Bulletin of Mathematical Biology

, Volume 35, Issue 4, pp 475–486 | Cite as

On adjoint dynamical systems

  • Ion Bâianu
  • Dragoş Scripcariu
Article

Abstract

Transformations of dynamical systems are discussed in terms of adjoint, simple adjoint and weak adjoint functors. The relevance of this approach to interpretations of nuclear transplant experiments is suggested, and three new theorems concerning the development of biological systems are presented. Another three theorems concerning adjoint dynamical systems are proved. The connection of these results with the theory of organismic sets developed by Rashevsky (1966, 1967a-c, 1968a-c, 1969a-c, 1971a, b) is also investigated.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  1. Bâianu, I. 1970. “Organismic Supercategories: II. On Multistable Systems”.Bull. Math. Biophysics,32, 540–561.CrossRefGoogle Scholar
  2. —. 1971. “Organismic Supercategories and Qualitative Dynamics of Systems”. —Ibid..33, 339–354.MATHCrossRefGoogle Scholar
  3. — and M. Marinescu. 1968. “Organismic Supercategories: I. Proposals for a General Unitary Theory of Systems.” —Ibid.,,30, 625–636.MATHCrossRefGoogle Scholar
  4. Bâianu, I. and M. Marinescu. 1973. “A Functorial Construction of (M, R)-Systems.”Rev. Roum. Math. Pures et Appl (in press).Google Scholar
  5. — 1973. “Some Algebraic Properties of (M, R.)-Systems.”Bull. Math. Biology,35, 213–217.MATHCrossRefMathSciNetGoogle Scholar
  6. Briggs, R. and T. King. 1952. “Transplantation of Living Nuclei from Blastula Cells into Enucleated Frogs’ Eggs”Proc. Natl. Acad. Sci. U.S. 38, 455–463.CrossRefGoogle Scholar
  7. Bucur, I. and Deleanu, A. 1968.Introduction to the Theory of Categories and Functors, pp. 16–52. London, New York, Sydney: Wiley.MATHGoogle Scholar
  8. Burgess, M. A., 1967. “The Developmental Potentialities of Regeneration Blastema Cell Nuclei as Determined by Nuclear Transplantation”J. Embryol. Exp. Morph.,18, 27–41.Google Scholar
  9. Denis, H. 1970. “Importance des Interactions Nucleo-Cytoplasmiques au Cours du Développement Embryonnaire”Arch. Int. Physiol. Biochim. 78, 367–380.Google Scholar
  10. 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.CrossRefGoogle Scholar
  11. Graham, C. F.et al. 1966. “The Induction of DNA Synthesis by Frog Egg Cytoplasm”.Develop. Biol.,14, 349–381.CrossRefGoogle Scholar
  12. Gurdon, J. B. 1967. “On the Origin and Persistence of a Cytoplasmic State Inducing Nuclear DNA Synthesis in Frogs’ Eggs”Proc. Natl. Acad. Sci. U.S.,58, 545–552.CrossRefGoogle Scholar
  13. Kainen, P. 1971. “Weak Adjoint Functors”Math. Z.,122, 1–9.MATHCrossRefMathSciNetGoogle Scholar
  14. Kan, D. M. 1958. “Adjoint Functors”Trans. A.M.S.,87, 294–330.MATHCrossRefMathSciNetGoogle Scholar
  15. King, T. J. and R. Briggs. 1956. “Serial Transplantation of Embryonic Nuclei”.Cold Spring Harbor Symp. Quant. Biol.,21, 271–290.Google Scholar
  16. Mitchell, Barry. 1965.The Theory of Categories. New York and London: Academic Press.Google Scholar
  17. Popescu, D. 1970. “Some Remarks on Complete Cogenerated Categories”Rev. Roum. Math. Pures et Appl.,15, 1027–1033.MATHGoogle Scholar
  18. Popescu, N. 1971.Abelian Categories (in Romanian). Bucharest: Ed. Academy of R.S. Romania.MATHGoogle Scholar
  19. Rashevsky, Nicolas. 1966. “Physics, Biology and Sociology: A Reappraisal.”Bull. Math. Biophysics,28 283–308.CrossRefMathSciNetGoogle Scholar
  20. —, 1967a. “Organismic Sets: Outline of a General Theory of Biological and Social Organisms.” —Ibid.,,29, 139–152.MATHCrossRefGoogle Scholar
  21. — 1967b. “Physics, Biology and Sociology: II. Suggestions for a Synthesis.” —Ibid.,,29, 643–648.CrossRefGoogle Scholar
  22. —. 1967c. “Organismic Sets and Biological Epimorphism.” —Ibid.,,29, 389–393.CrossRefGoogle Scholar
  23. —. 1968a. “Organismic Sets: II. Some General Considerations.” —Ibid.,30, 163–173.MATHCrossRefGoogle Scholar
  24. —. 1968b. “Neurocybernetics as a Particular Case of General Regulatory Mechanisms in Biological and Social Organisms”Concepts de l’Age de la Science,3, 243–258.Google Scholar
  25. —. 1968c. “A Note on the Development of Organismic Sets.”Bull. Math. Biophysics,30, 355–358.CrossRefGoogle Scholar
  26. —. 1969a. “Outline of a Unified Approach to Physics, Biology and Sociology.” —Ibid.,31, 159–198.MATHCrossRefGoogle Scholar
  27. —. 1969b. “Multiple Relational Equilibria: Polymorphism, Metamorphosis and Other Possibly Similar Phenomena”. —Ibid.,31, 417–427.MATHCrossRefGoogle Scholar
  28. —, 1969c. “Some Considerations of Relational Equilibria.” —Ibid.,,31, 605–617.MATHCrossRefGoogle Scholar
  29. —. 1971a. “Two Definitions of Stability of Equilibria.” —Ibid.,33, 157–164.Google Scholar
  30. —. 1971b. “Relational Forces and Structures Produced by Them.” —Ibid.,33, 321–338.MATHCrossRefGoogle Scholar
  31. Rosen, Robert. 1958. “The Representation of Biological Systems from the Standpoint of the Theory of Categories.” —Ibid.,20, 317–342.CrossRefGoogle Scholar
  32. —. 1968. “On Analogous Systems.” —Ibid.,30, 481–492.MATHCrossRefGoogle Scholar
  33. —. 1971. “Some Realizations of (M, R)-Systems and Their Possible Interpretations” —Ibid.,33, 303–320.MATHCrossRefGoogle Scholar
  34. Signoret, J. and B. Picheral. 1962. “Transplantations de Noyaux chez Pleurodeles Waltlii Michah”.C.R. Acad. Sci. Paris,254, 1150–1151.Google Scholar
  35. — 1965. “Transplantations Nucléaires et Différenciation Embryonnaire”Archives de biologie (Liege),76, 591–606.Google Scholar
  36. Smith, L. D. 1965. “Transplantation of Nuclei of Primordial Germ Cells into Enucleated Eggs ofRana pipiens”.Proc. Nat. Acad. Sci. U.S. 54, 101–107.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1973

Authors and Affiliations

  • Ion Bâianu
    • 1
  • Dragoş Scripcariu
    • 2
  1. 1.Faculty of PhysicsBiophysics LaboratoryBucharest
  2. 2.Faculty of BiologyLaboratory of Embryology and Cell BiologyBucharest

Personalised recommendations