Two-layer Network Model Research Articles

Network structure analysis based on embodied energy of the Australian economy

Energy and economic growth are closely linked and have negative impacts on the environment. Both environmental protection and economic development are significant global focal points of concern. Australian economic growth has slowed but energy consumption has increased. The relationship between economic growth and energy consumption has changed significantly. However, existing methods for accounting energy transfers between industries overlook the role of embodied energy, making them insufficient to fully capture the actual energy usage in both domestic and international trade. This study investigates the structural changes in embodied energy in the Australian economy. The paper integrates sectors as the section nodes for a network and constructs a two-layer network model to analyze energy flows both between and within nodes. The results show that the Australian embodied energy network exhibited significant variations in efficiency and interconnectedness over time, with a trend toward shorter, more interconnected paths from 2015 to 2019, enhancing overall network efficiency. The Australian embodied energy network currently faces significant funding constraints. The findings show that the Australian economic sectors have increased energy consumption in production without contributing to economic growth due to the concentration of resources within the network.

Aviation armament system-of-systems modeling and identification method of vulnerable nodes based on interdependent network

Aiming at the problem that it is difficult to build model and identify the vulnerable equipment for aviation armament System-of-Systems (SoS) due to complex equipment interaction relationships and high confrontation, the interdependent network theory is introduced to solve it. Firstly, a two-layer heterogeneous interdependent network model for aviation armament SoS is proposed, which reflects the information interaction, functional dependency and inter-network dependence effectively. Secondly, using the attack cost to describe the confrontation process and taking the comprehensive impact on kill chains as the entry point, the node importance index and the attack cost measurement method are constructed. Thirdly, the identification of vulnerable nodes is transformed into the optimization problem of node combinatorial selection, and the vulnerable node identification method based on tabu search is proposed. Based on vulnerable nodes, a robustness enhancement strategy for aviation armament SoS network is presented. Finally, the above methods are used to an aerial confrontation SoS, and the results verify the rationality and effectiveness of the proposed methods.

Distributed Nash equilibrium seeking in noncooperative game with partial decision information of neighbors.

In the real world, individuals may conceal some of their real decision information to their neighbors due to competition. It is a challenge to explore the distributed Nash equilibrium when individuals play the noncooperative game with partial decision information in complex networks. In this paper, we investigate the distributed Nash equilibrium seeking problem with partial decision information of neighbors. Specifically, we construct a two-layer network model, where players in the first layer engage in game interactions and players in the second layer exchange estimations of real actions with each other. We also consider the case where the actions of some players remain unchanged due to the cost of updating or personal reluctance. By means of the Lyapunov function method and LaSalle's invariance principle, we obtain the sufficient conditions in which the consensus of individual actions and estimations can be achieved and the population actions can converge to the Nash equilibrium point. Furthermore, we investigate the case with switched topologies and derive the sufficient conditions for the convergence of individual actions to Nash equilibrium by the average dwell time method. Finally, we give numerical examples for cases of fixed and switched topologies to verify our theoretical results.

Coupled propagation between one communicable disease and related two types of information on multiplex networks with simplicial complexes

Currently, regarding the coupling transmission of information and disease, most researches only focus on the impact of one type of information on disease transmission, and some works may be correlated with two types of information, but they are usually based upon pairwise interactions, which ignored the complexity and diversity of information transmission. In real life, the characteristics of interpersonal networks often involve both group interactions and pairwise interactions. Aiming to explore the influence of active or passive information diffusion on the transmission of epidemics on a higher-order network, the coupled two-layered multiplex network model between communicable disease and information transmission is presented. Here, the upper layer characterizes the information transmission network constructed from random simplicial complexes, while the lower layer provides the underlying network that can transmit communicable diseases. First, on the basis of micro Markov chain (MMC) method, the epidemic threshold is analytically derived for the proposed model, indicating that the diffusion of positive and negative preventive information can exert a substantial influence on the critical threshold. Then, by comparing the results acquired by MMC and Monte Carlo simulations (MCS), it can be explicitly expressed that the differences between them are minimal, which implies that the model can predict the transmission of epidemics in the network well. Finally, through extensive MCS, it is also indicated that introducing a 2-simplex into the information layer helps to suppress the propagation or outbreak of communicable diseases, which offers some new ideas or routes for formulating strategies to inhibit communicable diseases.

Unveiling and Evaluating the Collaboration in Engineering Projects through a Two-Layer Information Collaboration Network Model

Unveiling and Evaluating the Collaboration in Engineering Projects through a Two-Layer Information Collaboration Network Model

A multilayer network model of interaction between rumor propagation and media influence.

