相关论文: Function integration, reconstruction and approxima…

In quantum gas microscopy experiments, reconstructing the site-resolved lattice occupation with high fidelity is essential for the accurate extraction of physical observables. For short interatomic separations and limited signal-to-noise…

Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

We study quasi-Monte Carlo (QMC) methods for numerical integration of multivariate functions defined over the high-dimensional unit cube. Lattice rules and polynomial lattice rules, which are special classes of QMC methods, have been…

Flexible boundary condition methods couple an isolated defect to bulk through the bulk lattice Green's function. The inversion of the force-constant matrix for the lattice Green's function requires Fourier techniques to project out the…

We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when…

This work is concerned with approximating a trivariate function defined on a tensor-product domain via function evaluations. Combining tensorized Chebyshev interpolation with a Tucker decomposition of low multilinear rank yields function…

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…

Recent work in the matrix completion literature has shown that prior knowledge of a matrix's row and column spaces can be successfully incorporated into reconstruction programs to substantially benefit matrix recovery. This paper proposes a…

Using normalized Hermite functions, we construct bases in the space of square integrable functions on the unit circle ($L^2(\mathcal C)$) and in $l_2(\mathbb Z)$, which are related to each other by means of the Fourier transform and the…

Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…

It has been observed by several authors that well-known periodization strategies like tent or Chebychev transforms lead to remarkable results for the recovery of multivariate functions from few samples. So far, theoretical guarantees are…

We address in this paper the following two closely related problems: 1. How to represent functions with singularities (up to a prescribed accuracy) in a compact way? 2. How to reconstruct such functions from a small number of measurements?…

We investigate convexification for convex quadratic optimization with step function penalties. Such problems can be cast as mixed-integer quadratic optimization problems, where binary variables are used to encode the non-convex step…

We introduce several associative algebras and series of vector spaces associated to these algebras. Using lattice vertex operators, we obtain dimension and character formulae for these spaces. In particular, we a series of representations…

A lattice fermion model is formulated in Fock space using the Jordan-Wigner representation for the fermion creation and annihilation operators. The resulting path integral is a sum over configurations of lattice site occupation numbers…

We investigate relations between symmetrizations of quasi-Banach function spaces and constructions such as Calderon-Lozanovskii spaces, pointwise product spaces and pointwise multipliers. We show that under reasonable assumptions the…

This paper studies how to sketch element-wise functions of low-rank matrices. Formally, given low-rank matrix A = [Aij] and scalar non-linear function f, we aim for finding an approximated low-rank representation of the (possibly high-rank)…

We propose a recursive lattice reduction framework for finding short non-zero vectors or dense sublattices of a lattice. The framework works by recursively searching for dense sublattices of dense sublattices (or their duals) with…

Bayesian inference for Continuous-Time Markov Chains (CTMCs) on countably infinite spaces is notoriously difficult because evaluating the likelihood exactly is intractable. One way to address this challenge is to first build a non-negative…