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Introduction: Mind-wandering is a highly dynamic phenomenon involving frequent fluctuations in cognition. However, the dynamics of functional connectivity between brain regions during mind-wandering have not been extensively studied. Methods: We employed an analytical approach aimed at extracting recurring network states of multilayer networks built using amplitude envelope correlation and imaginary phase-locking value of delta, theta, alpha, beta, or gamma frequency band. These networks were constructed based on electroencephalograph (EEG) data collected while participants engaged in a video-learning task with mind-wandering and focused learning conditions. Recurring multilayer network states were defined via clustering based on overlapping node closeness centrality. Results: We observed similar multilayer network states across the five frequency bands. Furthermore, the transition patterns of network states were not entirely random. We also found significant differences in metrics that characterize the dynamics of multilayer network states between mind-wandering and focused learning. Finally, we designed a classification algorithm, based on a hidden Markov model using state sequences as input, that achieved a 0.888 mean area under the receiver operating characteristic curve for within-participant detection of mind-wandering. Discussion: Our approach offers a novel perspective on analyzing the dynamics of EEG data and shows potential application to mind-wandering detection. [ABSTRACT FROM AUTHOR]

Researchers have long been intrigued by cooperative behavior in populations of selfish individuals. Recently, the focus has shifted to how social networks shape human interactions, as well as cooperation and moral behavior in general. Real-world situations often require an interdependent network, combining multiple layers of sub-networks. Previous studies have mostly examined cases with similar network structures across layers. Here, we go beyond this by investigating a coupled bilayer network, comprising a real-world collaborative network and a scale-free network, using the Prisoner's Dilemma to study its evolutionary dynamics. Individuals make decisions through social learning, moving within or between layers. We introduce a parameter that measures individuals' ability to communicate across layers. Without this communication, both trans-layer mobility and network structures impact cooperation. A small trans-layer mobility probability boosts cooperation, but excessive mobility erodes network reciprocity, decreasing cooperation in the collaborative layer network. Cooperation frequency is generally lower in the collaborative layer network compared to isolated networks, with individuals migrating to the scale-free layer network. However, with some information exchange, trans-layer mobility facilitates mutual social learning, reversing the decline in cooperation in the collaborative layer network and promoting overall cooperation. These findings may offer insights into population migration as well as regional development strategies. [ABSTRACT FROM AUTHOR]

With the development of social networks, misinformation including rumors is spreading through multiple channels, which brings many negative effects to society. The government and several Nongovernmental Organizations (NGOs) use relevant rumor rebuttal tactics to control the spread of rumors to prevent these detrimental impacts. In this paper, we consider the responses of different individuals to rumors and classify individuals into three categories: active, normal and inactive, with different activity rates for the three categories. In order to study the interaction between rumor repudiation mechanisms and rumor propagation, we propose a rumor propagation model that considers global and local rumor repudiation mechanisms as well as activity rates in multiplex networks. The upper layer represents the rumor refutation information propagation and the lower layer expresses the rumor propagation. And mean-field equations describing the dynamics of this model in multiplex networks are derived. We found that the threshold of rumor propagation is significantly affected by individual activity rates. Another interesting finding is that the global rumor refutation mechanism suppresses rumor propagation more than the local disinformation mechanism. [ABSTRACT FROM AUTHOR]

Link prediction methods can help to reconstruct systems from incomplete datasets, to understand the structure dynamic complex networks, and to predict future interactions in evolving networks. Link prediction in multiplex networks is the problem of finding missing links between users based on information from other layers. Although the link prediction problem has been widely studied in multiplex networks, most methods do not consider both interlayer and intralayer features at the same time. Similarity metrics are one of the most common approaches to solving the link prediction problem. However, the development of similarity metrics over multiple layers with the definition of multiplex networks has become an important challenge that has caught the attention of many researchers. In this article, a novel similarity metric is introduced by considering reliable paths between users for link prediction in multiplex networks. The proposed method maps the network to a weighted network by extracting different interlayer and intralayer features from multiplex networks. Finally, the proposed similarity metric develops the FriendLink metric by considering the weight of links and reliable paths. The proposed method is evaluated in comparison with classical similarity metrics and equivalence algorithms such as SEM-Path, LPIS, and SOIDP. Two real datasets based on multiplex networks including Twitter–Foursquare and Twitter–Instagram have been used to evaluate. Experiments prove the superiority of link prediction in the proposed method over other algorithms. [ABSTRACT FROM AUTHOR]

Core–periphery detection aims to separate the nodes of a complex network into two subsets: a core that is densely connected to the entire network and a periphery that is densely connected to the core but sparsely connected internally. The definition of core–periphery structure in multiplex networks that record different types of interactions between the same set of nodes on different layers is non-trivial since a node may belong to the core in some layers and to the periphery in others. We propose a nonlinear spectral method for multiplex networks that simultaneously optimizes a node and a layer coreness vector by maximizing a suitable non-convex homogeneous objective function by a provably convergent alternating fixed-point iteration. We derive a quantitative measure for the quality of a given multiplex core–periphery structure that allows the determination of the optimal core size. Numerical experiments on synthetic and real-world networks illustrate that our approach is robust against noisy layers and significantly outperforms baseline methods while improving the latter with our novel optimized layer coreness weights. As the runtime of our method depends linearly on the number of edges of the network, it is scalable to large-scale multiplex networks. [ABSTRACT FROM AUTHOR]

