Related papers: p-Adic numbers in bioinformatics: from genetic cod…
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…
Using basic properties of p-adic numbers, we consider a simple new approach to describe main aspects of DNA sequence and genetic code. Central role in our investigation plays an ultrametric p-adic information space which basic elements are…
The genetic code is connection between 64 codons, which are building blocks of the genes, and 20 amino acids, which are building blocks of the proteins. In addition to coding amino acids, a few codons code stop signal, which is at the end…
We introduce the simple parametrization for the space of codons (triples of nucleotides) by 8\times 8 table. This table (which we call the dyadic plane) possesses the natural 2-adic ultrametric. We show that after this parametrization the…
The present paper is devoted to foundations of p-adic modelling in genomics. Considering nucleotides, codons, DNA and RNA sequences, amino acids, and proteins as information systems, we have formulated the corresponding p-adic formalisms…
We perform geometrization of genetics by representing genetic information by points of the 4-adic {\it information space.} By well known theorem of number theory this space can also be represented as the 2-adic space. The process of…
The conception of multi-alphabetical genetics is represented. Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have revealed algebraic properties of this system. These properties are connected with…
The structure of the genetic code is discussed in formal terms. A rectangular table of the code ("the code matrix"), whose properties reveal its arithmetical content tagged with the information symbols in several notations. New parameters…
Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have revealed algebraic properties of this system. Families of genetic (4*4)- and (8*8)-matrices show unexpected connections of the genetic system…
Degeneracy of the genetic code is a biological way to minimize effects of the undesirable mutation changes. Degeneration has a natural description on the 5-adic space of 64 codons $\mathcal{C}_5 (64) = \{n_0 + n_1 5 + n_2 5^2 : n_i = 1, 2,…
New analyses of the organization of the genetic code system together with their relation to the two classes of aminoacyl-tRNA synthetases are reported in this work. A closer inspection revealed how the enzymes and the 20 amino acids of the…
The p-adic formulation of replica symmetry breaking is presented. In this approach ultrametricity is a natural consequence of the basic properties of the p-adic numbers. Many properties can be simply derived in this approach and p-adic…
The systematics of indices of physico-chemical properties of codons and amino acids across the genetic code are examined. Using a simple numerical labelling scheme for nucleic acid bases, data can be fitted as low-order polynomials of the 6…
We present a new method to propagate $p$-adic precision in computations, which also applies to other ultrametric fields. We illustrate it with many examples and give a toy application to the stable computation of the SOMOS 4 sequence.
In biology, predicting RNA secondary structures plays a vital role in determining its physical and chemical properties. Although we have powerful energy models to predict them as well as parametric analysis to understand the models…
A computational framework utilizes the traditional similarity measures for mining the significant relationships in biological annotations is recently proposed by Tatiana V. Karpinets et al. [2]. In this paper, an improved approximation…
This paper introduces new tools for genomic signal processing, which can assist for genomic attribute extracting or describing biologically meaningful features embedded in a DNA. The codongrams and a2grams are offered as an alternative to…
Bit-level sparsity in neural network models harbors immense untapped potential. Eliminating redundant calculations of randomly distributed zero-bits significantly boosts computational efficiency. Yet, traditional digital SRAM-PIM…
The rank metric measures the distance between two matrices by the rank of their difference. Codes designed for the rank metric have attracted considerable attention in recent years, reinforced by network coding and further motivated by a…
Identifying similar protein sequences is a core step in many computational biology pipelines such as detection of homologous protein sequences, generation of similarity protein graphs for downstream analysis, functional annotation and gene…