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A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
The synchrosqueezing method aims at decomposing 1D functions as superpositions of a small number of "Intrinsic Modes", supposed to be well separated both in time and frequency. Based on the unidimensional wavelet transform and its…
Many examples of signals and images cannot be modeled by locally bounded functions, so that the standard multifractal analysis, based on the H\"older exponent, is not feasible. We present a multifractal analysis based on another quantity,…
Biosignals are nowadays important subjects for scientific researches from both theory and applications especially with the appearance of new pandemics threatening humanity such as the new Coronavirus. One aim in the present work is to prove…
Some techniques for the study of intermittency by means of wavelet transforms, are presented on an example of synthetic turbulent signal. Several features of the turbulent field, that cannot be probed looking at standard structure function…
Tight wavelet frames are computationally and theoretically attractive, but most existing multivariate constructions have various drawbacks, including low vanishing moments for the wavelets, or a large number of wavelet masks. We further…
Decomposing discrete signals such as images into components is vital in many applications, and this paper propose a framework to produce filtering banks to accomplish this task. The framework is an equation set which is ill-posed, and thus…
The new concept of multilevel network is introduced in order to embody some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classical models. This new model, which…
Samplets are data adapted multiresolution analyses of localized discrete signed measures. They can be constructed on scattered data sites in arbitrary dimension such that they exhibit vanishing moments with respect to any prescribed set of…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…
The use of machine learning interatomic potentials (MLIPs) in simulations of materials is a state-of-the-art approach, which allows achieving nearly \textit{ab initio} accuracy with orders of magnitude less computational cost.…
The interest in a system often resides in the interplay among different parameters governing its evolution. It is thus often required to access many of them at once for a complete description. Assessing how quantum enhancement in such…
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…
All wavelets can be associated to a multiresolution like structure, i.e. an incr easing sequence of subspaces of L^2(R). We consider the interaction of a wavel et and the translation operator in terms of which of the subspaces in this multi…
Unsupervised deep learning has recently demonstrated the promise of producing high-quality samples. While it has tremendous potential to promote the image colorization task, the performance is limited owing to the high-dimension of data…
The simultaneous quantum estimation of multiple parameters can provide a better precision than estimating them individually. This is an effect that is impossible classically. We review the rich background of multi-parameter quantum…
The recently proposed empirical wavelet transform was based on a particular type of filter. In this paper, we aim to propose a general framework for the construction of empirical wavelet systems in the continuous case. We define a…
The construction of needlet-type wavelets on sections of the spin line bundles over the sphere has been recently addressed in Geller and Marinucci (2008), and Geller et al. (2008,2009). Here we focus on an alternative proposal for needlets…
We propose a novel framework to investigate lead-lag relationships between two financial assets. Our framework bridges a gap between continuous-time modeling based on Brownian motion and the existing wavelet methods for lead-lag analysis…