This paper proposes two local multifractal measures motivated by blanket method for calculation of fractal dimension. They cover both fractal approaches familiar in image processing. The first two measures (proposed Methods 1 and 3) support model of image with embedded dimension three, while the other supports model of image embedded in space of dimension three (proposed Method 2). While the cl...

High concentrations of ground-level ozone have a negative impact on human health and the environment, especially in urban places. Detailed knowledge on the effects of nitrogen dioxide on the ozone seasonal pattern is convenient to prevent these undesirable effects. Thus, the joint multifractal approach has been used to complete the information provided by descriptive statistics. The joint multi...

The intraday pattern, long memory, and multifractal nature of the intertrade durations, which are defined as the waiting times between two consecutive transactions, are investigated based upon the limit order book data and order flows of 23 liquid Chinese stocks listed on the Shenzhen Stock Exchange in 2003. An inverse U -shaped intraday pattern in the intertrade durations with an abrupt drop i...

Moments of the measure defined by products of random deviates are considered with the aim of reproducing the multifractal spectrum of the DiffusionLimited Aggregation (DLA) . appeared in: Journal of Technical Physics 37 (1996), pp.441-444 In 1981 Witten and Sander have proposed the Diffusion-Limited Aggregation (DLA) model [1] leading to the formation of fractal patterns. The growth process of ...

Power spectral density is an accepted measure of heart rate variability. Two estimators of multifractal properties: Wavelet Transform Modulus Maxima and Multifractal Detrended Fluctuation Analysis are used to investigate multifractal properties for the three strongly physiologically grounded components of power spectra: low frequency (LF), very low frequency (VLF) and ultra low frequency (ULV)....

Abstract. Recently it was discovered that the 3-fold convolution of the Cantor measure μ has intricate fractal structure [HL]: the set of local dimensions μ has an isolated point and therefore the standard multifractal formalism does not hold. Our purpose here is to give a detail study of such class of examples and to understand the dilemma. This will shed some light on the multifractal structu...

In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with such data. We show that because of strong correlations, the standard extreme value approach is not valid and classical tail exponent estimators should be int...

Using renormalization group methods we study multifractality in percolation at the instance of noisy random resistor networks. We introduce the concept of master operators. The multifractal moments of the current distribution (which are proportional to the noise cumulants C (l) R (x, x ′) of the resistance between two sites x and x′ located on the same cluster) are related to such master operat...

Two methods for enhancing the microcalcifications in digitized mammograms are under consideration. First method is based on multifractal approach, and second on modern mathematical morphology. In multifractal approach, from initial mammogram image, a corresponding multifractal “images” are created, from which a radiologist has a freedom to change the level of segmentation in an interactive mann...

This work is a contribution to the analysis of the procedure, based on wavelet coeecient partition functions, commonly used to estimate the Legendre multifractal spectrum. The procedure is applied to two examples, a fractional Brownian motion in multifractal time and a self-similar-stable process , whose sample paths exhibit irregularities that by eye appear very close. We observe that, for the...