biogroupoids and mathematical models of species evolution

Biogroupoids and mathematical models of species evolution

Introduction

Biogroupoids, $ \mathcal{G_B}$ , were introduced as mathematical representations of evolving biological species ([1,2]) that are defined by (or `consist of') weakly equivalent classes of living organisms, $ E_O$ , specified by inter-breeding organisms;in this case, the weak equivalence relation, $ \sim_w$ , is defined on the set of evolving organisms modeled in terms of functional, isomorphic genome networks, $ G_{iso}^N$ , such as those described by $ LM_n$ -logic networks in Łukasiewicz-Moisil, $ \mathcal{L}M$ topoi ([1]).

AT-Formulation

This biogroupoid concept allows an algebraic topology formulation of the origin of species and biological evolution both at organismal/organismic and biomolecular levels; it represents a new approach to biological evolution from the standpoint of super-complex systems biology.

Bibliography

1
Baianu I. C., Brown R., Georgescu G. and J. F. Glazebrook: 2006, Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz-Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks., Axiomathes, 16 Nos. 1-2: 65-122.

2
Baianu, I.C., R. Brown and J.F. Glazebrook. : 2007, Categorical Ontology of Complex Spacetime Structures: The Emergence of Life and Human Consciousness, Axiomathes, 17: 35-168.



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