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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...

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Autor Principal: Carb?-Dorca, Carr?
Formato: Artículos
Lenguaje:eng
Publicado: 2016
Materias:
QUANTUM SIMILARITY
COMMUNICATIONS
COLLECTIVE DISTANCES COMPUTED
MULTIMOLECULAR POLYHEDRA
Acceso en línea:http://repositorio.educacionsuperior.gob.ec/handle/28000/3103
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spelling oai:localhost:28000-31032017-04-17T21:01:47Z Comunications on Quantum Similarity distances computed by means of Similarity Matrices, as generators of intrinsic ordering among Quantum Multimolecular Polyhedra. Carb?-Dorca, Carr? QUANTUM SIMILARITY COMMUNICATIONS COLLECTIVE DISTANCES COMPUTED 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, 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. Universidad T?cnica Particular de Loja http://onlinelibrary.wiley.com/doi/10.1002/wcms.1223/abstract 2016-11-09T17:26:50Z 2016-11-09T17:26:50Z 2015 article Carb?-Dorca, Carr?.; Barragan, Diego. (2015). Comunications on Quantum Similarity distances computed by means of Similarity Matrices, as generators of intrinsic ordering among Quantum Multimolecular Polyhedra. Computational Molecular Science. Vol.5, N?5. pp.380-404 1759-0884 http://repositorio.educacionsuperior.gob.ec/handle/28000/3103 eng restrictedAccess pp.380-404
institution SENESCYT
collection Repositorio SENESCYT
biblioteca Biblioteca Senescyt
language eng
format Artículos
topic QUANTUM SIMILARITY
COMMUNICATIONS
COLLECTIVE DISTANCES COMPUTED
MULTIMOLECULAR POLYHEDRA
spellingShingle QUANTUM SIMILARITY
COMMUNICATIONS
COLLECTIVE DISTANCES COMPUTED
MULTIMOLECULAR POLYHEDRA
Carb?-Dorca, Carr?
Comunications on Quantum Similarity distances computed by means of Similarity Matrices, as generators of intrinsic ordering among Quantum Multimolecular Polyhedra.
description 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.
author Carb?-Dorca, Carr?
author_facet Carb?-Dorca, Carr?
author_sort Carb?-Dorca, Carr?
title Comunications on Quantum Similarity distances computed by means of Similarity Matrices, as generators of intrinsic ordering among Quantum Multimolecular Polyhedra.
title_short Comunications on Quantum Similarity distances computed by means of Similarity Matrices, as generators of intrinsic ordering among Quantum Multimolecular Polyhedra.
title_full Comunications on Quantum Similarity distances computed by means of Similarity Matrices, as generators of intrinsic ordering among Quantum Multimolecular Polyhedra.
title_fullStr Comunications on Quantum Similarity distances computed by means of Similarity Matrices, as generators of intrinsic ordering among Quantum Multimolecular Polyhedra.
title_full_unstemmed Comunications on Quantum Similarity distances computed by means of Similarity Matrices, as generators of intrinsic ordering among Quantum Multimolecular Polyhedra.
title_sort comunications on quantum similarity distances computed by means of similarity matrices, as generators of intrinsic ordering among quantum multimolecular polyhedra.
publishDate 2016
url http://repositorio.educacionsuperior.gob.ec/handle/28000/3103
_version_ 1634995109206425600
score 11,871979

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