Percolation transitions in edge-coupled interdependent networks with directed dependency links

We propose a model of edge-coupled interdependent networks with directed dependency links(EINDDLs)and develop the theoretical analysis framework of this model based on the self-consistent probabilities method.The phase transition behaviors and parameter thresholds of this model under random attacks are analyzed theoretically on both random regular(RR)networks and Erd¨os-Renyi(ER)networks,and computer simulations are performed to verify the results.In this EINDDL model,a fractionβof connectivity links within network B depends on network A and a fraction(1-β)of connectivity links within network A depends on network B.It is found that randomly removing a fraction(1-p)of connectivity links in network A at the initial state,network A exhibits different types of phase transitions(first order,second order and hybrid).Network B is rarely affected by cascading failure whenβis small,and network B will gradually converge from the first-order to the second-order phase transition asβincreases.We present the critical values ofβfor the phase change process of networks A and B,and give the critical values of p andβfor network B at the critical point of collapse.Furthermore,a cascading prevention strategy is proposed.The findings are of great significance for understanding the robustness of EINDDLs.

Assessing edge-coupled interdependent network disintegration via rank aggregation and elite enumeration

The disintegration of networks is a widely researched topic with significant applications in fields such as counterterrorism and infectious disease control. While the traditional approaches for achieving network disintegration involve identifying critical sets of nodes or edges, limited research has been carried out on edge-based disintegration strategies. We propose a novel algorithm, i.e., a rank aggregation elite enumeration algorithm based on edge-coupled networks(RAEEC),which aims to implement tiling for edge-coupled networks by finding important sets of edges in the network while balancing effectiveness and efficiency. Our algorithm is based on a two-layer edge-coupled network model with one-to-one links, and utilizes three advanced edge importance metrics to rank the edges separately. A comprehensive ranking of edges is obtained using a rank aggregation approach proposed in this study. The top few edges from the ranking set obtained by RAEEC are then used to generate an enumeration set, which is continuously iteratively updated to identify the set of elite attack edges.We conduct extensive experiments on synthetic networks to evaluate the performance of our proposed method, and the results indicate that RAEEC achieves a satisfactory balance between efficiency and effectiveness. Our approach represents a significant contribution to the field of network disintegration, particularly for edge-based strategies.

Impact of asymptomatic infected individuals on epidemic transmission dynamics in multiplex networks with partial coupling

The theory of network science has attracted great interest of many researchers in the realm of biomathematics and public health,and numerous valuable epidemic models have been developed.In previous studies,it is common to set up a one-to-one correspondence between the nodes of a multi-layer network,ignoring the more complex situations in reality.In the present work,we explore this situation by setting up a partially coupled model of a two-layer network and investigating the impact of asymptomatic infected individuals on epidemics.We propose a self-discovery mechanism for asymptomatic infected individuals,taking into account situations such as nucleic acid testing in the community and individuals performing self-antigen testing during the epidemic.Considering these factors together,through the microscopic Markov chain approach(MMCA)and extensive Monte Carlo(MC)numerical simulations,we find that the greater the coupling between the networks,the more information dissemination is facilitated.In order to control the epidemics,more asymptomatic infected individuals should be made aware of their infection.Massive adoption of nucleic acid testing and individual adoption of antigenic self-testing can help to contain epidemic outbreaks.Meanwhile,the epidemic threshold of the proposed model is derived,and then miscellaneous factors affecting the epidemic threshold are also discussed.Current results are conducive to devising the prevention and control policies of pandemics.

The Invulnerability of Directed Interdependent Networks with Multiple Dependency Relations

The paper aims to study the invulnerability of directed interdependent networks with multiple dependency relations: dependent and supportive. We establish three models and simulate in three network systems to deal with this question. To improve network invulnerability, we’d better avoid dependent relations transmission and add supportive relations symmetrically.

Assessing Air Traffic Management Performance Interdependencies through Bayesian Networks： Preliminary Applications and Results

The performance model proposed by this study represents an innovative approach to deal with performance assessment in ATM （air traffic management）. It is based on Bayesian networks methodology, which presents several advantages but also some drawbacks as highlighted along the paper. We illustrate the main steps required for building the model and present a number of interesting results. The contribution of the paper is two-fold： （1） It presents a new methodological approach to deal with a problem which is of strategic importance for ANSPs （air navigation service providers）; （2） It provides insights on the interdependencies between factors influencing performance. Both results are considered particularly important nowadays, due to the SES （Single European Sky） performance scheme and its related target setting process.

