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In recent years, link prediction in multiplex networks has attracted increasing interest of researchers. Multiplex social networks that model different types of social relationships between the same set of entities in separate layers are a special case of multiplex networks. However, most existing methods usually ignore that new links can also be formed through information transmission. Therefore, we propose a novel link prediction method that applies information transmission approach to multiplex social networks in this paper. To begin with, we define a new index and three new ways of information transmission in a multiplex network. In this regard, the similarities of potential links in the target layer are computed based on the total amount of information they transmit each other via fusing information from all layers. At last, the interlayer relevance method is used to weight all layers. To evaluate the prediction performance of the proposed method, extensive experiments are implemented on eight real-world multiplex networks, and the experimental results demonstrate that the proposed method significantly outperforms several competing state-of-the-art methods in most cases. • An information transmission-based multiplex link prediction method is proposed. • A new index and three new ways of information transmission are defined. • Similarities of node pairs are computed using information transmitted. • Experiments show the proposed method achieves superior performance. [ABSTRACT FROM AUTHOR]

The digital age has seen an exponential increase in the creation and dissemination of information, while the post-truth era has amplified the role of emotion in the spread of news. To prevent the outbreak of negative public sentiment due to uncontrolled emotional responses, it is critical to investigate the interplay between these two factors during the propagation. Therefore, we develop an emotion-information multiplex network based on the topic discussion function of social media. According to the influence of emotion on information transmission, emotion is divided into positive, negative and uninterested which are introduced into the standard SIR model. The microscopic Markov chain approach (MMCA) is used to analyze the outbreak threshold proving that emotion affects the threshold of information propagation. The extensive Monte Carlo (MC) simulations show that the average degree of information layer affects the emotional atmosphere. Secondly, the rapid dissemination of information will widen the emotional differences between people. Finally, positive or uninterested can easily become the dominant emotion of the group, and the group effect is more easily reflected in the user's supportive attitude rather than the opposition attitude. • We build an emotion-information coupled network. • We propose a mechanism for the influence of the emotional atmosphere. • When the system is in steady state, the users with positive emotions or uninterested account for the highest proportion. • The denser network and the increase of spreading probability will both intensify emotion difference among users. • The emotional dominance of the system is an important index to influence information diffusion. [ABSTRACT FROM AUTHOR]

The diffusion of individual awareness has a significant impact on the dynamic spread of epidemics. In previous studies, the individual's state of awareness is mainly divided into two states: awareness and unawareness. However, in the real world, the factors that change the awareness state of individuals with different health states are often different, and there are differences when they are aware of the epidemic. In order to study the influence of the strength of awareness on epidemic transmission, this article proposes a two-layer network epidemic transmission model based on the individual health state. The upper-layer network constructs an APA (Asthenic awareness - Powerful awareness - Asthenic awareness) propagation model, which is used to represent the diffusion process of information about epidemic awareness. Meanwhile, the epidemic pain level is introduced to describe the awareness changes in infected persons. The lower-layer network adopts the SIS (Susceptible–Infected–Susceptible) virus model to describe the epidemic transmission process influenced by awareness information. Then we validate the efficiency of the proposed two-layer network propagation model through Monte Carlo numerical simulation. The epidemic threshold is determined using the microscopic Markov chain approach (MMCA), while analyzing key factors such as the epidemic pain level, the attenuation factor and network topology. The results demonstrate that individuals with powerful awareness exhibit a more pronounced inhibitory effect on the spread of the epidemic. Furthermore, individuals who are more sensitive to the pain of the epidemic are better at sustaining powerful awareness, thereby facilitating more effective containment of the epidemic. The systematic findings of this study provide valuable insights for exploring the interplay between individual awareness and epidemic transmission in real-world scenarios. • Proposing an APA-SIS model that considers health state in awareness propagation. • MMCA is utilized to gain detailed insights into the dynamics of the epidemic. • The results show that powerful awareness can effectively delay outbreaks and limit the scale of an epidemic. • Reducing the pain level of the epidemic can effectively promote powerful awareness diffusion. [ABSTRACT FROM AUTHOR]

