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Brain network analysis can offer useful information to guide the rehabilitation of post-stroke patients. We applied functional network connection models based on multiplex-multilayer network analysis (MMN) to explore functional network connectivity changes induced by robot-aided gait training (RAGT) using the Ekso, a wearable exoskeleton, and compared it to conventional overground gait training (COGT) in chronic stroke patients. We extracted the coreness of individual nodes at multiple locations in the brain from EEG recordings obtained before and after gait training in a resting state. We found that patients provided with RAGT achieved a greater motor function recovery than those receiving COGT. This difference in clinical outcome was paralleled by greater changes in connectivity patterns among different brain areas central to motor programming and execution, as well as a recruitment of other areas beyond the sensorimotor cortices and at multiple frequency ranges, contemporarily. The magnitude of these changes correlated with motor function recovery chances. Our data suggest that the use of RAGT as an add-on treatment to COGT may provide post-stroke patients with a greater modification of the functional brain network impairment following a stroke. This might have potential clinical implications if confirmed in large clinical trials.

In complex networks, the existing link prediction methods primarily focus on the internal structural information derived from single-layer networks. However, the role of interlayer information is hardly recognized in multiplex networks, which provide more diverse structural features than single-layer networks. Actually, the structural properties and functions of one layer can affect that of other layers in multiplex networks. In this paper, the effect of interlayer structural properties on the link prediction performance is investigated in multiplex networks. By utilizing the intralayer and interlayer information, we propose a novel “Node Similarity Index” based on “Layer Relevance” (NSILR) of multiplex network for link prediction. The performance of NSILR index is validated on each layer of seven multiplex networks in real-world systems. Experimental results show that the NSILR index can significantly improve the prediction performance compared with the traditional methods, which only consider the intralayer information. Furthermore, the more relevant the layers are, the higher the performance is enhanced.

In this paper, the interplay of epidemic spreading and the strategy-mixed awareness diffusion within the framework of multiplex networks is studied. In the model, epidemics can spread through a physical-contact layer and the awareness can diffuse through a virtual-contact layer. Each node on physical-contact layer is randomly matched one-to-one with a node of virtual-contact layer, but the connectivity is distinct in each of them. In view of the complexity of human behaviors, we assume that the diffusion of awareness is ruled by two mixed contagion dynamics: a fraction $m$ of individuals adopt the herd-like dynamics and the others follow the epidemic-like dynamics. We analyze the epidemic threshold based on the microscopic Markov chain approach. Meanwhile, combing with the Monte Carlo (MC) simulations, we show that the strategy-mixed awareness diffusion mechanism can enrich the dynamics of epidemic spreading, including the crossover phenomenon of the final epidemic size, the two-stage effect of the local awareness rate, and so forth.

Cooperate epidemic spreading dynamics has attracted much attention from the field of network science. In this paper, we study the cooperate epidemic spreading dynamics on multiplex networks with heterogeneous populations, which induces the heterogeneous coinfection susceptibility. We propose a spreading model to describe the evolution mechanisms. To predict the final state of the epidemic outbreak size, a generalized bond percolation theory is suggested. Through numerical simulations and theoretical analyses, we find that the system exhibits a discontinuous phase transition for large average and small variance of the distribution of coinfection susceptibility on ER–ER multiplex networks, while the phase transition is continuous on SF–SF networks. In addition, the final outbreak size increases with the average coinfection susceptibility and decreases with the variance of the coinfection susceptibility. Our suggested bond percolation theory can well predict the numerical simulations.

It is common that the spreading of epidemics is influenced by other simultaneous spreading diseases and preventive reactions due to the awareness of people. In this paper, we study the co-evolution dynamics of two competing epidemics and the awareness process for prevention related to the epidemics, where the former represents the biological suppression impact and the latter represents social suppression impact. Our analysis reveals that when the two factors act simultaneously their impact is not guaranteed to be suppression, but may even prompt the spreading of an epidemic. Detailed analyses are provided to account for these phenomena which are supported by numerical simulations.

