biogroupoids: mathematical models of species evolution

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0.1 Introduction

Biogroupoids, $\\mathcal{G_{B}}$ , were introduced as mathematical representations ofevolving biological species ([1, 2]) generated by weakly equivalent classes of living organisms, $E_{O}$ , specified by inter-breeding organisms;in this case, a 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, ${\\mathcal{L}M}_{n}$ topoi ([1]).

0.2 AT-Formulation

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

References

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.

单词	BiogroupoidsMathematicalModelsOfSpeciesEvolution
释义	biogroupoids: mathematical models of species evolution \\xyoption curve 0.1 Introduction Biogroupoids, $\\mathcal{G_{B}}$ , were introduced as mathematical representations ofevolving biological species ([1, 2]) generated by weakly equivalent classes of living organisms, $E_{O}$ , specified by inter-breeding organisms;in this case, a 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, ${\\mathcal{L}M}_{n}$ topoi ([1]). 0.2 AT-Formulation This concept allows an algebraic topology formulation of the origin of species and biological evolutionboth at organismal/organismic and biomolecular levels; it represents a new approach to biological evolutionfrom the standpoint of super-complex systems biology. References 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.
随便看	MinimalPolynomial minimal polynomial MinimalPolynomialendomorphism minimal polynomial (endomorphism) MinimalPrime minimal prime MinimalPrimeIdeal minimal prime ideal MinimalProjectivePresentation minimal projective presentation MinimalSurface minimal surface MinimalUnitizationsOfAlgebrasWithAdditionalStructure minimal unitizations of algebras with additional structure MinimaxInequality minimax inequality MinimumSpanningTree minimum spanning tree MinimumWeightedPathLength minimum weighted path length MinkowskiFunctional Minkowski functional MinkowskiInequality Minkowski inequality MinkowskisConstant