Rumors spread among the crowd have an impact on media influence, while media influence also has an impact on rumor dissemination. This article constructs a two-layer rumor media interaction network model, in which the rumors spread in the crowd are described using the susceptibility-apathy-propagation-recovery model, and the media influence is described using the corresponding flow model. The rationality of the model is studied, and then a detailed analysis of the model is conducted. In the simulation section, we undertake a sensitivity analysis of the crucial parameters within our model, focusing particularly on their impact on the basic reproduction number. According to data simulation analysis, the following conclusion can be drawn: First, when the media unilaterally influences the crowd and does not accept feedback from the crowd, the influence of the media will decrease to zero over time, which has a negative effect on the spread of rumors among the crowd (the degree of rumor dissemination decreases). Second, when the media does not affect the audience and accepts feedback from the audience, this state is similar to the media collecting information stage, which is to accept rumors from the audience but temporarily not disclose their thoughts. At this time, both the media influence and the spread of rumors in the audience will decrease. Finally, the model is validated using an actual dataset of rumors. The simulation results show an R-squared value of 0.9606, indicating that the proposed model can accurately simulate rumor propagation in real social networks.

Modelling the impact of human behavior using a two-layer Watts-Strogatz network for transmission and control of Mpox

PurposeThis study aims to evaluate the effectiveness of mitigation strategies and analyze the impact of human behavior on the transmission of Mpox. The results can provide guidance to public health authorities on comprehensive prevention and control for the new Mpox virus strain in the Democratic Republic of Congo as of December 2023.MethodsWe develop a two-layer Watts-Strogatz network model. The basic reproduction number is calculated using the next-generation matrix approach. Markov chain Monte Carlo (MCMC) optimization algorithm is used to fit Mpox cases in Canada into the network model. Numerical simulations are used to assess the impact of mitigation strategies and human behavior on the final epidemic size.ResultsOur results show that the contact transmission rate of low-risk groups and susceptible humans increases when the contact transmission rate of high-risk groups and susceptible humans is controlled as the Mpox epidemic spreads. The contact transmission rate of high-risk groups after May 18, 2022, is approximately 20% lower than that before May 18, 2022. Our findings indicate a positive correlation between the basic reproduction number and the level of heterogeneity in human contacts, with the basic reproduction number estimated at 2.3475 (95% CI: 0.0749–6.9084). Reducing the average number of sexual contacts to two per week effectively reduces the reproduction number to below one.ConclusionWe need to pay attention to the re-emergence of the epidemics caused by low-risk groups when an outbreak dominated by high-risk groups is under control. Numerical simulations show that reducing the average number of sexual contacts to two per week is effective in slowing down the rapid spread of the epidemic. Our findings offer guidance for the public health authorities of the Democratic Republic of Congo in developing effective mitigation strategies.

Interplay of simplicial information propagation and epidemic spreading on multiplex metapopulation networks

Disease-related information inevitably enhances people’s awareness to prevent themselves from being infected. The traditional information propagation mainly presents in the form of individual to individual, without revealing the effects of herd-awareness on individuals. That is, individuals can perceive the disease-related information not only from their resident herd but also surrounding high-order herds. Thus, to further explore the effects information propagation of herd-awareness on spatial spreading of the epidemic, we construct a two-layer metapopulation network model, in which the upper layer is responsible for the information propagation by the patterns of self-herd awareness (0-simplex), neighboring herd awareness (1-simplex), and high-order herd-awareness (2-simplex), while the lower layer is responsible for spatial spreading of the epidemic.The results show that strengthening self-herd awareness can properly curb the epidemic spreading, and enhancing neighboring herd-awareness propagation apparently decrease the final infection scale. Nevertheless, enhancing high-order herd-awareness of 2-simplex propagation is not evident. This study may provide helpful guidance for the intervention of the epidemic in reality.

A two-layer model with partial mapping: Unveiling the interplay between information dissemination and disease diffusion

This study delves into the pivotal role of information dissemination in public health, particularly how it influences the spread of diseases. By implementing a sophisticated two-layer partial mapping network model (UAU-SIRS), we investigate the dynamic relationship between information flow and disease transmission. Our approach utilizes extensive multiplexed network data, processed through a micro Markov chain (MMC) model, to simulate the interplay between information spread and disease dynamics. The findings reveal a noteworthy positive correlation between the rates of information dissemination, recovery in the network, and the epidemic threshold. Conversely, the conversion rate is inversely related to this threshold. A critical observation is that Scale-free (SF) networks, characterized by their uneven node distribution, are more susceptible to the impacts of information spread on their outbreak thresholds compared to Erdős-Rényi (ER) networks. This research offers crucial insights for epidemic prevention strategies and provides valuable guidance for managing the dissemination of disease-related information within complex network structures.

