Email this article Multidimensional p-adic metric and genetic code
- Authors: Kozyrev S.V1, Khrennikov A.Y.2
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Affiliations:
- Steklov Mathematical Institute, Russian Academy of Sciences
- Linnæus University
- Issue: Vol 15, No 1 (2011)
- Pages: 113-117
- Section: Articles
- URL: https://journals.eco-vector.com/1991-8615/article/view/21096
- ID: 21096
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Abstract
We discuss the family of metrics in multimensional p-adic spaces. For a metric under consideration the set of balls differs from the set of balls for the standard multidimensional metric. Moreover, we it is possible to consider the metrics for which the form of the sets of balls depends on the scale and position. As the example of the introduced metric spaces we study the 2-adic parametrization of the genetic code. We show that the degeneracy of the genetic code is described by the metric space from the considered family, i.e. the map of the genetic code is constant for the balls with respect to the metric from the introduced class.
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About the authors
Sergey V Kozyrev
Steklov Mathematical Institute, Russian Academy of Sciences
Email: kozyrev@mi.ras.ru
(д.ф.-м.н.), ведущий научный сотрудник, отдел математической физики; Математический институт им. В. А. Стеклова РАН; Steklov Mathematical Institute, Russian Academy of Sciences
Andrei Yu Khrennikov
Linnæus University
Email: kozyrev@mi.ras.ru
; Linnæus University
References
- Albeverio S., Kozyrev S. V. Multidimensional p-adic wavelets for the deformed metric // p-Adic Numbers, Ultrametric Analysis, and Applications, 2010. Vol. 2, no. 4. Pp. 265-277.
- Albeverio S., Kozyrev S. V. Pseudodifferential p-adic vector fields and pseudodifferentiation of a composite p-adic function // p-Adic Numbers, Ultrametric Analysis, and Applications, 2010. Vol. 2, no. 1. Pp. 21-34.
- Koonin E. V., Novozhilov A. S. Origin and Evolution of the Genetic Code: The Universal Enigma // IUBMB Life, 2009, February. Vol. 61(2). Pp. 99-111, arXiv: 0807.4749.
- Khrennikov A. Yu., Kozyrev S. V. Genetic code on the dyadic plane // Physica A, 2007. Vol. 381. Pp. 265-272, arXiv: q-bio/0701007.
- Khrennikov A. Yu., Kozyrev S. V. 2-Adic clustering of the PAM matrix // Journal of Theoretical Biology, 2009. Vol. 261. Pp. 396-406, arXiv: 0903.0137.
- Козырев С. В., Хренников А. Ю. 2-Адические числа в генетике и симметрия Румера // Докл. Акад. Наук, 2010. Т. 430, № 1. С. 32-34
- Dragovich B., Dragovich A. A p-Adic Model of DNA Sequence and Genetic Code // p- Adic Numbers, Ultrametric Analysis and Applications, 2009. Vol. 1, no. 1. Pp. 34-41, arXiv: q-bio/0607018v1.
- Khrennikov A. Yu. Gene expression from polynomial dynamics in the 2-adic information space // Chaos, Solitons, and Fractals, 2009. Vol. 42, no. 1. Pp. 341-347.
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