Natasa Misic

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...

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 incl...

The genetic code (GC) plays a central role in all living organisms. From a mathematical point of view, the GC is a map from a set of 64 elements (which are codons) onto a set of 21 elements (which are 20 amino acids and 1 stop signal). The GC is the result of evolution, experimentally deciphered as early as the mid-1960s, but its satisfactory theor...

The genetic code is a mapping from the set of 64 codons onto the set of 20 amino acids and one stop signal. The codons are ordered triplets composed of the nucleotides cytosine (C), adenine (A), uracil (U) (or thymine (T)), guanine (G) and they are contained in the genes. The amino acids are building blocks of the proteins. The vertebrate mitochond...

Ultrametric approach to the genetic code and the genome is considered and developed. $p$-Adic degeneracy of the genetic code is pointed out. Ultrametric tree of the codon space is presented. It is shown that codons and amino acids can be treated as $p$-adic ultrametric networks. Ultrametric modification of the Hamming distance is defined and noted...

This paper represents the preliminary results and conclusions on the one of fundamental questions of the genetic code related to the underlying selective mechanisms involved in its origin and evolution, in particular their hypothetical different nature, originally considered in [1,2,3]. A novel approach is introduced, based on known arithmetic regu...

Summation of a large class of the functional series, which terms contain factorials, is considered. We first investigated finite partial sums for integer arguments. These sums have the same values in real and all p-adic cases. The corresponding infinite functional series are divergent in the real case, but they are convergent and have p-adic invari...

We consider summation of some finite and infinite functional p-adic series with factorials. In particular, we are interested in the infinite series which are convergent for all primes p, and have the same integer value for an integer argument. In this paper, we present rather large class of such p-adic functional series with integer coefficients wh...

Numerous arithmetical regularities of nucleon numbers of canonical amino acids for quite different systematizations of the genetic code, which are dominantly based on decimal number 037, indicate the hidden existence of a more universal ordering principle. Mathematical analysis of number 037 reveals that it is a unique decimal number from which an...

The genetic code is analyzed as one of the major natural codes, which as such can reveal the deeper principles of optimal coding. The analysis is based on a discovery that the symmetrical architecture of genetic code and the nucleon number of its constituents - the free canonical amino acids and bases, are strictly determined by the prime number wi...

A completely new doublet-triplet system of amino acids in module 3/2 is given, determined with stereochemical specificity and polarity of amino acids presented either separately, or within four stereochemical types (alanine, valine, proline, and glycine types).

Science and technology related to Fullerene C60 and related compounds have attracted the attention and research stems from the Fullerenes' beautiful symmetry, dazzling chemical and physical technologies and nanotechnologies. Modern history of fivefold symmetry and the icosahedron began in 1985, when Kroto/Smally research team discovered the C60 mol...