--- 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.' altloc: - http://www.springerlink.com/content/31784n16758x3353/ chapter: ~ commentary: ~ commref: ~ confdates: ~ conference: ~ confloc: ~ contact_email: ~ creators_id: - ibaianu@illinois.edu creators_name: - family: Baianu given: 'I. C. ' honourific: Prof. Dr. lineage: '' date: 1980-09-21 date_type: published datestamp: 2011-12-16 00:58:34 department: ~ dir: disk0/00/00/77/55 edit_lock_since: ~ edit_lock_until: 0 edit_lock_user: ~ editors_id: [] editors_name: - family: Rashevsky given: 'Nicolas ' honourific: Prof.Dr. lineage: ~ eprint_status: archive eprintid: 7755 fileinfo: application/pdf;http://cogprints.org/7755/1/NatTransf_orig80.pdf full_text_status: public importid: ~ institution: ~ isbn: ~ ispublished: pub issn: ~ item_issues_comment: [] item_issues_count: ~ item_issues_description: [] item_issues_id: [] item_issues_reported_by: [] item_issues_resolved_by: [] item_issues_status: [] item_issues_timestamp: [] item_issues_type: [] keywords: 'Categories, supercategories, organisms development and evolution, functors and natural transformations in organismic set theory, (M,R)-systems and molecular set theories' lastmod: 2011-12-16 00:58:34 latitude: ~ longitude: ~ metadata_visibility: show note: ~ number: 3 pagerange: 431-446 pubdom: TRUE publication: 'BULLETIN OF MATHEMATICAL BIOLOGY , DOI: 10.1007/BF02460794' publisher: 'Pergamon Press, Ltd, reprinted by Springer ' refereed: TRUE referencetext: "LITERATURE\r\n\r\nArbib, M. 1966. \"Categories of (M, R)-Systems.\" Bull. Math. Biophys. 28, 511-517.\r\nBaianu, I. and M. Marinescu. 1968. \"Organismic Supercategories: I. Proposals for a\r\nGeneral Unitary Theory of Systems.\" Bull. Math. Biophys. 30, 625 635.\r\nBaianu, I. 1970. \"Organismic Supercategories: II. On Multistable Systems,\" Bull. Math.\r\nBiophys. 32, 539-561.\r\nBaianu, I. 1971a. \"Organismic Supercategories and Qualitative Dynamics of Systems.\" Bull.\r\nMath. Biophys. 33, 339 354.\r\nBaianu, I. 1971b. \"Categories, Functors and Automata Theory.\" 4th Int. Congress L.M.P.S.\r\nBucharest (1971).\r\nBaianu, I. 1972. \"Energetic Considerations in E.E.G. Interpretations.\" Ann. Univ. Bucuresti\r\n(Physics) 21, 61-67.\r\nBaianu, I. 1973. \"Some Algebraic Properties of (M, R)-Systems.\" Bull. Math. Biol. 35, 213-\r\n217.\r\nBaianu, I. and D. Scripcariu. 1973. \"On Adjoint Dynamical Systems.\" Bull. Math. Biol. 35,\r\n475~486.\r\nBaianu, I. and M. Marinescu. 1974. \"A Functorial Construction of (M,R)-Systems.\" Rev.\r\nRoum. Math. Put. Appl. 19, 389-391. (received in final form in June 1971).\r\nBaianu, I. 1977. \"A Logical Model of Genetic Activities in Lukasiewicz Algebras: The\r\nNon-Linear Theorey.\" Bull. Math. Biol. 39, 249 258.\r\nBaianu, I. 1980. \"Structural Order and Partial Disorder in Biological Systems.\"\r\nBull. Math. Biol. 42, 137-141.\r\nBartholomay, Anthony F. 1960. \"Molecular Set Theory: A Mathematical Representation\r\nfor Chemical Reaction Mechanisms.\" Bull. Math. Biophys. 22, 285-307.\r\nBartholomay, Anthony E. 1965. \"Molecular Set Theory. I: An Aspect of the\r\nBiomathematical Theory of Sets.\" Bull. Math. Biophys., Special Issue, 27, 235-251.\r\nBartholomay, Anthony F. 1971. \"Molecular Set Theory. III: The Wide Sense Kinetics of\r\nMolecular Sets.\" Bull. Math. Biophys. 33, 355-372.\r\nComorosan, S. and I. Baianu. 1969. \"Abstract Representations of Biological Systems in\r\nSupercategories.\" Bull. Math. Biophys. 31, 59-70.\r\nEilenberg, S. and S. MacLane. 1945. \"General Theory of Natural Equivalences.\" Trans. Am.\r\nMath. Soc. 58, 231 294.\r\nLawvere, F. W. 1963. \"Functorial Semantics of Algebraic Theories.\" Proc. Natn. Acad. Sci.\r\nU.S.A. 50, 869-872.\r\nL6fgren, L. 1968. \"An Axiomatic Explanation of Complete Self-Reproduction?' Bull. Math.\r\nBiophys. 30, 317 348.\r\nMitchell, Barry. 1965. The Theory of Categories. New York and London: Academic Press.\r\nPopescu, Nicolae. 1973. Abelian Categories with Applications to Rings and Modules.\r\nNew York and London: Academic Press.\r\nRashevsky, Nicolas. 1954. \"Topology and Life: In Search of General Mathematical\r\nPrinciples in Biology and Sociology.\" Bull. Math. Biophys. 16, 317 348.\r\nRashevsky, Nicolas. 1960. Mathematical Biophysics, 3rd Edn. New York: Dover\r\nPublications.\r\nRashevsky, Nicolas. 1966a. \"Physics, Biology and Sociology: A Reappraisal.