I-Ching, dyadic groups of binary numbers and the geno-logic coding in living bodies

2018

Preprint

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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: -05 *(R80+r82)mentioning

confidence: 99%

The Genetic Coding System and Unitary Matrices

2018

Preprint

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“…One can note that our study belongs to the field of applications of algebraic methods and notions of quantum mechanics for modeling moleculargenetic structures where works of many authors exist, for example, the following [Dragovich, Dragovich, 2007;Dragovich, Khrennikov, Misic, 2017;Fimmel, Danielli, Strüngmann, 2013;Fimmel, Strüngmann, 2016;Igamberdiev, 1993;Ji, 2015Ji, , 2017Hu, Petoukhov, Petukhova, 2017;Matsuno, 1999Matsuno, , 2003Matsuno, , 2015Matsuno, Paton, 2000;Moon Ho Lee et al, 2017;Pellionis, 2008;Pellionisz et al, 2012;Penrose, 1996;Perez, 2010Perez, , 2013Perez, , 2017Petoukhov, 2008Petoukhov, , 2010aPetoukhov, ,b, 2011Petoukhov, , 2012Petoukhov, , 2015aPetoukhov, ,b,c,d,c, 2016Petoukhov, , 2017aPetoukhov, He, 2009;Petoukhov, Petukhova, 2017a,b;Petoukhov, Svirin, 2012;Rapoport, 2016a,b,c;Rumer, 1968;Simeonov, 2013;Stambuk, 1999].…”

Section: Connections Among Amino Acids and Triplets From The Standpoimentioning

confidence: 99%

The Genetic Coding System and Unitary Matrices

2018

Preprint

Self Cite

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.

“…Many structural features of genetic coding systems indicate the important role of dyadic groups of binary numbers [Petoukhov, 2008[Petoukhov, , 2016cHu Z.B., Petoukhov S.V., Petukhova E.S., 2017]. Binary numbers and their dyadic groups occupy a very important place in modern science and technology including computers, digital noise-immune communication, systems of artificial intelligence, etc.…”

Section: The Genetic Code Dyadic Groups and The Matrix Of Dyadic Shiftsmentioning

confidence: 99%

The Genetic Code, Algebraic Codes and Double Numbers

2019

Preprint

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The article shows materials to the question on algebraic features of the genetic code. Presented 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. Algebraic features of the genetic code are associated with hypercomplex double (or hyperbolic) numbers. The article also presents data on structural relations of some genetically inherited macrobiological phenomena with double numbers and with their algebraic extentions. 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 organization. This allows one to think that living organisms are algebraically encoded entities.