The mental lexicon is a complex cognitive system representing information about the words/concepts that one knows. Over decades psychological experiments have shown that conceptual associations across multiple, interactive cognitive levels can greatly influence word acquisition, storage, and processing. How can semantic, phonological, syntactic, and other types of conceptual associations be mapped within a coherent mathematical framework to study how the mental lexicon works? Here we review cognitive multilayer networks as a promising quantitative and interpretative framework for investigating the mental lexicon. Cognitive multilayer networks can map multiple types of information at once, thus capturing how different layers of associations might co-exist within the mental lexicon and influence cognitive processing. This review starts with a gentle introduction to the structure and formalism of multilayer networks. We then discuss quantitative mechanisms of psychological phenomena that could not be observed in single-layer networks and were only unveiled by combining multiple layers of the lexicon: (i) multiplex viability highlights language kernels and facilitative effects of knowledge processing in healthy and clinical populations; (ii) multilayer community detection enables contextual meaning reconstruction depending on psycholinguistic features; (iii) layer analysis can mediate latent interactions of mediation, suppression, and facilitation for lexical access. By outlining novel quantitative perspectives where multilayer networks can shed light on cognitive knowledge representations, including in next-generation brain/mind models, we discuss key limitations and promising directions for cutting-edge future research. [ABSTRACT FROM AUTHOR]

A central puzzle of international relations research is understanding how groups of cooperative states form. While in theory cooperative groups of states can be made up of states with diverse domestic organizations, in practice, groups of cooperative states tend to have similar domestic characteristics. In this regard, the current state of knowledge on international cooperation is lacking. I fill this research gap by analyzing how network relations simultaneously affect the domestic organization of and conflict among states. Specifically, I argue that frequent interactions and dynamic network formation help states signal their preferences, interests, and capabilities. This information helps spread the political institutions of more powerful states, while alleviating information and coordination problems within groups of states. Over time, this creates cooperative communities or politically homophilous groups of states that are more internally cooperative. When these processes are jointly considered, shared institutional characteristics have a null effect on interstate conflict. [ABSTRACT FROM AUTHOR]

Communication and interaction of individuals in the real world cannot be represented by one-layer networks, and in our paper we use multiplex networks capturing the complexity of their interactions. We define players' utilities taking into account a multilayer structure of the network by specifying different ways of accounting players' costs. Using two approaches, we obtain stability conditions for special multilplex structures including all-layer complete, all-layer star with unique or different centers, and all-layer unique networks. [ABSTRACT FROM AUTHOR]

Multiplex networks convey more valuable information than single-layer networks; thus, performing the community detection task involving these networks has become a subject of extensive research on the exploration of latent community structures. The non-negative matrix factorization (NMF) algorithm has proven successful in community detection scenarios by offering good interpretations of community structures. However, directly obtaining consensus community assignments using the traditional NMF algorithm poses a challenge due to the presence of complex structures spanning across different layers in the multiplex network. In this paper, we propose a novel algorithm called Deep Structure-Preserving Non-negative Matrix Factorization (DSP-NMF) to perform community detection in multiplex networks. Specifically, DSP-NMF constructs a deep autoencoder-like NMF model to generate meaningful network embeddings that are represented by multiple basis matrices and reconstructed by corresponding transposed basis matrices. By integrating the similarity relationships of nodes into the proposed DSP-NMF algorithm, the corresponding Laplacian matrices in each network layer are regularized to preserve the community structure during the learning process. Simultaneously, a consensus network embedding can be learned to obtain the final community partition. In this manner, the proposed DSP-NMF algorithm not only uncovers robust community structures in multiplex networks but also maintains the coherence between layers without losing complementary features. The experimental results obtained on five multiplex network datasets show that our proposed DSP-NMF algorithm outperforms other competitive methods in community detection tasks involving multiplex networks. [ABSTRACT FROM AUTHOR]

Abstract A wide variety of complex systems are characterized by interactions of different types involving varying numbers of units. Multiplex hypergraphs serve as a tool to describe such structures, capturing distinct types of higher-order interactions among a collection of units. In this work, we introduce a comprehensive set of measures to describe structural connectivity patterns in multiplex hypergraphs, considering scales from node and hyperedge levels to the system’s mesoscale. We validate our measures with three real-world datasets: scientific co-authorship in physics, movie collaborations, and high school interactions. This validation reveals new collaboration patterns, identifies trends within and across movie subfields, and provides insights into daily interaction dynamics. Our framework aims to offer a more nuanced characterization of real-world systems marked by both multiplex and higher-order interactions.

