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On Adjoint Dynamical Systems

Baianu, Prof. Dr. I. C. and Scripcariu, Prof.Dr. Dragos (1973) On Adjoint Dynamical Systems. [Journal (Paginated)]

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Abstract

Transformations of dynamical systems and organismic structures are discussed in terms of adjoint, simple adjoint and weak adjoint functors of organismic supercategories during development and evolution of organisms on markedly different timescales. A representation of nuclear transplants in terms of adjoint functors and a novel interpretation of nuclear transplant experiments is proposed. Three new theorems are proven for adjoint dynamical systems representing multi-potent developing cells and additional results are obtained for weak adjoint systems such as differentiated (specialized) cells.

Item Type:Journal (Paginated)
Additional Information:http://www.springerlink.com/content/c163r4620w44g532/ BULLETIN OF MATHEMATICAL BIOLOGY Volume 35, Number 4, 475-486, DOI: 10.1007/BF02575191
Keywords:Development and Evolution of biological organisms represente in terms of adjoint and weak functors of organismic supercategories; analysis of nuclear transplant experiments in terms of dynamic transformations of interacting cells; progresive restrictions of transformation potentiality leading to cell and tissue differentiation in multicellular organisms; cloning criteria in terms of adjoint functors of organismic structures.
Subjects:Computer Science > Dynamical Systems
Computer Science > Complexity Theory
Biology > Sociobiology
Biology > Evolution
Computer Science > Neural Nets
Biology > Theoretical Biology
Biology > Animal Cognition
Biology > Behavioral Biology
Biology > Ecology
ID Code:7753
Deposited By: Baianu, Professor I. C.
Deposited On:16 Dec 2011 00:58
Last Modified:16 Dec 2011 00:58

References in Article

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LITERATURE

Baianu, I. 1970. "Organismic Supercategories: II. On Multistable Systems." Bull.

Math. Biophysics, 32, 540-561.

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

Ibid., 33, 339-354.

Baianu, I. and M. Marinescu. 1968. "Organismic Supercategories: I. Proposals for a

General Unitary Theory of Systems." Ibid., 30, 625-636.

- - and 1973. "A Functorial Construction of (M, R)-Systems." Rev.

Roum. Math. Purcs et Appl. (in press).

1973. "Some Algebraic Properties of (M, R)-Systems." Bull. Math. Biology,

35, 213-217.

Briggs, R. and T. King. 1952. "Transplantation of Living Nuclei from Blastula Cells

into Enucleated Frogs' Eggs." Proc. Natl. Acad. Sei. U.S., 38, 455~463.

Bueur, I. and Deleanu, A. 1968. Introduction to the Theory of Categories and t~unetors,

pp. 16-52. London, New York, Sydney: Wiley.

Burgess, M.A. 1967. "The Developmental Potentialities of Regeneration Blastema Cell

Nuclei as Determined by Nuclear Transplantation." J. Embryol. Exp. Morph., 18,

27-41.

Denis, H. 1970. "Importance des Interactions Nucleo-Cytoplasmiques au Cours du

Dbveloppement Embryonnaire." Arch. Int. Physiol. Biochim., 78, 367-380.

Di Berardino, A. M. and Nancy Hoffner. 1970. "Origin of Chromosomal Abnormalities

in Nuclear Transplants--A Reevaluation of Nuclear Differentiation and Nuclear

Equivalence in Amphibians." Develop. Biol., 23, No. 2, 185-209.

1. Ashby, W. R. 1960. Design for a brain, 2nd ed., New York: J. Wiley & Sons, Inc.

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

3. Ashby, W. R 1956.An Introduction to Oybernetics, New York: J. Wiley & Sons, Inc.

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

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

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

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

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

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

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

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

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

13. Baianu, I.C. 1980. Structural Order and Partial Disorder in Biological Systems. Bull. Math. Biology, 42: 464-468

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

15. 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.

16. 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.

17. Bourbaki, N. 1958. Elements de Mathematique, Paris: Hermann & Cle, Editeurs.

18. Carnap. R. 1938. "'The Logical Syntax of Language" New York: Harcourt, Brace and Co.

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

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

21. Ehresmann, Ch. 1966. "Trends Toward Unity in Mathematics." Cahiers de Topologie Et Geometrie Differentielle, 8,1-7.

22. Eilenberg, S. and S. MacLane. 1945. "General Theory of Natural Equivalences."Trans. .Am. Math. Soo., 58, 231-294.

23. Eilenberg, S. and J. Wright. 1967. "Automata. in General Algebras." Seventy-Second Meeting American

Math. Soc., 1-17.

24. Georgescu, G. and D. Popescu. 1968. "On Algebraic Categories." Rev. Roum. Math. Pures et Appl., 13, 337-342.

25. Georgescu, G. and C. Vraciu 1970. "On the Characterization of Lukasiewicz Algebras." J. Algebra, 16 (4), 486-495.

26. Hilbert, D. and W. Ackerman. 1927. Grunduge.der Theoretischen Logik, Berlin: Springer.

27. Lawvere, F. W. 1963. "Functional Semantics of Algebraic Theories." Proc. Natl.Acad. Sci., 50, 869-872.

28. 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, Heidelberg and New York: Springer-Verlag, pp. 1-20.

29. Lawvere, F. W. 1969. "Closed Cartesian Categories." (Lecture held as a guest of the Romanian Academy of Sciences).

30. Lofgren; L. 1968. "An Axiomatic Explanation of Complete Self-Reproduction." Bull.Math. Biophysics, 30, 317-348

31. Mitchell, B. 1965. The Theory of Categories. New York and London: Academic Press.

32. Rashevsky, N. 1954. "Topology and Life: In Search of General Mathematical Principles in Biology and Sociology." Bull. Math. Biophysics, 16, 317-348.

33. McCulloch, W and W. Pitts. 1943. "A logical Calculus of Ideas Immanent in Nervous Activity" Ibid., 5, 115-133.

34. Pitts, W. 1943. “The Linear Theory of Neuron Networks” Bull. Math. Biophys., 5, 23-31.

35. Rosen, R.1958a. "A relational Theory of Biological Systems" Bull. Math. Biophys., 20, 245-260.

36. Rosen, R. 1958b. "The Representation of Biological Systems from the Standpoint of the Theory of Categories." Bull. Math. Biophys., 20, 317-341.

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

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

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

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

The authors would like to dedicate this paper to the memory of Professor Nicolas Rashevsky who, in more than one way, initiated this approach.

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