Modelling Accelerating Growth with IntermittentProcesses in Evolving Networks

In this paper, the acceleratingly growing network model with intermittent processes is proposed. In the growing network, there exist both accelerating and intermittent processes. The network is grown from the number of nodes m₀ and the number of links added with each new node is a nonlinearly increasing function m+aN^β(t)f(t), where N(t) is the number of nodes present at time t. f(t) is the periodic and bistable function with period T, whose values are 1 and 0 indicating accelerating and intermittent processes, respectively. Here we denote the ratio τ of acceleration time to whole one. We study the degree distribution p(k) of the model, focusing on the dependence of p(k) on the network parameters τ, T, m, a, N, and β. It is found that there exists a phase transition point k_c such that if k<k_c, then p(k) obeys a power-law distribution with exponent -γ₁, while if k>k_c, then p(k) exhibits a power-law distribution with exponent -γ₂. Moreover, the exponents γ₁ and γ₂ are independent of τ, T, m, a, and N, while they depend only on the parameter β. More interesting, the phase transition point is described by k_c=aN^β, which is equal to the value at which p(k) is maximum in GM model.     

Resilience of the internet to random breakdowns

A common property of many large networks, including the Internet, is that the connectivity of the various nodes follows a scale-free power-law distribution, P(k) = ck(-alpha). We study the stability of such networks with respect to crashes, such as random removal of sites. Our approach, based on percolation theory, leads to a general condition for the critical fraction of nodes, p(c), that needs to be removed before the network disintegrates. We show analytically and numerically that for alpha0.99.     

动态随机最短路径算法研究

静态最短路径问题已经得到很好解决, 然而现实中的网络大多具有动态性和随机性. 网络弧和节点的状态及耗费不仅具有不确定性且相互关联, 弧和节点的耗费都服从一定的概率分布, 因此把最短路径问题看作是一个动态随机优化问题更具有一般性. 文中分析了网络弧和节点的动态随机特性及其相互关系, 定义了动态随机最短路径; 给出了动态随机最短路径优化数学模型, 提出了一种动态随机最短路径遗传算法; 针对网络的拓扑特性设计了高效合理的遗传算子. 实验结果表明, 文中提出的模型和算法能有效地解决动态随机最短路径问题, 可以运用到交通、通信等网络的网络流随机优化问题中.     

Voter model on heterogeneous graphs

We study the voter model on heterogeneous graphs. We exploit the nonconservation of the magnetization to characterize how consensus is reached. For a network of N nodes with an arbitrary but uncorrelated degree distribution, the mean time to reach consensus T(N) scales as Nmu(2)1/mu(2), where mu(k) is the kth moment of the degree distribution. For a power-law degree distribution n(k) approximately k(-nu), T(N) thus scales as N for nu > 3, as N/ln(N for nu = 3, as N((2nu-4)/(nu-1)) for 2 < nu < 3, as (lnN)2 for nu = 2, and as omicron(1) for nu < 2. These results agree with simulation data for networks with both uncorrelated and correlated node degrees.     

Investigation of seismicity after the initiation of a Seismic Electric Signal activity until the main shock

The behavior of seismicity in the area candidate to suffer a main shock is investigated after the observation of the Seismic Electric Signal activity until the impending main shock. This is based on the view that the occurrence of earthquakes is a critical phenomenon to which statistical dynamics may be applied. In the present work, analysing the time series of small earthquakes, the concept of natural time chi was used and the results revealed that the approach to criticality itself can be manifested by the probability density function (PDF) of kappa(1) calculated over an appropriate statistical ensemble. Here, kappa(1) is the variance kappa(1)(=-(2)) resulting from the power spectrum of a function defined as Phi(omega)= summation operator(k=1)(N) p(k) exp(iomegachi(k)), where p(k) is the normalized energy of the k-th small earthquake and omega the natural frequency. This PDF exhibits a maximum at kappa(1) asymptotically equal to 0.070 a few days before the main shock. Examples are presented, referring to the magnitude 6 approximately 7 class earthquakes that occurred in Greece.     

