Genetic Code

2010 ◽  
pp. 1-30
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Genetic Code ◽  
Noise Immunity ◽  
Matrix Analysis ◽  
Matrix Methods ◽  
Genetic Coding ◽  
Discrete Signals ◽  
Genetic Structures

This chapter is devoted to symmetrical analysis for genetic code systems. The genetic coding possesses the noise-immunity. Mathematical theories of the noise-immunity coding and discrete signals processing are based on matrix methods of representation and analysis of information. These matrix methods, which are connected closely with relations of symmetry, are borrowed for a matrix analysis of ensembles of molecular elements of the genetic code. This chapter describes a uniform representation of ensembles of genetic multiplets in the form of matrices of a cumulative Kronecker family. The analysis of molecular peculiarities of the system of nitrogenous bases reveals the first significant relations of symmetry in these genetic matrices. It permits to introduce a natural numbering the multiplets in each of the genetic matrices and to give the basis for further analysis of genetic structures. The connection of the numerated genetic matrices with famous matrices of dyadic shifts is demonstrated.

Mathematical fundamentals for the noise immunity of the genetic code

Biosystems ◽  
2018 ◽  
Vol 164 ◽  
pp. 186-198 ◽  
Author(s):  
Elena Fimmel ◽  
Lutz Strüngmann
Keyword(s):  
Genetic Code ◽  
Noise Immunity

scholarly journals Theoretical approaches to the synthesis of discrete signals with necessary properties

Radiotekhnika ◽  
2021 ◽  
pp. 25-32
Author(s):  
I.D. Gorbenko ◽  
A.A. Zamula
Keyword(s):  
Information Security ◽  
Information Exchange ◽  
Communication Systems ◽  
Noise Immunity ◽  
Hadamard Matrix ◽  
General Characteristic ◽  
Software Complex ◽  
Theoretical Approaches ◽  
Discrete Signals ◽  
Information And Communication

Methods for information exchange, formation and processing of data used in information and communication systems (ICS), as well as classes of broadband signals used as a physical data carrier, do not provide the necessary (for individual ICS applications) indicators of cyber and information security, noise immunity of reception signals and secrecy of IKS functioning. Most of the existing systems use signals, the construction of which is based on linear laws, which allows an attacker, based on the establishment of the parameters of the signals used in the system, to carry out deliberate interference in the operation of the ICS with minimal energy consumption. The article presents conceptual approaches to the construction of secure ICS, which determine the need to cover the entire spectrum of information transformations in the complex, and based on the synthesis of signal systems with improved ensemble, correlation, structural properties. A method is proposed for synthesizing discrete derivatives of signals based on nonlinear discrete complex cryptographic signals (CS) and orthogonal signals formed on the basis of the rows of the Hadamard matrix (initial signals),. Based on computer modeling and the performed calculations, it is shown that the derivative signals formed on the basis of cryptographic sequences and rows of the Hadamard matrix have improved properties compared to orthogonal and linear classes of signals. Approaches to the construction are stated and a general characteristic of the hardware-software complex for synthesis, analysis, study of properties, generation, processing of a number of studied signal classes is given. It is shown that the use of such signals will improve such indicators of the system functioning as information security, noise immunity of signal reception and secrecy of functioning.

scholarly journals Comparative analysis of noise immunity of reception of nonlinear complex discrete signals with standard signals AFM-16 BPSK

Radiotekhnika ◽  
2020 ◽  
pp. 133-140
Author(s):  
S.G. Rassomakhin ◽  
A.A. Zamula ◽  
I.D. Gorbenko ◽  
Ho Tri Luc
Keyword(s):  
Comparative Analysis ◽  
Error Probability ◽  
Noise Immunity ◽  
Signal To Noise Ratio ◽  
Statistical Simulation ◽  
Gaussian Channel ◽  
Signal To Noise ◽  
Discrete Signals ◽  
Noise Ratio ◽  
Correlation Properties

The article shows that the solution to the problem of increasing the noise immunity (noise immunity and secrecy of functioning) of the ICS can be achieved using systems of nonlinear signals with improved ensemble, structural and correlation properties. Two classes of nonlinear complex discrete signals are considered: characteristic discrete signals (CDS) and cryptographic signals (CS). Methods for the synthesis of these signals are presented. The paper gives a statistical simulation model for studying the noise immunity of various classes of signals in the Gaussian channel. Using this model, estimates of the dependence of the error probability on the signal-to-noise ratio were obtained for various classes of signals, namely: CDS, KS and standard BPSK AFM-16 signals. It is shown that for the signal-to-noise ratio – 10 the error probability for the CDR is 4.6875e-06, for the CS is 3.515625e-06, and for the AFM-16 is 0.002025. Thus, the use of nonlinear complex discrete signals, in particular, CDS and KS, can significantly increase the noise immunity of signal reception in modern ICS. At the same time, taking into account the improved ensemble and structural properties of these nonlinear signals, it is possible to improve significantly the indicators of crypto- and imitation security of the systems functioning.

