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.     

复杂网络病毒传播的局域控制研究

从复杂网络的节点路径长度范围的角度来研究病毒传播的局域控制，分析了在不同拓扑结构的复杂网络中进行局域控制的有效性.研究表明，局域控制对WS小世界网络、BA无标度网络和ER随机网络三类复杂网络均有效，但只有WS小世界网络存在零感染的控制范围最优值d=3；对于长程连边的分布存在距离偏好的Kleinberg小世界网络，随着依赖度的增大，病毒传播率临界值增加，同时局域范围控制的效果得到加强. 关键词： 复杂网络 病毒传播 局域控制 路径长度     

长程作用下Gauss系统的临界温度

利用傅里叶变换的方法，严格求解了d维(d=1，2和3)超立方晶格和二维三角晶格上具有长程 相互作用的Gauss模型(这里考虑的长程作用有幂指数、指数和对数三种形式).得到了这些情 况下系统的临界点(温度)，并对不同形式的长程作用对临界点的影响进行了比较.结果表明 ，长程相互作用的存在，使得系统的临界温度有了一定程度的升高，它们对系统临界温度的 影响与其衰减的快慢有关. 关键词： Gauss模型 临界点 超立方晶格 三角晶格     

基于有限资源提升网络可生存性的拓扑重构方法

给定网络拓扑结构和有限添加边资源,如何优化配置添加边使重构后的网络拓扑结构具有最优可生存性是非常有价值的研究问题.本文首先明确网络可生存性的量化评估指标,以移除节点后网络结构的鲁棒性和有效性为优化目标,提出网络拓扑重构优化问题的建模与分析方法.同时在给定资源代价的约束下,为实现添加边资源配置效率的最大化,提出优先配置节点加强保护圈的启发式算法.仿真实验表明,该算法在有限资源约束的随机局部故障和选择性攻击环境中,能兼顾改善网络鲁棒性和传输效率,有效提升网络结构的可生存性.     

水分子凝聚体系的介孔结构分形学

透射电镜研究表明，4,40-双硬脂酰胺基二苯醚在水中聚集、自组装成缠绕细纤维状聚集体，进而使整个体系形成三维网络结构．水分子被包囊在这个网络结构中，形成一种新型的凝聚体系(水分子凝胶)．水分子凝胶是一种典型的纳米介孔物质，其复杂的微孔结构可以用分形维数D来表征，通过气体吸附方法(孔度法和比表面积法)计算，求得水分子凝胶体系的微孔结构的分形维数为2.1?2.2．对于纤维状三维网络结构的分形表征，通过粘度法和Cayley分形树模型得出分形维数为1.98．由此推测其分形网络形成的过程是一个初始成核-生长-枝化的循环过程．     

大规模软件系统的无标度特性与演化模型

在软件工程中，常用类图来描述类之间的关系. 以软件系统网为研究对象，通过对Sun和IBM公司提供的大规模软件系统进行实证分析，发现Java软件系统网的度分布是无标度分布，标度指数γ≈2.5. 在软件系统网的演化过程中，除加点之外，还存在边的添加、边的随机移除与边的重连等局部事件. 由此建立了软件系统演化模型. 由该模型演化生成的网络，其度分布服从幂律分布. 实际应用与数值仿真验证了该模型的有效性. 关键词： 软件系统 复杂网络 度分布 无标度     

基于改进免疫遗传算法的K覆盖异构传感器节点调度

为了实现无线传感器网络监测区域目标点的多重覆盖,设计了一种基于改进免疫遗传算法的异构传感器节点调度算法实现目标点的K重覆盖;首先,在传统的概率感知模型中加入剩余能量和感知能力因素,得到改进的概率感知模型,并设计了以最小化节点数并满足覆盖度约束的目标函数;然后,采用改进的免疫遗传算法对节点进行调度,最后,给出了具体的采用改进免疫遗传算法实现WSN异构节点调度的具体算法;仿真实验表明:文中方法能在满足K覆盖约束前提下实现监测区域的节点调度,与其他方法相比,活动节点数平均多7%,具有较长的网络生命周期和较少的网络能耗。     

