• Corpus ID: 180461

The genetic code, 8-dimensional hypercomplex numbers and dyadic shifts

@article{Petoukhov2011TheGC,
  title={The genetic code, 8-dimensional hypercomplex numbers and dyadic shifts},
  author={Sergey V. Petoukhov},
  journal={arXiv: Other Quantitative Biology},
  year={2011}
}
  • S. Petoukhov
  • Published 17 February 2011
  • Computer Science
  • arXiv: Other Quantitative Biology
The article is devoted to algebraic features of structural phenomena of molecular ensembles of the genetic code. Matrix forms of presentations of the genetic code allow showing deep relations of the genetic code with dyadic shifts and algebras of 8-dimensional hypercomplex numbers. Hadamard matrices and orthogonal systems of Rademacher and Walsh functions, which are well-known formalisms from discrete signal processing, participate in this discovery of hidden structural features of the genetic… 

Figures from this paper

Relations of the Genetic Code with Algebraic Codes and Hypercomplex Double Numbers
TLDR
The received results confirm that multidimensional numerical systems is effective for modeling and revealing the interconnections of structures of biological bodies at various levels of their organisation and allow one to think that living organisms are algebraically encoded entities.
The Genetic Code, Algebraic Codes and Double Numbers
TLDR
Results testify in favor that the genetic code is an algebraic code related with a wide class of algebraic codes, which are a basis of noise-immune coding of information in communication technologies.
Matrix Genetics and Algebraic Properties of the Multi-Level System of Genetic Alphabets
TLDR
Algebraic properties of the multi-level system of molecular-genetic alphabets, taking into account the important role of dyadic shifts, hypercomplex numbers and Hadamard matrices, testify that living matter has a profound algebraic essence which is interconnected with 8-dimensional vector spaces.
Dyadic groups, dyadic trees and symmetries in long nucleotide sequences
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
The term “ octet ” is also used frequently in phenomenologic laws of science : the Eightfold
The article is devoted to algebraic properties of the multi-level system of moleculargenetic alphabets. It leads to help solve the problem of algebraic unity of inherited information systems in
The genetic code, algebra of projection operators and problems of inherited biological ensembles
TLDR
This article is devoted to applications of projection operators to simulate phenomenological properties of the molecular-genetic code system and proposes and describes special systems of multidimensional numbers under names united-hypercomplex numbers.
Symmetries in Genetic Systems and the Concept of Geno-Logical Coding
TLDR
Basic pieces of evidence are described in favor of the existence of the geno-logical code, which exists in p­arallel with the known genetic code of amino acid sequences but which serves for transferring inherited processes along chains of generations.
The Matrix Method of Representation, Analysis and Classification of Long Genetic Sequences
TLDR
A matrix method of comparative analysis of long nucleotide sequences by means of presenting each sequence in the form of three digital binary sequences, which can be visually represented as an individual fractal-like mosaic or another regular mosaic of binary type.
Algebraic Rules for the Percentage Composition of Oligomers in Genomes
TLDR
Unexpected rules of invariance of total sums of percentages in certain tetra-groupings of n-plets in different layers of genomic DNA sequences are revealed and are candidates for the role of universal genomic rules.
Tensor Rules in the Stochastic Organization of Genomes and Genetic Stochastic Resonance in Algebraic Biology
TLDR
The tensor product of matrices and vectors is used as an effective analytical tool borrowed from the arsenal of quantum mechanics in this study of studying hidden rules and symmetries in structures of long single-stranded DNA sequences in eukaryotic and prokaryotic genomes.
...
...

References

SHOWING 1-10 OF 206 REFERENCES
SYMMETRIES, GENERALIZED NUMBERS AND HARMONIC LAWS IN MATRIX GENETICS
This paper is devoted to the presentation and analysis of matrix representations of the genetic code. Principal attention is paid to a family of the genetic matrices which are constructed on the
The degeneracy of the genetic code and Hadamard matrices
TLDR
A special decomposition of numeric genetic matrices reveals their close relations with a family of 8-dimensional hypercomplex numbers (not Cayley's octonions). Some hypothesis and thoughts are formulated on the basis of these phenomenological facts.
THE GENETIC CODE, HADAMARD MATRICES AND ALGEBRAIC BIOLOGY
Algebraic theory of coding is one of modern fields of applications of algebra. This theory uses matrix algebra intensively. This paper is devoted to an application of Kronecker's matrix forms of
Matrix genetics, part 2: the degeneracy of the genetic code and the octave algebra with two quasi-real units (the genetic octave Yin-Yang-algebra)
TLDR
The investigations of the genetic code on the basis of matrix approaches ("matrix genetics") and the results are related with the problem of algebraization of bioinformatics take attention to the question: what is life from the viewpoint of algebra.
Matrix genetics, part 2: the degeneracy of the genetic code and the octave algebra with two quasi-real units (the "Yin-Yang octave algebra")
Algebraic properties of the genetic code are analyzed. The investigations of the genetic code on the basis of matrix approaches ("matrix genetics") are described. The degeneracy of the vertebrate
Conversion of nucleotides sequences into genomic signals
  • P. Cristea
  • Biology
    Journal of cellular and molecular medicine
  • 2002
TLDR
An original tetrahedral representation of the Genetic Code that better describes its structure, degeneration and evolution trends is defined and it is shown that some essential features of the nucleotide sequences can be better extracted using this representation.
Generalized DNA matrices , Silver Means , and Pythagorean Triples
TLDR
A family of bisymmetric 2 n x 2 n matrices that code the structure of the four DNA bases, the 64 codons that make up the 20 amino acids in all living structures, and beyond that, the proteins assembled from the amino acids as building blocks are studied.
A Striking Property of Genetic Code-like Transformations
TLDR
This paper shows that genetic code-like transformations (GCTs) introduce very interesting properties to the representation of a genetic fitness function and points out that such transformations can convert some function representations of exponential description in Fourier basis to a description that is highly suitable for polynomial-complexity approximation.
HYPERCOMPLEX CROSS-CORRELATION OF DNA SEQUENCES
TLDR
A hypercomplex representation of DNA is proposed to facilitate comparing DNA sequences with fuzzy composition and a new scoring system has been proposed to accommodate the hypercomplex number representation and integrated with dynamic programming alignment method.
Commutative hypercomplex Fourier transforms of multidimensional signals
In Chap. 8 the approach of the Clifford Fourier transform (CFT) and of the quaternionic Fourier transform (QFT) have been introduced. We have shown that the CFT yields an extended and more efficient
...
...