Robustness analysis of interdependent network accounting for failure probability and coupling patterns.

The robustness of interdependent networks against perturbations is an important problem for network design and operation. This paper focuses on establishing a cascading failure dynamics model and analyzing the robustness for interdependent networks, in which the states of the nodes follow certain failure probability and various connectivity patterns. First, to describe the removal mechanism of an overloaded node, the failure probability associated with the load distribution of components was proposed. Then, we present the node capacity cost and the average capacity cost of the network to investigate the propagation of cascading failures. Finally, to discuss the impact of the configuration parameters on robustness, some numerical examples are conducted, where the robustness was analyzed based on the proposed method and different interdependence types. Our results show that, the larger the overload parameter, the more robust the network is, but this also increases the network cost. Furthermore, we find that allocating more protection resources to the nodes with higher degree can enhance the robustness of the interdependent network. The robustness of multiple-to-multiple interdependent networks outperforms that of one-to-one interdependent networks under the same coupling pattern. In addition, our results unveil that the impact of coupling strategies on the robustness of multiple-to-multiple interdependent networks is smaller than that of one-to-one interdependent networks.

[Clinical effect of Yisui decoction plus western medicine in treating multiple system atrophy].

To observe the clinical effect of Yisui decoction plus western medicine in treating multiple system atrophy patients, totally 65 patients from China-Japan Friendship hospital during 2008-2012 with complete clinical data and received consecutive traditional Chinese medicine and western medicine treatment for more than 3 months were observed changes of traditional Chinese medicine symptom score, part 1 of unified multiple system atrophy rating scale, orthostatic hypotension before treatment and after 3 months treatment. After 3 months treatment, total effective rate of traditional Chinese medicine symptom was 70.8%. Compared with before treatment, score of part 1 of unified multiple system atrophy rating scale was obviously reduced after 3 month treatment (P < 0.001). Ex- cept swallow function without significant improvement, the remaining projects of unified multiple system atrophy rating scale were im- proved obviously (P < 0.05), of which the most obvious differences were orthostatic symptoms, falls and intestinal function (P < 0.001). Orthostatic hypotension after 1 month treatment and 3 month treatment was obviously better than before treatment (P < 0.001). There was no significant difference in orthostatic hypotension between 1 month treatment and 3 month treatment. The research results show that Yisui decoction plus western medicine has a certain effect on improving clinical symptoms of multiple system atrophy patients, especially has a significant effect on orthostatic hypotension, and can maintain a stable clinical effect in a certain period of time.

Nonlocal delay gives rise to vegetation patterns in a vegetation-sand model.

The vegetation pattern generated by aeolian sand movements is a typical type of vegetation patterns in arid and semi-arid areas. This paper presents a vegetation-sand model with nonlocal interaction characterized by an integral term with a kernel function. The instability of the Turing pattern was analyzed and the conditions of stable pattern occurrence were obtained. At the same time, the multiple scales method was applied to obtain the amplitude equations at the critical value of Turing bifurcation. The spatial distributions of vegetation under different delays were obtained by numerical simulation. The results revealed that the vegetation biomass increased as the interaction intensity decreased or as the nonlocal interaction distance increased. We demonstrated that the nonlocal interaction between vegetation and sand is a crucial mechanism for forming vegetation patterns, which provides a theoretical basis for preserving and restoring vegetation.