Application Of Multifractal Analysis Research Articles

Application of Multifractal Analysis in Estimating the Reaction of Energy Markets to Geopolitical Acts and Threats

Since the industrial revolution, the geopolitics of energy has been a driver of global prosperity and security, and determines the survival of life on our planet. This study examines the nonlinear structure and multifractal behavior of the cross-correlation between geopolitical risk and energy markets (West Texas Intermediate (WTI), Brent, natural gas and heating oil), using the multifractal detrended cross-correlation analysis. Furthermore, an in-depth analysis reveals different associations of the indices of overall geopolitical risk, geopolitical acts, and geopolitical threats against the four energy products. Based on daily data ranging from 1 January 1985 to 30 August 2021, the findings confirm the presence of nonlinear dependencies, suggesting that geopolitical risk and energy markets are interlinked. Furthermore, significant multifractal characteristics are found and the degree of multifractality is stronger between the overall geopolitical risk and WTI while the lowest degree of multifractality is with Brent. Overall, for the WTI and heating-oil markets, the influence of geopolitical threats is more pronounced rather than their fulfilment. Contrarily, the Brent and natural gas are more correlated to geopolitical acts. Energy products exhibit heterogeneous persistence levels of cross-correlation with all the indicators of geopolitical risk, being more persistent in the case of small fluctuations compared to large fluctuations.

Application of Multifractal Analysis for Research of Structural Materials

Application of multifractal analysis for qualitative and quantitative description of structural materials is demonstrated. This makes it possible to evaluate the system’s characteristics of structures and to characterize the processes of self-organization in the materials. Formation of friction surface structures for aluminum alloys with Al2O3 and SiC additives in the scuffing mode is considered under comparable thermodynamic conditions. The addition of SiC, in comparison with Al2O3 , is less conducive to fragmentation and increase in the frequency of seizure and rupture processes. The addition of graphite into a composite material reinforced with SiC leads to increase in the degree of non-equilibrium of the thermodynamic conditions for the formation of the structures. Additional introduction of graphite further enhances the difference between materials with additions of Al2O3 and SiC, and this leads to the formation of the least ordered structures of the friction surface.

Application of multifractal analysis to the study of SAR features and oil spills on the ocean surface

Abstract. The use of synthetic aperture radar (SAR) to investigate the ocean surface provides a wealth of useful information that is very seldom used to its full potential. Here we will discuss the application of multifractal techniques to detect oil spills and the dynamic state of the sea regarding turbulent diffusion. We present different techniques in order to relate the shape of the multifractal spectral functions and the maximum fractal dimension to the behaviour of the ocean surface. We compare eddy and sheared dominated flows with convective driven flows and discuss the different features and observation methods. We also compare the scaling of different oil spills detected by means of SAR images. Recent spills and weathered ones are selected and compared to investigate their behaviour in different spatial and temporal ranges. We calculate the partition function based on the grey intensity value of each SAR pixel deriving several types of multifractal spectra as a function of spill residence time estimated for each image. Image manipulations are seen to reduce the speckle noise and thus distinguish much better the texture of the oil spill images. The results are used to discuss how eddy diffusivity may be estimated and used in a description of the ocean surface using a simple turbulence kinematic simulation model to predict the shape of oil spills. Differences in the multifractal spectrum among SAR images may detect the slicks due to plankton and also provide information on the age of the oil spills, on the Lagrangian turbulent structure and on ocean surface diffusivity.

