In this paper we compute the multifractal analysis for local dimensions of Bernoulli measures supported on the self-affine carpets introduced by Bedford-McMullen. This extends the work of King where the multifractal analysis is computed with strong additional separation assumptions.

This paper provides an introduction to recent advances in the study of scale-invariance and related phenomena, namely the concept of infinitely divisible scaling which encompasses statistical self-similarity and multifractal scaling. Further the paper develops path properties and scaling of Poisson products of multiplicative and exponential shot-noise processes. Acknowledgement: Financial suppo...

In order to ensure continued availability of high-performance network for the nation's research and education community and to continue supporting the development of new high performance Internet capabilities, the National Science Foundation (NSF) established the very-high-speed Backbone Network Service (vBNS) through a cooperative agreement with MCI telecommunications Corporation. To ensure qu...

BACKGROUND Histologic image analysis plays an important role in cancer diagnosis. It describes the structure of the body tissues and abnormal structure gives the suspicion of the cancer or some other diseases. Observing the structural changes of these chaotic textures from the human eye is challenging process. However, the challenge can be defeat by forming mathematical descriptor to represent ...

We present a multiplicative multifractal process to model tra$c which exhibits long-range dependence. Using tra$c 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 also model the frame size sequences of VBR video tra$c process. We prove a number of properties of multiplicative multifrac...

We study the multifractal e ects of nonlinear transformations of monofractal, stationary time series and apply the found results to measure the true unbiased multifractality generated only by multiscaling properties of initial (primary) data before transformations. A di erence is stressed between naive observed multifractal e ects calculated directly within detrended multifractal analysis as th...

In recent decades multifractal analysis has been successfully applied to characterize the complex temporal and spatial organization of such diverse natural phenomena as heartbeat dynamics, the dendritic shape of neurons, retinal vessels, rock fractures, and intricately shaped volcanic ash particles. The characterization of multifractal properties of closed contours has remained elusive because ...

Multifractal analysis is considered a promising tool for image processing, notably for texture characterization. However, practical operational estimation procedures based on a theoretically well established multifractal analysis are still lacking for image (as opposed to signal) processing. In the present contribution, a wavelet Leader based multifractal analysis, known to be theoretically str...

A considerable portion of Canada’s landmass is covered by grassland ecosystems. Insight into the grassland spatial heterogeneity will not only contribute to better understanding of the scale dependent ecological processes but will also help in management and monitoring. Leaf area index (LAI) is a key structural attribute of grassland that reflects primary production. It is well-known that topog...