Narrow Results

In interdependent networks, link addition strategies can enhance the connectivity of networks, thus improving robustness in the face of cascading failures. In this paper, first, interdependent networks models under various coupling methods and cascading failures model are proposed. Moreover, link addition strategies and node importance metrics are obtained. Finally, this paper analyzes the influence of link addition strategies and node importance metrics on robustness under three coupling methods. Besides, the effects of coupling ratio and link addition ratio on robustness in the interdependent network under different coupling methods are also analyzed. The simulation results show in partial coupled networks, intra-layer link addition strategy (Intra LAS) is more robust. In one-to-one coupled networks, inter-layer link addition strategy (Inter LAS) yields better performance in improving robustness when the number of initial attacked nodes is fewer, and intra-layer link addition strategy (Intra LAS) is more robust when more nodes are attacked initially. The effect of network size and the average degree of network on this result are also discussed. The variation trend of networks with multiple dependencies is similar to that of partial coupled network with high coupling rate, but it has less robust than partial coupled network. The conclusions can provide guidance on how to select link addition strategy and node importance metric under different coupling methods.

We introduce the notion of coupling distances on the space of Lévy measures in order to quantify rates of convergence towards a limiting Lévy jump diffusion in terms of its characteristic triplet, in particular in terms of the tail of the Lévy measure. The main result yields an estimate of the Wasserstein–Kantorovich–Rubinstein distance on path space between two Lévy diffusions in terms of the coupling distances. We want to apply this to obtain precise rates of convergence for Markov chain approximations and a statistical goodness-of-fit test for low-dimensional conceptual climate models with paleoclimatic data.