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Genetic coalgebras and their cubic stochastic matrices

机译:遗传结合及其立方随机矩阵

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摘要

We study the structure of genetic coalgebras and prove the existence of a decomposition as the direct sum of indecomposable subcoalgebras with genetic realization. To obtain such a decomposition, we first define a new multiplication for their related cubic stochastic matrices of type (1,2) and then, considering these matrices as cubic non-negative, we show how this new multiplication induces an index classification which can be used to study the genetic coalgebra structure. Genetically, the given coalgebra decomposition can be understood as a genetic clustering of the different types for the genetic trait defining the genetic coalgebra, which allows us to identify isolated ancestral populations.
机译:我们研究了遗传结合的结构,并证明了分解的存在作为具有遗传实现的不可分解的亚古格拉斯的直接和。 为了获得这样的分解,我们首先为其相关的立方随机矩阵定义一个新的乘法(1,2),然后将这些矩阵视为立方体非负,我们展示了这一新乘法如何引起可以是索引分类 用于研究遗传结合结构。 遗传上,给定的基地资料分解可以被理解为不同类型的遗传性状的遗传聚类,用于定义遗传结合的遗传特征,这使我们能够识别孤立的祖传人群。

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