--- abstract: "The representation of physical and complex biological systems in terms of organismic supercategories was introduced in 1968 by Baianu and Marinescu in the attached paper which was published in the Bulletin of Mathematical Biophysics, edited by Nicolas Rashevsky. The different approaches to relational biology, developed by Rashevsky, Rosen and by Baianu et al.(1968,1969,1973,1974,1987,2004)were later discussed. \r\nThe present paper is an attempt to outline an abstract unitary theory of systems. In the introduction some of the previous abstract representations of systems are discussed. Also a possible connection of abstract representations of systems with a general theory of measure is proposed. Then follow some necessary definitions and authors' proposals for an axiomatic theory of systems. Finally some concrete examples are analyzed in the light of the proposed theory.\r\n\r\nAn abstract representation of biological systems from the standpoint of the theory of supercategories is presented. The relevance of such representations forG-relational biologies is suggested. In section A the basic concepts of our representation, that is class, system, supercategory and measure are introduced. Section B is concerned with the mathematical representation starting with some axioms and principles which are natural extensions of the current abstract representations in biology. Likewise, some extensions of the principle of adequate design are introduced in section C. Two theorems which present the connection between categories and supercategories are proved. Two other theorems concerning the dynamical behavior of biological and biophysical systems are derived on the basis of the previous considerations. Section D is devoted to a general study of oscillatory behavior in enzymic systems, some general quantitative relations being derived from our representation. Finally, the relevance of these results for a quantum theoretic approach to biology is discussed.\r\n\r\nhttp://www.springerlink.com/content/141l35843506596h/" altloc: [] chapter: ~ commentary: ~ commref: ~ confdates: ~ conference: ~ confloc: ~ contact_email: ~ creators_id: - icb - ~ creators_name: - family: Baianu given: I.C. honourific: Prof. Dr. lineage: '' - family: Marinescu given: Mircea M. honourific: Dr. lineage: '' date: 1968-12-21 date_type: published datestamp: 2004-10-06 department: ~ dir: disk0/00/00/38/31 edit_lock_since: ~ edit_lock_until: 0 edit_lock_user: ~ editors_id: [] editors_name: - family: Rashevsky given: Nicolas honourific: Professor lineage: '' eprint_status: archive eprintid: 3831 fileinfo: application/pdf;http://cogprints.org/3831/2/Orgsuper_cats1icb.pdf full_text_status: public importid: ~ institution: ~ isbn: ~ ispublished: pub issn: ~ item_issues_comment: [] item_issues_count: 0 item_issues_description: [] item_issues_id: [] item_issues_reported_by: [] item_issues_resolved_by: [] item_issues_status: [] item_issues_timestamp: [] item_issues_type: [] keywords: 'Complex Systems Biology, Categories and Functors; Homology Theory applications to Qualitative Dynamics; Quantum Genetics; Relational Oscillations; Organismic Supercategories; Qualitative Dynamics of Systems in Organismic Supercategories; Categorical Dynamic Systems; Observables Generating Diagram, Relational Biology; Quantum, Electron Tunneling mechanisms in Enzyme Catalized reactions; ' lastmod: 2011-12-16 00:59:02 latitude: ~ longitude: ~ metadata_visibility: show note: "Recent developments of this unified theory include applications to: Cell Transformations to Malignant Cancer; Telomerase and Reverse Transcriptase roles; c-Myc , TP53 and Ras tumor suppressor genes; p27 and p21 inhibition and uncontrolled cell cycling leading to neoplastic transformation/ malignant cell re-differentiation; rational, individualized therapy of cancers; rational clinical trials; molecular medicine, high-throughput genomics