Self-similarity of complex networks

Complex networks have been studied extensively owing to their relevance to many real systems such as the world-wide web, the Internet, energy landscapes and biological and social networks. A large number of real networks are referred to as 'scale-free' because they show a power-law distribution of the number of links per node. However, it is widely believed that complex networks are not invariant or self-similar under a length-scale transformation. This conclusion originates from the 'small-world' property of these networks, which implies that the number of nodes increases exponentially with the 'diameter' of the network, rather than the power-law relation expected for a self-similar structure. Here we analyse a variety of real complex networks and find that, on the contrary, they consist of self-repeating patterns on all length scales. This result is achieved by the application of a renormalization procedure that coarse-grains the system into boxes containing nodes within a given 'size'. We identify a power-law relation between the number of boxes needed to cover the network and the size of the box, defining a finite self-similar exponent. These fundamental properties help to explain the scale-free nature of complex networks and suggest a common self-organization dynamics.     

Functional cartography of complex metabolic networks

High-throughput techniques are leading to an explosive growth in the size of biological databases and creating the opportunity to revolutionize our understanding of life and disease. Interpretation of these data remains, however, a major scientific challenge. Here, we propose a methodology that enables us to extract and display information contained in complex networks. Specifically, we demonstrate that we can find functional modules in complex networks, and classify nodes into universal roles according to their pattern of intra- and inter-module connections. The method thus yields a 'cartographic representation' of complex networks. Metabolic networks are among the most challenging biological networks and, arguably, the ones with most potential for immediate applicability. We use our method to analyse the metabolic networks of twelve organisms from three different superkingdoms. We find that, typically, 80% of the nodes are only connected to other nodes within their respective modules, and that nodes with different roles are affected by different evolutionary constraints and pressures. Remarkably, we find that metabolites that participate in only a few reactions but that connect different modules are more conserved than hubs whose links are mostly within a single module.     

基于搜索效率的复杂网络多模型并行演化分析

很多真实的复杂网络呈现无标度性．但是,这些网络为什么在增长过程中遵从优先连接规则？现有研究尚未给出有力的解释．一个合理的猜想是：这些网络如果不遵从优先连接规则,则将处于不利的地位．为证实这一猜想,采用搜索效率作为评价指标,量化评价不同演化模型的优劣．首先提出一种新的复杂网络并行演化模式,使得同一网络中不同的局部遵从不同的演化模型,从而在统一的基础上比较不同演化模型搜索效率的优劣．以BA无标度网络、WS小世界网络和随机网络为基础,构建了异质复杂网络．其次,采用随机游走搜索策略和DS最大度搜索策略,比较遵从不同演化模型的异质子网的搜索效率,力图解释复杂网络中演化模式同质化的原因．实验发现一种“信息壁垒”现象,即处于劣势的网络模型,其所属节点很难被其他模型的节点访问到．实验结果表明：对于以搜索为重要功能的复杂网络,无标度网络具有最强的适应性,从而在一定程度上解释了无标度现象在众多现实复杂网络中存在的原因．     

多产品供应链网络的建模与绩效分析

为了研究多产品供应链库存控制问题,构建了一种网络模型,提出了一种解析方法求解模型的主要性能指标.该方法通过任务队列分解分析求解各节点的主要性能指标,通过合并输入流和分解输出流来连接网络中的各个节点.数值试验验证了文中所提方法的有效性.     

融合节点影响力与多标签传播的重叠社区发现算法

重叠社区发现是复杂网络分析研究的重要目标之一。针对传统多标签传播算法存在的社区发现结果具有随机性、不稳定性,以及忽视节点影响力对标签传播的影响等问题,提出一种基于节点影响力与多标签传播的能够生成稳定社区的重叠社区发现算法。算法在节点影响力的计算、排序和核心节点识别基础上,通过邻居节点初始标签的再处理和基于平衡系数的节点标签异步更新策略,实现复杂网络重叠社区的有效识别。在真实数据集和人工数据集上的实验综合表明,算法性能优于各对比算法,适用于大规模复杂网络。     

Error and attack tolerance of complex networks

Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network. Complex communication networks display a surprising degree of robustness: although key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these and other complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. Here we demonstrate that error tolerance is not shared by all redundant systems: it is displayed only by a class of inhomogeneously wired networks, called scale-free networks, which include the World-Wide Web, the Internet, social networks and cells. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates. However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks (that is, to the selection and removal of a few nodes that play a vital role in maintaining the network's connectivity). Such error tolerance and attack vulnerability are generic properties of communication networks.     