• Network setup effectively structures huge amounts of heterogeneous financial data. • Multilayer financial networks encode the effect of time correlation between assets. • We propose new clustering coefficients for the multilayer context. • Tensor-based approach to clustering coefficients unifies their formal expressions. • The proposed indicators catch critical features of temporal financial networks. Big data and the use of advanced technologies are relevant topics in the financial market. In this context, complex networks became extremely useful in describing the structure of complex financial systems. In particular, the time evolution property of the stock markets have been described by temporal networks. However, these approaches fail to consider the interactions over time between assets. To overcome this drawback, financial markets can be described by multiplex networks where the different relations between nodes can be conveniently expressed structuring the network through different layers. To catch this kind of interconnections we provide new local clustering coefficients for multiplex networks, looking at the network from different perspectives depending on the node position, as well as a global clustering coefficient for the whole network. We also prove that all the well-known expressions for clustering coefficients existing in the literature, suitably extended to the multiplex framework, may be unified into our proposal. By means of an application to the multiplex temporal financial network, based on the returns of the S&P100 assets, we show that the proposed measures prove to be effective in describing dependencies between assets over time. [ABSTRACT FROM AUTHOR]

Diffusion dynamics in multiplex networks can model a diverse number of real-world processes. In some specific configurations of these systems, the super-diffusion phenomenon arises, in which the diffusion is faster in the multiplex network than in any of its layers. Many studies attempt to characterize this phenomenon by examining its dependency on structural properties of the network, such as overlap, average degree, network dissimilarity, and others. While certain properties show a correlation with super-diffusion in specific networks, a broader characterization is still missing. Here, we introduce a structural parameter based on the minimum node strength that effectively predicts the occurrence of super-diffusion in multiplex networks. Additionally, we propose a novel framework for deriving analytical bounds for several multiplex networks structures. Finally, we analyze and justify why certain arrangements of the inter-layer connections induce super-diffusion. These findings provide novel insights into the super-diffusion phenomenon and the interplay between network structure and dynamics. • Structural parameter to predict super-diffusion in multiplex networks. • Super-diffusion analytical bounds for multiplex networks. • Inducing super-diffusion by selecting inter-layer connections based on node strength. • Strength distribution plays a pivotal role in the diffusion dynamics of networks. [ABSTRACT FROM AUTHOR]

Every outbreak of a serious infectious disease has the potential to pose unprecedented challenges to humanity. Understanding how epidemic spreads among populations is a key step in preventing and controlling it to spread. In this paper, for modeling the epidemic spreading and its associated information spreading, we put forward a novel coupled two-layered networking framework. One layer deals with the modeling of an SI 1 I 2 R process, where each node in the network may be in four states: susceptible, mildly infected, severely infected and recovery. Whereas, for the other layer, the transmission dynamics can be represented by an unaware–aware–refractory (UAT) model, which is significantly different from the classical unaware–aware–unaware (UAU) process since there exist individuals who are unwilling to share information. Moreover, we set a group of discrete time Microscopic Markov equations and derive the epidemic threshold. Finally, some numerical simulations are carried out to validate the analytical results. This work is of great significance to prevent epidemic, and it can be applicable in guiding the input on disease-related information on complex networks. [ABSTRACT FROM AUTHOR]

Compared with single-layer networks, multiplex networks can describe real-world scenarios in more detail while suffering from requiring considerable computing and storage resources at the same time. Network feature learning, which aims to embed networks into a low dimensional space, is an effective method for solving these problems. Currently, research on multiplex network embedding faces two major challenges: how to make full use of the connected information in different layers and how to embed multiplex networks into a unified space. In this paper, a novel multiplex network embedding model is proposed to solve these two problems. It preserves all the first-, second- and multi-order proximities in multiplex networks by optimizing the corresponding objective functions. The network reconstruction step combines information of different types of relations in other layers while maintaining their distinctive properties. The proposed synchronous learning strategy provides a path to embed multiplex networks into a unified space. Extensive experiments on three real applications: visualization, link prediction and node classification are conducted to validate the effectiveness of the proposed method. The experimental results show that it achieves better or comparable performance compared with several state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The duration of the accumulation rate (physical image) is a key factor in analysis of counterintuitive phenomena involving relative timescales on multiplex networks. Typically, the relative timescales are represented by multiplying any layer by the same factor. However, researchers often overlook the changes in the relative timescales caused by local parameters, resulting in incomplete analysis of phenomena. This paper examines the survival time of stifler individuals in the information-epidemic model on multiplex networks. The relative timescales can be affected by the survival time (only one parameter), reversing the monotonically increasing phenomenon into a monotonically decreasing one, that is, a counterintuitive phenomenon under incomplete analysis. Additionally, the relative timescales can influence the epidemic threshold, which is different from the previous studies. Our work suggests that considering the physical image of relative timescales is crucial when analyzing multiplex networks, even when only one parameter is altered. • Relative timescales are essential for coevolutionary dynamics on multiplex networks. • Changing just one parameter can significantly change the relative timescales. • Epidemic threshold in information-epidemic model is affected by relative timescales. • Reducing the survival time of stifler individuals is a "double-edged sword". [ABSTRACT FROM AUTHOR]

