Publications associées à Fondements des mathématiques

Geometric Learning: Leveraging differential geometry for learning and control

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

Extractable Witness Encryption for the Homogeneous Linear Equations Problem

Serge Vaudenay, Bénédikt Minh Dang Tran

Witness encryption is a cryptographic primitive which encrypts a message under an instance of an NP language and decrypts the ciphertext using a witness associated with that instance. In the current state of the art, most of the witness encryption construc ...

Springer2023

Deep Learning Meets Sparse Regularization

Rahul Parhi

Deep learning (DL) has been wildly successful in practice, and most of the state-of-the-art machine learning methods are based on neural networks (NNs). Lacking, however, is a rigorous mathematical theory that adequately explains the amazing performance of ...

2023

Dynamical Low-Rank 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 stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of basis vectors with r ...

American Mathematical Society (AMS)2024

A data fusion approach for ride-sourcing demand estimation: A discrete choice model with sampling and endogeneity corrections

Michel Bierlaire, Prateek Bansal

Ride-sourcing services offered by companies like Uber and Didi have grown rapidly in the last decade. Understanding the demand for these services is essential for planning and managing modern transportation systems. Existing studies develop statistical mod ...

2023

Mathematical Foundations of Adaptive Isogeometric Analysis

Annalisa Buffa, Rafael Vazquez Hernandez

This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of ...

SPRINGER2022

Improved spiking neural network for intershaft bearing fault diagnosis

Jun Wang, Tianfu Li

The intershaft bearing is located between the high and low-pressure rotors of the aero-engine, where the working environment is harsh, the load variation range is large, and the lubrication and heat dissipation are poor. The fault of the intershaft bearing ...

ELSEVIER SCI LTD2022

The irreducibility of vision: Gestalt, crowding and the fundamentals of vision

Michael Herzog

What is fundamental in vision has been discussed for millennia. For philosophical realists and the physiological approach to vision, the objects of the outer world are truly given, and failures to perceive objects properly, such as in illusions, are just s ...

2022

Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes

Alexis Arnaudon

Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model ...

NATURE PORTFOLIO2022

Analysis of barrette foundations subjected to mechanical and thermal loads

Lyesse Laloui, Alessandro Francesco Rotta Loria

In recent years, there has been increasing interest in the use of rectangular barrette foundations for the structural support and energy supply of tall buildings when circular piles become inefficient or uneconomical. In such applications, so-called energy ...

2022