基于DynamicRank的重要节点集挖掘算法

为了更为有效地挖掘复杂网络中综合影响力高的节点集、提高重要节点集挖掘算法的准确性,针对节点集中各节点在信息传播中不同程度的相互促进和相互抑制作用,基于DynamicRank算法设计了一种新的级联概率计算模型。通过增强贪心策略,优先从种子集邻居以外的节点中选取备选节点,减小种子集内重叠邻居对信息传播引发的抑制作用;利用级联概率计算模型,增强种子集对信息传播的级联促进作用。在4个实际网络上采用SIR模型进行了测试,实验结果表明,相较于已有重要节点挖掘方法H-index、Degree、DynamicRank、VoteRank和EnRenew,提出的算法挖掘出的节点集具有更高影响力。特别地,在Grid数据集上,本文方法挖掘出的种子集的传播范围比对比算法平均提升了49.3%。提出的算法针对信息传播概率和贪心策略的改进有利于重要节点集的挖掘和识别。     

Uncovering the overlapping community structure of complex networks in nature and society

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the coexistence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins, industrial sectors and groups of people) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large networks find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping communities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties.     

复杂网络的控制及计算机数值算法

针对复杂网络存在稳定的同步现象问题,采用了一种节点为三元二次迭代方程的复杂网络的控制方法.以相同结构动力学系统作为节点构造复杂网络,通过多控制信号和单一正弦控制信号来分别控制该动力学系统,通过计算机仿真模拟.结果表明:复杂网络存在稳定的同步现象,仿真模拟证明多控制信号和单一正弦控制信号对该动力学系统的控制方法是有效的.     

复杂网络上具有分布式传染速率的流行病传播行为

提出一个改进的SI模型来研究分布式传染速率对复杂网络上的流行病传播的影响.与标准的SI模型不同,假定传播速率为几种典型的分布参数,如二值分布、均匀分布和指数分布.这种分布式的速率可以表示个体在传染性上的差异,这种差异可在很多真实的传染病中观察到.大量的数值仿真表明,这种分布式的传染速率能大大减小被感染结点的密度,减缓其动态传播过程,并且允许有更长的时间来采取相应的控制措施.因而,当前的研究结果对进一步理解网络上真实流行病的传播特性具有重要意义.     

旅游目的地虚拟网络结构特征研究——-以黄山市为例

以黄山市为案例, 采用复杂网络理论和方法研究分析目的地虚拟网络的结构特征。结果显示该网络是具有小世界特征的稀疏网络, 其度分布符合幂律分布且幂指数位于1与2之间, 其节点倾向于链接不同类型的节点, 并且节点之间的距离和度值对节点互联的影响较弱。将黄山网络与随机网络、万维网以及其他旅游虚拟网络进行对比分析, 探讨目的地虚拟网络和现实网络之间的关系, 认为虚拟网络不仅只是信息网路, 也是社会网络, 它是现实网络在虚拟空间中的映射。在这个意义下, 目的地虚拟网络的结构特征反映了其现实网络的特征。     

移动自组织网络中一种能量有效的跨层协议

提出了一种移动自组织网络中能量有效的跨层协议,将网络层的能量感知路由协议与MAC层的功率控制协议相结合,以提高节点的能量利用效率.在路由协议中根据节点剩余能量决定节点接入路由的延迟时间,从而使剩余能量较多的节点能够更快地接入路由,以使网络中的能量消耗更公平.在MAC层中实现功率控制,减少节点的实际能量消耗.仿真结果表明,在移动自组织网络中,该能量有效的跨层协议不但能延长网络的生存时间,减少端到端延迟,而且可以提高网络吞吐率.     

Entanglement of spin waves among four quantum memories

Quantum networks are composed of quantum nodes that interact coherently through quantum channels, and open a broad frontier of scientific opportunities. For example, a quantum network can serve as a 'web' for connecting quantum processors for computation and communication, or as a 'simulator' allowing investigations of quantum critical phenomena arising from interactions among the nodes mediated by the channels. The physical realization of quantum networks generically requires dynamical systems capable of generating and storing entangled states among multiple quantum memories, and efficiently transferring stored entanglement into quantum channels for distribution across the network. Although such capabilities have been demonstrated for diverse bipartite systems, entangled states have not been achieved for interconnects capable of 'mapping' multipartite entanglement stored in quantum memories to quantum channels. Here we demonstrate measurement-induced entanglement stored in four atomic memories; user-controlled, coherent transfer of the atomic entanglement to four photonic channels; and characterization of the full quadripartite entanglement using quantum uncertainty relations. Our work therefore constitutes an advance in the distribution of multipartite entanglement across quantum networks. We also show that our entanglement verification method is suitable for studying the entanglement order of condensed-matter systems in thermal equilibrium.     

