Multifractal characteristics of external anal sphincter based on sEMG signals

This work presents the application of Multifractal Detrended Fluctuation Analysis for the surface electromyography signals obtained from the patients suffering from rectal cancer. The electrical activity of an external anal sphincter at different levels of medical treatment is considered. The results from standard MFDFA and the EMD--based MFDFA method are compared. Two distinct scaling regions were identified. Within the region of short time scales the calculated spectra exhibit the shift towards higher values of the singularity exponent for both methods. In addition obtained spectra are shifted towards the lower values of singularity exponent for the EMD--based MFDFA.Comment: 10 pages, 6 figures, 2 table

The graph, range and level set singularity spectra of bb-adic independent cascade function

With the "iso-H\"older" sets of a function we naturally associate subsets of the graph, range and level set of the function. We compute the associated singularity spectra for a class of statistically self-similar multifractal functions, namely the $b$-adic independent cascade function.Comment: 37 pages, 10 figure

Tuning of tunneling current noise spectra singularities by localized states charging

We report the results of theoretical investigations of tunneling current noise spectra in a wide range of applied bias voltage. Localized states of individual impurity atoms play an important role in tunneling current noise formation. It was found that switching "on" and "off" of Coulomb interaction of conduction electrons with two charged localized states results in power law singularity of low-frequency tunneling current noise spectrum ($1/f^{\alpha}$) and also results on high frequency component of tunneling current spectra (singular peaks appear).Comment: 7 pages, 4 figure

Solution of Two-Body Bound State Problems with Confining Potentials

The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to remove the singularity of the kernel of the integral equation, a regularized form of the potentials is used. As an application of the method, the mass spectra of heavy quarkonia, mesons consisting from heavy quark and antiquark $(\Upsilon(b\bar{b}), \psi(c\bar{c}))$, are calculated for linear and quadratic confining potentials. The results are in good agreement with configuration space and experimental results.Comment: 6 pages, 5 table

Connection Conditions and the Spectral Family under Singular Potentials

To describe a quantum system whose potential is divergent at one point, one must provide proper connection conditions for the wave functions at the singularity. Generalizing the scheme used for point interactions in one dimension, we present a set of connection conditions which are well-defined even if the wave functions and/or their derivatives are divergent at the singularity. Our generalized scheme covers the entire U(2) family of quantizations (self-adjoint Hamiltonians) admitted for the singular system. We use this scheme to examine the spectra of the Coulomb potential $V(x) = - e^2 / | x |$ and the harmonic oscillator with square inverse potential $V(x) = (m \omega^2 / 2) x^2 + g/x^2$, and thereby provide a general perspective for these models which have previously been treated with restrictive connection conditions resulting in conflicting spectra. We further show that, for any parity invariant singular potentials $V(-x) = V(x)$, the spectrum is determined solely by the eigenvalues of the characteristic matrix $U \in U(2)$.Comment: TeX, 18 page

Nonlinear stratospheric variability: multifractal detrended fluctuation analysis and singularity spectra

Characterising the stratosphere as a turbulent system, temporal fluctuations often show different correlations for different time scales as well as intermittent behaviour that cannot be captured by a single scaling exponent. In this study, the different scaling laws in the long term stratospheric variability are studied using Multifractal de-trended Fluctuation Analysis. The analysis is performed comparing four re-analysis products and different realisations of an idealised numerical model, isolating the role of topographic forcing and seasonal variability, as well as the absence of climate teleconnections and small-scale forcing. The Northern Hemisphere (NH) shows a transition of scaling exponents for time scales shorter than about one year, for which the variability is multifractal and scales in time with a power law corresponding to a red spectrum, to longer time scales, for which the variability is monofractal and scales in time with a power law corresponding to white noise. Southern Hemisphere (SH) variability also shows a transition at annual scales. The SH also shows a narrower dynamical range in multifractality than the NH, as seen in the generalised Hurst exponent and in the singularity spectra. The numerical integrations show that the models are able to reproduce the low-frequency variability but are not able to fully capture the shorter term variability of the stratosphere