In many natural and man-made networks, nodes communicate with each other through different types of interconnections giving rise to so-called multiplex networks. In this paper, we study the interplay between synchronous steady state solutions and the topology of multiplex networks of Chua’s circuits. In particular, we consider all circuits to be simultaneously interconnected through a network of resistors (static diffusive coupling) and a network of capacitors (dynamic diffusive coupling) each with its own structure. We find that the presence of dynamic links and the structure of the multiplex network affect the stability of the emerging synchronous solutions. Theoretical results are discussed and validated using a dedicated experimental set-up. [ABSTRACT FROM AUTHOR]

Abstract Rumor propagation and behavior spreading are usually closely coupled with each other and the interaction will have great influence on the spreading dynamics. In this paper, we propose a novel interacting model of rumor propagation and behavior spreading in multiplex networks. Specifically, coupled reinforcements are introduced in the derived mean-field equations to describe the interplay between these two dynamical processes. Then the basic reproduction number and the final sizes of rumor and behavior spreading are estimated. Monte Carlo simulations results show that the interacting model are much more consistent with the real data than the classical model. Besides, the attractiveness of rumor and behavior and couple reinforcements are crucial factors affecting the interactive spreading processes. Especially, influenced by the coupled reinforcements, any attractiveness increasing can enhance maximum influences and final spreading sizes of rumor and behavior simultaneously. What's more, the coupled reinforcements will extend the duration of rumor and behavior spreading. Moreover, the reinforcement of spreaders or infecteds to promote spreading is far stronger than that of stiflers and recovered to suppress spreading. Interestingly, we also find that the final size of rumor propagation is larger than that of behavior spreading, while the range of the final size variation resulting from the coupled reinforcements is opposite. This work may shed some lights on understanding the interaction between rumor and behavior and suggest a promising way to control rumors and irrational behaviors. [ABSTRACT FROM AUTHOR]

Higher-order networks are gaining significant scientific attention due to their ability to encode the many-body interactions present in complex systems. However, higher-order networks have the limitation that they only capture many-body interactions of the same type. To address this limitation, we present a mathematical framework that determines the topology of higher-order multiplex networks and illustrates the interplay between their topology and dynamics. Specifically, we examine the diffusion of topological signals associated not only to the nodes but also to the links and to the higher-dimensional simplices of multiplex simplicial complexes. We leverage on the ubiquitous presence of the overlap of the simplices to couple the dynamics among multiplex layers, introducing a definition of multiplex Hodge Laplacians and Dirac operators. We show that the spectral properties of these operators determine higher-order diffusion on higher-order multiplex networks and encode their multiplex Betti numbers. Our numerical investigation of the spectral properties of synthetic and real (connectome, microbiome) multiplex simplicial complexes indicates that the coupling between the layers can either speed up or slow down the higher-order diffusion of topological signals. This mathematical framework is very general and can be applied to study generic higher-order systems with interactions of multiple types. In particular, these results might find applications in brain networks which are understood to be both multilayer and higher-order. • We focus on higher-order multiplex networks that encode the many-body interactions of different types existing in real complex systems. • We formulate a mathematical framework to capture the topology of higher-order multiplex networks and predict their multiplex Betti numbers. • We define multiplex Hodge Laplacians and multiplex Dirac operator whose spectral properties dictate the diffusion dynamics of topological signals on higher-order multiplex networks. • We study the spectral properties of synthetic and real higher-order multiplex networks showing that their topology can control the diffusion dynamics of higher-order multiplex networks. [ABSTRACT FROM AUTHOR]

Multiplex networks formed by a set of nodes connected through different types of edges are widely used to model interactions between different systems. In many real-world scenarios, the properties of nodes in different layers are characterized by non-topological features such as age, flow, and geographical location. On this basis, the associations between different layers are caused by the coupling of features. Here, we propose a percolation framework to investigate the properties of such interlayer feature-correlated multiplex networks (FCN). Based on this framework, the robustness of the networks correlated through completely unequal discrete features, discrete features with repetition, and continuous features is analyzed. Theoretical and numerical results show that the interlayer degree–degree correlation (IDDC) of the network is controlled by both the correlation between degrees and features, and the correlation between the features of different layers. When there are repeating features, the network structure is randomized due to the decrease in the differentiation of nodes in the feature space. This randomization substantially reduces the IDDC of the network even if the above correlations are fixed. Our findings provide new insight into revealing the origins of the complexities of real-world multiplex networks. • We focus on multiplex networks whose layers are coupled by non-topological features. • A percolation framework for feature-correlated networks is proposed. • How three typical features affect network robustness are analyzed. [ABSTRACT FROM AUTHOR]

