Impact of core-periphery structure on cascading failures in interdependent scale-free networks

Core-periphery structure is a typical meso-scale structure in networks. Previous studies on core-periphery structure mainly focus on the improvement of detection methods, while the research on the impact of core-periphery structure on cascading failures in interdependent networks is still missing. Therefore, we investigate the cascading failures of interdependent scale-free networks with different core-periphery structures and coupling preferences in the paper. First, we introduce an evaluation index to calculate the goodness of core-periphery structure. Second, we propose a new scale-free network evolution model, which can generate tunable core-periphery structures, and its degree distribution is analyzed mathematically. Finally, based on a degree-load-based cascading failure model, we mainly investigate the impact of goodness of core-periphery structure on cascading failures in both symmetrical and asymmetrical interdependent networks. Through numerical simulations, we find that with the same average degree, the networks with weak core-periphery structure will be more robust, while the initial load on node will influence the improvement of robustness. In addition, we also find that the inter-similarity coupling performs better than random coupling. These findings may be helpful for building resilient interdependent networks.     

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.     

Modeling and simulations of the cascading failure of multiple interdependent R&D networks under risk propagation

In this paper, we study the robustness of multiple interrelated R&D networks under risk propagation. Firstly, using a bi-partite graph to represent the interrelated R&D networks is emphasized and proposed. Secondly, a risk propagation model is built by defining risk load and risk capacity of each enterprise on a specific R&D network, Thirdly, we use simulations to study risk propagation in interrelated R&D networks. Our results indicate that there exist three critical thresholds to quantify the robustness of R&D networks. Risk propagation in R&D networks is highly affected by the heterogeneity of all enterprises' scales and risk capacities.     

On the robustness of Spanish telecommunication networks

Complex networks are considered robust against random failures but sensitive to failures in target. Under this perspective we analyze the robustness of the Spanish telecommunication networks for digital transmission, the Synchronous Digital Hierarchy (SDH), considering failures in the equipments that control the flow of information. Our results suggest that the robustness depends not only on the connectivity of equipments removed but also on the capacity and types of links associated with that removal. We have also observed that the robustness of SDH networks depends on the particular initial design and evolution of each Spanish province.     

Impact of local coupling on the vulnerability of 2D spatially embedded interdependent networks

Real networks are always interdependent and spatially embedded. Considering the space constraint, dependency links between networks may be established not globally but locally. In this paper, we study how the spatial coupling will impact the robustness of interdependent scale-free networks located in a 2D square plane where dependent nodes are connected within a connecting radius $r_{connect}$. Besides the traditional assortative degree–degree coupling (GD) and random coupling (GR), some novel spatial couplings are also introduced, i.e., spatial assortative degree–degree coupling (SD), spatial random coupling (SR) and nearest neighbor coupling (NN). Simulation results indicate that assortative couplings, GD and SD, can improve the robustness under topological attacks while under localized attacks, NN coupling is the best one. In addition, for SD coupling under topological attacks, we find that the robustness for small $r_{connect}$ decreases with $r_{connect}$ from 0 to the critical value $r_{c1}$, and for larger $r_{connect}$ gradually increases with $r_{connect}$ from $r_{c1}$ to the maximum value ${(r_{connect})}_{max}$. However, opposite results will be obtained under localized attacks. These findings may be helpful to understand and analyze some real interdependent infrastructures.     

社交网络中基于贝叶斯和半环代数模型的节点影响力计算机理

本文综合考虑网络结构及节点间的互动等关键因素, 提出了一种节点影响力分布式计算机理. 首先根据节点交互行为在时域上的自相似特性, 运用带折扣因子的贝叶斯模型计算节点间的直接影响力; 然后运用半环模型来分析节点间接影响力的聚合; 最后根据社交网络的小世界性质及传播门限, 综上计算出节点的综合影响力. 仿真结果表明, 本文给出的模型能有效抑制虚假粉丝导致的节点影响力波动, 消除了虚假粉丝的出现对节点影响力计算带来的干扰, 从中选择影响力高的若干节点作为传播源节点, 可以将信息传播到更多数目的节点, 促进了信息在社交网络中的传播. 关键词： 社交网络 影响力 贝叶斯 半环代数     

Effects of friend-making resources/costs and remembering on acquaintance networks

We consider two overlooked yet important factors that affect acquaintance network evolution and formation—friend-making resources and remembering—and propose a bottom-up, network-oriented simulation model based on three rules representing human social interactions. Our proposed model reproduces many topological features of real-world acquaintance networks, including a small-world phenomenon and a sharply peaked connectivity distribution feature that mixes power-law and exponential distribution types. We believe that this is an improvement over fieldwork sampling methods that fail to capture acquaintance network node connectivity distributions. Our model may produce valuable results for sociologists working with social opinion formation and epidemiologists studying epidemic dynamics.     

