Notes on Quantitative Structure-Properties Relationships (QSPR) Part Four: Quantum Multimolecular Polyhedra, Collective Vectors, Quantum Similarity, and Quantum QSPR Fundamental Equation

Carbó‐Dorca, Ramon; González, Silvia

doi:10.17265/2328-2185/2016.01.004

Cited by 7 publications

(5 citation statements)

References 36 publications

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“…Other computational algorithms have been described so far, see for example references [49][50][51][52][53][54]. The present algorithm in the Eq.…”

Section: The Appropriate Quantum Qspr Algorithmsmentioning

confidence: 99%

“…The real predictive quantum QSPR procedure consists to set up a molecular set with some molecules possessing known properties and some with unknown values. An equation of type (30) is set for the known molecular property subset, the proposed algorithms use the whole molecular set to determine the values of the property for all the structures, see for example references [49][50][51][52][53][54], or propose new applications and algorithms related to chemical problems and QSPR [94][95][96][97][98]…”

Section: The Appropriate Quantum Qspr Algorithmsmentioning

confidence: 99%

See 1 more Smart Citation

Quantum similarity and QSPR in Euclidean-, and Minkowskian–Banach spaces

Carbó‐Dorca

2023

J Math Chem

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This paper describes first how Euclidian- and Minkowskian–Banach spaces are related via the definition of a metric or signature vector. Also, it is discussed later on how these spaces can be generated using homothecies of the unit sphere or shell. Such possibility allows for proposing a process aiming at the dimension condensation in such spaces. The condensation of dimensions permits the account of the incompleteness of classical QSPR procedures, independently of whether the algorithm used is statistical bound or AI-neural network related. Next, a quantum QSPR framework within Minkowskian vector spaces is discussed. Then, a well-defined set of general isometric vectors is proposed, and connected to the set of molecular density functions generating the quantum similarity metric matrix. A convenient quantum QSPR algorithm emerges from this Minkowskian mathematical structure and isometry.

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“…Other computational algorithms have been described so far, see for example references [49][50][51][52][53][54]. The present algorithm in the Eq.…”

Section: The Appropriate Quantum Qspr Algorithmsmentioning

confidence: 99%

Section: The Appropriate Quantum Qspr Algorithmsmentioning

confidence: 99%

Quantum similarity and QSPR in Euclidean-, and Minkowskian–Banach spaces

Carbó‐Dorca

2023

J Math Chem

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“…Broadly speaking, one can consider vector semispaces, as defined over the positive real, rational or natural numbers. One can consider natural vector spaces V N (N) , defined over the set of natural numbers, as recently discussed, see references [23]- [24]., directly constructed in the guise of semispaces.…”

Section: Vector Spaces and Vector Semispacesmentioning

confidence: 99%

Boolean hypercubes and the structure of vector spaces

Carbó‐Dorca¹

2018

Journal of Mathematical Sciences and Modelling

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The present study pretends to describe an alternative way to look at Vector Spaces as a scaffold to produce a meaningful new theoretical structure to be used in both classical and quantum QSPR. To reach this goal it starts from the fact that N-Dimensional Boolean Hypercubes contain as vertices the whole information maximally expressible by means of strings of N bits. One can use this essential property to construct the structure of N-Dimensional Vector Spaces, considering vector classes within a kind of Space Wireframe related to a Boolean Hypercube. This way of deconstruct-reconstruct Vector Spaces starts with some newly coined nomenclature, because, through the present paper, any vector set is named as a Vector Polyhedron, or a polyhedron for short if the context allows it. Also, definition of an Inward Vector Product allows to easily build up polyhedral vector structures, made of inward powers of a unique vector, which in turn one might use as Vector Space basis sets. Moreover, one can construct statistical-like vectors of a given Vector Polyhedron as an extended polyhedral sequence of vector inward powers. Furthermore, the Complete Sum of a vector is defined simply as the sum of all its elements. Once defined, one can use it to compute, by means of inward products, generalized scalar products, generalized vector norms and statistical-like indices attached to a Vector Polyhedron. Along this paper will be used the well-known Dirac notation to represent vectors. According to this choice, N-Dimensional column vectors will be written as: |a = (a 1 , a 2 , ..., a N) T = {a I |I = 1, N } and the associated dual row vectors as: a| = (a 1 , a 2 , ..., a N). An N-Dimensional vector space defined over some scalar numerical set S will be represented by: V N (S). Symbolized by H N an N-Dimensional Boolean Hypercube is described by a set of 2 N vertices, which might be also noted by: |h I I = 0, 2 N − 1. Each vertex is made by all the possible combinations of sets of N binary digits. That is, sets in the form of vectors of N elements just made by two number-symbols as: B = {0, 1}. H N might be seen as the unique set of distinct vector elements, which can be contained within a vector space defined as:V N (B) .

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“…Being the molecular DF positive definite, the nature of the similarity integrals (Bultinck, Gironés, & Carbó-Dorca, 2005;Bultinck, Van Damme, & Carbó-Dorca, 2009;Carbó, Besalú, Amat, & Fradera, 1996;Carbó, Calabuig, Vera, & Besalú, 1994;Carbó & Besalú, 1995;Carbó & Calabuig, 1990;Carbó-Dorca & Besalú, 1998;Carbó-Dorca, 2013d), a basic notion in QS, is attached in any circumstance to a measure. This fact, resulting into the similarity measures definite positiveness, encompassed the discussions about the use of similarity matrices in QQSPR applications (Carbó-Dorca & Besalú, 1998;Carbó-Dorca, 2013d, 2014a, 2014b, and has to be considered the source of a large variety of mathematical definitions and algorithms (Carbó-Dorca & Barragán, n. d.;Carbó-Dorca & Besalú, 2012a;Carbó-Dorca & González, 2016;Carbó-Dorca, 2013b, 2015a) related to the QS problems.…”

Section: The Three Directions Of Quantum Similaritymentioning

confidence: 99%

“…Moreover, the condensed collective variance of any polyhedron can be considered as a collective distance involving all its vector vertices (Carbó-Dorca & Barragán, 2015). Collective distances have been recently described in several papers (Carbó-Dorca & Barragán, n. d.;Carbó-Dorca & González, 2016Carbó-Dorca, 2013b, 2014a, 2014b.…”

Section: Collective Distances In Polyhedramentioning

confidence: 99%

Molecular Spaces Quantum Quantitative Structure-Properties Relations (QQSPR)

Carbó‐Dorca

González

2016

International Journal of Quantitative Structure-Property Relationships

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Quantum QSPR can be described as a set of procedures, which can be obtained from molecular space structure, where quantum (multi)molecular polyhedra (QMP) can be defined. The collective vectors, which can be described characteristic of a given QMP and their condensed scalar values, can be used in turn to construct Hermitian QQSPR operators, which can be further employed to obtain expectation values of complex molecular properties. The linear QQSPR fundamental equation constructed from this quantum mechanical idea is able to fundament, not only an algorithm capable to obtain estimates of unknown molecular properties from the knowledge of quantum mechanical density functions, but also from the empirical, classical numerical description of molecular sets.

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Notes on Quantitative Structure-Properties Relationships (QSPR) Part Four: Quantum Multimolecular Polyhedra, Collective Vectors, Quantum Similarity, and Quantum QSPR Fundamental Equation

Cited by 7 publications

References 36 publications

Quantum similarity and QSPR in Euclidean-, and Minkowskian–Banach spaces

Quantum similarity and QSPR in Euclidean-, and Minkowskian–Banach spaces

Boolean hypercubes and the structure of vector spaces

Molecular Spaces Quantum Quantitative Structure-Properties Relations (QQSPR)

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