{"title":"空间填充图的加权高斯曲率导数","authors":"A. Akopyan, H. Edelsbrunner","doi":"10.1515/cmb-2020-0101","DOIUrl":null,"url":null,"abstract":"Abstract The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy.","PeriodicalId":34018,"journal":{"name":"Computational and Mathematical Biophysics","volume":"8 1","pages":"74 - 88"},"PeriodicalIF":0.0000,"publicationDate":"2019-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/cmb-2020-0101","citationCount":"4","resultStr":"{\"title\":\"The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram\",\"authors\":\"A. Akopyan, H. Edelsbrunner\",\"doi\":\"10.1515/cmb-2020-0101\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy.\",\"PeriodicalId\":34018,\"journal\":{\"name\":\"Computational and Mathematical Biophysics\",\"volume\":\"8 1\",\"pages\":\"74 - 88\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-08-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/cmb-2020-0101\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational and Mathematical Biophysics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/cmb-2020-0101\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational and Mathematical Biophysics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/cmb-2020-0101","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram
Abstract The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy.
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