The genetic code and its p-adic ultrametric modeling.

The genetic code plays a central role in all living organisms and its modeling is important for describing and understanding involved the coding rules. There are many approaches to modeling various aspects of the genetic code. One of the simple and successful mathematical tools for modeling the similarity both between codons and between amino acids, is the ultrametrics and especially the p-adic distance.

On Entropy of Probability Integral Transformed Time Series.

The goal of this paper is to investigate the changes of entropy estimates when the amplitude distribution of the time series is equalized using the probability integral transformation. The data we analyzed were with known properties-pseudo-random signals with known distributions, mutually coupled using statistical or deterministic methods that include generators of statistically dependent distributions, linear and non-linear transforms, and deterministic chaos. The signal pairs were coupled using a correlation coefficient ranging from zero to one.

p-Adic mathematics and theoretical biology.

The principal objective of this article is a brief overview of the main parts of p-adic mathematics, which have already had valuable applications and may have a significant impact in the near future on the further development of some fields of theoretical and mathematical biology. In particular, we present the basics of ultrametrics, p-adic numbers and p-adic analysis, as well as insight into their applications for modeling some cognitive processes, genetic code and protein dynamics. We also argue that ultrametric concepts and p-adic mathematics are natural tools for the viable description of biological systems and phenomena with a hierarchical structure.

p-Adic hierarchical properties of the genetic code.

In this article, we consider p-adic modeling of the standard genetic code and the vertebrate mitochondrial one. To this end, we use 5-adic and 2-adic distance as a mathematical tool to describe closeness (nearness, similarity) between codons as elements of a bioinformation space. Codons which are simultaneously at the smallest 5-adic and 2-adic distance code the same (or similar) amino acid or stop signal.