夸克－胶子等离子体对高能碰撞多重产生的可能描述

以ＱＣＤ袋模型和统计流体力学模型为基础，在二维平衡态近似下得到多重数和质心系能量的关系式，和高能　碰撞非单衍过程产生的多重数实验数据吻合得很好；在三维平衡态近似下得到中心在快度较大区域的产生粒子的源Ⅱ的大小和横动量的关系，关系式和三火球模型计算结果符合．     

黎曼面上的温度对偶性与亏格数g=1和2的弦宇宙学解

考察了一个在引力场g_μv和dilaton场背景下的有限温度玻色弦模型,导出了高亏格黎曼面上能量动量张量满足的对偶关系式;同时,还在四维Robertson–Walker(R–W)度规下证明了弦气体物质作用量的温度对偶不变性,获得了亏格数g=1和2的弦宇宙学解,并研究了运动方程的温度变换性质.     

基于超图结构的科研合作网络演化模型

基于科研论文作者的合作方式, 用超图理论构建了一个科研合作超网络演化模型. 利用平均场理论分析了作者发表论文的演化规律, 发现作者的超度 (即发表论文数) 分布符合幂律分布. 进一步理论分析得到分布的幂指数γ与合作领域作者增长速度相关. γ越大, 新作者增长速度越快, 且存在关系: γ=1+L/M (L/M为作者增长率). 并通过对《物理学报》与《中国科学》2003–2012年期间作者发表论文进行了数据分析, 实证结果与理论分析及模拟结果能很好地符合. 本文对科研合作网络的理论和实证研究有一定的借鉴意义. 关键词： 复杂网络 超图 科研合作网络 演化模型     

Generating weighted community networks based on local events

Many realistic networks have community structures, namely, a network consists of groups of nodes within which links are dense but among which links are sparse. This paper proposes a growing network model based on local processes, the addition of new nodes intra-community and new links intra- or inter-community. Also, it utilizes the preferential attachment for building connections determined by nodes' strengths, which evolves dynamically during the growth of the system. The resulting network reflects the intrinsic community structure with generalized power-law distributions of nodes' degrees and strengths.     

Reducing congestion on complex networks by dynamic relaxation processes

We study the effects of relaxational dynamics on the congestion pressure in general transport networks. We show that the congestion pressure is reduced in scale-free networks if a relaxation mechanism is utilized, while this is in general not the case for non-scale-free graphs such as random graphs. We also present evidence supporting the idea that the emergence of scale-free networks arise from optimization mechanisms to balance the load of the networks nodes.     

Growing community networks with local events

The study of community networks has attracted considerable attention recently. In this paper, we propose an evolving community network model based on local processes, the addition of new nodes intra-community and new links intra- or inter-community. Employing growth and preferential attachment mechanisms, we generate networks with a generalized power-law distribution of nodes’ degrees.     

Local model of a scientific collaboration in physics network compared with the global model

We have constructed a collaboration network for physicists based in Iran working in different disciplines. By discussing properties like collaborators per author, shortest path, betweenness, and the concept of power in networks for this local model, and comparing with the global model, we understand how a developing country in the Middle East is contributing to the scientific growth in the world statistically. In this comparison, we found some properties of the local model which were not in accordance with the standard global society of science, which should be considered in developing the future policies. Our results show significant differences in factors like the degree and the diameter of the networks. Even though the diversity of disciplines is low in contrast with the rest of the world according to the diameter of networks, people are reluctant to collaborate as their degree shows.     

Line graphs as social networks

It was demonstrated recently that the line graphs are clustered and assortative. These topological features are known to characterize some social networks [M.E.J. Newman, Y. Park, Why social networks are different from other types of networks, Phys. Rev. E 68 (2003) 036122]; it was argued that this similarity reveals their cliquey character. In the model proposed here, a social network is the line graph of an initial network of families, communities, interest groups, school classes and small companies. These groups play the role of nodes, and individuals are represented by links between these nodes. The picture is supported by the data on the LiveJournal network of about 8×10⁶ people.     

