This chapter is build from three 1.5 hours lectures given in Udine in april 2018 on various aspects of Earth's core dynamics. The chapter starts with a short historical note on the discovery of Earth's magnetic field and core (section 1). We then turn to an introduction of magnetohydrodynamics (section 2), introducing and discussing the induction e...
We consider robust power-distance functions that approximate the distance function to a compact set, from a noisy sample. We pay particular interest to robust power-distance functions that are anisotropic, in the sense that their sublevel sets are unions of ellipsoids, and not necessarily unions of balls. Using persistence homology on such power-di...
Nous présentons un dispositif pédagogique transdisciplinaire commun à trois formations de l'Université de Nantes (métiers du livre/métiers du numérique/design). Après une présentation du contexte et du dispositif, nous en problématisons les enjeux à partir d'une question principale : comment amener des étudiant.e.s de cultures et de compétences dif...
This work considers systems described by the heat equation on the interval [0, π] with L^2 boundary controls and it studies the reachable space at some instant τ > 0. The main results assert that this space is generally sandwiched between two Hilbert spaces of holomorphic functions defined on a square in the complex plane and which has [0, π] as on...
Graph databases have received a lot of attention recently as they are particularly useful in many applications such as social networks or for the semantic web. Various languages have emerged to query such graph databases. At the heart of many of those query languages, there is a construction to navigate through the graph which allows some form of r...
We study multiplayer stochastic multi-armed bandit problems in which the players cannot communicate,and if two or more players pull the same arm, a collision occurs and the involved players receive zero reward.Moreover, we assume each arm has a different mean for each player. Let $T$ denote the number of rounds.An algorithm with regret $O((\log T)^...
We investigate and provide new insights on the sampling rule called Top-Two Thompson Sampling (TTTS). In particular, we justify its use for fixed-confidence best-arm identification. We further propose a variant of TTTS called Top-Two Transportation Cost (T3C), which disposes of the computational burden of TTTS. As our main contribution, we provide ...
We propose an expression for the joint density / distribution function for the endpoint of an Ornstein-Uhlenbeck process and its supremum. This law is expressed as an expansion involving parabolic cylinder functions. We obtain this law faster than with a Monte Carol's method. Numerical applications illustrate the interest of this result.
The construction of optimal resultant formulae for polynomial systems is one of the main areas of research in computational algebraic geometry. However, most of the constructions are restricted to formulae for unmixed polynomial systems, that is, systems of polynomials which all have the same support. Such a condition is restrictive, since mixed sy...
This paper is devoted to the study of reflected Stochastic Differential Equationswith jumps when the constraint is not on the paths of the solution but acts on the law of thesolution. This type of reflected equations have been introduced recently by Briand, Elie and Hu[BEH18] in the context of BSDEs, when no jumps occur. In [BCdRGL16], the authors ...
