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

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.\u

Łukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models

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 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

Two-dimensional models of type theory

We describe a non-extensional variant of Martin-L\"of type theory which we call two-dimensional type theory, and equip it with a sound and complete semantics valued in 2-categories.Comment: 46 pages; v2: final journal versio

Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models

Operational logic and bioinformatics models of nonlinear dynamics in complex functional systems such as neural networks, genomes and cell interactomes are 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 Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis