Quote:
Originally Posted by roachboy
on what basis do you assume that theories rooted in equilibrium obtain for bio-systems?
if you can't explain that, you can't do the mapping.
but the distribution is interesting on it's own--thinking about it.
so thanks.
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Thank you, roachboy. The only answer I can give is that the equilibrium can only be reached if the function s(x) is constant. If it varies with time, the process may only strive to a maximum - foillowing the gradient of P - which will perhaps never be reached. Expressions of the gradients may be found in the papers of Kjellström, 1970, and Kjellström & Taxén, 1981. For references see my next post.
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Bergström, R. M., 1969. An Entropy model of the Developing Brain. Developmental Psychobiology, 2(3): 139-152.
Bergström, M. Hjärnans resurser. Brain Books, ISBN 91-88410-07-2, Jönköping, 1992. (Swedish).
Bergström, M. Neuropedagogik. En skola för hela hjärnan. Wahlström & Widstrand, 1995. (Swedish).
Brooks, D. R. & Wiley, E. O. Evolution as Entropy, Towards a unified theory of Biology. The University of Chicago Press, 1986.
Brooks, D. R. Evolution in the Information Age: Rediscovering the Nature of the Organism. Semiosis, Evolution, Energy, Development, Volume 1, Number 1, March 2001
Cramér, H. Mathematical Methods of Statistics. Princeton, Princeton University Press, 1961.
Dawkins, R. The Selfish Gene. Oxford University Press, 1976.
Eigen, M. Steps towards life. Oxford University Press, 1992.
Gaines, Brian R. Knowledge Management in Societies of Intelligent Adaptive Agents. Journal of intelligent Information systems 9, 277-298 (1997).
Goldberg, D. E. Genetic Algorithms in Search Optimization & Machine Learning. Addison-Wesley, New York, 1989.
Hamilton, WD. 1963. The evolution of altruistic behavior. American Naturalist 97:354-356
Hartl, D. L. A Primer of Population Genetics. Sinauer, Sunderland, Massachusetts, 1981.
Kandel, E. R., Schwartz, J. H., Jessel, T. M. Essentials of Neural Science and Behavior. Prentice Hall International, London, 1995.
Kjellström, G. Network Optimization by Random Variation of component values. Ericsson Technics, vol. 25, no. 3, pp. 133-151, 1969.
Kjellström, G. Optimization of electrical Networks with respect to Tolerance Costs. Ericsson Technics, no. 3, pp. 157-175, 1970.
Kjellström, G. & Taxén, L. Stochastic Optimization in System Design. IEEE Trans. on Circ. and Syst., vol. CAS-28, no. 7, July 1981.
Kjellström, G. On the Efficiency of Gaussian Adaptation. Journal of Optimization Theory and Applications, vol. 71, no. 3, Dec. 1991.
Kjellström, G. & Taxén, L. Gaussian Adaptation, an evolution-based efficient global optimizer; Computational and Applied Mathematics, In, C. Brezinski & U. Kulish (Editors), Elsevier Science Publishers B. V., pp 267-276, 1992.
Kjellström, G. Evolution as a statistical optimization algorithm. Evolutionary Theory 11:105-117 (January, 1996).
Kjellström, G. The evolution in the brain. Applied Mathematics and Computation, 98(2-3):293-300, February, 1999.
Kjellström, G. Evolution in a nutshell and some consequences concerning valuations. EVOLVE, ISBN 91-972936-1-X, Stockholm, 2002.
Levine, D. S. Introduction to Neural & Cognitive Modeling. Laurence Erlbaum Associates, Inc., Publishers, 1991.
MacLean, P. D. A Triune Concept of the Brain and Behavior. Toronto, Univ. Toronto Press, 1973.
Maynard Smith, J. 1964. Group Selection and Kin Selection, Nature 201:1145-1147.
Maynard Smith, J. Evolutionary Genetics. Oxford University Press, 1998.
Mayr, E. What Evolution is. Basic Books, New York, 2001.
Middleton, D. An Introduction to Statistical Communication Theory. McGraw-Hill, 1960.
Rechenberg, I. Evolutionsstrategie. Stuttgart: Fromann - Holzboog, 1973.
Reif, F. Fundmentals of Statistical and Thermal Physics. McGraw-Hill, 1985.
Ridley, M. Evolution. Blackwell Science, 1996.
Shannon, C. E. A Mathematical Theory of Communication, Bell Syst. Techn. J., Vol. 27, pp 379-423, (Part I), 1948.
Stehr, G. On the Performance Space Exploration of Analog Integrated Circuits. Technischen Universität Munchen, Dissertation 2005.
Taxén, L. A Framework for the Coordination of Complex Systems’ Development. Institute of Technology, Linköping University, 2003.
Zohar, D. The quantum self : a revolutionary view of human nature and consciousness rooted in the new physics. London, Bloomsbury, 1990
Åslund, N. The fundamental theorems of information theory (Swedish). Nordisk Matematisk Tidskrift, Band 9, Oslo 1961.