In this paper we obtain multifractal generalizations of classical results by Lévy and Khintchin in metrical Diophantine approximations and measure theory of continued fractions. We give a complete multifractal analysis for Stern–Brocot intervals, for continued fractions and for certain Diophantine growth rates. In particular, we give detailed discussions of two multifractal spectra closely rela...

Incidence of infection time-series data for the childhood diseases measles, chicken pox, rubella and whooping cough are described in the language of multifractals. We explore the potential of using the wavelet transform maximum modulus (WTMM) method to characterize the multiscale structure of the observed time series and of simulated data generated by the stochastic susceptible-exposed-infectio...

We present a stochastic model of gait rhythm dynamics, based on transitions between di'erent “neural centers”, that reproduces distinctive statistical properties of normal human walking. By tuning one model parameter, the transition (hopping) range, the model can describe alterations in gait dynamics from childhood to adulthood—including a decrease in the correlation and volatility exponents wi...

In this paper, a systematic analysis of hourly wind speed data obtained from four potential wind generation sites in North Dakota is conducted. The power spectra of the data exhibited a power law decay characteristic of 1/fα processes with possible long range correlations. The temporal scaling properties of the records were studied using multifractal detrended fluctuation analysis MFDFA. It is ...

The dependence of the statistics of energy dissipation on the Reynolds number is investigated in an experimental jet flow. In a range of about one decade of Reλ (from about 200 to 2000) the adimensional mean energy dissipation is found to be independent on Reλ, while the higher moments of dissipation show a power-law dependence. The scaling exponents are found to be consistent with a simple pre...

We simulate advective transport in bond percolation clusters at the critical point. We compute the histogram of flow speeds in each bond of the backbone and find the multifractal spectrum for two-dimensional lattices with linear dimension L2000 and in three dimensions for L250 . We demonstrate that in the limit of large systems all the negative moments of the velocity distribution become ill-de...

In this paper, a new Multifractal Wavelet Model (MWM) is studied and simulation results are presented. We conclude that MWM has captured most of the properties of network traffic and the computational complexity of MWM is only O(N). The efficiency of MWM makes it possible in the real-time applications. 1.Introduction Network traffic modeling is one of the key topics in the application of networ...

We prove that the multifractal decomposition behaves as expected for a family of sets K known as digraph recursive fractals, using measures ^ of Markov type. For each value of a parameter a between a minimum amin and maximum amax, we define 'multifractal components' K^ a) of K, and show that they are fractals in the sense of Taylor. The dimension /(or) of K^ is computed from the data of the pro...

Walking is regulated through the motorcontrol system (MCS). The MCS consists of a network of neurons from the central nervous system (CNS) and the intraspinal nervous system (INS), which is capable of producing a syncopated output. The coupling of the latter two systems produces a complex stride interval time series that is characterized by fractal and multifractal properties that depend upon s...