Multilayer networks are used to represent the interdependence between the relational data of individuals interacting with each other via different types of relationships. To study the information-theoretic phase transitions in detecting the presence of planted partition among the nodes of a multilayer network with additional nodewise covariate information and diverging average degree, Ma and Nandy (2023, IEEE Trans. Inf. Theory , 69, 3203–3239) introduced Multi-Layer Contextual Stochastic Block Model. In this paper, we consider the problem of detecting planted partitions in the Multi-Layer Contextual Stochastic Block Model, when the average node degrees for each network are greater than |$1$|⁠. We establish the sharp phase transition threshold for detecting the planted bi-partition. Above the phase-transition threshold testing the presence of a bi-partition is possible, whereas below the threshold no procedure to identify the planted bi-partition can perform better than random guessing. We further establish that the derived detection threshold coincides with the threshold for weak recovery of the partition and provides a quasi-polynomial time algorithm to estimate it. [ABSTRACT FROM AUTHOR]

The outbreak of an epidemic often stimulates the generation of public awareness about epidemic prevention. This heightened awareness encourages individuals to take proactive protective measures, thereby curbing the transmission of the epidemic. Previous research commonly adopts an assumption that each individual has the same probability of awakening self-protection awareness after infection. However, in the real-world process, different individuals may generate varying awareness responses due to the differences in the amount of information received. Therefore, in this study, we first propose a coupled awareness-epidemic spreading model, where the self-initiated awareness of each individual can be influenced by the number of aware neighbors. Subsequently, we develop a Micro Markov Chain Approach to analyze the proposed model and explore the effects of different dynamic and structural parameters on the coupled dynamics. Findings indicate that individual awareness awakening can effectively promote awareness diffusion within the proposed coupled dynamics and inhibit epidemic transmission. Moreover, the influence of awareness diffusion on epidemic transmission exhibits a metacritical point, from which the epidemic threshold increases with the increase in the awareness diffusion probability. The research findings also suggest that the increase in the average degree of virtual-contact networks can reduce the value of the metacritical point, while the change in the average degree of the physical-contact networks does not affect the metacritical point. Finally, we conduct extensive experiments on four real networks and obtain results consistent with the above conclusions. The systematic research findings of this study provide new insights for exploring the interaction between individual awareness and epidemic transmission in the real world. [ABSTRACT FROM AUTHOR]

This paper aims to understand how a group of academics cite each others' work through time, considering the simultaneous co-evolution of three networks representing their scientific collaboration, the journals in which they publish and institutional membership. It argues that both social and cognitive processes contribute to these dynamics. Two types of network mechanisms are considered specifically: closures by affiliation and closures by association. To assess whether these mechanisms generate the macro features of the network under study, we propose new features for three-mode multilevel networks such as the mixed geodesic distances, mixed degree distributions, and the mixed quadrilateral census. We investigate whether a micro-level model that considers the above-mentioned network mechanisms is able to correctly reproduce these features. We apply stochastic actor-oriented models (SAOMs) for one-mode and two-mode networks to link the micro-macro processes using a dataset of a scientific community of astronomers from 2013 to 2015. The results suggest that social relationships grounded on scientific collaboration and proximity based on institutional affiliation are more accurately suited to understanding the co-evolution of the network of citations than an alternative approach that merely considers cognitive-based networks measured as the similarity in publishing in the same journals. • We investigate how a group of academics cite each others' work through time considering the co-evolution of a multilevel network. • The co-evolution of a three-mode multilevel network is analysed considering cross-level effects. • New and already available measures for diagnostics are used for statistical models for social networks to identify how micro-mechanisms trigger different structures at the macro level. • Social relationships grounded on scientific collaboration and space proximity based on institutional affiliation are more accurately suited to understand the co-evolution of the networks in a scientific network. [ABSTRACT FROM AUTHOR]

Influence maximization (IM) in dynamic social networks is an optimization problem to analyze the changes in social networks for different periods. However, the existing IM methods ignore the context propagation of interaction behaviors among users. Hence, context-based IM in multiplex networks is proposed here. Initially, multiplex networks along with their contextual data are taken as input. Community detection is performed for the network using the Wilcoxon Hypothesized K-Means (WH-KMA) algorithm. From the detected communities, the homogeneous network is used for extracting network topological features, and the heterogeneous networks are used for influence path analysis based on which the node connections are weighted. Then, the influence-path-based features along with contextual features are extracted. These extracted features are given for the link prediction model using the Parametric Probability Theory-based Long Short-Term Memory (PPT-LSTM) model. Finally, from the network graph, the most influencing nodes are identified using the Linear Scaling based Clique (LS-Clique) detection algorithm. The experimental outcomes reveal that the proposed model achieves an enhanced performance. [ABSTRACT FROM AUTHOR]

IntroductionMind-wandering is a highly dynamic phenomenon involving frequent fluctuations in cognition. However, the dynamics of functional connectivity between brain regions during mind-wandering have not been extensively studied.MethodsWe employed an analytical approach aimed at extracting recurring network states of multilayer networks built using amplitude envelope correlation and imaginary phase-locking value of delta, theta, alpha, beta, or gamma frequency band. These networks were constructed based on electroencephalograph (EEG) data collected while participants engaged in a video-learning task with mind-wandering and focused learning conditions. Recurring multilayer network states were defined via clustering based on overlapping node closeness centrality.ResultsWe observed similar multilayer network states across the five frequency bands. Furthermore, the transition patterns of network states were not entirely random. We also found significant differences in metrics that characterize the dynamics of multilayer network states between mind-wandering and focused learning. Finally, we designed a classification algorithm, based on a hidden Markov model using state sequences as input, that achieved a 0.888 mean area under the receiver operating characteristic curve for within-participant detection of mind-wandering.DiscussionOur approach offers a novel perspective on analyzing the dynamics of EEG data and shows potential application to mind-wandering detection.

