Oriented Conformal Geometric Algebra and the Molecular Distance Geometry Problem

作     者：Lavor, Carlile Alves, Rafael 

作者机构：Univ Estadual Campinas UNICAMP IMECC BR-13081970 Campinas SP Brazil Fed Univ ABC UFABC CMCC BR-09210580 Santo Andre SP Brazil 

出 版 物：《ADVANCES IN APPLIED CLIFFORD ALGEBRAS》 (克里福德几何代数高级应用)

年 卷 期：2019年第29卷第1期

页      面：9-9页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：CNPq CAPES FAPESP 

主　　题：Oriented conformal geometric algebra Distance geometry Branch and prune algorithm 3D protein structure 

摘      要：The problem of 3D protein structure determination using distance information from nuclear magnetic resonance (NMR) experiments is a classical problem in distance geometry. NMR data and the chemistry of proteins provide a way to define a protein backbone order such that the distances related to the pairs of atoms are available, implying a combinatorial method to solve the problem, called branch-and-prune (BP). There are two main steps in BP algorithm: the first one (the branching phase) is to intersect three spheres centered at the positions for atoms , respectively, to obtain two possible positions for atom i;and the second one (the pruning phase) is to check if additional spheres (related to distances can be used to select one of the two possibilities for atom i. Differently from distances , may not be precise. BP algorithm has difficulties to deal with uncertainties, and this paper proposes the oriented conformal geometric algebra to take care of intersection of spheres when their centers and radius are not precise.