An effective method to improve the robustness of small-world networks under attack

In this study, the robustness of small-world networks to three types of attack is investigated. Global efficiency is introduced as the network coefficient to measure the robustness of a small-world network. The simulation results prove that an increase in rewiring probability or average degree can enhance the robustness of the small-world network under all three types of attack. The effectiveness of simultaneously increasing both rewiring probability and average degree is also studied, and the combined increase is found to significantly improve the robustness of the small-world network.Furthermore, the combined effect of rewiring probability and average degree on network robustness is shown to be several times greater than that of rewiring probability or average degree individually. This means that small-world networks with a relatively high rewiring probability and average degree have advantages both in network communications and in good robustness to attacks. Therefore, simultaneously increasing rewiring probability and average degree is an effective method of constructing realistic networks. Consequently, the proposed method is useful to construct efficient and robust networks in a realistic scenario.     

Dynamical robustness of networks based on betweenness against multi-node attack

We explore the robustness of a network against failures of vertices or edges where a fraction f of vertices is removed and an overload model based on betweenness is constructed. It is assumed that the load and capacity of vertex i are correlated with its betweenness centrality B_i as B_i~θ and(1 + α)Bθi(θ is the strength parameter, α is the tolerance parameter).We model the cascading failures following a local load preferential sharing rule. It is found that there exists a minimal αc when θ is between 0 and 1, and its theoretical analysis is given. The minimal αc characterizes the strongest robustness of a network against cascading failures triggered by removing a random fraction f of vertices. It is realized that the minimalαc increases with the increase of the removal fraction f or the decrease of average degree. In addition, we compare the robustness of networks whose overload models are characterized by degree and betweenness, and find that the networks based on betweenness have stronger robustness against the random removal of a fraction f of vertices.     

Optimization of robustness of network controllability against malicious attacks

As the controllability of complex networks has attracted much attention recently, how to design and optimize the robustness of network controllability has become a common and urgent problem in the engineering field. In this work, we propose a method that modifies any given network with strict structural perturbation to effectively enhance its robustness against malicious attacks, called dynamic optimization of controllability. Unlike other structural perturbations, the strict perturbation only swaps the links and keeps the in- and out-degree unchanged. A series of extensive experiments show that the robustness of controllability and connectivity can be improved dramatically. Furthermore, the effectiveness of our method is explained from the views of underlying structure. The analysis results indicate that the optimization algorithm makes networks more homogenous and assortative.     

Enhancement of scale-free network attack tolerance

Despite the large size of most communication and transportation systems,there are short paths between nodes in these networks which guarantee the efficient information,data and passenger delivery;furthermore these networks have a surprising tolerance under random errors thanks to their inherent scale-free topology.However,their scale-free topology also makes them fragile under intentional attacks,leaving us a challenge on how to improve the network robustness against intentional attacks without losing their strong tolerance under random errors and high message and passenger delivering capacity.Here we propose two methods (SL method and SH method) to enhance scale-free network’s tolerance under attack in different conditions.     

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.     

面向级联失效的相依网络鲁棒性研究

针对相依网络耦合强度、子网络边以及耦合边对网络鲁棒性影响的问题,基于三种典型网络模型,建立对称相依网络和不对称相依网络模型.针对六种不同的相依网络模型,计算其网络临界成本,比较耦合边权值和子网络边权值对相依网络成本的贡献程度,发现耦合边对网络的贡献更大.采用仿真和理论证明的方法,获得使网络具有最小网络成本时的子网络负载参数α值和耦合强度参数β值,并证明了网络成本变化趋势与该参数对有关.以网络成本作为鲁棒性测度的变量,通过对六种相依网络模型进行级联失效仿真,给出了网络具有最强鲁棒性时参数对的取值,以及网络鲁棒性与耦合强度之间的关系,发现网络鲁棒性并不是随着耦合强度单调地增加或减少.     

基于度的正/负相关相依网络模型及其鲁棒性研究

利用典型的Barabási-Albert无标度网络构建了基于度的正/负相关相依网络模型, 该模型考虑子网络间的相依方式及相依程度, 主要定义了两个参数F和K, F表示相依节点比例, K表示相依冗余度. 在随机攻击及基于度的蓄意攻击模式下, 针对网络的级联失效问题, 研究了不同的F值和K值对该相依网络模型鲁棒性的影响, 与随机相依网络模型进行了对比研究. 仿真结果表明:无论是随机相依或是基于度的正/负相关相依网络, 其鲁棒性都是随着F的增大而减弱, 随着K的增大而增强; 在随机攻击下, 全相依模式(F=1)时, 基于度正相关相依网络模型鲁棒性最优, 部分相依模式 (F =0.2, 0.5, 0.8)时, 基于度的负相关相依网络模型则表现出更好的鲁棒性. 而在基于度的蓄意攻击下, 无论F为何值, 基于度的正相关相依网络模型表现出弱鲁棒性.     

