--- abstract: 'Molecular models in terms of Categories, Functors and Natural Transformations are introduced for unimolecular chemical transformations, multi-molecular chemical and biochemical transformations. Novel approaches to realization of Relational Biology Models of Complex System Biology are introduced in terms of Natural Transformations between Functors of Molecular Categories. Several applications of such natural transformations are then presented to protein biosynthesis, embryogenesis and nuclear transplant experiments. Other possible realizations in Molecular Biology and Relational Biology of Organisms are also suggested. Future developments will include: Fuzzy Relations in Biology; Categories of Lukasiewicz Logic Algebras and Intuitionistic Logic Algebras for Modeling of Complex Neural Network Processes; Stochastic, Genetic Networks in Lukn-Algebras, and Relational Biology Models of Complex Hormonal Controls. ' altloc: [] chapter: ~ commentary: ~ commref: ~ confdates: 1983 conference: Proceed. SIAM & Society for Mathematical Biology Meeting confloc: 'Colorado, USA.' contact_email: ~ creators_id: - icb creators_name: - family: Baianu given: Ion honourific: Professor lineage: '' date: 1983-09 date_type: published datestamp: 2004-07-06 department: ~ dir: disk0/00/00/36/75 edit_lock_since: ~ edit_lock_until: ~ edit_lock_user: ~ editors_id: [] editors_name: - family: Landahl given: H.D. honourific: Professor lineage: Sr. eprint_status: archive eprintid: 3675 fileinfo: /style/images/fileicons/application_pdf.png;/3675/1/Naturaltransfmolbionu6.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: "Quantum Automata and Quantum Computation, Quantum Dynamics in terms of The Theory of Categories, Functors and Natural Transformations,Natural Transformations in Molecular Biology, Protein Biosynthesis Models, Embryogenesis models, Models of Nuclear Transplant Experiments in terms of Natural Transformations, Uni-molecular and multi-molecular transformations, Variable-Molecular-sets, molecular-set-variable (MSVs), Natural Transformations in Molecular Evolution \n\n" lastmod: 2011-03-11 08:55:37 latitude: ~ longitude: ~ metadata_visibility: show note: |+ New approaches to realization of Relational Biology Modeling of Complex System Biology in terms of Natural Transformations between Functors of Molecular Categories; Future developments will include: FUZZY RELATIONS ; Categories of Lukasiewicz Logic Algebras and Intuitionistic Logic Algebras for Modeling of Complex Neural Network Processes; STOCHASTIC, GENETIC NETWORKS in Lukn, L-ALGEBRAS; Relational Biology Models of Complex HORMONAL CONTROL and other METABOLIC PROCESSES. New approaches to realization of Relational Biology Modeling of Complex System Biology in terms of Natural Transformations between Functors of Molecular Categories; Future developments will include: FUZZY RELATIONS ; Categories of Lukasiewicz Logic Algebras and Intuitionistic Logic Algebras for Modeling of Complex Neural Network Processes; STOCHASTIC, GENETIC NETWORKS in Lukn, L-ALGEBRAS; Relational Biology Models of Complex HORMONAL CONTROL and other METABOLIC PROCESSES. number: 3 pagerange: 230-232 pubdom: FALSE publication: Proceedings of SIAM & Society for Mathematical Biology Meeting publisher: AMS (SIAM) refereed: TRUE referencetext: |+ REFERENCES Baianu, I. and Marinescu, M. 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. Biophysics., 32: 539-561. Baianu, I.1971 "Organismic Supercategories and Qualitative Dynamics of Systems." Ibid, 33, 339-353. Baianu, I. 1973. "Some Algebraic Properties of (M, R).Systems." Bull. Math. Biol., 35. 213-217. Carnap. R. 1938. "'The Logical Syntax of Language" New York: Harcourt, Brace and Co. Georgescu, G. and C. Vraciu 1970. "On the Characterization of Lukasiewicz Algebras." J Algebra, 16 4, 486-495. Hilbert, D. and W. Ackerman. 1927. Grunduge.der Theoretischen Logik, Berlin: Springer. McCulloch, W and W. Pitts. 