In practice, an epidemic might be spreading among multi-communities; while the communities are usually intra-connected. In this manuscript, each community is modeled as a multiplex network (i.e., virtual layer and physical one). The connections inside certain community are referred as inter-contacts while the intra-contacts denote the connections among communities. For the epidemic spreading process, the traditional susceptible-infected-recovered (SIR) model is adopted. Then, corresponding state transition trees are determined and simulations are conducted to study the epidemic spreading process in multi-communities. Here, the effect of incorporating virtual layer on the range of individual affected by the epidemic is pursued. As illustrated, multi-summits are incurred if the spreading in multi-communities is considered; furthermore, the disparity between summits varies. This is affected by various factors. As indicated, the incorporation of virtual layer is capable of reducing the proportion of individuals being affected; moreover, disparity of different summits is likely to be increased regarding with scenarios of excluding virtual layer. Furthermore, the summit is likely to be postponed if virtual layer is incorporated. [ABSTRACT FROM AUTHOR]

Detecting influential nodes in multiplex networks is a complex task due to the presence of multiple layers. In this study, we propose a method for identifying important layers with strong spreaders based on several key parameters. These include a layer's position within a well-connected neighborhood, the number of active edges and critical nodes, the ratio of active nodes to all possible connections, and the intersection of intra-layer communication compared to other layers. To accomplish this, we have formulated a layer weighting method which takes into account these parameters, and developed an algorithm for mapping and computing the rank of nodes based on their spreading capability within multiplex networks. The resulting layer weighting is then used to map and compress centrality vector values to a scalar value, allowing us to calculate node centrality in multiplex networks via a coupled set of equations. Moreover, our method combines the important layer parameters to compute the influence of nodes from different layers. Our experimental results, conducted on both synthetic and real-world networks, demonstrate that the proposed approach significantly outperforms existing methods in detecting high influential spreaders. These findings highlight the importance of using a suitable layer weighting measure for identifying potential spreaders in multiplex networks. • New criteria are defined for calculating layer's influence in identifying influential nodes. • For the first time, the important layer parameters are combined to utilize in layer weighting method. • A new local layer weighting method is formulated for multiplex networks. • Optimal layer measures and their effective combinations is proposed to identify spreaders. • Compressing centrality vector and mapping it to scalar value for layer weighting. [ABSTRACT FROM AUTHOR]

In recent years, public health emergencies have occurred frequently around the world, and infectious diseases are one of the most destructive and influential events. The coupling effect between infectious disease transmission and information dissemination has been a research hotspot that scholars have focused on in recent years. Analyzing how to effectively prevent the impact of information dissemination on the process of infectious disease transmission from the perspective of government prevention and control has important theoretical significance. Firstly, this paper investigates the COVID-19 epidemic and establishes a coupled multi-channel network UFAT-SEIR transmission model under government prevention and management based on the characteristics of infectious disease transmission and information transmission. Considering the individual's ability to recognize information, the interaction between false information and real information, and the impact of group polarization, the step function is used to explore the results of the user's information decision-making process. Secondly, the microscopic Markov chain approach (MMCA) is constructed to derive the transmission threshold of infectious diseases related to the information transmission layer. Finally, simulation is performed based on the impact of government prevention and management actions on parameters. The research findings can provide relevant strategies and suggestions for the government to prevent and control the spread of infectious diseases. [ABSTRACT FROM AUTHOR]

Real networks in our surrounding are usually complex and composite by nature and they consist of many interwoven layers. The commutation of agents (nodes) across layers in these composite multiplex networks heavily influences the underlying dynamical processes, such as information, idea and disease spreading, synchronization, consensus, etc. In order to understand how the agents’ dynamics and the compositeness of multiplex networks influence the spreading dynamics, we develop a susceptible-infected-susceptible-based model on the top of these networks, which is integrated with the transition of agents across layers. Moreover, we analytically obtain a critical infection rate for which an epidemic dies out in a multiplex network, and latter show that this rate can be higher compared with the isolated networks. Finally, using numerical simulations we confirm the epidemic threshold and we show some interesting insights into the epidemic onset and the spreading dynamics in several real and generic multiplex networks. [ABSTRACT FROM PUBLISHER]

