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We investigate multifractal properties for an Abelian directed model of self-organized criticality that describes the growth of droplets inside a cloud and the subsequent rainfall. The probability distribution of events of the model satisfies finite-size scaling. We obtain the singularity spectra f(α) associated with temporal records for avalanche size and for the potential energy, defined by the total sum of the product between mass and height of each site. The measure defined by avalanche size has a clear cut multifractal character, while the obtained f(α) for potential energy may include a spurious branch.

Multifractal detrended cross-correlation analysis (MF-DXA) has been developed to detect the long-range power-law cross-correlation of two simultaneous series. However, the synchronization of underlying data can not be guaranteed integrated by a variety of factors. We artificially imbed a time delay in considered series and study its influence on the multifractal cross-correlation analysis. Time delay is found to affect the multifractal characterization, where a larger time delay causes a weaker multifractality. We also propose an alternative modification on MF-DXA to make the process more robust. The logarithmic return and volatility of Chinese stock indices show cross-correlation scaling behavior and strong multifractality by MF-DXA as well as singularity spectrum analysis.

This paper presents the basic scheme and the log-normal, log-gamma and log-negative-inverted-gamma scenarios to establish the Rényi function for infinite products of homogeneous isotropic random fields on Rⁿ; in particular for random fields on the sphere in R³. The motivation of this paper is the test of (non-)Gaussianity on the Cosmic Microwave Background Radiation (CMBR) in Cosmology. In the presentation, we need to employ spherical harmonics for some concrete computations.

Automatic voice pathology detection enables an objective assessment of pathologies that influence the voice production strategy. By utilizing the conventional pipeline model as well as the modern deep learning-centric end-to-end methodology, numerous pathological voice analyzing techniques have been developed. The conventional methodology is still a valid choice owing to the lack of enormous amounts of training data in the study region of pathological voice. In the meantime, obtaining higher precision, higher accuracy, and stability is still a complicated task. Therefore, by amalgamating the nonlinear measure, the pathological voices are analyzed to abate such risks. The viability of six nonlinear discriminating measures derived from the phase space realm, involving healthy and pathological voice signals, is studied in this work. The analyzed parameters are Singularity spectrum coefficients (${\alpha }_{min}$, ${\alpha }_{max},{\gamma }_1$ and ${\gamma }_2$). Correlation entropy at optimum embedding dimension ($K_{2m}$) and correlation dimension at optimum embedding dimension ($D_{2m}$). Analyzing the pathological voices with better accuracy rates is the major objective of the proposed methodology. Here, the Support Vector Machine (SVM) was utilized as the classifier. Experimentations were performed on VOiceICarfEDerico (VOICED) databases subsuming 208 healthy, as well as pathological voices, amongst these 50 samples, were utilized. Here, the model obtained 97% of accuracy with 99% as of the classifier with Gaussian kernel function. Therefore, to differentiate normal as well as pathological subjects, the six proposed characteristics are highly beneficial; in addition, they will be supportive in pathology diagnosis.

In this paper, multifractal analysis together with wavelet transform modulus maxima (WTMM) method is used to analyze the fluctuating signals of circulating fluidized bed (CFB). Singularity spectrum shows that the gas-particle flow in CFB has multifractal character. Motion behavior of the particle-fluid system of CFB can be described by singularity spectrum. Intermittency index can be used to determine the transition of flow regime from fast fluidization to pneumatic conveying.