Hyperbolic Numbers in Modeling Genetic Phenomena

Petoukhov, Sergey V.

doi:10.20944/preprints201908.0284.v1

Cited by 2 publications

(3 citation statements)

References 26 publications

(11 reference statements)

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“…The author's works are aimed at studying algebraic properties of the genetic coding system for revealing hidden information rules algebraically encoded in the molecular genetic system. This article is part of a set of long-term author's studies of the genetic system by the methods of matrix analysis and modeling combined under the general name “matrix genetics” ( Petoukhov, 2008 , 2011 , 2016 , 2017 , 2019b , c ; Petoukhov, He, 2010 ; Petoukhov, Petukhova, 2017a , b ).…”

Section: The Representation Of the Dna Alphabets By Their Binary-oppomentioning

confidence: 99%

“…Both of them reflect in different languages the oligomeric cooperative organization of genomes. This is useful to note because the author has published an effective mathematical model for the rules of collective probability, which is obviously applicable also to the above formulated hyperbolic rule № 1 ( Petoukhov, 2018b ; Petoukhov et al, 2019e , Petoukhov, 2020d , Petoukhov, 2020 , Petoukhov, 2019d , Petoukhov, 2019c , Petoukhov, 2019b , Petoukhov, 2019a ).…”

Section: The Quantum-information Model Of the Oligomer Cooperative Ormentioning

confidence: 99%

“…Let us turn to the above-mentioned author's model of properties of genomic sequences expressed by the expressions (11.2) and (11.3) ( Petoukhov, 2018b ; Petoukhov, 2019a , Petoukhov, 2019b , Petoukhov, 2019c , Petoukhov, 2019d , Petoukhov et al, 2019e ). This model is based on the tensor products and some other formalisms of quantum informatics and concerns, first of all, the hyperbolic rule №1 of the oligomer cooperative organization of genomes.…”

Section: The Quantum-information Model Of the Oligomer Cooperative Ormentioning

confidence: 99%

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Hyperbolic rules of the cooperative organization of eukaryotic and prokaryotic genomes

Petoukhov

2020

Biosystems

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The author's method of oligomer sums for analysis of oligomer compositions of eukaryotic and prokaryotic genomes is described. The use of this method revealed the existence of general rules for the cooperative oligomeric organization of a wide list of genomes. These rules are called hyperbolic because they are associated with hyperbolic sequences including the harmonic progression 1, 1/2, 1/3, .., 1/ n . These rules are demonstrated by examples of quantitative analysis of many genomes from the human genome to the genomes of archaea and bacteria. The hyperbolic (harmonic) rules, speaking about the existence of algebraic invariants in full genomic sequences, are considered as candidates for the role of universal rules for the cooperative organization of genomes. The results concerns additionally the problem of the origin of life. The described phenomenological results were obtained as consequences of the previously published author's quantum-information model of long DNA sequences. The oligomer sums method was also applied to the analysis of long genes and viruses including the COVID-19 virus; this revealed, in characteristics of many of them, the phenomenon of such rhythmically repeating deviations from model hyperbolic sequences, which are associated with DNA triplets. In addition, an application of the oligomer sums method is shown to the analysis of amino acid sequences in long proteins like the protein Titin. The topics of the algebraic harmony in living bodies and of the quantum-information approach in biology are discussed.

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Section: The Representation Of the Dna Alphabets By Their Binary-oppomentioning

confidence: 99%

Section: The Quantum-information Model Of the Oligomer Cooperative Ormentioning

confidence: 99%

Section: The Quantum-information Model Of the Oligomer Cooperative Ormentioning

confidence: 99%

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Hyperbolic rules of the cooperative organization of eukaryotic and prokaryotic genomes

Petoukhov

2020

Biosystems

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Inheritance is a Surjection: Description and Consequence

Ballonoff¹

2019

The 5th International Electronic Conference on Entropy and Its Applications

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Consider an evolutionary process. In genetic inheritance and in human cultural systems, each new offspring is assigned to be produced by a specific pair of the previous population. This form of mathematical arrangement is called a surjection. We have thus briefly described the mechanics of genetics-physical mechanics describes the possible forms of loci, and normal genetic statistics describe the results as viability of offspring in actual use. However, we have also described much of the mechanics of mathematical anthropology. Understanding that what we know as inheritance is the result of finding surjections and their consequences is useful in understanding, and perhaps predicting, biological-as well as human-evolution.

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Hyperbolic Numbers in Modeling Genetic Phenomena

Cited by 2 publications

References 26 publications

Hyperbolic rules of the cooperative organization of eukaryotic and prokaryotic genomes

Hyperbolic rules of the cooperative organization of eukaryotic and prokaryotic genomes

Inheritance is a Surjection: Description and Consequence

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