In this paper, a meaningful representation of the road network using multiplex networks and a novel feature selection framework that enhances the predictability of future traffic conditions of an entire network are proposed. Using data on traffic volumes and tickets’ validation from the transportation network of Athens, we were able to develop prediction models that not only achieve very good performance but are also trained efficiently, do not introduce high complexity and, thus, are suitable for real-time operation. More specifically, the network’s nodes (loop detectors and subway/metro stations) are organized as a multilayer graph, each layer representing an hour of the day. Nodes with similar structural properties are then classified in communities and are exploited as features to predict the future demand values of nodes belonging to the same community. The results reveal the potential of the proposed method to provide reliable and accurate predictions.

When do domestic events affect international relations? Our answer to this puzzle emphasizes patterns of interaction in domestic networks. Leaders depend on coalitions of subnational actors—civilians, parties, militaries, and so on—for political survival. Structural imbalance emerges when the higher-order relations of subnational actors contradict their revealed preferences, such as when actors cooperate with enemies of friends or conflict with friends of friends. Imbalance generates uncertainty about the preferences and future behaviors of subnational actors, which in turn diminishes the government’s confidence in domestic coalitions. Imbalance thus increases the probability that leaders will turn to survival strategies, such as manipulating foreign relations in order to show competence. At the same time, foreign governments respond to imbalance by implementing preventive measures or intervening for strategic gain. We develop and test these arguments from a networks-of-networks approach. We introduce generalizable metrics of structural imbalance and foreign-relations shifts. Extensive empirical analysis shows that the greater the imbalance generated by domestic events, the greater the probability that those events will affect foreign relations.

AbstractThe reuse of well-established medicines using computational modeling has gained a lot of attention due to its tremendous benefits. Based on this perspective, a new method for linking known medicines to diseases is proposed. The creation of a new treatment or medicine can be financially and temporally costly and the reuse of medicines is one possibility to accelerate this process efficiently. The main purpose of the reuse of medicines is to reduce some stages of the development of new medicines, motivating the proposition of several methods nowadays. In this work, a new method is developed aiming to connect known medicines to diseases based on available networks of protein interactions and available lists of medicines that affect protein action. The concepts of multiplex networks are used to connect subgraphs of vertices that represent medicines and proteins. The core of the procedure is determined by a weighting strategy constructed to define precisely the more relevant connections. The method was compared to other network link methods in the literature and a case study was presented and evaluated by the proposed method. [ABSTRACT FROM AUTHOR]

In recent years, the exponential growth of online social networks as complex networks has presented challenges in expanding networks and forging new connections. Link prediction emerges as a crucial technique to anticipate future relationships among users, leveraging the current network state to address this challenge effectively. While link prediction models on monoplex networks have a well-established history, the exploration of similar tasks on multilayer networks has garnered considerable attention. Extracting topological and multimodal features for weighting links can improve link prediction in weighted complex networks. Meanwhile, establishing reliable and trustworthy paths between users is a useful way to create metrics that convert unweighted to weighted similarity. The local random walk is a widely used technique for predicting links in weighted monoplex networks. The aim of this paper is to develop a semi-local random walk over reliable paths to improve link prediction on a multilayer social network as a complex network, which is denoted as Reliable Multiplex semi-Local Random Walk (RMLRW). RMLRW leverages the semi-local random walk technique over reliable paths, integrating intra-layer and inter-layer information from multiplex features to conduct a trustworthy biased random walk for predicting new links within a target layer of multilayer networks. In order to make RMLRW scalable, we develop a semi-local random walk-based network embedding to represent the network in a lower-dimensional space while preserving its original characteristics. Extensive experimental studies on several real-world multilayer networks demonstrate the performance assurance of RMLRW compared to equivalent methods. Specifically, RMLRW improves the average f-measure of the link prediction by 3.2% and 2.5% compared to SEM-Path and MLRW, respectively. [ABSTRACT FROM AUTHOR]

Using a 22-year study of an elite university's faculty networks and their work activities, we extend network ecology to concern top-down processes of environmental selection and bottom-up processes of individual adaptation. We argue that faculty enact distinct types of collaborative work activity that are central to their role: research training (co-advising), publishing (co-authoring), and financing (co-granting). STEM (hard science) and HSS (humanities and social science) cultures train and expect their members to perform these activities in different ways reflective of distinct networking styles. STEM faculty anchor their work relations in grants and extend those relations liberally to advising and publishing collaborations, forming an egalitarian interdisciplinary network reflective of a guild system. HSS faculty anchor their work relations in advising and layer and extend their ties locally around star faculty to form a restrictive patronage system. However, individual faculty vary in their adherence to these styles, and those adopting the STEM style of networking are more likely to survive in the university and achieve tenure. New faculty increasingly learn and adapt to this, and the STEM model increasingly diffuses and transforms the university social structure, illustrating the salience of top-down and bottom-up processes of network ecology in explaining social structural change. • We advance network ecology in multiple ways. • Multiple types of ties and forms of tie refunctioning are key mechanisms of network formation. • Internal contextual variation within the university corresponds with the distinct networking practices of STEM and HSS faculty. • The university selects faculty for tenure that use a STEM networking strategy and faculty learn to adopt such a strategy. • This results in top-down and bottom-up structural change that dramatically alters the university collaboration network. [ABSTRACT FROM AUTHOR]

