PlanetPhysics/Biogroupoids and Mathematical Models of Species Evolution

Biogroupoids and mathematical models of species evolution

Introduction

Biogroupoids , ${\mathcal {G_{B}}}$ , were introduced as mathematical \htmladdnormallink{representations {http://planetphysics.us/encyclopedia/CategoricalGroupRepresentation.html} of evolving biological species} (^[1]) 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 \L{}ukasiewicz-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.

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References

↑ ^1.0 ^1.1 ^1.2 Baianu I. C., Brown R., Georgescu G. and J. F. Glazebrook: 2006, Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and \L ukasiewicz-Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks., Axiomathes , 16 Nos. 1-2: 65-122.
↑ Baianu, I.C., R. Brown and J.F. Glazebrook. : 2007, Categorical Ontology of Complex Spacetime Structures: The Emergence of Life and Human Consciousness, Axiomathes, \textbf {17}: 35-168.

[BBGG2k6-1] 1.0 ^1.1 ^1.2 Baianu I. C., Brown R., Georgescu G. and J. F. Glazebrook: 2006, Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and \L ukasiewicz-Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks., Axiomathes , 16 Nos. 1-2: 65-122.

[BBG2k7-2] Baianu, I.C., R. Brown and J.F. Glazebrook. : 2007, Categorical Ontology of Complex Spacetime Structures: The Emergence of Life and Human Consciousness, Axiomathes, \textbf {17}: 35-168.

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