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QuantumAutnu2_ICB.pdf
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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 nvalued, 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 unimolecular chemical transformations, multimolecular 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 computationassisted 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, ncategories 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.

Baianu
I. C.
Professor
icb
Quantum Automata and Quantum Computation, Quantum Genetics;
Relational Biology models of Complex genetic networks,
Carcinogenesis, Human Neural Networks, Hormonal and Immune
Regulatory Systems, Molecular Interactions in terms of Catgeories,Functors and natural transformations, Lukasiewicz Topos modeling of Nonlinear Genetic Networks,
Intuitionistic Heyting Logic Algebra of Quantum Hilbert Spaces, Adjunctions between Hilbert Spaces of Quantum Automata; Genetic Expression as an adjunction of Quantum Genetic processes in stable Hilbert Spaces.
TRUE
FALSE
Baianu, I. and Marinescu, M. 1968. Organismic Supercategories: I. Proposals for a General Unitary Theory of Systems. Bull. Math. Biophys., 30: 625635.
Baianu, I. 1970. "Organismic Supercategories: II On Multistable Systems."Bull. Math.
Biophysics., 32: 539561.
Baianu, I.1971 "Organismic Supercategories and Qualitative Dynamics of Systems."
Ibid, 33, 339353.
Baianu, I. 1973. "Some Algebraic Properties of (M, R).Systems." Bull. Math. Biol., 35.
213217.
Carnap. R. 1938. "'The Logical Syntax of Language" New York: Harcourt, Brace and Co.
Georgescu, G. and C. Vraciu 1970. "On the Characterization of Lukasiewicz Algebras." J Algebra, 16 4, 486495.
Hilbert, D. and W. Ackerman. 1927. Grunduge.der Theoretischen Logik, Berlin: Springer.
McCulloch, W and W. Pitts. 1943. “A logical Calculus of Ideas Immanent in Nervous Activity” Ibid., 5, 115133.
Pitts, W. 1943. “The Linear Theory of Neuron Networks” Bull. Math. Biophys., 5, 2331.
Rosen, R.1958.a.”A relational Theory of Biological Systems” Bull. Math. Biophys., 20, 245260.
Rosen, R. 1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories” Bull. Math. Biophys., 20, 317341.
Russel, Bertrand and A.N. Whitehead, 1925. Principia Mathematica, Cambridge: Cambridge Univ. Press.
Applications of the Theory of Categories, Functors and
Natural Transformations, Ncategories, Abelian or NonAbelian to:
Automata Theory/ Sequential Machines, Bioinformatics, Complex Biological Systems /Complex Systems Biology, Computer Simulations and Modeling, Dynamical Systems , Quantum Dynamics, Quantum Field Theory, Quantum Groups,Topological Quantum Field Theory (TQFT), Quantum Automata, Cognitive Systems, Graph Transformations, Logic, Mathematical Modeling, etc.
1. Rosen, R. 1958. The Representation of Biological Systems from the Standpoint of the Theory of Categories." (of sets). Bull. Math. Biophys. 20: 317341.
2. Rosen, Robert. 1964. Abstract Biological Systems as Sequential Machines, Bull. Math. Biophys., 26: 103111; 239246; 27:1114;28:141148.
3. Arbib, M. 1966. Categories of (M,R)Systems. Bull. Math. Biophys., 28: 511517.
4. Cazanescu, D. 1967. On the Category of Abstract Sequential Machines. Ann. Univ. Buch., Maths & Mech. series, 16 (1):3137.
5. Rosen, Robert. 1968. On Analogous Systems. Bull. Math. Biophys., 30: 481492.
6. Baianu, I.C. and Marinescu, M. 1968. Organismic Supercategories:I. Proposals for a General Unitary Theory of Systems. Bull. Math. Biophys., 30: 625635.
7. Comorozan,S. and Baianu, I.C. 1969. Abstract Representations of Biological Systems in Supercategories. Bull. Math. Biophys., 31: 5971.
8. Baianu, I. 1970. Organismic Supercategories: III. On Multistable Systems. Bull. Math. Biophys., 32: 539561.
9. Baianu, I. 1971. Organismic Supercategories and Qualitative Dynamics of Systems. Bull. Math. Biophys., 33: 339354.
10. Baianu, I. 1971. Categories, Functors and Automata Theory. The 4th Intl. Congress LMPS, AugustSept. 1971.
11. Baianu, I. and Scripcariu, D. 1973. On Adjoint Dynamical Systems. Bull. Math. Biology., 35: 475486.
12. Rosen, Robert. 1973. On the Dynamical realization of (M,R)Systems. Bull. Math. Biology., 35:110.
13. Baianu, I. 1973. Some Algebraic Properties of (M,R)Systems in Categories. Bull. Math. Biophys, 35: 213218.
14. Baianu, I. and Marinescu, M. 1974. A Functorial Construction of (M,R)Systems. Rev. Roum. Math. Pures et Appl., 19: 389392.
15. Baianu, I.C. 1977. A Logical Model of Genetic Activities in Lukasiewicz Algebras: The NonLinear Theory., Bull. Math. Biol.,39:249258.
16. Baianu, I.C. 1980. Natural Transformations of Organismic Structures. Bull.Math. Biology, 42:431446.
17. Warner, M. 1982. Representations of (M,R)Systems by Categories of Automata., Bull. Math. Biol., 44:661668.
18. Baianu, I.C.1983. Natural Transformations Models in Molecular Biology. SIAM Natl. Meeting, Denver, CO, USA.
19. Baianu, I.C. 1984. A MolecularSetVariable Model of Structural and Regulatory Activities in Metabolic and Genetic Systems., Fed. Proc. Amer. Soc. Experim. Biol. 43:917.
19. Baianu, I.C. 1987. Computer Models and Automata Theory in Biology and Medicine. In: "Mathematical models in Medicine.",vol.7., M. Witten, Ed., Pergamon Press: New York, pp.15131577.
 compscimachdynamsys
 compscicomplextheory
 compsciartintel
 biotheory
Quantum Genetics, Quantum Automata and Quantum Computation
published
200405
A novel approach is applied to a wide range of complex biosysytems and biodynamic processes is presented that has numerous potential applications to neurosciences,human neural networks, cognitive processes, molecular biology, protein biosynthesis, proteomics and cell interactomics. Such applications utilize advanced mathematical tools from the theories of Topos, Intuitionistic Heyting Logics, Lukasiewicz Logic Algebras, Adjunctions, Limits and Colimits, Categories, Functors and Natural Transformations of Functors. These concepts have applications in developing very advanced computation systems, such as quantum automata and quantum computers, novel Artificial Inteligence Systems,
and the fundamental aspects of Nonlinear Dynamic Systems.
public