Contagion dynamics on adaptive multiplex networks with awareness-dependent rewiring

Over the last few years,the interplay between contagion dynamics of social influences(e.g.,human awareness,risk perception,and information dissemination)and biological infections has been extensively investigated within the framework of multiplex networks.The vast majority of existing multiplex network spreading models typically resort to heterogeneous mean-field approximation and microscopic Markov chain approaches.Such approaches usually manifest richer dynamical properties on multiplex networks than those on simplex networks;however,they fall short of a subtle analysis of the variations in connections between nodes of the network and fail to account for the adaptive behavioral changes among individuals in response to epidemic outbreaks.To transcend these limitations,in this paper we develop a highly integrated effective degree approach to modeling epidemic and awareness spreading processes on multiplex networks coupled with awareness-dependent adaptive rewiring.This approach keeps track of the number of nearest neighbors in each state of an individual;consequently,it allows for the integration of changes in local contacts into the multiplex network model.We derive a formula for the threshold condition of contagion outbreak.Also,we provide a lower bound for the threshold parameter to indicate the effect of adaptive rewiring.The threshold analysis is confirmed by extensive simulations.Our results show that awareness-dependent link rewiring plays an important role in enhancing the transmission threshold as well as lowering the epidemic prevalence.Moreover,it is revealed that intensified awareness diffusion in conjunction with enhanced link rewiring makes a greater contribution to disease prevention and control.In addition,the critical phenomenon is observed in the dependence of the epidemic threshold on the awareness diffusion rate,supporting the metacritical point previously reported in literature.This work may shed light on understanding of the interplay between epidemic dynamics and social contagion on adaptive networks.

Influence Diffusion Model in Multiplex Networks

The problem of influence maximizing in social networks refers to obtaining a set of nodes of a specified size under a specific propagation model so that the aggregation of the node-set in the network has the greatest influence.Up to now,most of the research has tended to focus on monolayer network rather than on multiplex networks.But in the real world,most individuals usually exist in multiplex networks.Multiplex networks are substantially different as compared with those of a monolayer network.In this paper,we integrate the multi-relationship of agents in multiplex networks by considering the existing and relevant correlations in each layer of relationships and study the problem of unbalanced distribution between various relationships.Meanwhile,we measure the distribution across the network by the similarity of the links in the different relationship layers and establish a unified propagation model.After that,place on the established multiplex network propagation model,we propose a basic greedy algorithm on it.To reduce complexity,we combine some of the characteristics of triggering model into our algorithm.Then we propose a novel MNStaticGreedy algorithm which is based on the efficiency and scalability of the StaticGreedy algorithm.Our experiments show that the novel model and algorithm are effective,efficient and adaptable.

Impact of individual behavior adoption heterogeneity on epidemic transmission in multiplex networks

In recent years, the impact of information diffusion and individual behavior adoption patterns on epidemic transmission in complex networks has received significant attention. In the immunization behavior adoption process, different individuals often make behavioral decisions in different ways, and it is of good practical importance to study the influence of individual heterogeneity on the behavior adoption process. In this paper, we propose a three-layer coupled model to analyze the process of co-evolution of official information diffusion, immunization behavior adoption and epidemic transmission in multiplex networks, focusing on individual heterogeneity in behavior adoption patterns. Specifically, we investigate the impact of the credibility of social media and the risk sensitivity of the population on behavior adoption in further study of the effect of heterogeneity of behavior adoption on epidemic transmission. Then we use the microscopic Markov chain approach to describe the dynamic process and capture the evolution of the epidemic threshold. Finally, we conduct extensive simulations to prove our findings. Our results suggest that enhancing the credibility of social media can raise the epidemic transmission threshold, making it effective at controlling epidemic transmission during the dynamic process. In addition, improving an individuals' risk sensitivity, and thus their taking effective protective measures, can also reduce the number of infected individuals and delay the epidemic outbreak. Our study explores the role of individual heterogeneity in behavior adoption in real networks, more clearly models the effect of the credibility of social media and risk sensitivity of the population on the epidemic transmission dynamic, and provides a useful reference for managers to formulate epidemic control and prevention policies.

