A New Derivation and Recursive Algorithm Based on Wronskian Matrix for Vandermonde Inverse Matrix

For an analytical expression of Vandermonde inverse matrix, a new derivation process based on Wronskian matrix and Lagrange interpolation polynomial basis is presented. Recursive formula and implementation cases for the direct formula of Vandermonde inverse matrix are given based on deriving the unified formula of Wronskian inverse matrix. For the calculation of symbol-type Vandermonde inverse matrix, the direct formula and recursive method are verified to be more efficient than Mathematica which is good at symbolic computation by comparing the computing time in Mathematica. The process and steps of recursive algorithm are relatively simple. The derivation process and idea both have very important values in theory and practice of Vandermonde and generalized Vandermonde inverse matrix

Prediction of Metabolic Syndrome for the Survival of Patients With Digestive Tract Cancer: A Meta-Analysis

Background and Objectives: Growing evidence indicates that metabolic syndrome confers a differential risk for the development and progression of many types of cancer, especially in the digestive tract system. We here synthesized the results of published cohort studies to test whether baseline metabolic syndrome and its components can predict survival in patients with esophageal, gastric, or colorectal cancer.Methods: Literature retrieval, publication selection and data extraction were performed independently by two authors. Analyses were done using STATA software (version 14.1).Results: A total of 15 publications involving 54,656 patients were meta-analyzed. In overall analyses, the presence of metabolic syndrome was associated with a non-significant 19% increased mortality risk for digestive tract cancer (hazard ratio [HR]: 1.19; 95% confidence interval [CI]: 1.45 to 2.520.95 to 1.49, P = 0.130; I2: 94.8%). In stratified analyses, the association between metabolic syndrome and digestive tract cancer survival was statistically significant in prospective studies (HR: 1.64, 95% CI: 1.18 to 2.28), in studies involving postsurgical patients (HR: 1.42, 95% CI: 1.06 to 1.92), and in studies assessing cancer-specific survival (HR: 1.91, 95% CI: 1.45 to 2.52). Further meta-regression analyses indicated that age and smoking were potential sources of between-study heterogeneity (both P < 0.001). The shape of the Begg's funnel plot seemed symmetrical (Begg's test P = 0.945 and Egger's test P = 0.305).Conclusions: Our findings indicate that metabolic syndrome is associated with an increased risk of postsurgical digestive tract cancer-specific mortality. Continued investigations are needed to uncover the precise molecule mechanism linking metabolic syndrome and digestive tract cancer