likely to play an important role in developing future innovative strategies in neurorehabilitation therapy.
- ItemSleep as a Novel Biomarker and a Promising Therapeutic Target for Cerebral Small Vessel Disease: A Review Focusing on Alzheimer’s Disease and the Blood-Brain Barrier(Basel : Molecular Diversity Preservation International, 2020) Semyachkina-Glushkovskaya, Oxana; Postnov, Dmitry; Penzel, Thomas; Kurths, JürgenCerebral small vessel disease (CSVD) is a leading cause of cognitive decline in elderly people and development of Alzheimer’s disease (AD). Blood–brain barrier (BBB) leakage is a key pathophysiological mechanism of amyloidal CSVD. Sleep plays a crucial role in keeping health of the central nervous system and in resistance to CSVD. The deficit of sleep contributes to accumulation of metabolites and toxins such as beta-amyloid in the brain and can lead to BBB disruption. Currently, sleep is considered as an important informative platform for diagnosis and therapy of AD. However, there are no effective methods for extracting of diagnostic information from sleep characteristics. In this review, we show strong evidence that slow wave activity (SWA) (0–0.5 Hz) during deep sleep reflects glymphatic pathology, the BBB leakage and memory deficit in AD. We also discuss that diagnostic and therapeutic targeting of SWA in AD might lead to be a novel era in effective therapy of AD. Moreover, we demonstrate that SWA can be pioneering non-invasive and bed–side technology for express diagnosis of the BBB permeability. Finally, we review the novel data about the methods of detection and enhancement of SWA that can be biomarker and a promising therapy of amyloidal CSVD and CSVD associated with the BBB disorders. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.
- ItemBrain anomaly networks uncover heterogeneous functional reorganization patterns after stroke([Amsterdam u.a.] : Elsevier, 2018) Zou, Yong; Zhao, Zhiyong; Yin, Dazhi; Fan, Mingxia; Small, Michael; Liu, Zonghua; Hilgetag, Claus C.; Kurths, JürgenStroke has a large physical, psychological, and financial burden on patients, their families, and society. Based on functional networks (FNs) constructed from resting state fMRI data, network connectivity after stroke is commonly conjectured to be more randomly reconfigured. We find that this hypothesis depends on the severity of stroke. Head movement-corrected, resting-state fMRI data were acquired from 32 patients after stroke, and 37 healthy volunteers. We constructed anomaly FNs, which combine time series information of a patient with the healthy control group. We propose data-driven techniques to automatically identify regions of interest that are stroke relevant. Graph analysis based on anomaly FNs suggests consistently that strong connections in healthy controls are broken down specifically and characteristically for brain areas that are related to sensorimotor functions and frontoparietal control systems, but new links in stroke patients are rebuilt randomly from all possible areas. Entropic measures of complexity are proposed for characterizing the functional connectivity reorganization patterns, which are correlated with hand and wrist function assessments of stroke patients and show high potential for clinical use.
- ItemSee–saw relationship of the Holocene East Asian–Australian summer monsoon(London : Nature Publishing Group, 2016) Eroglu, Deniz; McRobie, Fiona H.; Ozken, Ibrahim; Stemler, Thomas; Wyrwoll, Karl-Heinz; Breitenbach, Sebastian F.M.; Marwan, Norbert; Kurths, JürgenThe East Asian–Indonesian–Australian summer monsoon (EAIASM) links the Earth’s hemispheres and provides a heat source that drives global circulation. At seasonal and inter-seasonal timescales, the summer monsoon of one hemisphere is linked via outflows from the winter monsoon of the opposing hemisphere. Long-term phase relationships between the East Asian summer monsoon (EASM) and the Indonesian–Australian summer monsoon (IASM) are poorly understood, raising questions of long-term adjustments to future greenhouse-triggered climate change and whether these changes could ‘lock in’ possible IASM and EASM phase relationships in a region dependent on monsoonal rainfall. Here we show that a newly developed nonlinear time series analysis technique allows confident identification of strong versus weak monsoon phases at millennial to sub-centennial timescales. We find a see–saw relationship over the last 9,000 years—with strong and weak monsoons opposingly phased and triggered by solar variations. Our results provide insights into centennial- to millennial-scale relationships within the wider EAIASM regime.
- ItemPartial cross mapping eliminates indirect causal influences([London] : Nature Publishing Group UK, 2020) Leng, Siyang; Ma, Huanfei; Kurths, Jürgen; Lai, Ying-Cheng; Lin, Wei; Aihara, Kazuyuki; Chen, LuonanCausality detection likely misidentifies indirect causations as direct ones, due to the effect of causation transitivity. Although several methods in traditional frameworks have been proposed to avoid such misinterpretations, there still is a lack of feasible methods for identifying direct causations from indirect ones in the challenging situation where the variables of the underlying dynamical system are non-separable and weakly or moderately interacting. Here, we solve this problem by developing a data-based, model-independent method of partial cross mapping based on an articulated integration of three tools from nonlinear dynamics and statistics: phase-space reconstruction, mutual cross mapping, and partial correlation. We demonstrate our method by using data from different representative models and real-world systems. As direct causations are keys to the fundamental underpinnings of a variety of complex dynamics, we anticipate our method to be indispensable in unlocking and deciphering the inner mechanisms of real systems in diverse disciplines from data.