We propose a dynamic model for a system consisting of self-propelled agents in which the influence of an agent on another agent is weighted by geographical distance. A parameter $alpha$ is introduced to adjust the influence: the smaller value of $alp
ha$ means that the closer neighbors have stronger influence on the moving direction. We find that there exists an optimal value of $alpha$, leading to the highest degree of direction consensus. The value of optimal $alpha$ increases as the system size increases, while it decreases as the absolute velocity, the sensing radius and the noise amplitude increase.
Understanding spreading dynamics will benefit society as a whole in better preventing and controlling diseases, as well as facilitating the socially responsible information while depressing destructive rumors. In network-based spreading dynamics, edg
es with different weights may play far different roles: a friend from afar usually brings novel stories, and an intimate relationship is highly risky for a flu epidemic. In this article, we propose a weighted susceptible-infected-susceptible model on complex networks, where the weight of an edge is defined by the topological proximity of the two associated nodes. Each infected individual is allowed to select limited number of neighbors to contact, and a tunable parameter is introduced to control the preference to contact through high-weight or low-weight edges. Experimental results on six real networks show that the epidemic prevalence can be largely promoted when strong ties are favored in the spreading process. By comparing with two statistical null models respectively with randomized topology and randomly redistributed weights, we show that the distribution pattern of weights, rather than the topology, mainly contributes to the experimental observations. Further analysis suggests that the weight-weight correlation strongly affects the results: high-weight edges are more significant in keeping high epidemic prevalence when the weight-weight correlation is present.
In this paper, we consider the Fefferman-Stein decomposition of $Q_{alpha}(mathbb{R}^{n})$ and give an affirmative answer to an open problem posed by M. Essen, S. Janson, L. Peng and J. Xiao in 2000. One of our main methods is to study the structure
of the predual space of $Q_{alpha}(mathbb{R}^{n})$ by the micro-local quantities. This result indicates that the norm of the predual space of $Q_{alpha}(mathbb{R}^{n})$ depends on the micro-local structure in a self-correlation way.
Background: Controlling global epidemics in the real world and accelerating information propagation in the artificial world are of great significance, which have activated an upsurge in the studies on networked spreading dynamics. Lots of efforts hav
e been made to understand the impacts of macroscopic statistics (e.g., degree distribution and average distance) and mesoscopic structures (e.g., communities and rich clubs) on spreading processes while the microscopic elements are less concerned. In particular, roles of ties are not yet clear to the academic community. Methodology/Principle Findings: Every edges is stamped by its strength that is defined solely based on the local topology. According to a weighted susceptible-infected-susceptible model, the steady-state infected density and spreading speed are respectively optimized by adjusting the relationship between edges strength and spreading ability. Experiments on six real networks show that the infected density is increased when strong ties are favored in the spreading, while the speed is enhanced when weak ties are favored. Significance of these findings is further demonstrated by comparing with a null model. Conclusions/Significance: Experimental results indicate that strong and weak ties play distinguishable roles in spreading dynamics: the former enlarge the infected density while the latter fasten the process. The proposed method provides a quantitative way to reveal the qualitatively different roles of ties, which could find applications in analyzing many networked dynamical processes with multiple performance indices, such as synchronizability and converging time in synchronization and throughput and delivering time in transportation.
