3,552 research outputs found
Bootstrap for log Wavelet Leaders Cumulant based Multifractal Analysis.
Multifractal analysis, which mostly consists of estimating scaling exponents related to the power law behaviors of the moments of wavelet coefficients, is becoming a popular tool for empirical data analysis. However, little is known about the statistical performance of such procedures. Notably, despite their being of major practical importance, no confidence intervals are available. Here, we choose to replace wavelet coefficients with wavelet Leaders and to use a log-cumulant based multifractal analysis. We investigate the potential use of bootstrap to derive confidence intervals for wavelet Leaders log-cumulant multifractal estimation procedures. From numerical simulations involving well-known and well-controlled synthetic multifractal processes, we obtain two results of major importance for practical multifractal analysis : we demonstrate that the use of Leaders instead of wavelet coefficients brings significant improvements in log-cumulant based multifractal estimation, we show that accurate bootstrap designed confidence intervals can be obtained for a single finite length time series
Multifractal detrended fluctuation analysis of nonstationary time series
We develop a method for the multifractal characterization of nonstationary
time series, which is based on a generalization of the detrended fluctuation
analysis (DFA). We relate our multifractal DFA method to the standard partition
function-based multifractal formalism, and prove that both approaches are
equivalent for stationary signals with compact support. By analyzing several
examples we show that the new method can reliably determine the multifractal
scaling behavior of time series. By comparing the multifractal DFA results for
original series to those for shuffled series we can distinguish multifractality
due to long-range correlations from multifractality due to a broad probability
density function. We also compare our results with the wavelet transform
modulus maxima (WTMM) method, and show that the results are equivalent.Comment: 14 pages (RevTex) with 10 figures (eps
Application of multifractal wavelet analysis to spontaneous fermentation processes
An algorithm is presented here to get more detailed information, of mixed
culture type, based exclusively on the biomass concentration data for
fermentation processes. The analysis is performed with only the on-line
measurements of the redox potential being available. It is a two-step procedure
which includes an Artificial Neural Network (ANN) that relates the redox
potential to the biomass concentrations in the first step. Next, a multifractal
wavelet analysis is performed using the biomass estimates of the process. In
this context, our results show that the redox potential is a valuable indicator
of microorganism metabolic activity during the spontaneous fermentation. In
this paper, the detailed design of the multifractal wavelet analysis is
presented, as well as its direct experimental application at the laboratory
levelComment: 12 pages, 3 figures, Physica A, to appea
Numerical Methods of Multifractal Analysis in Information Communication Systems and Networks
In this chapter, the main principles of the theory of fractals and multifractals are stated. A singularity
spectrum is introduced for the random telecommunication traffic, concepts of fractal dimensions and
scaling functions, and methods used in their determination by means of Wavelet Transform Modulus
Maxima (WTMM) are proposed. Algorithm development methods for estimating multifractal spectrum
are presented. A method based on multifractal data analysis at network layer level by means of WTMM
is proposed for the detection of traffic anomalies in computer and telecommunication networks. The
chapter also introduces WTMM as the informative indicator to exploit the distinction of fractal dimen-
sions on various parts of a given dataset. A novel approach based on the use of multifractal spectrum
parameters is proposed for estimating queuing performance for the generalized multifractal traffic on
the input of a buffering device. It is shown that the multifractal character of traffic has significant impact
on queuing performance characteristics
Application of Fractal and Wavelets in Microcalcification Detection
Breast cancer has been recognized as one or the most frequent, malignant tumors in women, clustered microcalcifications in mammogram images has been widely recognized as an early sign of breast cancer. This work is devote to review the application of Fractal and Wavelets in microcalcifications detection
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