Quantum Genetics, Quantum Automata and Quantum Computation

The concepts of quantum automata and quantum computation are studied in the context of quantum genetics and genetic networks with nonlinear dynamics. In a previous publication (Baianu,1971a) the formal concept of quantum automaton was introduced and its possible implications for genetic and metabolic activities in living cells and organisms were considered. This was followed by a report on quantum and abstract, symbolic computation based on the theory of categories, functors and natural transformations (Baianu,1971b). The notions of topological semigroup, quantum automaton,or quantum computer, were then suggested with a view to their potential applications to the analogous simulation of biological systems, and especially genetic activities and nonlinear dynamics in genetic networks. Further, detailed studies of nonlinear dynamics in genetic networks were carried out in categories of n-valued, Lukasiewicz Logic Algebras that showed significant dissimilarities (Baianu, 1977) from Bolean models of human neural networks (McCullough and Pitts,1945). Molecular models in terms of categories, functors and natural transformations were then formulated for uni-molecular chemical transformations, multi-molecular chemical and biochemical transformations (Baianu, 1983,2004a). Previous applications of computer modeling, classical automata theory, and relational biology to molecular biology, oncogenesis and medicine were extensively reviewed and several important conclusions were reached regarding both the potential and limitations of the computation-assisted modeling of biological systems, and especially complex organisms such as Homo sapiens sapiens(Baianu,1987). Novel approaches to solving the realization problems of Relational Biology models in Complex System Biology are introduced in terms of natural transformations between functors of such molecular categories. Several applications of such natural transformations of functors were then presented to protein biosynthesis, embryogenesis and nuclear transplant experiments. Other possible realizations in Molecular Biology and Relational Biology of Organisms are here suggested in terms of quantum automata models of Quantum Genetics and Interactomics. Future developments of this novel approach are likely to also include: Fuzzy Relations in Biology and Epigenomics, Relational Biology modeling of Complex Immunological and Hormonal regulatory systems, n-categories and Topoi of Lukasiewicz Logic Algebras and Intuitionistic Logic (Heyting) Algebras for modeling nonlinear dynamics and cognitive processes in complex neural networks that are present in the human brain, as well as stochastic modeling of genetic networks in Lukasiewicz Logic Algebras

Symbolic Knowledge Extraction from Trained Neural Networks Governed by Lukasiewicz Logics

This work describes a methodology to extract symbolic rules from trained neural networks. In our approach, patterns on the network are codified using formulas on a Lukasiewicz logic. For this we take advantage of the fact that every connective in this multi-valued logic can be evaluated by a neuron in an artificial network having, by activation function the identity truncated to zero and one. This fact simplifies symbolic rule extraction and allows the easy injection of formulas into a network architecture. We trained this type of neural network using a back-propagation algorithm based on Levenderg-Marquardt algorithm, where in each learning iteration, we restricted the knowledge dissemination in the network structure. This makes the descriptive power of produced neural networks similar to the descriptive power of Lukasiewicz logic language, minimizing the information loss on the translation between connectionist and symbolic structures. To avoid redundance on the generated network, the method simplifies them in a pruning phase, using the "Optimal Brain Surgeon" algorithm. We tested this method on the task of finding the formula used on the generation of a given truth table. For real data tests, we selected the Mushrooms data set, available on the UCI Machine Learning Repository

Quantum Genetics and Quantum Automata Models of Quantum-Molecular Evolution Involved in the Evolution of Organisms and Species

Previous theoretical or general approaches to the problems of Quantum Genetics and Molecular Evolution are considered in this article from the point of view of Quantum Automata Theory first published by the author in 1971 and further developed in several recent articles. The representation of genomes and Interactome networks in categories of many-valued logic LMn –algebras that are naturally transformed during biological evolution, or evolve through interactions with the environment provide a new insight into the mechanisms of molecular evolution, as well as organismal evolution, in terms of sequences of quantum automata. Phenotypic changes are expressed only when certain environmentally-induced quantum-molecular changes are coupled with an internal re-structuring of major submodules of the genome and Interactome networks related to cell cycling and cell growth. Contrary to the commonly held view of `standard’ Darwinist models of evolution, the evolution of organisms and species occurs through coupled multi-molecular transformations induced not only by the environment but actually realized through internal re-organizations of genome and interactome networks. The biological, evolutionary processes involve certain epigenetic transformations that are responsible for phenotypic expression of the genome and Interactome transformations initiated at the quantum-molecular level. It can thus be said that only quantum genetics can provide correct explanations of evolutionary processes that are initiated at the quantum--multi-molecular levels and propagate to the higher levels of organismal and species evolution.

Biological evolution should be therefore regarded as a multi-scale process which is initiated by underlying quantum (coupled) multi-molecular transformations of the genomic and interactomic networks, followed by specific phenotypic transformations at the level of organism and the variable biogroupoids associated with the evolution of species which are essential to the survival of the species. The theoretical framework introduced in this article also paves the way to a Quantitative Biology approach to biological evolution at the quantum-molecular, as well as at the organismal and species levels. This is quite a substantial modification of the 'established’ modern Darwinist, and also of several so-called `molecular evolution’ theories

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