Publications associées à Problèmes du prix du millénaire

Hands-on tasks make learning visible: a learning analytics lens on the development of mechanistic problem-solving expertise in makerspaces

Richard Lee Davis, Bertrand Roland Schneider

This study investigated the impact of participating in a year-long digital-fabrication course on high-school seniors' problem-solving skills, with a focus on problems involving mechanistic systems. The research questions centered on whether working in a ma ...

Springer2023

The double exponential runtime is tight for 2-stage stochastic ILPs

Kim-Manuel Klein, Klaus Jansen, Alexandra Anna Lassota

We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage stochastic ILP is an integer program of the form min{c(T)x vertical bar Ax = ...

SPRINGER HEIDELBERG2022

Continuation Methods For Riemannian Optimization

Daniel Kressner, Axel Elie Joseph Séguin

Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target function on a Riemann ...

SIAM PUBLICATIONS2022

Knapsack and Subset Sum with Small Items

Adam Teodor Polak, Lars Rohwedder

Knapsack and Subset Sum are fundamental NP-hard problems in combinatorial optimization. Recently there has been a growing interest in understanding the best possible pseudopolynomial running times for these problems with respect to various parameters. In t ...

Schloss Dagstuhl -- Leibniz-Zentrum für Informatik2021

Global Frobenius liftability I

Maciej Emilian Zdanowicz

We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo p(2)-we expect that such varieties, after a finite stale cover, admit a toric fibration over an ordinary abelian v ...

2021

Atomistic modeling of the solid-liquid interface of metals and alloys

Edoardo Baldi

Solidification is a phase transformation of utmost importance in material science, for it largely controls materials' microstructure on which a wide range of mechanical properties depends. Almost every human artifact undergoes a transformation that leads t ...

EPFL2020

Stationary Structures near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations

Klaus Martin Widmayer

We study the behavior of solutions to the incompressible 2d Euler equations near two canonical shear flows with critical points, the Kolmogorov and Poiseuille flows, with consequences for the associated Navier-Stokes problems. We exhibit a large family of ...

2020

Constraint-aware neural networks for Riemann problems

Jan Sickmann Hesthaven, Deep Ray

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtai ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks

Jan Sickmann Hesthaven, Niccolo' Discacciati, Deep Ray

High-order numerical solvers for conservation laws suffer from Gibbs phenomenon close to discontinuities, leading to spurious oscillations and a detrimental effect on the solution accuracy. A possible strategy to reduce it comprises adding a suitable amoun ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

On the asymptotic behavior of the solutions to parabolic variational inequalities

Maria Colombo

We consider various versions of the obstacle and thin-obstacle problems, we interpret them as variational inequalities, with non-smooth constraint, and prove that they satisfy a new constrained Lojasiewicz inequality. The difficulty lies in the fact that, ...

2020