In this paper, we study the interplay between the epidemic spreading and the diffusion of awareness in multiplex networks. In the model, an infectious disease can spread in one network representing the paths of epidemic spreading (contact network), leading to the diffusion of awareness in the other network (information network), and then the diffusion of awareness will cause individuals to take social distances, which in turn affects the epidemic spreading. As for the diffusion of awareness, we assume that, on the one hand, individuals can be informed by other aware neighbors in information network, on the other hand, the susceptible individuals can be self-awareness induced by the infected neighbors in the contact networks (local information) or mass media (global information). Through Markov chain approach and numerical computations, we find that the density of infected individuals and the epidemic threshold can be affected by the structures of the two networks and the effective transmission rate of the awareness. However, we prove that though the introduction of the self-awareness can lower the density of infection, which cannot increase the epidemic threshold no matter of the local information or global information. Our finding is remarkably different to many previous results on single-layer network: local information based behavioral response can alter the epidemic threshold. Furthermore, our results indicate that the nodes with more neighbors (hub nodes) in information networks are easier to be informed, as a result, their risk of infection in contact networks can be effectively reduced. [ABSTRACT FROM AUTHOR]

To get further insight into the mechanism behind driving the social behaviors for a compartmental flow model of corruption on multiplex networks, we apply the model to the duplex networks, where different flows among three states (H o n e s t , C o r r u p t , O s t r a c i s m) take place separately on a particular layer. In our work, we aim to unravel the impact of edge overlap and interlayer degree correlations on the evolution of corruption by considering different underlying contact networks. To assess the role of the edge overlap (m) on the diffusion of corruption, we produce various values of m by rewiring the edges of one of two synthetic networks. In addition, to explore the significance of interlayer degree correlations, we generate the duplex networks with specific degree correlated patterns giving rise to different values of m. The results show that the influence of the structural properties becomes gradually prominent as the corruption and delation rate decrease. The smaller m produced by rewiring the biased edges makes the extension of the stability region of full honesty state though not clearly noticeable. However, the larger m determined by the degree correlation patterns is prone to the presence of the stability region of the full H state. The findings reveal that edge overlap caused by rewiring links barely has an effect on the evolution regardless of duplex networks being uncorrelated or correlated. Nevertheless, the interlayer correlated coupling plays a major role in the stationary states of the corruption dynamics. [Display omitted] • Propose a compartmental flow model of corruption applied to multiplex networks. • Explore the impact of edge overlap and interlayer degree correlations on evolution. • Generate various degree-correlated patterns to investigate behaviors diffusion. • Edge overlap due to interlayer correlated coupling makes a difference in the dynamics. • Rewiring links barely affects dynamics whether networks are uncorrelated or correlated. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has resulted in a proliferation of conflicting opinions on physical distancing across various media platforms, which has had a significant impact on human behavior and the transmission dynamics of the disease. Inspired by this social phenomenon, we present a novel UAP-SIS model to study the interaction between conflicting opinions and epidemic spreading in multiplex networks, in which individual behavior is based on diverse opinions. We distinguish susceptibility and infectivity among individuals who are unaware, pro-physical distancing and anti-physical distancing, and we incorporate three kinds of mechanisms for generating individual awareness. The coupled dynamics are analyzed in terms of a microscopic Markov chain approach that encompasses the aforementioned elements. With this model, we derive the epidemic threshold which is related to the diffusion of competing opinions and their coupling configuration. Our findings demonstrate that the transmission of the disease is shaped in a significant manner by conflicting opinions, due to the complex interaction between such opinions and the disease itself. Furthermore, the implementation of awareness-generating mechanisms can help to mitigate the overall prevalence of the epidemic, and global awareness and self-awareness can be interchangeable in certain instances. To effectively curb the spread of epidemics, policymakers should take steps to regulate social media and promote physical distancing as the mainstream opinion. • We present an UAP-SIS model to study the interaction dynamics. • Awareness-generating mechanisms can mitigate the prevalence of the epidemic. • Conflicting opinions weaken people's protective behavior. • Conflicting opinions increase the disease's final size. • Global awareness and self-awareness can be interchangeable in certain instances. [ABSTRACT FROM AUTHOR]