Noise immunity of the genetic code

Biosystems ◽  
1983 ◽  
Vol 16 (1) ◽  
pp. 9-29 ◽  
Author(s):  
Georges Cullmann ◽  
Jean-Michel Labouygues
Keyword(s):  
Genetic Code ◽  
Noise Immunity

scholarly journals Optimization for the quick-code methods for the synthesis of discrete signals – physical carriers of data in information-communication systems

2021 ◽  
pp. 126-130
Author(s):  
Alexander Zamula ◽  
Ivan Gorbenko
Keyword(s):  
Communication Systems ◽  
Noise Immunity ◽  
Random Processes ◽  
Signal Generation ◽  
Data Generation ◽  
Information Communication ◽  
Signal Systems ◽  
Discrete Signals ◽  
Discrete Programming ◽  
Theoretical Foundations

The paper presents the theoretical foundations of synthesis and analysis of complex nonlinear discrete cryptographic signals, the basis for the synthesis of which are random (pseudo-random) processes, including algorithms for cryptographic transformation of information, as well as methods for optimizing the synthesis of these signals using decimation and discrete programming. namely, the method of branches and boundaries. In order to improve the performance of signal generation and processing, estimates of the effectiveness of the decimation procedure are proposed and presented. It is shown that the use of the studied signal systems will improve the efficiency of modern ICS (speed of data generation and processing devices, noise immunity, information security, secrecy, protection against input (imposition) of false messages, message falsification, data integrity, etc.).

Genetic System, Fibonacci Numbers, and Phyllotaxis Laws

2010 ◽  
pp. 207-221
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Mathematical Biology ◽  
Genetic Code ◽  
Golden Section ◽  
Fibonacci Numbers ◽  
Biological Evolution ◽  
Genetic System ◽  
Huge Number ◽  
Matrix Methods ◽  
Long Time

This chapter describes data suggesting a connection between matrix genetics and one of the most famous branches of mathematical biology: phyllotaxis laws of morphogenesis. Thousands of scientific works are devoted to this morphogenetic phenomenon, which relates with Fibonacci numbers, the golden section, and beautiful symmetrical patterns. These typical patterns are realized by nature in a huge number of biological bodies on various branches and levels of biological evolution. Some matrix methods are known for a long time to simulate in mathematical forms these phyllotaxis phenomena. This chapter describes connections of the famous Fibonacci (2x2)-matrices with genetic matrices. Some generalizations of the Fibonacci matrices for cases of (2nx2n)-matrices are proposed. Special geometrical invariants, which are connected with the golden section and Fibonacci numbers and which characterize some proportions of human and animal bodies, are described. All these data are related to matrices of the genetic code in some aspects.

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 From chemical metabolism to life: the origin of the genetic coding process

2017 ◽  
Vol 13 ◽  
pp. 1119-1135 ◽  
Author(s):  
Antoine Danchin
Keyword(s):  
Carbon Dioxide ◽  
Amino Acids ◽  
Solar System ◽  
Genetic Code ◽  
Metabolic Pathways ◽  
Origins Of Life ◽  
Genetic Coding ◽  
Carbon Molecules ◽  
Carry Over

Looking for origins is so much rooted in ideology that most studies reflect opinions that fail to explore the first realistic scenarios. To be sure, trying to understand the origins of life should be based on what we know of current chemistry in the solar system and beyond. There, amino acids and very small compounds such as carbon dioxide, dihydrogen or dinitrogen and their immediate derivatives are ubiquitous. Surface-based chemical metabolism using these basic chemicals is the most likely beginning in which amino acids, coenzymes and phosphate-based small carbon molecules were built up. Nucleotides, and of course RNAs, must have come to being much later. As a consequence, the key question to account for life is to understand how chemical metabolism that began with amino acids progressively shaped into a coding process involving RNAs. Here I explore the role of building up complementarity rules as the first information-based process that allowed for the genetic code to emerge, after RNAs were substituted to surfaces to carry over the basic metabolic pathways that drive the pursuit of life.

scholarly journals The concept of synthesis of one class of self-synchronizing discrete signals

Radiotekhnika ◽  
2021 ◽  
pp. 24-29
Author(s):  
I.D. Gorbenko ◽  
O.V. Potii ◽  
A.A. Zamula
Keyword(s):  
Structural Properties ◽  
Correlation Functions ◽  
Performance Indicators ◽  
Communication Systems ◽  
Noise Immunity ◽  
Signal Systems ◽  
Discrete Signals ◽  
Information And Communication ◽  
Modern Information ◽  
Correlation Properties

The use of broadband signals (BSS) makes it possible to increase the noise immunity of information and communication systems (ICS) when exposed to structural (mutual) and organized interference. The real noise immunity will be lower than the potential one. The reason for the decrease in noise immunity, when entering synchronism and when distinguishing signals, is the presence of side peaks of the correlation functions. Proceeding from this, the NLS used in ICS should have such correlation properties when the side peaks of the NLS CF are as small as possible, i.e. ideally should tend to zero. In this case, it is necessary to determine the influence of side peaks on the characteristics of signal detection, measure their parameters, distinguish signals, and find the conditions for obtaining small side peaks. The problem of synthesizing a class of signals with given correlation, ensemble and structural properties, as well as properties of "blurring" in correlation characteristics, is formulated and solved in general form. The specified property ("fuzziness") means that increasing or decreasing the length of the discrete signal does not change the correlation properties of the discrete sequence on the basis of which the signal is synthesized. The use of many of these signal systems in modern information and communication systems will improve the performance indicators of such systems, first of all, noise immunity, secrecy, information security, noise immunity of signal reception.

Sign in / Sign up

Export Citation Format

Share Document