Related papers: Localisation of directional scale-discretised wave…
If a droplet is placed on a substrate with a conical shape it spontaneously starts to spread in the direction of a growing fibre radius. We describe this capillary spreading dynamics by developing a lubrication approximation on a cone and…
We propose a method of solving partial differential equations on the $n$-dimen\-sional unit sphere with methods based on the continuous wavelet transform derived from approximate identities.
Spherical data is found in many applications. By modeling the discretized sphere as a graph, we can accommodate non-uniformly distributed, partial, and changing samplings. Moreover, graph convolutions are computationally more efficient than…
Hydroelastic surface waves propagate at the surface of water covered by a thin elastic sheet and can be directly measured with accurate space and time resolution. We present an experimental approach using hydroelastic waves that allows us…
We investigate dimension-theoretic properties of concentric topological spheres, which are fractal sets emerging both in pure and applied mathematics. We calculate the box dimension and Assouad spectrum of such collections, and use them to…
In this Letter we present discrete wave turbulence (DWT) as a counterpart of classical statistical wave turbulence (SWT). DWT is characterized by resonance clustering, not by the size of clusters, i.e. it includes, but is not reduced to,…
In this paper, we propose a new two-dimensional directional discrete wavelet transform that can decompose an image into 12 multiscale directional edge components. The proposed transform is designed in a fully discrete setting and thus is…
We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on larger parameter…
We consider modeling for strong-strong beam-beam interactions beyond preceding linearized/perturbative methods such as soft gaussian approximation or FMM (HFMM) etc. In our approach discrete coherent modes, discovered before, and possible…
In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on…
This paper argues that curvelets provide a powerful tool for representing very general linear symmetric systems of hyperbolic differential equations. Curvelets are a recently developed multiscale system in which the elements are highly…
We propose and study a new quasi-interpolation method on spheres featuring the following two-phase construction and analysis. In Phase I, we analyze and characterize a large family of zonal kernels (e.g., the spherical version of Poisson…
Wavelets are known to be closely related to atomic orbital. A new approach of 2D, 3D and multidimensional wavelet system is proposed from a paralell with anti-symmetric systems of several isolated particles. The theory of fermionic states…
We revisit the feasibility approach to the construction of compactly supported smooth orthogonal wavelets on the line. We highlight its flexibility and illustrate how symmetry and cardinality properties are easily embedded in the design…
Motivated by recent interest in the spectrum of the Laplacian of incomplete surfaces with isolated conical singularities, we consider more general incomplete m-dimensional manifolds with singularities on sets of codimension at least 2. With…
We present a definition of discrete channel surfaces in Lie sphere geometry, which reflects several properties for smooth channel surfaces. Various sets of data, defined at vertices, on edges or on faces, are associated with a discrete…
Wavelets are scaleable, oscillatory functions that deviate from zero only within a limited spatial regime and have average value zero. In addition to their use as source characterizers, wavelet functions are rapidly gaining currency within…
In this paper we introduce a new localization framework for wavelet transforms, such as the 1D wavelet transform and the Shearlet transform. Our goal is to design nonadaptive window functions that promote sparsity in some sense. For that,…
Diffusion wavelets extract information from graph signals at different scales of resolution by utilizing graph diffusion operators raised to various powers, known as diffusion scales. Traditionally, these scales are chosen to be dyadic…
We present a detailed review of large-scale structure (LSS) study using the discrete wavelet transform (DWT). After describing how one constructs a wavelet decomposition we show how this bases can be used as a complete statistical…