Identification of Important FPGA Modules Based on Complex Network

The globalization of hardware designs and supply chains,as well as the integration of third-party intellectual property(IP)cores,has led to an increased focus from malicious attackers on computing hardware.However,existing defense or detection approaches often require additional circuitry to perform security verification,and are thus constrained by time and resource limitations.Considering the scale of actual engineering tasks and tight project schedules,it is usually difficult to implement designs for all modules in field programmable gate array(FPGA)circuits.Some studies have pointed out that the failure of key modules tends to cause greater damage to the network.Therefore,under limited conditions,priority protection designs need to be made on key modules to improve protection efficiency.We have conducted research on FPGA designs including single FPGA systems and multi-FPGA systems,to identify key modules in FPGA systems.For the single FPGA designs,considering the topological structure,network characteristics,and directionality of FPGA designs,we propose a node importance evaluationmethod based on the technique for order preference by similarity to an ideal solution(TOPSIS)method.Then,for the multi-FPGA designs,considering the influence of nodes in intra-layer and inter-layers,they are constructed into the interdependent network,and we propose a method based on connection strength to identify the important modules.Finally,we conduct empirical research using actual FPGA designs as examples.The results indicate that compared to other traditional indexes,node importance indexes proposed for different designs can better characterize the importance of nodes.

Recovery of coupled networks after cascading failures

With society＇s increasing dependence on critical infrastructure such as power grids and communications systems, the robustness of these systems has attracted significant attention.Failure of some nodes can trigger a cascading failure, which completely fragments the network, necessitating recovery efforts to improve robustness of complex systems. Inspired by real-world scenarios, this paper proposes repair models after two kinds of network failures, namely complete and incomplete collapse. In both models, three kinds of repair strategies are possible, including random selection（RS）, node selection based on single network node degree（SD）, and node selection based on double network node degree（DD）. We find that the node correlation in each of the two coupled networks affects repair efficiency. Numerical simulation and analysis results suggest that the repair node ratio and repair strategies may have a significant impact on the economics of the repair process. The results of this study thus provide insight into ways to improve the robustness of coupled networks after cascading failures.

基于相依网络的无人机集群通信系统鲁棒性分析

作为地震灾害救援和侦察战场等的主力设备,无人机集群通信系统的鲁棒性是抗毁性的重要指标,本文借助复杂相依网络理论建模无人机集群通信系统,引入相对网络效能比作为通信系统网络整体鲁棒性的指标,准确地反映节点之间的相互依赖关系,为评估通信系统在目标攻击下的鲁棒性提供了一种全新的视角。基于经典M-L模型和动态信息的负载重分配策略,建立相依同构ER-ER和异构ER-BA网络模型,考虑两层网络中相依节点度数的特性进行目标攻击,分析其在攻击下的级联失效动态过程,以及任意两节点的连边概率、平均度数和容量系数等特征参数,对通信网络整体鲁棒性的影响。研究表明,网络鲁棒性和网络相依强度负相关,在级联失效过程中可考虑降低52.09%~72.9%相依强度,以抵抗更严重的通信网络崩塌;对同构网络来说,相依模式的不同,RL、AL较DL整体鲁棒性分别降低了9.25%和15.95%。

城市关联基础设施多层网络韧性评估模型

为了探究城市基础设施系统关联关系对城市韧性的影响,采用理论分析和python模拟相结合的方法研究城市关联基础设施系统在扰动下的韧性变化过程。首先,基于韧性机制和多层网络理论,构建城市关联基础设施网络;然后,探究在功能关联下,城市关联基础设施网络受到3种外界扰动后的级联失效过程,并基于基础设施系统机能曲线法,构建城市关联基础设施网络韧性评估模型;最后,以湖南省中部偏北某县作为研究对象进行实例研究。结果表明:关联网络中电力节点的聚类系数明显高于整体平均水平;通信网络的抵御能力和恢复能力是5类基础设施网络中最强的,韧性水平也最高;随着网络中节点失效概率增大和网络层数的增加,整体关联基础设施网络及其子网络的可靠性逐渐降低;网络效率在介数恢复策略下恢复至较高水平时间较短,说明对此基础设施网络使用介数恢复策略更为合适。

相互依赖网络上级联故障鲁棒性悖论研究

相互依赖网络中的级联故障过程一直是网络级联分析的一个重要领域.与以往研究不同的是,本文考虑了人们在出行时最小化成本的需求,提出了基于成本约束的网络动力学模型.同时,研究了相互依赖网络中不同层次的特性,定义了不同的负载传播模式.在此基础上,本文通过改变网络结构和模型中的参数,仿真现实中的网络防护策略并验证这些措施的防护效果,并发现了一些有趣的结论.一般认为,增加网络中连边的数量或提高连边的质量可以有效地增强网络的鲁棒性.然而,本文的实验结果表明,这些方法在某些情况下实际上可能会降低网络的鲁棒性.一方面,网络中一些特殊边的复活是导致边能力提升网络鲁棒性却下降的主要原因,因为这些边会破坏原有网络的稳定结构;另一方面,无论是提高单层网络的内部连通性来增加网络连边数量,还是提高相互依赖的网络之间的耦合强度来增加连边数量,都不能完全有效地提高网络的鲁棒性.这是因为随着边数量的增加,网络中可能会出现一些关键边,这些边会吸引大量的网络负载,导致网络的鲁棒性下降.

