A p-adic model of DNA sequence and genetic code

Драгович, Бранко; Dragovich, A. Yu.

doi:10.1134/s2070046609010038

Cited by 75 publications

(55 citation statements)

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“…В работе [142] Б. Дра-говича и А. Драгович генетический код был представлен как ло-кально постоянное отображение на информационном 5-адическом пространство кодонов, при этом вырождение генетического ко-да описывалось локальным постоянством этого отображения от-носительно 2-адической и 5-адической метрик. В работе Козы-рева и Хренникова [183] для описания вырождения и физико-химических свойств генетического кода использовалось двумер-ное 2-адическое пространство.…”

Section: библиографический обзорunclassified

“…В работе [142] Б. Дра-говича и А. Драгович для описания вырождения генетическо-го кода использовалось информационное 5-адическое простран-ство. Был предложен новый подход -генетический код был пред-ставлен как локально постоянное отображение, определённое на ультраметрическом пространстве кодонов, при этом вырождение генетического кода описывается локальным постоянством этого отображения.…”

Section: главаunclassified

“…Наша конструкция отличается от конструкции ра-боты [142] другой параметризацией пространства кодонов и дру-гой конструкцией ультраметрики.…”

Section: главаunclassified

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Козырев¹

2008

Sovrem. Probl. Mat.

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Section: библиографический обзорunclassified

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Козырев¹

2008

Sovrem. Probl. Mat.

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“…Recently, a new interesting application of m-adic information space was found in the domain of genetics, (m = 2, 4, 5 depending on a model); see B. Dragovich and A. Dragovich [206], A. Khrennikov [207], M. Pitkänen [208], A. Khrennikov and S. Kozyrev [211].…”

Section: P-adic Models Of the Genetic Codementioning

confidence: 99%

On p-adic mathematical physics

Драгович¹,

Khrennikov

Козырев

et al. 2009

P-Adic Num Ultrametr Anal Appl

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A brief review of some selected topics in p-adic mathematical physics is presented.1 Numbers: Rational, Real, p-AdicWe present a brief review of some selected topics in p-adic mathematical physics. More details can be found in the references below and the other references are mainly contained therein. We hope that this brief introduction to some aspects of p-adic mathematical physics could be helpful for the readers of the first issue of the journal p-Adic Numbers, Ultrametric Analysis and Applications.The notion of numbers is basic not only in mathematics but also in physics and entire science. Most of modern science is based on mathematical analysis over real and complex numbers. However, it is turned out that for exploring complex hierarchical systems it is sometimes more fruitful to use analysis over p-adic numbers and ultrametric spaces. p-Adic numbers (see, e.g. [1]), introduced by Hensel, are widely used in mathematics: in number theory, algebraic geometry, representation theory, algebraic and arithmetical dynamics, and cryptography.The following view how to do science with numbers has been put forward by Volovich in [2,3]. Suppose we have a physical or any other system and we 1 make measurements. To describe results of the measurements, we can always use rationals. To do mathematical analysis, one needs a completion of the field Q of the rational numbers. According to the Ostrowski theorem there are only two kinds of completions of the rationals. They give real R or p-adic Q p number fields, where p is any prime number with corresponding p-adic norm |x| p , which is non-Archimedean. There is an adelic formula p |x| p = 1 valid for rational x which expresses the real norm |x| ∞ in terms of p-adic ones. Any p-adic number x can be represented as a series x = ∞ i=k a i p i , where k is an integer and a i ∈ {0, 1, 2, ..., p − 1} are digits. To build a mathematical model of the system we use real or p-adic numbers or both, depending on the properties of the system [2,3].Superanalysis over real and p-adic numbers has been considered by Vladimirov and Volovich [4,5]. An adelic approach was emphasized by Manin [6].One can argue that at the very small (Planck) scale the geometry of the spacetime should be non-Archimedean [2,3,7]. There should be quantum fluctuations not only of metrics and geometry but even of the number field. Therefore, it was suggested [2] the following number field invariance principle: Fundamental physical laws should be invariant under the change of the number field.One could start from the ring of integers or the Grothendieck schemes. Then rational, real or p-adic numbers should appear through a mechanism of number field symmetry breaking, similar to the Higgs mechanism [8, 9].Recently (for a review, see [10,11,12,13,14]) there have been exciting achievements exploring p-adic, adelic and ultrametric structures in various models of physics: from the spacetime geometry at small scale and strings, via spin glasses and other complex systems, to the universe as a whole. There has been al...

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“…Completing the affine line to the projective line P 1 and then taking an extra puncture ∞, allows us to see the dendrogram as a subtree of the Bruhat-Tits tree, which is an important object in the study of p-adic algebraic curves. A first application is in the coding of DNA sequences [9], which is a special case of p-adic methods for processing strings over a given alphabet, as explained in [7], where also new invariants of time series of dendrograms are developped.…”

Section: Introductionmentioning

confidence: 99%

Degenerating Families of Dendrograms

Bradley

2008

J Classif

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Abstract. Dendrograms used in data analysis are ultrametric spaces, hence objects of nonarchimedean geometry. It is known that there exist p-adic representation of dendrograms. Completed by a point at infinity, they can be viewed as subtrees of the Bruhat-Tits tree associated to the p-adic projective line. The implications are that certain moduli spaces known in algebraic geometry are p-adic parameter spaces of (families of) dendrograms, and stochastic classification can also be handled within this framework. At the end, we calculate the topology of the hidden part of a dendrogram.

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A p-adic model of DNA sequence and genetic code

Cited by 75 publications

References 13 publications

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On p-adic mathematical physics

Degenerating Families of Dendrograms

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