Related papers: Constructing efficient spatial discretizations of …
In this article, we propose several quantization-based stratified sampling methods to reduce the variance of a Monte Carlo simulation. Theoretical aspects of stratification lead to a strong link between optimal quadratic quantization and…
We introduce a lattice random walk discretisation scheme for stochastic differential equations (SDEs) that samples binary or ternary increments at each step, suppressing complex drift and diffusion computations to simple 1 or 2 bit random…
We present a robust and efficient multigrid method for single-patch isogeometric discretizations using tensor product B-splines of maximum smoothness. Our method is based on a stable splitting of the spline space into a large subspace of…
In the framework of mapped pseudospectral methods, we introduce a new polynomial-type mapping function in order to describe accurately the dynamics of systems developing almost singular structures. Using error criteria related to the…
Elliptical slice sampling, when adapted to linearly truncated multivariate normal distributions, is a rejection-free Markov chain Monte Carlo method. At its core, it requires analytically constructing an ellipse-polytope intersection. The…
A piecewise Chebyshevian spline space is good for design when it possesses a B-spline basis and this property is preserved under knot insertion. The interest in such kind of spaces is justified by the fact that, similarly as for polynomial…
We generalize the sparsification algorithm of Batson, Spielman and Srivastava, making one part of the result dimension-independent. In particular, we recover discretization inequalities in $L_2$- and sup-norms on general finite-dimensional…
In this paper we present new constructive methods, random and deterministic, for the efficient subsampling of finite frames in $\mathbb C^m$. Based on a suitable random subsampling strategy, we are able to extract from any given frame with…
Convection-diffusion-reaction equations are a class of second-order partial differential equations widely used to model phenomena involving the change of concentration/population of one or more substances/species distributed in space.…
Sampling from binary quadratic distributions (BQDs) is a fundamental but challenging problem in discrete optimization and probabilistic inference. Previous work established theoretical guarantees for stochastic localization (SL) in…
Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various tree-like…
The Cholesky decomposition is a fundamental tool for solving linear systems with symmetric and positive definite matrices which are ubiquitous in linear algebra, optimization, and machine learning. Its numerical stability can be improved by…
We propose an implementation of the Smooth Selection Embedding Method (SSEM) in the setting of Chebyshev polynomials. The SSEM is a hybrid fictitious domain / collocation method which solves boundary value problems in complex domains by…
Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…
Building upon score-based learning, new interest in stochastic localization techniques has recently emerged. In these models, one seeks to noise a sample from the data distribution through a stochastic process, called observation process,…
This paper studies the complexity of distributed construction of purely additive spanners in the CONGEST model. We describe algorithms for building such spanners in several cases. Because of the need to simultaneously make decisions at far…
In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…
We present a novel method to significantly speed up cosmological parameter sampling. The method relies on constructing an interpolation of the CMB-log-likelihood based on sparse grids, which is used as a shortcut for the…
Efficient handling of sparse data is a key challenge in Computer Science. Binary convolutions, such as polynomial multiplication or the Walsh Transform are a useful tool in many applications and are efficiently solved. In the last decade,…
Single-pixel imaging (SPI) is significant for applications constrained by transmission bandwidth or lighting band, where 3D SPI can be further realized through capturing signals carrying depth. Sampling strategy and reconstruction algorithm…