Related papers: Higher-Order Properties of Analytic Wavelets
Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real data applications, the correlation between time series is crucial. Usual…
The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated…
In Floquet engineering, we apply a time-periodic modulation to change the effective behavior of a wave system. In this work, we generalize Floquet engineering to exploit spatial degrees of freedom, expanding the scope of effective behaviors…
The detection of power-laws in real data is a demanding task for several reasons. The two, more frequently met, being: (i) real data possess noise which affects significantly the power-law tails and (ii) there is no solid tool for the…
Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The…
Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint…
Many complex systems that exhibit temporal non-pairwise interactions can be represented by means of generative higher-order network models. Here, we propose a hidden variables formalism to analytically characterize a general class of…
The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction…
Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. This article gives an overview over some well known results about the continuous and discrete wavelet transforms and…
Wind Energy is a useful resource for Renewable energy purpose. Wind speed plays a vital role for wind energy calculation of certain location. So, it is very much necessary to know the wind speed data characteristics. In this paper fourier…
In this work, the orientation adapter, a species of active particles that adapt their direction of motion from the other active particles, is introduced. The orientation adapters exist besides the usual Vicsek-like particles; both are…
The mechanism of preferential attachment underpins most recent social network formation models. Yet few authors attempt to check or quantify assumptions on this mechanism. We call generalized preferential attachment any kind of preference…
This work presents an original experimental device conceived to characterise the viscoelastic properties of wood. Classically, the dynamic mechanical analysis of wood is performed using a commercial apparatus like a DMA (Dynamic Mechanical…
Persistent homology has been studied to better understand the structural properties and topology features of weighted networks. It can reveal hidden layers of information about the higher-order structures formed by non-pairwise interactions…
Collaborative filtering is a popular approach in recommender systems, whose objective is to provide personalized item suggestions to potential users based on their purchase or browsing history. However, personalized recommendations require…
Quantum sensitivity is an important issue in the field of quantum metrology where sub-Planck scale structures play crucial role in the Heisenberg limited measurement. We investigate the mesoscopic superposition structures, particularly for…
The Talbot effect describes periodic revivals of field patterns and is ubiquitous across wave systems. In optics, it is mostly known for its manifestations in space and time, but is also observed in the wavevector and frequency spectra…
In this paper we define a new class of continuous fractional wavelet transform (CFrWT) and study its properties in Hardy space and Morrey space. The theory developed generalize and complement some of already existing results.
In the analysis of empirical signals, detecting correlations that capture genuine interactions between the elements of a complex system is a challenging task with applications across disciplines. Here we analyze a global data set of surface…
Standard transformer attention computes pairwise token similarity but treats all tokens as equally salient and all positions as equally local, regardless of the informational structure of the input. We identify two complementary inductive…