Effects of node buffer and capacity on network traffic

In this paper, we study the optimization of network traffic by considering the effects of node buffer ability and capacity. Two node buffer settings are considered. The node capacity is considered to be proportional to its buffer ability. The node effects on network traffic systems are studied with the shortest path protocol and an extension of the optimal routing [Phys. Rev. E 74 046106 (2006)]. In the diagrams of flux-density relationships, it is shown that a nodes buffer ability and capacity have profound effects on the network traffic.     

网络计算环境下大容量数据安全存储策略研究

近年来,随着计算机技术的发展,网络环境下的数据运算能力愈来愈强。加之,大数据时代的来临将人们日常生活、工作、学习的物质化信息转化为数据化关联性链条,通过网络进行大数据资源共享,简化了工作学习的繁杂,提升了工作学习效率。但是,传统的网络储存策略常常出现数据泄露、储存服务器数据溢出等一系列储存安全问题。针对问题产生原因,提出网络计算环境下大容量数据安全存储策略研究方法。通过采用数据修正单元、逻辑补偿单元与节点加密单元,对传统网络储存策略进行动态化针对性解决。通过仿真实验证明,提出的网络计算环境下大容量数据安全存储策略研究方法,具有数据储存响应速度快、反渗透逻辑性强、数据安全级别高、易用性强的优点。     

数字水印的鲁棒性评测模型

数字水印的鲁棒性是水印技术实用化的一个重要指标.与通过StirMark测试和各种仿真测试不同,定义互信息作为代价函数,建立水印系统鲁棒性描述和度量的一般模型.以扩频水印和量化水印为范例,推导出评测鲁棒性的互信息度量计算模型,并仿真分析了高斯噪声和JPEG压缩条件下互信息函数对鲁棒性的评估结果.实验以统计误比特率的方法计算图像DCT域中低频系数为载体的扩频水印误码率和一段音频数据三级小波细节系数为载体的量化水印误码率.互信息函数和误码率之间的匹配关系验证了互信息度量模型的有效性,互信息函数可以作为代价函数预测误码率的变化趋势. 关键词： 数字水印 鲁棒性 互信息 误码率     

The effects of degree correlations on network topologies and robustness

Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial to an understanding of the function, performance and evolution of complex systems. In the last few years, many network metrics and models have been proposed to investigate the network topology, dynamics and evolution. Since these network metrics and models are derived from a wide range of studies, a systematic study is required to investigate the correlations among them. The present paper explores the effect of degree correlation on the other network metrics through studying an ensemble of graphs where the degree sequence (set of degrees) is fixed. We show that to some extent, the characteristic path length, clustering coefficient, modular extent and robustness of networks are directly influenced by the degree correlation.     

Dynamical robustness analysis of weighted complex networks

Robustness of weighted complex networks is analyzed from nonlinear dynamical point of view and with focus on different roles of high-degree and low-degree nodes. We find that the phenomenon for the low-degree nodes being the key nodes in the heterogeneous networks only appears in weakly weighted networks and for weak coupling. For all other parameters, the heterogeneous networks are always highly vulnerable to the failure of high-degree nodes; this point is the same as in the structural robustness analysis. We also find that with random inactivation, heterogeneous networks are always more robust than the corresponding homogeneous networks with the same average degree except for one special parameter. Thus our findings give an integrated picture for the dynamical robustness analysis on complex networks.     

远红外窄带滤光片厚度的鲁棒性分析

鉴于在制备过程中存在介质层厚度的随机扰动,计算了远红外窄带滤光片厚度的鲁棒性。结果表明:当随机度小于0.05时,窄带滤光片全向带隙和带隙率变化不大,但缺陷层的透射率只有原来的1/3左右;当随机度大于0.1时,随着厚度的随机扰动逐渐增大,窄带滤光片的全向带隙和带隙率都逐渐减小;当随机度达到0.2时,窄带滤光片的第一个全向带隙消失,第二个全向带隙向短波方向偏移明显,缺陷层的透射率也只有原来的1/3左右;当随机度达到0.5时,窄带滤光片的两个全向带隙全部消失。制备了一种远红外窄带滤光片,其结果较好地验证了厚度的随机扰动对滤光片的影响。     

Analysis of robustness of urban bus network

In this paper,the invulnerability and cascade failures are discussed for the urban bus network.Firstly,three static models(bus stop network,bus transfer network,and bus line network) are used to analyse the structure and invulnerability of urban bus network in order to understand the features of bus network comprehensively.Secondly,a new way is proposed to study the invulnerability of urban bus network by modelling two layered networks,i.e.,the bus stop-line network and the bus line-transfer network and then the interactions between different models are analysed.Finally,by modelling a new layered network which can reflect the dynamic passenger flows,the cascade failures are discussed.Then a new load redistribution method is proposed to study the robustness of dynamic traffic.In this paper,the bus network of Shenyang City which is one of the biggest cities in China,is taken as a simulation example.In addition,some suggestions are given to improve the urban bus network and provide emergency strategies when traffic congestion occurs according to the numerical simulation results.     

