Levels of complexity in scale-invariant neural signals
Many physical and physiological signals exhibit complex scale-invariant features
characterized by 1/f scaling and long-range power-law correlations, indicating a possibly …
characterized by 1/f scaling and long-range power-law correlations, indicating a possibly …
Simulation methods for linear fractional stable motion and FARIMA using the Fast Fourier Transform
We present efficient methods for simulation, using the Fast Fourier Transform (FFT)
algorithm, of two classes of processes with symmetric α-stable (SαS) distributions. Namely,(i) …
algorithm, of two classes of processes with symmetric α-stable (SαS) distributions. Namely,(i) …
Fractional Lévy stable motion can model subdiffusive dynamics
We show in this paper that the sample (time average) mean-squared displacement (MSD) of
the fractional Lévy α-stable motion behaves very differently from the corresponding …
the fractional Lévy α-stable motion behaves very differently from the corresponding …
On the wavelet spectrum diagnostic for Hurst parameter estimation in the analysis of Internet traffic
The fluctuations of Internet traffic possess an intricate structure which cannot be simply
explained by long-range dependence and self-similarity. In this work, we explore the use of …
explained by long-range dependence and self-similarity. In this work, we explore the use of …
LASS: a tool for the local analysis of self-similarity
The Hurst parameter H characterizes the degree of long-range dependence (and asymptotic
self-similarity) in stationary time series. Many methods have been developed for the …
self-similarity) in stationary time series. Many methods have been developed for the …
Multiscale aspects of cardiac control
We report some recent attempts to understand the dynamics of complex physiologic
fluctuations by adapting and extending concepts and methods developed very recently in …
fluctuations by adapting and extending concepts and methods developed very recently in …
Wavelet estimation for operator fractional Brownian motion
Supplement to “Wavelet estimation for operator fractional Brownian motion”. In Section B of
the supplementary file Abry and Didier [2], we provide several additional auxiliary results …
the supplementary file Abry and Didier [2], we provide several additional auxiliary results …
Time-dependent scaling patterns in high frequency financial data
We measure the influence of different time-scales on the intraday dynamics of financial
markets. This is obtained by decomposing financial time series into simple oscillations …
markets. This is obtained by decomposing financial time series into simple oscillations …
An overview of fractional order signal processing (FOSP) techniques
This paper presents a brief overview of some existing fractional order signal processing
(FOSP) techniques where the developments in the mathematical communities are …
(FOSP) techniques where the developments in the mathematical communities are …
Irregularities and scaling in signal and image processing: multifractal analysis
B. Mandelbrot gave a new birth to the notions of scale invariance, self-similarity and non-
integer dimensions, gathering them as the founding corner-stones used to build up fractal …
integer dimensions, gathering them as the founding corner-stones used to build up fractal …