Optimal paths in disordered complex networks

We study the optimal distance in networks, l(opt), defined as the length of the path minimizing the total weight, in the presence of disorder. Disorder is introduced by assigning random weights to the links or nodes. For strong disorder, where the maximal weight along the path dominates the sum, we find that l(opt) approximately N(1/3) in both Erdos-Rényi (ER) and Watts-Strogatz (WS) networks. For scale-free (SF) networks, with degree distribution P(k) approximately k(-lambda), we find that l(opt) scales as N((lambda-3)/(lambda-1)) for 3 or =4. Thus, for these networks, the small-world nature is destroyed. For 2相似文献   

Periodic solution and chaotic strange attractor for shunting inhibitory cellular neural networks with impulses

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence, uniqueness, and global exponential stability of periodic solution for shunting inhibitory cellular neural networks with impulses, dx(ij)dt=-a(ij)x(ij)- summation operator(C(kl)inN(r)(i,j))C(ij) (kl)f(ij)[x(kl)(t)]x(ij)+L(ij)(t), t>0,t not equal t(k); Deltax(ij)(t(k))=x(ij)(t(k) (+))-x(ij)(t(k) (-))=I(k)[x(ij)(t(k))], k=1,2,...] . Furthermore, the numerical simulation shows that our system can occur in many forms of complexities, including periodic oscillation and chaotic strange attractor. To the best of our knowledge, these results have been obtained for the first time. Some researchers have introduced impulses into their models, but analogous results have never been found.     

Weighted percolation on directed networks

We present and numerically test an analysis of the percolation transition for general node removal strategies valid for locally treelike directed networks. On the basis of heuristic arguments we predict that, if the probability of removing node i is p(i), the network disintegrates if p(i) is such that the largest eigenvalue of the matrix with entries A(ij)(1-p(i)) is less than 1, where A is the adjacency matrix of the network. The knowledge or applicability of a Markov network model is not required by our theory, thus making it applicable to situations not covered by previous works.     

Connectivity of growing random networks

A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites that link to earlier sites with a probability A(k) which depends on the number of preexisting links k to that site. For homogeneous connection kernels, A(k) approximately k(gamma), different behaviors arise for gamma<1, gamma>1, and gamma = 1. For gamma<1, the number of sites with k links, N(k), varies as a stretched exponential. For gamma>1, a single site connects to nearly all other sites. In the borderline case A(k) approximately k, the power law N(k) approximately k(-nu) is found, where the exponent nu can be tuned to any value in the range 2相似文献   

Stability and topology of scale-free networks under attack and defense strategies

We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree k of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an intentional attack with insufficient knowledge of the network. We determine, for all strategies, the critical fraction p(c) of nodes that must be removed for disintegrating the network. We find that, for an intentional attack, little knowledge of the well-connected sites is sufficient to strongly reduce p(c). At criticality, the topology of the network depends on the removal strategy, implying that different strategies may lead to different kinds of percolation transitions.     

Model for cascading failures with adaptive defense in complex networks

<正>This paper investigates cascading failures in networks by considering interplay between the flow dynamic and the network topology,where the fluxes exchanged between a pair of nodes can be adaptively adjusted depending on the changes of the shortest path lengths between them.The simulations on both an artificially created scale-free network and the real network structure of the power grid reveal that the adaptive adjustment of the fluxes can drastically enhance the robustness of complex networks against cascading failures.Particularly,there exists an optimal region where the propagation of the cascade is significantly suppressed and the fluxes supported by the network are maximal. With this understanding,a costless strategy of defense for preventing cascade breakdown is proposed.It is shown to be more effective for suppressing the propagation of the cascade than the recent proposed strategy of defense based on the intentional removal of nodes.     

In-plane thermal conductivity of Nd2CuO4: evidence for magnon heat transport

We report the temperature and magnetic field dependence of the in-plane thermal conductivity (kappa(ab)) of high-quality monocrystalline Nd2CuO4. Isothermal measurements of the field dependence of kappa(ab) at low temperatures (2 K相似文献   

Clique percolation in random networks

The notion of k-clique percolation in random graphs is introduced, where k is the size of the complete subgraphs whose large scale organizations are analytically and numerically investigated. For the Erdos-Rényi graph of N vertices we obtain that the percolation transition of k-cliques takes place when the probability of two vertices being connected by an edge reaches the threshold p(c) (k) = [(k - 1)N](-1/(k - 1)). At the transition point the scaling of the giant component with N is highly nontrivial and depends on k. We discuss why clique percolation is a novel and efficient approach to the identification of overlapping communities in large real networks.     

智能光网络中一种新型的分布式恢复方法

提出了一种基于固定备用路由和目的端触发的智能光网络中的分布式恢复方法,所选择的任一对源端节点和目的的端节点之间的固定备用路由包括该节点对之间的k条最短路径路由和基于部分链路无关的路由.目的端节点一旦探测到业务通道的失效将立即启动恢复进程,根据网络当前的资源使用情况,在这些备用路由中按照一定的次序选择一条恢复路由并为此分配一条可用的波长(对于没有波长变换器的光网络),然后将恢复通道的建立请求消息发送给该恢复通道的相关节点,这些相关节点可以锁定相关的网络资源,以避免来自其他恢复通道的竞争.所提出的算法增加了固定备用路由的数量,从仿真结果可以看出,该方法明显改善了失效连接的阻塞性能.     

