Fractal processes, like trees or coastlines, are defined by self-similarity or power law scaling controlled by a single exponent, simply related to the fractal dimension or Hurst exponent (H) of the process. Multifractal processes, like turbulence, have more complex behaviours defined by a spectrum of possible local scaling behaviours or singularity exponents (h). Here, we report two experiment...

Myeloperoxidase (MPO), hemoprotein present in neutrophils and monocytes, has an essential role in immune surveillance and host defense mechanisms. Upon phagocyte activation in peripheral tissues and fluids, MPO is secreted into both the extracellular milieu and the phagolysosome where it uses hydrogen peroxide (H2O2) generated during a respiratory burst by activated NADPH as co-substrate. (Hurs...

Long-range dependent (LRD) self-similar chaotic behaviour has been found to be present in internet traffic by many researchers. The ‘Hurst exponent’, H, is used as a measure of the degree of long-range dependence. A variety of techniques exist for estimating the Hurst exponent; these deliver a variable efficacy of estimation. Whilst ways of exploiting these techniques for control and optimizati...

As it moves through an aquifer, a dissolved solute plume will evolve according to the complex heterogeneities that are present at many scales. Some statistical model must account for the aquifer structure. A fractional Brownian motion (fBm) model has been shown to create the long-range correlation that can produce continually faster-than-Fickian plume growth. Previous fBm models have assumed is...

We consider the problem of estimating the Hurst parameter for long-range dependent processes using wavelets. Wavelet techniques have shown to effectively exploit the asymptotic linear relationship that forms the basis of constructing an estimator. However, it has been noticed that the commonly adopted standard wavelet estimator is vulnerable to various non-stationary phenomena that increasingly...

Experimental measurements show that many relevant processes in telecommunication engineering exhibit self-similarity and long-range dependence (LRD) characteristics. Internet traffic is a significant example. A traditional parameter used to characterize self-similarity and LRD is the Hurst parameter H. Recently, the Modified Allan Variance (MAVAR) has been proposed to estimate the power-law spe...

The discrete-time fractional Gaussian noise (DFGN) has been proven to be a regular process. Therefore, an autoregressive (AR) model of an infinite order can describe DFGN based on Wold and Kolmogorov theorems. A fast estimation algorithm on the Hurst exponent of DFGN or discrete-time fractional Brownian motion (DFBM) has been proposed, but the algorithm did not consider the order selection of A...

Fractional Brownian motion is known to be a realistic model for many natural rough surfaces. It is defined by means of a single parameter, the Hurst exponent, which determines the fractal characteristics of the surface. We propose a method to estimate the Hurst exponent of a fractional Brownian profile from the electromagnetic scattering data. The method is developed in the framework of three u...

We study the possible link between “local turbulence strength” in a flow which is represented by a finite time series and a “chaotic invariant”, namely, the leading Lyaponuv exponent that characterizes this series. To validate a conjecture about this link, we analyze several time series of measurements taken by a plane flying at constant height in the upper troposphere. For each of these time s...

This paper describes some of the results in [5] for a stochastic calculus for a fractional Brownian motion with the Hurst parameter in the interval (1/2, 1). Two stochastic integrals are defined with explicit expressions for their first two moments. Multiple and iterated integrals of a fractional Browinian motion are defined and various properties of these integrals are given. A square integrab...