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NATURAL TRANSFORMATIONS OF MULTI-LEVEL ORGANISMAL STRUCTURES REPRESENTED AS ORGANISMIC SUPERCATEGORIES: I. Generation of Categorical Limits and Colimits during Biological Development and Evolution

Baianu, Dr. Ion (1983) NATURAL TRANSFORMATIONS OF MULTI-LEVEL ORGANISMAL STRUCTURES REPRESENTED AS ORGANISMIC SUPERCATEGORIES: I. Generation of Categorical Limits and Colimits during Biological Development and Evolution. [Journal (Paginated)]

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Abstract

A current update of our original 1980 publication entitled "Natural Transformations of Organismic Structures" is here presented, along with the original (1980) article. A unifying approach to the realization of Relational Biology models and Complex System Biology was reported in 1980 for the first time in terms of Natural Transformations between Functors of Organismic Supercategories and their generating categorical diagrams. The representation of organismal structures in terms of Organismic-Supercategories, Functors and their Natural Transformations was introduced for the investigation of developmental and evolutionary processes. Several applications of such natural transformations were presented in relation to embryogenesis and evolutionary processes involving natural selection and the emergence of 'optimally designed' organismal structures. Other molecular realizations in Relational Biology and the underlying Molecular Biology of organisms were also discussed. Current developments of this approach to Complex Systems Biology include: Fuzzy Relations in Biological Dynamics and Structural Biology, Categories of Lukasiewicz Logic Algebras as representations of Functional Genomics and Cell Interactomics, and Intuitionistic Logic Algebras in Topoi and Higher-Dimensional Algebras as possible models of the emergence of Human Consciousness through 'long-range' correlations and partially coherent, multi-level Neural Network processes.

Item Type:Journal (Paginated)
Additional Information:New approaches to realizations of Relational Biology Modeling in Complex System Biology in terms of Natural Transformations between Functors of Organismic Supercategories and their underlying Molecular Categories; Current developments include: Fuzzy Relations in Complex Systems Biology, Categories of Lukasiewicz Logic Algebras and Intuitionistic Logic Algebras for Modeling Complex Neural Network Processes' realization of Relational Biology models in Complex System Biology in terms of Natural Transformations between Functors of Molecular Categories;
Keywords:Organismal Bioynamics and Evolutionary Processes in terms of The Theory of Organismic Supercategories, Functors and Natural Transformations; Natural Transformations in Molecular Biology and Embryogenesis ; multi-molecular transformations, Variable-Molecular-sets, molecular-set-variable (MSVs); Natural Transformations in Molecular Evolution; The Principle of Optimal Design in Biology in relation to Natural Selection;
Subjects:Computer Science > Dynamical Systems
Computer Science > Complexity Theory
Computer Science > Artificial Intelligence
Biology > Theoretical Biology
ID Code:3829
Deposited By:Baianu, Professor I.C.
Deposited On:06 Oct 2004
Last Modified:11 Mar 2011 08:55

References in Article

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REFERENCES

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.1971 "Organismic Supercategories and Qualitative Dynamics of Systems."

Ibid, 33, 339-353.

Baianu, I. 1973. "Some Algebraic Properties of (M, R).Systems." Bull. Math. Biol., 35.

213-217.

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.

Russel, Bertrand and A.N. Whitehead, 1925. Principia Mathematica, Cambridge: Cambridge Univ. Press.

Applications of the Theory of Categories, Functors and

Natural Transformations, N-categories, 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: 317-341.

2. Rosen, Robert. 1964. Abstract Biological Systems as Sequential Machines, Bull. Math. Biophys., 26: 103-111; 239-246; 27:11-14;28:141-148.

3. Arbib, M. 1966. Categories of (M,R)-Systems. Bull. Math. Biophys., 28: 511-517.

4. Cazanescu, D. 1967. On the Category of Abstract Sequential Machines. Ann. Univ. Buch., Maths & Mech. series, 16 (1):31-37.

5. Rosen, Robert. 1968. On Analogous Systems. Bull. Math. Biophys., 30: 481-492.

6. Baianu, I.C. and Marinescu, M. 1968. Organismic Supercategories:I. Proposals for a General Unitary Theory of Systems. Bull. Math. Biophys., 30: 625-635.

7. Comorosan,S. and Baianu, I.C. 1969. Abstract Representations of Biological Systems in Supercategories. Bull. Math. Biophys., 31: 59-71.

8. Baianu, I. 1970. Organismic Supercategories: III. On Multistable Systems. Bull. Math. Biophys., 32: 539-561.

9. Baianu, I. 1971. Organismic Supercategories and Qualitative Dynamics of Systems. Bull. Math. Biophys., 33: 339-354.

10. Baianu, I. 1971. Categories, Functors and Automata Theory. The 4th Intl. Congress LMPS, August-Sept. 1971.

11. Baianu, I. and Scripcariu, D. 1973. On Adjoint Dynamical Systems. Bull. Math. Biology., 35: 475-486.

12. Rosen, Robert. 1973. On the Dynamical realization of (M,R)-Systems. Bull. Math. Biology., 35:1-10.

13. Baianu, I. 1973. Some Algebraic Properties of (M,R)-Systems in Categories. Bull. Math. Biophys, 35: 213-218.

14. Baianu, I. and Marinescu, M. 1974. A Functorial Construction of (M,R)-Systems. Rev. Roum. Math. Pures et Appl., 19: 389-392.

15. Baianu, I.C. 1977. A Logical Model of Genetic Activities in Lukasiewicz Algebras: The Non-Linear Theory., Bull. Math. Biol.,39:249-258.

16. Baianu, I.C. 1980. Natural Transformations of Organismic Structures. Bull.Math. Biology, 42:431-446.

17. Warner, M. 1982. Representations of (M,R)-Systems by Categories of Automata., Bull. Math. Biol., 44:661-668.

18. Baianu, I.C.1983. Natural Transformations Models in Molecular Biology. SIAM Natl. Meeting, Denver, CO, USA.

19. 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.

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.1513-1577.

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