From Tarski's Plank Problem to Simultaneous Approximation

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one -phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions n >= 3 is completely open. In this context, axial ...

In this thesis, we concentrate on advancing high-level behavioral control policies for robotic systems within the framework of Dynamical Systems (DS). Throughout the course of this research, a unifying thread weaving through diverse fields emerges, and tha ...

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental ...

Dynamical system (DS) based motion planning offers collision-free motion, with closed-loop reactivity thanks to their analytical expression. It ensures that obstacles are not penetrated by reshaping a nominal DS through matrix modulation, which is construc ...

In this thesis, we apply cochain complexes as an algebraic model of space in a diverse range of mathematical and scientific settings. We begin with an algebraic-discrete Morse theory model of auto-encoding cochain data, connecting the homotopy theory of d ...

This paper presents a comparison of machine learning (ML) methods used for three-dimensional localization of partial discharges (PD) in a power transformer tank. The study examines ML and deep learning (DL) methods, ranging from support vector machines (SV ...

This paper introduces a novel method for data-driven robust control of nonlinear systems based on the Koopman operator, utilizing Integral Quadratic Constraints (IQCs). The Koopman operator theory facilitates the linear representation of nonlinear system d ...

Entanglement and correlation are at the basis of quantummechanicsand have been used in optics to create a framework for "ghostimaging". We propose that a similar scheme can be used in anelectron microscope to exploit the correlation of electrons with theco ...

Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- (PT-) and anti-PT-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian sp ...

The task of discovering equivalent entities in knowledge graphs (KGs), so-called KG entity alignment, has drawn much attention to overcome the incompleteness problem of KGs. The majority of existing techniques learns the pointwise representations of entiti ...

Dimensionality provides a clear fingerprint on the dispersion of infrared-active, polar-optical phonons. For these phonons, the local dipoles parametrized by the Born effective charges drive the LO-TO splitting of bulk materials; this splitting actually br ...

This thesis is a study of the global well-posedness of the Cauchy problems for half-wave maps from the Minkowski space of dimension n+1 to the 2-dimensional sphere and the hyperbolic plane. The work is mainly based on the results from Krieger-Sire 17' in ...

Recently, substantial progress has been made in the understanding of microresonators frequency combs based on dissipative Kerr solitons (DKSs). However, most of the studies have focused on the single-resonator level. Coupled resonator systems can open new ...

We investigate the mechanics of bistable, hard-magnetic, elastic beams, combining experiments, finite-element modelling (FEM) and a reduced-order theory. The beam is made of a hard magneto-rheological elastomer, comprising two segments with antiparallel ma ...

We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form of supervised le ...

We study elastic ribbons subject to large, tensile pre-stress confined to a central region within the cross-section. These ribbons can buckle spontaneously to form helical shapes, featuring regions of alternating chirality (phases) that are separated by so ...

Digital brain atlases define a hierarchy of brain regions and their locations in three-dimensional space. They provide a standard coordinate system in which diverse datasets can be integrated for visualization and analysis. They also enable building of dat ...

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

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 ...

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

From Tarski's Plank Problem to Simultaneous Approximation

Chat with Graph Search

Stable cones in the thin one-phase problem

Geometric Learning: Leveraging differential geometry for learning and control

Anomalous and Chern topological waves in hyperbolic networks

Reactive collision-free motion generation in joint space via dynamical systems and sampling-based MPC

Cochains are all you need

Partial discharge localization in power transformer tanks using machine learning methods

Koopman-based Data-driven Robust Control of Nonlinear Systems Using Integral Quadratic Constraints

One-Dimensional "Ghost Imaging" in Electron Microscopy of Inelastically Scattered Electrons

Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems

Complex Representation Learning with Graph Convolutional Networks for Knowledge Graph Alignment

Infrared-active phonons in one-dimensional materials and their spectroscopic signatures

Well-posedness Issues For the Half-Wave Maps Equation With Hyperbolic And Spherical Targets

Nonlinear dynamics and Kerr frequency comb formation in lattices of coupled microresonators

Snap buckling of bistable beams under combined mechanical and magnetic loading

A structured prediction approach for robot imitation learning

Twisting instabilities in elastic ribbons with inhomogeneous pre-stress: A macroscopic analog of thermodynamic phase transition

Enhancement of brain atlases with region-specific coordinate systems: flatmaps and barrel column annotations

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Localization errors of the stochastic heat equation

Reduced representations of complexes, signals, and multifiltrations