Physiological Cycles and Their Algebraic Models in Matrix Genetics

2010 ◽  
pp. 222-247
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Genetic Code ◽  
Hadamard Matrices ◽  
Algebraic Models ◽  
Natural Systems ◽  
Biological Time ◽  
Circular Permutations ◽  
Yin Yang ◽  
The Matrix ◽  
Cyclic Processes ◽  
Cyclic Changes

This chapter presents data about cyclic properties of the genetic code in its matrix forms of presentation. These cyclic properties concern cyclic changes of genetic Yin-Yang-matrices and their Yin-Yangalgebras (bipolar algebras) at many kinds of circular permutations of genetic elements in genetic matrices. These circular permutations lead to such reorganizations of the matrix form of presentation of the initial genetic Yin-Yang-algebra that arisen matrices serve as matrix forms of presentations of new Yin-Yang-algebras, as well. They are connected algorithmically with Hadamard matrices. New patterns and relations of symmetry are described. The discovered existence of a hierarchy of the cyclic changes of genetic Yin-Yang-algebras allows one to develop new algebraic models of cyclic processes in bioinformatics and in other related fields. These cycles of changes of the genetic 8-dimensional algebras and of their 8-dimensional numeric systems have many analogies with famous facts and doctrines of modern and ancient physiology, medicine, and so forth. This viewpoint proposes that the famous idea by Pythagoras (about organization of natural systems in accordance with harmony of numerical systems) should be combined with the idea of cyclic changes of Yin-Yang-numeric systems in considered cases. This second idea reminds of the ancient idea of cyclic changes in nature. From such algebraic-genetic viewpoint, the notion of biological time can be considered as a factor of coordinating these hierarchical ensembles of cyclic changes of the genetic multi-dimensional algebras.

The Evolution of the Genetic Code from the Viewpoint of the Genetic 8-Dimensional Yin-Yang-Algebra

2010 ◽  
pp. 168-192
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Genetic Code ◽  
Quantum Computer ◽  
Hadamard Matrices ◽  
Algebraic Model ◽  
Sexual Relationships ◽  
Algebraic Properties ◽  
Yin Yang ◽  
The Matrix ◽  
First Results ◽  
Biophysical Factor

The set of known dialects of the genetic code is analyzed from the viewpoint of the genetic 8-dimensional Yin-Yang-algebra. This algebra was described in Chapter 7. The octet Yin-Yang-algebra is considered as the model of the genetic code. From the viewpoint of this algebraic model, for example, the sets of 20 amino acids and of 64 triplets consist of sub-sets of “male,” “female,” and “androgynous” molecules, and so forth. This algebra allows one to reveal hidden peculiarities of the structure and evolution of the genetic code and to propose the conception of “sexual” relationships among genetic molecules. The first results of the analysis of the genetic code systems from such an algebraic viewpoint speak about the close connection between evolution of the genetic code and this algebra. They include 7 phenomenological rules of evolution of the dialects of the genetic code. The evolution of the genetic code appears as the struggle between male and female beginnings. The hypothesis about new biophysical factor of “sexual” interactions among genetic molecules is proposed. The matrix forms of presentation of elements of the genetic octet Yin-Yang-algebra are connected with Hadamard matrices by means of the simple U-algorithm. Hadamard matrices play a significant role in the theory of quantum computers, in particular. It leads to new opportunities for the possible understanding of genetic code systems as quantum computer systems. Revealed algebraic properties of the genetic code allow one to put forward the problem of algebraization of bioinformatics on the basis of the algebras of the genetic code. The described investigations are connected with the question: what is life from the viewpoint of algebra?

