A Comparative Analysis of Associative Properties of Fourier versus Walsh Digital Holograms

2018

Preprint

Information molecules of DNA and RNA should obey principles of quantum mechanics where unitary operators in form of unitary matrices have key meanings. Unitary matrices are the basis of calculations in quantum computers. This article presents some author's results, which show that matrix forms of the representation of structured systems of molecular-genetic alphabets can be considered as sets of sparse unitary matrices related with phenomenologic features of the degeneracy of the genetic code. These sparse unitary matrices have orthogonal systems of functions in their rows and columns. A complementarity exists among some unitary genetic matrices in relation each other.  Decompositions of numeric genetic matrices into sets of sparse unitary matrices are connected with the logical operation of modulo-2 addition used in quantum computers as well. Tensor (or Kronecker)  families of unitary genetic matrices with their fractal-like properties are also considered. The described results are discussed in the frame of development of quantum-information approaches for modeling genetic systems.

Section: Introductionmentioning

confidence: 99%

The Genetic Coding System and Unitary Matrices

2018

Preprint

“…Hadamard operators are also widely used for spectral representations of signal vectors in the technique of noise-immune communication [Seberry, Wysocki, Wysocki, 2005], the sequency analysis of Harmuth [Harmuth, 1977[Harmuth, , 1989, the digital logical holography [Derzhypolskyy, Melenevskyy, Gnatovskyy, 2007;Morita, Sakurai, 1973;Soroko, 1974] and algorithms of quantum informatics [Nielsen, Chuang, 2010]. But the Hadamard matrices with their complete systems of orthogonal functions are not the only unitary matrices with complete systems of orthogonal functions in them.…”

Section: Introductionmentioning

confidence: 99%

The Genetic Coding System and Unitary Matrices

2018

Preprint

Abstract. Information molecules of DNA and RNA should obey principles of quantum mechanics where unitary operators in form of unitary matrices have key meanings. Unitary matrices are the basis of calculations in quantum computers. This article presents some author's results, which show that matrix forms of the representation of structured systems of molecular-genetic alphabets can be considered as sets of sparse unitary matrices related with phenomenologic features of the degeneracy of the genetic code. These sparse unitary matrices have orthogonal systems of functions in their rows and columns. A complementarity exists among some unitary genetic matrices in relation each other. Decompositions of numeric genetic matrices into sets of sparse unitary matrices are connected with the logical operation of modulo-2 addition used in quantum computers as well. Tensor (or Kronecker) families of unitary genetic matrices with their fractal-like properties are also considered. The described results are discussed in the frame of development of quantuminformation approaches for modeling genetic systems.

“…This algebra-logical Walsh-holography under the title «logical holography» was also considered later in [Derzhypolskyy, Melenevskyy, Gnatovskyy, 2007;Golubov, Efimov, Skvortsov, 1987]. All these and other works about logical Walsh-holography considered possibilities of its applications in engineering technologies of digital signals processing without any supposition of its application in biology, in particular, in genetics.…”

Section: Logical Holography By Walsh Functionsmentioning

confidence: 99%

Algebraic Rules for the Percentage Composition of Oligomers in Genomes

2021

Preprint

The article presents the author's results of studying hidden rules of structural organizations of long DNA sequences in eukaryotic and prokaryotic genomes. The results concern some rules of percentages (or probabilities) of n-plets in genomes. To reveal such rules, the author considers genomic DNA nucleotide sequences as multilayers sequences of n-plets and studies the percentage contents of n-plets in different layers. 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. These discovered rules are candidates for the role of universal genomic rules. A tensor family of matrix representations of interrelated DNA-alphabets of 4 nucleotides, 16 doublets, 64 triplets, and 256 tetraplets is used in the study. This matrix approach allows revealing algebraic properties of the mentioned genetic rules of probabilities, which are useful for developing algebraic and quantum biology. Some analogies of the discovered genetic phenomena with phenomena of Gestalt psychology are noted and discussed. The author connects the received results about the genomic percentages rules with a supposition of P. Jordan, who is one of the creators of quantum mechanics and quantum biology, that life's missing laws are the rules of chance and probability of the quantum world. Additional attention is paid to the algebraic features of the system of structured DNA alphabets and their relationship with the methods of algebraic holography, known in the technique of processing discrete signals. The concept of algebraic-holographic genetics is being developed for the understanding of inherited holographic properties of organisms.