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abstract: "The concepts of quantum automata and quantum computation are studied in the context of quantum genetics and genetic networks with nonlinear dynamics. In previous publications (Baianu,1971a, b) the formal concept of quantum automaton and quantum computation, respectively, were introduced and their possible implications for genetic processes 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; 1977; 1987; 2004; Baianu et al, 2004). 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, Łukasiewicz Logic Algebras that showed significant dissimilarities (Baianu, 1977; 2004a; Baianu et al, 2004b) from Boolean models of human neural networks (McCullough and Pitts, 1943). 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, 1987, 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. Topoi of Łukasiewicz Logic Algebras and Intuitionistic Logic (Heyting) Algebras are being considered 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 Łukasiewicz Logic Algebras. \n"
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- family: Baianu
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date: 2004-06
date_type: published
datestamp: 2004-07-06
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keywords: '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; applications of the Theory of Categories, Functors and Natural Transformations; pushouts, pullbacks, presheaves, sheaves, Categories of sheaves, Topos, n-valued Logic, N-categories/ higher dimensional algebra, Homotopy theory;apllications to physical theories, quantum gravity, complex systems biology, bioengineering, informatics, Bioinformatics, Computer simulations, Mathematical Biology of complex systems and phenomena in various types of Dynamical Systems; bioengineering, Computing, Neurosciences, Bioinformatics, biological and/or social networks; quantitative ecology and quantitative biology/'
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It is often assumed incorrectly that Quantum Computation was introduced in 1982 and that Quantum Automata were introduced in 1997. Actually, the formal concepts of Quantum Automata and Quantum Computation were introduced in 1971, in relation to Quantum Genetics (Rosen, 1960) in a paper published in the Bulletin of Mathematical Biophysics, 33:339-354 (Baianu, 1971a). There are also numerous citations of Quantum Automata papers printed in the late 80’s and also recent quantum computation textbooks that fail to report the first introduction of the concepts of “quantum automaton” and
“quantum computation”. Categorical computations, both algebraic and topological, were also introduced in 1971 (Baianu, 1971b) that propose to employ symbolic programming for adjoint functor pairs in the theory of categories, functors and natural transformations (Baianu, 1971b). The notions of topological semigroup, quantum automaton, or computer, were then suggested for applications and modeling, 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 Boolean models of human neural networks (McCullough and Pitts,1943). 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; 2004a; Baianu et al, 2004b) from Boolean models of human neural networks (McCullough and Pitts, 1943).
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referencetext: |+
Baianu, I. and Marinescu, M. 1968. Organismic Supercategories: I. Proposals for a General Unitary Theory of Systems. Bull. Math. Biophys., 30: 625-635.
Baianu, I. 1970. "Organismic Supercategories: II On Multistable Systems."Bull. Math.Biophysics., 32: 539-561.
Baianu, I.1971a. "Organismic Supercategories and Qualitative Dynamics of Systems." Ibid., 33, 339-353.
Baianu, I. 1971. Categories, Functors and Automata Theory. The 4th Intl. Congress LMPS, August-Sept. 1971b.
Baianu, I. and Scripcariu, D. 1973. On Adjoint Dynamical Systems. Bull. Math. Biology., 35: 475-486.
Baianu, I. 1973. Some Algebraic Properties of (M,R)-Systems in Categories. Bull. Math. Biophys, 35: 213-218.
Baianu, I. and Marinescu, M. 1974. A Functorial Construction of (M,R)-Systems. Rev. Roum. Math. Pures et Appl., 19: 389-392.
Baianu, I.C. 1977. A Logical Model of Genetic Activities in Lukasiewicz Algebras: The Non-Linear Theory., Bull. Math. Biol.,39:249-258.Baianu, I.C. 1977.
Baianu, I.C. 1980. Natural Transformations of Organismic Structures. Bull.Math. Biology, 42:431-446.
Baianu, I.C.1983. Natural Transformations Models in Molecular Biology. SIAM Natl. Meeting, Denver, CO, USA.
Baianu, I.C. 1984. A Molecular-Set-Variable Model of Structural and Regulatory Activities in Metabolic and Genetic Systems., Fed. Proc. Amer. Soc. Experim. Biol. 43:917.
Baianu, I.C. 1987. “Computer Models and Automata Theory in Biology and Medicine” (A Review). In: "Mathematical models in Medicine.",vol.7., M. Witten, Ed., Pergamon Press: New York, pp.1513-1577.
Baianu, I.C. 2004. “Cell Genome and Interactome Nonlinear Dynamic Models in Łukasiewicz Logic Algebras. Neoplastic Transformation Models in a Łukasiewicz Topos.” Submitted archive preprint, June 25th 2004. # GN 0406050.
Baianu, I.C., J. Glazebrook, G. Georgescu and R.Brown, 2004. “A Novel Approach to Complex Systems Biology and Observation Strategies based on Categories, Higher Dimensional Algebra and Łukasiewicz Topos. “ Manuscript in preparation, 16 pp.