Synchronization in a network of connected elements is essential to the proper functioning of both natural and engineered systems and is thus of increasing interest across disciplines. In many cases, synchronization phenomena involve not just actions within a single network in isolation, but the coordinated and coherent behaviors of several networks interacting with each other. The interactions between multiple systems play a crucial role in determining the emergent dynamics. One paradigm capable of representing real-world complex systems is that of multiplex networks, where the same set of nodes exists in multiple layers of the network. Recent studies have made significant progress in understanding synchronization in multiplex networks. In this review, we primarily focus on two key aspects: structural complexity and dynamical complexity. From the perspective of structural complexity, we present how the topological setting, such as the interlayer coupling pattern, affects the synchronizability of a multiplex network. The structural characteristics of a multiplex network, in particular, give rise to dynamical complexity, including the emergence of intralayer synchronization (within each layer) and interlayer synchronization (between layers). We also discuss the major methods for studying the stability of complete, intralayer, and interlayer synchronization, as well as synchronization control in multiplex networks. Additionally, we briefly introduce some relevant applications. Lastly, the review provides a comprehensive summary of the notable findings in the study of synchronization in multiplex networks, emphasizing the interplay between their structural and dynamical complexities, and identifies open problems that present opportunities for future research in this field. [ABSTRACT FROM AUTHOR]

The idea of predicting links in multiplex networks has gained increasing interest in recent years. In this paper, we propose a comprehensive framework which benefits from the structural information of auxiliary layers to predict links on a target layer of multiplex networks. Specifically, we assume that the likelihood of the existence of a link between two nodes is determined by the contributions from both the nodes' neighbors on the target layer and their counterparts' neighbors on a manually network generated by auxiliary layers. The final likelihood matrix is acquired by an iterative algorithm. In addition, we show advantages of our methods for predicting links on sparse and dense networks as well as on networks with assortative and disassortative structural layers. The effectiveness of the proposed methods are evaluated through extensive experiments on real-world multiplex networks. [ABSTRACT FROM AUTHOR]

Nowadays, community detection is one of the important fields for understanding network topology and has many applications in information diffusion, interaction mining and migration behaviour analysis. Therefore, community detection in social networks can help to understand user behaviour and network characteristics. There are many community detection methods, which are often designed for single-layer social networks. However, real-world networks use several types of relationships to establish connections between users, each of which has different characteristics. Hence, real-world networks can be modelled as multiplex networks. In general, multiplex networks are an example of multilayer networks in which the relationships between users in different networks can be considered simultaneously. In these networks, each layer represents the connections between users in a social network. Meanwhile, communities in multiplex networks are identified based on the structure and connections between overlapping users in different layers of the network. In this article, the nonnegative matrix tri-factorization (NMTF) strategy is used to model multiplex social networks, and a solution for community detection is developed based on it. According to this strategy, a common consensus matrix and then an alignment matrix are extracted based on similarity metrics and network structure. The use of these matrices as a flexible modelling framework enables the detection of coherent community between overlapping users in multiplex social networks. We evaluate the proposed NMTF method through various metrics on a multiplex social network. The results of this evaluation show the better performance of NMTF in terms of community quality compared to equivalent methods. [ABSTRACT FROM AUTHOR]

The outbreak of an epidemic often stimulates the generation of public awareness about epidemic prevention. This heightened awareness encourages individuals to take proactive protective measures, thereby curbing the transmission of the epidemic. Previous research commonly adopts an assumption that each individual has the same probability of awakening self-protection awareness after infection. However, in the real-world process, different individuals may generate varying awareness responses due to the differences in the amount of information received. Therefore, in this study, we first propose a coupled awareness-epidemic spreading model, where the self-initiated awareness of each individual can be influenced by the number of aware neighbors. Subsequently, we develop a Micro Markov Chain Approach to analyze the proposed model and explore the effects of different dynamic and structural parameters on the coupled dynamics. Findings indicate that individual awareness awakening can effectively promote awareness diffusion within the proposed coupled dynamics and inhibit epidemic transmission. Moreover, the influence of awareness diffusion on epidemic transmission exhibits a metacritical point, from which the epidemic threshold increases with the increase in the awareness diffusion probability. The research findings also suggest that the increase in the average degree of virtual-contact networks can reduce the value of the metacritical point, while the change in the average degree of the physical-contact networks does not affect the metacritical point. Finally, we conduct extensive experiments on four real networks and obtain results consistent with the above conclusions. The systematic research findings of this study provide new insights for exploring the interaction between individual awareness and epidemic transmission in the real world.

Towards 6G, a key challenge lies in the placement of virtual network functions on physical resources. This becomes complex due to the dynamic nature of mobile environments, making the design a major point of research. We propose a framework that sees this challenge as a complex and dynamic collective process, presenting a novel perspective which encompasses transport network and wireless segment aspects. The framework is built around an analytical modeling and algorithmic tools that rely on complex systems’ paradigm as multiplex networks and evolutionary game theory. The multiplex network enables capturing the layered and heterogeneous nature of the environment. Evolutionary game theory models the dynamical behavior of the system as a collective social process, where each decision on functions influences the overall outcome. Our model allows us to achieve a placement scheme that optimizes 6G functions deployment and minimizes the number of active computational nodes. Compared to traditional transport network centric approach, it effectively reduces interference, ensuring the network’s effective operation and performance. Results show the efficacy of the strategy, enabling the dynamic distribution of functions as the outcome of a social dilemma, and highlight the potential applicability of this approach to tackle the network function placement problem in 6G networks.

