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- ItemEmotional tendencies in online social networking: a statistical analysis(London : Taylor & Francis Open, 2016) Zhang, Xianhan; Zhang, Nan; Zhao, Letong; Zhang, Ruihan; Cao, Jinde; Lu, Jianquan; Kurths, Jürgen; Qian, ChengNumerous previous studies suggested that people's emotional tendency (ET) towards an issue can often be affected by others. But in some cases, people are unwilling to believe opposite points. This paper aims to study whether people's emotional tendencies (ET) are susceptible with exposures to others' ET concerning a special topic. ET contained in 798,057 pieces of private-information-deleted Chinese Weibo posts are carefully investigated via a revised genetic algorithm, a nonlinear method. Note that nearly all of the posts are closely related to a special topic, the terrible earthquake happen in Japan, 11 March 2011. By conducting statistical analysis including coefficient calculations and hypothesis testing, this study shows that concerning this particular topic, Chinese citizens' first impressions about Japan are solid enough to form their ET and would not be easily altered. Moreover, according to analysis and discussion, we discover that node-to-node impact is exaggerated in some theoretical information diffusion models. Instead it is actually the interaction between nodes' properties and the spread information that matters in the process of information diffusions.
- ItemSurvivability of deterministic dynamical systems(London : Nature Publishing Group, 2016) Hellmann, Frank; Schultz, Paul; Grabow, Carsten; Heitzig, Jobst; Kurths, JürgenThe notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel stability measure by considering models from climate science, neuronal networks and power grids. We also show that a semi-analytic lower bound for the survivability of linear systems allows a numerically very efficient survivability analysis in realistic models of power grids. Our numerical and semi-analytic work underlines that the type of stability measured by survivability is not captured by common asymptotic stability measures.
- ItemMultiscale Spatiotemporal Analysis of Extreme Events in the Gomati River Basin, India(Basel : MDPI, 2021) Kalyan, AVS; Ghose, Dillip Kumar; Thalagapu, Rahul; Guntu, Ravi Kumar; Agarwal, Ankit; Kurths, Jürgen; Rathinasamy, MaheswaranAccelerating climate change is causing considerable changes in extreme events, leading to immense socioeconomic loss of life and property. In this study, we investigate the characteristics of extreme climate events at a regional scale to ‐understand these events’ propagation in the near fu-ture. We have considered sixteen extreme climate indices defined by the World Meteorological Or-ganization’s Expert Team on Climate Change Detection and Indices from a long‐term dataset (1951– 2018) of 53 locations in Gomati River Basin, North India. We computed the present and future spatial variation of theses indices using the Sen’s slope estimator and Hurst exponent analysis. The periodicities and non‐stationary features were estimated using the continuous wavelet transform. Bivariate copulas were fitted to estimate the joint probabilities and return periods for certain com-binations of indices. The study results show different variation in the patterns of the extreme climate indices: D95P, R95TOT, RX5D, and RX showed negative trends for all stations over the basin. The number of dry days (DD) showed positive trends over the basin at 36 stations out of those 17 stations are statistically significant. A sustainable decreasing trend is observed for D95P at all stations, indi-cating a reduction in precipitation in the future. DD exhibits a sustainable decreasing trend at almost all the stations over the basin barring a few exceptions highlight that the basin is turning drier. The wavelet power spectrum for D95P showed significant power distributed across the 2–16‐year bands, and the two‐year period was dominant in the global power spectrum around 1970–1990. One interest-ing finding is that a dominant two‐year period in D95P has changed to the four years after 1984 and remains in the past two decades. The joint return period’s resulting values are more significant than values resulting from univariate analysis (R95TOT with 44% and RTWD of 1450 mm). The difference in values highlights that ignoring the mutual dependence can lead to an underestimation of extremes. © 2021 by the author. Licensee MDPI, Basel, Switzerland.
- 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.
- ItemInteracting tipping elements increase risk of climate domino effects under global warming(Göttingen : Copernicus, 2021) Wunderling, Nico; Donges, Jonathan F.; Kurths, Jürgen; Winkelmann, RicardaWith progressing global warming, there is an increased risk that one or several tipping elements in the climate system might cross a critical threshold, resulting in severe consequences for the global climate, ecosystems and human societies. While the underlying processes are fairly well-understood, it is unclear how their interactions might impact the overall stability of the Earth's climate system. As of yet, this cannot be fully analysed with state-of-the-art Earth system models due to computational constraints as well as some missing and uncertain process representations of certain tipping elements. Here, we explicitly study the effects of known physical interactions among the Greenland and West Antarctic ice sheets, the Atlantic Meridional Overturning Circulation (AMOC) and the Amazon rainforest using a conceptual network approach. We analyse the risk of domino effects being triggered by each of the individual tipping elements under global warming in equilibrium experiments. In these experiments, we propagate the uncertainties in critical temperature thresholds, interaction strengths and interaction structure via large ensembles of simulations in a Monte Carlo approach. Overall, we find that the interactions tend to destabilise the network of tipping elements. Furthermore, our analysis reveals the qualitative role of each of the four tipping elements within the network, showing that the polar ice sheets on Greenland and West Antarctica are oftentimes the initiators of tipping cascades, while the AMOC acts as a mediator transmitting cascades. This indicates that the ice sheets, which are already at risk of transgressing their temperature thresholds within the Paris range of 1.5 to 2 ∘C, are of particular importance for the stability of the climate system as a whole.
- 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.
- ItemComplex network approach for detecting tropical cyclones(Berlin ; Heidelberg : Springer, 2021) Gupta, Shraddha; Boers, Niklas; Pappenberger, Florian; Kurths, JürgenTropical cyclones (TCs) are one of the most destructive natural hazards that pose a serious threat to society, particularly to those in the coastal regions. In this work, we study the temporal evolution of the regional weather conditions in relation to the occurrence of TCs using climate networks. Climate networks encode the interactions among climate variables at different locations on the Earth’s surface, and in particular, time-evolving climate networks have been successfully applied to study different climate phenomena at comparably long time scales, such as the El Niño Southern Oscillation, different monsoon systems, or the climatic impacts of volcanic eruptions. Here, we develop and apply a complex network approach suitable for the investigation of the relatively short-lived TCs. We show that our proposed methodology has the potential to identify TCs and their tracks from mean sea level pressure (MSLP) data. We use the ERA5 reanalysis MSLP data to construct successive networks of overlapping, short-length time windows for the regions under consideration, where we focus on the north Indian Ocean and the tropical north Atlantic Ocean. We compare the spatial features of various topological properties of the network, and the spatial scales involved, in the absence and presence of a cyclone. We find that network measures such as degree and clustering exhibit significant signatures of TCs and have striking similarities with their tracks. The study of the network topology over time scales relevant to TCs allows us to obtain crucial insights into the effects of TCs on the spatial connectivity structure of sea-level pressure fields.
- 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.
- ItemPath integral solutions for n-dimensional stochastic differential equations under α-stable Lévy excitation(College Park, Md : [Verlag nicht ermittelbar], 2023) Zan, Wanrong; Xu, Yong; Kurths, JürgenIn this paper, the path integral solutions for a general n-dimensional stochastic differential equations (SDEs) with α-stable Lévy noise are derived and verified. Firstly, the governing equations for the solutions of n-dimensional SDEs under the excitation of α-stable Lévy noise are obtained through the characteristic function of stochastic processes. Then, the short-time transition probability density function of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski (CKS) equation and the characteristic function, and its correctness is demonstrated by proving that it satisfies the governing equation of the solution of the SDE, which is also called the Fokker-Planck-Kolmogorov equation. Besides, illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method, and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.