Journal of Mathematical Chemistry

, Volume 53, Issue 8, pp 1876–1884 | Cite as

An isometric representation problem in quantum multimolecular polyhedra and similarity: (2) synisometry

  • Ramon Carbó-DorcaEmail author
Original Paper


Collective distances in quantum multimolecular polyhedra (QMP), which can be set as a scalar indices associated to the QMP variance vector, enhance the role of the pair density similarity matrix. This paper describes a simplified efficient algorithm to compute triple, quadruple or higher order density similarity hypermatrices via an approximate isometry: a synisometric decomposition of the pair similarity matrix. Synisometries pretend to avoid the use of Minkowski metrics in QMP description problems, where the double density similarity matrix possesses negative eigenvalues. The synisometric decomposition of the similarity matrix opens the way to the general use of higher order approximate similarity elements in quantum QSAR and in the construction of scalar condensed vector statistical-like indices, for instance skewness and kurtosis. This might lead the way to describe, without excessive complication and within a real field computational framework, the collective structure of quantum multimolecular polyhedra.


Quantum molecular similarity Quantum multimolecular polyhedra Quantum object sets Density functions discrete isometric and Synisometric representation Collective distances  Collective similarity indices 



The author wishes to specify that this work has been developed under a Prometeo fellowship, and acknowledges the SENESCYT, Government of Ecuador, for granting it.

Conflict of interest

The author confirms that this paper contents have no conflict of interest.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institut de Química Computacional i CatàlisiUniversitat de GironaGironaSpain
  2. 2.Departamento de QuímicaUniversidad Técnica Particular de LojaLojaEcuador

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