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Hand, foot, and mouth disease (HFMD) is a common childhood infectious disease. The incidence of HFMD has a pronounced seasonal tendency and is closely related to meteorological factors such as temperature, rainfall, and wind speed. In this paper, we propose a combined SARIMA-XGBoost model to improve the prediction accuracy of HFMD in 15 regions of Xinjiang, China. The SARIMA model is used for seasonal trends, and the XGBoost algorithm is applied for the nonlinear effects of meteorological factors. The geographical and temporal weighted regression model is designed to analyze the influence of meteorological factors from temporal and spatial perspectives. The analysis results show that the HFMD exhibits seasonal characteristics, peaking from May to August each year, and the HFMD incidence has significant spatial heterogeneity. The meteorological factors affecting the spread of HFMD vary among regions. Temperature and daylight significantly impact the transmission of the disease in most areas. Based on the verification experiment of forecasting, the proposed SARIMA-XGBoost model is superior to other models in accuracy, especially in regions with a high incidence of HFMD. [ABSTRACT FROM AUTHOR]

The n -dimensional augmented cube A Q n , proposed by Choudum and Sunitha in 2002, is one of the most famous interconnection networks of the distributed parallel system. Reliability evaluation of underlying topological structures is vital for fault tolerance analysis of this system. As one of the most extensively studied parameters, the k -conditional edge-connectivity of a connected graph G , λ k (G) , is defined as the minimum number of the cardinality of the edge-cut of G , if exists, whose removal disconnects this graph and keeps each component of G − F having minimum degree at least k. Let n , t and δ be three integers, where δ = 1 , if t = 0 and δ = 0 , if t > 0. In this paper, we determine the exact value of the (2 t − 1) -conditional edge-connectivity of A Q n , λ 2 t − 1 (A Q n) = 2 t (2 n − 2 t) − δ for each positive integer 0 ≤ t ≤ n − 1 and n ≥ 1 , and give an affirmative answer to Shinde and Borse's corresponding conjecture on this topic in [On edge-fault tolerance in augmented cubes, J. Interconnection Netw. 20(4) (2020), DOI:10.1142/S0219265920500139 ]. [ABSTRACT FROM AUTHOR]