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"keywords": "Cognitive Neural Networks simulation by quantum computers;\nalgebraic-topological, symbolic computation; Genetic Networks\/Genome; Interactome simulations by computers;\nRecursive and digital computability limitations for biological and chaotic dynamics simulations;Kauffman, random networks and Boolean algebra; Lukasiewics Logic Algebra isomporphic to MV-logic algebra as model of biological system networks; Quantum MV-Logic algebras for\nmicrophysical modelling in Quantum Genetics and Enzyme Kinetics; Categories, functors, natural transformations and\nTopos as adequate tools for modelling hierarchical organization in biological systems and especially super-structures involved in cognitive processes supported by multi-layered neural networks.",
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"commref": "This is a 2004 update of the original section on Computer Simulation of Biosystems and Computability",
"datestamp": "2004-07-13",
"uri": "http:\/\/cogprints.org\/id\/eprint\/3718",
"title": "COMPUTER SIMULATION AND COMPUTABILITY\nOF BIOLOGICAL SYSTEMS",
"publication": "Mathematical Modelling, Vol. 7: \"Mathematical Modelling in Biology and Medicine.\"",
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"abstract": "The ability to simulate a biological organism by employing a computer is related to the\nability of the computer to calculate the behavior of such a dynamical system, or the \"computability\" of the system.* However, the two questions of computability and simulation are not equivalent. Since the question of computability can be given a precise answer in terms of recursive functions, automata theory and dynamical systems, it will be appropriate to consider it first. The more elusive question of adequate simulation of biological systems by a computer will be then addressed and a possible connection between the two answers given will be considered. A conjecture is formulated that suggests the possibility of employing an algebraic-topological, \"quantum\" computer (Baianu, 1971b)\nfor analogous and symbolic simulations of biological systems that may include chaotic processes that are not, in genral, either recursively or digitally computable. Depending on the biological network being modelled, such as the Human Genome\/Cell Interactome or a trillion-cell Cognitive Neural Network system, the appropriate logical structure for such simulations might be either the Quantum MV-Logic (QMV) discussed in recent publications (Chiara, 2004, and references cited therein)or Lukasiewicz Logic Algebras that were shown to be isomorphic to MV-logic algebras (Georgescu et al, 2001). ",
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"suggestions": "Related subject fields would involve general models of Cognition and Neurosciences",
"referencetext": "1. Arbib, M. 1966. Categories of (M,R)-Systems. Bull. Math. Biophys., 28: 511-517.\n2. Ashby, W. R. 1960. Design for a brain, 2nd ed., New York: J. Wiley & Sons, Inc.\n3. Ashby, W. R 1956. An Introduction to Oybernetics, New York: J. Wiley & Sons, Inc.\n4. Baianu, I.C. and Marinescu, M. 1968. Organismic Supercategories:I. Proposals for a General\nUnitary Theory of Systems. Bull. Math. Biophys., 30: 625-635.\n5. Baianu, I. 1970. Organismic Supercategories: II. On Multistable Systems. Bull. Math. Biophys., 32:\n539-561.\n6. Baianu, I. 1971. Organismic Supercategories and Qualitative Dynamics of Systems. Bull. Math. Biophys., 33: 339-354.\n7. Baianu, I. 1971. Categories, Functors and Automata Theory: A Novel Approach through Algebraic-Topological Quantum Computation., Proceed. 4th Intl. Congress LMPS, August-Sept. 1971.\n8. Baianu, I. and Scripcariu, D. 1973. On Adjoint Dynamical Systems. Bull. Math. Biology.,35: 475-486.\n9. Baianu, I. 1973. Some Algebraic Properties of (M,R)-Systems in Categories. Bull. Math. Biophys, 35: 213-218.\n10. Baianu, I. and Marinescu, M. 1974. A Functorial Construction of (M,R)-Systems. Rev. Roum. Math. Pures et Appl., 19: 389-392.\n11. Baianu, I.C. 1977. A Logical Model of Genetic Activities in Lukasiewicz Algebras: The Non-Linear Theory., Bull. Math. Biology, 39:249-258.