scholarly journals Local Fractal Dimensions and Multifractal Analysis of the Root System of Legumes

2000 ◽  
Vol 3 (3) ◽  
pp. 289-295 ◽  
Author(s):  
Kalyani Weerasinghe Ketipearachchi ◽  
Jiro Tatsumi
Keyword(s):  
Root System ◽  
Multifractal Analysis ◽  
Fractal Dimensions

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.

scholarly journals MULTIFRACTAL ANALYSIS OF MOUNT St. HELENS SEISMICITY AS A TOOL FOR IDENTIFYING ERUPTIVE ACTIVITY

Fractals ◽  
2006 ◽  
Vol 14 (03) ◽  
pp. 179-186 ◽  
Author(s):  
FILIPPO CARUSO ◽  
SERGIO VINCIGUERRA ◽  
VITO LATORA ◽  
ANDREA RAPISARDA ◽  
STEPHEN MALONE
Keyword(s):  
Time Distribution ◽  
Multifractal Analysis ◽  
Mechanical Response ◽  
Fractal Dimensions ◽  
Distribution Patterns ◽  
Fixed Number ◽  
Short Time Scale ◽  
Eruptive Activity ◽  
Seismic Swarms ◽  
Mount St Helens

We present a multifractal analysis of Mount St. Helens seismic activity during 1980–2002. The seismic time distribution is studied in relation to the eruptive activity, mainly marked by the 1980 major explosive eruptions and by the 1980–1986 dome building eruptions. The spectrum of the generalized fractal dimensions, i.e. Dq versus q, extracted from the data, allows us to identify two main earthquake time distribution patterns. The first one exhibits a multifractal clustering correlated to the intense seismic swarms of the dome building activity. The second one is characterized by an almost constant value of Dq ≈ 1, as for a random uniform distribution. The time evolution of Dq (for q = 0.2), calculated on a fixed number of events window and at different depths, shows that the brittle mechanical response of the shallow layers to rapid magma intrusions, during the eruptive periods, is revealed by sharp changes, acting at a short time scale (order of days), and by the lowest values of Dq (≈ 0.3). Conversely, for deeper earthquakes, characterized by intense seismic swarms, Dq do not show obvious changes during the whole analyzed period, suggesting that the earthquakes, related to the deep magma supply system, are characterized by a minor degree of clustering, which is independent of the eruptive activity.

FRACTAL BEHAVIOR OF NUCLEAR FRAGMENTS IN HIGH ENERGY INTERACTIONS

Fractals ◽  
2003 ◽  
Vol 11 (04) ◽  
pp. 331-343 ◽  
Author(s):  
DIPAK GHOSH ◽  
ARGHA DEB ◽  
MITALI MONDAL ◽  
SWARNAPRATIM BHATTACHARYYA ◽  
JAYITA GHOSH
Keyword(s):  
Specific Heat ◽  
Multifractal Analysis ◽  
Fractal Dimensions ◽  
High Energy ◽  
Factorial Moments

The multifractal analysis of data on nuclear fragments obtained from 28 Si-AgBr interactions at 14.5 A GeV is performed using three different methods (the factorial moments, G-moments and Takagi moments). The generalized fractal dimensions Dq is determined from all these methods. Data reflects multifractal geometry for the nuclear fragments. From the knowledge of Dq, the multifractal specific heat is calculated for this data and also for 16 O-AgBr interactions at 60 A GeV and 32 S-AgBr interactions at 200 A GeV.

scholarly journals Wavelet and multifractal analysis of the nonlinear structures in chaotic processes for hydroecological systems

2017 ◽  
pp. 171-175
Author(s):  
N.G. Serbov ◽  
O. Yu. Khetselius ◽  
A.A. Svinarenko ◽  
O.N. Grushevsky
Keyword(s):  
Time Series ◽  
Numerical Modelling ◽  
Multifractal Analysis ◽  
Theoretical Data ◽  
Fractal Dimensions ◽  
Nonlinear Structures ◽  
Dynamical Chaos ◽  
Fractal Structures ◽  
Linear Dynamical Systems ◽  
Multifractal Formalism

This paper goes on our investigations of the fractal structures in the chaotic and turbulent processes and connected with a great importance the experimental and theoretical studying of the non-linear dynamical systems with aim to discover the fractal features and elements of dynamical chaos. In this paper on the basis of wavelet analysis and multifractal formalism it is carried out an analysis of fractal structures in the chaotic processes (the time series of the nitrates concentrations in the Small Carpathians river’s watersheds Svidnik-Ondrava in the Earthen Slovakia) and the spectrum of the fractal dimensions has been computed. It is carried out numerical modelling and fulfilled a comparison of theoretical data with the earlier received estimates on the basis of other fractal formalism algorithm.

