305 research outputs found
Convergence rates of Gibbs measures with degenerate minimum
We study convergence rates for Gibbs measures, with density proportional to
, as where admits a unique global minimum at . We focus on the case
where the Hessian is not definite at . We assume instead that the
minimum is strictly polynomial and give a higher order nested expansion of
at , which depends on every coordinate. We give an algorithm yielding
such a decomposition if the polynomial order of is no more than ,
in connection with Hilbert's problem. However, we prove that
the case where the order is 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
where is the solution to some stochastic differential equation and is a
test function. The new estimator is , where and
have same marginal law as but are pathwise correlated so that to
reduce the variance. The optimal correlation function is approximated by
a deep neural network and is calibrated along the trajectories of
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 particuliÚrement 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
âLa littĂ©rature, câest la mise en forme dâun dĂ©sirâ
Dans cet entretien, Annie Ernaux revient sur lâimportance quâa pour elle la sociologie, notamment celle de Pierre Bourdieu, et montre comment le travail littĂ©raire se distingue, et doit ĂȘtre distinguĂ©, des Ă©crits 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 hiĂ©rarchisĂ©e du monde social et lui permet aussi dâexprimer la rĂ©alitĂ© occultĂ©e de ce dernier. Ernaux insiste : elle part de cette rĂ©alitĂ© pour atteindre le rĂ©el, et cette dĂ©marche se fait par des voies propres Ă la littĂ©rature ; malgrĂ© lâexistence de concepts et de thĂ©matiques communs entre littĂ©rature et sciences sociales, il faut ĂȘtre conscient de la spĂ©cificitĂ© de la littĂ©rature et de la façon dont sâarticule lâĂ©criture par rapport Ă la thĂ©orie. En somme, rester dans ce qui est le plus probable, dans la rĂšgle gĂ©nĂ©rale sociologique, lorsquâon Ă©crit de la fiction ou autres textes Ă visĂ©e littĂ©raire, ce nâest pas faire de la littĂ©rature. Au-delĂ des questions dâĂ©criture, Ernaux revient sur dâautres questions de sociologie, notamment sur le fait que lâon reproduit dans le champ littĂ©raire la position que lâon a dans la vie.In this interview, Annie Ernaux reminds us of the importance of sociology for her own writing, in particular Bourdieuâs 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 littĂ©raire) 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
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