creators_name: Baianu, I. C. creators_id: ibaianu@illinois.edu editors_name: Rashevsky, Nicolas type: journalp datestamp: 2011-12-16 00:58:34 lastmod: 2011-12-16 00:58:34 metadata_visibility: show title: Natural Transformations of Organismic Structures ispublished: pub subjects: bio-evo subjects: bio-theory subjects: comp-neuro-sci subjects: comp-sci-complex-theory subjects: comp-sci-mach-dynam-sys subjects: comp-sci-neural-nets subjects: neurgen subjects: phil-logic subjects: phil-sci full_text_status: public keywords: Categories, supercategories, organisms development and evolution, functors and natural transformations in organismic set theory, (M,R)-systems and molecular set theories abstract: The mathematical structures underlying the theories of organismic sets, (M, R)-systems and molecular sets are shown to be transformed naturally within the theory of categories and functors. Their natural transformations allow the comparison of distinct entities, as well as the modelling of dynamics in “organismic” structures. date: 1980-09-21 date_type: published publication: BULLETIN OF MATHEMATICAL BIOLOGY , DOI: 10.1007/BF02460794 volume: 42 number: 3 publisher: Pergamon Press, Ltd, reprinted by Springer pagerange: 431-446 refereed: TRUE referencetext: LITERATURE Arbib, M. 1966. "Categories of (M, R)-Systems." Bull. Math. Biophys. 28, 511-517. Baianu, I. and M. Marinescu. 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. Biophys. 32, 539-561. Baianu, I. 1971a. "Organismic Supercategories and Qualitative Dynamics of Systems." Bull. Math. Biophys. 33, 339 354. Baianu, I. 1971b. "Categories, Functors and Automata Theory." 4th Int. Congress L.M.P.S. Bucharest (1971). Baianu, I. 1972. 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"A Note on the Development of Organismic Sets." Bull. Math. Biophys. 30, 355-358. Rashevsky, Nicolas. 1969a. "Outline of a Unified Approach to Physics, Biology and Sociology." Bull. Math. Biophys. 31, 159-198. Rashevsky, Nicolas. 1969b. "Multiple Relational Equilibria: Polymorphism, Metamorphosis and Other Possibly Similar Phenomena." Bull. Math. Biophys. 31, 417 427. Rashevsky, Nicolas. 1969c. "Some Considerations on Relational Equilibria." Bull. Math. Biophys. 31,605 617. Rashevsky, Nicolas. 1970a. "Contributions to the Theory of Organismic Sets: Why are There Only Two Sexes?". Bull. Math. Biophys. 32, 293-301. Rashevsky, Nicolas. 1970b. "Contributions to the Theory of Organismic Sets: Leadership." Bull. Math. Biophys. 32, 391M01. Rashevsky, Nicolas. 1970c. "The Approximation Method, Relational Biology and Organismic Sets." Bull. Math. Biophys. 32, 485~,98. Rashevsky, Nicolas. 1971a. "Two Definitions of Stability of Equilibria." Bull. Math. Biophys. 33, 157-164. 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(1980) Natural Transformations of Organismic Structures. [Journal (Paginated)] document_url: http://cogprints.org/7755/1/NatTransf_orig80.pdf