Natural Transformations of Organismic Structures

Baianu, Prof. Dr. I. C. (1980) Natural Transformations of Organismic Structures. [Journal (Paginated)]

This is the latest version of this eprint.

Full text available as:

PDF (A unified theory of natural transformations of organisms, metabolic-replication biochemical systems and quantum molecular sets) - Published Version
Available under License Creative Commons Attribution Non-commercial.



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.

Item Type:Journal (Paginated)
Keywords:Categories, supercategories, organisms development and evolution, functors and natural transformations in organismic set theory, (M,R)-systems and molecular set theories
Subjects:Biology > Evolution
Biology > Theoretical Biology
Neuroscience > Computational Neuroscience
Computer Science > Complexity Theory
Computer Science > Dynamical Systems
Computer Science > Neural Nets
Neuroscience > Neurogenetics
Philosophy > Logic
Philosophy > Philosophy of Science
ID Code:7755
Deposited By: Baianu, Professor I. C.
Deposited On:16 Dec 2011 00:58
Last Modified:16 Dec 2011 00:58

Available Versions of this Item

References in Article

Select the SEEK icon to attempt to find the referenced article. If it does not appear to be in cogprints you will be forwarded to the paracite service. Poorly formated references will probably not work.


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. "Energetic Considerations in E.E.G. Interpretations." Ann. Univ. Bucuresti

(Physics) 21, 61-67.

Baianu, I. 1973. "Some Algebraic Properties of (M, R)-Systems." Bull. Math. Biol. 35, 213-


Baianu, I. and D. Scripcariu. 1973. "On Adjoint Dynamical Systems." Bull. Math. Biol. 35,


Baianu, I. and M. Marinescu. 1974. "A Functorial Construction of (M,R)-Systems." Rev.

Roum. Math. Put. Appl. 19, 389-391. (received in final form in June 1971).

Baianu, I. 1977. "A Logical Model of Genetic Activities in Lukasiewicz Algebras: The

Non-Linear Theorey." Bull. Math. Biol. 39, 249 258.

Baianu, I. 1980. "Structural Order and Partial Disorder in Biological Systems."

Bull. Math. Biol. 42, 137-141.

Bartholomay, Anthony F. 1960. "Molecular Set Theory: A Mathematical Representation

for Chemical Reaction Mechanisms." Bull. Math. Biophys. 22, 285-307.

Bartholomay, Anthony E. 1965. "Molecular Set Theory. I: An Aspect of the

Biomathematical Theory of Sets." Bull. Math. Biophys., Special Issue, 27, 235-251.

Bartholomay, Anthony F. 1971. "Molecular Set Theory. III: The Wide Sense Kinetics of

Molecular Sets." Bull. Math. Biophys. 33, 355-372.

Comorosan, S. and I. Baianu. 1969. "Abstract Representations of Biological Systems in

Supercategories." Bull. Math. Biophys. 31, 59-70.

Eilenberg, S. and S. MacLane. 1945. "General Theory of Natural Equivalences." Trans. Am.

Math. Soc. 58, 231 294.

Lawvere, F. W. 1963. "Functorial Semantics of Algebraic Theories." Proc. Natn. Acad. Sci.

U.S.A. 50, 869-872.

L6fgren, L. 1968. "An Axiomatic Explanation of Complete Self-Reproduction?' Bull. Math.

Biophys. 30, 317 348.

Mitchell, Barry. 1965. The Theory of Categories. New York and London: Academic Press.

Popescu, Nicolae. 1973. Abelian Categories with Applications to Rings and Modules.

New York and London: Academic Press.

Rashevsky, Nicolas. 1954. "Topology and Life: In Search of General Mathematical

Principles in Biology and Sociology." Bull. Math. Biophys. 16, 317 348.

Rashevsky, Nicolas. 1960. Mathematical Biophysics, 3rd Edn. New York: Dover


Rashevsky, Nicolas. 1966a. "Physics, Biology and Sociology: A Reappraisal." Bull. Math.

Biophys. 28, 283-308.

Rashevsky, Nicolas. 1966b. "A Sociological Approach to Biology." Bull. Math. Biophys. 28,


Rashevsky, Nicolas. 1967a. "Organismic Sets: Outline of a General Theory of Biological

and Social Organisms." Bull. Math. Biophys. 29, 139 152.

Rashevsky, Nicolas. 1967b.


Rashevsky, Nicolas. 1967c. "Physics, Biology and Sociology: II. Suggestion for a Synthesis."

Bull. Math. Biophys. 29, 643-648.

Rashevsky, Nicolas. 1968a. "Organismic Sets: II. Some General Considerations." Bull.

Math. Biophys. 30, 163-174.

Rashevsky, Nicolas. 1968b. "Neurocybernetics as a Particular Case of General Regulatory

Mechanisms in Biological and Social Organisms." Concepts de l'ftge de la Science 3, 243


Rashevsky, Nicolas. 1968c. "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


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.

Rashevsky, Nicolas. 1971b. "Contributions to the Theory of Organismic Sets. II:

Aggressiveness and Submissiveness." Bull. Math. Biophys. 33, 49-54.

Rashevsky, Nicolas. 1971c. "Relational Forces and Structures Produced by Them." Bull.

Math. Biophys. 33, 321-338.

Rosen, Robert. 1958a. "A Relational Theory of Biological Systems." Bull. Math. Biophys.

20, 245 260.

Rosen, Robert. 1958b. "The Representation of Biological Systems from the Standpoint of

the Theory of Categories." Bull. Math. Biophys. 20, 317-342.

Rosen, Robert. 1959. "A Relational Theory of Biological Systems II." Bull. Math. Biophys.

21, 109 127.

Rosen, Robert. 1961. "A Relational Theory of Structural Changes Induced in Biological

Systems by Alterations in Environment." Bull. Math. Biophys. 23, 165-171.

Rosen, Robert, 1963a. "On the Reversibility of Environmentally Induced Alterations in

Abstract Biological Systems." Bull. Math. Biophys. 25, 41-50.

Rosen, Robert. 1963b. "Some Results in Graph Theory and Their Application to Abstract

Relational Biology." Bull. Math. Biophys. 25, 231 241.

Rosen, Robert. 1964a. "Abstract Biological Systems as Sequential Machines." Bull. Math.

Biophys. 26, 103-111.

Rosen, Robert, 1964b. "Abstract Biological Systems as Sequential Machines II: Strong

Connectedness and Reversibility." Bull. Math. Biophys. 26, 239-246.

Rosen, Robert. 1966a. "Abstract Biological Systems as Sequential Machines: III. Some

Algebraic Aspects." Bull. Math. Biophys. 28, 141-148.

Rosen, Robert, 1966b. "A Note on Replication in (M, R)-Sys.tems." Bull. Math. Biophys. 28,


Rosen, Robert. 1968. "On Analogous Systems." Bull. Math. Biophys. 30, 481~492.

Rosen, Robert. 1971. "Some Realizations of (M, R)-Systems and Their Interpretation." Bull.

Maths. Biophys. 33, 303-319.

Rosen, Robert, 1973. "On the Dynamical Realization of

(M, R)-Systems." Bull. Math. Biol.

35, 1-9.


Repository Staff Only: item control page