Multifractal Analysis for Nutritional Assessment

The concept of multifractality is currently used to describe self-similar and complex scaling properties observed in numerous biological signals. Fractals are geometric objects or dynamic variations which exhibit some degree of similarity (irregularity) to the original object in a wide range of scales. This approach determines irregularity of biologic signal as an indicator of adaptability, the capability to respond to unpredictable stress, and health. In the present work, we propose the application of multifractal analysis of wavelet-transformed proton nuclear magnetic resonance (1H NMR) spectra of plasma to determine nutritional insufficiency. For validation of this method on 1H NMR signal of human plasma, standard deviation from classical statistical approach and Hurst exponent (H), left slope and partition function from multifractal analysis were extracted from 1H NMR spectra to test whether multifractal indices could discriminate healthy subjects from unhealthy, intensive care unit patients. After validation, the multifractal approach was applied to spectra of plasma from a modified crossover study of sulfur amino acid insufficiency and tested for associations with blood lipids. The results showed that standard deviation and H, but not left slope, were significantly different for sulfur amino acid sufficiency and insufficiency. Quadratic discriminant analysis of H, left slope and the partition function showed 78% overall classification accuracy according to sulfur amino acid status. Triglycerides and apolipoprotein C3 were significantly correlated with a multifractal model containing H, left slope, and standard deviation, and cholesterol and high-sensitivity C-reactive protein were significantly correlated to H. In conclusion, multifractal analysis of 1H NMR spectra provides a new approach to characterize nutritional status.

Application of multifractal analysis on microscopic images in the classification of metastatic bone disease

The paper considers the method, based on multifractal (MF) analysis, for classifying the shape of tissue cells from microscopis images, identifying the primary cancer in cases of metastasis bone disease. Diagnosis of primary cancer is of great importance, because further treatment depends on how successful and accurate that diagnosis is. This method can be applied as an additional and objective tool in primary cancer diagnosis, as well as in decreasing of the subjective factor and error probability. The method is tested over a large number (1050) of clinical cases from the Institute of Pathology, University of Belgrade. The results of computer-aided analysis of images have been presented and discussed.

Applying Multifractal Analysis to Remotely Sensed Data for Assessing PYVV Infection in Potato (Solanum tuberosum L.) Crops

Multispectral reflectance imagery and spectroradiometry can be used to detect stresses affecting crops. Previously, we have shown that changes in spectral reflectance and vegetation indices detected viral infection 14 days before visual symptoms were noticed by the trained eye. Herein we present evidence that shows that the application of multifractal analysis and wavelet transform to spectroradiometrical data improves the diagnostic power of the remote sensing-based methodology proposed in our previous work. The diagnosis of viral infection was effectively enhanced, providing the earliest detection ever reported, as anomalies were detected 29 and 33 days before appearance of visual symptoms in two experiments.

Correlation of mosaic-structurepeculiarities with electric characteristics and surfacemultifractal parameters for GaN epitaxial layers

The first successful results of the application ofmultifractal analysis to a quantitative description ofmosaic-structure peculiarities, that are typical of aGaN epitaxial layer with hexagonal modification grown on (0001)sapphire substrates, have been obtained. The characteristic sizeof the mosaic structure has been measured to be 200-800 nm. Thedirect dependence of mobility on the multifractal parameters(the Renyi dimension or the self-organization degree and theorder-degree index) of the surface topology of the mosaicstructure has been observed for all GaN layers investigated.

Multifractal analysis: Pitfalls of standard procedures and alternatives.

When applied to measures that are not multifractal at all, standard methods of multifractal analysis (MFA) may produce results that make the measures appear multifractal. This is because such methods, which are based on the scaling properties of moments of the measure of interest, tend to produce envelopes of the actual spectrum that look like the {\ensuremath{\alpha},f(\ensuremath{\alpha})} spectra of legitimate multifractal measures. We show examples and consequences of this property through the application of MFA to analytic functions, for which the actual spectrum can be easily evaluated, and to measures obtained from empirical data. It is shown specifically that application of MFA to the ``width function'' of river basins has led in the past to erroneous conclusions. We develop tools to distinguish between legitimate and spurious multifractal spectra, in part by using existing MFA procedures in unusual ways and in part by modifying such procedures. Finally, we discuss the extension of MFA to properties other than the scaling of local integrals. We illustrate this possibility by considering increments and integrals of increments of a function. We find that width functions are to a first approximation monofractal relative to differences, with an \ensuremath{\alpha} of about 0.3. This means that at small scales, such functions behave like fractional Brownian motion with a fractal dimension of about 1.7. This is in essential agreement with previous findings. Numerical issues in the application of MFA algorithms are briefly discussed.