\" Bull. Math.\r\nBiophys. 28, 283-308.\r\nRashevsky, Nicolas. 1966b. \"A Sociological Approach to Biology.\" Bull. Math. Biophys. 28,\r\n655-661.\r\nRashevsky, Nicolas. 1967a. \"Organismic Sets: Outline of a General Theory of Biological\r\nand Social Organisms.\" Bull. Math. Biophys. 29, 139 152.\r\nRashevsky, Nicolas. 1967b.\r\nNATURAL TRANSFORMATIONS OF ORGANISMIC STRUCTURES 445\r\nRashevsky, Nicolas. 1967c. \"Physics, Biology and Sociology: II. Suggestion for a Synthesis.\"\r\nBull. Math. Biophys. 29, 643-648.\r\nRashevsky, Nicolas. 1968a. \"Organismic Sets: II. Some General Considerations.\" Bull.\r\nMath. Biophys. 30, 163-174.\r\nRashevsky, Nicolas. 1968b. \"Neurocybernetics as a Particular Case of General Regulatory\r\nMechanisms in Biological and Social Organisms.\" Concepts de l'ftge de la Science 3, 243\r\n258.\r\nRashevsky, Nicolas. 1968c. \"A Note on the Development of Organismic Sets.\" Bull. Math.\r\nBiophys. 30, 355-358.\r\nRashevsky, Nicolas. 1969a. \"Outline of a Unified Approach to Physics, Biology and\r\nSociology.\" Bull. Math. Biophys. 31, 159-198.\r\nRashevsky, Nicolas. 1969b. \"Multiple Relational Equilibria: Polymorphism,\r\nMetamorphosis and Other Possibly Similar Phenomena.\" Bull. Math. Biophys. 31, 417\r\n427.\r\nRashevsky, Nicolas. 1969c. \"Some Considerations on Relational Equilibria.\" Bull. Math.\r\nBiophys. 31,605 617.\r\nRashevsky, Nicolas. 1970a. \"Contributions to the Theory of Organismic Sets: Why are\r\nThere Only Two Sexes?\". Bull. Math. Biophys. 32, 293-301.\r\nRashevsky, Nicolas. 1970b. \"Contributions to the Theory of Organismic Sets: Leadership.\"\r\nBull. Math. Biophys. 32, 391M01.\r\nRashevsky, Nicolas. 1970c. \"The Approximation Method, Relational Biology and\r\nOrganismic Sets.\" Bull. Math. Biophys. 32, 485~,98.\r\nRashevsky, Nicolas. 1971a. \"Two Definitions of Stability of Equilibria.\" Bull. Math. Biophys.\r\n33, 157-164.\r\nRashevsky, Nicolas. 1971b. \"Contributions to the Theory of Organismic Sets. II:\r\nAggressiveness and Submissiveness.\" Bull. Math. Biophys. 33, 49-54.\r\nRashevsky, Nicolas. 1971c. \"Relational Forces and Structures Produced by Them.\" Bull.\r\nMath. Biophys. 33, 321-338.\r\nRosen, Robert. 1958a. \"A Relational Theory of Biological Systems.\" Bull. Math. Biophys.\r\n20, 245 260.\r\nRosen, Robert. 1958b. \"The Representation of Biological Systems from the Standpoint of\r\nthe Theory of Categories.\" Bull. Math. Biophys. 20, 317-342.\r\nRosen, Robert. 1959. \"A Relational Theory of Biological Systems II.\" Bull. Math. Biophys.\r\n21, 109 127.\r\nRosen, Robert. 1961. \"A Relational Theory of Structural Changes Induced in Biological\r\nSystems by Alterations in Environment.\" Bull. Math. Biophys. 23, 165-171.\r\nRosen, Robert, 1963a. \"On the Reversibility of Environmentally Induced Alterations in\r\nAbstract Biological Systems.\" Bull. Math. Biophys. 25, 41-50.\r\nRosen, Robert. 1963b. \"Some Results in Graph Theory and Their Application to Abstract\r\nRelational Biology.\" Bull. Math. Biophys. 25, 231 241.\r\nRosen, Robert. 1964a. \"Abstract Biological Systems as Sequential Machines.\" Bull. Math.\r\nBiophys. 26, 103-111.\r\nRosen, Robert, 1964b. \"Abstract Biological Systems as Sequential Machines II: Strong\r\nConnectedness and Reversibility.\" Bull. Math. Biophys. 26, 239-246.\r\nRosen, Robert. 1966a. \"Abstract Biological Systems as Sequential Machines: III. Some\r\nAlgebraic Aspects.\" Bull. Math. Biophys. 28, 141-148.\r\nRosen, Robert, 1966b. \"A Note on Replication in (M, R)-Sys.tems.\" Bull. Math. Biophys. 28,\r\n149-151.\r\nRosen, Robert. 1968. \"On Analogous Systems.\" Bull. Math. Biophys. 30, 481~492.\r\nRosen, Robert. 1971. \"Some Realizations of (M, R)-Systems and Their Interpretation.\" Bull.\r\nMaths. Biophys. 33, 303-319.\r\nRosen, Robert, 1973. \"On the Dynamical Realization of \r\n(M, R)-Systems.\" Bull. Math. Biol.\r\n35, 1-9.\r\n" relation_type: [] relation_uri: [] reportno: ~ rev_number: 5 series: ~ source: ~ status_changed: 2011-12-16 00:58:34 subjects: - bio-evo - bio-theory - comp-neuro-sci - comp-sci-complex-theory - comp-sci-mach-dynam-sys - comp-sci-neural-nets - neurgen - phil-logic - phil-sci succeeds: 7745 suggestions: ~ sword_depositor: ~ sword_slug: ~ thesistype: ~ title: Natural Transformations of Organismic Structures type: journalp userid: 4959 volume: 42