Human awareness plays an important role in the spread of infectious diseases and the control of propagation patterns. The dynamic process with human awareness is called awareness cascade, during which individuals exhibit herd-like behavior because they are making decisions based on the actions of other individuals [Borge-Holthoefer et al., J. Complex Networks 1, 3 (2013)]. In this paper, to investigate the epidemic spreading with awareness cascade, we propose a local awareness controlled contagion spreading model on multiplex networks. By theoretical analysis using a microscopic Markov chain approach and numerical simulations, we find the emergence of an abrupt transition of epidemic threshold ${\beta }_c$ with the local awareness ratio $\alpha$ approximating $0.5$, which induces two-stage effects on epidemic threshold and the final epidemic size. These findings indicate that the increase of $\alpha$ can accelerate the outbreak of epidemics. Furthermore, a simple 1D lattice model is investigated to illustrate the two-stage-like sharp transition at ${\alpha }_c\approx 0.5$. The results can give us a better understanding of why some epidemics cannot break out in reality and also provide a potential access to suppressing and controlling the awareness cascading systems.

There has been growing interest in exploring the interplay between epidemic spreading with human response, since it is natural for people to take various measures when they become aware of epidemics. As a proper way to describe the multiple connections among people in reality, multiplex network, a set of nodes interacting through multiple sets of edges, has attracted much attention. In this paper, to explore the coupled dynamical processes, a multiplex network with two layers is built. Specifically, the information spreading layer is a time varying network generated by the activity driven model, while the contagion layer is a static network. We extend the microscopic Markov chain approach to derive the epidemic threshold of the model. Compared with extensive Monte Carlo simulations, the method shows high accuracy for the prediction of the epidemic threshold. Besides, taking different spreading models of awareness into consideration, we explored the interplay between epidemic spreading with awareness spreading. The results show that the awareness spreading can not only enhance the epidemic threshold but also reduce the prevalence of epidemics. When the spreading of awareness is defined as susceptible-infected-susceptible model, there exists a critical value where the dynamical process on the awareness layer can control the onset of epidemics; while if it is a threshold model, the epidemic threshold emerges an abrupt transition with the local awareness ratio α approximating 0.5. Moreover, we also find that temporal changes in the topology hinder the spread of awareness which directly affect the epidemic threshold, especially when the awareness layer is threshold model. Given that the threshold model is a widely used model for social contagion, this is an important and meaningful result. Our results could also lead to interesting future research about the different time-scales of structural changes in multiplex networks.

The information diffusion process in single complex networks has been extensively studied, especially for modeling the spreading activities in online social networks. However, individuals usually use multiple social networks at the same time, and can share the information they have learned from one social network to another. This phenomenon gives rise to a new diffusion process on multiplex networks with more than one network layer. In this paper we account for this multiplex network spreading by proposing a model of information diffusion in two-layer multiplex networks. We develop a theoretical framework using bond percolation and cascading failure to describe the intralayer and interlayer diffusion. This allows us to obtain analytical solutions for the fraction of informed individuals as a function of transmissibility $T$ and the interlayer transmission rate $\theta$. Simulation results show that interaction between layers can greatly enhance the information diffusion process. And explosive diffusion can occur even if the transmissibility of the focal layer is under the critical threshold, due to interlayer transmission.

With the security requirements of networks, biometrics authenticated schemes which are applied in the multi-server environment come to be more crucial and widely deployed. In this paper, we propose a novel biometric-based multi-server authentication and key agreement scheme which is based on the cryptanalysis of Mishra et al.’s scheme. The informal and formal security analysis of our scheme are given, which demonstrate that our scheme satisfies the desirable security requirements. The presented scheme provides a variety of significant functionalities, in which some features are not considered in the most of existing authentication schemes, such as, user revocation or re-registration and biometric information protection. Compared with several related schemes, our scheme has more secure properties and lower computation cost. It is obviously more appropriate for practical applications in the remote distributed networks.

We investigate the collective dynamics of excitatory-inhibitory excitable networks in response to external stimuli. How to enhance the dynamic range, which represents the ability of networks to encode external stimuli, is crucial to many applications. We regard the system as a two-layer network (E layer and I layer) and explore the criticality and dynamic range on diverse networks. Interestingly, we find that phase transition occurs when the dominant eigenvalue of the E layer's weighted adjacency matrix is exactly 1, which is only determined by the topology of the E layer. Meanwhile, it is shown that the dynamic range is maximized at a critical state. Based on theoretical analysis, we propose an inhibitory factor for each excitatory node. We suggest that if nodes with high inhibitory factors are cut out from the I layer, the dynamic range could be further enhanced. However, because of the sparseness of networks and passive function of inhibitory nodes, the improvement is relatively small compared to the original dynamic range. Even so, this provides a strategy to enhance the dynamic range.