In the course of individual consumption decision-making, the interaction between online product-attributes information propagation and face-to-face word-of-mouth (WOM) communication is an important influencing factor, and due to the heterogeneity of individuals and the involvement of enterprise, the interaction becomes more complicated. In this paper, we establish a multi-layer network model to explore the effect of individual and enterprise behaviors on the interaction between product-attributes information propagation and WOM communication, and derive mean-field equations to describe the dynamics process on complex social networks. We use analytical and numerical solutions of these equations to examine the threshold for the product-attributes information propagation and the WOM communication (both positive WOM and negative WOM). It also finds that individual behavior promotes both product-attributes information propagation and WOM communication, but the marginal utility of such promotion is diminishing; enterprise behavior promotes the communication of positive WOM and suppresses the communication of negative WOM.

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.

Modeling multiple complex systems as multiplex networks has refreshed our opinions about the structure and dynamics of assorted real-world systems. By studying the traffic dynamics of two-layer multiplex networks, it can be found that the limited buffer queue length of each node in both the logical and physical layers is one of the factors that restrict the whole network traffic capacity. Since high degree nodes in the network may bear heavier load, it is necessary to allocate a larger buffer queue to them. In order to enhance the transport efficiency, a new queue allocation strategy is proposed to alleviate the congestion of the two-layer multiplex networks. By extensive computer simulations, the proposed strategy can effectively improve the traffic capacity of the multiplex networks.

Controlling the virus spreading in complex networks is very important to the research fields ranging from social science to technology. However, recent researches only consider information transmission and virus spreading as independent and uncorrelated, which neglect their interactive process in real systems. To study the interactive process between information transmission and virus spreading, in this paper, we propose a new virus information interactive spreading model on multiplex network. The multiplex networks can be divided into information transmission layer and virus spreading layer. The interactive spreading model considers the inherent characteristics of information by introducing the information forgetting and information loss mechanisms. Specially, by utilizing the mean field theory, the information transmission and virus process are unified to deduce the critical threshold of virus breakout. It shows that the critical threshold is not only related to the spreading properties of virus, but also influenced by the information density of individuals. We also find that the critical threshold is independent of the information generation probability, and the loss of the information will lead to a decrease. Finally, to verify the theoretical derivations, we apply it on both artificial network and real social network. The experimental results show that the simulations perfectly coincide with theoretical results, which verified the effectiveness of our model.

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.

By incorporating multi-community attachments into the continuous opinion formation model, we investigate the driving force for reaching consensus in networked systems. A phase transition from fragmentation to consensus is determined by the multiplex network structures and the coupling of different communities. A moderate number of layers and weak coupling are beneficial for consensus. The evolutionary dynamics in the present model is governed by the prolonged evolutionary time, which results from the disparities of individual opinions in different communities. Increasing the multiple layers is similar to promoting coupling between different communities. A functional relation between the convergence time and the coupling coefficient is found.

We study the resilience of a multiplex socio-ecological system (SES) which we structure from the spheres composing the sustainability Venn diagram. The SES network is subject to dynamics of spread of a global reform through a knock-on effect, as a direct and indirect repercussion of a small-scale reform process that spreads out over time through network connectivity. The model outcomes reveal that high probability of reform completion on an SES layer through nodes previously reformed on other SES layers is necessary and sufficient to propagate the desired reform on that layer. The maximum asymptotic density of reformed nodes can only be achieved in the absence of risk of reform abrogation. When the risk is significant, it prevents the equilibrium density from reaching a steady state. The numerical simulation results show that the combination of likely probability of reform completion and of proportional influence of all layers yields the maximum magnitude of efficiency of the knock-on effect. We provide a formal argument that favors assigning equal weight to all aspects of sustainable development.

Recent studies on international networks have investigated the role of global cities as catalysts of knowledge flows. In this paper, we examine global cities in transnational networks of innovators. To assess the likelihood of scientists and inventors from different cities to take part in international teams, we propose a measure based on 3-hyperedges in the collaboration network constructed from scientific publications and patents. This measure is used to identify the most competitive global cities in the international network of innovators. To this end, we construct a null model based on the hypergeometric ensembles of random graphs. We find that five US cities play a leading role in transnational networks of innovators. Among them, San Francisco stands out as the most globalized city.

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.