Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow p(k) ∼ ck −α . We study the robustness of scale-free networks to random failures from the character of their heterogeneity. Entropy of the degree distribution can be an average measure of a network's heterogeneity. Optimization of scale-free network robustness to random failures with average connectivity constant is equivalent to maximize the entropy of the degree distribution. By examining the relationship of the entropy of the degree distribution, scaling exponent and the minimal connectivity, we get the optimal design of scale-free network to random failures. We conclude that the entropy of the degree distribution is an effective measure of network's resilience to random failures.
PACS 89.75.Hc -Networks and genealogical trees PACS 05.10.-a -Computational methods in statistical physics and nonlinear dynamics PACS 89.20.Hh -World Wide Web, Internet PACS 89.75.Fb -Structures and organization in complex systemsAbstract. -We study numerically the cascading failure problem by using artificially created scale-free networks and the real network structure of the power grid. The capacity for a vertex is assigned as a monotonically increasing function of the load (or the betweenness centrality). Through the use of a simple functional form with two free parameters, revealed is that it is indeed possible to make networks more robust while spending less cost. We suggest that our method to prevent cascade by protecting less vertices is particularly important for the design of more robust real-world networks to cascading failures.
Objective
: To evaluate the efficacy and safety of Hua Shi Bai Du Granule (Q-14) plus standard care compared with standard care alone in adults with coronavirus disease (COVID-19).
Study Design
: A single-center, open-label, randomized controlled trial.
Setting
: Wuhan Jinyintan Hospital, Wuhan, China, February 27 to March 27, 2020.
Participants
: A total of 204 patients with laboratory-confirmed COVID-19 were randomized into the treatment group and control group, consisting of 102 patients in each group.
Interventions
: In the treatment group, Q-14 was administered at 10 g (granules) twice daily for 14 days, plus standard care. In the control group, patients were provided standard care alone for 14 days.
Main Outcome Measure
: The primary outcome was the conversion time for the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) viral assay. Adverse events were analyzed in the safety population.
Results
: Among the 204 patients, 195 were analyzed according to the intention-to-treat principle. A totalof 149 patients (71 vs. 78 in the treatment and control groups, respectively) tested negative via the SARS-CoV-2 viral assay. There was no statistical significance in the conversion time between the treatment group and control group (full analysis set: median (interquartile range): 10.00 (9.00-11.00) vs. 10.00 (9.00-11.00); mean rank: 67.92 vs. 81.44; P=0.051.). The recovery time for fever was shorter in the treatment group than in the control group. The disappearance rate of symptomslike cough, fatigue, and chest discomfort was significantly higher in the treatment group. In chest computed tomography (CT) examinations, the overall evaluation of chest CT examination after treatment compared with baseline showed that more patients showed improvement in the treatment group. There were no significant differences in the other outcomes.
Conclusion
: The combination of Q-14 and standard care for COVID-19 was useful for the improvement of symptoms (such as fever, cough, fatigue, and chest discomfort), but did not result in a significantly higher probability of negative conversion in the SARS-CoV-2 viral assay. No serious adverse events were observed.
Trial Registration
: ChiCTR2000030288
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