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?

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 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.

scholarly journals Connectivity matrix model of quantum circuits and its application to distributed quantum circuit optimization

2021 ◽  
Vol 20 (7) ◽  
Author(s):  
Ismail Ghodsollahee ◽  
Zohreh Davarzani ◽  
Mariam Zomorodi ◽  
Paweł Pławiak ◽  
Monireh Houshmand ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Connectivity Matrix ◽  
Circuit Optimization ◽  
Novel Approach ◽  
The Matrix ◽  
Minimum Number ◽  
Two Phases

AbstractAs quantum computation grows, the number of qubits involved in a given quantum computer increases. But due to the physical limitations in the number of qubits of a single quantum device, the computation should be performed in a distributed system. In this paper, a new model of quantum computation based on the matrix representation of quantum circuits is proposed. Then, using this model, we propose a novel approach for reducing the number of teleportations in a distributed quantum circuit. The proposed method consists of two phases: the pre-processing phase and the optimization phase. In the pre-processing phase, it considers the bi-partitioning of quantum circuits by Non-Dominated Sorting Genetic Algorithm (NSGA-III) to minimize the number of global gates and to distribute the quantum circuit into two balanced parts with equal number of qubits and minimum number of global gates. In the optimization phase, two heuristics named Heuristic I and Heuristic II are proposed to optimize the number of teleportations according to the partitioning obtained from the pre-processing phase. Finally, the proposed approach is evaluated on many benchmark quantum circuits. The results of these evaluations show an average of 22.16% improvement in the teleportation cost of the proposed approach compared to the existing works in the literature.

scholarly journals Measurements on pointing error and field of view of Cimel-318 Sun photometers in the scope of AERONET-Europe

2013 ◽  
Vol 6 (2) ◽  
pp. 3013-3057
Author(s):  
B. Torres ◽  
C. Toledano ◽  
A. Berjón ◽  
D. Fuertes ◽  
V. Molina ◽  
...  
Keyword(s):  
Calibration Method ◽  
Field Of View ◽  
Pointing Error ◽  
Vicarious Calibration ◽  
Movement Correction ◽  
Measurement Protocol ◽  
The Matrix ◽  
First Results ◽  
Sensitivity Studies

Abstract. Sensitivity studies indicate that among the different error sources of ground-based sky radiometer observations, the pointing error has an important role in the correct retrieving of aerosol properties, being specially critical for the characterization of desert dust aerosol. The present work analyzes the first results of two new measurements, cross and matrix, specifically designed for an evaluation of the pointing error in the standard instrument of the Aerosol Robotic Network, the Cimel CE-318 sun-photometer. The first part of the analysis contains a preliminary study whose results conclude on the need of a sun movement correction for the correct evaluation of the pointing error from both new measurements. Once this correction is applied, both measurements show an equivalent behavior with differences under 0.01° in the evaluation of the pointing error. The second part of the analysis includes the incorporation of the cross scenario in the AERONET routine measurement protocol in order to monitor the pointing error in field instruments. Using the data collected for more than a year, the pointing error is evaluated on 7 sun-photometers belonging to AERONET-Europe. The pointing error values registered are generally smaller than 0.01° though in some instruments values up to 0.03° have been observed. Moreover, the pointing error evaluation has shown that this measure can be used to detect mechanical problems in the robots or dirtiness in the quadrant detector due to the stable behavior of the values against time and solar zenith angle. At the same time, the matrix scenario can be used to derive the value of the field of view. The methodology implemented and the characterization of five sun-photometers is presented in the last part of the study. To validate the method, a comparison with field of view values obtained from the vicarious calibration method was developed. The differences between both techniques are under 3%.

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 Computation of parton distributions from the quasi-PDF approach at the physical point

2018 ◽  
Vol 175 ◽  
pp. 14008 ◽  
Author(s):  
Constantia Alexandrou ◽  
Simone Bacchio ◽  
Krzysztof Cichy ◽  
Martha Constantinou ◽  
Kyriakos Hadjiyiannakou ◽  
...  
Keyword(s):  
Pion Mass ◽  
Distribution Functions ◽  
Matrix Elements ◽  
Parton Distribution Functions ◽  
Physical Point ◽  
Parton Distributions ◽  
The Matrix ◽  
First Results ◽  
Perturbative Renormalization ◽  
Vector Combination

We show the first results for parton distribution functions within the proton at the physical pion mass, employing the method of quasi-distributions. In particular, we present the matrix elements for the iso-vector combination of the unpolarized, helicity and transversity quasi-distributions, obtained with Nf = 2 twisted mass cloverimproved fermions and a proton boosted with momentum [see formula in PDF] = 0.83 GeV. The momentum smearing technique has been applied to improve the overlap with the proton boosted state. Moreover, we present the renormalized helicity matrix elements in the RI’ scheme, following the non-perturbative renormalization prescription recently developed by our group.

scholarly journals A Convenient Method to Obtain Stellar Eigenfrequencies

1983 ◽  
Vol 66 ◽  
pp. 331-341
Author(s):  
M. Knölker ◽  
M. Stix
Keyword(s):  
Eigenvalue Problem ◽  
Model Comparison ◽  
Symmetric Matrix ◽  
Outer Boundary ◽  
Solar Model ◽  
Pressure Perturbation ◽  
Stellar Oscillations ◽  
The Matrix ◽  
First Results ◽  
Algebraic Eigenvalue Problem

AbstractThe differential equations describing stellar oscillations are transformed into an algebraic eigenvalue problem. Frequencies of adiabatic oscillations are obtained as the eigenvalues of a banded real symmetric matrix. We employ the Cowling-approximation, i.e. neglect the Eulerian perturbation of the gravitational potential, and, in order to preserve selfadjointness, require that the Eulerian pressure perturbation vanishes at the outer boundary. For a solar model, comparison of first results with results obtained from a Henyey method shows that the matrix method is convenient, accurate, and fast.

A Trust Evaluation of Networks Utilizing Matrix Operations Based on t-norms and t-conorms

2012 ◽  
Vol 16 (1) ◽  
pp. 154-161
Author(s):  
Masaya Nohmi ◽  
◽  
Aoi Honda ◽  
Yoshiaki Okazaki
Keyword(s):  
Trust Evaluation ◽  
Matrix Operations ◽  
Fuzzy Graphs ◽  
Algebraic Properties ◽  
The Matrix ◽  
Membership Value

A new scheme for numerical trust evaluation of networks is proposed. Matrix operations based on t-norms and t-conorms are used for the evaluation. The algebraic properties of the matrix operations are studied. Fuzzy graphs, in which nodes are linked with some membership value, are proposed, using the matrices as adjacent matrices. Furthermore, the fuzzinesses of the trustability distribution are calculated.

Sign in / Sign up

Export Citation Format

Share Document