一种全局同质化相依网络耦合模式

相依网络的相依模式(耦合模式)是影响其鲁棒性的重要因素之一.本文针对具有无标度特性的两个子网络提出一种全局同质化相依网络耦合模式.该模式以子网络的总度分布均匀化为原则建立相依网络的相依边,一方面压缩度分布宽度,提高其对随机失效的抗毁性,另一方面避开对度大节点(关键节点)的相依,提高其对蓄意攻击的抗毁性.论文将其与常见的节点一对一的同配、异配及随机相依模式以及一对多随机相依模式作了对比分析,仿真研究其在随机失效和蓄意攻击下的鲁棒性能.研究结果表明,本文所提全局同质化相依网络耦合模式能大大提高无标度子网络所构成的相依网络抗级联失效能力.本文研究成果能够为相依网络的安全设计等提供指导意义.     

相依网络的条件依赖群逾渗

相依网络鲁棒性研究多集中于满足无反馈条件的一对一依赖,但现实网络节点往往依赖于多节点构成的依赖群,即使群内部分节点失效也不会导致依赖节点失效.针对此现象提出了一种相依网络的条件依赖群逾渗模型,该模型允许依赖群内节点失效比例不超过容忍度γ时,依赖节点仍可正常工作.通过理论分析给出了基于生成函数方法的模型巨分量方程,仿真结果表明方程理论解与相依网络模拟逾渗值相吻合,增大γ值和依赖群规模可提高相依网络鲁棒性.本文模型有助于更好地理解现实网络逾渗现象,对如何增强相依网络鲁棒性有一定指导作用.     

负荷作用下相依网络中的级联故障

研究负荷作用下相依网络中的级联故障具有重要的现实意义, 可为提高相依网络的鲁棒性提供参考. 构建了双层相依网络级联故障模型, 主要研究了外部度和内部度对负荷贡献比、耦合因素、层内度-度相关性对相依网络级联故障的影响. 研究表明, 当外部度和内部度对负荷贡献比达到一定值时, 相依网络抵抗级联故障的鲁棒性最强. 而耦合因素的影响是多方面的, 为了达到较高鲁棒性, 建议采用异配耦合方式和尽可能大的平均外部度, 并尽量使外部度保持均匀分布. 另外, 与不考虑负荷作用时相反, 当表征层内度-度相关性的相关系数越大时, 其抵抗级联故障的能力越强.     

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.     

异质弱相依网络鲁棒性研究

传统研究认为网络间相依边的引入使网络鲁棒性大幅降低,但现实相依网络的鲁棒性往往优于理论结果.通过观察现实相依网络的级联失效过程,发现节点不会因相依节点失效而损失所有连接边,且由于网络节点的异质性,每个节点的连接边失效概率也不尽相同.针对此现象,提出一种异质弱相依网络模型,与传统网络逾渗模型不同,本文认为两个弱相依节点的其中一个失效后,另一个节点的连接边以概率g失效而不是全部失效,并且不同节点连接边失效概率g会因节点的异质性而不同.通过理论分析给出模型基于生成函数的逾渗方程,求解出任意随机分布异质对称弱相依网络的连续相变点.仿真结果表明方程的理论解与随机网络逾渗模拟值相符合,网络鲁棒性随着弱相依关系异质程度的增大而提高.     

相依网络上基于相连边的择优恢复算法

如何有效地应对和控制故障在相依网络上的级联扩散避免系统发生结构性破碎,对于相依网络抗毁性研究具有十分重要的理论价值和现实意义.最新的研究提出一种基于相依网络的恢复模型,该模型的基本思想是通过定义共同边界节点,在每轮恢复阶段找出符合条件的共同边界节点并以一定比例实施恢复.当前的做法是按照随机概率进行选择.这种方法虽然简单直观,却没有考虑现实世界中资源成本的有限性和择优恢复的必然性.为此,针对相依网络的恢复模型,本文利用共同边界节点在极大连通网络内外的连接边数计算边界节点的重要性,提出一种基于相连边的择优恢复算法(preferential recovery based on connectivity link,PRCL)算法.利用渗流理论的随机故障模型,通过ER随机网络和无标度网络构建的不同结构相依网络上的级联仿真结果表明,相比随机方法和度数优先以及局域影响力优先的恢复算法,PRCL算法具备恢复能力强、起效时间早且迭代步数少的优势,能够更有效、更及时地遏制故障在网络间的级联扩散,极大地提高了相依网络遭受随机故障时的恢复能力.     

