A Fuzzy Theory Based Topological Distance Measurement for Undirected Multigraphs

The topological distance is to measure the structural difference between two graphs in a metric space. Graphs are ubiquitous, and topological measurements over graphs arise in diverse areas, including, e.g. COVID-19 structural analysis, DNA/RNA alignment, discovering the Isomers, checking the code plagiarism. Unfortunately, popular distance scores used in these applications, that scale over large graphs, are not metrics, and the computation usually becomes NP-hard. While, fuzzy measurement is an uncertain representation to apply for a polynomial-time solution for undirected multigraph isomorphism. But the graph isomorphism problem is to determine two finite graphs that are isomorphic, which is not known with a polynomial-time solution. This paper solves the undirected multigraph isomorphism problem with an algorithmic approach as NP=P and proposes a polynomial-time solution to check if two undirected multigraphs are isomorphic or not. Based on the solution, we define a new fuzzy measurement based on graph isomorphism for topological distance/structural similarity between two graphs. Thus, this paper proposed a fuzzy measure of the topological distance between two undirected multigraphs. If two graphs are isomorphic, the topological distance is 0;if not, we will calculate the Euclidean distance among eight extracted features and provide the fuzzy distance. The fuzzy measurement executes more efficiently and accurately than the current methods.

China's experience in COVID-19 prevention and control among children in its different regions.

OBJECTIVE: To summarize the experience of three Chinese cities (Wuhan, Shanghai and Haikou) and provide a reference for global efforts to combat COVID-19 spread among children. MATERIALS AND METHODS: Through collecting the measures and outcomes of preventing and controlling COVID-19 in China's three hospitals, we compared the effect of different strategies. RESULTS: From January to March 2020, the number of suspected and confirmed COVID-19 cases in Wuhan increased exponentially, and Wuhan Children's Hospital as a whole was transformed into a designated quarantine and treatment facility, which is the "Wuhan Model". Shanghai has more children's hospitals with better capabilities to tackle public health emergency. Besides, it is far away from Wuhan and had a small caseload. Children's Hospital of Fudan University, a facility in Shanghai to treat pediatric infectious diseases, is famous for its well-equipped building for infectious disease treatment and professional medical team, and therefore no major transformation was required. That is the "Shanghai Model". Haikou is located on an island. Amid the outbreak, large numbers of tourists and travelers from Hubei had already arrived in Haikou. Hainan Women and Children's Medical Center, as the only pediatric care hospital in Hainan Province, did not have a separate building for infectious disease treatment. After a citywide survey of the medical resources and facilities available, a temporarily idle hospital 3 kilometers away from Hainan Women and Children's Medical Center was requisitioned as the quarantine and treatment facility for pediatric cases. That is the "Hainan Model". The three models enabled the treatment of all suspected and confirmed cases and no fatality was reported. CONCLUSIONS: The COVID-19 coping strategies for children should be designed according to the existing conditions of the local children's hospitals and the risk levels of the epidemic.