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Complex Non-linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks
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Complex Non-linear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz–Moisil Topos: Transformations of
Neuronal, Genetic and Neoplastic Networks
I. C. Baianu, R. Brown, G. Georgescu and J. F. Glazebrook
Abstract A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of
non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models
of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear
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–Moisil Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network
activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories
of organismic sets, molecular sets and Robert Rosen’s ( M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional
algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks,
such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum
logics are considered in the context of an emerging Quantum Relational Biology.
Keywords adjoint functors and dynamically analogous systems - biogroupoids and organismal development - biological principles - nuclear equivalence and cell differentiation - categories - n-valued logics and higher dimensional algebra in neuroscience and genetics - cognitive and anticipatory processes - learning and quantum wave-pattern recognition - colimits - limits and adjointness relations in biology - generalized (M,R)-systems - neuro-categories and consciousness - quantum automata and relational biology - quantum bionetworks and their underlying quantum logics - quantum computers
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