Impact of environmental factors on the coevolution of information-emotions-epidemic dynamics in activity-driven multiplex networks

During public health emergencies,the diffusion of negative information can exacerbate the transmission of adverse emotions,such as fear and anxiety.These emotions can adversely affect immune function and,consequently,influence the spread of the epidemic.In this study,we established a coupled model incorporating environmental factors to explore the coevolution dynamic process of information-emotions-epidemic dynamics in activity-driven multiplex networks.In this model,environmental factors refer to the external conditions or pressures that affect the spread of information,emotions,and epidemics.These factors include media coverage,public opinion,and the prevalence of diseases in the neighborhood.These layers are dynamically cross-coupled,where the environmental factors in the information layer are influenced by the emotional layer;the higher the levels of anxious states among neighboring individuals,the greater the likelihood of information diffusion.Although environmental factors in the emotional layer are influenced by both the information and epidemic layers,they come from the factors of global information and the proportion of local infections among surrounding neighbors.Subsequently,we utilized the microscopic Markov chain approach to describe the dynamic processes,thereby obtaining the epidemic threshold.Finally,conclusions are drawn through numerical modeling and analysis.The conclusions suggest that when negative information increases,the probability of the transmission of anxious states across the population increases.The transmission of anxious states increases the final size of the disease and decreases its outbreak threshold.Reducing the impact of environmental factors at both the informational and emotional levels is beneficial for controlling the scale of the spread of the epidemic.Our findings can provide a reference for improving public health awareness and behavioral decision-making,mitigating the adverse impacts of anxious states,and ultimately controlling the spread of epidemics.

Impact of asymmetric activity on interactions between information diffusion and disease transmission in multiplex networks

Disease is a serious threat to human society.Understanding the characteristics of disease transmission is helpful for people to effectively control disease.In real life,it is natural to take various measures when people are aware of disease.In this paper,a novel coupled model considering asymmetric activity is proposed to describe the interactions between information diffusion and disease transmission in multiplex networks.Then,the critical threshold for disease transmission is derived by using the micro-Markov chain method.Finally,the theoretical results are verified by numerical simulations.The results show that reducing the activity level of individuals in the physical contact layer will have a continuous impact on reducing the disease outbreak threshold and suppressing the disease.In addition,the activity level of individuals in the virtual network has little impact on the transmission of the disease.Meanwhile,when individuals are aware of more disease-related information,the higher their awareness of prevention will be,which can effectively inhibit the transmission of disease.Our research results can provide a useful reference for the control of disease transmission.

Modeling the COVID-19 epidemic and awareness diffusion on multiplex networks

The coronavirus disease 2019(COVID-19)has been widely spread around the world,and the control and behavior dynamics are still one of the important research directions in the world.Based on the characteristics of COVID-19’s spread,a coupled disease-awareness model on multiplex networks is proposed in this paper to study and simulate the interaction between the spreading behavior of COVID-19 and related information.In the layer of epidemic spreading,the nodes can be divided into five categories,where the topology of the network represents the physical contact relationship of the population.The topological structure of the upper network shows the information interaction among the nodes,which can be divided into aware and unaware states.Awareness will make people play a positive role in preventing the epidemic diffusion,influencing the spread of the disease.Based on the above model,we have established the state transition equation,through the microscopic Markov chain approach(MMCA),and proposed the propagation threshold calculation method under the epidemic model.Furthermore,MMCA iteration and the Monte Carlo method are simulated on the static network and dynamic network,respectively.The current results will be beneficial to the study of COVID-19,and propose a more rational and effective model for future research on epidemics.

Multi-Core Virtual Concatenation Scheme Considering Inter-Core Crosstalk in Spatial Division Multiplexing Enabled Elastic Optical Networks

Spatial division multiplexing enabled elastic optical networks(SDM-EONs) are the potential implementation form of future optical transport networks, because it can curve the physical limitation of achievable transmission capacity in single-mode fiber and single-core fiber. However, spectrum fragmentation issue becomes more serious in SDM-EONs compared with simple elastic optical networks(EONs) with single mode fiber or single core fiber. In this paper, multicore virtual concatenation(MCVC) scheme is first proposed considering inter-core crosstalk to solve the spectrum fragmentation issue in SDM-EONs. Simulation results show that the proposed MCVC scheme can achieve better performance compared with the baseline scheme, i.e., single-core virtual concatenation(SCVC) scheme, in terms of blocking probability and spectrum utilization.