Data mining and spatio-temporal characteristics of urban road traffic emissions: A case study in Shijiazhuang, China

Accurate estimation of traffic emissions and analysis of spatio-temporal distribution on urban roads play a crucial role in the development of low-carbon transportation system. Traditionally, a region’s emission characteristics have been studied using numerous emission models with GPS-based spatio-temporal data. Due to the heavy data processing needs of GPS-based data, emission characteristics for a large region have been studied by dividing the region into a limited number of smaller areas or units. Additionally, GPS data are based on a few vehicles in the traffic which does not fully reflect road conditions. This paper proposed an approach that can be used to study and calculate the spatio-temporal emission pattern of a region at a roadway section level by using Baidu’s online traffic data and COPERT model. The proposed method can be used to estimate road-level emission patterns while avoiding the impact of redundant data in large datasets, making the dataset more reliable, applicable, and scalable. The proposed approach has been demonstrated through a study of spatio-temporal emission patterns in the Qiaoxi district within city of Shijiazhuang, China. Online data crawling technology was used to obtain data on urban road traffic speed and driving distance. The linear reference technology was used to construct a two-layer road network model to conduct the coupling and matching of traffic data with the road network data. The COPERT model was implemented to calculate the average traffic emissions on each road in the road network, and a traffic emission intensity index was proposed to quantify the CO, VOC, NOx and CO2 emissions on urban roads in the study area. The analysis results show that the traffic emission intensity of the expressway, trunk road, secondary road, and branch road is high during the morning peak (7 AM-9 AM) and evening peak (5 PM—7 PM). The sections with higher traffic emission intensity are mainly concentrated on the main roads and secondary roads such as Jiefang South Street, Shitong Road and Xinhua Road. Nearly one-third of 2nd Ring and 3rd Ring roads also have relatively high emission intensity. The research results provide new ideas for estimating traffic emissions in urban road networks and analyzing the spatio-temporal distribution of traffic emissions. The research results can also provide a decision-making basis for traffic management departments to formulate energy-saving and emission-reduction measures and promote the development of urban green and low-carbon transportation.

Hierarchical Relational Graph Learning for Autonomous Multirobot Cooperative Navigation in Dynamic Environments

As a specific kind of Cyber-Physical Systems (CPSs), autonomous robot clusters play an important role in various intelligent manufacturing fields. However, due to the increasing design complexity of robot clusters, it is becoming more and more challenging to guarantee the safety and efficiency for multi-robot cooperative navigation in dynamic and complex environments. Although Deep Reinforcement Learning (DRL) shows great potential in learning multi-robot cooperative navigation policies, existing DRL-based approaches suffer from scalability issues and rarely consider the transferability of trained policies to new tasks. To address these problems, this paper presents a novel DRL-based multi-robot cooperative navigation approach named HRMR-Navi that equips each robot with both a two-layered hierarchical graph network model and an attention-based communication model. In our approach, the hierarchical graph network model can efficiently figure out hierarchical relations among all agents that either cooperate for efficiency or avoid obstacles for safety to derive more advanced strategies, and the communication model can accurately form a global view of the environment for a specific robot, thus the multi-robot cooperation efficiency can be further strengthened. Meanwhile, we propose an improved Proximal Policy Optimization (PPO) algorithm based on the Maximum Entropy reinforcement learning, named MEPPO, to enhance the robot exploration ability. Comprehensive experimental results demonstrate that, compared with state-of-the-art approaches, HRMR-Navi can achieve more efficient cooperative navigation with less time cost, lower collision rate, higher scalability, and better knowledge transferability.

Studying the co-evolution of information diffusion, vaccination behavior and disease transmission in multilayer networks with local and global effects

