Optimization-based structure identification of dynamical networks

The topological structure of a dynamical network plays a pivotal part in its properties, dynamics and control. Thus, understanding and modeling the structure of a network will lead to a better knowledge of its evolutionary mechanisms and to a better cottoning on its dynamical and functional behaviors. However, in many practical situations, the topological structure of a dynamical network is usually unknown or uncertain. Thus, exploring the underlying topological structure of a dynamical network is of great value. In recent years, there has been a growing interest in structure identification of dynamical networks. As a result, various methods for identifying the network structure have been proposed. However, in most of the previous work, few of them were discussed in the perspective of optimization. In this paper, an optimization algorithm based on the projected conjugate gradient method is proposed to identify a network structure. It is straightforward and applicable to networks with or without observation noise. Furthermore, the proposed algorithm is applicable to dynamical networks with partially observed component variables for each multidimensional node, as well as small-scale networks with time-varying structures. Numerical experiments are conducted to illustrate the good performance and universality of the new algorithm.     

复杂网络系统拓扑连接优化控制方法

为了增加实际网络系统连接增益、减少网络连接成本, 提出了一种基于网络效率和平均连接度的网络拓扑连接优化控制方法, 该方法利用网络效率来表征网络连接收益、用网络平均连接度来表征网络连接成本, 并提出了其计算优化算法, 该算法的时间复杂性为O(Mpn²). 实验分析表明, 可以采取一定的方式对实际复杂网络拓扑连接进行优化控制, 小世界和无标度网络均存在一个最佳的网络平均度值能够使网络连接增益达到最大. 关键词： 复杂网络 拓扑连接 优化控制 连接增益     

Accelerating distributed average consensus by exploring the information of second-order neighbors

The problem of accelerating distributed average consensus by using the information of second-order neighbors in both the discrete- and continuous-time cases is addressed in this Letter. In both two cases, when the information of second-order neighbors is used in each iteration, the network will converge with a speed faster than the algorithm only using the information of first-order neighbors. Moreover, the problem of using partial information of second-order neighbors is considered, and the edges are not chosen randomly from second-order neighbors. In the continuous-time case, the edges are chosen by solving a convex optimization problem which is formed by using the convex relaxation method. In the discrete-time case, for small network the edges are chosen optimally via the brute force method. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed algorithm.     

Adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions

<正>The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper.Based on Lyapunov stability theory and Barbalat’s lemma,generalized matrix projective lag synchronization criteria are derived by using the adaptive control method.Furthermore,each network can be undirected or directed,connected or disconnected,and nodes in either network may have identical or different dynamics.The proposed strategy is applicable to almost all kinds of complex networks.In addition,numerical simulation results are presented to illustrate the effectiveness of this method,showing that the synchronization speed is sensitively influenced by the adaptive law strength,the network size,and the network topological structure.     

一类输出耦合时延复杂动态网络故障诊断研究

文章针对一类输出耦合时延复杂动态网络模型,考虑节点动力学参数未知的情况,基于网络外部同步思想,提出一种对该类复杂动态网络进行故障诊断的方法.利用节点的输出变量作为反馈变量设计控制器,根据Lyapunov稳定性理论,推导网络达到外部同步的条件.该方法可以实时监控时延网络拓扑结构的变化情况,对网络进行故障诊断.通过仿真验证本文方法的有效性. 关键词： 复杂动态网络 时延 故障诊断 节点参数     

Topology identification of the complex networks with non-delayed and delayed coupling

In practical situation, there exists many uncertain information in complex networks, such as the topological structures. So the topology identification is an important issue in the research of the complex networks. Based on LaSalle's invariance principle, in this Letter, an adaptive controlling method is proposed to identify the topology of a weighted general complex network model with non-delayed and delayed coupling. Finally, simulation results show that the method is effective.     