and proteomics technologies, tumor cell lines separation and complete genomic analysis; cancer cell biomarker pattern identification; Early, Reliable and Sensitive Detection of Cancers by Ultra-sensitive, in vivo, Non-Invasive Detection methods. cell interactomics, dynamics of coupled genetic-proteomic networks; Quantum Computation,Quantum Automata and Quantum Gravity (in preparation in 2004); Carcinogenesis; Single Molecule Dynamics; Malignant Tumors; Cancer Cell Interactomics; dynamics of genetic-proteomic networks and signalling pathways, development, regeneration, the control mechanisms of cell dynamic programming in cells; Cancer Cell Cycling; Neoplastic Transformations and Oncogenesis;Complex Systems Biology, Łukasiewicz-Topos and Higher-Dimensional Algebraic Models of Cell Interactomics; cell interactomics, dynamics of coupled genetic-proteomic networks and signaling pathways, development, regeneration, and control mechanisms of cell dynamic programming in cells, neoplastic transformations and oncogenesis; complex system modeling and biomolecular network representations in categories of Łukasiewicz Logic Algebras and Łukasiewicz-Topos Relational and Molecular Biology, Cell Genomics and Proteomics, and Cancer Cell Interactomics are represented in Supercategories defined currently as n-categories (or higher dimensional algebra), Axiomatic definitions of Categories and Supercategories of Relational, Complex Biological Systems, Dynamic Computations with Algebraic Varieties, Cell Transformations to Malignant Cancer.\r\nEarly, Reliable and Sensitive Detection of Cancers by Ultra-sensitive, in vivo, Non-Invasive detection methods. " number: 1 pagerange: 625-635 pubdom: TRUE publication: The Bulletin of Mathematical Biophysics publisher: 'Pergamon Press, Ltd., and Springer reprints' refereed: TRUE referencetext: "Baianu, I. and Marinescu, M. 1968. Organismic Supercategories: I. Proposals for a General Unitary Theory of Systems., Bull. Math. Biophys., 30: 625-635.\r\nBaianu, I. 1970. Organismic Supercategories: II. On Multistable Systems. Bull. Math. Biophys., 32: 539-561.\r\nBaianu, I. 1971. Organismic Supercategories and Qualitative Dynamics of Systems. Bull. Math. Biophys., 33: 339-354.\r\nBaianu, I. 1971. Categories, Functors and Automata Theory: “Symbolic Computation of Categories, Topological Semigroup Categories by Quantum Automata and Quantum Computers.”,Proceed. 4th Intl. Congress LMPS, Bucharest, August-Sept. 1971.\r\nBaianu, I. 1970 \"Organismic Supercategories: II. On Multistable Systems.\" Bull. Math.Biophysics., 32:539-561.\r\nBaianu, I.1971 \"Organismic Supercategories and Qualitative Dynamics of Systems.\", Ibid., 33: 339-353.\r\nBaianu, I. 1973. \"Some Algebraic Properties of \r\n(M,R)-Systems.\" Bull. Math. Biol., 35: 213-217.\r\nBaianu, I. and Scripcariu, D. 1973. On Adjoint Dynamical Systems. Bull. Math. Biology., 35: 475-486.\r\nBaianu, I. and Marinescu, M. 1974. A Functorial Construction of (M,R)-Systems. Rev. Roum. Math. Pures et Appl., 19: 389-392.\r\nBaianu, I.C. 1977. A Logical Model of Genetic Activities in Łukasiewicz Algebras: The Non-Linear Theory., Bull. Math. Biology, 39:249-258.\r\nBaianu, I.C. 1980. Natural Transformations of Organismic Structures. Bull. Math. Biology, 42: 431-446.\r\nBaianu, I.C. 1980. Structural Order and Partial Disorder in Biological Systems. Bull. Math. Biology, 42: 464-468 \r\nBaianu, I.C.1983. Natural Transformations Models in Molecular Biology. SIAM Natl. Meeting, Denver, CO, USA.\r\nBaianu, I.C. 1984. A Varying-Molecular-Set Model of Structural and Regulatory Activities in Metabolic and Genetic Systems., Fed. Proc. Amer. Soc. Experim. Biol. 43: 917.\r\nBaianu, I.C. 1987. Computer Models and Automata Theory in Biology and Medicine. In: \"Mathematical Models in Medicine.\", vol.7., M. Witten, Ed., Pergamon Press: New York, pp.1513-1577.\r\nBaianu, I.C. 2004a. “Relational Quantum Biology”. CERN Preprint.