1943. “A logical Calculus of Ideas Immanent in Nervous Activity” Ibid., 5, 115-133. Pitts, W. 1943. “The Linear Theory of Neuron Networks” Bull. Math. Biophys., 5, 23-31. Rosen, R.1958.a.”A relational Theory of Biological Systems” Bull. Math. Biophys., 20, 245-260. Rosen, R. 1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories” Bull. Math. Biophys., 20, 317-341. Russel, Bertrand and A.N. Whitehead, 1925. Principia Mathematica, Cambridge: Cambridge Univ. Press. Applications of the Theory of Categories, Functors and Natural Transformations, N-categories, Abelian or NonAbelian to: Automata Theory/ Sequential Machines, Bioinformatics, Complex Biological Systems /Complex Systems Biology, Computer Simulations and Modeling, Dynamical Systems , Quantum Dynamics, Quantum Field Theory, Quantum Groups,Topological Quantum Field Theory (TQFT), Quantum Automata, Cognitive Systems, Graph Transformations, Logic, Mathematical Modeling, etc. 1. Rosen, R. 1958. The Representation of Biological Systems from the Standpoint of the Theory of Categories." (of sets). Bull. Math. Biophys. 20: 317-341. 2. Rosen, Robert. 1964. Abstract Biological Systems as Sequential Machines, Bull. Math. Biophys., 26: 103-111; 239-246; 27:11-14;28:141-148. 3. Arbib, M. 1966. Categories of (M,R)-Systems. Bull. Math. Biophys., 28: 511-517. 4. Cazanescu, D. 1967. On the Category of Abstract Sequential Machines. Ann. Univ. Buch., Maths & Mech. series, 16 (1):31-37. 5. Rosen, Robert. 1968. On Analogous Systems. Bull. Math. Biophys., 30: 481-492. 6. Baianu, I.C. and Marinescu, M. 1968. Organismic Supercategories:I. Proposals for a General Unitary Theory of Systems. Bull. Math. Biophys., 30: 625-635. 7. Comorosan,S. and Baianu, I.C. 1969. Abstract Representations of Biological Systems in Supercategories. Bull. Math. Biophys., 31: 59-71. 8. Baianu, I. 1970. Organismic Supercategories: III. On Multistable Systems. Bull. Math. Biophys., 32: 539-561. 9. Baianu, I. 1971. Organismic Supercategories and Qualitative Dynamics of Systems. Bull. Math. Biophys., 33: 339-354. 10. Baianu, I. 1971. Categories, Functors and Automata Theory. The 4th Intl. Congress LMPS, August-Sept. 1971. 11. Baianu, I. and Scripcariu, D. 1973. On Adjoint Dynamical Systems. Bull. Math. Biology., 35: 475-486. 12. Rosen, Robert. 1973. On the Dynamical realization of (M,R)-Systems. Bull. Math. Biology., 35:1-10. 13. Baianu, I. 1973. Some Algebraic Properties of (M,R)-Systems in Categories. Bull. Math. Biophys, 35: 213-218. 14. Baianu, I. and Marinescu, M. 1974. A Functorial Construction of (M,R)-Systems. Rev. Roum. Math. Pures et Appl., 19: 389-392. 15. Baianu, I.C. 1977. A Logical Model of Genetic Activities in Lukasiewicz Algebras: The Non-Linear Theory., Bull. Math. Biol.,39:249-258. 16. Baianu, I.C. 1980. Natural Transformations of Organismic Structures. Bull.Math. Biology, 42:431-446. 17. Warner, M. 1982. Representations of (M,R)-Systems by Categories of Automata., Bull. Math. Biol., 44:661-668. 18. Baianu, I.C.1983. Natural Transformations Models in Molecular Biology. SIAM Natl. Meeting, Denver, CO, USA. 19. Baianu, I.C. 1984. A Molecular-Set-Variable Model of Structural and Regulatory Activities in Metabolic and Genetic Systems., Fed. Proc. Amer. Soc. Experim. Biol. 43:917. 19. Baianu, 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. relation_type: [] relation_uri: [] reportno: ~ rev_number: 12 series: ~ source: ~ status_changed: 2007-09-12 16:52:41 subjects: - comp-sci-mach-dynam-sys - comp-sci-complex-theory - comp-sci-art-intel - bio-theory succeeds: ~ suggestions: | The paper is relevant to both Dynamic Systems and Artificial Intelligence in addition to Theoretical Biology as it introduces a series of novel concepts with potential for a wide range of applications in Artificial Intelligence Bioinformatics, and Nonlinear Dynamical Systems Theory. sword_depositor: ~ sword_slug: ~ thesistype: ~ title: NATURAL TRANSFORMATION MODELS IN MOLECULAR BIOLOGY type: confpaper userid: 4959 volume: N/A