Related papers: Re-Embeddings of Special Border Basis Schemes
We give a criterion for a collection of polynomials to be a universal Gr\"{o}bner basis for an ideal in terms of the multidegree of the closure of the corresponding affine variety in $(\mathbb{P}^1)^N$. This criterion can be used to give…
ADER schemes are numerical methods, which can reach an arbitrary order of accuracy in both space and time. They are based on a reconstruction procedure and the solution of generalized Riemann problems. However, for general boundary…
In recent years there have been tremendous advances in the theoretical understanding of boundary integral equations for Maxwell problems. In particular, stable dual pairing of discretisation spaces have been developed that allow robust…
Score-based diffusion models achieve state-of-the-art performance for inverse problems, but their practical deployment is hindered by long inference times and cumbersome hyperparameter tuning. While pretrained diffusion models can be reused…
Emulation has been successfully applied across a wide variety of scientific disciplines for efficiently analysing computationally intensive models. We develop known boundary emulation strategies which utilise the fact that, for many…
We answer a question of Serre from the 1980s on rational points of bounded height on projective thin sets, in degree at least $4$. For degrees $2$ and $3$ we improve the known bounds in general. The focus is on thin sets of type II, namely…
The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…
Numerical homogenization and multiscale finite element methods construct effective properties on a coarse grid by solving local problems and extracting the average effective properties from these local solutions. In some cases, the…
The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence…
Border bases arise as a canonical generalization of Gr\"obner bases. We provide a polyhedral characterization of all order ideals (and hence border bases) that are supported by a zero-dimensional ideal: order ideals that support a border…
We study the relationship between operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space $\mathcal{H}$. We get sufficient conditions on an orthonormal basis of subspaces…
Given an algorithm of resolution of singularities satisfying certain conditions (``good algorithms''), natural notions of simultaneous algorithmic resolution, or equiresolution, for families of embedded schemes (parametrized by a reduced…
We introduce a framework for spline spaces of hierarchical type, based on a parent-children relation, which is very convenient for the analysis as well as the implementation of adaptive isogeometric methods. Such framework makes it simple…
Binary embedding is the problem of mapping points from a high-dimensional space to a Hamming cube in lower dimension while preserving pairwise distances. An efficient way to accomplish this is to make use of fast embedding techniques…
We propose a unique scheme to construct fully optimized atomic basis sets for density-functional calculations. The shapes of the radial functions are optimized by minimizing the {\it spillage} of the wave functions between the atomic…
This paper proposes a novel neural-network-based adaptive hybrid-reflectance three-dimensional (3-D) surface reconstruction model. The neural network combines the diffuse and specular components into a hybrid model. The proposed model…
Let G be a reductive algebraic group and H a closed subgroup of G. An affine embedding of the homogeneous space G/H is an affine G-variety with an open G-orbit isomorphic to G/H. We start with some basic properties of affine embeddings and…
Recurrent neural language models are the state-of-the-art models for language modeling. When the vocabulary size is large, the space taken to store the model parameters becomes the bottleneck for the use of recurrent neural language models.…
We present a novel approach for the construction of basis functions to be employed in selective or adaptive h-refined finite element applications with arbitrary-level hanging node configurations. Our analysis is not restricted to…
We analyze the "eigenbundle" (localization bundle) of certain Hilbert modules over bounded symmetric domains of rank $r,$ giving rise to complex-analytic fibre spaces which are stratified of length $r+1.$ The fibres are described in terms…