Multiplex network infomax:Multiplex network embedding via information fusion

For networking of big data applications,an essential issue is how to represent networks in vector space for further mining and analysis tasks,e.g.,node classification,clustering,link prediction,and visualization.Most existing studies on this subject mainly concentrate on monoplex networks considering a single type of relation among nodes.However,numerous real-world networks are naturally composed of multiple layers with different relation types;such a network is called a multiplex network.The majority of existing multiplex network embedding methods either overlook node attributes,resort to node labels for training,or underutilize underlying information shared across multiple layers.In this paper,we propose Multiplex Network Infomax(MNI),an unsupervised embedding framework to represent information of multiple layers into a unified embedding space.To be more specific,we aim to maximize the mutual information between the unified embedding and node embeddings of each layer.On the basis of this framework,we present an unsupervised network embedding method for attributed multiplex networks.Experimental results show that our method achieves competitive performance on not only node-related tasks,such as node classification,clustering,and similarity search,but also a typical edge-related task,i.e.,link prediction,at times even outperforming relevant supervised methods,despite that MNI is fully unsupervised.

CoLM^(2)S:Contrastive self‐supervised learning on attributed multiplex graph network with multi‐scale information

Contrastive self‐supervised representation learning on attributed graph networks with Graph Neural Networks has attracted considerable research interest recently.However,there are still two challenges.First,most of the real‐word system are multiple relations,where entities are linked by different types of relations,and each relation is a view of the graph network.Second,the rich multi‐scale information(structure‐level and feature‐level)of the graph network can be seen as self‐supervised signals,which are not fully exploited.A novel contrastive self‐supervised representation learning framework on attributed multiplex graph networks with multi‐scale(named CoLM^(2)S)information is presented in this study.It mainly contains two components:intra‐relation contrast learning and interrelation contrastive learning.Specifically,the contrastive self‐supervised representation learning framework on attributed single‐layer graph networks with multi‐scale information(CoLMS)framework with the graph convolutional network as encoder to capture the intra‐relation information with multi‐scale structure‐level and feature‐level selfsupervised signals is introduced first.The structure‐level information includes the edge structure and sub‐graph structure,and the feature‐level information represents the output of different graph convolutional layer.Second,according to the consensus assumption among inter‐relations,the CoLM^(2)S framework is proposed to jointly learn various graph relations in attributed multiplex graph network to achieve global consensus node embedding.The proposed method can fully distil the graph information.Extensive experiments on unsupervised node clustering and graph visualisation tasks demonstrate the effectiveness of our methods,and it outperforms existing competitive baselines.

FAIRNESS OF SHARING PROTECTION FOR MULTICAST IN WDM NETWORKS

In this paper,the sharing schemes of multicast in survivable Wavelength-Division Multi-plexed(WDM) networks are studied and the concept of Shared Risk Link Group(SRLG) is considered.While the network resources are shared by the backup paths,the sharing way is possible to make the backup paths selfish.This selfishness leads the redundant hops of the backup route and a large number of primary lightpaths to share one backup link.The sharing schemes,especially,the self-sharing and cross-sharing,are investigated to avoid the selfishness when computing the backup light-tree.In order to decrease the selfishness of the backup paths,it is important to make the sharing links fair to be used.There is a trade-off between the self-sharing and cross-sharing,which is adjusted through simulation to adapt the sharing degree of each sharing scheme and save the network resources.

Equilibrium Analysis for Anycast in WDM Networks

In this paper, the wavelength-routed WDM network was analyzed for the dynamic case where the arrival of anycast requests was modeled by a state-dependent Poisson process. The equilibrium analysis was also given with the UWNC algorithm.

Research on Weighted Directed Dynamic Multiplexing Network of World Grain Trade Based on Improved MLP Framework

As the main food source for humans, the global movement of the three major grains significantly impacts human survival and development. To investigate the evolution of the world cereal trade network and its development trend, a weighted directed dynamic multiplexed network was established using historical data on cereal trade, cereal import dependency ratio, and arable land per capita. Inspired by the MLP framework, we redefined the weight determination method for computing layer weights and edge weights of the target layer, modified the CN, RA, AA, and PA indicators, and proposed the node similarity indicator for weighted directed networks. The AUC metric, which measures the accuracy of the algorithm, has also been improved in order to finally obtain the link prediction results for the grain trading network. The prediction results were processed, such as web-based presentation and community partition. It was found that the number of generalized trade agreements does not have a decisive impact on inter-country cereal trade. The former large grain exporters continue to play an important role in this trade network. In the future, the world trade in cereals will develop in the direction of more frequent intercontinental trade and gradually weaken the intracontinental cereal trade.