Pion production and multifractality in ultrarelativistic nuclear collision – evidence of constant specific heat

2005 ◽  
Vol 83 (11) ◽  
pp. 1169-1175 ◽  
Author(s):  
D Ghosh ◽  
A Deb ◽  
M B Lahiri ◽  
R Das
Keyword(s):  
Specific Heat ◽  
Multifractal Analysis ◽  
Pion Production ◽  
Collision Energy ◽  
Fractal Dimensions ◽  
Nuclear Collision ◽  
Multiparticle Production

Multifractal analysis of the pions produced in 32S–AgBr and 16O–AgBr interactions at 200 and 60 AGeV, respectively, is performed following the method proposed by Takagi. The generalized fractal dimensions Dq's are determined and found to decrease with order, thereby supporting multifractality in multiparticle production. From the knowledge of Dq, the multifractal specific heat is calculated for each interaction. It has been observed that the value of the specific heat is independent of the collision energy. PACS Nos.: 25.75–q, 24.60.Ky, 12.40.Ee

scholarly journals Fuzzy Generalized Fractal Dimensions Using Inter-Heartbeat Interval Dynamics in ECG Signals for Age Related Discrimination

2018 ◽  
Vol 7 (4.10) ◽  
pp. 900
Author(s):  
D. Easwaramoorthy ◽  
P. S. Eliahim Jeevaraj ◽  
A. Gowrisankar ◽  
A. Manimaran ◽  
S. Nandhini
Keyword(s):  
Multifractal Analysis ◽  
Fractal Theory ◽  
Age Groups ◽  
Fractal Dimensions ◽  
Elderly Subjects ◽  
Classification Rate ◽  
Ecg Signals ◽  
Age Related ◽  
Graphical Comparison ◽  
Chaotic Nature

Fractal theory is the propelled technique to analyze the non-linear signals with more complexity.  Quantification of chaotic nature and complexity of the multifaceted therapeutic signals requires the estimation of the spectrum of Generalized Fractal Dimensions (GFD) where the complexity means greater inconstancy in the general form of fractal dimension range.  This paper has proposed a fuzzy multifractal technique to analyze the age related classifications by using the Fuzzy Generalized Fractal Dimensions (F–GFD) with Gaussian fuzzy valued function through the cardiac inter-beat interval dynamics in electrocardiogram (ECG) signals.  It has been revealed that, the designed Fuzzy GFD method accurately categorizes the young and old age subjects by graphical comparison with the typical GFD method.  The classification rate of young and elderly subjects has also supported statistically by ANOVA test.   Hence the fuzzified multifractal analysis accomplishes significantly to discriminate age groups than the classical multifractal analysis in heartbeat rate time series from ECG signals and also the conventional GFD is a specific case of the proposed F–GFD.   

scholarly journals Bifractal nature of chromosome contact maps

2019 ◽  
Author(s):  
Simone Pigolotti ◽  
Mogens H. Jensen ◽  
Yinxiu Zhan ◽  
Guido Tiana
Keyword(s):  
Experimental Data ◽  
Stem Cells ◽  
Conformational Changes ◽  
Multifractal Analysis ◽  
Fractal Dimensions ◽  
Multifractal Spectrum ◽  
Quantitative Agreement ◽  
Scaling Exponent ◽  
Human Stem Cells ◽  
Contact Maps

Modern biological techniques such as Hi–C permit to measure probabilities that different chromosomal regions are close in space. These probabilities can be visualised as matrices called contact maps. In this paper, we introduce a multifractal analysis of chromosomal contact maps. Our analysis reveals that Hi–C maps are bifractal, i.e. complex geometrical objects characterized by two distinct fractal dimensions. To rationalize this observation, we introduce a model that describes chromosomes as a hierarchical set of nested domains and we solve it exactly. The predicted multifractal spectrum is in excellent quantitative agreement with experimental data. Moreover, we show that our theory yields to a more robust estimation of the scaling exponent of the contact probability than existing methods. By applying this method to experimental data, we detect subtle conformational changes among chromosomes during differentiation of human stem cells.

scholarly journals Multifractal analysis of electron images of fossil coal surface

2018 ◽  
Vol 56 ◽  
pp. 01020 ◽  
Author(s):  
Vasiliy Malinnikov ◽  
Valeriy Zakharov ◽  
Denis Uchaev ◽  
Dmitry Uchaev ◽  
Olga Malinnikova
Keyword(s):  
Surface Structure ◽  
Multifractal Analysis ◽  
Structural Organization ◽  
Quantitative Difference ◽  
Fractal Dimensions ◽  
Coal Surface ◽  
Coal Specimen ◽  
Fossil Coal ◽  
Multifractal Spectra ◽  
The Right

The multifractal spectra of electronic images of fossil coal surfaces obtained from outburst-hazardous zones, outburst-nonhazardous (quiet) zones and outburst zones are studied. It is shown that the structural organization of coal surface elements can be represented by a multifractal with a corresponding f (α) -spectrum of fractal dimensions, which is suitable to determine quantitative difference in microstructures of coal specimens from outburst-hazardous and outburst-nonhazardous beds. Coals from outburst-hazardous and outburst-nonhazardous beds differ in the direction of skewness of multifractal spectra characterizing their surface structure. If the f (α) -spectrum is skewed to the right, then the analyzed coal specimen belongs to an outburst-hazardous bed, and on the contrary, if f (α) is skewed to the left, then it can be concluded that the coal specimen most likely belongs to an outburst-nonhazardous bed.

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