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Second-order hyperbolic S.P.D.E.'s driven by homogeneous Gaussian noise on a hyperplane

Related publications (45)

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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

Dynamically Orthogonal Approximation for Stochastic Differential Equations

Fabio Nobile, Yoshihito Kazashi, Fabio Zoccolan

In this paper, we set the mathematical foundations of the Dynamical Low Rank Approximation (DLRA) method for high-dimensional stochastic differential equations. DLRA aims at approximating the solution as a linear combination of a small number of basis vect ...

2023

Biobased surfactants

Jeremy Luterbacher, Songlan Sun, Stefania Bertella, Anastasiia Komarova

Compound of the general formula (Ia), (Ib) and (Ic) R50 and R60 are different form each other and are selected from the group consisting of -R70, -ZR70, -Z-OH, -Z-NH2, -Z-SH, -Z-OC(O)R70, -OC(O)R70, - COOH and its corresponding salts, -C(O)NH2, -C(O)NH-R70 ...

2023

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

Singularities of general fibers and the LMMP

Zsolt Patakfalvi, Joseph Allen Waldron

We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to a divisor with positive integer coefficients divisible by p - 1. We deduce ...

JOHNS HOPKINS UNIV PRESS2022

On Gaussian Process based Koopman Operator

Colin Neil Jones

Enabling analysis of non-linear systems in linear form, the Koopman operator has been shown to be a powerful tool for system identification and controller design. However, current data-driven methods cannot provide quantification of model uncertainty given ...

2020

Relax and Recover: Guaranteed Range-Only Continuous Localization

Adam James Scholefield, Frederike Dümbgen, Michalina Wanda Pacholska

Range-only localization has applications as diverse as underwater navigation, drone tracking and indoor localization. While the theoretical foundations of lateration---range-only localization for static points---are well understood, there is a lack of unde ...

2020

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Range-only localization has applications as diverse as underwater navigation, drone tracking and indoor localization. While the theoretical foundations of lateration-range-only localization for static points-are well understood, there is a lack of understa ...

2020

Matrix recovery from bilinear and quadratic measurements

Martin Vetterli, Adam James Scholefield, Michalina Wanda Pacholska, Karen Adam

Matrix (or operator) recovery from linear measurements is a well-studied problem. However, there are situations where only bilinear or quadratic measurements are available. A bilinear or quadratic problem can easily be transformed into a linear one, but it ...

ArXiv2020

Multi-channel Time Encoding for Improved Reconstruction of Bandlimited Signals

Martin Vetterli, Adam James Scholefield, Karen Adam

Traditional sampling involves encoding a signal through (time, value)-pairs. In contrast, time encoding machines (TEMs) characterize a signal by recording time points which depend on the integral of the signal over time. We study multi-channel TEMs where c ...

2019

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