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	Arabic numerals ArbelosAndParbelos arbelos and parbelos ArbitraryJoin arbitrary join ARBSymmetryAndGroupoidRepresentations ARB symmetry and groupoid representations ArchimedeanOrderedFieldsAreReal Archimedean ordered fields are real ArchimedeanProperty Archimedean property ArchimedeanSemigroup Archimedean semigroup ArchimedeanSpiral Archimedean spiral ArchimedesCalculus ArchimedesCylindersInCube Archimedes’ calculus Archimedes’ cylinders in cube ArcLength arc length ArclengthAsFilteredLimit arclength as filtered limit ArcLengthOfLogarithmicCurve arc length of logarithmic curve