%A Professor I.C. Baianu %O 14 pages of .doc.ODT and PDF files; this version is peer-reviewed %T Nonlinear Models of Neural and Genetic Network Dynamics: Natural Transformations of ?ukasiewicz Logic LM-Algebras in a ?ukasiewicz-Topos as Representations of Neural Network Development and Neoplastic Transformations %X A categorical and ?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. ?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 ?ukasiewicz Topos with an N-valued ?ukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis. %N 1-2 %K ?ukasiewicz models of Neural and Genetic Networks; Genome and cell interactomics models in terms of categories of ?ukasiewicz logic Algebras and Lukasiewicz Topos;?ukasiewicz Topos with an n-valued ?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 %P 1-14 %E Dr. Barna Iantovics %V 1 %D 2011 %I Springer %L cogprints7739