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 Submitted to: Studies in Computational Intelligence, 8-9 September 2011 ISSN: 1860-949X, Springer
Ion C. Băianu · 2011
A categorical and Łukasiewicz-Topos framework for Łukasiewicz LM-Algebraic Logic models of nonlinear dynamics in complex functional systems such as neural networks, genomes and cell interactomes is proposed. Łukasiewicz Algebraic Logic models of 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 Łukasiewicz Topos with an n-valued Łukasiewicz LM-Algebraic Logic subobject classifier description that represents nonrandom and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis. Kan extensions are also considered in the context of neural network development.