技术创新合作网的演化机理与特征研究

自然界和人类社会中的网络系统既具有某些已被发现的组织结构的共性,也还有未被发现的内在演化机理和特性．本文在对复杂网络理论研究的基础上,结合企业技术创新合作实际,提出了节点具有竞争力的社会合作网络多阶段演化模型和算法,并通过数值模拟和实证研究,对网络的演化机理和小世界、无标度等特征进行了分析,得到了一些有意义的启示．     

Effect of spatial distance on search information correlation in complex systems

Spatial distance has a remarkable effect on the attended mode of a network embedded in a certain space. First, we investigate how spatial restriction leads to information-information correlation that is strong, linear and positive in real networks. We then construct a two-dimensional space, define the action radius R for nodes of networks, and propose a class of models that depend on spatial distance. Information correlation of the models is consistent with that of real networks. The spatial distance plays ...     

Surface Coverage Algorithm in Directional Sensor Networks for Three-Dimensional Complex Terrains

Coverage is an important issue in the area of wireless sensor networks, which reflects the monitoring quality of the sensor networks in scenes. Most sensor coverage research focuses on the ideal two-dimensional(2-D) plane and full three-dimensional(3-D) space. However, in many real-world applications, the target field is a3-D complex surface, which makes conventional methods unsuitable. In this paper, we study the coverage problem in directional sensor networks for complex 3-D terrains, and design a new surface coverage algorithm. Based on a 3-D directional sensing model of nodes, this algorithm employs grid division, simulated annealing, and local optimum ideas to improve the area coverage ratio by optimizing the position coordinates and the deviation angles of the nodes, which results in coverage enhancement for complex 3-D terrains. We also conduct extensive simulations to evaluate the performance of our algorithms.     

基于B—P神经网络的非线性系统预测控制的研究

预测控制是以计算机为手段基于模型预测进行控制的方法,但是已有的预测控制算法通常是针对线性渐进稳定对象的,或者即使针对非线性使用了非线性模型,但由于算法过于复杂不能适用于快速系统,本文对复杂非线性系统提出了一种基于Ｂ－神经网络的预测控制方法,仿真和实际结果表明该方法的有效性和快速性,能够实现对非线性系统的实时智能优化控制。     

Efficient Algorithm for Energy-Aware Virtual Network Embedding

Network virtualization is a promising approach for resource management that allows customized Virtual Networks(VNs) to be multiplexed on a shared physical infrastructure. A key function that network virtualization can provide is Virtual Network Embedding(VNE), which maps virtual networks requested by users to a shared substrate network maintained by an Internet service provider. Existing research has worked on this, but has primarily focused on maximizing the revenue of the Internet service provider. In this paper, we consider energy-aware virtual network embedding, which aims at minimizing the energy consumption for embedding virtual networks in a substrate network. In our optimization model, we consider energy consumption of both links and nodes. We propose an efficient heuristic to assign virtual nodes to appropriate substrate nodes based on priority, where existing activated nodes have higher priority for hosting newly arrived virtual nodes. In addition, our proposed algorithm can take advantage of activated links for embedding virtual links so as to minimize total energy consumption. The simulation results show that, for all the cases considered, our algorithm can improve upon previous work by an average of12.6% on acceptance rate, while the consumed energy can be reduced by 12.34% on average.     

复杂网络中众多混沌运动电机的同步控制研究

以混沌运动的永磁同步电机作为节点构建线性耦合的复杂动力网络,研究了网络中众多电机的同步控制方法.该方法根据线性耦合网络全局同步的牵制控制条件,设计出电机交轴和直轴电压的比例调节控制器,并给出施加牵制控制后电机网络的状态方程.模拟结果表明:在网络耦合强度、电机节点参数时变情况下,对于小世界拓扑或无标度拓扑构建的电机网络,一个电机节点的线性反馈牵制控制就能实现网络所有电机同步,控制方法具有控制效率高、代价小、可调节等优点.     

两个时变复杂网络的自适应同步(英文)

研究了两个时变复杂网络的自适应同步。根据Lyapunov稳定性理论,分析了两个时变复杂网络的同步条件,并且证明了它的有效性。为了验证理论结果,以不同参数下的Lorenz系统作为两个时变网络的节点动力学系统进行仿真分析,从仿真结果可以得到:如果不施加控制,这两个时变复杂网络不能实现同步;如果设计合适的自适应控制器,这两个时变复杂网络将达到同步。不管是对相同结构的复杂网络,还是对不同结构的复杂网络,仿真结果和理论分析均一致。