Two-layer Network Model Research Articles

Enhancing traffic capacity of two-layer networks by link deletion

Two-layer or multilayer networks can more accurately reveal the transmission dynamics of the actual network and increase the traffic capacity. Therefore, we considered optimising the physical layer topology of the two-layer network, and proposed a link deletion strategy at the physical layer. The nodes with maximum weight ( $$k_i$$ * $$k_j$$ ) were deleted, where $$k_i$$ and $$k_j$$ are the degrees of nodes i and j, respectively, and the traffic load was redistributed from the central node to the non-central nodes. The simulation results showed that the strategy significantly increased the network traffic capacity. In two-layer network model, the logical layer network structure is unchanged and the shortest path routing strategy is used.

The Spread of Information in Virtual Communities

With the growth of online commerce, companies have created virtual communities (VCs) where users can create posts and reply to posts about the company’s products. VCs can be represented as networks, with users as nodes and relationships between users as edges. Information propagates through edges. In VC studies, it is important to know how the number of topics concerning the product grows over time and what network features make a user more influential than others in the information-spreading process. The existing literature has not provided a quantitative method with which to determine key points during the topic emergence process. Also, few researchers have considered the link between multilayer physical features and the nodes’ spreading influence. In this paper, we present two new ideas to enrich network theory as applied to VCs: a novel application of an adjusted coefficient of determination to topic growth and an adjustment to the Jaccard coefficient to measure the connection between two users. A two-layer network model was first used to study the spread of topics through a VC. A random forest method was then applied to rank various factors that might determine an individual user’s importance in topic spreading through a VC. Our research provides insightful ways for enterprises to mine information from VCs.

Double-Layer Network Model of Bank-Enterprise Counterparty Credit Risk Contagion

Banks and enterprises constitute a multilayered, multiattribute, multicriteria credit-related super network due to financial transaction behaviors, such as credit, wealth management, savings, and derivatives. Such a network has become an important channel for credit risk cross-contagion. This study constructs a two-layer network model of credit risk contagion between the bank and corporate counterparties from the perspective that banks do not withdraw loans from enterprises by considering the influence of corporate credit defaults on their counterparties under the credit linkage. This study analyzes the mechanism of influencing the evolution of bank-enterprise counterparty credit risk contagion in the two-tier network through theoretical analysis, including the following: the enterprises’ coping ability, risk preference, influence, level of interenterprise credit risk contagion and its network heterogeneity in the interenterprise credit association network, the risk prevention and control ability, business correlation degree, interbank credit risk contagion and its network heterogeneity in the interbank credit association network, the level of credit risk contagion between bank-enterprise counterparty credit association networks, and other factors in the case that banks do not withdraw loans from enterprises. In addition, this study performs a calculation experiment to analyze the characteristics of the evolution of counterparty credit risk contagion of bank and corporate counterparties under the double-layer network. The following four major conclusions can be drawn from the results. First, in the interenterprise credit-related network, the threshold of credit risk contagion rate is positively correlated with the marginal increase in risk perception and risk leveling ability of the enterprise. By contrast, such threshold is negatively correlated with the marginal decrease in the initial economic impact, leverage level, and influence of the enterprise. Moreover, the scale of corporate counterparty credit risk contagion is negatively correlated with the enterprise’s risk perception level and risk spillover ability but positively correlated with the enterprise’s initial economic shock level, the enterprise’s leverage level, and influence. Second, in the interbank credit association network, the threshold of the rate of credit risk contagion is negatively correlated with the marginal decrease in the degree of interbank business association but positively correlated with the marginal increase in the bank’s risk resistance ability and risk information processing ability. Furthermore, the scale of credit risk contagion of bank counterparties is positively correlated with the degree of interbank business association but negatively correlated with the bank’s ability to resist risks and process risk information. Third, if the heterogeneity of the credit-related network of bank-enterprise counterparties is high, then the rate threshold of credit risk contagion is high and the scale of credit risk diffusion is low. Moreover, the scale of credit risk contagion of bank counterparties is positively correlated with the marginal decrease in the degree of corporate and bank counterparties. Finally, the scale of bank counterparty credit risk contagion is a monotonically increasing convex function of the credit risk contagion rate in the enterprise credit association network and among the bank-enterprise networks.