The Genetic Code, Hadamard Matrices, Noise Immunity, and Quantum Computers

2010 ◽  
pp. 115-131
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Genetic Code ◽  
Cyclic Codes ◽  
Hadamard Matrices ◽  
Matrix Form ◽  
Quantum Computers ◽  
Black And White ◽  
Discrete Signals ◽  
Mitochondrial Genetic Code ◽  
The Matrix ◽  
Genetic Alphabet

This chapter continues an analysis of the degeneracy of the vertebrate mitochondrial genetic code in the matrix form of its presentation, which possesses the symmetrical black-and-white mosaic. Taking into account a symmetry breakdown in molecular compositions of the four letters of the genetic alphabet, the connection of this matrix form of the genetic code with a Hadamard (8x8)-matrix is discovered. Hadamard matrices are one of the most famous and the most important kinds of matrices in the theory of discrete signals processing and in spectral analysis. The special U-algorithm of transformation of the symbolic genetic matrix [C A; U G](3) into the appropriate Hadamard matrix is demonstrated. This algorithm is based on the molecular parameters of the letters A, C, G, U/T of the genetic alphabet. In addition, the analogical relations is shown between Hadamard matrices and other symmetrical forms of genetic matrices, which are produced from the symmetrical genomatrix [C A; U G](3) by permutations of positions inside triplets. Many new questions arise due to the described fact of the connection of the genetic matrices with Hadamard matrices. Some of them are discussed here, including questions about an importance of amino-group NH2 in molecular-genetic systems, and about possible relations with the theory of quantum computers, where Hadamard gates are utilized. A new possible answer is proposed to the fundamental question concerning reasons for the existence of four letters in the genetic alphabet. Some thoughts about cyclic codes and a principle of molecular economy in genetic informatics are presented as well.

Recupero di energia dai rifiuti: dall'economia del danno all'economia del benessere

2009 ◽  
pp. 56-66
Author(s):  
Andrea Masullo
Keyword(s):  
Life Cycle ◽  
Life Cycle Analysis ◽  
External Environment ◽  
Natural Systems ◽  
Positive Effects ◽  
Cyclic Processes ◽  
Economical System ◽  
Far From Equilibrium ◽  
Economical Process ◽  
It Success

- The organization of an economical system is based on a flux of energy and materials that receive from the external environment. In nature evolution move systems to a growing efficiency in circulating energy and materials to let them producing positive effects implementing the internal organization, to create new opportunities to move far from equilibrium, to create differences. But while natural systems operate cyclic processes, economical systems are linear, and using concentrated resources as input and producing wastes that spread in the environment in a way that make them no more reusable, as much it success in growth as much it approximate its end. From an energy life cycle analysis of a material used in an economical process we can see that is much more efficient reuse goods and recycle materials than incinerate them. For instance we study the case of a PET bottle to deduce that reusing 20 times a 50g PET bottle can save 5 times more energy than electricity produced by burning 20 one-use 25g bottles in an incinerator.

Multidimensional Numbers and the Genomatrices of Hydrogen Bonds

2010 ◽  
pp. 193-206
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Hydrogen Bonds ◽  
Genetic Code ◽  
Structural Features ◽  
Hyperbolic Type ◽  
Complex Numbers ◽  
Hypercomplex Numbers ◽  
Molecular Systems ◽  
Natural Systems ◽  
Double Numbers ◽  
Mathematical Properties

This chapter returns to the kind of numeric genetic matrices, which were considered in Chapter 4-6. This kind of genomatrices is not connected with the degeneracy of the genetic code directly, but it is related to some other structural features of the genetic code systems. The connection of the Kronecker families of such genomatrices with special categories of hypercomplex numbers and with their algebras is demonstrated. Hypercomplex numbers of these two categories are named “matrions of a hyperbolic type” and “matrions of a circular type.” These hypercomplex numbers are a generalization of complex numbers and double numbers. Mathematical properties of these additional categories of algebras are presented. A possible meaning and possible applications of these hypercomplex numbers are discussed. The investigation of these hyperbolic numbers in their connection with the parameters of molecular systems of the genetic code can be considered as a continuation of the Pythagorean approach to understanding natural systems.

