We consider the self-similar phase space with reduced fractal dimension d being distributed within domain 0 < d < 1 with spectrum f(d). Related thermostatistics is shown to be governed by the Tsallis’ formalism of the non-extensive statistics, where role of the non-additivity parameter plays inverted value τ̄(q) ≡ 1/τ(q) > 1 of the multifractal function τ(q) = qd(q)− f(d(q)), being the specific ...

The properties of several multifractal formalisms based on wavelet coefficients are compared from both mathematical and numerical points of view. When it is based directly on wavelet coefficients, the multifractal formalism is shown to yield, at best, the increasing part of the weak scaling exponent spectrum. The formalism has to be based on new multiresolution quantities, the wavelet leaders, ...

Nonlinear phenomena in animal vocalizations fundamentally includes known features, namely, frequency jump, subharmonics, biphonation, and deterministic chaos. In the present study, the multifractal detrended fluctuation analysis (MFDFA) has been employed to characterize the phase couplings revealed in the feeding clicks of Hippocampus kuda yellow seahorse. The fluctuation function Fq(s), genera...

When common factors strongly influence two power-law cross-correlated time series recorded in complex natural or social systems, using detrended cross-correlation analysis (DCCA) without considering these common factors will bias the results. We use detrended partial cross-correlation analysis (DPXA) to uncover the intrinsic power-law cross correlations between two simultaneously recorded time ...

By applying the multifractal detrended fluctuation analysis to the high-frequency tick-bytick data from Deutsche Börse both in the price and in the time domains, we investigate multifractal properties of the time series of logarithmic price increments and inter-trade intervals of time. We show that both quantities reveal multiscaling and that this result holds across different stocks. The origi...

In this paper, we investigate the queueing behavior of multifractal traffic flows. Initially, we derive a global scaling parameter for multifractal processes. Next, we obtain a global scaling based expression for the effective bandwidth of multifractal flows. Relating this effective bandwidth estimate to the statistical network calculus, we propose performance bounds for high-speed networks. Ou...

In this paper, we propose an approach to estimate the byte loss probability in computer network links considering multifractal properties of traffic flows. More specifically, we obtain a mathematical expression for the loss probability for finite buffer servers fed by multifractal traffic flows. The proposed approach is based on the Many Sources theory and on the multiplicative cascade based mu...

The multifractal scaling exponents are calculated for the critical wave function of a two-dimensional Dirac fermion in the presence of a random magnetic field. It is shown that the problem of calculating the multifractal spectrum maps into the thermodynamics of a static particle in a random potential. The multifractal exponents are simply given in terms of thermodynamic functions, such as free ...

We analyze the multifractal spectra of daily foreign exchange rates for Japan, Hong-Kong, Korea, and Thailand with respect to the United States in the period from 1991 until 2005. We find that the return time series show multifractal spectrum features for all four cases. To observe the effect of the Asian currency crisis, we also estimate the multifractal spectra of limited series before and af...

Čerenkov images of air showers can also be classified using multifractal and wavelet parameters, as compared to the conventional Hillas image parameters. This new technique was applied to the images recorded by the cameras of the stereoscopic imaging air Čerenkov-telescopes operated by the HEGRA collaboration. With respect to the identification of particles, the performance of multifractal and ...