An increasing number of studies have attempted to build a multiplex network (MN) model to generalize the traditional network theory and have proposed various centrality measures for MNs. In this paper, we proposed an improved centrality measure, the Adaptive PageRank Algorithm Modified by the Gravity Model (APAMGM), to identify critical nodes in MNs. We modified the idea that the transition probability of a node is only related to its outgoing connections (or degree in an undirected network) in the adapted PageRank algorithm. In APAMGM, the transition probability is positively correlated with the quality of nodes and inversely correlated with the interaction impedance between nodes. We conducted a case study using a multiplex urban transportation network in Shenzhen, China, which consists of a bus, metro, taxi, and shared bike network. The results show that APAGMG can identify critical nodes with good interpretability and it displays potential for application in networks where spatial interactions exist between nodes. The interdependencies in the network were explored and discussed with the characterization of nodes. This study might provide insights into applying complex network theory and centrality measures to some MNs, especially urban transportation networks. • An improved centrality measure for multiplex networks is proposed. • The modification allows the identification of nodes with active features or close proximity. • The method shows potential for node identification in multiplex networks where nodes have spatial interactions. • The method can identify the most critical areas in urban public transport systems. [ABSTRACT FROM AUTHOR]

Clustering and closure coefficients are among the most widely applied indicators in the description of the topological structure of a network. Many distinct definitions have been proposed over time, particularly in the case of weighted networks, where the choice of the weight attributed to the triangles is a crucial aspect. In the present work, in the framework of weighted directed multilayer networks, we extend the classical clustering and closure coefficients through the introduction of the clumping coefficient, which generalizes them to incomplete triangles of any type. We then organize the class of these coefficients in a systematic taxonomy in the more general context of weighted directed multilayer networks. Such cohesion coefficients have also been adapted to the different scales that characterize a multilayer network, in order to grasp their structure from different perspectives. We also show how the tensor formalism allows incorporating the new definitions, as well as all those existing in the literature, in a single unified writing, in such a way that a suitable choice of the involved adjacency tensors allows obtaining each of them. Finally, through some applications to simulated networks, we show the effectiveness of the proposed coefficients in capturing different peculiarities of the network structure on different scales. • We propose new general cohesion coefficients for multilayer networks. • New coefficients extend clustering and closure coefficients for monoplex networks. • Tensor-based approach to cohesion coefficients unifies their formal expressions. • We prove the effectiveness of the coefficients on class of synthetic networks. [ABSTRACT FROM AUTHOR]

We study numerically the spatiotemporal dynamics and anti-phase synchronization of complex structures in a two-layer multiplex network of bidirectionally and repulsively coupled two-dimensional lattices. Each layer consists of locally and attractively coupled identical van der Pol oscillators. Depending on randomly distributed initial conditions the isolated layers can exhibit either a spiral or a target wave regime. The latter is found for first time for the locally coupled van der Pol lattice considered in this work. We vary the inter-layer coupling strength for either fixed or changing intra-layer coupling strengths in the interacting layers. The numerical results are summarized in the two-dimensional diagrams plotted in the "intra-layer coupling strength – inter-layer coupling strength" parameter plane. Anti-phase synchronization is identified by evaluating the local and global cross-correlation coefficients which are equal to −1. We also explore the impact of random de-multiplexing on the robustness of the observed spatiotemporal structures and anti-phase synchronized regimes in the two-layer network. • Target waves have been found for the first time in a 2D network of locally coupled van der Pol oscillators. • Anti-phase synchronization of wave structures has been shown in a two repulsively coupled 2D lattices. • The robustness of anti-phase synchronization has been explored for sparse inter-layer coupling. [ABSTRACT FROM AUTHOR]

We analyzed the interaction processes between disease and disease-based information on multiplex networks. Unlike previous models, an epidemic can spread in parallel with the information diffusion during a time step. We used the probability theory to derive a novel individual-based transmission model, which is different from the reported methods, and developed a pairwise formulation of this model. Interestingly, when the infection rate is enough large, the infection curve firstly achieves a large peak, then rapidly decreases to a steady state. In addition, we considered the other two coexistence mechanisms of disease and information during a time step, and found that all mechanisms have the same condition of epidemic outbreak. The theoretical results strongly agree with discrete-time stochastic simulations, and may provide insights for a wide application range for multi-dynamic spreading processes. • The coexistence mechanism between information and disease processes is studied. • This paper assumes that two processes simultaneously evolve during a atime step. • We derive the microscopic Markov-chain approximation model and its pair formulation rigorously. • Compared to previous models, the present model has a simpler formulation and same outbreak condition of an epidemic. • Our models agree well with stochast simulations on heterogeneous multiplex networks. [ABSTRACT FROM AUTHOR]

