Numerical approximation of BSDEs using local polynomial drivers and branching processes

We propose a new numerical scheme for Backward Stochastic Differential Equations based on branching processes. We approximate an arbitrary (Lipschitz) driver by local polynomials and then use a Picard iteration scheme. Each step of the Picard iteration can be solved by using a representation in terms of branching diffusion systems, thus avoiding the need for a fine time discretization. In contrast to the previous literature on the numerical resolution of BSDEs based on branching processes, we prove the convergence of our numerical scheme without limitation on the time horizon. Numerical simulations are provided to illustrate the performance of the algorithm.Comment: 28 page

Ingénierie pédagogique des systèmes d'enseignement supérieur

Our works are set in the field of higher-education systems pedagogical engineering. Our early works deal with the modeling of university practices. We expressed a conceptual framework for the evolution of acquiring knowledge modules to integrate the acquisition of high-level cognitive skills and professional competencies. Next, we have defined a frame to help define pedagogical scenarios more formally. The challenge was to get pedagogical scenarios that favored a higher pedagogical expressiveness compared to existing standards such as IMS-Learning Design (IMS-LD), while begin formal enough to be implemented, at least semi-automatically, on different e-learning platforms. This approach was validated thanks to the Assistance for Contextualized MoDeling of learning systems (ACoMoD) method. Finally, we developed a project-based learning pedagogical method, Multi-Role Project, applied to the teaching of Science, Technology, Engineering, and Mathematics (STEM). One goal is to project our results in Massive Open Online Courses (MOOC), which raise challenges of their ownNos travaux s'inscrivent dans le domaine de l'ingénierie pédagogique des systèmes d'enseignement supérieur. Nos premiers travaux se sont portés sur la modélisation des pratiques universitaires. Nous avons ainsi dégagé un cadre conceptuel d’évolution d’acquisition de connaissances disciplinaires en vue d'intégrer l’acquisition de compétences cognitives professionnelles et de haut niveau. Ensuite, nous avons travaillé à définir un cadre de définition de scénarios pédagogiques plus formel. L'enjeu était d'obtenir des scénarios pédagogiques qui permettent une expressivité pédagogique qui dépasse celle des standards existants tels IMS-Learning Design (IMS-LD) tout en étant suffisamment formalisé pour se prêter à un traitement informatique et être implémenté, au moins semi automatiquement, dans différentes plateformes de e-learning. Cette approche a été validée en utilisant la méthode Assistance for Contextualized MoDeling of learning systems (ACoMoD). Enfin nous développons une méthode de pédagogie par projet, Multi-Rôles Project, autour des problématiques de l'enseignement en Science, Technology, Engineering, and Mathematics (STEM). Un des buts est de projeter nos résultats dans l'implémentation des Massive Open Online Courses (MOOC) qui pose des défis particuliers

Numerical approximation of general Lipschitz BSDEs with branching processes

We extend the branching process based numerical algorithm of Bouchard et al. [3], that is dedicated to semilinear PDEs (or BSDEs) with Lipschitz nonlinearity, to the case where the nonlinearity involves the gradient of the solution. As in [3], this requires a localization procedure that uses a priori estimates on the true solution, so as to ensure the well-posedness of the involved Picard iteration scheme, and the global convergence of the algorithm. When, the nonlinearity depends on the gradient, the later needs to be controlled as well. This is done by using a face-lifting procedure. Convergence of our algorithm is proved without any limitation on the time horizon. We also provide numerical simulations to illustrate the performance of the algorithm

Les images non pathologiques et incidentalomes en IRM du genou ( une étude transversale sur 500 examens)