ROUTING AND WAVELENGTH ASSIGNMENT ALGORITHMS BASED ON EQUIVALENT NETWORKS

In this paper, a Wavelength Division Multiplexing (WDM) network model based on the equivalent networks is described, and wavelength-dependent equivalent arc, equivalent networks, equivalent multicast tree and some other terms are presented. Based on this model and relevant Routing and Wavelength Assign- ment (RWA) strategy, a unicast RWA algorithm and a multicast RWA algorithm are presented. The wave- length-dependent equivalent arc expresses the schedule of local RWA and the equivalent network expresses the whole topology of WDM optical networks, so the two algorithms are of the flexibility in RWA and the optimi- zation of the whole problem. The theoretic analysis and simulation results show the two algorithms are of the stronger capability and the lower complexity than the other existing algorithms for RWA problem, and the complexity of the two algorithms are only related to the scale of the equivalent networks. Finally, we prove the two algorithms’ feasibility and the one-by-one corresponding relation between the equivalent multicast tree and original multicast tree, and point out the superiorities and drawbacks of the two algorithms respectively.

Robust Design of Virtual Topology for WDM Networks under Bandwidth Demand Uncertainties

In this paper, a novel method is proposed to address the problem of designing virtual topology over wavelength division multiplexing （WDM） networks under bandwidth demand uncertainties. And a bandwidth demand model under uncertainties is presented. The optimization goal of virtual topology design is defined as minimizing the maximum value amongp percentiles of the bandwidth demand distribution on all Hght-paths. Correspondingly, we propose a heuristic algorithm called an improved decreasing multi-hop logical topology design algorithm （ID-MLTDA） that involves with a degree of uncertainties to design virtual topology. The proposed algorithm yields better performance than previous algorithms. Additionally, the simplicity and efficiency of the proposed algorithm can be in favor of the feasibility for topology design of large networks.

A cost-effective structure of a centralized-light-source WDM-PON utilizing inverse-duobinary-RZ downstream and DPSK upstream

In this paper, we propose a new structure of a centralized-light-source wavelength division multiplexed passive op- tical network （WDM-PON） utilizing inverse-duobinary-return-to-zero （inverse-duobinary-RZ） downstream and DPSK up- stream. It reuses downstream light for the upstream modulation, which retrenches lasers assembled at each optical network unit （ONU）, and ultimately cuts down the cost of ONUs a great deal. Meanwhile, a 50-km-reach WDM-PON experiment with 10-Gb/s inverse-duobinary-RZ downstream and 6-Gb/s DPSK upstream is demonstrated here. It is revealed to be a novel cost-effective alternative for the next generation access network.

Multiplex network reconstruction for the coupled spatial diffusion of infodemic and pandemic of COVID-19

The pandemic of COVID-19 witnessed a massive infodemic with the public being bombarded with vast quantities of information.The spreading of neutral and highly accurate reports can guide the public to self-protect and reduce the pandemic.Mis-and dis-information would intrigue panic and high exposure risk to epidemic.Although the infodemic has attracted attentions from the academia,it is still not known to what degree and in which direction the information flows contribute to the COVID-19 pandemic.To fill the gap,we apply network reconstruction techniques to rebuild the hidden multiplex network of information and COVID-19 spreading by which we aim at quantifying the interaction between the propagation of information and the spatial outbreak of COVID-19,and delineate between the positive and negative impact of information on the pandemic.By differentiating the types of media that participated in the information process,we find that in the early stage of COVID-19 pandemic,infodemic does play a critical role to amplify the risk of virus outbreak in China and the risk is even larger for those highly developed regions.Compared to the old-fashion media,the new mobile platforms impose a greater risk to reinforce the positive feedback between infodemic and COVID-19 pandemic.

