Soil complexity and environmental heterogeneity may be viewed as a consequence of deterministic chaotic dynamics and therefore highly irregular patterns with so-called multifractal behavior should be common. This approach introduces a distinct viewpoint as compared with fractal models for soil surface roughness based on fractional Brownian motion. It suggests that it would be useful to move awa...

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...

Segmentation plays a vital role in determining the tumor in brain MR Images. The analysis is done using multifractional Brownian motion (mBm) to devise the tumor in brain MR images. The spatially varying feature is extracted using mBm and corresponding algorithm. Then segmentation is carried out based on multifractal features. An algorithm for segmentation is proposed by modifying the well-know...

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...

In this paper, we describe a new multiscale model for characterizing positive-valued and long-range dependent data. The model uses the Haar wavelet transform and puts a constraint on the wavelet coefficients to guarantee positivity, which results in a swift O(N) algorithm to synthesize N -point data sets. We elucidate our model’s ability to capture the covariance structure of real data, study i...

We present a multiplicative multifrac-tal process to model long-range dependent traac. Using traac trace data captured by Bellcore from operations across local and wide area networks, we examine the interarrival time series and the packet length sequences. We show the multiplicative process to effectively characterize the stochastic behavior exhibited by these processes. Furthermore we consider...

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...

Long-range dependence (LRD) or second-order self-similarity has been found to be an ubiquitous feature of internet traffic. In addition, several traffic data sets have been shown to possess multifractal behavior. In this paper, we present an algorithm to generate traffic traces that match the LRD and multifractal properties of the parent trace. Our algorithm is based on the decorrelating proper...

We test for the presence of multifractality in the daily returns of the three most important stock market indices from Central and Eastern Europe, Czech PX, Hungarian BUX and Polish WIG using the Empirical Mode Decomposition based Multifractal Detrended Fluctuation Analysis. We found that the global Hurst coefficient varies with the q coefficient and that there is multifractality evidenced thro...