This paper introduces multifractal theory into the research of chaotic channels, and a novel model of chaotic channel is established from nonlinear science standpoint. By studying the relationship between multifractal dimensions and work environments, increments probability distribution, and statistical self-similarity of low power line communication (L-PLC) channel which is a typical chaotic c...

Analysis of the cardiovascular system (CVS) activity is important for several purposes, including better understanding of heart physiology, diagnosis and forecast of cardiac events. The central CVS, through the study of heart rate variability (HRV), has been shown to exhibit multifractal properties, possibly evolving with physiologic or pathologic states of the organism. An additional viewpoint...

This is an easy read introduction to multifractals We start with a thorough study of the Binomial measure from a multifractal point of view introducing the main multifractal tools We then continue by showing how to generate more general multiplicative measures and close by presenting an extensive set of examples on which we elaborate how to read a multifractal spectrum

Abstract. We present the results on the modelling and synthesis of broadband traffic processes namely ethernet inter-arrival times using the VVGM (variable variance gaussian multiplier) multiplicative multifractal model. This model is shown to be more appropriate for modelling network traffic which possess time varying scaling/self-similarity and burstiness. The model gives a simple and efficie...

The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at criticality. The multifractal analysis of local measures is extended to more general observables including scaling variables such as the conductance in the localizat...

Software development is difficult to model, particularly the noisy, non-stationary signals of changes per time unit, extracted from version control systems (VCSs). Currently researchers are utilizing timeseries analysis tools such as ARIMA to model these signals extracted from a project’s VCS. Unfortunately current approaches are not very amenable to the underlying power-law distributions of th...

Multifractal fluctuations in the time dynamics of geoelectrical data, recorded in a seismic area of southern Italy, have been revealed using the Multifractal Detrended Fluctuation Analysis (MF-DFA), which allows to detect multifractality in nonstationary signals. Our findings show that the geoelectrical time series, recorded in the seismic area of southern Apennine Chain (Italy), is multifracta...

We introduce the mathematical concept of multifractality and describe various multifractal spectra for dynamical systems, including spectra for dimensions and spectra for entropies. We support the study by providing some physical motivation and describing several nontrivial examples. Among them are subshifts of finite type and one-dimensional Markov maps. An essential part of the article is dev...

The crossing tree of a signal has been recently used to construct monofractal and multifractal processes. In this paper, we use the crossing tree of a signal for the purpose of analysis. Given a realisation of a signal, its crossing tree is calculated, whose characteristics are used to estimate the multifractal spectrum. More precisely, a partition function is evaluated at each resolution to su...

This paper investigates new properties concerning the multifractal structure of a class of statistically self-similar measures. These measures include the well-known Mandelbrot multiplicative cascades, sometimes called independent random cascades. We evaluate the scale at which the multifractal structure of these measures becomes discernible. The value of this scale is obtained through what we ...