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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oai:localhost:28000310320170417T21:01:47Z 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 Ndimensionalgeometry 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 20161109T17:26:50Z 20161109T17:26:50Z 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.380404 17590884 http://repositorio.educacionsuperior.gob.ec/handle/28000/3103 eng restrictedAccess pp.380404 
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QUANTUM SIMILARITY COMMUNICATIONS COLLECTIVE DISTANCES COMPUTED MULTIMOLECULAR POLYHEDRA 
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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 Ndimensionalgeometry 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 
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http://repositorio.educacionsuperior.gob.ec/handle/28000/3103 
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1634995109206425600 
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11,871979 