Today, with the rapid development of the internet, a large amount of information often accompanies the rapid transmission of disease outbreaks, and increasing numbers of scholars are studying the relationship between information and the disease transmission process using complex networks. In fact, the disease transmission process is very complex. Besides this information, there will often be individual behavioral measures and other factors to consider. Most of the previous research has aimed to establish a two-layer network model to consider the impact of information on the transmission process of disease, rarely divided into information and behavior, respectively. To carry out a more in-depth analysis of the disease transmission process and the intrinsic influencing mechanism, this paper divides information and behavior into two layers and proposes the establishment of a complex network to study the dynamic co-evolution of information diffusion, vaccination behavior, and disease transmission. This is achieved by considering four influential relationships between adjacent layers in multilayer networks. In the information layer, the diffusion process of negative information is described, and the feedback effects of local and global vaccination are considered. In the behavioral layer, an individual’s vaccination behavior is described, and the probability of an individual receiving a vaccination is influenced by two factors: the influence of negative information, and the influence of local and global disease severity. In the disease layer, individual susceptibility is considered to be influenced by vaccination behavior. The state transition equations are derived using the micro Markov chain approach (MMCA), and disease prevalence thresholds are obtained. It is demonstrated through simulation experiments that the negative information diffusion is less influenced by local vaccination behavior, and is mainly influenced by global vaccination behavior; vaccination behavior is mainly influenced by local disease conditions, and is less influenced by global disease conditions; the disease transmission threshold increases with the increasing vaccination rate; and the scale of disease transmission increases with the increasing negative information diffusion rate and decreases with the increasing vaccination rate. Finally, it is found that when individual vaccination behavior considers both the influence of negative information and disease, it can increase the disease transmission threshold and reduce the scale of disease transmission. Therefore, we should resist the diffusion of negative information, increase vaccination proportions, and take appropriate protective measures in time.

Dynamics analysis of the two-layer complex propagation network with individual heterogeneous decreased behavior

Due to the differences in society stratum, personal profession, and social acceptability, information propagation can be impacted by the contact capabilities of individuals. Importantly, we found that with the changes in individual psychology, their response to a phenomenon will gradually weaken. This phenomenon is called heterogeneous decreased behavior and applied in the fields of economics, sociology, and ecology. In the social network, people show a gradually decreasing degree of interest for information, named individual heterogeneous decreased behavior (IHDB). We structure a two-layer network model to describe individual behavioral contact and propose a threshold function to represent IHDB. Meanwhile, we use partition theory to explain the information propagation mechanism. Through experiments, it is demonstrated that there is a continuous information outbreak in the ultimate adoption size when individuals exhibit a positive IHDB. However, when individuals exhibit a passive IHDB, there is a discontinuous information outbreak in the ultimate adoption size. Eventually, our experiments show that the theoretical analysis coincides with the results of the simulations.

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 counter-terrorism 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.

Epidemic trajectories and awareness diffusion among unequals in simplicial complexes

The interplay between awareness diffusion and epidemic spreading has been an active topic of research in recent years. Studies have shown that group interactions are an important consideration in contagion processes, and that thus higher-order interactions should be introduced into epidemic modeling. Research has also shown that individual responses to an unfolding epidemic are often strongly heterogeneous. We therefore present a two-layer network model, where the diffusion of awareness unfolds over 2-simplicial complexes in one layer, and the actual epidemic spreading unfolds over pairwise physical contacts in the other layer. The model takes into account individual differences in the degree of acceptance of information and self-protection measures once the epidemic is perceived. We use the micro Markov chain approach to determine the epidemic threshold of the model, which agrees well with the results obtained by Monte Carlo simulations. We show that the synergistic reinforcement due to 2-simplicial complexes in the virtual layer can restrain epidemic spreading by facilitating awareness diffusion, and moreover, that individual heterogeneity in the physical layer can increase the epidemic threshold and decrease the size of epidemic transmission. However, heterogeneity in the perception can also have the opposite effect because it inhibits the diffusion of awareness. Our results reveal the intricate interplay between awareness diffusion and epidemic spreading, and we hope they can help determine effective control measures.

Co-evolution of regional integration and green innovation under two-layer network

With global low-carbon development, green innovation has becoming a key factor for countries to obtain and maintain core competitive advantages. However, the division of scientific research resources often fails to meet the requirements of economic development. Therefore, regional integration cooperation has become an inevitable choice for innovation and development. However, the effect of the impact, direction, and interaction of regional integration policies on green innovation decision-making remains uncertain. To study the synergistic development mechanism between the two, this study constructs a two-layer network model that includes the decision and influence layers and uses a graph neural network model to map the relationship between the two-layer networks. With the help of opinion dynamics model and public goods game model, we draw the following conclusions. (1) Limited communication between regions can encourage all parties to adopt active green innovation strategies. However, excessive communication can lead to disunity of opinions among all parties, which may not be conducive to green innovation and result in an increase in free-rider behavior. (2) Regional integration development can effectively prompt all parties to choose active green innovation strategies. (3) Increasing the breadth of regional integration cooperation is more effective in promoting the active participation of all parties in green innovation, compared to increasing the depth of regional integration cooperation. This study provides theoretical support for decision-making in regional integration and green innovation development.

The impact of nodes of information dissemination on epidemic spreading in dynamic multiplex networks.