Memory-based prisoner's dilemma game with history optimal strategy learning promotes cooperation on interdependent networks

Cooperation is regarded as the architect of the evolution process. The research on the influence of memory mechanism on human cooperative behavior has been a hot issue in recent years. However, most previous researchers usually concentrated their efforts on the single-layer networks and the impact of memory length on cooperative behavior, but paid less attention to the interdependent networks and other factors affecting the decision-making. In this paper, we presented a two-layer interdependent Holme-Kim network model with scale-free, high clustering and interconnection characteristics and a history optimal strategy learning mechanism fully considering the historical strategy, payoffs information and memory length, and combined them to discuss the emergence and maintenance of cooperation behavior. Through modeling simulation, we studied the parameter r for network construction, memory length M and defection to temptation T. Game participants, equipped with the same memory length, played Prisoner's dilemma games with their neighbors located on home or adjacent layer (if any), and selected their following strategies for the next game round through the history optimal strategy learning mechanism. The results show that density of cooperation is inversely related to parameter r and positively related to memory length M. The newly proposed network model can improve network reciprocity and the history optimal strategy learning mechanism can find out the strategy that can bring the maximum revenue in a certain period of time. The smaller r is, the larger M is, the more conductive to cooperation.

Scholar’s career switch adhesive with research topics: An evidence from China

Despite persistent efforts in untangling the mechanism of scientists switching between research topics, little is investigated for the relationship of scholars’ career stage switch leading to dynamics of research topics. In this paper, aiming to reveal career stage and its influence on research topics, we construct a two-layer network model, coauthors collaboration network (α-layer) for scholars research career stages and papers similarity network (β-layer) for research topic types, and analyze the relationship between the career stage switch and the topic type change. Applying the data set SMSEC from China to the model, the different statistics of the two layers show different forming mechanisms, the preference attachment and the rule of similarity inherited in the two layers, respectively. The coupling mechanism of the two layers is displayed by correlation of career stages and topic types, and presented by a framework with contributions of new added papers and associated scholars. The results show that the longer of research career is, the bigger contribution on the type of divided topics is; a scholar with large topic scopes would more likely insist in his/her research.

Impact of inter-layer hopping on epidemic spreading in a multilayer network

Hopping of individuals among distinct layers can induce inter-layer coupling and consequently affect the spreading process in each layer of real world multilayer networks. We articulate a two-layer network model where a fraction of nodes are inter-layer travelers that can hop between layers. We develop a theoretical framework based on the quenched mean-field approximation to accurately predict the epidemic thresholds and final states in both layers. Extensive numerical simulations on synthetic and empirical networks demonstrate that, in the general setting where the structures of the two network layers are asymmetric, intense hopping can lead to simultaneous epidemic outbreak in both layers. In general, the impacts of hopping on the spreading dynamics in the two layers can be quite distinct. As the inter-layer coupling strength is increased, the epidemic threshold of the denser layer increases monotonically, while for the sparser layer, a surprising non-monotonic behavior of the threshold with a minimize value arises. Another finding is that, as a result of hopping, recurrent outbreaks can occur in the sparser layer, providing a plausible explanation for the phenomenon of multiple outbreaks observed from real health data.

A Ladder Transmission Line Model for the Extraction of Ultralow Specific Contact Resistivity—Part I: Theoretical Design and Simulation Study

A ladder transmission line model (LTLM) that features capability to eliminate parasitic metal resistance from contact metal and access electrodes, a simple fabrication process, and a sub- $10^{-{10}}\,\, \Omega \cdot $ cm2 resolution is demonstrated for accurate extraction of the specific contact resistivity $\rho _{c}$ . The proposed LTLM is verified by technology computer-aided design (TCAD) simulation and a two-layer distributed-resistor network model. After eliminating the parasitic metal resistance, the current spreading and crowding effects are the main factors that contribute to the extraction error in LTLM. The effects of current spreading and crowding on the extraction of $\rho _{c}$ in LTLM are further quantitatively analyzed and design guidelines to achieve a sub- $10^{-{10}}\,\, \Omega \cdot $ cm2 resolution of $\rho _{c}$ extraction are provided. The details of theoretical modeling and simulation of LTLM are documented in Part I. The experimental demonstration of extracting sub- $10^{-{9}}\,\, \Omega \cdot $ cm $^{{2}} \rho _{c}$ using the proposed LTLM is provided in Part II.

A two-layer social network model for manufacturing service composition based on synergy: A case study on an aircraft structural part

Abstract Cloud manufacturing is an emerging manufacturing paradigm, with the issue of service composition being one of its most significant challenges. The current researches take the view that all manufacturing services are of equal importance. However, in fact, manufacturing services that owns scarce resources are more important than ordinary one, especially in the production of complex products. Hence, it is significant to meet the requirements of manufacturing services that own scarce resources first. Meanwhile, due to the increasing complexity of products, a high degree of synergy is required in service composition. Our study explores a new framework of social relationships from the perspective of synergy. A two-layer social network model is first proposed for resource allocation that takes synergy and priority into account. The upper layer of this model is occupied by the manufacturing services with scare resources. The lower layer is occupied by ordinary manufacturing services. All services are connected by social relationships. For the master-slave characteristic of the model, the two-layer network is embedded into bi-level programming. Then, an improved genetic algorithm is designed to solve the problem. Finally, the effectiveness of the model and algorithm are verified using a structural part of the Modern Ark 60 as an example.

