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Shadows’ hypercube, vector spaces, and non-linear optimization of QSPR procedures

Abstract:

The role of the shadows’ hypercube is presented first to define a classification of the vectors in a vector space defined over the rational field. Up from this step, the inward product of vectors is presented as the basis for non-linear optimization of several vector scalar and matrix functions. The first use of the inward power of a vector shows that the simple least-squares fitting can be non-linearly optimized. Then the shadows’ hypercube is connected with the topological description of molecules. Further application of the developed theoretical background to the QSPR problem permits us to have some insight into the role of descriptor representation of molecular structures and the non-linear optimization of the involved equations.