高低阶耦合网络的鲁棒性研究

为了深入理解现实网络系统中的相互依赖关系,解决复杂网络及其高阶网络面临的级联故障问题。提出了一种高低阶耦合网络模型,该模型用于描述复杂网络(低阶网络)及其高阶组织(高阶网络)之间的相互依赖。通过对高低阶耦合网络进行随机攻击来分析其脆弱性。研究表明,与单独的低阶网络相比,高低阶耦合网络在面对随机攻击时表现出更高的脆弱性。这一结果强调了在设计和管理复杂网络系统时考虑高低阶网络相互依赖关系的重要性,尤其是在防止级联故障时需要特别关注这些相互依赖结构的脆弱性。

基于相依失效的“空-基-地”编队可靠性分析

针对大规模多域无人设备之间难以进行可靠性分析的问题,根据实际“空-基-地”分布式协同编队特征,提出了一种基于多域无人平台运作规则与层网络间逻辑连接失效关系的空基地集群编队可靠性分析算法。用空中网络、通信网络、地面网络组成的3层轻量化方格拓扑结构代替现实中的集群,在综合考虑随机攻击、蓄意攻击以及区域失效关系、关联失效关系、级联失效关系等依赖关系的条件下设计算法,以网络中最大连通子图为可靠性测度,进行不同编队状态及编队形式下的网络可靠性分析。最后与标准仿真平台进行对比,试验结果验证了算法的可行性、快速性以及资源占用率小等优势。该研究为提升多域无人平台协同编队时的可靠性及相关的防控策略的研究提供了研究基础。

二元双层耦合网络渗流行为分析

本文建立了节点和连边耦合的二元相互依赖网络模型(binary interdependent networks with node and edge coupling,BINNEC).该模型中,网络A节点随机依赖网络B多条边从而形成边依赖群,当边依赖群的失效比例超过网络失效容忍度μ时,导致网络A的节点失效.基于自平衡概率法建立起理论分析框架,通过对3种经典网络结构下的BINNEC网络进行计算机仿真验证,并分析了该模型面对随机攻击下的相变行为和关键阈值.研究结果表明3种网络结构下的BINNEC网络和一元耦合网络一样脆弱,网络的相变行为都是一阶相变.当网络节点的边依赖群规模m越大,网络鲁棒性增强;在网络的边依赖群规模一定时,节点的失效容忍度μ越大网络鲁棒性越强.本文进一步研究在m和μ相同条件下,网络的度分布对BINNEC的影响.研究可以为此类二元耦合网络鲁棒性提供一定的理论依据,同时也为现实网络的安全设计提供指导意义.

负载目标下基于延迟分配的多层级相依网络级联失效模型

在负载具有目标节点的多层级相依网络中,为了避免大规模级联失效的发生、增加网络鲁棒性、提高负载完成效率,提出一种可调参数的级联失效模型。该模型设置了新的初始负载和节点容量,构建了负载延迟分配机制,在负载分配的异质性和均匀性基础上制定了负载重分配规则。解析分析模型的级联失效条件,并通过WS-BA相依网络进行了仿真实验,结果表明,在网络容量一定条件下,合理调节异质性参数和均匀性参数可以提高网络的鲁棒性和效率。

Resilience assessment framework toward interdependent bus-rail transit network:Structure,critical components,and coupling mechanism

Understanding the interdependent nature of multimodal public transit networks(PTNs)is vital for ensuring the resilience and robustness of transportation systems.However,previous studies have predominantly focused on assessing the vulnerability and characteristics of single-mode PTNs,neglecting the impacts of heterogeneous disturbances and shifts in travel behavior within multimodal PTNs.Therefore,this study introduces a novel resilience assessment framework that comprehensively analyzes the coupling mechanism,structural and functional characteristics of bus-rail transit networks(BRTNs).In this framework,a network performance metric is proposed by considering the passengers’travel behaviors under various disturbances.Additionally,stations and subnetworks are classified using the k-means algorithm and resilience metric by simulating various disturbances occurring at each station or subnetwork.The proposed framework is validated via a case study of a BRTN in Beijing,China.Results indicate that the rail transit network(RTN)plays a crucial role in maintaining network function and resisting external disturbances in the interdependent BRTN.Furthermore,the coupling interactions between the RTN and bus transit network(BTN)exhibit distinct characteristics under infrastructure component disruption and functional disruption.These findings provide valuable insights into emergency management for PTNs and understanding the coupling relationship between BTN and RTN.