This paper investigates the synchronization problem for multiplex networks with the stochastic perturbations via intermittent control. In the control schemes, the topologies of different layers of multiplex networks can be different, the control strategy adopts aperiodically intermittent and pinning control methods, and the number of pinned nodes can be different in different layers. Based on the stochastic theory and the Lyapunov stability theory, linear feedback and adaptive controllers are constructed respectively, some sufficient conditions are derived for guaranteeing synchronization of multiplex networks. Furthermore, for the different connectivity of multiplex networks, the conditions for achieving synchronization are discussed. Finally, two numerical simulations are provided to verify the theoretical results.

We consider both leaderless and leader-follower, possibly nonlinear, networks affected by time-varying communication delays. For such systems, we give a set of sufficient conditions that guarantee the convergence of the network towards some desired behaviour while simultaneously ensuring the rejection of polynomial disturbances and the non-amplification of other classes of disturbances across the network. To fulfill these desired properties, and prove our main results, we propose the use of a control protocol that implements a multiplex architecture. The use of our results for control protocol design is then illustrated in the context of formation control. The protocols are validated both in-silico and via an experimental set-up with real robots. All experiments confirm the effectiveness of our approach.

Networks are commonly used to model complex systems. The different entities in the system are represented by nodes of the network and their interactions by edges. In most real life systems, the different entities may interact in different ways necessitating the use of multiplex networks where multiple links are used to model the interactions. One of the major tools for inferring network topology is community detection. Although there are numerous works on community detection in single-layer networks, existing community detection methods for multiplex networks mostly learn a common community structure across layers and do not take the heterogeneity across layers into account. In this paper, we introduce a new multiplex community detection method that identifies communities that are common across layers as well as those that are unique to each layer. The proposed method, Multiplex Orthogonal Nonnegative Matrix Tri-Factorization, represents the adjacency matrix of each layer as the sum of two low-rank matrix factorizations corresponding to the common and private communities, respectively. Unlike most of the existing methods which require the number of communities to be pre-determined, the proposed method also introduces a two stage method to determine the number of common and private communities. The proposed algorithm is evaluated on synthetic and real multiplex networks, as well as for multiview clustering applications, and compared to state-of-the-art techniques.

Multiplex networks have become increasingly more prevalent in many fields, and have emerged as a powerful tool for modeling the complexity of real networks. There is a critical need for developing inference models for multiplex networks that can take into account potential dependencies across different layers, particularly when the aim is community detection. We add to a limited literature by proposing a novel and efficient Bayesian model for community detection in multiplex networks. A key feature of our approach is the ability to model varying communities at different network layers. In contrast, many existing models assume the same communities for all layers. Moreover, our model automatically picks up the necessary number of communities at each layer (as validated by real data examples). This is appealing, since deciding the number of communities is a challenging aspect of community detection, and especially so in the multiplex setting, if one allows the communities to change across layers. Borrowing ideas from hierarchical Bayesian modeling, we use a hierarchical Dirichlet prior to model community labels across layers, allowing dependency in their structure. Given the community labels, a stochastic block model (SBM) is assumed for each layer. We develop an efficient slice sampler for sampling the posterior distribution of the community labels as well as the link probabilities between communities. In doing so, we address some unique challenges posed by coupling the complex likelihood of SBM with the hierarchical nature of the prior on the labels. An extensive empirical validation is performed on simulated and real data, demonstrating the superior performance of the model over single-layer alternatives, as well as the ability to uncover interesting structures in real networks. [ABSTRACT FROM AUTHOR]

The higher brain functions arise from coordinated neural activity between distinct brain regions, but the spatial, temporal, and spectral complexity of these functional connectivity networks (FCNs) has challenged the identification of correlates with neurobehavioral phenotypes. Characterizing behavioral correlates of early life FCNs is important to understand the activity dependent emergence of neurodevelopmental performance and for improving health outcomes. Here, we develop an analysis pipeline for identifying multiplex dynamic FCNs that combine spectral and spatiotemporal characteristics of the newborn cortical activity. This data‐driven approach automatically uncovers latent networks that show robust neurobehavioral correlations and consistent effects by in utero drug exposure. Altogether, the proposed pipeline provides a robust end‐to‐end solution for an objective assessment and quantitation of neurobehaviorally meaningful network constellations in the highly dynamic cortical functions. [ABSTRACT FROM AUTHOR]

