scholarly journals Wavelet-based multifractal analysis and fractal Signature of SARS-Cov-2 Coronavirus Variants genomes.

2021 ◽  
Author(s):  
Sid-Ali Ouadfeul
Keyword(s):  
Hurst Exponent ◽  
Multifractal Analysis ◽  
Fractal Dimensions ◽  
Dna Coding ◽  
Wavelet Transform Modulus Maxima ◽  
Range Correlation ◽  
Indicator Matrix ◽  
Correlated Characters ◽  
Modulus Maxima ◽  
Virus Genomes

Abstract In this paper, the SARS-CoV-2 coronavirus variants of concern and of interest genomes are analyzed using the wavelet transform modulus maxima lines (WTMM) method. The goal is to track the monofractal behavior of the virus genomes and to investigate the Long-Range-Correlation (LRC) character through the estimation of the Hurst exponent. The obtained results demonstrate the multifractal and the anti-correlated characters in the variants of concern for the Knucleotidic and GC DNA coding. The fractal signatures of SARS-CoV-2 coronavirus variants are investigated through the indicator matrix maps of the genomes, they exhibit the same patterns for the variants (Alpha, Delta) and (Eta, Lota, Kappa) with moving positions, while the variants Beta, Gamma and Epsilon have different indicator matrixes. The fractal dimensions of SARS-CoV-2 variants are oscillating aroundI, except the Epsilon variant from USA, where the fractal dimension is 1.70.

scholarly journals Multifractal Analysis of SARS-CoV-2 Coronavirus genomes using the wavelet transform

2020 ◽  
Author(s):  
Sid-Ali Ouadfeul
Keyword(s):  
Wavelet Transform ◽  
Hurst Exponent ◽  
Multifractal Analysis ◽  
Genome Structure ◽  
The Self ◽  
Self Organization ◽  
Dna Coding ◽  
Wavelet Transform Modulus Maxima ◽  
Range Correlation ◽  
Modulus Maxima

AbstractIn this paper, the 1D Wavelet Transform Modulus Maxima lines (WTMM) method is used to investigate the Long-Range Correlation (LRC) and to estimate the so-called Hurst exponent of 21 isolate RNA sequence downloaded from the NCBI database of patients infected by SARS-CoV-2, Coronavirus, the Knucleotidic, Purine, Pyramidine, Ameno, Keto and GC DNA coding are used. Obtained results show the LRC character in the most sequences; except some sequences where the anti-correlated or the Classical Brownian motion character is observed, demonstrating that the SARS-Cov2 coronavirus undergoes mutation from a country to another or in the same country, they reveals also the complexity and the heterogeneous genome structure organization far from the equilibrium and the self-organization.

Numerical Methods of Multifractal Analysis in Information Communication Systems and Networks

2013 ◽  
pp. 16-46
Author(s):  
Oleg I. Sheluhin ◽  
Artem V. Garmashev
Keyword(s):  
Communication Systems ◽  
Multifractal Analysis ◽  
Fractal Dimensions ◽  
Multifractal Spectrum ◽  
Telecommunication Networks ◽  
Information Communication ◽  
Novel Approach ◽  
Wavelet Transform Modulus Maxima ◽  
Modulus Maxima ◽  
Development Methods

In this chapter, the main principles of the theory of fractals and multifractals are stated. A singularity spectrum is introduced for the random telecommunication traffic, concepts of fractal dimensions and scaling functions, and methods used in their determination by means of Wavelet Transform Modulus Maxima (WTMM) are proposed. Algorithm development methods for estimating multifractal spectrum are presented. A method based on multifractal data analysis at network layer level by means of WTMM is proposed for the detection of traffic anomalies in computer and telecommunication networks. The chapter also introduces WTMM as the informative indicator to exploit the distinction of fractal dimensions on various parts of a given dataset. A novel approach based on the use of multifractal spectrum parameters is proposed for estimating queuing performance for the generalized multifractal traffic on the input of a buffering device. It is shown that the multifractal character of traffic has significant impact on queuing performance characteristics.

