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 N. N Kozlov Journal of Computer and Communications (JCC) , 2018, DOI: 10.4236/jcc.2018.67007 Abstract: The disclosure of many secrets of the genetic code was facilitated by the fact that it was carried out on the basis of mathematical analysis of experimental data: the diversity of genes, their structures and genetic codes. New properties of the genetic code are presented and its most important integral characteristics are established. Two groups of such characteristics were distinguished. The first group refers to the integral characteristics for the areas of DNA, where genes are broken down in pairs and all 5 cases of overlap, allowed by the structure of DNA, were investigated. The second group of characteristics refers to the most extended areas of DNA in which there is no genetic overlap. The interrelation of the established integral characteristics in these groups is shown. As a result, a number of previously unknown effects were discovered. It was possible to establish two functions in which all the over-understood codons in mitochondrial genetic codes (human and other organizations) participate, as well as a significant difference in the integral characteristics of such codes compared to the standard code. Other properties of the structure of the genetic code following from the obtained results are also established. The obtained results allowed us to set and solve one of the new breakthrough problems—the calculation of the genetic code. The full version of the solution to this problem was published in this journal in August 2017.
 Computer Science , 2012, Abstract: In Search Based Software Engineering, Genetic Programming has been used for bug fixing, performance improvement and parallelisation of programs through the modification of source code. Where an evolutionary computation algorithm, such as Genetic Programming, is to be applied to similar code manipulation tasks, the complexity and size of source code for real-world software poses a scalability problem. To address this, we intend to inspect how the Software Engineering concepts of modularity, granularity and localisation of change can be reformulated as additional mechanisms within a Genetic Programming algorithm.
 Quantitative Biology , 2009, Abstract: We propose a physical model to describe the mechanisms of two major scenarios of the genetic code evolution, the codon capture and ambiguous intermediate scenarios, in a consistent manner. We sketch the lowest dimensional version of our model, a minimal model, by introducing a physical quantity, codon level. On the basis of the hierarchical structure of the codon levels two scenarios are classified into two different routes of the evolutional process. In the case of the ambiguous intermediate scenario we perform a simulation implemented cost selection of amino acids and confirm a rapid transition of the code change. Such rapidness reduces uncomfortableness of the non-unique translation of the code at intermediate state that is the weakness of the scenario.
 O. Babatunde Okunoye Computer Science , 2009, Abstract: We Propose 22 unique Solutions to the Genetic Code. An Alternative Cracking, from the Perspective of a Mathematician.
 Branko Dragovich Quantitative Biology , 2009, Abstract: Living organisms are the most complex, interesting and significant objects regarding all substructures of the universe. Life science is regarded as a science of the 21st century and one can expect great new discoveries in the near futures. This article contains an introductory brief review of genetic information, its coding and translation of genes to proteins through the genetic code. Some theoretical approaches to the modelling of the genetic code are presented. In particular, connection of the genetic code with number theory is considered and the role of $p$-adic numbers is underlined.
 Quantitative Biology , 2007, DOI: 10.1016/j.physa.2007.03.018 Abstract: 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 genetic code will be a locally constant map of the simple form. The local constancy of this map will describe degeneracy of the genetic code. The map of the genetic code defines 2-adic ultrametric on the space of amino acids. We show that hydrophobic amino acids will be clustered in two balls with respect to this ultrametric. Therefore the introduced parametrization of space of codons exhibits the hidden regularity of the genetic code.
 Physics , 2006, DOI: 10.1073/pnas.0603780103 Abstract: A dynamical theory for the evolution of the genetic code is presented, which accounts for its universality and optimality. The central concept is that a variety of collective, but non-Darwinian, mechanisms likely to be present in early communal life generically lead to refinement and selection of innovation-sharing protocols, such as the genetic code. Our proposal is illustrated using a simplified computer model, and placed within the context of a sequence of transitions that early life may have made, prior to the emergence of vertical descent.
 Quantitative Biology , 2015, Abstract: A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick on the origin and evolution of the code as well as with the chronological order of appearence of the amino acids along the evolution as inferred from work that mixtures known experimental results with theoretical speculations. Suggested by the diagram we propose a Hamilton quaternions based mathematical representation of the code as it stands now-a-days. The central object in the description is a codon function that assigns to each amino acid an integer quaternion in such a way that the observed code degeneration is preserved. We emphasize the advantages of a quaternionic representation of amino acids taking as an example the folding of proteins. With this aim we propose an algorithm to go from the quaternions sequence to the protein three dimensional structure which can be compared with the corresponding experimental one stored at the Protein Data Bank. In our criterion the mathematical representation of the genetic code in terms of quaternions merits to be taken into account because it describes not only most of the known properties of the genetic code but also opens new perspectives that are mainly derived from the close relationship between quaternions and rotations.
 Quantitative Biology , 2002, Abstract: A representation of the genetic code as a six-dimensional Boolean hypercube is proposed. It is assumed here that this structure is the result of the hierarchical order of the interaction energies of the bases in codon-anticodon recognition. The proposed structure demonstrates that in the genetic code there is a balance between conservatism and innovation. Comparing aligned positions in homologous protein sequences two different behaviors are found: a) There are sites in which the different amino acids present may be explained by one or two "attractor nodes" (coding for the dominating amino acid(s)) and their one-bit neighbors in the codon hypercube, and b) There are sites in which the amino acids present correspond to codons located in closed paths in the hypercube. The structure of the code facilitates evolution: the variation found at the variable positions of proteins do not corresponds to random jumps at the codon level, but to well defined regions of the hypercube.
 Tidjani Negadi Quantitative Biology , 2009, Abstract: We present a completely new version of our arithmetic model of the standard genetic code and compute in a straightforward manner the exact numeric degeneracies of the five multiplets without any trick for the doublets and the sextets, as we have done previously. We give also some interesting applications.
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