糖的原子电距矢量表达及其核磁共振碳谱模拟

提出以原子电性距离矢量(VAED),描述上百种糖分子中数百个不同等价碳原子的化学环境;并结合γ效应校正,建立核磁共振碳谱(¹³C NMR)化学位移(CS)的五参数线性模型.用于糖分子中四类不同的等价碳原子化学位移的估计,复相关系数R和均方根误差RMS及标准偏差SD和F-统计量F分别为:伯碳n=62,R=0.991 0,RMS=1.960 2(SD=1.9762,F=5 0 2.32 94,EV=0.980 5);仲碳n=79,R=0.9886,RMS=2.5 40 5(SD=2.5 5 67,F=5 1 5.60 4 6,EV=0.975 7);叔碳n=30 2,R=0.95 1 4,RMS=3.6884(SD=3.694 5,F=4 68.82 76,EV=0.90 35)及季碳n=1 4,R=0.5 772,RMS=8.862 6(SD=9.1 972,F=0.5 82 8,EV=-0.0 837).经交互校验,伯仲叔碳的化学位移模型稳定性较好.并综合几种处理方法,找到一种较好的建模方法,将它用于几个外部样本的定量预测,结果良好.     

强度应力干涉下多态多系统的可靠性研究

基于多元随机分析以及统计物理,建立了在系统强度与应力干涉下具有初始失效的多个状态以及多个相依子系统的可靠性模型. 在条件序列统计量的定义下推导了系统随机强度向量的概率密度函数;考虑各个子系统内零部件间的相干性,给出了不同结构的系统可靠性评估,将任意干涉系统可靠性表示为所有(n－i+1)/n(1≤i≤n)型冗余系统可靠性的线性组合. 为验证模型的有效性,基于二维Pareto分布给出了一个工程上的实例分析. 关键词： 干涉系统 可靠性 应力强度 条件序列统计     

电网在三种边攻击方式下的级联失效

研究美国西部电网在三种边攻击方式下级联失效差异性.定义边ij的初始负载为(k_ik_j)^θ,k_i,k_j分别表示节点i和j的度,θ为一可调参数.三种边攻击方式分别为:最小负载边攻击方式(LL)、最大负载边攻击方式(HL)和容量比最小边攻击方式(SPC).通过分析电网的拓扑结构,研究三种攻击方式级联失效差异性.研究表明:HL和LL攻击方式下,受攻击边的范围不随θ而改变,HL的攻击效果随θ的增大而增强,LL的攻击效果随θ的增大而减弱.而SPC法选中的被攻击边随θ变化,当θ取值较小时,SPC攻击边是拓扑结构较特殊的一种最小负载边,随着θ的增大,SPC攻击边趋向于高负载边,因此θ较小时,SPC的攻击效果和LL接近,当θ较大时,SPC的攻击效果和HL接近.     

非均匀磁场和杂质磁场对自旋1系统量子关联的影响

通过负值度和测量诱导的扰动, 研究了非均匀磁场和杂质磁场对自旋为1的Heisenberg系统量子关联的影响. 研究发现非均匀磁场的增加会降低纠缠, 但也可用来产生纠缠, 并且会提高临界非线性作用K_c的值, 测量诱导的扰动的临界磁场要高于负值度的临界磁场, 而且测量诱导的扰动不会随着非线性作用|K| 的减小而消失, 它能全面反映量子关联的存在. 研究还发现, 不同杂质磁场对测量诱导的扰动的影响彼此间无交叉. 杂质磁场下, 相互作用|J| 必须小于非线性作用|K| 才会有纠缠存在, 但是测量诱导的扰动却可以在相互作用|J| 大于非线性作用|K| 时依然存在, |J| 与|K| 相同时只是测量诱导的扰动的最小取值点. 此外, 系统粒子数目对量子关联也具有重要影响.     

复杂网络的顶点着色及其在疾病免疫中的应用

在复杂网络研究中, 对于网络结构特征的分析已经引起了人们的极大关注, 而其中的网络着色问题却没有得到足够的重视. 为了理解网络结构与着色之间的关系, 本文研究了WS, BA网络以及不同宏观结构参量对于正常K色数的影响, 发现最大团数可以大致反映正常K色数的变化趋势, 而网络的平均度和匹配系数比异质性和聚类系数对于色数的影响更大. 对于一些实际网络的正常着色验证了本文的分析结果. 对复杂网络的顶点进行着色后, 根据独立集内任意两个顶点均不相邻的特点, 我们提出了基于独立集的免疫策略. 与全网随机免疫相比, 基于独立集的免疫策略可令网络更为脆弱, 从而有效抑制疾病的传播. 基于网络着色的独立集提供了一种崭新的免疫思路, 作为一个简单而适用的平台,有助于设计更为有效的免疫策略. 关键词： 复杂网络 正常着色 独立集 免疫策略     

False Positive and False Negative Effects on Network Attacks

Robustness against attacks serves as evidence for complex network structures and failure mechanisms that lie behind them. Most often, due to detection capability limitation or good disguises, attacks on networks are subject to false positives and false negatives, meaning that functional nodes may be falsely regarded as compromised by the attacker and vice versa. In this work, we initiate a study of false positive/negative effects on network robustness against three fundamental types of attack strategies, namely, random attacks (RA), localized attacks (LA), and targeted attack (TA). By developing a general mathematical framework based upon the percolation model, we investigate analytically and by numerical simulations of attack robustness with false positive/negative rate (FPR/FNR) on three benchmark models including Erd?s-Rényi (ER) networks, random regular (RR) networks, and scale-free (SF) networks. We show that ER networks are equivalently robust against RA and LA only when FPR equals zero or the initial network is intact. We find several interesting crossovers in RR and SF networks when FPR is taken into consideration. By defining the cost of attack, we observe diminishing marginal attack efficiency for RA, LA, and TA. Our finding highlights the potential risk of underestimating or ignoring FPR in understanding attack robustness. The results may provide insights into ways of enhancing robustness of network architecture and improve the level of protection of critical infrastructures.     

