相关论文: Convergence of the cascade algorithm at irregular …
We sketch an application of proximal algorithms to the deformation of de Rham currents into cycles, which is presented as a convex optimization problem. Emphasis is placed on the use of total variation denoising for differential forms,…
Capsule networks(CapsNet) are recently proposed neural network models with new processing layers, specifically for entity representation and discovery of images. It is well known that CapsNet have some advantages over traditional neural…
In the present paper, a wavelet family over the $n$-dimensional sphere is constructed such that for each scale the wavelet is a polynomial and the inverse wavelet transform of a continuous function converges in the supremum norm.
The arrangement of brine above water across a micro porous permeable membrane is used to study high Rayleigh Number($10^{11}- 10^{10}$) high Schmidt number(650)turbulent convection. The flux shows 4/3$^{rd}$ scaling with line plume as the…
A method is described for predicting statistical properties of turbulence. Collections of Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics of the full dynamics can be…
In this paper we present a general approach to multivariate periodic wavelets generated by scaling functions of de la Vall\'ee Poussin type. These scaling functions and their corresponding wavelets are determined by their Fourier…
The role of turbulence in a spherically symmetric accreting system has been studied on very large spatial scales of the system. This is also a highly subsonic flow region and here the accreting fluid has been treated as nearly…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
A multiresolution analysis is a nested chain of related approximation spaces.This nesting in turn implies relationships among interpolation bases in the approximation spaces and their derived wavelet spaces. Using these relationships, a…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…
We generalize the recent invariant polytope algorithm for computing the joint spectral radius and extend it to a wider class of matrix sets. This, in particular, makes the algorithm applicable to sets of matrices that have finitely many…
We characterize the scaling function of a crystal Multiresolution Analysis in terms of the vector-scaling function for a Multiresolution Analysis associated to a lattice. We give necessary and sufficient conditions in terms of the symbol…
We analyze a family of fourth-order non-linear diffusion models corresponding to local approximations of 4-wave kinetic equations of weak wave turbulence. We focus on a class of parameters for which a dual cascade behaviour is expected with…
We investigate the neural Actor Critic algorithm using shallow neural networks for both the Actor and Critic models. The focus of this work is twofold: first, to compare the convergence properties of the network outputs under various…
We analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank…
This paper offers a new regard on compactly supported wavelets derived from FIR filters. Although being continuous wavelets, analytical formulation are lacking for such wavelets. Close approximations for daublets (Daubechies wavelets) and…
Large deviations for additive path functionals of stochastic dynamics and related numerical approaches have attracted significant recent research interest. We focus on the question of convergence properties for cloning algorithms in…
We introduce and validate a theoretical framework for coherent control of multichannel scattering of linear waves to route waves through complex geometries with multiple scattering. We show that steady-state perfect routing solutions are…
This paper examines the wavelet multiplicity function. An explicit formula for the multiplicity function is derived. An application to operator interpolation is then presented. We conclude with several remarks regarding the wavelet…