DETECTION OF ATMOSPHERIC TURBULENCE BY MULTIFRACTAL ANALYSIS USING WAVELETS

Fractals ◽  
2004 ◽  
Vol 12 (02) ◽  
pp. 211-221 ◽  
Author(s):  
M. NICOLLET ◽  
A. LEMARCHAND ◽  
N. CAVACIUTI
Keyword(s):  
Wavelet Transform ◽  
Atmospheric Turbulence ◽  
Multifractal Analysis ◽  
Function Method ◽  
Lower Stratosphere ◽  
Thin Layers ◽  
Scaling Exponents ◽  
Wavelet Transform Modulus Maxima ◽  
Modulus Maxima ◽  
Balloon Measurements

We study the singularities of a temperature profile obtained by means of balloon measurements in the troposphere and lower stratosphere. The data give the evolution of the temperature as the altitude of the probe increases. We compare the scaling exponents deduced from the Wavelet Transform Modulus Maxima (WTMM) method and the structure function method. In the lower stratosphere, the variations in the multifractal properties with the altitude deduced from wavelets allow us to detect thin layers of about 200 m depth exhibiting atmospheric turbulence.

scholarly journals DETERMINING LOCAL SINGULARITY STRENGTHS AND THEIR SPECTRA WITH THE WAVELET TRANSFORM

Fractals ◽  
2000 ◽  
Vol 08 (02) ◽  
pp. 163-179 ◽  
Author(s):  
ZBIGNIEW R. STRUZIK
Keyword(s):  
Wavelet Transform ◽  
Multifractal Analysis ◽  
Real Life ◽  
Life Time ◽  
Hölder Exponent ◽  
Multifractal Formalism ◽  
Wavelet Transform Modulus Maxima ◽  
Local Singularity ◽  
Modulus Maxima ◽  
Multiplicative Cascade

We present a robust method of estimating the effective strength of singularities (the effective Hölder exponent) locally at an arbitrary resolution. The method is motivated by the multiplicative cascade paradigm, and implemented on the hierarchy of singularities revealed with the wavelet transform modulus maxima (WTMM) tree. In addition, we illustrate the direct estimation of the scaling spectrum of the effective singularity strength, and we link it to the established partition function-based multifractal formalism. We motivate both the local and the global multifractal analysis by showing examples of computer-generated and real-life time series.

Study for Detection Algorithm of QRS Complex in ECG Signal

2013 ◽  
Vol 765-767 ◽  
pp. 2105-2108
Author(s):  
Xu Wen Li ◽  
Bi Wei Zhang ◽  
Qiang Wu
Keyword(s):  
Wavelet Transform ◽  
Detection Algorithm ◽  
Automatic Analysis ◽  
Detection Accuracy ◽  
Ecg Signal ◽  
Good Precision ◽  
Qrs Complex ◽  
Noise Interference ◽  
Wavelet Transform Modulus Maxima ◽  
Modulus Maxima

In ECG signals accurate detection to the position of QRS complex is a key to automatic analysis and diagnosis system. And its premise is that effectively remove all kinds of noise interference in ECG signal. Here, a method of detecting QRS based on EMD and wavelet transform was presented which is aim to improve the anti-noise performance of the detection algorithm. It is combined EMD with the theory of singularity detecting based on wavelet transform modulus maxima method. It has the high detection accuracy and good precision that can give an effective way to the automatic analysis for ECG signal.

Dynamical Variation of Weierstrass-Mandelbrot Function in Higher Dimensional Space

2013 ◽  
Vol 470 ◽  
pp. 767-771
Author(s):  
L. Zhang ◽  
Shu Tang Liu
Keyword(s):  
Hurst Exponent ◽  
Dimensional Space ◽  
Dynamical Behavior ◽  
Fractal Dimensions ◽  
Statistical Characteristics ◽  
3 Dimensional ◽  
Higher Dimensional ◽  
Complex Phenomena ◽  
Real Complex

Many real complex phenomena are related with Weierstrass-Mandelbrot function (WMF). Most researches focus on the systems as parameters fixed, such as calculations of its different fractal dimensions or the statistical characteristics of its generalized form and so on. Moreover, real systems always change according to different environments, so that to study the dynamical behavior of these systems as parameters change is important. However, there is few results about this aim. In this paper, we propose simulated results for the effects of parameters changeably on the graph of WMF in higher dimensional space. In addition, the relationships between the Hurst exponent of WMF and its parameters dynamically in 2-and 3-dimensional spaces are also given.

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