Optimal weighting scheme and the role of coupling strength against load failures in degree-based weighted interdependent networks

The optimal weighting scheme and the role of coupling strength against load failures on symmetrically and asymmetrically coupled interdependent networks were investigated. The degree-based weighting scheme was extended to interdependent networks, with the flow dynamics dominated by global redistribution based on weighted betweenness centrality. Through contingency analysis of one-node removal, we demonstrated that there still exists an optimal weighting parameter on interdependent networks, but it might shift as compared to the case in isolated networks because of the break of symmetry. And it will be easier for the symmetrically and asymmetrically coupled interdependent networks to achieve robustness and better cost configuration against the one-node-removal-induced cascade of load failures when coupling strength was weaker. Our findings might have great generality for characterizing load-failure-induced cascading dynamics in real-world degree-based weighted interdependent networks.     

Stabilization of stochastic cycles and control of noise-induced chaos

We study the robustness of symmetrically coupled and clustering-based weighted heterogeneous inter-connected networks with respect to load-failure-induced cascades. This is done under the assumption that the flow dynamics are governed by global redistribution of loads based on weighted betweenness centrality. Our results indicate that no weighting bias should be assigned to inter-links when calculating shortest path between node pairs under the clustering-based weighting scheme; i.e., inter-links shall be treated no differently than intra-links. In contrast with local load redistribution cases, we show that increasing connectivity is preferred for the robustness against global load redistribution-based cascading failures in clustering-based weighted inter-connected networks. Furthermore, comparisons among weighting schemes reveal that, both the clustering-based and degree-based schemes outperform the random one in the sense of requiring lower initial and total investments required to ensure robustness. We also find that clustering-based scheme outperforms degree-based one in terms of requiring lower initial investments. Except in a limited range where weighting is heavily suppressed, clustering-based scheme is shown to outperform degree-based one in terms of total investments. Finally, when there exists a hard investment budget constraint, clustering-based weighting scheme would be a better choice against a two-nodes-induced failure than the degree-based weighting, and the clustering-based scheme is more stable than degree-based scheme against one-or-two-nodes-induced failure. We expect our findings to be significantly useful in designing real-world weighted inter-connected networks that are robust against load-failure-induced cascades.     

Random anisotropy studies in amorphous FeTmB

We have studied the magnetization of melt spun amorphous Fe_{80 −x}Tm_xB₂₀ alloys with 0 x 15 under magnetic fields up to 18 kOe, and have analyzed the results at different temperatures based on the random magnetic anisotropy model. Exchange interactions J_FeFe and J_FeTm evaluated by the fitting of M-T curves are discussed. The local random anisotropy K_L and the exchange constant A are found to decrease with increasing temperature. Experimental data show that the ferromagnetic correlation length R_f decreases with increasing Tm content.     

Robustness analysis of network controllability

Structural controllability, which is an interesting property of complex networks, attracts many researchers from various fields. The maximum matching algorithm was recently applied to explore the minimum number of driver nodes, where control signals are injected, for controlling the whole network. Here we study the controllability of directed Erdös–Rényi and scale-free networks under attacks and cascading failures. Results show that degree-based attacks are more efficient than random attacks on network structural controllability. Cascade failures also do great harm to network controllability even if they are triggered by a local node failure.     

Robustness measurement of scale-free networks based on motif entropy

As a classical complex network model, scale-free network is widely used and studied. And motifs, as a high-order subgraph structure, frequently appear in scale-free networks, and have a great influence on the structural integrity, functional integrity and dynamics of the networks. In order to overcome the shortcomings in the existing work on the robustness of complex networks, only nodes or edges are considered, while the defects of high-order structure in the network are ignored. From the perspective of network motif, we propose an entropy of node degree distribution based on motif to measure the robustness of scale-free networks under random attacks. The effectiveness and superiority of our method are verified and analyzed in the BA scale-free networks.     

Error and attack tolerance of evolving networks with local preferential attachment

Networks generated by local-world evolving network model display a transition from exponential network to power-law network with respect to connectivity distribution. We investigate statistical properties of the evolving networks and the responses of these networks under random errors and intentional attacks. It has been found that local world size M has great effect on the network's heterogeneity, thus leading to transitional behaviors in network's robustness against errors and attacks. Numerical results show that networks constructed with local preferential attachment mechanism can maintain the robustness of scale-free networks under random errors and concurrently improve reliance against targeted attacks on highly connected nodes.