Algebraic computation of genetic patterns related to three-dimensional evolution algebras
Rings and Algebras
2019-01-08 v1
Abstract
The mitosis process of an eukaryotic cell can be represented by the structure constants of an evolution algebra. Any isotopism of the latter corresponds to a mutation of genotypes of the former. This paper uses Computational Algebraic Geometry to determine the distribution of three-dimensional evolution algebras over any field into isotopism classes and hence, to describe the spectrum of genetic patterns of three distinct genotypes during a mitosis process. Their distribution into isomorphism classes is also determined in case of dealing with algebras having a one-dimensional annihilator.
Keywords
Cite
@article{arxiv.1705.04157,
title = {Algebraic computation of genetic patterns related to three-dimensional evolution algebras},
author = {Óscar J. Falcón and Raúl M. Falcón and Juan Núñez},
journal= {arXiv preprint arXiv:1705.04157},
year = {2019}
}
Comments
17 pages. . Accepted for publication in Applied Mathematics and Computation