![]() Subsequently, multinomial generating functions for colorings of all (6-q)-hyperplanes of the 6D-hypercube are constructed for q = 1 through 6. ![]() Computational techniques are comprised of computing the generalized character cycle indices of 65 irreducible representations for all hyperplanes of the 6D-hypercube using the Möbius inversion technique followed by the construction of polynomial generators for different cycle types under the hyperoctahedral group action for all six types of hyperplanes of the 6D-hypercube. The computational techniques are inspired by a number of physico-chemical and biological applications to molecular chirality, molecular clusters, isomerization reaction graphs, relativistic effects, massively-large data sets, visualization, and genetic regulatory networks. Some aspects of the Quantum Analogy Functor approach, with focus on Molecular Shapes and QShAR are discussed in this contribution.Ĭomputational generating function techniques are outlined for combinatorics of colorings of all hyperplanes of the 6D-hypercube for 65 irreducible representations of the 6D-hyperoctahedral group isomorphic to the wreath product S6 group of order 46,080. The Quantum Similarity Measures and alternative measures based on quantum chemistry are combined into a Quantum Analogy Functor model, with special emphasis on the 3D molecular shapes represented by the electron density clouds, and the associated Quantitative Shape-Activity Relations, QShAR. Such analogies are highly relevant in the interpretation of complex biochemical actions, as well as in pharmaceutical drug design. ![]() Some of the relevant background important in molecular applications, especially, in studies of chemical and biochemical activity problems are discussed, where several factors of various levels of similarities are determining the overall chemical processes. An analogy can be regarded as a relation between two families of similarities, and the mathematical tool of functor has been proposed for certain chemical applications where not just one type of similarity, but entire families of similarities, hence, analogies, are playing important roles. ![]()
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