The representation of biological systems from the standpoint of the theory of categories
- 270 Downloads
A mathematical framework for a rigorous theory of general systems is constructed, using the notions of the theory of Categories and Functors introduced by Eilenberg and MacLane (1945,Trans. Am. Math. Soc.,58, 231–94). A short discussion of the basic ideas is given, and their possible application to the theory of biological systems is discussed. On the basis of these considerations, a number of results are proved, including the possibility of selecting a unique representative (a “canonical form”) from a family of mathematical objects, all of which represent the same system. As an example, the representation of the neural net and the finite automaton is constructed in terms of our general theory.
KeywordsBiological System Block Diagram Covariant Functor Oriented Graph Oriented Edge
Unable to display preview. Download preview PDF.
- Eilenberg, S. 1957.Categories and Fiber Bundles. Mimeographed Lecture Notes, (Unpublished, The University of Chicago.)Google Scholar
- Kleene, S. C. 1955. “Representation of Events in Nerve Nets”, Automata Studies, Annals of Mathematics Studies, #34, 3–41. (Ed. C. E. Shannon and J. McCarthy.) Princeton: Princeton University Press.Google Scholar
- McCulloch, W. and W. Pitts. 1943. “A Logical Calculus of the Ideas Immanent in Nervous Activity”.Bull. Math. Biophysics,10, 1–10.Google Scholar
- Neumann, J. von 1951. “The General and Logical Theory of Automata”.Cerebral Mechanisms in Behavior (Ed. Lloyd A. Jeffress.) New York: John Wiley & Sons.Google Scholar
- — 1955. “Probabilistic Logics and the Synthesis of Reliable Organisms From Unreliable Components”.Automata Studies, Annals of Mathematics Studies, #34 43–98. (Ed. C. E. Shannon and J. McCarthy.) Princeton: Princeton University Press.Google Scholar
- Rosen, R. 1958. “A Relational Theory of Biological Systems”.Bull. Math. Biophysics,20, 245–60.Google Scholar