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@misc{cogprints7739, volume = {1}, number = {1-2}, month = {November}, author = {Professor I.C. Baianu}, note = {14 pages of .doc.ODT and PDF files; this version is peer-reviewed}, editor = {Dr. Barna Iantovics}, title = {Nonlinear Models of Neural and Genetic Network Dynamics: Natural Transformations of {\L}ukasiewicz Logic LM-Algebras in a {\L}ukasiewicz-Topos as Representations of Neural Network Development and Neoplastic Transformations }, publisher = {Springer}, year = {2011}, pages = {1--14}, keywords = {{\L}ukasiewicz models of Neural and 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;Neural and genetic network dynamics, LM-logic algebra, LM-Topoi, neural network development, morphogenesis, neoplastic transformations, LM-logic algebra categories, Lukasiewicz-Moisil Logic Algebras }, url = {http://cogprints.org/7739/}, 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/transfer 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. } }