genetic nets

0.1 Introduction

Genetic ‘nets’, or networks, $G N$ – that represent a living organism’s genome –are mathematical models of functional genes linked through their non-linear, dynamic interactions.

A simple genetic (or gene) network $GN_{s}$ may be thus represented by a directed graph $G_{D}$ whose nodes (or vertices) are the genes $g_{i}$ of a cell or a multicellular organism and whose edges (arcs) are arrows representing the actions of a gene $a_{g}^{i}$ on a linked gene or genes; such a directed graph representing a gene network has a canonically associated biogroupoid $\\mathcal{G}_{B}$ which is generated or directly computed from the directed graph $G_{D}$ .

0.2 Boolean vs. N-state models of genetic networks in $LM_{n}$ - logic algebras

The simplest, Boolean, or two-state models of genomes represented by such directed graphs of gene networks form a proper subcategory of the category of n-state genetic networks, $\\textbf{GN}_{\\L{}M_{n}}$ that operate on the basis of a Łukasiewicz-Moisil n-valued logic algebra $LM_{n}$ . Then, the category of genetic networks, $\\textbf{GN}_{\\L{}M_{n}}$ was shown in ref. [2] to form a subcategory of thealgebraic category of Łukasiewicz algebras (http://planetmath.org/AlgebraicCategoryOfLMnLogicAlgebras), $\\mathcal{LM}$ [1, 2]. There are several published, extensive computer simulations of Boolean two-state models of both genetic and neuronal networks (for a recent summary of such computations see, for example, ref. [2]. Most, but not all, such mathematical models are Bayesian, and therefore involve computations for random networks that may have limited biological relevance as the topology of genomes, defined as their connectivity, is far from being random.

The category of automata (or sequential machines based on Chrysippean or Boolean logic) and the category of $(M,R)$ -systems (which can be realized as concrete metabolic-repair biosystems of enzymes, genes, and so on) are subcategories of the category of gene nets $\\textbf{GN}_{\\L{}M_{n}}$ . The latter corresponds to organismic sets of zero-th order $S_{0}$ in the simpler, Rashevsky’s theory of organismic sets.

References

1 Baianu, I.C. (1977). A Logical Model of Genetic Activities in Łukasiewicz Algebras: TheNon-linear Theory., Bulletin of Mathematical Biology, 39:249-258.
2 Baianu, I.C., Brown, R., Georgescu, G., Glazebrook, J.F. (2006). Complex nonlinear biodynamics incategories, higher dimensional algebra and Łukasiewicz-Moisil topos: transformations of neuronal,genetic and neoplastic networks. Axiomathes 16(1-2):65-122.
3 Baianu, I.C., J. Glazebrook, G. Georgescu and R.Brown. (2008). A Novel Approach toComplex Systems Biology based on Categories, Higher Dimensional Algebra and Łukasiewicz Topos.Manuscript in preparation, 16 pp.
4 Georgescu, G. and C. Vraciu (1970). On the Characterization of Łukasiewicz Algebras.,J. Algebra, 16 (4), 486-495.

单词	GeneticNets
释义	genetic nets 0.1 Introduction Genetic ‘nets’, or networks, $G N$ – that represent a living organism’s genome –are mathematical models of functional genes linked through their non-linear, dynamic interactions. A simple genetic (or gene) network $GN_{s}$ may be thus represented by a directed graph $G_{D}$ whose nodes (or vertices) are the genes $g_{i}$ of a cell or a multicellular organism and whose edges (arcs) are arrows representing the actions of a gene $a_{g}^{i}$ on a linked gene or genes; such a directed graph representing a gene network has a canonically associated biogroupoid $\\mathcal{G}_{B}$ which is generated or directly computed from the directed graph $G_{D}$ . 0.2 Boolean vs. N-state models of genetic networks in $LM_{n}$ - logic algebras The simplest, Boolean, or two-state models of genomes represented by such directed graphs of gene networks form a proper subcategory of the category of n-state genetic networks, $\\textbf{GN}_{\\L{}M_{n}}$ that operate on the basis of a Łukasiewicz-Moisil n-valued logic algebra $LM_{n}$ . Then, the category of genetic networks, $\\textbf{GN}_{\\L{}M_{n}}$ was shown in ref. [2] to form a subcategory of thealgebraic category of Łukasiewicz algebras (http://planetmath.org/AlgebraicCategoryOfLMnLogicAlgebras), $\\mathcal{LM}$ [1, 2]. There are several published, extensive computer simulations of Boolean two-state models of both genetic and neuronal networks (for a recent summary of such computations see, for example, ref. [2]. Most, but not all, such mathematical models are Bayesian, and therefore involve computations for random networks that may have limited biological relevance as the topology of genomes, defined as their connectivity, is far from being random. The category of automata (or sequential machines based on Chrysippean or Boolean logic) and the category of $(M,R)$ -systems (which can be realized as concrete metabolic-repair biosystems of enzymes, genes, and so on) are subcategories of the category of gene nets $\\textbf{GN}_{\\L{}M_{n}}$ . The latter corresponds to organismic sets of zero-th order $S_{0}$ in the simpler, Rashevsky’s theory of organismic sets. References 1 Baianu, I.C. (1977). A Logical Model of Genetic Activities in Łukasiewicz Algebras: TheNon-linear Theory., Bulletin of Mathematical Biology, 39:249-258. 2 Baianu, I.C., Brown, R., Georgescu, G., Glazebrook, J.F. (2006). Complex nonlinear biodynamics incategories, higher dimensional algebra and Łukasiewicz-Moisil topos: transformations of neuronal,genetic and neoplastic networks. Axiomathes 16(1-2):65-122. 3 Baianu, I.C., J. Glazebrook, G. Georgescu and R.Brown. (2008). A Novel Approach toComplex Systems Biology based on Categories, Higher Dimensional Algebra and Łukasiewicz Topos.Manuscript in preparation, 16 pp. 4 Georgescu, G. and C. Vraciu (1970). On the Characterization of Łukasiewicz Algebras.,J. Algebra, 16 (4), 486-495.
随便看	Galois criterion for solvability of a polynomial by radicals GaloisExtension Galois extension GaloisGroup Galois group GaloisGroupOfABiquadraticExtension Galois group of a biquadratic extension GaloisGroupOfACubicPolynomial Galois group of a cubic polynomial GaloisGroupOfAQuarticPolynomial Galois group of a quartic polynomial GaloisGroupOfTheCompositumOfTwoGaloisExtensions Galois group of the compositum of two Galois extensions GaloisGroupsOfFiniteAbelianExtensionsOfmathbbQ Galois groups of finite abelian extensions of ℚ GaloisIsNotTransitive Galois is not transitive GaloisRepresentation Galois representation GaloisSubfieldsOfRealRadicalExtensionsAreAtMostQuadratic Galois subfields of real radical extensions are at most quadratic GaloistheoreticDerivationOfTheCubicFormula Galois-theoretic derivation of the cubic formula GaloistheoreticDerivationOfTheQuarticFormula Galois-theoretic derivation of the quartic formula

genetic nets

0.1 Introduction

0.2 Boolean vs. N-state models of genetic networks in L⁢Mn- logic algebras

References

0.2 Boolean vs. N-state models of genetic networks in $LM_{n}$ - logic algebras