Knowledge transmission research based on complex networks mainly focuses on the pattern of transmission with consideration of a single channel. However, both online and offline channels have been adopted for transmitting knowledge in reality, and two channels have some interactions. In this paper, we explore the spread mechanism of a kind of knowledge in the multiplex networks with consideration of online and offline channels. First, a knowledge transmission model in the multiplex networks is established and the mean-field equations are derived. Specifically, the transmission rate parameters are tuned to characterize the interaction of knowledge transmission between two channels and the relevance of networks structure is considered in the model. Then, we obtain the threshold conditions to distinguish whether a kind of knowledge spreads or not among employees by using two channels. Finally, simulation experiments are carried out. The results show that if individuals spread a kind of knowledge too many times by using two channels in a period of time, or they spread a kind of knowledge too many times only by using one of the two channels in a period of time, it is likely to have the negative impact on the spread of the kind of knowledge in the two cases. In addition, the simulation results indicate that it can promote the spread of knowledge among employees to review what they have learned in time. Compared with the multiplex networks with two homogeneous subnetworks, the speed of spread is faster and the range of spread is wider in the multiplex networks with scale-free and homogeneous subnetworks. • We explore the spread mechanism of a kind of knowledge in the multiplex networks with consideration of online and offline channels. • The transmission rate parameters are tuned to characterize the interaction of knowledge transmission between two channels and the relevance of networks structure is considered in the model. • If individuals spread a kind of knowledge too many times by using two channels, or using only one channel in a period of time, it has the negative impact on the spread of the kind of knowledge. [ABSTRACT FROM AUTHOR]

This paper studies the identification and estimation of social parameters in a general version of the Linear-in-Means model commonly fitted in the Social Sciences with multilayered network data. A Monte Carlo exercise showcases its good small-sample properties while an empirical application to Canadian consumers' credit usage demonstrates its applicability. Our estimates show that one's credit-card balance increases by $0.31 for an extra $1 owed by surrounding neighbors. [ABSTRACT FROM AUTHOR]

• We provide a random walk-based solution for the problem of link prediction in multiplex networks. • We use biasing functions to compute the interlayer weights between different layers. • Extensive experiments are conducted on real-world datasets collected from different types of social networks, and the proposed model is shown to outperform state-of-the-art link prediction methods. Link prediction is a technique to forecast future new or missing relationships between nodes based on the current network information. However, the link prediction in monoplex networks seems to have a long background, the attempts to accomplish the same task on multiplex networks are not abundant, and it was often a challenge to apply conventional similarity methods to multiplex networks. The issue of link prediction in multiplex networks is the way of predicting the links in one layer, taking structural information of other layers into account. One of the most important methods of link prediction in a monoplex network is a local random walk (LRW) that captures the network structure using pure random walking to measure nodes similarity of the graph and find unknown connections. The goal of this paper is to propose an extended version of local random walk based on pure random walking for solving link prediction in the multiplex network, referred to as the Multiplex Local Random Walk (MLRW). We explore approaches for leveraging information mined from inter-layer and intra-layer in a multiplex network to define a biased random walk for finding the probability of the appearance of a new link in one target layer. Experimental studies on seven multiplex networks in the real world demonstrate that a multiplex biased local random walk performs better than the state-of-the-art methods of link prediction and corresponding unbiased case and improves prediction accuracy. [ABSTRACT FROM AUTHOR]

• A new computationally and temporally efficient methodology to represent the relationships between assets through a multiplexed network whose edges include temporal attributes. • A combination of two mathematical domains (signal processing and complex networks) increases the accuracy of each of them separately. • An application of a new methodology in the cybersecurity domain provides promising results with a more computationally efficient effort. Intrusion Detection Systems (IDS) are fundamental tools in cybersecurity environments. In this paper, we present a new methodology for the creation of intrusion detection systems (IDS) based on a strategy that combines the use of multiplex networks and time series analysis to provide a probability that an IP address be an attacker in a certain time. This approach reduces the number of alerts to a small number of IP addresses as well as the computation effort by not having to analyze each event independently. The evaluation of all traffic happens only at pre-defined times. The methodology relies on both the original utilization of some unsupervised machine learning techniques and on the use of certain time series attributes and their representation as a complex multiplex network, achieving a very significant reduction in the dimensionality of the resulting data representation. The result is a very effective intrusion detection system in large corporate environments and a new approach in the representation of the analyzed data as shown in the real case presented. [ABSTRACT FROM AUTHOR]

