Related papers: Non-equispaced B-spline wavelets
We obtain a characterization of all wavelets leading to analytic wavelet transforms (WT). The characterization is obtained as a by-product of the theoretical foundations of a new method for wavelet phase reconstruction from magnitude-only…
Recent investigations of turbulent circulation fluctuations have uncovered substantial insights into the statistical organization of flow structures and revealed unexpected geometric features of turbulent intermittency. Of particular…
This paper develops the use of wavelets as a basis set for the solution of physical problems exhibiting behavior over wide-ranges in length scale. In a simple diagrammatic language, this article reviews both the mathematical underpinnings…
The interaction between turbulent axisymmetric wakes plays an important role in many industrial applications, notably in the modelling of wind farms. While the non-equilibrium high Reynolds number scalings present in the wake of…
Numerically predicting the performance of heterogenous structures without scale separation represents a significant challenge to meet the critical requirements on computational scalability and efficiency -- adopting a mesh fine enough to…
Most data processing techniques, applied to biomedical and sociological time series, are only valid for random fluctuations that are stationary in time. Unfortunately, these data are often non stationary and the use of techniques of…
In nonparametric statistical problems, we wish to find an estimator of an unknown function f. We can split its error into bias and variance terms; Smirnov, Bickel and Rosenblatt have shown that, for a histogram or kernel estimate, the…
Nonlinear machine learning for turbulent flows can exhibit robust performance even outside the range of training data. This is achieved when machine-learning models can accommodate scale-invariant characteristics of turbulent flow…
The underlying mathematics of the wavelet formalism is a representation of the inhomogeneous Lorentz group or the affine group. Within the framework of wavelets, it is possible to define the ``window'' which allows us to introduce a…
We show how it is possible to assess the rate of convergence in the Gaussian approximation of triangular arrays of $U$-statistics, built from wavelets coefficients evaluated on a homogeneous spherical Poisson field of arbitrary dimension.…
Recent work by Webb {\it et al.} has provided indications of spatial variations of the fine-structure constant, $\alpha$, at a level of a few parts per million. Using a dataset of 293 archival measurements, they further show that a dipole…
Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the…
In this paper, we will outline a novel data-driven method for estimating functions in a multivariate nonparametric regression model based on an adaptive knot selection for B-splines. The underlying idea of our approach for selecting knots…
This paper introduces a novel data driven framework for constructing accurate and general equivariant models of multiscale phenomena which does not rely on specific assumptions about the underlying physics. This framework is illustrated…
Previous numerical investigations of the stability and bifurcation properties of different nonlinear combination structures of spiral vortices in a counterrotating Taylor-Couette system that were done for fixed axial wavelengths are…
In the paper, we construct a new quadratic spline-wavelet basis on the interval and a unit square satisfying homogeneous Dirichlet boundary conditions of the first order. Wavelets have one vanishing moment and the shortest support among…
Gravitational wave detectors produce time series of the gravitational wave strain co-added with instrument noise. For evenly sampled data, such as from laser interferometers, it has been traditional to Fourier transform the data and perform…
In a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological…
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as…
In the second paper of this series we extend our Bayesian reanalysis of the evidence for a cosmic variation of the fine structure constant to the semi-parametric modelling regime. By adopting a mixture of Dirichlet processes prior for the…