, Volume 16, Issue 1–2, pp 25–34 | Cite as

Robert Rosen’s Work and Complex Systems Biology

  • I.  C. Baianu


Complex Systems Biology approaches are here considered from the viewpoint of Robert Rosen’s (M,R)-systems, Relational Biology and Quantum theory, as well as from the standpoint of computer modeling. Realizability and Entailment of (M,R)-systems are two key aspects that relate the abstract, mathematical world of organizational structure introduced by Rosen to the various physicochemical structures of complex biological systems. Their importance for understanding biological function and life itself, as well as for designing new strategies for treating diseases such as cancers, is pointed out. The roles played by multiple metastable states in the “continuous uphill flow of Life” supported through internal bioenergetic processes that are coupled to essential inflows are also discussed in relation to dynamic realizations of (M,R)-systems. Furthermore, the roles played by the underlying, many-valued, quantum logics and symbolic computations for ultra-complex biological systems are also briefly discussed.


Categories classical logic paradoxes of replication entailment in (M,R)-systems complex versus simple systems Complex Systems Biology and the underlying Quantum Logics generalized (M,R)-systems Multiple metastable states and “Chaotic” trajectories coupled to Bioenergetic processes and the Anticipatory Organization of Information Flows that are supporting Life N-valued logics and higher dimensional algebra in Complex Systems Biology Quantum Automata and Relational Biology Quantum computers and symbolic computation versus numerical simulations of ultra-complex systems realization and entailment problem for (M,R)-systems) Thermodynamic linkage of metastable states to essential Bioenergetic processes 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Baianu, I. C., R. Brown, G. Georgescu, and J. F. Glazebrook: 2006, ‘Complex Nonlinear Biodynamics in Categories, Higher Dimensional Algebra and Łukasiewicz-Moisil Topos: Transformations of Neuronal, Genetic and Neoplastic Networks’, Axiomathes (this volume).Google Scholar
  2. Baianu, I. C., R. Brown, and J. F. Glazebrook: 2005, ‘Quantum Algebraic Topology and Field Theories’, (in preparation):
  3. Baianu, I.C., Marinescu, M. 1968‘Organismic Supercategories: Towards a Unified Theory of Systems’Bulletin of Mathematical Biophysics30148165Google Scholar
  4. Baianu, I.C. 1971a“Organismic Supercategories and Qualitative Dynamics of Systems”Ibid.33339353Google Scholar
  5. Baianu, I. C.: 1971b, ‘Categories, Functors, Quantum Automata and Quantum Computation’, in P. Suppes (ed.), Proceedings of the 4th Intl. Congress LMPS, BucharestGoogle Scholar
  6. Baianu, I.C. 1973‘Some Algebraic Properties of (M,R)-Systems’Bulletin of Mathematical Biophysics35213217Google Scholar
  7. Baianu, I.C., Marinescu, M. 1974‘A Functorial Construction of (M,R) Systems’Revue Roumaine de Mathematiques Pures et Appliquees19388391Google Scholar
  8. Baianu, I.C. 1977“A Logical Model of Genetic Activities in Łukasiewicz Algebras: The Non-linear Theory”Bulletin of Mathematical Biophysics39249258Google Scholar
  9. Baianu, I.C. 1980‘Natural Transformations of Organismic Structures’Bulletin of Mathematical Biophysics42431446Google Scholar
  10. Baianu, I. C.: 1983, ‘Natural Transformation Models in Molecular Biology’, in Proceedings of the SIAM Natl. Meet., Denver, CO.; Eprint:;
  11. Baianu, I.C. 1984‘A Molecular-Set-Variable Model of Structural and Regulatory Activities in Metabolic and Genetic Networks’FASEB Proceedings43917Google Scholar
  12. Baianu, I. C.: 1987a, ‘Computer Models and Automata Theory in Biology and Medicine’ in M. Witten (ed.), Mathematical Models in Medicine, vol. 7., Pergamon Press, New York, 1513–1577; CERN Preprint No. EXT-2004-072:
  13. Baianu, I. C.: 1987b, ‘Molecular Models of Genetic and Organismic Structures’, in Proceed. Relational Biology Symp., Argentina; CERN Preprint No. EXT-2004-067,–2004–067/Molecular Models ICB3.doc.Google Scholar
  14. Ehresmann, C. 1965Catégories et StructuresDunodParisGoogle Scholar
  15. Ehresmann, C. 1966‘Trends Toward Unity in Mathematics’Cahiers de Topologie et Géometric Differentielle817Google Scholar
  16. Eilenberg, S., MacLane, S. 1945‘The General Theory of Natural Equivalences’Transactions of the American Mathematical Society58231294Google Scholar
  17. Elsasser, M.W. 1981‘A Form of Logic Suited for Biology’Robert, Rosen eds. Progress in Theoretical Biology, Volume 6Academic PressNew York and London2362Google Scholar
  18. Georgescu, G., Popescu, D. 1968‘On Algebraic Categories’Revue Roumaine de Mathematiques Pures et Appliquees13337342Google Scholar
  19. Georgescu, G.: 2006, ‘N-valued Logics and Łukasiewicz-Moisil Algebras’, Axiomathes (in this volume).Google Scholar
  20. Löfgren,  L. 1968“An Axiomatic Explanation of Complete Self-Reproduction”Bulletin of Mathematical Biophysics30317348Google Scholar
  21. Mitchell,  B. 1965Theory of CategoriesAcademic PressLondonGoogle Scholar
  22. Rashevsky,  N. 1965The Representation of Organisms in Terms of PredicatesBulletin of Mathematical Biophysics27477491Google Scholar
  23. Rashevsky,  N. 1969‘Outline of a Unified Approach to Physics, Biology and Sociology’Bulletin of Mathematical Biophysics31159198Google Scholar
  24. Rosen,  R. 1958a‘A Relational Theory of Biological Systems’Bulletin of Mathematical Biophysics20245260Google Scholar
  25. Rosen,  R. 1958b‘The Representation of Biological Systems from the Standpoint of the Theory of Categories’Bulletin of Mathematical Biophysics20317341Google Scholar
  26. Rosen,  R. 1971‘Some Realizations of (M,R)-Systems and Their Interpretation’Bulletin of Mathematical Biophysics33303319Google Scholar
  27. Rosen,  R. 1973‘On the Dynamical Realization of (M,R)-Systems’Bulletin of Mathematical Biology3519CrossRefGoogle Scholar
  28. Rosen,  R. 1977‘Book Review: Structural Stability and Morphogensis by René Thom’Bulletin of Mathematical Biology39629632Google Scholar
  29. Rosen,  R. 1991Life ItselfColumbia University PressNew YorkGoogle Scholar
  30. Rosen, R. 1999Essays on Life ItselfColumbia University PressNew York(also 2nd edn., 2004)Google Scholar
  31. Rosen, R.: 2006, ‘Autobiographical Reminiscences, with an Epilogue by Judith Rosen’, Axiomathes (this volume).Google Scholar
  32. Rosen, J.: 2005. ‘How to define a living organism according to Robert Rosen?’ (personal communication to the author)Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • I.  C. Baianu

There are no affiliations available

Personalised recommendations