Related papers: Using wave packet decompositions to construct func…
Arnold, Falk, & Winther, in "Finite element exterior calculus, homological techniques, and applications" (2006), show how to geometrically decompose the full and trimmed polynomial spaces on simplicial elements into direct sums of…
We develop a sparse multiscale operator-adapted wavelet decomposition-based finite element method (FEM) on unstructured polygonal mesh hierarchies obtained via a coarsening procedure. Our approach decouples different resolution levels,…
We consider orthogonal decompositions of invariant subspaces of Hardy spaces, these relate to the Blaschke based phase unwinding decompositions. We prove convergence in Lp. In particular we build an explicit multiscale wavelet basis. We…
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux…
From any graph $G$ arises a flat space wavefunction, obtained by integrating a product of propagators associated to the vertices and edges of $G$. This function is a key ingredient in the computation of cosmological correlators, and several…
One approach to ease the construction of frames is to first construct local components and then build a global frame from these. In this paper we will show that the study of the relation between a frame and its local components leads to the…
Turbulent flows are chaotic and multi-scale dynamical systems, which have large numbers of degrees of freedom. Turbulent flows, however, can be modelled with a smaller number of degrees of freedom when using the appropriate coordinate…
Real-space refinement of atomic models in macromolecular crystallography or in cryo electron microscopy fits a model to a map obtained experimentally. This requires generating model maps of a limited resolution which moreover may vary from…
The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…
We consider the problem of atmospheric tomography, as it appears for example in adaptive optics systems for extremely large telescopes. We derive a frame decomposition, i.e., a decomposition in terms of a frame, of the underlying…
We consider the expansion of wave packets governed by the free Schr\"odinger equation. This seemingly simple task plays an important role in simulations of various quantum experiments and in particular in the field of matter-wave…
The space mapping technique is used to efficiently solve complex optimization problems. It combines the accuracy of fine model simulations with the speed of coarse model optimizations to approximate the solution of the fine model…
We develop the wave packet decomposition to study the Schrodinger evolution with rough potential. As an application, we obtain the improved bound on the wave propagation for the generic value of a parameter.
Optical full-field techniques have a great importance in modern experimental mechanics. Even if they are reasonably spread among the university laboratories, their diffusion in industrial companies remains very narrow for several reasons,…
We present the results from a two-day study in which we discussed various implementations of Smooth Particle Hydrodynamics (SPH), one of the leading methods used across a variety of areas of large-scale astrophysical simulations. In…
Wavelets are closely related to the Schr\"odinger's wave functions and the interpretation of Born. Similarly to the appearance of atomic orbital, it is proposed to combine anti-symmetric wavelets into orbital wavelets. The proposed approach…
This article concerns the predictive modeling for spatio-temporal data as well as model interpretation using data information in space and time. We develop a novel approach based on supervised dimension reduction for such data in order to…
Spherical harmonics (SH) have been extensively used as a basis for analyzing the morphology of particles in granular mechanics. The use of SH is facilitated by mapping the particle coordinates onto a unit sphere, in practice often a…
Recent work introduced a unified framework for steerable and directional wavelets in two and three dimensions that ensures many desirable properties, such as a multi-scale structure, fast transforms, and a flexible angular localization. We…
Within an increasing number of domains an important emerging need is the ability for technically naive users to compose computational elements into novel configurations. Examples include astronomers who create new analysis pipelines to…