基于博弈论的关联网络攻防博弈分析

根据现实中关联网络复杂的关联特性和网络中重要的评估指标,提出了5种不同的耦合方式,建立了9种关联网络模型;考虑到网络中信息的传输,再分配和级联故障,建立了基于介数虚拟流的级联失效模型;基于博弈论,从复杂网络的角度分析了关键基础设施的攻防问题,分析了多种关联网络的鲁棒性。发现了关联网络中博弈参与者的偏好,为基础设施网络的保护提供了决策支持。

边耦合相依网络动态修复策略研究

为应对边耦合相依网络中因少部分的连边失效引起的网络大面积的结构性破坏甚至崩溃,本文提出了一种基于共同边界连边的边耦合相依网络级联失效修复模型。将修复过程与网络级联失效过程动态结合,同时根据边耦合网络的特征提出了复合冗余度择优修复策略和一种改进的复合冗余度择优修复策略。分别在随机故障和蓄意攻击情况下对ER-ER(Erdős-Rényi随机网络)、SF-SF(scale-free无标度网络)边耦合相依网络进行仿真,与随机修复策略及介数择优修复策略对比,寻找最优修复策略。研究发现在不同结构的边耦合相依网络中的最优修复策略,随着网络连边初始存留比例及故障类型的不同而发生改变,并且能够在更大的连边初始攻击比例下修复网络至初始状态的修复策略,其所需要的迭代步数并不一定最少。

MODELING AND SIMULATION OF THE VULNERABILITY OF INTERDEPENDENT POWER-WATER INFRASTRUCTURE NETWORKS TO CASCADING FAILURES

Critical infrastructures are becoming increasingly interdependent and vulnerable to cascading failures. Existing studies have analyzed the vulnerability of interdependent networks to cascading failures from the static perspective of network topology structure. This paper develops a more realistic cascading failures model that considers the dynamic redistribution of load in power network to explore the vulnerability of interdependent power-water networks. In this model, the critical tolerance threshold is originally proposed to indicate the vulnerability of network to cascading failures. In addition, some key parameters that are important to network vulnerability are identified and quantified through numerical simulation. Results show that cascading failures can be prevented when the values of tolerance parameter are above a critical tolerance threshold. Otherwise interdependent networks collapse after attacking a critical fraction of power nodes. Interdependent networks become more vulnerable with the increase in interdependence strength, which implies the importance of protecting those interconnected nodes to reduce the consequences of cascading failures. Interdependent networks are most vulnerable under high-load attack, which shows the significance of protecting high-load nodes.

考虑灰色攻击的多制式区域轨道交通网络韧性评估

为有效刻画多制式区域轨道交通(MRRT)网络,提高其网络韧性评估的准确性,依据MRRT评估系统内不同子网络间的协同工作关系以及运输服务特征,基于复杂网络理论构建MRRT相依网络模型;兼顾网络拓扑结构和服务质量,从抵抗能力、吸收能力、缓冲能力和恢复能力4个维度构建网络韧性评估指标,改进了基于引力模型识别其关键站点的方法;因MRRT网络复杂度高,其遭受突发事件扰动的潜在攻击信息具有灰色特征,故使用Matlab模拟不同信息精确度α下的灰色攻击策略,探究α对MRRT相依网络韧性的影响。结果表明:MRRT相依网络具有无标度网络特征;基于引力模型识别关键站点,可提高网络节点关键性评价的准确性;降低灰色攻击的信息精确度α,可提高网络韧性,且α对网络韧性的影响存在阈值,当α∈(02,08)时,网络遭受攻击后的性能损失会随α的降低而减小,当α≥08∪α≤02时,降低α并不会对网络韧性有显著影响。

经济“双循环”背景下中国与国际产业相依结构研究

完备的产业体系能够保障国民经济的平稳运行和国家在对外发展中的主导地位,是当前我国打造双循环的坚实根基。文章从金融市场角度出发,选取MSCI中国与发达市场一级行业指数,以2016年8月31日至2022年8月10日为样本区间,通过R藤Copula模型和基于Copula Glasso方法改进的复杂网络模型研究中国与国际行业间的非线性相依结构与关联网络;通过扩展的分块R藤Copula方法研究国内外产业间相依关系。研究发现:国内外行业间均存在显著的正向联动关系;国内行业中,信息技术行业、工业行业、非日常消费行业和原材料行业占主导地位;传统产业和民生产业在国内外产业结构中均占据重要地位,且行业、产业间国内循环相对独立于国际循环。