Network evolution by nonlinear preferential rewiring of edges

The mathematical framework for small-world networks proposed in a seminal paper by Watts and Strogatz sparked a widespread interest in modeling complex networks in the past decade. However, most of research contributing to static models is in contrast to real-world dynamic networks, such as social and biological networks, which are characterized by rearrangements of connections among agents. In this paper, we study dynamic networks evolved by nonlinear preferential rewiring of edges. The total numbers of vertices and edges of the network are conserved, but edges are continuously rewired according to the nonlinear preference. Assuming power-law kernels with exponents α and β, the network structures in stationary states display a distinct behavior, depending only on β. For β>1, the network is highly heterogeneous with the emergence of starlike structures. For β<1, the network is widely homogeneous with a typical connectivity. At β=1, the network is scale free with an exponential cutoff.     

Partially connected feedforward neural networks on Apollonian networks

This paper presents a novel and data-independent method to construct a type of partially connected feedforward neural network (FNN). The proposed networks, called Apollonian network-based partially connected FNNs (APFNNs), are constructed in terms of the structures of two-dimensional deterministic Apollonian networks. The APFNNs are then applied in various experiments to solve function approximation, forecasting and classification problems. Their results are compared with those generated by partially connected FNNs with random connectivity (RPFNNs), different learning algorithm-based traditional FNNs and other benchmark methods. The results demonstrate that the proposed APFNNs have a good capacity to fit complicated input and output relations, and provide better generalization performance than traditional FNNs and RPFNNs. The APFNNs also demonstrate faster training speed in each epoch than traditional FNNs.     

复杂网络上动力系统同步的研究进展

本文简要介绍复杂网络的基本概念并详细总结了近年来复杂网络上动力学系统的同步的研究进展，主要内容有复杂网络同步的稳定性分析，复杂网络上动力学系统同步的特点，网络的几何特征量对同步稳定性的影响，以及提高网络同步能力的方法等。最后文章提出了这一领域的几个有待解决的问题及可能的发展方向。     

基于Sierpinski分形垫的确定性复杂网络演化模型研究

近年来,人们发现大量真实网络都表现出小世界和无尺度的特性,由此复杂网络演化模型成为学术界研究的热点问题.本文基于Sierpinski分形垫,通过迭代的方式构造了两个确定性增长的复杂网络模型,即小世界网络模型(S-DSWN)和无尺度网络模型(S-DSFN);其次,给出了确定性网络模型的迭代生成算法,解析计算了其主要拓扑特性,结果表明两个网络模型在度分布、集聚系数和网络直径等结构特性方面与许多现实网络相符合;最后,提出了一个确定性的统一模型(S-DUM),将S-DSWN与S-DSFN纳入到一个框架之下,为复杂网络的相关研究提供理论基础.特别地,发现这些网络模型都是极大平面图.     

Deterministic scale-free small-world networks of arbitrary order

In many real-life networks, both the scale-free distribution of degree and small-world behavior are important features. There are many random or deterministic models of networks to simulate these features separately. However, there are few models that combine the scale-free effect and small-world behavior, especially in terms of deterministic versions. What is more, all the existing deterministic algorithms running in the iterative mode generate networks with only several discrete numbers of nodes. This contradicts the purpose of creating a deterministic network model on which we can simulate some dynamical processes as widely as possible. According to these facts, this paper proposes a deterministic network generation algorithm, which can not only generate deterministic networks following a scale-free distribution of degree and small-world behavior, but also produce networks with arbitrary number of nodes. Our scheme is based on a complete binary tree, and each newly generated leaf node is further linked to its full brother and one of its direct ancestors. Analytical computation and simulation results show that the average degree of such a proposed network is less than 5, the average clustering coefficient is high (larger than 0.5, even for a network of size 2 million) and the average shortest path length increases much more slowly than logarithmic growth for the majority of small-world network models.