Publications associées à New Foundations

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

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

A Unified Theory of Robust and Distributionally Robust Optimization via the Primal-Worst-Equals-Dual-Best Principle

Daniel Kuhn, Jianzhe Zhen, Wolfram Wiesemann

Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from within an ambigu ...

2023

Electromagnetic waves under nonstationary conditions, the connection with parity-time symmetry and studies on resonant systems

Theodoros Koutserimpas

In this thesis, the electromagnetic wave propagation is studied in nonstationary-medium scenarios. The electromagnetic fields under material time-modulation are shown to conserve their momentum but not their energy. The mathematical foundations and analysi ...

EPFL2021

Time- and Angle-Resolved Photoelectron Spectroscopy of Solar Materials

Serhii Polishchuk

Natural foundations defining the manner in which a solid material interacts with optical radiation are primarily encoded in the material's momentum-dependent band structure and the microscopic details of the electron-lattice interactions. An access to this ...

EPFL2021

An Ink–and–Paper Automaton: The Conceptual Mechanization of Cognition and the Practical Automation of Reasoning in Leibniz’s De Affectibus (1679)

Simon François Dumas Primbault

On ten loose handwritten folios dating back from April 1679, Leibniz gradually devised, in the course of three days, a full-blown theory of thought that nonetheless remained unpublished and still has received little attention from scholars. Conceiving of a ...

2020

Tropical Ehrhart Theory and Tropical Volume

Matthias Schymura, Georg Peter Loho

We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes. We exhibit the basic properties and compare it to existing measures. Our exposit ...

2019

Replicating portfolio approach to capital calculation

Mathieu Jacques David Cambou, Damir Filipovic

The replicating portfolio (RP) approach to the calculation of capital for life insurance portfolios is an industry standard. The RP is obtained from projecting the terminal loss of discounted asset–liability cash flows on a set of factors generated by a fa ...

2018