Identifying influential nodes in multiplex complex networks have a critical importance to implement in viral marketing and other real-world information diffusion applications. However, selecting suitable influential spreaders in multiplex networks are more complex due to existing multiple layers. Each layer of multiplex networks has its particular importance. Based on this research, an important layer with strong spreaders is a layer positioned in a well-connected neighborhood with more active edges, active critical nodes, the ratio of active nodes and their connections to all possible connections, and the intersection of intralayer communication compared to other layers. In this paper, we have formulated a layer weighting method based on mentioned layer's parameters and proposed an algorithm for mapping and computing the rank of nodes based on their spreading capability in multiplex networks. Thus, the result of layer weighting is used in mapping and compressing centrality vector values to a scalar value for calculating the centrality of nodes in multiplex networks by a coupled set of equations. In addition, based on this new method, the important layer parameters are combined for the first time to utilize in computing the influence of nodes from different layers. Experimental results on both synthetic and real-world networks show that the proposed layer weighting and mapping method significantly is effective in detecting high influential spreaders against compared methods. These results validate the specific attention to suitable layer weighting measure for identifying potential spreaders in multiplex network. [ABSTRACT FROM AUTHOR]

Understanding the interplay between human behavioral phenomena and infectious disease dynamics has been one of the central challenges of mathematical epidemiology. However, socio-cognitive processes critical for the initiation of desired behavioral responses during an outbreak have often been neglected or oversimplified in earlier models. Combining the microscopic Markov chain approach with the law of total probability, we herein institute a mathematical model describing the dynamic interplay between stage-based progression of awareness diffusion and endemic disease transmission in multiplex networks. We analytically derived the epidemic thresholds for both discrete-time and continuous-time versions of our model, and we numerically demonstrated the accuracy of our analytic arguments in capturing the time course and the steady state of the coupled disease-awareness dynamics. We found that our model is exact for arbitrary unclustered multiplex networks, outperforming a widely adopted probability-tree-based method, both in the prediction of the time-evolution of a contagion and in the final epidemic size. Our findings show that informing the unaware individuals about the circulating disease will not be sufficient for the prevention of an outbreak unless the distributed information triggers strong awareness of infection risks with adequate protective measures, and that the immunity of highly-aware individuals can elevate the epidemic threshold, but only if the rate of transition from weak to strong awareness is sufficiently high. Our study thus reveals that awareness diffusion and other behavioral parameters can nontrivially interact when producing their effects on epidemiological dynamics of an infectious disease, suggesting that future public health measures should not ignore this complex behavioral interplay and its influence on contagion transmission in multilayered networked systems. [ABSTRACT FROM AUTHOR]

The problem of sequential formation control in multiagent systems is studied in this paper, where a team of agents is required to establish needed formations in order at user-defined times. To address this problem, our contribution is a finite-time distributed control architecture predicated on multiplex networks over directed graph topologies. The key feature of the multiplex networks is that it allows leader agent(s) to spatially alter the size and orientation of the resulting formation without requiring global information exchange ability. In addition, the key feature of the finite-time approach is to ensure that the overall multiagent system establishes a particular formation determined by the leader agent(s) at user-defined times. System-theoretical analysis of the proposed architecture is given using the time transformation approach along with Lyapunov stability theory, and an illustrative numerical example is also included to demonstrate the ability of the proposed architecture in addressing the sequential formation control problem. [ABSTRACT FROM AUTHOR]

In recent years, community detection has received increasing interest. In network analysis, community detection refers to the identification of tightly connected subsets of nodes, which are called “communities” or “groups”, in the network. Non-negative matrix factorization models are often used to solve the problem. Orthogonal non-negative matrix tri-factorization (ONMTF) exhibits significant potential as an approach for community detection within multiplex networks. This paper explores the application of ONMTF in multiplex networks, aiming to detect both shared and exclusive communities simultaneously. The model decomposes each layer within the multiplex network into two low-rank matrices. One matrix corresponds to shared communities across all layers, and the other to unique communities within each layer. Additionally, graph regularization and the diversity of private communities are taken into account in the algorithm. The Hilbert Schmidt Independence Criterion (HSIC) is used to constrain the independence of private communities. The results prove that ONMTF effectively addresses community detection in multiplex networks. It also offers strong interpretability and feature extraction capabilities. Therefore, it is an advanced method for community detection in multiplex networks.

Multiplex networks have proven to be valuable tools for modeling and analyzing real complex system. Extensive work has been done on the traffic dynamics on multiplex networks, but there remains a lack of sufficient attention towards studying routing strategies for the purpose of suppressing epidemic spreading. In this paper, the impact of global awareness routing (GAR), improved global awareness routing (IGAR), and improved active routing (IAR) strategies on traffic-driven epidemic spreading are investigated. Our findings indicate that in the case of infinite node-delivery capacity and no traffic congestion in the network, adjusting routing parameters can effectively suppress epidemic spreading. In this context, these three strategies show better abilities on the multiplex network built by WS or ER model to minimize the density of infected nodes, thus contributing to the overall inhibition of the epidemic spread. However, in the multiplex network constructed by BA model, GAR strategy has a promoting effect on epidemic spreading compared with the shortest routing strategy. In addition, by controlling traffic flow, limiting node delivery capabilities can contain outbreaks. Our results suggest that adopting appropriate routing strategies in multiplex networks can play a proactive role in controlling epidemic spreading. This is crucial for formulating effective prevention and control measures and improving public health security. [ABSTRACT FROM AUTHOR]

