Publications associées à On discrete Fourier uniqueness sets in Euclidean space

Verification of the Fourier-enhanced 3D finite element Poisson solver of the gyrokinetic full-f code PICLS

Stephan Brunner, Laurent Villard, Alberto Bottino, Moahan Murugappan

We introduce and derive the Fourier -enhanced 3D electrostatic field solver of the gyrokinetic full -f PIC code PICLS. The solver makes use of a Fourier representation in one periodic direction of the domain to make the solving of the system easily paralle ...

Elsevier2024

Geometric Learning: Leveraging differential geometry for learning and control

Bernardo Fichera

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 ...

EPFL2024

Anomalous and Chern topological waves in hyperbolic networks

Romain Christophe Rémy Fleury, Aleksi Antoine Bossart, Haoye Qin, Zhechen Zhang

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 ...

Nature Research2024

Impact of beam-coupling impedance on the Schottky spectrum of bunched beam

Tatiana Pieloni, Nicolas Frank Mounet, Christophe Emmanuel R. Lannoy

The Schottky monitors of the Large Hadron Collider (LHC) can be used for non-invasive beam diagnostics to estimate various bunch characteristics, such as tune, chromaticity, bunch profile or synchrotron frequency distribution. However, collective effects, ...

Iop Publishing Ltd2024

Unified Harmonic Power-Flow and Stability Analysis of Power Grids with Converter-Interfaced Distributed Energy Resources

Johanna Kristin Maria Becker

Modern power distribution systems are experiencing a large-scale integration of Converter-Interfaced Distributed Energy Resources (CIDERs). Their presence complicates the analysis and mitigation of harmonics, whose creation and propagation may be amplified ...

EPFL2024

Adding Color to Mass Spectra of Biopolymers: Charge Determination Analysis (CHARDA) Assigns Charge State to Every Ion Peak

Yury Tsybin, Laure Menin, Anton Kozhinov, Natalia Gasilova, Konstantin Nagornov

Traditionally, mass spectrometry (MS) output is the ion abundance plotted versus the ionic mass-to-charge ratio m/z. While employing only commercially available equipment, Charge Determination Analysis (CHARDA) adds a third dimension to MS, estimating for ...

Amer Chemical Soc2024

Cochains are all you need

Kelly Spry Maggs

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 ...

EPFL2024

An optimal preconditioned FFT-accelerated finite element solver for homogenization

Till Junge, Ali Falsafi, Martin Ladecký

We generalize and provide a linear algebra-based perspective on a finite element (FE) ho-mogenization scheme, pioneered by Schneider et al. (2017)[1] and Leuschner and Fritzen (2018)[2]. The efficiency of the scheme is based on a preconditioned, well-scale ...

ELSEVIER SCIENCE INC2023

Complex Representation Learning with Graph Convolutional Networks for Knowledge Graph Alignment

Quoc Viet Hung Nguyen, Thành Tâm Nguyên, Thanh Trung Huynh

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 ...

Wiley-Hindawi2023

Exploring the effectiveness of using internal CNC system signals for chatter detection in milling process

Dimitrios Kyritsis, Roberto Pérez, Xiaochen Zheng

Chatter is a harmful self-excited vibration that commonly occurs during milling processes. Data -driven chatter detection and prediction is critical to achieve high surface quality and process efficiency. Most existing chatter detection approaches are base ...

ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD2023

Computation of the attenuation function of the lightning return-stroke current from electromagnetic fields measured in a short-duration time-window, Part I: Theoretical investigation

Farhad Rachidi-Haeri, Marcos Rubinstein

In a recent paper, a procedure to reconstruct the attenuation function of a return-stroke current from the simultaneous measurements of the channel-base current and the radiated electromagnetic fields was presented. One of the assumptions of the whole fram ...

Elsevier2023

A structured prediction approach for robot imitation learning

Aude Billard, Iason Batzianoulis, Anqing Duan

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 ...

Sage Publications Ltd2023

Towards Stable and Efficient Adversarial Training against $l_1$ Bounded Adversarial Attacks

Mathieu Salzmann, Sabine Süsstrunk, Chen Liu, Zhuoyi Huang, Yulun Jiang

We address the problem of stably and efficiently training a deep neural network robust to adversarial perturbations bounded by an

l_1

norm. We demonstrate that achieving robustness against

l_1

-bounded perturbations is more challenging than in the

l_2

...

2023

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

Axel Elie Joseph Séguin

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 ...

EPFL2023

Hybrid Quadratic Programming - Pullback Bundle Dynamical Systems Control

Aude Billard, Bernardo Fichera

Dynamical System (DS)-based closed-loop control is a simple and effective way to generate reactive motion policies that well generalize to the robotic workspace, while retaining stability guarantees. Lately the formalism has been expanded in order to handl ...

SPRINGER INTERNATIONAL PUBLISHING AG2023

Fourier uniqueness and interpolation in Euclidean space

Martin Peter Stoller

We prove that every Schwartz function in Euclidean space can be completely recovered given only its restrictions and the restrictions of its Fourier transform to all origin-centered spheres whose radii are square roots of integers. In particular, the only ...

EPFL2022

Localization errors of the stochastic heat equation

David Jean-Michel Candil

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

pyFFS: A Python Library for Fast Fourier Series Computation and Interpolation with GPU Acceleration

Martin Vetterli, Paul Hurley, Sepand Kashani, Matthieu Martin Jean-André Simeoni, Eric Bezzam

Fourier transforms are an often necessary component in many computational tasks, and can be computed efficiently through the fast Fourier transform (FFT) algorithm. However, many applications involve an underlying continuous signal, and a more natural choi ...

SIAM2022

Fourier non-uniqueness sets from totally real number fields

Martin Peter Stoller

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

EUROPEAN MATHEMATICAL SOC-EMS2022

midiVERTO: A Web Application to Visualize Tonality in Real Time

Daniel Harasim, Fabian Claude Moss

This paper presents a web application for visualizing the tonality of a piece of music-the organization of its chords and scales-at a high level of abstraction and with coordinated playback. The application applies the discrete Fourier transform to the pit ...

SPRINGER INTERNATIONAL PUBLISHING AG2022