Adding a bias to vector models of association memory provides item memory for free

Anderson (1970) introduced two models that are at the core of artificial neural network models as well as cognitive mathematical models of memory. The first, a simple summation of items, represented as vectors, can support rudimentary item-recognition. The second, a heteroassociative model consisting of a summation of outer products between paired item vectors, can support cued recall of associations. Anderson recommended fixing the element-value mean to zero, for tractability, and with minimal loss of generality. However, in a neural network model, if element values are represented by firing rates, this mean-centering is violated, because firing rates cannot be negative. We show, analytically, that adding a bias to item representations produces interference from other studied list items. Although this worsens cued recall, it also tempts the model to make intrusion responses to other studied items, not unlike human participants. Moreover, an unexpected feature appears: when probed with a constant vector, containing no “information,” the model retrieves a weighted sum of studied items, formally equivalent to Anderson’s item-memory model. This speaks to Hockley and Cristi’s (1996) findings that associative study strategies led to high item-recognition, but not vice versa. We show that such a model can achieve high levels of performance (d′), when the bias is greater than zero but not too large relative to the standard deviation of element values. We demonstrate these effects in a two-layer spiking-neuron network model. Thus, when modelers have striven for realism and relaxed mean-centering, such models may not only still function at adequate levels, but acquire a spin-off functionality that can actually be used, without the need for additional encoding terms specific to item-memory.

Vaccination behavior by coupling the epidemic spreading with the human decision under the game theory

When confronting the epidemics or pandemics, there often exists an interplay between epidemic incidence and the vaccination strategies of individuals. Recently, the characteristics of human behaviors, such as imitating nature or bandwagon effect, have been proven critical to the final herd immunity. In this paper, by establishing a two-layered multiplex network model which combines SIR epidemic process, vaccination decision-making and imitating human nature, we discover that imitating behavior would restrain the increase of herd immunity, which is verified by Monte Carlo simulations and mean-field equations, respectively. Interestingly, a suitable quantity of conformity motivated individual, counter-intuitively, could be beneficial to save the social costs. At the same time, we analytically determine the precise conditions for the minimum total social costs. The current results can help to understand the behavior of social group in depth and then explore public attitudes concerning the vaccine, which usually has a tremendous impact on social vaccine take-up within the population.

Asymmetric interdependent networks with multiple-dependence relation.

In this paper, we study the robustness of interdependent networks with multiple-dependence (MD) relation which is defined that a node is interdependent on several nodes on another layer, and this node will fail if any of these dependent nodes are failed. We propose a two-layered asymmetric interdependent network (AIN) model to address this problem, where the asymmetric feature is that nodes in one layer may be dependent on more than one node in the other layer with MD relation, while nodes in the other layer are dependent on exactly one node in this layer. We show that in this model the layer where nodes are allowed to have MD relation exhibits different types of phase transitions (discontinuous and hybrid), while the other layer only presents discontinuous phase transition. A heuristic theory based on message-passing approach is developed to understand the structural feature of interdependent networks and an intuitive picture for the emergence of a tricritical point is provided. Moreover, we study the correlation between the intralayer degree and interlayer degree of the nodes and find that this correlation has prominent impact to the continuous phase transition but has feeble effect on the discontinuous phase transition. Furthermore, we extend the two-layered AIN model to general multilayered AIN, and the percolation behaviors and properties of relevant phase transitions are elaborated.

A Two-Layer Network Model Reveals the Adhesion Scientist Career Stage and Research Topic in China

Despite persistent efforts in untangling the mechanism of scientists switching between research topics, little is investigated the relationship of the career stage switch and the dynamic of research topics. Here, a two-layer network model, the coauthor collaboration network(α-layer) and the paper similarity network(β-layer) with the coupled information between them, is presented, and the relationship between the scientist career stage switch and research topics is analyzed. Utilizing the data of published papers and authors with at least one at Society of Management Science and Engineering of China, it is found that the career stages in α-layer display vivid stage switching behaviors respect to the publications, and β-layer has a clear community structure where each community represents a research topic. Computing the frequency of the state switch in α-layer, it is also found that scholars with a few topics in their early career have great probability to give up the research work, yet scholars with broad scopes would stay in research fields. The analysis result reveals that the coupling mechanism of the two layers is simulated by a linear correlation of the number of evolving topics with the changing career stages. The career stage switch is closely related with his/her collaborators in China, which the novice collaborating with the reputation scholar would help them find popular topics and projects, while the experienced scholars working with the novices would help to explore new knowledge frontiers.