\r\nBaianu, I.C. 2004b. “Computer simulation and computability of biological systems”. Cogprints, UK.\r\nBaianu, I.C. 2004c. “Complex Systems Analysis of Cell Cycling Models in Carcinogenesis.” Preprint arXiv/q-bio.OT/0406045 [abs, pdf] :23 pages, 1 Figure.\r\nBourbaki, N. 1958. Elements de Mathematique, Paris: Hermann & Cie, Editeurs.\r\nBrown, R. 1967. \"Groupoids and van Kampen's Theorem.\", Proc. London Math. Soc. 17(3):385-401. \r\nBrown, R. 1976. Groupoids II.\r\nBrown, R. 2002. \"Crossed Complexes and Homotopy Groupoids as NonCommutative tools for Higher Dimensional Local-to-Global Problems.\", Maths Preprint 02.26 of the University of Wales, Bangor, UK.\r\nBrown, Ronald and G. Danesh-Naruie. 1975.``The fundamental groupoid as a topological groupoid'' Proc. Edinborough Math. Soc. 19: 237-244. \r\nBrown, R. and Porter,S. 2003. Higher Dimensional Algebra and Neurosciences. arXiv Preprint 2003.\r\nCarnap. R. 1938. \"'The Logical Syntax of Language\" New York: Harcourt, Brace and Co. \r\nDupre, P. and Glazebrook, J. 2001. \r\nGeorgescu, G. and C. Vraciu.1970. \"On the Characterization of Łukasiewicz Algebras.\" J Algebra, 16 (4): 486-495.\r\nGeorgescu, G. and Popescu, D. 1973. On Algebraic Categories. Rev. Roum. Math. 18: 212-226.\r\nGlazebrook, J. and Brown,R.2002. Groupoid Actions and Holonomy. J. Algebra. \r\nHilbert, D. and W. Ackerman. 1927. Grunduge.der Theoretischen Logik, Berlin: Springer.\r\nMcCulloch, W and W. Pitts. 1943. “A Logical Calculus of Ideas Immanent in Nervous Activity” Ibid., 5, 115-133.\r\nPitts, W.1943. “The Linear Theory of Neuron Networks” Bull. Math. Biophys., 5, 23-31.\r\n\r\nPrisecaru, V.I. and I.C. Baianu.2004. Complex Systems Analysis of Cell Cycling Models in Carcinogenesis. Preprint at Cogprints, UK. (accepted/archived in July 2004). \r\nRosen, R.1958a.”A Relational Theory of Biological Systems” Bull. Math. Biophys., 20: 245-260.\r\nRosen, R.1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories” Bull. Math. Biophys., 20, 317-341.\r\nRussel, Bertrand and A.N. Whitehead, 1925. Principia Mathematica, Cambridge: Cambridge Univ. Press\r\nWarner, M. 1982. Representations of (M, R)-Systems by Categories of Automata., Bull. Math. Biol., 44:661-668.\r\nWoese.C.1987. Bacterial evolution. Microbiol Rev. 1987 June, 51 (2): 221–271. (Archea).\r\nWoese, Carl, R. 2002. On the evolution of cells. Proceed. Natl. Acad. Sci. USA, June 25, 2002: vol. 99, no. 13 : 8742-8747. (Archea)\r\n" relation_type: [] relation_uri: [] reportno: ~ rev_number: 27 series: ~ source: ~ status_changed: 2011-12-16 00:59:02 subjects: - comp-sci-stat-model - comp-sci-mach-dynam-sys - comp-sci-complex-theory - bio-socio - bio-evo - comp-sci-neural-nets - comp-sci-hci - bio-theory - bio-pop - bio-ani-behav - bio-ani-cog - bio-behav - bio-eco - comp-sci-art-intel succeeds: ~ suggestions: "Currently I own the copyright for this article and am allowing the posting on the web of my original article. Important related areas of the topic presented in this archived continuation of my published work are:\r\nRepresentations of Biological and Quantum Systems in terms of Categories, Functors and Natural Tranformations (Functorial Morphisms); Homology and Homotopy Theory applications to Qualitative Dynamics; \r\n-Quantum Genetics; Relational Oscillations; Organismic Supercategories; \r\n-Qualitative Dynamics of Systems in Organismic Supercategories; Algebraic Geometry in Biology, Cell Division Control and Dynamic Programnming;\r\n-Categorical Dynamic Systems; Observables Generating Diagram, Relational Biology;\r\n-Single Molecule Dynamics; Quantum, Electron Tunneling mechanisms in Enzyme Catalized reactions; \r\n" sword_depositor: ~ sword_slug: ~ thesistype: ~ title: "Organismic Supercategories: I. Proposals for a General Unified Theory of Systems- Classical, Quantum, and Complex Biological Systems.\r\n\r\n\r\n" type: journalp userid: 4959 volume: 30