Recovering unknown topology in a two-layer multiplex network:One layer infers the other layer

There have been increasing interests in studying multiplex dynamical networks recently.This paper focuses on topology identiflcation of two-layer multiplex networks with peer-to-peer interlayer couplings.For a two-layer network model in which different layers have different coupling patterns,we propose novel methods to recover unknown topological structure of one layer,using the information of the other layer known as a prior.The proposed methods make full use of the measured evolutional states of the multiplex network itself,and treat the layer with a known structure as an auxiliary layer which is designed to identify the unknown topological layer.Compared with the traditional synchronization-based identiflcation method,the proposed methods are in no need of constructing an additional auxiliary network to identify the unknown topological layer,and thus greatly reduce the cost of topology identiflcation.Finally,numerical simulations validate the effectiveness of the proposed methods.

Synchronizability of time-varying structured duplex dynamical networks with different intra-layer rewiring mechanisms

Global synchronizability of duplex networks induced by three different intra-layer rewiring mechanisms is explored in this paper.The rewiring mechanisms are named as model-preserving rewiring(MPR), simply direct rewiring(SDR), and degree-preserving rewiring(DPR), respectively. It is found that high switching frequencies will certainly enhance global synchronizability for WSWS duplex networks(i.e., each layer is independently formed by the algorithm proposed by Watts and Strogatz for generating small-world networks), ER-ER duplex networks(i.e., each layer is independently generated by the algorithm proposed by Erd ¨os and Renyi) and BA-BA duplex networks(i.e., each layer is independently formed by the classical BA algorithm). Namely,the faster the intra-layer couplings are reconnected, the faster the duplex networks reach global synchronization. Furthermore,we find that by increasing the intra-or inter-coupling strengths, the WS-WS time-varying network’s global synchronizability is enhanced. Take the WS-WS time-varying network as an example, we find that SDR mechanism has greater impact on global synchronizability than MPR mechanism and DPR mechanism. The related dynamical networks can arrive at synchronization faster by SDR than by MPR or DPR. Thus, we only study the effects of SDR on ER-ER duplex networks and BA-BA duplex networks. In addition, we obtain the fact via numerical simulations that, switching intra-layer coupling topologies under SDR mechanism has the greatest impact on the BA-BA duplex network, followed by the ER-ER network, and has the weakest influence on the WS-WS duplex network in terms of improving the global synchronizability when all the intra-layer networks are sparse and have the same average degree. Finally, the global synchronizability of WS-WS and BA-BA time-varying networks is improved compared with static duplex networks, the reason being that the networks tend to be randomized under SDR according to analysis of the networks’ average clustering coefficients and degree distributions.

Quantifying multiple social relationships based on a multiplex stochastic block model

Online social networks have attracted great attention recently, because they make it easy to build social connections for people all over the world. However, the observed structure of an online social network is always the aggregation of multiple social relationships. Thus, it is of great importance for real-world networks to reconstruct the full network structure using limited observations. The multiplex stochastic block model is introduced to describe multiple social ties, where different layers correspond to different attributes(e.g., age and gender of users in a social network). In this letter, we aim to improve the model precision using maximum likelihood estimation, where the precision is defined by the cross entropy of parameters between the data and model. Within this framework, the layers and partitions of nodes in a multiplex network are determined by natural node annotations, and the aggregate of the multiplex network is available. Because the original multiplex network has a high degree of freedom, we add an independent functional layer to cover it, and theoretically provide the optimal block number of the added layer.Empirical results verify the effectiveness of the proposed method using four measures, i.e., error of link probability,cross entropy, area under the receiver operating characteristic curve, and Bayes factor.

2 Tbit/s based coherent wavelength division multiplexing passive optical network for 5G transport

Future high-speed mobile communication systems require low latency and high capacity networks.Coherent wavelength division multiplexing(WDM)passive optical network(PON)scheme is expected to play a vital role in these systems.In this paper,coherent WDM-PON scheme based on dual-polarization 16-quadrature amplitude modulation(DP-16 QAM)transceiver has been investigated.The aim of this scheme is to build a 2 Tbit/s(125 Gbit/s/λ×16 wavelengths)network that will be used in the construction of the transport architecture of fifth generation(5 G)and beyond 5 G(B5 G)cellular networks either in mobile front haul(MFH)or mobile back haul(MBH).The results indicate that the proposed scheme is very adequate for both 5 G and B5 G cellular networks requirements.