Comunications on Quantum Similarity distances computed by means of Similarity Matrices, as generators of intrinsic ordering among Quantum Multimolecular Polyhedra.

This study generalizes the notion of distance via de?ning an axiomatic collectivedistance, between arbitrary vector sets. A ?rst part discusses conceptual tools,which can be later useful for general mathematical practice or as computationalquantum similarity indices. After preliminary de?nitions, tw...

Full description

Saved in:
Bibliographic Details
Main Author: Carb?-Dorca, Carr?
Format: Artículos
Language:eng
Published: 2016
Subjects:
Online Access:http://repositorio.educacionsuperior.gob.ec/handle/28000/3103
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This study generalizes the notion of distance via de?ning an axiomatic collectivedistance, between arbitrary vector sets. A ?rst part discusses conceptual tools,which can be later useful for general mathematical practice or as computationalquantum similarity indices. After preliminary de?nitions, two elements, whichcan be associated with arbitrary sets of a vector space, are described: the centroidand the variance vectors. The Minkowski norm of the variance vector is shownto comply with the axioms of a collective distance. The role of the Gram matrix,associated with a vector set, is linked to the de?nition of numerical variance.Several simple application examples involving linear algebra and N-dimensionalgeometry are given. In a second part, all previous de?nitions are applied toquantum multimolecular polyhedra (QMP), where a set of molecular quantummechanical density functions act as vertices. The numerical Minkowski norm of thevariance vector in any QMP could be considered as a superposition of molecularcontributions, corresponding to a new set of quantum similarity indices, which cangenerate intrinsic ordering among QMP vertices. In this way, the role of quantumsimilarity matrix elements is evidenced. Application to collections of molecularstructures is analyzed as an illustrative practical exercise. The connection of theQMP framework with classical and quantum quantitative structure?propertiesrelation (QSPR) becomes evident with the aid of numerical examples computedover several molecular sets acting as QMP.