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Über die wahrscheinlichkeit eines quasiergodischen wortes im grenzfall unendlich grosser wortlänge

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Abstract

According to Rosen (Bull. Math. Biophysics,23, 305–318, 1961) the forming of the first genes in natural history can be understood in terms of stochastic building of words. The genes are supposed to represent quasiergodic words of great length. For a word of lengthN, belonging to the free monoid with base ofn elements, a formula is given for the probability of its belonging to some quasiergodic submonoid.

Restricting ourselves ton=2, we give an estimate for an upper and a lower bound of the limit of this probability asN tends to infinity. Result: If the tolerance ε does not exceed a certain value depending only on the mean relative frequencies (p 1,p 2,...) of the quasiergodic submonoid, the upper bound for the limit of the probability is zero. Concluding remarks are added to show the meaning of our results to the biologists.

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Literatur

  • Khinchin, A. I. 1957.Mathematical Foundations of Information Theory. New York: Dover Publications, Inc.

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  • Rosen, R. 1959a. “The DNA-Protein Coding Problem.”Bull. Math. Biophysics,21, 71–95.

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  • — 1959b. “Some Further Comments on the DNA-Protein Coding Problem.”Ibid.,21, 289–297.

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Authors and Affiliations

  1. Lehrgebiet Biologie und Anthropologie, Technische Universität Berlin, Berlin, Germany

    Uwe Klemm

Authors
  1. Uwe Klemm
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Additional information

Rosen 1959a, b, 1960, 1961) behandelt das DNS-Protein-Coding-Problem mit Hilfe der mathematischen Theorie der freien Halbgruppen. Anknüpfend an (1961) wollen wir im folgenden eine Abschätzung für die

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Klemm, U. Über die wahrscheinlichkeit eines quasiergodischen wortes im grenzfall unendlich grosser wortlänge. Bulletin of Mathematical Biophysics 24, 429–439 (1962). https://doi.org/10.1007/BF02477999

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  • DOI: https://doi.org/10.1007/BF02477999

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