The multifractal detrended fluctuation analysis of time series is able to reveal the presence of longrange correlations and, at the same time, to characterize the self-similarity of the series. The rich information derivable from the characteristic exponents and the multifractal spectrum can be further analyzed to discover important insights about the underlying dynamical process. In this paper...

Context. Cosmic voids are observed in the distribution of galaxies and, to some extent, in the dark matter distribution. If these distributions have fractal geometry, it must be reflected in the geometry of voids; in particular, we expect scaling sizes of voids. However, this scaling is not well demonstrated in galaxy surveys yet. Aims. Our objective is to understand the geometry of cosmic void...

We discuss a general concept of multifractality, and give a complete description of the multifractal spectra for Gibbs measures on two-dimensional horseshoes. We discuss a multifractal characterization of surface diffeomorphisms.

For hyperbolic diffeomorphisms, we describe the variational properties of the dimension spectrum of equilibrium measures on locally maximal hyperbolic sets, when the measure or the dynamical system are perturbed. We also obtain explicit expressions for the first derivative of the dimension spectra and the associated Legendre transforms. This allows us to establish a local version of multifracta...

In this paper we analyze a number of IP packet level very-high-speed Backbone Network Service (vBNS) tra c traces collected by the San Diego Supercomputer Center (SDSC) National Laboratory for Applied Network Research (NLANR) measurement and analysis group passive monitors at a number of highperformance connection (HPC) sites. Speci cally, we show that the vBNS tra c traces also have long-range...

A new expression for cell/packet loss probability in an ATM and packet switched queue system with a finite buffer is presented. Cell and packet loss analysis is based on the new concept of a “buffer overflow cluster” and the overflow probability for a queue with an infinite buffer. This approach holds for a wide variety of long-range dependent traffic sources typical of wide-area networks, as w...

We introduce a model for simulating mutation of prokaryote DNA sequences. Using that model we can then evaluated traditional techniques like parsimony and maximum likelihood methods for computing phylogenetic relationships. We also use the model to mimic large scale genomic changes, and use this to evaluate multifractal and related information theory techniques which take into account these lar...

Most results in multifractal analysis are obtained using either a thermodynamic approach based on existence and uniqueness of equilibrium states or a saturation approach based on some version of the specification property. A general framework incorporating the most important multifractal spectra was introduced by Barreira and Saussol, who used the thermodynamic approach to establish the multifr...

Fractal structures are found in biomedical time series from a wide range of physiological phenomena. The multifractal spectrum identifies the deviations in fractal structure within time periods with large and small fluctuations. The present tutorial is an introduction to multifractal detrended fluctuation analysis (MFDFA) that estimates the multifractal spectrum of biomedical time series. The t...

It is now clear that natural texture images can be discriminated by multifractal exponents. Most natural images, such as geographical images , are all textural in nature. In remote sensing images, different regions possess different texture and have different multifractal exponents. These properties are thus ideal for use in image segmentation. Like fractal dimensions, multifractal exponents ar...