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Nonlinear Models of Neural and Genetic Network Dynamics: Natural Transformations of Łukasiewicz Logic LM-Algebras in a Łukasiewicz-Topos as Representations of Neural Network Development and Neoplastic Transformations

Baianu, Professor I.C. (2011) Nonlinear Models of Neural and Genetic Network Dynamics: Natural Transformations of Łukasiewicz Logic LM-Algebras in a Łukasiewicz-Topos as Representations of Neural Network Development and Neoplastic Transformations. [Conference Paper] (In Press)

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Abstract

A categorical and Łukasiewicz-Topos framework for Algebraic Logic models of nonlinear dynamics in complex functional systems such as Neural Networks, Cell Genome and Interactome Networks is introduced. Łukasiewicz Algebraic Logic models of both neural and genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable next-state/transfer functions is extended to a Łukasiewicz Topos with an N-valued Łukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis.

Item Type:Conference Paper
Additional Information:14 pages of .doc.ODT and PDF files; this version is peer-reviewed
Keywords:Łukasiewicz models of Neural and Genetic Networks; Genome and cell interactomics models in terms of categories of Łukasiewicz logic Algebras and Lukasiewicz Topos;Łukasiewicz Topos with an n-valued Łukasiewicz Algebraic Logic subobject classifier; genetic network transformations in Carcinogenesis, developmental processes and Evolution/ Evolutionary Biology; Relational Biology of Archea, yeast and higher eukaryotic organisms; nonlinear dynamics in non-random, hierarchic genetic networks; proteomics coupled genomes via signaling pathways;mechanisms of neoplastic transformations of cells and topological grupoid models of genetic networks in cancer cells; natural transformations of organismic structures in Molecular Biology;Neural and genetic network dynamics, LM-logic algebra, LM-Topoi, neural network development, morphogenesis, neoplastic transformations, LM-logic algebra categories, Lukasiewicz-Moisil Logic Algebras
Subjects:Biology > Theoretical Biology
Neuroscience > Computational Neuroscience
Computer Science > Artificial Intelligence
Computer Science > Complexity Theory
Computer Science > Dynamical Systems
Computer Science > Neural Nets
Neuroscience > Neurogenetics
Neuroscience > Neural Modelling
ID Code:7739
Deposited By: Baianu, Professor I. C.
Deposited On:16 Dec 2011 00:58
Last Modified:16 Dec 2011 00:58

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References in Article

Select the SEEK icon to attempt to find the referenced article. If it does not appear to be in cogprints you will be forwarded to the paracite service. Poorly formated references will probably not work.

Baianu, I. and Marinescu, M. 1968. Organismic Supercategories: I. Proposals for a General Unitary Theory of Systems. Bull. Math. Biophys., 30: 625-635.

Baianu, I. 1970. "Organismic Supercategories: II On Multistable Systems." Bull. Math.

Biophysics., 32,539-561.

Baianu, I. 1971 "Organismic Supercategories and Qualitative Dynamics of Systems."

Ibid., 33, 339-353.

Baianu, I. 1973. "Some Algebraic Properties of (M, R).Systems." Bull. Math. Biol., 35.

213-217.

Baianu, I.C. 1977. “A Logical Model of Genetic Activities in Łukasiewicz Algebras: The Non-linear Theory.” Bulletin of Mathematical Biology, 39:249-258 (1977).

Baianu, I.C., J. Glazebrook, G. Georgescu and R.Brown. 2010. “Łukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems in Biology and Medicine” BRAIN, vol. 1, pp.1-11; ISSN 2067-3957.

Carnap. R. 1938. "'The Logical Syntax of Language" New York: Harcourt, Brace and Co.

Georgescu, G. and C. Vraciu 1970. "On the Characterization of Łukasiewicz Algebras." J. Algebra, 16 (4), 486-495.

Hilbert, D. and W. Ackerman. 1927. Grunduge der Theoretischen Logik, Berlin: Springer.

McCulloch, W and W. Pitts. 1943. “A logical Calculus of Ideas Immanent in Nervous Activity” Bull. Math. Biophys., 5, 115-133.

Pitts, W. 1943. “The Linear Theory of Neuron Networks” Bull. Math. Biophys., 5, 23-31.

Rosen, R.1958.a.”A Relational Theory of Biological Systems” Bull. Math. Biophys., 20, 245-260.

Rosen, R. 1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories” Bull. Math. Biophys., 20, 317-341.

Rosen, Robert. 1973. On the Dynamical realization of (M,R)-Systems. Bull. Math. Biology., 35:1-10.

Rosen, Robert. 2001. “Essays on Life Itself “. New York: Columbia University Press, 221 pp.

Russel, Bertrand and A.N. Whitehead, 1925. Principia Mathematica, Cambridge: Cambridge Univ. Press.

Warner, M. 1982. Representations of (M,R)-Systems by Categories of Automata., Bull. Math. Biol., 44:661-668.

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