Community detection with consideration of non-topological information

In a network described by a graph, only topological structure information is considered to determine how the nodes are connected by edges. Non-topological information denotes that which cannot be determined directly from topological information. This paper shows, by a simple example where scientists in three research groups and one external group form four communities, that in some real world networks non-topological information (in this example, the research group affiliation) dominates community division. If the information has some influence on the network topological structure, the question arises as to how to find a suitable algorithm to identify the communities based only on the network topology. We show that weighted Newman algorithm may be the best choice for this example. We believe that this idea is general for real-world complex networks.     

Adaptive projective synchronization in complex networks with time-varying coupling delay

In this Letter, adaptive projective synchronization (PS) between two complex networks with time-varying coupling delay is investigated by the adaptive control method, and this method has been applied to identify the exact topology of a weighted general complex network. To validate the proposed method, the Lü and Qi systems as the nodes of the networks are detailed analysis, and some numerical results show the effectiveness of the present method.     

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.     

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.     

基于时间序列符号化模式表征的有向加权复杂网络

时间序列复杂网络分析近些年已发展成为非线性信号分析领域的一个国际热点课题.为了能更有效地挖掘时间序列(特别是非线性时间序列)中的结构特征,同时简化时间序列分析的复杂度,提出了一种新的基于时间序列符号化结合滑窗技术模式表征的有向加权复杂网络建网方法.该方法首先按照等概率区段划分的方式将时间序列做符号化处理,结合滑窗技术确定不同时刻的符号化模式作为网络的节点;然后将待分析时间序列符号化模式的转换频次和方向作为网络连边的权重和方向,从而建立时间序列有向加权复杂网络.通过对Logistic系统不同参数设置对应的时间序列复杂网络建网测试结果表明,相比经典的可视图建网方法,本文方法的网络拓扑能更简洁、直观地展示时间序列的结构特征.进而,将本文方法应用于规则排列采集的自然风场信号分析,其网络特性指标能较准确地预测采集信号的排布规律,而可视图建网方法的网络特性指标没有任何规律性的结果.     

Structure identification and adaptive synchronization of uncertain general complex dynamical networks

This Letter proposes an approach to identify the topological structure and unknown parameters for uncertain general complex networks simultaneously. By designing effective adaptive controllers, we achieve synchronization between two complex networks. The unknown network topological structure and system parameters of uncertain general complex dynamical networks are identified simultaneously in the process of synchronization. Several useful criteria for synchronization are given. Finally, an illustrative example is presented to demonstrate the application of the theoretical results.     

Improved Local Search with Momentum for Bayesian Networks Structure Learning

Bayesian Networks structure learning (BNSL) is a troublesome problem that aims to search for an optimal structure. An exact search tends to sacrifice a significant amount of time and memory to promote accuracy, while the local search can tackle complex networks with thousands of variables but commonly gets stuck in a local optimum. In this paper, two novel and practical operators and a derived operator are proposed to perturb structures and maintain the acyclicity. Then, we design a framework, incorporating an influential perturbation factor integrated by three proposed operators, to escape current local optimal and improve the dilemma that outcomes trap in local optimal. The experimental results illustrate that our algorithm can output competitive results compared with the state-of-the-art constraint-based method in most cases. Meanwhile, our algorithm reaches an equivalent or better solution found by the state-of-the-art exact search and hybrid methods.     

Community detection in networks by using multiobjective evolutionary algorithm with decomposition

Community structure is an important property of complex networks. Most optimization-based community detection algorithms employ single optimization criteria. In this study, the community detection is solved as a multiobjective optimization problem by using the multiobjective evolutionary algorithm based on decomposition. The proposed algorithm maximizes the density of internal degrees, and minimizes the density of external degrees simultaneously. It can produce a set of solutions which can represent various divisions to the networks at different hierarchical levels. The number of communities is automatically determined by the non-dominated individuals resulting from our algorithm. Experiments on both synthetic and real-world network datasets verify that our algorithm is highly efficient at discovering quality community structure.     

Community detection in complex networks by density-based clustering

We proposed a method to find the community structure in a complex network by density-based clustering. Physical topological distance is introduced in density-based clustering for determining a distance function of specific influence functions. According to the distribution of the data, the community structures are uncovered. The method keeps a better connection mode of the community structure than the existing algorithms in terms of modularity, which can be viewed as a basic characteristic of community detection in the future. Moreover, experimental results indicate that the proposed method is efficient and effective to be used for community detection of medium and large networks.     