Anomalous transport in scale-free networks

To study transport properties of scale-free and Erdos-Rényi networks, we analyze the conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k)-k(-lambda) in which all links have unit resistance. We predict a broad range of values of G, with a power-law tail distribution phi(SF)(G)-G(-g(G)), where g(G)=2lambda-1, and confirm our predictions by simulations. The power-law tail in phi(SF)(G) leads to large values of G, signaling better transport in scale-free networks compared to Erdos-Rényi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical "transport backbone" picture we show that the conductances of scale-free and Erdos-Rényi networks are well approximated by ck(A)k(B)/(k(A)+k(B)) for any pair of nodes A and B with degrees k(A) and k(B), where c emerges as the main parameter characterizing network transport.     

空间网络上的随机游走

本文以一维均匀环为基础, 通过添加有限数量的长程连接构造出了一维有限能量约束下的空间网络, 环上任意节点i与j之间存在一条长程连接的概率满足p_ijα d_ij^-α (α≥ 0),其中d_ij为节点i与j之间的网格距离, 并且所有长程连接长度总和受到总能量∧=cN(c≥ 0)的约束, N为网络节点总数.通过研究该空间网络上的随机游走过程,存在最优幂指数α₀ 使得陷阱问题的平均首达时间最短.进一步研究发现,平均首达时间与网络规模N之间存在着幂律关系, 随着网络规模N和总能量∧的增加,最优幂指数α₀单调增加,并趋近最优值1.5.     

A temporal ant colony optimization approach to the shortest path problem in dynamic scale-free networks

A large number of networks in the real world have a scale-free structure, and the parameters of the networks change stochastically with time. Searching for the shortest paths in a scale-free dynamic and stochastic network is not only necessary for the estimation of the statistical characteristics such as the average shortest path length of the network, but also challenges the traditional concepts related to the “shortest path” of a network and the design of path searching strategies. In this paper, the concept of shortest path is defined on the basis of a scale-free dynamic and stochastic network model, and a temporal ant colony optimization (TACO) algorithm is proposed for searching for the shortest paths in the network. The convergence and the setup for some important parameters of the TACO algorithm are discussed through theoretical analysis and computer simulations, validating the effectiveness of the proposed algorithm.     

Hybrid gap structure of the heavy-fermion superconductor CeIrIn5

The thermal conductivity kappa of the heavy-fermion superconductor CeIrIn5 was measured as a function of temperature down to T(c)/8, for current directions parallel (J parallel c) and perpendicular (J parallel a) to the tetragonal c axis. For J parallel a, a sizable residual linear term kappa(0)/T is observed, as previously, which confirms the presence of line nodes in the superconducting gap. For J parallel c, on the other hand, kappa/T-->0 as T-->0. The resulting precipitous decline in the anisotropy ratio kappa(c)/kappa(a) at low temperature rules out a gap structure with line nodes running along the c axis, such as the d-wave state favored for CeCoIn5, and instead points to a hybrid gap of E(g) symmetry.     

Structural changes in data communication in wireless sensor networks

Wireless sensor networks are an important technology for making distributed autonomous measures in hostile or inaccessible environments. Among the challenges they pose, the way data travel among them is a relevant issue since their structure is quite dynamic. The operational topology of such devices can often be described by complex networks. In this work, we assess the variation of measures commonly employed in the complex networks literature applied to wireless sensor networks. Four data communication strategies were considered: geometric, random, small-world, and scale-free models, along with the shortest path length measure. The sensitivity of this measure was analyzed with respect to the following perturbations: insertion and removal of nodes in the geometric strategy; and insertion, removal and rewiring of links in the other models. The assessment was performed using the normalized Kullback-Leibler divergence and Hellinger distance quantifiers, both deriving from the Information Theory framework. The results reveal that the shortest path length is sensitive to perturbations.     

Efficient and robust routing on scale-free networks

Information routing is one of the most important problems in large communication networks. In this paper we propose a novel routing strategy in which the optimal paths between all pairs of nodes are chosen according to a cost function that incorporates degrees of nodes in paths. Results on large scale-free networks demonstrate that our routing strategy is more efficient than the shortest path algorithm and the efficient routing strategy proposed by Yan et al. [Phys. Rev. E 73, 046108 (2006)]. Furthermore our routing strategy has strong robustness against cascading failure attacks on networks.