A model of the effects of authority on consensus formation in adaptive networks: Impact on network topology and robustness

Opinions of individuals in real social networks are arguably strongly influenced by external determinants, such as the opinions of those perceived to have the highest levels of authority. In order to model this, we have extended an existing model of consensus formation in an adaptive network by the introduction of a parameter representing each agent’s level of ‘authority’, based on their opinion relative to the overall opinion distribution. We found that introducing this model, along with a randomly varying opinion convergence factor, significantly impacts the final state of converged opinions and the number of interactions required to reach that state. We also determined the relationship between initial and final network topologies for this model, and whether the final topology is robust to node removals. Our results indicate firstly that the process of consensus formation with a model of authority consistently transforms the network from an arbitrary initial topology to one with distinct measurements in mean shortest path, clustering coefficient, and degree distribution. Secondly, we found that subsequent to the consensus formation process, the mean shortest path and clustering coefficient are less affected by both random and targeted node disconnection. Speculation on the relevance of these results to real world applications is provided.     

Assessment of robustness and transferability of classification models built for cancer diagnostics using Raman spectroscopy

Over recent years, Raman spectroscopy has been demonstrated as a prospective tool for application in cancer diagnostics. The use of Raman spectroscopy for this purpose relies on pattern recognition methods that have been developed to perform well on data achieved under laboratory conditions. However, the application of Raman spectroscopy as a routine clinical tool is likely to result in imperfect data due to instrument‐to‐instrument variation. Such corruption to the pure tissue spectral data is expected to negatively impact the classification performance of the diagnostic model. In this paper, we present a thorough assessment of the robustness of the Raman approach. This was achieved by perturbing a set of spectra in different ways, including various linear shifts, nonlinear shifts and random noise and using previously optimised classification models to predict the class membership of each spectrum in a testing set. The loss of predictive power with increased corruption was used to calculate a score, which allows an easy comparison of the model robustness. For this approach, three different types of classification models, including linear discriminant analysis (LDA), partial least square discriminant analysis (PLS‐DA) and support vector machine (SVM), built for lymph node diagnostics were the subject of the robustness testing. The results showed that a linear perturbation had the highest impact on the performance of all classification models. Among all linear corruption methods, a gradient y‐shift resulted in the highest performance loss. Thus, the factor most likely to affect the predictive outcome of models when using different systems is a gradient y‐shift. Copyright © 2010 John Wiley & Sons, Ltd.     

Non-monotonic increase of robustness with capacity tolerance in power grids

The robustness of different scale power grids is analyzed based on complex network theory in terms of electrical betweenness and weighted efficiency. The robustness of a power grid does not always increase monotonically with the capacity. This property is different from the results obtained in previous studies, which have indicated that the robustness increases monotonically with capacity. To understand the non-monotonic phenomenon, the cascading failure is divided into several sub-stages, and we analyze the number of overloaded nodes and the average remaining load in each sub-stage. The results indicate that the increasing capacity is barely able to reduce the number of overloaded nodes at the beginning of malfunction, which may lead to more nodes being removed subsequently, including certain nodes with many connections or large load. More loads remain in the power grid such that certain nodes cannot take the load. This eventually causes overloading of more nodes and a decline in the robustness of the power grid. The conclusion may be useful for power grid planners seeking to design grids with cost-effective capacity.     

Evaluation of network robustness using a node tearing algorithm

Until recently the study of failure and vulnerability in complex networks focused on the role of high degree nodes, and the relationship between their removal and network connectivity. Recent evidence suggested that in some network configurations, the removal of lower degree nodes can also cause network fragmentation. We present a disassembling algorithm that identifies nodes that are core to network connectivity. The algorithm is based on network tearing in which communities are defined and used to construct a hierarchical structure. Cut-nodes, which are located at the boundaries of the communities, are the key interest. Their importance in the overall network connectivity is characterized by their participation with neighbouring communities in each level of the hierarchy. We examine the impact of these cut-nodes by studying the change in size of the giant component, local and global efficiencies, and how the algorithm can be combined with other community detection methods to reveal the finer internal structure within a community.     

Evaluating the robustness of rogue waves under perturbations

Rogue waves, and their periodic counterparts, have been shown to exist in a number of integrable models. However, relatively little is known about the existence of these objects in models where an exact formula is unattainable. In this work, we develop a novel numerical perspective towards identifying such states as localized solutions in space-time. Importantly, we illustrate this methodology for different perturbations of nonlinear Schrödinger models. In particular, in addition to benchmarking known solutions (and confirming their numerical propagation under controllable error) this enables the continuation of such solutions over parametric variations to non-integrable models. As a result, we can answer in the positive the question about the parametric robustness of Peregrine-like waveforms and even of generalizations thereof on a cnoidal wave background.