By P. Baconnier, G. Benchetrit, J. Demongeot, T. Pham Dinh (auth.), Michel Cosnard, Jacques Demongeot, Alain Le Breton (eds.)
Read or Download Rhythms in Biology and Other Fields of Application: Deterministic and Stochastic Approaches Proceedings of the Journées de la Société Mathématique de France, held at Luminy, France, September 14–18,1981 PDF
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Additional info for Rhythms in Biology and Other Fields of Application: Deterministic and Stochastic Approaches Proceedings of the Journées de la Société Mathématique de France, held at Luminy, France, September 14–18,1981
To a morphologic problematics, replacing changes in the asymptotic states of gradient dynamical systems by changes of types (C p or else) of mappings. All the formalism is CP ,; let A, B, C, be manifolds; a mapping control from A to B is a mapping FAX C ~ B XC (where B X C stands for a certain fiber bundle with fibre B and base C) morphism of fiber bundles that leaves C fixed. A is the source, B the target, C the control space. One can thus define for any c E C a mapping fc from A' to B and such that F( ,c) = (fc'c).
J. 76 u J with R (s,a) (3. 2) s = [ATP J/ K, a = [F6P] / K, K = K MgATP = 5 micT(omoles; This reaction is characterized by a very strong inhibition by excess substrate. 0 , . , 0 and. 5, 1. and 2. millimoles. 2. 1). 1) was effected by two methods. 2) to be an unstable focus [17J • The latter was to continue a steady-state solution as one of these parameters varies, until finding an arc of unstable foci. 2. , Ao = 200. and p 450. 6. 4) gives a stable orbit, with a period on the order of 1/6. 3).
Type of embedding. p. types provide a rather refined, though qualitative, classification of plane curves. In fact, the diagram of contours can be used in pattern recognition to code such shapes into series of symbols and compare them to each other, to establish a morphological distance between them (counting the minimum number of co dimension one "bumps" necessary to transform one type into another), to extract features (subsequences of symbols), to write formal metaphors and study the constraints on them, etc ••• The mapping control tools thus transform gross classifications of the contour diagrams into finer ones for curves.