利用节点效率评估复杂网络功能鲁棒性

为了克服现有复杂网络鲁棒性研究模型只考虑节点失效的局部影响性和网络拓扑鲁棒性的缺陷, 提出了一种利用节点效率来评估复杂网络功能鲁棒性的方法. 该方法综合考虑节点失效的全局影响性, 利用网络中节点的效率来定义各节点的负载、极限负载和失效模型, 通过打击后网络中最终失效节点的比例来衡量网络的功能鲁棒性, 并给出了其评估优化算法. 实验分析表明该方法对考虑节点负载的复杂网络功能鲁棒性的评定可行有效, 对于大型复杂网络可以获得理想的计算能力.     

卷积神经网络的缺陷类型识别分析

该文提出一种基于卷积神经网络直接对阵列超声检测原始信号进行缺陷类型识别的方法,该方法无需对超声回波原始信号进行特征提取.文章研究对比了不同卷积神经网络及其优化的识别性能.首先采用超声相控阵系统对不同试块上的平底孔、球底孔、通孔三种缺陷进行超声检测,然后利用LeNet5、VGG16和ResNet三种卷积神经网络对一维和二...     

迟滞混沌神经元/网络的控制策略及应用研究

为了保持神经网络在优化计算求解过程中结构不被改变, 以迟滞混沌神经元和迟滞混沌神经网络为研究对象, 提出了一种基于滤波跟踪误差的控制策略来实现神经元/网络的稳定控制. 采用该控制策略, 在不改变非线性特性发生机理的情况下, 神经元/网络可实现函数优化计算问题的求解. 所设计的控制律包含两部分: 一部分是系统进入滤波跟踪误差面时的等效控制部分, 另一部分为确保系统快速进入滤波跟踪误差面的控制部分. 采用Lyapunov方法对神经元/网络的控制进行了稳定性证明. 根据待寻优函数直接求得神经元的控制律, 在该控制律的作用下, 神经元/网络可逐渐稳定到优化函数的极值点, 从而实现优化问题的求解, 仿真实验结果验证了该控制方法在优化计算中的可行性和有效性.     

基于改进教学优化算法的Hermite正交基神经网络混沌时间序列预测

针对传统预测模型对混沌时间序列预测精度低、收敛速度慢及模型结构复杂的问题, 提出了基于改进教学优化算法的Hermite正交基神经网络预测模型. 首先, 将自相关法和Cao方法相结合对混沌时间序列进行相空间重构, 以获得重构延迟时间向量; 其次, 以Hermite正交基函数为激励函数构成Hermite正交基神经网络, 作为预测模型; 最后, 将模型参数优化问题转化为多维空间上的函数优化问题, 利用改进教学优化算法对预测模型进行参数优化, 以建立预测模型并进行预测分析. 分别以Lorenz 系统和Liu系统为模型, 通过四阶Runge-Kutta法产生混沌时间序列作为仿真对象, 并进行单步及多步预测对比实验. 仿真结果表明, 与径向基函数神经网络、回声状态网络、最小二乘支持向量机及基于教学优化算法的Hermite正交基神经网络预测模型相比, 所提预测模型具有更高的预测精度、更快的收敛速度和更简单的模型结构, 验证了该模型的高效性, 便于推广和应用.     

Tapped granular packings described as complex networks

Abstract

We characterize the structure of simulated two-dimensional granular packings using concepts from complex networks theory. The packings are generated by a simulated tapping protocol, which allows us to obtain states in mechanical equilibrium in a wide range of densities. We show that our characterization method is able to discriminate non-equivalent states that have the same density. We do this by examining differences in the topological structure of the contact network of the packings. In particular, we find that the polygons of the network are specially sensitive probes for the contact structure. Additionally, we compare the network properties obtained in two different scenarios: the tapped and a compressed system.