Concept

Zero-dimensional space

Publications associées (33)

Localization errors of the stochastic heat equation

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

Maria Carola Colombo, Silja Noëmi Aline Haffter

We consider the SQG equation with dissipation given by a fractional Laplacian of order α

2021

Nearly-Tight and Oblivious Algorithms for Explainable Clustering

Ola Nils Anders Svensson, Adam Teodor Polak, Buddhima Ruwanmini Gamlath Gamlath Ralalage, Xinrui Jia

We study the problem of explainable clustering in the setting first formalized by Dasgupta, Frost, Moshkovitz, and Rashtchian (ICML 2020). A k-clustering is said to be explainable if it is given by a decision tree where each internal node splits data point ...

2021

A p-weighted limiter for the discontinuous Galerkin method on one-dimensional and two-dimensional triangular grids

Qian Wang

This paper presents an accuracy-preserving p-weighted limiter for discontinuous Galerkin methods on one-dimensional and two-dimensional triangular grids. The p-weighted limiter is the extension of the second-order WENO limiter by Li et al. [W. Li, J. Pan a ...

2020

Time-independent feedbacks for the null controllability of homogeneous quasilinear hyperbolic systems in one dimensional space

Hoài-Minh Nguyên

We consider the null controllability of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks for the null-controllability for

C^1

-solutions at any ...

2020

A Computational Comparison Between Isogeometric Analysis and Spectral Element Methods: Accuracy and Spectral Properties

Alfio Quarteroni, Ondine Gabrielle Chanon

In this paper, we carry out a systematic comparison between the theoretical properties of Spectral Element Methods and NURBS-based Isogeometric Analysis in its basic form, that is in the framework of the Galerkin method, for the approximation of the Poisso ...

SPRINGER/PLENUM PUBLISHERS2020

Continuous-Domain Signal Reconstruction Using L-p-Norm Regularization

Michaël Unser, Pakshal Narendra Bohra

We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Notes on functions of hyperbolic type

Nicolas Monod

Functions of hyperbolic type encode representations on real or complex hyperbolic spaces, usually infinite-dimensional. These notes set up the complex case. As applications, we prove the existence of a non-trivial deformation family of representations of S ...

BELGIAN MATHEMATICAL SOC TRIOMPHE2020

Path properties of the solution to the stochastic heat equation with Levy noise

Robert Dalang, Carsten Hao Ye Chong, Thomas Marie Jean-Baptiste Humeau

We consider sample path properties of the solution to the stochastic heat equation, in Rd or bounded domains of Rd, driven by a Levy space-time white noise. When viewed as a stochastic process in time with values in an infinite-dimensional space, the solut ...

SPRINGER2019

Dynamical Low Rank approximation of PDEs with random parameters

Eleonora Musharbash

In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...

EPFL2017

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Time-independent feedbacks for the null controllability of homogeneous quasilinear hyperbolic systems in one dimensional space

Hoài-Minh Nguyên

C^1

-solutions at any ...

2020