With the rapid development of network science, Turing patterns on complex networks have attracted extensive attention from researchers. In this paper, we focus on spatial patterns in multiplex ER (Erdös-Rényi) random networks, taking the predator–prey model with Allee effect and hyperbolic mortality as an example. In theory, the threshold condition for generating Turing patterns is given using the Turing instability theory of multiplex networks. Numerically, we design relevant experiments to explore the impact of network topology on Turing patterns. The factors considered include model parameters, diffusion rate, average degree of the network, and differences in the average degree of different layers. The results indicate that the importance of diffusion rate and network average degree for Turing patterns is affirmed on the single-layer network. For multiplex networks, the differentiation of average degrees in different layers controls the generation of Turing patterns, which are not affected by the diffusion rates of the two populations. More interestingly, we observe the switching of Turing patterns and spatiotemporal patterns. We believe that these findings contribute to a better understanding of self-organization on complex networks. [ABSTRACT FROM AUTHOR]

The emergence of epidemics has seriously threatened the running of human society, such as COVID-19. During the epidemics, some external factors usually have a non-negligible impact on the epidemic transmission. Therefore, we not only consider the interaction between epidemic-related information and infectious diseases, but also the influence of policy interventions on epidemic propagation in this work. We establish a novel model that includes two dynamic processes to explore the co-evolutionary spread of epidemic-related information and infectious diseases under policy intervention, one of which depicts information diffusion about infectious diseases and the other denotes the epidemic transmission. A weighted network is introduced into the epidemic spreading to characterize the impact of policy interventions on social distance between individuals. The dynamic equations are established to describe the proposed model according to the micro-Markov chain (MMC) method. The derived analytical expressions of the epidemic threshold indicate that the network topology, epidemic-related information diffusion and policy intervention all have a direct impact on the epidemic threshold. We use numerical simulation experiments to verify the dynamic equations and epidemic threshold, and further discuss the co-evolution dynamics of the proposed model. Our results show that strengthening epidemic-related information diffusion and policy intervention can significantly inhibit the outbreak and spread of infectious diseases. The current work can provide some valuable references for public health departments to formulate the epidemic prevention and control measures. [ABSTRACT FROM AUTHOR]

Heterogeneity among interacting units plays an important role in numerous biological and man-made complex systems. While the impacts of heterogeneity on synchronization, in terms of structural mismatch of the layers in multiplex networks, has been studied thoroughly, its influence on intralayer synchronization, in terms of parameter mismatch among the layers, has not been adequately investigated. Here, we study the intralayer synchrony in multiplex networks, where the layers are different from one other, due to parameter mismatch in their local dynamics. In such a multiplex network, the intralayer coupling strength for the emergence of intralayer synchronization decreases upon the introduction of impurity among the layers, which is caused by a parameter mismatch in their local dynamics. Furthermore, the area of occurrence of intralayer synchronization also widens with increasing mismatch. We analytically derive a condition under which the intralayer synchronous solution exists, and we even sustain its stability. We also prove that, in spite of the mismatch among the layers, all the layers of the multiplex network synchronize simultaneously. Our results indicate that a multiplex network with mismatched layers can induce synchrony more easily than a multiplex network with identical layers. [ABSTRACT FROM AUTHOR]

We consider data with multiple observations or reports on a network in the case when these networks themselves are connected through some form of network ties. We could take the example of a cognitive social structure where there is another type of tie connecting the actors that provide the reports; or the study of interpersonal spillover effects from one cultural domain to another facilitated by the social ties. Another example is when the individual semantic structures are represented as semantic networks of a group of actors and connected through these actors' social ties to constitute knowledge of a social group. How to jointly represent the two types of networks is not trivial as the layers and not the nodes of the layers of the reported networks are coupled through a network on the reports. We propose to transform the different multiple networks using line graphs, where actors are affiliated with ties represented as nodes, and represent the totality of the different types of ties as a multilevel network. This affords studying the associations between the social network and the reports as well as the alignment of the reports to a criterion graph. We illustrate how the procedure can be applied to studying the social construction of knowledge in local flood management groups. Here we use multilevel exponential random graph models but the representation also lends itself to stochastic actor-oriented models, multilevel blockmodels, and any model capable of handling multilevel networks. • A Network of Networks (NoN) is a graph whose nodes are graphs on a given node set. • An NoN can be represented as a single multilevel network. • Multilevel network configurations correspond to specific dependencies in the NoN. • We illustrate NoN for dependencies among socially tied actors' semantic networks [ABSTRACT FROM AUTHOR]

Many natural, engineered and social systems can be represented using the framework of a layered network, where each layer captures a different type of interaction between the same set of nodes. The study of such multiplex networks is a vibrant area of research. Yet, understanding how to quantify the correlations present between pairs of layers, and more so present in their co-evolution, is lacking. Such methods would enable us to address fundamental questions involving issues such as function, redundancy, and potential disruptions. Here, we show first how the edge set of a multiplex network can be used to construct an estimator of a joint probability distribution describing edge existence over all layers. We then adapt an information-theoretic measure of general correlation called the conditional mutual information, which uses the estimated joint probability distribution, to quantify the pairwise correlations present between layers. The pairwise comparisons can also be temporal, allowing us to identify if knowledge of a certain layer can provide additional information about the evolution of another layer. We analyse datasets from three distinct domains-economic, political, and airline networks-to demonstrate how pairwise correlation in structure and dynamical evolution between layers can be identified and show that anomalies can serve as potential indicators of major events such as shocks.