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The bulletin of mathematical biophysics

, Volume 33, Issue 3, pp 303–319 | Cite as

Some realizations of (M, R)-systems and their interpretation

  • Robert Rosen
Article

Abstract

Some years ago (Rosen 1958a, b; 1959) we described a class of metaphorical, relational paradigms for cellular activity which we termed (M, R)-systems. A sizable amount of subsequent work, to be itemized below, has been devoted to an exploration of some of the properties of these systems. The main purpose of the present paper is to put this class of paradigms into a general system-theoretic perspective, with a particular view to appraising the relation between the type of system description embodied in the (M, R)-system and other kinds of physical and mathematical descriptions of cellular systems. Thus, the principal aim is to establish the relationships and connections between the global relational formalism embodied in the (M, R)-systems and the empirical descriptions which still represent the bulk of our biological knowledge.

Keywords

Rosen System Description Sequential Machine Oriented Graph Dynamical Description 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature

  1. Arbib, M. 1965. “A Common Framework for Automata Theory and Control Theory.”J. SIAM Control, Ser. A,3, (No. 2), 206–222.MATHMathSciNetCrossRefGoogle Scholar
  2. — 1966. “Automata Theory and Control Theory—A Rapprochement.”Automatica,3, 161–189. Oxford, England: Pergamon Press.Google Scholar
  3. Higgins, J. 1967. “The Theory of Oscillating Reactions.”Industrial & Engineering Chemistry,59 (No. 5), 19–62.CrossRefGoogle Scholar
  4. Kalman, R. E. 1968. “New Developments in Systems Theory Relevant to Biology.”Systems Theory & Biology, edited by M. Mesarovich, pp. 222–232. New York: Springer-Verlag.Google Scholar
  5. Rosen, R. 1958a. “A Relational Theory of Biological Systems.”Bull. Math. Biophysics,20, 245–260.Google Scholar
  6. — 1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories.”Ibid.,,20, 317–341.Google Scholar
  7. Rosen, R. 1959. “A Relational Theory of Biological Systems II.”Ibid.,,21, 109–128.Google Scholar
  8. — 1961. “A Relational Theory of Structural Changes Induced in Biological Systems by Alterations in Environments.”Ibid.,,23, 165–171.Google Scholar
  9. — 1962a. “A Note on Abstract Relational Biologies.”Ibid.,,24, 31–38.MATHGoogle Scholar
  10. — 1963a. “On the Reversibility of Environmentally Induced Alterations in Abstract Biological Systems.”Ibid.,,25, 41–50.MATHGoogle Scholar
  11. — 1963b. “Some Results in Graph Theory and Their Application to Abstract Relational Biology.”Ibid.,,25, 231–241.MATHGoogle Scholar
  12. — 1964a. “Abstract Biological Systems as Sequential Machines.”Ibid.,,26, 103–111.MATHGoogle Scholar
  13. — 1964b. “Abstract Biological Systems as Sequential Machines II: Strong Connectedness.”Ibid.,26, 239–246.MATHGoogle Scholar
  14. — 1965. “Some Comments on Re-establishability.”Ibid.,,27, 11–14.Google Scholar
  15. — 1966a. “Biological and Physical Realizations of Abstract Metabolic Models.”Helgolander wiss. Meeresunters,14, 25–31.CrossRefGoogle Scholar
  16. — 1966b. “Abstract Biological Systems as Sequential Machines III: Some Algebraic Aspects.”Bull. Math. Biophysics,28, 141–148.MATHGoogle Scholar
  17. — 1966c. “A Note on Replication in (M, R)-Systems.”Ibid.,,28, 149–151.MATHGoogle Scholar
  18. — 1967a. “Two-Factor Models, Neural Nets and Biochemical Automata.”J. Theo. Biology,15, 282–297.CrossRefGoogle Scholar
  19. — 1967b. “Further Comments on Replication in (M, R)-Systems.”Bull. Math. Biophysics,29, 91–94.MATHGoogle Scholar
  20. — 1967c. Monograph:Optimality Principles in Biology. (Russian Translation.) London: Butterworth & Co., Ltd.Google Scholar
  21. — 1968a. “Relational Biology and Cybernetics.”Biokybernetik Band,1, 49–55. Berlin: Gustav-Fischer Verlag.Google Scholar
  22. — 1968b. “Some Comments on the Physico-chemical Description of Biological Activity.”J. Theo. Biology,18, 380–386.CrossRefGoogle Scholar
  23. — 1968c. “On Analogous Systems.”Bull. Math. Biophysics,30, 481–492.MATHGoogle Scholar
  24. — 1968d. “Turing’s Morphogens, Two-Factor Systems and Active Transport.”Ibid.,,30, 493–499.Google Scholar
  25. — 1969a. “Hierarchical Systems in Biology.” InHierarchical Structures, Wilson & Whyte. New York: American Elsevier.Google Scholar
  26. — 1969b. “Uber die Wahl der Zustandsvariablen für Metabilosche Systeme.”Studia Biophysica,14, 247–259.Google Scholar
  27. — 1970.Dynamical Systems in Biology. 2-volume Text-Monograph, Vol. 1, New York, N.Y.: John Wiley & Sons, Inc.Google Scholar
  28. Walter, C. F. 1969a. “Stability of Controlled Biological Systems.”J. Theo. Biology,23, 23–38.CrossRefGoogle Scholar
  29. — 1969b. “The Absolute Stability of Certain Types of Controlled Biological Systems.”Ibid.,,23, 39–52.CrossRefGoogle Scholar
  30. — 1970. “The Occurrence and the Significance of Limit Cycle Behavior in Controlled Biochemical Systems.”Ibid.,,27, 259–272.CrossRefGoogle Scholar
  31. Zadeh, L., and C. Desoer. 1963.Linear System Theory. New York: McGraw-Hill.MATHGoogle Scholar

Copyright information

© N. Rashevsky 1968

Authors and Affiliations

  • Robert Rosen
    • 1
  1. 1.Center for Theoretical BiologyState University of New York at BuffaloUSA

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