Data traffic capability of double-layer network based on coupling strength

The two-layer network model offers us a new viewpoint to observe the traffic dynamics of multilayer network systems. An efficient coupling mechanism is of great importance for alleviating the traffic congestion on two-layer networks. In order to reduce the network congestion and improve network transmission performance, the coupling mechanism between two layers of network and three coupling methods, which are random coupling, disassortative coupling and assortative coupling, are studied based on degree correlation. The packet transmission process is analyzed with both the shortest path routing strategy and degree-based weight routing strategy. The influences of the coupling mode and its corresponding routing strategy on the traffic capacity of the two-layer network are studied. In this paper, two scale-free networks are used to construct the two-layer network for simulation experiments. The network scale is in a range from 200 to 2400 with the value of average degree being 8. We focus on the traffic dynamics of two-layer network, and analyze the relationship between the traffic capacity and the three coupling modes, which are random coupling, disassortative coupling and assortative coupling, under the constraints of the shortest path routing strategy and the weight-based routing strategy. According to the characteristics of the coupling connection between the two layers of network, the best coupling method which is suitable for a certain routing strategy should be investigated. The suitable coupling connection between the two layers can effectively increase the traffic capacity. Both numerical result and analytical result show that the packet generation rate, average transmission time, and average throughput can be obviously improved under the shortest path routing strategy with the disassortative coupling method. When the degree-based static weight routing strategy is used, the traffic performance parameters such as packet generation rate, average transmission time, and average throughput can reach the optimal values with the assortative coupling method. It makes the traffic flow uniform that the routing strategy is chosen with the most suitable coupling method on the two-layer network, and the network traffic capacity may be effectively enhanced. More generally, the results indicate that the coupling modes can give rise to traffic behavior that relies subtly on the routing strategy on the two-layer network. Our work may shed some light on the design and optimization of some real traffic or communication networks.

Dynamic evaluation of the influence of drafting units in China’s air quality standards network

Abstract The setting of air quality standards is highly significant in controlling widespread pollutants and mitigating environmental risks. The selection of influential drafting units is a major step for the improvement of the systematicness, harmony, and compatibility of standard systems, which further leads to high air quality. To this end, this paper presents a novel social network-based methodology to assess the influence of drafting units based on a dynamic two-layer standard network model with the publicized data of the national air quality standards of China. Firstly, network theory metrics are aggregated with the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to evaluate their importance dynamically; Secondly, three measurements of participation degree, cooperation degree, and contribution degree are deliberately designed to assess the influence of drafting units. The results show that most of the key standards vary over time driven by policy reform, while the volatility of critical drafting units is relatively stable. It is also interesting to find that most of the influential drafting units are research institutes rather than enterprises. In view of the results, we assert that government agencies should strategically support influential drafting units and encourage them to make great efforts in drafting important standards.

Tree networks to assess financial contagion

We propose a two-layered tree network model that decomposes financial contagion into a global component, composed of inter-country contagion effects, and a local component, made up of inter-institutional contagion channels. The model is effectively applied to a database containing time series of daily CDS spreads of major European financial institutions (banks and insurance companies), and reveals the importance of monitoring both channels to assess financial contagion. Our empirical application reveals evidence of a high inter-country and inter-institutional vulnerability at the onset of the global financial crisis in 2008 and during the sovereign crisis in 2011. The results identify France as central to the inter-country contagion in the Euro area during the financial crisis, while Italy dominates during the sovereign crisis. The application of the model to detect contagion between sectors of the European economy reveals similar findings, and identifies the manufacturing sector as the most central, while, at the company level, financial institutions dominate during the 2008 crisis.

A two-layered brain network model and its chimera state

Based on the data of cerebral cortex, we present a two-layered brain network model of coupled neurons where the two layers represent the left and right hemispheres of cerebral cortex, respectively, and the links between the two layers represent the inter-couplings through the corpus callosum. By this model we show that abundant patterns of synchronization can be observed, especially the chimera state, depending on the parameters of system such as the coupling strengths and coupling phase. Further, we extend the model to a more general two-layered network to better understand the mechanism of the observed patterns, where each hemisphere of cerebral cortex is replaced by a highly clustered subnetwork. We find that the number of inter-couplings is another key parameter for the emergence of chimera states. Thus, the chimera states come from a matching between the structure parameters such as the number of inter-couplings and clustering coefficient etc and the dynamics parameters such as the intra-, inter-coupling strengths and coupling phase etc. A brief theoretical analysis is provided to explain the borderline of synchronization. These findings may provide helpful clues to understand the mechanism of brain functions.

