Publications related to On Polygons Excluding Point Sets

Related publications (32)

Dynamical system approach to navigation around obstacles

In this article, we propose a dynamical system to avoid obstacles which are star shaped and simultaneously converge to a goal. The convergence is almost-global in a domain and the stationary points are identified explicitly. Our approach is based on the id ...

2024

Hitting with Probability One for Stochastic Heat Equations with Additive Noise

Robert Dalang, Fei Pu

We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...

Springer/Plenum Publishers2024

A Note on Lenses in Arrangements of Pairwise Intersecting Circles in the Plane

Rom Pinchasi

Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...

Electronic Journal Of Combinatorics2024

Reliable data-driven decision-making through optimal transport

Bahar Taskesen

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

EPFL2024

Reducing uncertainties in response predictions of earthquake-damaged masonry buildings using data from image-based inspection

Ian Smith, Katrin Beyer, Bryan German Pantoja Rosero, Mathias Christian Haindl Carvallo

Image information about the state of a building after an earthquake, which can be collected without endangering the post-earthquake reconnaissance activities, can be used to reduce uncertainties in response predictions for future seismic events. This paper ...

Springer2024

Decentralized gradient tracking with local steps

Anastasiia Koloskova

Gradient tracking (GT) is an algorithm designed for solving decentralized optimization problems over a network (such as training a machine learning model). A key feature of GT is a tracking mechanism that allows us to overcome data heterogeneity between no ...

2024

Learning to Optimize with Convergence Guarantees Using Nonlinear System Theory

Luca Furieri, Andrea Martin

The increasing reliance on numerical methods for controlling dynamical systems and training machine learning models underscores the need to devise algorithms that dependably and efficiently navigate complex optimization landscapes. Classical gradient desce ...

2024

The first Grushin eigenvalue on cartesian product domains

Joachim Stubbe, Luigi Provenzano

In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed ...

WALTER DE GRUYTER GMBH2023

Thick points of the planar GFF are totally disconnected for all & gamma;=6 0*

Juhan Aru

We prove that the set of-y-thick points of a planar Gaussian free field (GFF) with Dirichlet boundary conditions is a.s. totally disconnected for all-y =6 0. Our proof relies on the coupling between a GFF and the nested CLE4. In particular, we show that th ...

INST MATHEMATICAL STATISTICS-IMS2023

Present design of the Steering Mirror Assembly (SMA) for ITER ECHUL

Timothy Goodman, René Chavan, Anastasia Xydou

In the ITER Tokamak, four Electron Cyclotron Heating Upper Launchers (ECHUL) are needed to control plasma instabilities at the rational surfaces, most importantly the q = 3/2 and q = 2/1 neoclassical tearing modes (NTMs). Each ECHUL is equipped with a set ...

2023

State of the Art in Dense Monocular Non-Rigid 3D Reconstruction

Pascal Fua

3D reconstruction of deformable (or non-rigid) scenes from a set of monocular 2D image observations is a long-standing and actively researched area of computer vision and graphics. It is an ill-posed inverse problem, since-without additional prior assumpti ...

WILEY2023

Discontinuous Galerkin methods for Fisher-Kolmogorov equation with application to a-synuclein spreading in Parkinson's disease

Alfio Quarteroni, Francesca Bonizzoni

This spreading of prion proteins is at the basis of brain neurodegeneration. This paper deals with the numerical modelling of the misfolding process of a-synuclein in Parkinson's disease. We introduce and analyse a discontinuous Galerkin method for the sem ...

Elsevier Science Sa2023

T-5 configurations and hyperbolic systems

Riccardo Tione, Carl Johan Peter Johansson

In this paper, we study the rank-one convex hull of a differential inclusion associated to entropy solutions of a hyperbolic system of conservation laws. This was introduced in [B. Kirchheim, S. Muller and V. S(sic)ver & aacute;k, Studying Nonlinear PDE by ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

Equivariant Neural Architectures for Representing and Generating Graphs

Clément Arthur Yvon Vignac

Graph machine learning offers a powerful framework with natural applications in scientific fields such as chemistry, biology and material sciences. By representing data as a graph, we encode the prior knowledge that the data is composed of a set of entiti ...

EPFL2023

Optimal containment control for a class of heterogeneous multi-agent systems with actuator faults

Ju Wu

This article investigates the optimal containment control problem for a class of heterogeneous multi-agent systems with time-varying actuator faults and unmatched disturbances based on adaptive dynamic programming. Since there exist unknown input signals i ...

WILEY2023

Stochastic homogenization of degenerate integral functionals with linear growth

Matthias Benjamin Ruf

We study the limit behaviour of sequences of non-convex, vectorial, random integral functionals, defined on W1,1, whose integrands are ergodic and satisfy degenerate linear growth conditions. The latter involve suitable random, scale-dependent weight-funct ...

2023

Results on Sparse Integer Programming and Geometric Independent Sets

Jana Tabea Cslovjecsek

An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

EPFL2023

Quadratic serendipity element shape functions on general planar polygons

Xiaodong Wei

This paper proposes a method for the construction of quadratic serendipity element (QSE) shape functions on planar convex and concave polygons. Existing approaches for constructing QSE shape functions are linear combinations of the pair-wise products of ge ...

ELSEVIER SCIENCE SA2022

Defects in III-N LEDs: experimental identification and impact on electro-optical characteristics

Nicolas Grandjean, Jean-François Carlin, Camille Haller

III-N light-emitting-diodes (LEDs) are subject of intense investigations, thanks to their high efficiency and great reliability. The quality of the semiconductor material has a significant impact on the electro-optical performance of LEDs: for this reason, ...

SPIE-INT SOC OPTICAL ENGINEERING2022

Removing Algorithmic Discrimination (With Minimal Individual Error)

Rachid Guerraoui, El Mahdi El Mhamdi, Alexandre David Olivier Maurer, Le Nguyen Hoang

We address for the first time the problem of correcting group discriminations within a score function, while minimizing the individual error. Each group is described by a probability density function on the set of profiles. We first solve the problem analy ...

2022