Analysis and models of bilateral investment treaties using a social networks approach

Bilateral investment treaties (BITs) are agreements between two countries for the reciprocal encouragement, promotion and protection of investments in each other’s territories by companies based in either country. Germany and Pakistan signed the first BIT in 1959 and since then, BITs are one of the most popular and widespread form of international agreement. In this work we study the proliferation of BITs using a social networks approach. We propose a network growth model that dynamically replicates the empirical topological characteristics of the BIT network.     

Analysis of thermal conductivity in tree-like branched networks

Asymmetric tree-like branched networks are explored by geometric algorithms. Based on the network, an analysis of the thermal conductivity is presented. The relationship between effective thermal conductivity and geometric structures is obtained by using the thermal-electrical analogy technique. In all studied cases, a clear behaviour is observed, where angle (δ ,θ ) among parent branching extended lines, branches and parameter of the geometric structures have stronger effects on the effective thermal conductivity. When the angle δ is fixed, the optical diameter ratio β^* is dependent on angle θ . Moreover, γ and m are not related to β ^* . The longer the branch is, the smaller the effective thermal conductivity will be. It is also found that when the angle θ < δ / 2, the higher the iteration m is, the lower the thermal conductivity will be and it tends to zero, otherwise, it is bigger than zero. When the diameter ratio β ₁< 0.707 and angle δ is bigger, the optimal k of the perfect ratio increases with the increase of the angle δ ; when β ₁> 0.707, the optimal k decreases. In addition, the effective thermal conductivity is always less than that of single channel material. The present results also show that the effective thermal conductivity of the asymmetric tree-like branched networks does not obey Murray's law.     

Analysis of epidemic models with demographics in metapopulation networks

In this paper, two susceptible–infected–susceptible (SIS) epidemic models are presented and analyzed by reaction–diffusion processes with demographics in metapopulation networks. Firstly, an SIS model with constant-inputting is discussed. The model has a disease-free equilibrium, which is locally asymptotically stable when the basic reproduction number is less than unity, otherwise it is unstable. It has an endemic equilibrium, which is globally asymptotically stable. Secondly, in another SIS model, the birth rate is the form of Logistic. Similarly, the stability of disease-free equilibrium and endemic equilibrium is also proved. Finally, numerical simulations are performed to illustrate the analytical results.     

Scaling and correlations in three bus-transport networks of China

We report the statistical properties of three bus-transport networks (BTN) in three different cities of China. These networks are composed of a set of bus lines and stations serviced by these. Network properties, including the degree distribution, clustering and average path length are studied in different definitions of network topology. We explore scaling laws and correlations that may govern intrinsic features of such networks. Besides, we create a weighted network representation for BTN with lines mapped to nodes and number of common stations to weights between lines. In such a representation, the distributions of degree, strength and weight are investigated. A linear behavior between strength and degree s(k)∼k$s(k)\sim k$ is also observed.     

Growth, percolation, and correlations in disordered fiber networks

This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameterp which controls the degree of clustering. Forp=1 the deposited network is uniformly random, while forp=0 only a single connected cluster can grow. Forp=0 we first derive the growth law for the average size of the cluster as well as a formula for its mass density profile. Forp>0 we carry out extensive simulations on fibers, and also needles and disks, to study the dependence of the percolation threshold onp. We also derive a mean-field theory for the threshold nearp=0 andp=1 and find good qualitative agreement with the simulations. The fiber networks produced by the model display nontrivial density correlations forp<1. We study these by deriving an approximate expression for the pair distribution function of the model that reduces to the exactly known case of a uniformly random network. We also show that the two-point mass density correlation function of the model has a nontrivial form, and discuss our results in view of recent experimental data on mss density correlations in paper sheets.     

Characterization of dynamical systems under noise using recurrence networks: Application to simulated and EEG data

In this letter, we study the influence of observational noise on recurrence network (RN) measures, the global clustering coefficient (C) and average path length (L  ) using the Rössler system and propose the application of RN measures to analyze the structural properties of electroencephalographic (EEG) data. We find that for an appropriate recurrence rate (RR>0.02$RR>0.02$) the influence of noise on C can be minimized while L is independent of RR for increasing levels of noise. Indications of structural complexity were found for healthy EEG, but to a lesser extent than epileptic EEG. Furthermore, C performed better than L in case of epileptic EEG. Our results show that RN measures can provide insights into the structural properties of EEG in normal and pathological states.     

