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Register a new userAdaptive Diffusion Processes of Time-Varying Local Information on Networks
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This paper mainly discusses the diffusion on complex networks with time-varying couplings. We propose a model to describe the adaptive diffusion process of local topological and dynamical information, and find that the Barabasi-Albert scale-free network (BA network) is beneficial to the diffusion and leads nodes to arrive at a larger state value than other networks do. The ability of diffusion for a node is related to its own degree. Specifically, nodes with smaller degrees are more likely to change their states and reach larger values, while those with larger degrees tend to stick to their original states. We introduce state entropy to analyze the thermodynamic mechanism of the diffusion process, and interestingly find that this kind of diffusion process is a minimization process of state entropy. We use the inequality constrained optimization method to reveal the restriction function of the minimization and find that it has the same form as the Gibbs free energy. The thermodynamical concept allows us to understand dynamical processes on complex networks from a brand-new perspective. The result provides a convenient means of optimizing relevant dynamical processes on practical circuits as well as related complex systems.
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The vast majority of strategies aimed at controlling contagion processes on networks considers the connectivity pattern of the system as either quenched or annealed. However, in the real world many networks are highly dynamical and evolve in time concurrently to the contagion process. Here, we derive an analytical framework for the study of control strategies specifically devised for time-varying networks. We consider the removal/immunization of individual nodes according the their activity in the network and develop a block variable mean-field approach that allows the derivation of the equations describing the evolution of the contagion process concurrently to the network dynamic. We derive the critical immunization threshold and assess the effectiveness of the control strategies. Finally, we validate the theoretical picture by simulating numerically the information spreading process and control strategies in both synthetic networks and a large-scale, real-world mobile telephone call dataset
Social interactions are stratified in multiple contexts and are subject to complex temporal dynamics. The systematic study of these two features of social systems has started only very recently mainly thanks to the development of multiplex and time-varying networks. However, these two advancements have progressed almost in parallel with very little overlap. Thus, the interplay between multiplexity and the temporal nature of connectivity patterns is poorly understood. Here, we aim to tackle this limitation by introducing a time-varying model of multiplex networks. We are interested in characterizing how these two properties affect contagion processes. To this end, we study SIS epidemic models unfolding at comparable time-scale respect to the evolution of the multiplex network. We study both analytically and numerically the epidemic threshold as a function of the overlap between, and the features of, each layer. We found that, the overlap between layers significantly reduces the epidemic threshold especially when the temporal activation patterns of overlapping nodes are positively correlated. Furthermore, when the average connectivity across layers is very different, the contagion dynamics are driven by the features of the more densely connected layer. Here, the epidemic threshold is equivalent to that of a single layered graph and the impact of the disease, in the layer driving the contagion, is independent of the overlap. However, this is not the case in the other layers where the spreading dynamics are sharply influenced by it. The results presented provide another step towards the characterization of the properties of real networks and their effects on contagion phenomena
Much effort has been devoted to understand how temporal network features and the choice of the source node affect the prevalence of a diffusion process. In this work, we addressed the further question: node pairs with what kind of local and temporal connection features tend to appear in a diffusion trajectory or path, thus contribute to the actual information diffusion. We consider the Susceptible-Infected spreading process with a given infection probability per contact on a large number of real-world temporal networks. We illustrate how to construct the information diffusion backbone where the weight of each link tells the probability that a node pair appears in a diffusion process starting from a random node. We unravel how these backbones corresponding to different infection probabilities relate to each other and point out the importance of two extreme backbones: the backbone with infection probability one and the integrated network, between which other backbones vary. We find that the temporal node pair feature that we proposed could better predict the links in the extreme backbone with infection probability one as well as the high weight links than the features derived from the integrated network. This universal finding across all the empirical networks highlights that temporal information are crucial in determining a node pairs role in a diffusion process. A node pair with many early contacts tends to appear in a diffusion process. Our findings shed lights on the in-depth understanding and may inspire the control of information spread.
The metapopulation framework is adopted in a wide array of disciplines to describe systems of well separated yet connected subpopulations. The subgroups or patches are often represented as nodes in a network whose links represent the migration routes among them. The connections have been so far mostly considered as static, but in general evolve in time. Here we address this case by investigating simple contagion processes on time-varying metapopulation networks. We focus on the SIR process and determine analytically the mobility threshold for the onset of an epidemic spreading in the framework of activity-driven network models. We find profound differences from the case of static networks. The threshold is entirely described by the dynamical parameters defining the average number of instantaneously migrating individuals and does not depend on the properties of the static network representation. Remarkably, the diffusion and contagion processes are slower in time-varying graphs than in their aggregated static counterparts, the mobility threshold being even two orders of magnitude larger in the first case. The presented results confirm the importance of considering the time-varying nature of complex networks.
The study of motifs in networks can help researchers uncover links between the structure and function of networks in biology, sociology, economics, and many other areas. Empirical studies of networks have identified feedback loops, feedforward loops, and several other small structures as motifs that occur frequently in real-world networks and may contribute by various mechanisms to important functions in these systems. However, these mechanisms are unknown for many of these motifs. We propose to distinguish between structure motifs (i.e., graphlets) in networks and process motifs (which we define as structured sets of walks) on networks and consider process motifs as building blocks of processes on networks. Using the steady-state covariances and steady-state correlations in a multivariate Ornstein--Uhlenbeck process on a network as examples, we demonstrate that the distinction between structure motifs and process motifs makes it possible to gain quantitative insights into mechanisms that contribute to important functions of dynamical systems on networks.
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