Curves in Hilbert modular varieties

We prove a boundedness-theorem for families of abelian varieties with real multiplication. More generally, we study curves in Hilbert modular varieties from the point of view of the Green Griffiths-Lang conjecture claiming that entire curves in complex projective varieties of general type should be contained in a proper subvariety. Using holomorphic foliations theory, we establish a Second Main Theorem following Nevanlinna theory. Finally, with a metric approach, we establish the strong Green-Griffiths-Lang conjecture for Hilbert modular varieties up to finitely many possible exceptions.Comment: Final version, to appear in Asian J. Mat

Compact leaves of codimension one holomorphic foliations on projective manifolds

This article studies codimension one foliations on projective man-ifolds having a compact leaf (free of singularities). It explores the interplay between Ueda theory (order of flatness of the normal bundle) and the holo-nomy representation (dynamics of the foliation in the transverse direction). We address in particular the following problems: existence of foliation having as a leaf a given hypersurface with topologically torsion normal bundle, global structure of foliations having a compact leaf whose holonomy is abelian (resp. solvable), and factorization results

L'intelligence existe-t-elle ?

Hors Série la Recherche - Tangente - Spécial logiqueL’intelligence se définit-elle scientifiquement ? Est-elle indépendante de l’apprentissage ? Comment ses différentes formes peuvent-elles être mesurées ? Pourquoi l’activité intellectuelle prolonge-t-elle l’efficacité du cerveau ? En quoi pratiquer jeux et tests rendent-ils plus intelligent ? Autant de réponses apportées par cette excellente introduction à un numéro exceptionnel de La Recherche - Tangent

Modeling and Simulation of Elementary Robot Behaviors using Associative Memories

International audienceToday, there are several drawbacks that impede the necessary and much needed use of robot learning techniques in real applications. First, the time needed to achieve the synthesis of any behavior is prohibitive. Second, the robot behavior during the learning phase is – by definition – bad, it may even be dangerous. Third, except within the lazy learning approach, a new behavior implies a new learning phase. We propose in this paper to use associative memories (self-organizing maps) to encode the non explicit model of the robot-world interaction sampled by the lazy memory, and then generate a robot behavior by means of situations to be achieved, i.e., points on the self-organizing maps. Any behavior can instantaneously be synthesized by the definition of a goal situation. Its performance will be minimal (not necessarily bad) and will improve by the mere repetition of the behavior

Q-learning for Robots

International audienceRobot learning is a challenging – and somewhat unique – research domain. If a robot behavior is defined as a mapping between situations that occurred in the real world and actions to be accomplished, then the supervised learning of a robot behavior requires a set of representative examples (situation, desired action). In order to be able to gather such learning base, the human operator must have a deep understanding of the robot-world interaction (i.e., a model). But, there are many application domains where such models cannot be obtained, either because detailed knowledge of the robot’s world is unavailable (e.g., spatial or underwater exploration, nuclear or toxic waste management), or because it would be to costly. In this context, the automatic synthesis of a representative learning base is an important issue. It can be sought using reinforcement learning techniques – in particular Q-learning which does not require a model of the robot-world interaction. Compared to supervised learning, Q-learning examples are triplets (situation, action, Q value), where the Q value is the utility of executing the action in the situation. The supervised learning base is obtained by recruiting the triplets with the highest utility

Robot Awareness in Cooperative Mobile Robot Learning

International audienceMost of the straight-forward learning approaches in cooperative robotics imply for each learning robot a state space growth exponential in the number of team members. To remedy the exponentially large state space, we propose to investigate a less demanding cooperation mechanism—i.e., various levels of awareness—instead of communication. We define awareness as the perception of other robots locations and actions. We recognize four different levels (or degrees) of awareness which imply different amounts of additional information and therefore have different impacts on the search space size (Θ(0), Θ(1), Θ(N), o(N),1 where N is the number of robots in the team). There are trivial arguments in favor of avoiding binding the increase of the search space size to the number of team members. We advocate that, by studying the maximum number of neighbor robots in the application context, it is possible to tune the parameters associated with a Θ(1) increase of the search space size and allow good learning performance. We use the cooperative multi-robot observation of multiple moving targets (CMOMMT) application to illustrate our method. We verify that awareness allows cooperation, that cooperation shows better performance than a purely collective behavior and that learned cooperation shows better results than learned collective behavior

Singular foliations with trivial canonical class

This paper describes the structure of singular codimension one foliations with numerically trivial canonical bundle on projective manifolds

The Theory of Neural Cognition Applied to Robotics

International audienceThe Theory of neural Cognition (TnC) states that the brain does not process information, it only represents informa‐ tion (i.e., it is 'only' a memory). The TnC explains how a memory can become an actor pursuing various goals, and proposes explanations concerning the implementation of a large variety of cognitive abilities, such as attention, memory, language, planning, intelligence, emotions, motivation, pleasure, consciousness and personality. The explanatory power of this new framework extends further though, to tackle special psychological states such as hypnosis, the placebo effect and sleep, and brain diseases such as autism, Alzheimer's disease and schizophrenia. The most interesting findings concern robotics: because the TnC considers the cortical column to be the key cognitive unit (instead of the neuron), it reduces the requirements for a brain implementation to only 160,000 units (instead of 86 billion). A robot exhibiting human-like cognitive abilities is therefore within our reach

Une version feuilletée d'un théorème de Bogomolov

9 pagesOn compact Kähler manifolds, we classify regular holomorphic foliations of codimension 1 whose canonical bundle is numerically trivial