节点中心性对复杂网络传播模式的影响分析

在众多的重要节点评估方法研究中,具有较高中心性的节点一直是关注的焦点,许多传播行为的研究也主要围绕高中心性节点展开,因此在一定程度上忽略了低中心性节点对传播行为的影响.本文从传播异构性角度,通过初始感染最大中心性节点和最小中心性节点揭示网络结构异构性对信息传播的影响.实验结果表明,传播过程中存在"链型"和"扇型"两种传播模式,在初始感染比例不断提升的情况下,两种传播模式的相互转换引发传播速率的变化,进一步促使非线性传播规模交叉现象的产生.这一现象说明,在宏观的信息传播过程中,最小中心性节点的影响力不容忽视,尤其在初始感染比例升高时,最小中心性节点比最大中心性节点更具传播优势.     

A review of fractality and self-similarity in complex networks

We review recent findings of self-similarity in complex networks. Using the box-covering technique, it was shown that many networks present a fractal behavior, which is seemingly in contrast to their small-world property. Moreover, even non-fractal networks have been shown to present a self-similar picture under renormalization of the length scale. These results have an important effect in our understanding of the evolution and behavior of such systems. A large number of network properties can now be described through a set of simple scaling exponents, in analogy with traditional fractal theory.     

STDP-driven networks and the C. elegans neuronal network

We study the dynamics of the structure of a formal neural network wherein the strengths of the synapses are governed by spike-timing-dependent plasticity (STDP). For properly chosen input signals, there exists a steady state with a residual network. We compare the motif profile of such a network with that of a real neural network of C. elegans and identify robust qualitative similarities. In particular, our extensive numerical simulations show that this STDP-driven resulting network is robust under variations of the model parameters.     

Analyzing topological characteristics of neuronal functional networks in the rat brain

In this study, we recorded spike trains from brain cortical neurons of several behavioral rats in vivo by using multi-electrode recordings. An NFN was constructed in each trial, obtaining a total of 150 NFNs in this study. The topological characteristics of NFNs were analyzed by using the two most important characteristics of complex networks, namely, small-world structure and community structure. We found that the small-world properties exist in different NFNs constructed in this study. Modular function Q was used to determine the existence of community structure in NFNs, through which we found that community-structure characteristics, which are related to recorded spike train data sets, are more evident in the Y-maze task than in the DM-GM task. Our results can also be used to analyze further the relationship between small-world characteristics and the cognitive behavioral responses of rats.     

UAV caching in 6G networks: A Survey on models,techniques, and applications

The rapid development road map of 6G networks has posed a new set of challenges to both industrial and academic sectors. On the one hand, it needs more disruptive technologies and solutions for addressing the threefold issues including enhanced mobile broadband, massive machine-type communications, and ultra-reliable and low-latency communications. On the other hand, the ever-massive number of mobile users and Internet of Things devices conveys the huge volume of traffic throughout the 6G networks. In this context, caching is one of the most feasible technologies and solutions that does not require any system architecture changes nor costly investments, while significantly improve the system performance, i.e., quality of service and resource efficiency. Ground caching models deployed at macro base stations, small-cell base stations, and mobile devices have been successfully studied and currently extended to the air done by unmanned aerial vehicles (UAVs) to deal with the challenges of 6G networks. This paper provides a comprehensive survey of UAV caching models, techniques, and applications in 6G networks. In particular, we first investigate the entire picture of caching models moving from the ground to the air as well as the related surveys on UAV communications. Then, we introduce a typical UAV caching system and describe how it works in connection with all types of the transceivers, end users, and applications and services (A&Ss). After that, we present the recent advancements and analyses of the UAV caching models and common system performance metrics. Furthermore, the UAV caching with assisted techniques, UAV caching-enabled mechanisms, and UAV caching A&Ss are discussed to demonstrate the role of UAV caching system in 6G networks. Finally, we highlight the ongoing challenges and potential research directions toward UAV caching in 6G networks.     

Spin glass,the travelling salesman problem,neural networks and all that

This paper presents an overview of diverse topics that are seemingly different but interrelated, with strong connections to statistical mechanics on the one hand and spin glass physics on the other. Written primarily for an inter-disciplinary audience, we start with a brief recapitulation of the relevant aspects of statistical mechanics, particularly those needed for understanding the recently-popular simulated-annealing technique used in optimization studies. Then follows a survey of the spin glass problem, with particular attention to the consequences of quenched randomness. The travelling-salesman problem is considered next, as also the impact made on it by the spin glass problem. Several examples are then presented of optimization studies wherein the simulated-annealing concept has been profitably used. Attention is also drawn in this context to the lessons provided by the spin glass problem. Finally, a brief survey of neural networks is made, essentially from a physicist’s point of view. The different learning schemes proposed are discussed, and the relevance of spin models and their statistical mechanics is also discussed.