DNA coding and Gödel numbering

Argyris Nicolaidis and Fotis Psomopoulos

Physica A: Statistical Mechanics and its Applications, 2022, vol. 594, issue C

Abstract: We consider a DNA strand as a mathematical statement. Inspired by the work of Kurt Gödel, we attach to each DNA strand a Gödel’s number, a product of prime numbers raised to appropriate powers. To each DNA chain corresponds a single Gödel’s number G, and inversely given a Gödel’s number G, we can specify the DNA chain it stands for. Next, considering a single DNA strand composed of N bases, we study the statistical distribution of g, the logarithm of G. Our assumption is that the choice of the mth term is random and with equal probability for the four possible outcomes. The ‘experiment’, to some extent, is similar to throwing N times a four-faces die. Through the moment generating function we obtain the discrete and then the continuum distribution of g. There is an excellent agreement between our formalism and simulated data. At the end we compare our formalism to actual data, to specify the presence of non-random fluctuations.

Keywords: Gödel numbering; Nucleotide sequences; Information theory; Language theory; Language representation of biological sequences (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437122001121
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:594:y:2022:i:c:s0378437122001121

DOI: 10.1016/j.physa.2022.127053

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().