Automated Detection of Coronal Loops using a Wavelet Transform Modulus Maxima Method

We propose and test a wavelet transform modulus maxima method for the au- tomated detection and extraction of coronal loops in extreme ultraviolet images of the solar corona. This method decomposes an image into a number of size scales and tracks enhanced power along each ridge corresponding to a coronal loop at each scale. We compare the results across scales and suggest the optimum set of parameters to maximise completeness while minimising detection of noise. For a test coronal image, we compare the global statistics (e.g., number of loops at each length) to previous automated coronal-loop detection algorithms

A three-dimensional wavelet based multifractal method : about the need of revisiting the multifractal description of turbulence dissipation data

We generalize the wavelet transform modulus maxima (WTMM) method to multifractal analysis of 3D random fields. This method is calibrated on synthetic 3D monofractal fractional Brownian fields and on 3D multifractal singular cascade measures as well as their random function counterpart obtained by fractional integration. Then we apply the 3D WTMM method to the dissipation field issue from 3D isotropic turbulence simulations. We comment on the need to revisiting previous box-counting analysis which have failed to estimate correctly the corresponding multifractal spectra because of their intrinsic inability to master non-conservative singular cascade measures.Comment: 5 pages, 3figures, submitted to Phys. Rev. Let

Long-range dependencies in heart rate signals- revisited

The RR series extracted from human electrocardiogram signal (ECG) is considered as a fractal stochastic process. The manifestation of long-range dependencies is the presence of power laws in scale dependent process characteristics. Exponents of these laws: $\beta$ - describing power spectrum decay, $\alpha$ - responsible for decay of detrended fluctuations or $H$ related to, so-called, roughness of a signal, are known to differentiate hearts of healthy people from hearts with congestive heart failure. There is a strong expectation that resolution spectrum of exponents, so-called, local exponents in place of global exponents allows to study differences between hearts in details. The arguments are given that local exponents obtained in multifractal analysis by the two methods: wavelet transform modulus maxima (WTMM) and multifractal detrended fluctuation analysis (MDFA), allow to recognize the following four stages of the heart: healthy and young, healthy and advance in years, subjects with left ventricle systolic dysfunction (NYHA I--III class) and characterized by severe congestive heart failure (NYHA III-IV class).Comment: 24 page

Scaling analyses based on wavelet transforms for the Talbot effect

The fractal properties of the transverse Talbot images are analysed with two well-known scaling methods, the wavelet transform modulus maxima (WTMM) and the wavelet transform multifractal detrended fluctuation analysis (WT-MFDFA). We use the widths of the singularity spectra, Delta alpha=alpha_H-alpha_min, as a characteristic feature of these Talbot images. The tau scaling exponents of the q moments are linear in q within the two methods, which proves the monofractality of the transverse diffractive paraxial field in the case of these imagesComment: 9 pages, 6 figures, version accepted at Physica

A Golden Age of Philanthropy Still Beckons: National Wealth Transfer and Potential for Philanthropy Technical Report

This report provides estimates of wealth transfer and philanthropic giving by households during the period from 2007 through 2011, with one study focused on the households in North Dakota, and another focused on household wealth transfer and charitable giving at the national level. Includes projections of individual charitable giving during the next half century. With bibliographical references

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