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@misc{cogprints3701, month = {June}, title = {{\L}ukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models }, author = {Professor I.C. Baianu}, year = {2004}, keywords = {{\L}ukasiewicz models of Genetic Networks; Genome and cell interactomics models in terms of categories of {\L}ukasiewicz logic Algebras and Lukasiewicz Topos;{\L}ukasiewicz Topos with an n-valued {\L}ukasiewicz 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.}, url = {http://cogprints.org/3701/}, abstract = {A categorical and {\L}ukasiewicz-Topos framework for Algebraic Logic models of nonlinear dynamics in complex functional systems such as Neural Networks, Cell Genome and Interactome Networks is introduced. {\L}ukasiewicz 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 functions' is extended to a {\L}ukasiewicz Topos with an n-valued {\L}ukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis. } }