45 research outputs found

    Robustness of Network of Networks with Interdependent and Interconnected links

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    Robustness of network of networks (NON) has been studied only for dependency coupling (J.X. Gao et. al., Nature Physics, 2012) and only for connectivity coupling (E.A. Leicht and R.M. D Souza, arxiv:0907.0894). The case of network of n networks with both interdependent and interconnected links is more complicated, and also more closely to real-life coupled network systems. Here we develop a framework to study analytically and numerically the robustness of this system. For the case of starlike network of n ER networks, we find that the system undergoes from second order to first order phase transition as coupling strength q increases. We find that increasing intra-connectivity links or inter-connectivity links can increase the robustness of the system, while the interdependency links decrease its robustness. Especially when q=1, we find exact analytical solutions of the giant component and the first order transition point. Understanding the robustness of network of networks with interdependent and interconnected links is helpful to design resilient infrastructures

    Percolation on interacting networks with feedback-dependency links

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    When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here we develop a mathematical framework and study numerically and analytically percolation of interacting networks with feedback-dependency links. We find that when nodes of between networks are lowly connected, the system undergoes from second order transition through hybrid order transition to first order transition as coupling strength increases. And, as average degree of each inter-network increases, first order region becomes smaller and second-order region becomes larger but hybrid order region almost keep constant. Especially, the results implies that average degree \bar{k} between intra-networks has a little influence on robustness of system for weak coupling strength, but for strong coupling strength corresponding to first order transition system become robust as \bar{k} increases. However, when average degree k of inter-network is increased, the system become robust for all coupling strength. Additionally, when nodes of between networks are highly connected, the hybrid order region disappears and the system first order region becomes larger and secondorder region becomes smaller. Moreover, we find that the existence of feedback dependency links between interconnecting networks makes the system extremely vulnerable by comparing non-feedback condition for the same parameters.First author draf

    Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application

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    The limited penetrable horizontal visibility algorithm is a new time analysis tool and is a further development of the horizontal visibility algorithm. We present some exact results on the topological properties of the limited penetrable horizontal visibility graph associated with random series. We show that the random series maps on a limited penetrable horizontal visibility graph with exponential degree distribution P(k)exp[λ(k2ρ2)],λ=ln[(2ρ+3)/(2ρ+2)],ρ=0,1,2,...,k=2ρ+2,2ρ+3,...P(k)\sim exp[-\lambda (k-2\rho-2)], \lambda = ln[(2\rho+3)/(2\rho+2)],\rho=0,1,2,...,k=2\rho+2,2\rho+3,..., independent of the probability distribution from which the series was generated. We deduce the exact expressions of the mean degree and the clustering coefficient and demonstrate the long distance visibility property. Numerical simulations confirm the accuracy of our theoretical results. We then examine several deterministic chaotic series (a logistic map, the Heˊ\acute{e}non map, the Lorentz system, and an energy price chaotic system) and a real crude oil price series to test our results. The empirical results show that the limited penetrable horizontal visibility algorithm is direct, has a low computational cost when discriminating chaos from uncorrelated randomness, and is able to measure the global evolution characteristics of the real time series.Comment: 23 pages, 12 figure

    Investigation of Carbon Tax Pilot in YRD Urban Agglomerations—Analysis and Application of a Novel ESER System with Carbon Tax Constraints

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    AbstractThis paper attempts to explore the dynamic behavior of energy-saving and emission-reduction (ESER) system in Yangtze River Delta (YRD) urban agglomerations, which has not yet been reported in present literature. The novel YRD urban agglomerations carbon tax attractor is achieved. A scenario study is carried out. The results show that, the ESER system in YRD urban agglomerations is superior to the average case in China, in which the impacts on economic growth are almost the same. The economic property of YRD urban agglomerations is the main cause why the ESER system of YRD urban agglomerations being superior

    Characteristics of Pollen from Transgenic Lines of Apple Carrying the Exogenous CpTI Gene

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    AbstractIt is fundamental for gene transformation and ecosystem hazard evaluation to study the pollen characteristics of transgenic plants. In this research, the characteristics of pollen from 7- or 8-year-old transgenic apple plants carrying an exogenous CpTI gene were analyzed. The results showed that there was no significant difference in terms of size, morphology, or exine ornamentation between the pollen of the transgenic plants and the non-transgenic control. However, the transgenic plants had more abnormal pollen grains. Of the 13 transgenic lines tested, 12 had a significantly lower amount of pollen and six exhibited a significantly lower germination rate when cultured in vitro. The pollen viability of three transgenic lines was determined, with two showing significantly lower viability than the control. The transgenic Gala apple pollen grains germinated normally via controlled pollination on Fuji apple stigmas. However, the pollen tubes extended relatively slowly during the middle and late development stages, and another 8h were needed to reach the ovules compared with the control. The gibberellic acid concentration in transgenic Gala apple flowers was lower than in the non-transgenic control during all development stages tested. The abscisic acid concentration in the transgenic flowers was lower during the pink stage, and higher during the ball and fully open stages. Microscopic observation of the anther structure showed no difference. The tapetum of the pollen sac wall in transgenic plants decomposed late and affected pollen grain development, which could be one of the reasons for the lower number of pollen grains and poor viability in the transgenic plants

    Percolation of partially interdependent networks under targeted attack

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    The study of interdependent networks, and in particular the robustness on networks, has attracted considerable attention. Recent studies mainly assume that the dependence is fully interdependent. However, targeted attack for partially interdependent networks simultaneously has the characteristics of generality in real world. In this letter, the comprehensive percolation of generalized framework of partially interdependent networks under targeted attack is analyzed. As α=0\alpha=0 and α=1\alpha=1, the percolation law is presented. Especially, when a=b=ka=b=k, p1=p2=pp_{1}=p_{2}=p, qA=qB=qq_{A}=q_{B}=q, the first and second lines of phase transition coincide with each other. The corresponding phase transition diagram and the critical line between the first and the second phase transition are found. We find that the tendency of critical line is monotone decreasing with parameter p1p_{1}. However, for different α\alpha, the tendency of critical line is monotone increasing with α\alpha. In a larger sense, our findings have potential application for designing networks with strong robustness and can regulate the robustness of some current networks.Comment: 6 pages, 9 figure
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