Detecting the significant nodes in two-layer flow networks: an interlayer non-failure cascading effect perspective

Detecting the significant nodes in multilayer networks is crucial for preventing the large-scale spread of disaster events. However, the existing model can hardly simulate the ubiquitous non-failure cascading effect process in social and economic systems. To solve this problem, first, we propose a mathematical method of constructing a two-layer network model. Then we define the non-failure cascading effect process in the two-layer network. Based on the model and spreading process, we propose a non-failure cascading effect index by using each node’s non-failure cascading affecting in uential degree on the two-layer network. We then applied the detecting model in theoretical two-layer networks. We find there exist significant nodes, and also exist several in uential factors of the interlayer cascading effect process. The detecting model is applied in the two-layer industrial input-output networks between the U.S. and China for testing the validity of the theoretical model. The hybrid network combination is relatively more sensitive to in uential factors; the significant nodes are more prominent in scale-free networks. Our research provides a solution for finding the significant nodes in two-layer social or economic networks based on the non-failure cascading effect process.

Autonomous Navigation Control of UAV Using Wireless Smart Meter Devices

In preparation for the upcoming home delivery services that rely on Unmanned Aerial Vehicles (UAVs), we developed a new multi-hop radio network that is laid over a smart meter network transferring electric energy information only. In this network, a UAV follows, for navigation purposes, the topology of a virtual network overlaid on the physical smart meter network. We established a service management control method which does not rely on image analysis or map information processing, i.e. processes that consume precious power resources of the UAV. Instead, navigation is based on the routing technology. The current distance between the UAV and a node of the smart meter network is measured by means of the radio transmission loss value, therefore determining the position of the UAV. A two-layer network model has been proposed. One layer consists of a network of nodes in a residential area with scattered buildings – a location that is safer to navigate – while the other is an access network of nodes in a densely populated area. Then, we proposed methods to determine the direction of movement towards the next hop node on the data-link layer and the end node on the network layer, which is the target destination. We implemented a software-based test system and verified the effectiveness of the proposed methods.

Explosive transitions induced by interdependent contagion-consensus dynamics in multiplex networks.

We introduce a model to study the interplay between information spreading and opinion formation in social systems. Our framework consists in a two-layer multiplex network where opinion dynamics takes place in one layer, while information spreads on the other one. The two dynamical processes are mutually coupled in such a way that the control parameters governing the dynamics of the node states at one layer depend on the dynamical states at the other layer. In particular, we consider the case in which consensus is favored by the common adoption of information, while information spreading is boosted between agents sharing similar opinions. Numerical simulations of the model point out that, when the coupling between the dynamics of the two layers is strong enough, a double explosive transition, i.e., a discontinuous transition both in consensus dynamics and in information spreading appears. Such explosive transitions lead to bi-stability regions in which the consensus-informed states and the disagreement-uninformed states are both stable solutions of the intertwined dynamics.

Investigation of epidemic spreading process on multiplex networks by incorporating fatal properties

Numerous efforts have been devoted to investigating the network activities and dynamics of isolated networks. Nevertheless, in practice, most complex networks might be interconnected with each other (due to the existence of common components) and exhibit layered properties while the connections on different layers represent various relationships. These types of networks are characterized as multiplex networks. A two-layered multiplex network model (usually composed of a virtual layer sustaining unaware-aware-unaware (UAU) dynamics and a physical one supporting susceptible-infected-recovered-dead (SIRD) process) is presented to investigate the spreading property of fatal epidemics in this manuscript. Due to the incorporation of the virtual layer, the recovered and dead individuals seem to play different roles in affecting the epidemic spreading process. In details, the corresponding nodes on the virtual layer for the recovered individuals are capable of transmitting information to other individuals, while the corresponding nodes for the dead individuals (which are to be eliminated) on the virtual layer should be removed as well. With the coupled UAU-SIRD model, the relationships between the focused variables and parameters of the epidemic are studied thoroughly. As indicated by the results, the range of affected individuals will be reduced by a large amount with the incorporation of virtual layers. Furthermore, the effects of recovery time on the epidemic spreading process are also investigated aiming to consider various physical conditions. Theoretical analyses are also derived for scenarios with and without required time periods for recovery which validates the reducing effects of incorporating virtual layers on the epidemic spreading process.