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Network systems with clustering have been given much attention due to their wide occurrence in the real world. One focus of these studies has been on robustness of single clustered networks and interdependent clustered networks under random attack (RA) or hub-targeted attack. However, infrastructure networks could suffer from a damage that is localized, i.e. a group of neighboring nodes attacked or fail, a topic that was not studied earlier on clustered networks. In this paper, we analytically and via simulations study the robustness under localized attack (LA) of single Erdős-Rényi clustered network and interdependent clustered network. For generating networks with clustering we use two models: (i) double Poisson distribution (DPD) and (ii) fixed degree distribution (FDD). For the LA case, the DPD model shows a second order phase transition behavior for a single clustered network, while for dependent networks, the system undergoes a change of percolation phase transition from a first order (abrupt transition) to a second order (continuous) transition when the coupling strength q decreases below a critical value q c . Our results imply that single networks become significantly more vulnerable with increasing clustering coefficient c with respect to LA. This is in contrast to RA where the robustness is almost independent of c. We obtain similar results when testing different real networks. For LA on dependent networks, we also observe that the system becomes more vulnerable as c increases. This is again in contrast to RA, where for, q<q c , the system robustness is almost unaffected by increasing clustering. We also solved analytically the case of LA on random regular networks which are clustered and interdependent and find that as m (the number of clustered networks that each network depends on) or c increases, the system becomes significantly more vulnerable. We also analyzed via simulations the case of generating clustering in networks for the model of keeping a FDD, and find that the influence of clustering on the robustness of two partially interdependent networks under LA is smaller than for DPD, which is very different from these cases under RA.

Objective: To analyze the relationship between the length from injury to first debridement (LFITFD) of open tibial fractures and perioperative infection, and explore independent risk factors related to infection.Methods: This retrospective study focused on 215 clinical patients with open tibial fractures who were admitted from January 2012 to January 2017. According to the time from injury to the operation, the patients were categorized into four groups: LFITFD ≤ 6 h, 6 < LFITFD ≤ 12 h, 12 < LFITFD≤24 h, and (LFITFD > 24 h). Infection risk factors were screened by univariate analysis, and multivariate logistic regression analysis was used to determine independent risk factors.Results: The infection rates of four groups were 9.2%, 9.5%, 11.1%, and 10.5% with six of 65, nine of 95, four of 36, and two of 19 patients being infected, respectively. There was no statistical significance between the four groups. The infection rates among fractures of different Gustilo-Anderson classifications were as follows. Of 62 cases of type I fractures, two were infected, and the infection rate was 3.2%. Among those with type II fractures, eight were infected, and the infection rate was 8.2%. Three of 26 cases of type IIIA fracture were infected, yielding an infection rate of 11.5%, seven of 25 cases of type III B fracture were infected (28% infection rate), and one of four cases of type III C fracture was infected (25% infection rate). There was a statistically significant difference between the five groups. Multivariate regression analysis showed that smoking, combined diabetes, surgical time, and fracture Gustilo-Anderson classification were independent risk factors for perioperative infection of open tibial fractures, and the difference in time from injury to first debridement was not related to infection. Conclusion:The incidence of perioperative infection in patients with open tibial fractures has little to do with the time of the first debridement, which is mainly related to the level of the fracture's Gustilo-Anderson classification. At the same time, smoking is prohibited before the operation, the patient's blood glucose is managed, and the debridement operation time is minimized conducive to reducing the incidence of infection.

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