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, 486-495.
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, 115-133.
Pitts, W. 1943. “The Linear Theory of Neuron Networks” Bull. Math. Biophys., 5, 23-31.
Rosen, R.1958.a.”A Relational Theory of Biological Systems” Bull. Math. Biophys., 20, 245-260.
Rosen, R. 1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories” Bull. Math. Biophys., 20, 317-341.
Rosen, Robert. 1973. On the Dynamical realization of (M,R)-Systems. Bull. Math. Biology., 35:1-10.
Rosen, Robert. 2001. “Essays on Life Itself “. New York: Columbia University Press, 221 pp.
Russel, Bertrand and A.N. Whitehead, 1925. Principia Mathematica, Cambridge: Cambridge Univ. Press.
Warner, M. 1982. Representations of (M,R)-Systems by Categories of Automata., Bull. Math. Biol., 44:661-668.
Baianu, I. and Marinescu, M. 1968. Organismic Supercategories: I. Proposals for a General Unitary Theory of Systems. Bull. Math. Biophys., 30: 625-635.
Baianu, I. 1970. "Organismic Supercategories: II On Multistable Systems."Bull. Math.Biophysics., 32: 539-561.
Baianu, I.1971a. "Organismic Supercategories and Qualitative Dynamics of Systems." Ibid., 33, 339-353.
Baianu, I. 1971. Categories, Functors and Automata Theory. The 4th Intl. Congress LMPS, August-Sept. 1971b.
Baianu, I. and Scripcariu, D. 1973. On Adjoint Dynamical Systems. Bull. Math. Biology., 35: 475-486.
Baianu, I. 1973. Some Algebraic Properties of (M,R)-Systems in Categories. Bull. Math. Biophys, 35: 213-218.
Baianu, I. and Marinescu, M. 1974. A Functorial Construction of (M,R)-Systems. Rev. Roum. Math. Pures et Appl., 19: 389-392.
Baianu, I.C. 1977. A Logical Model of Genetic Activities in Lukasiewicz Algebras: The Non-Linear Theory., Bull. Math. Biol.,39:249-258.Baianu, I.C. 1977.
Baianu, I.C. 1980. Natural Transformations of Organismic Structures. Bull.Math. Biology, 42:431-446.
Baianu, I.C.1983. Natural Transformations Models in Molecular Biology. SIAM Natl. Meeting, Denver, CO, USA.
Baianu, I.C. 1984. A Molecular-Set-Variable Model of Structural and Regulatory Activities in Metabolic and Genetic Systems., Fed. Proc. Amer. Soc. Experim. Biol. 43:917.
Baianu, I.C. 1987. “Computer Models and Automata Theory in Biology and Medicine” (A Review). In: "Mathematical models in Medicine.",vol.7., M. Witten, Ed., Pergamon Press: New York, pp.1513-1577.
Baianu, I.C. 2004. “Cell Genome and Interactome Nonlinear Dynamic Models in Łukasiewicz Logic Algebras. Neoplastic Transformation Models in a Łukasiewicz Topos.” Submitted archive preprint, June 25th 2004. # GN 0406050.
Baianu, I.C., J. Glazebrook, G. Georgescu and R.Brown, 2004. “A Novel Approach to Complex Systems Biology and Observation Strategies based on Categories, Higher Dimensional Algebra and Łukasiewicz Topos. “ Manuscript in preparation, 16 pp.
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, 486-495.
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, 115-133.
Pitts, W. 1943. “The Linear Theory of Neuron Networks” Bull. Math. Biophys., 5, 23-31.
Rosen, R.1958.a.”A Relational Theory of Biological Systems” Bull. Math. Biophys., 20, 245-260.
Rosen, R. 1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories” Bull. Math. Biophys., 20, 317-341.
Rosen, Robert. 1973. On the Dynamical realization of (M,R)-Systems. Bull. Math. Biology., 35:1-10.
Rosen, Robert. 2001. “Essays on Life Itself “. New York: Columbia University Press, 221 pp.
Russel, Bertrand and A.N. Whitehead, 1925. Principia Mathematica, Cambridge: Cambridge Univ. Press.
Warner, M. 1982. Representations of (M,R)-Systems by Categories of Automata., Bull. Math. Biol., 44:661-668.
relation_type: []
relation_uri: []
reportno: ~
rev_number: 12
series: ~
source: ~
status_changed: 2007-09-12 16:52:48
subjects:
- comp-sci-mach-dynam-sys
- comp-sci-complex-theory
- bio-theory
succeeds: ~
suggestions: |-
This article covers several research areas of interest to geneticists, theoretical biologists, quantum theorists,
genomic and proteomics, bioinformatics, quantum computation groups and fundamental automata theory/ quantum automata theory research.
sword_depositor: ~
sword_slug: ~
thesistype: ~
title: |
Quantum Genetics in terms of Quantum Reversible Automata and
Quantum Computation of Genetic Codes and Reverse Transcription
type: preprint
userid: 4959
volume: ~