Symmetries of the Degeneracy of the Vertebrate Mitochondrial Genetic Code in the Matrix Form

2010 ◽  
pp. 31-49
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Mathematical Modeling ◽  
Genetic Code ◽  
Matrix Form ◽  
Black And White ◽  
Mitochondrial Genetic Code ◽  
The Matrix

Symmetries of the degeneracy of the vertebrate mitochondrial genetic code in the mosaic matrix form of its presentation are described in this chapter. The initial black-and-white genomatrix of this code is reformed into a new mosaic matrix when internal positions in all triplets are permuted simultaneously. It is revealed unexpectedly that for all six variants of positional permutations in triplets (1-2-3, 2-3-1, 3-1-2, 1-3-2, 2-1-3, 3-2-1) the appropriate genetic matrices possess symmetrical mosaics of the code degeneracy. Moreover the six appropriate mosaic matrices in their binary presentation have the general non-trivial property of their “tetra-reproduction,” which can be utilized in particular for mathematical modeling of the phenomenon of the tetra-division of gametal cells in meiosis. Mutual interchanges of the genetic letters A, C, G, U in the genomatrices lead to new mosaic genomatrices, which possess similar symmetrical and tetra-reproduction properties as well.

scholarly journals Construction of generalized rotations and quasi-orthogonal matrices

2019 ◽  
Vol 7 (1) ◽  
pp. 107-113
Author(s):  
Luis Verde-Star
Keyword(s):  
Image Processing ◽  
Hadamard Matrices ◽  
Complex Numbers ◽  
Data Communications ◽  
Matrix Representations ◽  
Orthogonal Matrices ◽  
Orthogonal Designs ◽  
The Matrix ◽  
The One

Abstract We propose some methods for the construction of large quasi-orthogonal matrices and generalized rotations that may be used in applications in data communications and image processing. We use certain combinations of constructions by blocks similar to the one used by Sylvester to build Hadamard matrices. The orthogonal designs related with the matrix representations of the complex numbers, the quaternions, and the octonions are used in our construction procedures.

scholarly journals Water: the bloodstream of the biosphere

2003 ◽  
Vol 358 (1440) ◽  
pp. 1921-1934 ◽  
Author(s):  
Wilhelm Ripl
Keyword(s):  
Essential Role ◽  
Phase Changes ◽  
The Self ◽  
System Efficiency ◽  
Ecological Efficiency ◽  
Natural Systems ◽  
Self Organized ◽  
Sustainable Landscapes ◽  
Cyclic Processes

Water, the bloodstream of the biosphere, determines the sustainability of living systems. The essential role of water is expanded in a conceptual model of energy dissipation, based on the water balance of whole landscapes. In this model, the underlying role of water phase changes--and their energy-dissipative properties--in the function and the self-organized development of natural systems is explicitly recognized. The energy-dissipating processes regulate the ecological dynamics within the Earth's biosphere, in such a way that the development of natural systems is never allowed to proceed in an undirected or random way. A fundamental characteristic of self-organized development in natural systems is the increasing role of cyclic processes while loss processes are correspondingly reduced. This gives a coincidental increase in system efficiency, which is the basis of growing stability and sustainability. Growing sustainability can be seen as an increase of ecological efficiency, which is applicable at all levels up to whole landscapes. Criteria for necessary changes in society and for the design of the measures that are necessary to restore sustainable landscapes and waters are derived.

ON AMINO ACID AND CODON ASSIGNMENT IN ALGEBRAIC MODELS FOR THE GENETIC CODE

2010 ◽  
Vol 24 (04) ◽  
pp. 435-463 ◽  
Author(s):  
FERNANDO ANTONELI ◽  
MICHAEL FORGER ◽  
PAOLA A. GAVIRIA ◽  
JOSÉ EDUARDO M. HORNOS
Keyword(s):  
Amino Acid ◽  
Genetic Code ◽  
Lie Groups ◽  
Lie Algebras ◽  
Finite Groups ◽  
Algebraic Approach ◽  
Lie Superalgebras ◽  
Algebraic Models ◽  
Symmetry Principles

We give a list of all possible schemes for performing amino acid and codon assignments in algebraic models for the genetic code, which are consistent with a few simple symmetry principles, in accordance with the spirit of the algebraic approach to the evolution of the genetic code proposed by Hornos and Hornos. Our results are complete in the sense of covering all the algebraic models that arise within this approach, whether based on Lie groups/Lie algebras, on Lie superalgebras or on finite groups.

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