• Inter-layer synchronization is established in a network with frequency mismatch between layers. • Inter-layer structure and frequency synchronizations are studied. • Diagrams of regimes are plotted in the (frequency mismatch inter-layer coupling strength) parameter plane. We explore numerically inter-layer synchronization of spatiotemporal patterns in a heterogeneous bilayer network of nonlocally coupled Rössler oscillators. Both layers exhibit phase chimera regimes with similar cluster structures, but there is a mean frequency mismatch between the layers. We show that an entrainment of the mean frequency in the interacting layers is observed already for sufficiently weak inter-layer coupling even when the frequency mismatch is large. At the same time, frequency synchronization does not mean structure synchronization. Our numerical study indicates that inter-layer synchronization takes place within noticeably shorter ranges of the frequency mismatch and the inter-layer coupling strength than the frequency synchronization regime. Besides, we show that the weakest chaotic behavior is observed when both frequency and structure synchronizations occur, while the most developed chaotic oscillations are typical when the spatiotemporal structures in the layers are desynchronized. [ABSTRACT FROM AUTHOR]

• We study how to promote idea diffusion by using multiple communication channels based on an SIS model in the multiplex network. • The mutual promotion and competitive relationship of idea diffusion between any two of three communication channels are considered in the modeling. • The dynamics of the idea diffusion model is completely determined by a threshold value R 0. • The numerical simulations indicate that if we use the three channels in a balanced way to spread an idea, we can effectively promote its diffusion. This paper aims to study how to promote creative idea diffusion by using multiple channels. A variety of main communication channels, which are face to face communication channel at work, online communication channel in enterprise social media and electronic communication channel in non-working time, are considered. We propose an idea diffusion model in a multiplex network with the three channels. Furthermore, the threshold R 0 of idea diffusion is obtained. If R 0 < 1 , we can conclude that the free equilibrium without an idea in the multiplex network composed of the three channels is globally asymptotically stable; if R 0 > 1 , we prove that the creative idea spreads continuously in this system. Numerical simulations show that the speed of diffusion is fast and the scope of diffusion is wide among individuals when the average times of communication by using any of three channels in unit time are basically the same. If individuals communicate the creative idea only by using one or two online channels and ignore the offline communication channel at work, the diffusion of this creative idea is likely to be seriously hindered. [ABSTRACT FROM AUTHOR]

We investigate solitary states in a two-layer multiplex network of FitzHugh-Nagumo neurons in the oscillatory regime. We demonstrate how solitary states can be induced in a multiplex network consisting of two non-identical layers. More specifically, we show that these patterns can be introduced via weak multiplexing into a network that is fully synchronized in isolation. We show that this result is robust under variations of the inter-layer coupling strength and largely independent of the choice of initial conditions. Moreover, we study the vulnerability of solitary states with respect to changes in the inter-layer topology. In more detail, we remove links that connect two solitary nodes of each layer and evaluate the resulting pattern. We find a highly non-trivial dependence of the survivability of the solitary states on topological (position in the network) and dynamical (phase of the oscillation) characteristics. [ABSTRACT FROM AUTHOR]

• Considering FHN model on duplex network with nonlinear coupling. • The Laplacian matrices of monolayer networks are not commutable. • We studied patterns on duplex and proposed the approximation method from the perspective of network modes. • We found the dominant network modes are related to the most unstable modes. Patterns out of homogeneous equilibrium on monolayer networks have been well-documented. However, it is a challenge to understand patterns on multiplex networks. In this work, we study coupled FitzHugh–Nagumo model on duplex networks consisting of two layers. By numerical investigations, we find that the emergent patterns may be characterized by dominant network modes when the homogeneous equilibrium becomes unstable. These dominant network modes on duplex networks are related to the most unstable network modes in monolayer networks. Using these dominant networks modes, we develop approximation methods to deal with the instability of the homogeneous equilibrium on duplex networks. The comparison between theoretical and numerical results suggests that the approximation methods may serve as a tool for analyzing patterns on duplex networks. [ABSTRACT FROM AUTHOR]

• Anti-phase relay synchronization is established for the first time in a triplex network of 2D lattices. • The correlation coefficient measure is used for the first time as a relay synchronization criterion. • Strong inter-layer coupling induces in-phase complete synchronization. We explore numerically relay synchronization of wave structures in a heterogeneous three-layer network of coupled two-dimensional (2D) lattices of continuous-time systems. Remote layers, which are not directly connected but interact via a relay layer, consist of coupled van der Pol oscillators, while the middle layer is described by a lattice of interacting FitzHugh-Nagumo neurons. We show for the first time that already for weak inter-layer coupling, anti-phase relay synchronization of target wave patterns occurs in the considered network. This is a novel effect which can be observed in multiplex networks of interacting 2D lattices of oscillatory systems. Our numerical studies indicate that strong inter-layer coupling leads to in-phase synchronization of spatio-coherent structures in the network layers. We also analyze the impact of inter-layer coupling ranges in the relay and the remote layers on the relay synchronization effect. [ABSTRACT FROM AUTHOR]