Epidemic spreading processes on dynamic multiplex networks provide a more accurate description of natural spreading processes than those on single layered networks. To describe the influence of different individuals in the awareness layer on epidemic spreading, we propose a two-layer network-based epidemic spreading model, including some individuals who neglect the epidemic, and we explore how individuals with different properties in the awareness layer will affect the spread of epidemics. The two-layer network model is divided into an information transmission layer and a disease spreading layer. Each node in the layer represents an individual with different connections in different layers. Individuals with awareness will be infected with a lower probability compared to unaware individuals, which corresponds to the various epidemic prevention measures in real life. We adopt the micro-Markov chain approach to analytically derive the threshold for the proposed epidemic model, which demonstrates that the awareness layer affects the threshold of disease spreading. We then explore how individuals with different properties would affect the disease spreading process through extensive Monte Carlo numerical simulations. We find that individuals with high centrality in the awareness layer would significantly inhibit the transmission of infectious diseases. Additionally, we propose conjectures and explanations for the approximately linear effect of individuals with low centrality in the awareness layer on the number of infected individuals.

New insights into binocular rivalry from the reconstruction of evolving percepts using model network dynamics.

When the two eyes are presented with highly distinct stimuli, the resulting visual percept generally switches every few seconds between the two monocular images in an irregular fashion, giving rise to a phenomenon known as binocular rivalry. While a host of theoretical studies have explored potential mechanisms for binocular rivalry in the context of evoked model dynamics in response to simple stimuli, here we investigate binocular rivalry directly through complex stimulus reconstructions based on the activity of a two-layer neuronal network model with competing downstream pools driven by disparate monocular stimuli composed of image pixels. To estimate the dynamic percept, we derive a linear input-output mapping rooted in the non-linear network dynamics and iteratively apply compressive sensing techniques for signal recovery. Utilizing a dominance metric, we are able to identify when percept alternations occur and use data collected during each dominance period to generate a sequence of percept reconstructions. We show that despite the approximate nature of the input-output mapping and the significant reduction in neurons downstream relative to stimulus pixels, the dominant monocular image is well-encoded in the network dynamics and improvements are garnered when realistic spatial receptive field structure is incorporated into the feedforward connectivity. Our model demonstrates gamma-distributed dominance durations and well obeys Levelt's four laws for how dominance durations change with stimulus strength, agreeing with key recurring experimental observations often used to benchmark rivalry models. In light of evidence that individuals with autism exhibit relatively slow percept switching in binocular rivalry, we corroborate the ubiquitous hypothesis that autism manifests from reduced inhibition in the brain by systematically probing our model alternation rate across choices of inhibition strength. We exhibit sufficient conditions for producing binocular rivalry in the context of natural scene stimuli, opening a clearer window into the dynamic brain computations that vary with the generated percept and a potential path toward further understanding neurological disorders.

Analysis of Failure Propagation in Cyber-Physical Power Systems Based on an Epidemic Model

From the perspective of propagation dynamics in complex networks, failure propagation in cyber-physical power systems is analogous to the spread of diseases; subsequently, the cyber nodes and power nodes are regarded as individuals in each of their groups. In this study, a two-layer interdependent network model of the cyber-physical power system is proposed, where each subnetwork adopts the Susceptible-Infected-Susceptible (SIS) epidemic-spreading model. On this basis, we construct a failure cooperation propagation model of cyber-physical power systems. Furthermore, we introduce the node protection mechanism to ensure the normal operation of key nodes. The generated scale-free cyber network and IEEE118-bus power system are used for simulation to analyze the influence of the coupling effect between them on the final failure scale.

Analysis of Influence of Behavioral Adoption Threshold Diversity on Multi-Layer Network.

The same people exhibit various adoption behaviors for the same information on various networks. Previous studies, however, did not examine the variety of adoption behaviors on multi-layer networks or take into consideration this phenomenon. Therefore, we refer to this phenomenon, which lacks systematic analysis and investigation, as behavioral adoption diversity on multi-layered networks. Meanwhile, individual adoption behaviors have LTI (local trend imitation) characteristics that help spread information. In order to study the diverse LTI behaviors on information propagation, a two-layer network model is presented. Following that, we provide two adoption threshold functions to describe diverse LTI behaviors. The crossover phenomena in the phase transition is shown to exist through theoretical derivation and experimental simulation. Specifically, the final spreading scale displays a second-order continuous phase transition when individuals exhibit active LTI behaviors, and, when individuals behave negatively, a first-order discontinuous phase transition can be noticed in the final spreading scale. Additionally, the propagation phenomena might be impacted by the degree distribution heterogeneity. Finally, there is a good agreement between the outcomes of our theoretical analysis and simulation.