\n12. Baianu, I.C. 1980. Natural Transformations of Organismic Structures. Bull. Math. Biology, 42: 431-446.\n13. Baianu, I.C. 1980. Structural Order and Partial Disorder in Biological Systems. Bull. Math. Biology, 42: 464-468\n14. Baianu, I.C.1983. Natural Transformations Models in Molecular Biology. SIAM Natl. Meeting, Denver, CO, USA.\n15. 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:\n917.\n16. 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,\npp.1513-1577.\n17. Bourbaki, N. 1958. Elements de Mathematique, Paris: Hermann & Cle, Editeurs.\n18. Carnap. R. 1938. \"'The Logical Syntax of Language\" New York: Harcourt, Brace and Co.\n19. Cazanescu, D. 1967. On the Category of Abstract Sequential Machines. Ann. Univ. Buch., Maths & Mech. series, 16 (1):31-37.\n20. Comorozan, S. and Baianu, I.C. 1969. Abstract Representations of Biological Systems in Supercategories. Bull. Math. Biophys., 31: 59-71.\n21. Ehresmann, Ch. 1966. \"Trends Toward Unity in Mathematics.\" Cahiers de Topologie Et Geometrie Differentielle, 8,1-7.\n22. Eilenberg, S. and S. MacLane. 1945. \"General Theory of Natural Equivalences.\", Trans.Am. Math.Soc.,58,231-294.\n23. Eilenberg, S. and J. Wright. 1967. \"Automata in General Algebras.\" Seventy-Second Meeting American Math. Soc., 1-17.\n24. Georgescu, G. and D. Popescu. 1968. \"On Algebraic Categories.\" Rev. Roum. Math. Pures et Appl.,24:13,337-342.\n25. Georgescu, G. and C. Vraciu 1970. \"On the Characterization of Lukasiewicz Algebras.\" J Algebra,16(4), 486-495.\n26. Hilbert, D. and W. Ackerman. 1927. Grunduge.der Theoretischen Logik, Berlin: Springer.\n27. Lawvere, F. W. 1963. \"Functional Semantics of Algebraic Theories.\" Proc. Natl.Acad. Sci.USA,50,869-872.\n28. Lawvere, F. W. 1966. \"The Category of Categories as a Foundation for Mathematics.\" In the Proc. Conf. Categorical Algebra-La Jolla. 1965, Eilenberg, S., et al. eds., Berlin,\nHeidelberg and New York: Springer-Verlag, pp. 1-20.\n29. Lawvere, F. W. 1969. \"Closed Cartesian Categories.\" (Lecture held as a guest of the Romanian Academy of Sciences).\n30. Lofgren; L. 1968. \"An Axiomatic Explanation of Complete Self-Reproduction.\" Bull.Math. Biophysics, 30, 317-348\n.\n31. M. Conrad and O. Rössler. 1982. Example of a system which is computation universal but not effectively programmable. Bull. Math. Biol. 44: 443-448.\n32. McCulloch, W and W. Pitts. 1943. “A logical Calculus of Ideas Immanent in Nervous Activity” Ibid., 5, 115-133.\n33. Mitchell, B. 1965. The Theory of Categories., New York and London: Academic Press.\n34. O. Rössler. 1979. Chaos and strange at tractors in chemical kinetics, in Synthetics-Far from Equilibrium. Edited by A. Pacault and C. Vidal. Springer-Verlag, Heidelberg. 107-113.\n35. Rashevsky, N. 1954. \"Topology and Life: In Search of General Mathematical Principles in Biology and Sociology.\" Bull. Math. Biophysics, 16, 317-348.\n36. Pitts, W. 1943. “The Linear Theory of Neuron Networks” Bull. Math. Biophys., 5, 23-31.\n37. Rosen, R.1958.a.”A relational Theory of Biological Systems” Bull. Math. Biophys.,20,245-260.\n38. Rosen, R. 1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories” Bull. Math. Biophys., 20, 317-341.\n39. Rosen, Robert. 1968. On Analogous Systems. Bull. Math. Biophys., 30: 481-492.\n40. Rosen, Robert. 1973. On the Dynamical realization of (M,R)-Systems. Bull. Math.Biology., 35:1-10.\n41. Russel, Bertrand and A.N. Whitehead, 1925. Principia Mathematica, Cambridge: Cambridge Univ. Press.\n42. Warner, M. 1982. Representations of (M,R)-Systems by Categories of Automata., Bull. Math. Biol., 44:661-668.",
"note": "This updated paper addresses recent developments in quantum computation models of cognitive processes in the brain as well as in genetic networks, based on QMV- Logic and Lukasiewicz Logic Algebras (LLA)on the basis of the original published section that raised the question of biomimetics, or simulation of biosystems beyond recursive computation-based modeling, by means of n-valued logic, \nQuantum Computation, Quantum Automata and algebraic-topological symbolic models of both neural and genetic networks with very large numbers of components and complex, hierarchically organized brain structures.",
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