Convergence rates of Gibbs measures with degenerate minimum

We study convergence rates for Gibbs measures, with density proportional to $e^{-f(x)/t}$, as $t \rightarrow 0$ where $f : \mathbb{R}^d \rightarrow \mathbb{R}$ admits a unique global minimum at $x^\star$. We focus on the case where the Hessian is not definite at $x^\star$. We assume instead that the minimum is strictly polynomial and give a higher order nested expansion of $f$ at $x^\star$, which depends on every coordinate. We give an algorithm yielding such a decomposition if the polynomial order of $x^\star$ is no more than $8$, in connection with Hilbert's $17^{\text{th}}$ problem. However, we prove that the case where the order is $10$ or higher is fundamentally different and that further assumptions are needed. We then give the rate of convergence of Gibbs measures using this expansion. Finally we adapt our results to the multiple well case.Comment: 25 page

Policy Gradient Optimal Correlation Search for Variance Reduction in Monte Carlo simulation and Maximum Optimal Transport

We propose a new algorithm for variance reduction when estimating $f(X_T)$ where $X$ is the solution to some stochastic differential equation and $f$ is a test function. The new estimator is $(f(X^1_T) + f(X^2_T))/2$, where $X^1$ and $X^2$ have same marginal law as $X$ but are pathwise correlated so that to reduce the variance. The optimal correlation function $\rho$ is approximated by a deep neural network and is calibrated along the trajectories of $(X^1, X^2)$ by policy gradient and reinforcement learning techniques. Finding an optimal coupling given marginal laws has links with maximum optimal transport.Comment: 7 page

Simulation of Reflected Brownian motion on two dimensional wedges

We study a correlated Brownian motion in two dimensions, which is reflected, stopped or killed in a wedge represented as the intersection of two half spaces. First, we provide explicit density formulas, hinted by the method of images. These explicit expressions rely on infinite oscillating sums of Bessel functions and may demand computationally costly procedures. We propose suitable recursive algorithms for the simulation of the laws of reflected and stopped Brownian motion which are based on generalizations of the reflection principle in two dimensions. We study and give bounds for the complexity of the proposed algorithms.Comment: 36 page

De l'espace-temps dans l'analyse du discours

International audienceThis paper describes a dynamic approach to discourse interpretation that focusses on computing the spatio-temporal structure of texts. The theoretical framework is Segmented Discourse Representation Theory, an extension of DRT which accounts for both discourse semantics and pragmatics. It is shown that several components are necessary in the interpretation process. These components model information about: discourse (rhetorical) structure, grammatical semantics, lexical semantics, space-time ontology, and extra-linguistic background knowledge. To illustrate the approach, texts describing trajectories in French are analyzed and their Segmented Discourse Representation Structures are built.Cet article décrit une approche dynamique de l'interprétation du discours qui s'intéresse plus particulièrement au calcul de la structure spatio-temporelle des textes. Le cadre théorique choisi est la Théorie des Représentations Discursives Structurées, une extension de la DRT qui rend compte à la fois de la sémantique et de la pragmatique du discours. On montre que plusieurs composants sont nécessaires au processus d'interprétation. Ces composants modélisent des informations sur : la structure (rhétorique) des discours, la sémantique grammaticale, la sémantique lexicale, l'ontologie de l'espace-temps et la connaissance extra-linguistique sur le monde. Afin d'illustrer cette approche, des textes décrivant des trajectoires en français sont analysés et leurs représentations (dénommées SDRS, pour structures de représentation du discours segmentées, en anglais) sont construites

“La littérature, c’est la mise en forme d’un désir”

Dans cet entretien, Annie Ernaux revient sur l’importance qu’a pour elle la sociologie, notamment celle de Pierre Bourdieu, et montre comment le travail littéraire se distingue, et doit être distingué, des écrits de sciences sociales. Ernaux pense en termes de sociologie et utilise sciemment le lexique de la sociologie, ce qui lui permet de ne pas reproduire dans ses textes la vision hiérarchisée du monde social et lui permet aussi d’exprimer la réalité occultée de ce dernier. Ernaux insiste : elle part de cette réalité pour atteindre le réel, et cette démarche se fait par des voies propres à la littérature ; malgré l’existence de concepts et de thématiques communs entre littérature et sciences sociales, il faut être conscient de la spécificité de la littérature et de la façon dont s’articule l’écriture par rapport à la théorie. En somme, rester dans ce qui est le plus probable, dans la règle générale sociologique, lorsqu’on écrit de la fiction ou autres textes à visée littéraire, ce n’est pas faire de la littérature. Au-delà des questions d’écriture, Ernaux revient sur d’autres questions de sociologie, notamment sur le fait que l’on reproduit dans le champ littéraire la position que l’on a dans la vie.In this interview, Annie Ernaux reminds us of the importance of sociology for her own writing, in particular Bourdieu’s work. Yet she also emphasizes that we ought to distinguish literary work from social sciences writings. Ernaux thinks in terms of sociology and deliberately uses the terminology of sociology, which helps her avoid reproducing the hierarchical stratification of social groups as well as expose a concealed social reality. To do so, however, she uses tools belonging to literature. Although literature and the social sciences share concepts and themes, we need to be aware of the specificity of literature, and pay attention to the specific ways in which literary writing takes theory into account. In short, despite their claim to belong to literature, texts that only reproduce general sociological rules should not be seen as literary works. In addition to issues pertaining to literary writing, Ernaux returns to questions raised by sociology; in particular, the fact that writers often adopt in the literary field (le champ littéraire) the same social position they hold in life

Challenges in Collaborative HRI for Remote Robot Teams

Collaboration between human supervisors and remote teams of robots is highly challenging, particularly in high-stakes, distant, hazardous locations, such as off-shore energy platforms. In order for these teams of robots to truly be beneficial, they need to be trusted to operate autonomously, performing tasks such as inspection and emergency response, thus reducing the number of personnel placed in harm's way. As remote robots are generally trusted less than robots in close-proximity, we present a solution to instil trust in the operator through a `mediator robot' that can exhibit social skills, alongside sophisticated visualisation techniques. In this position paper, we present general challenges and then take a closer look at one challenge in particular, discussing an initial study, which investigates the relationship between the level of control the supervisor hands over to the mediator robot and how this affects their trust. We show that the supervisor is more likely to have higher trust overall if their initial experience involves handing over control of the emergency situation to the robotic assistant. We discuss this result, here, as well as other challenges and interaction techniques for human-robot collaboration.Comment: 9 pages. Peer reviewed position paper accepted in the CHI 2019 Workshop: The Challenges of Working on Social Robots that Collaborate with People (SIRCHI2019), ACM CHI Conference on Human Factors in Computing Systems, May 2019, Glasgow, U