Lors de l interprétation d une IRM de genou, on peut rencontrer un certain nombre d images non pathologiques ou à la limite entre une variante de la normale et le pathologique, et sans rapport apparent avec la symptomatologie du patient. Cette étude rétrospective sur 500 examens réalisés au CHU d Amiens a pour but de faciliter l interprétation des examens d IRM de genou en pratique courante par une meilleure connaissance et reconnaissance de ces images. Nous avons donc répertorié de la façon la plus exhaustive possible ces images qui ont été préalablement définies à l aide d une étude bibliographique. Nous en avons calculé la prévalence, la répartition par sexe, l âge moyen au diagnostic, la répartition en fonction de la présence ou non d un épanchement, ainsi que les dimensions et le volume moyens. Nous en avons aussi précisé le contexte pathologique. Ensuite, nous avons procédé à des tests de corrélation sur l ensemble des images non pathologiques retrouvées, concernant le sexe, l âge, la présence d un épanchement et les six gammes diagnostiques principales retenues (normal, ligament/tendon, ménisque, arthrose, fracture/contusion osseuse et inflammatoire). L ensemble des résultats a été confronté aux données de la littérature. Globalement, ils sont plutôt concordants, si ce n est que certaines de nos prévalences sont parfois supérieures car notre étude concerne des examens d IRM sur genoux symptomatiques très souvent pathologiques avec des images non pathologiques ou incidentalomes parfois liés à une pathologie. De plus, notre étude est plus récente que celles de la littérature, avec environ un tiers d examens réalisés sur une machine à 3 Tesla, présentant une résolution supérieure. Les tests de corrélation sont également concordants avec les données actuelles des connaissances médicales, si ce n est que d après notre étude, un genou inflammatoire serait un facteur protecteur vis-à-vis des enostoses et que les bourses prétibiales seraient favorisées par les lésions méniscales. Pour conclure, notre étude a effectivement atteint son but en permettant une meilleure connaissance et reconnaissance de ces images en pratique quotidienne des examens d IRM du genou.Throughout our review of knee MRI series, we have encountered numerous incidental findings that were considered non pathological or borderline but not apparently related to the patient s main symptomatology. We decided to conduct a retrospective analytic study of 500 knee MR exams performed in the Amiens university centre hospital with an aim to simplify the images interpretation in daily practice through better knowledge and recognition of these fortuitous findings. We have hence listed these findings in the most comprehensive way possible following a bibliographic database review of their definitions. Then, we determined the prevalence, gender distribution, mean age at presentation, distribution according to the coexistence or not of a joint effusion, as well as the dimensions and mean volume. The pathological setting was again specified. We subsequently proceeded to a statistical correlation analysis of all studied incidental images with gender, age, joint effusion presence and six main diagnostic headings (normal, meniscus, tendons & ligaments, degeneration, inflammation and bony contusions/fractures). Our results were compared to literature data. They were roughly concordant on the whole, were it not for occasional higher prevalence encountered in our study which dealt with symptomatic patients with often pathological knees. Our study is also comparatively more recent with about a third of the exams conducted on a 3T magnet yielding higher image resolution. Furthermore, some findings previously reported as incidental may have been misperceived as such with our study suggesting inflammation may serve a protective role against enostoses formation, at the same time meniscal lesions may boost the possibility of associated pretibial bursitis. As a conclusion, we think this study has achieved its goal by allowing a better knowledge and recognition of the various findings encountered during the daily interpretation practice of knee MR exams.AMIENS-BU Santé (800212102) / SudocSudocFranceF

Assistance To Project-Based Learning Support: From Learning Models To Platforms

International audienceFor the research domain we study, Technology Enhanced Learning Systems (TELS), these systems do not consider pedagogical and computer science aspects be unrelated. One of the teachers' major objectives is to define the way of designing, adapting or choosing the accurate platform to support the pedagogy they need to implement. Therefore our work aims to propose an approach to help the teachers to choose a platform of e-learning and deploy their lessons according to the objectives of a Project-Based Collaborative Learning (PBCL) framework. We focused on the choice and adaptation strategy rather than on the design development aspects. In this publication, we define an MDA based approach in order to establish a methodological framework of our research project and therefore meet with our objectives. We will also report on our research progress and propose a state of our work in PBCL modeling

Projet en milieu universitaire : vers une gestion collaborative assistée par le Web

Cet article présente une méthodologie de gestion de projets étudiants assistée par le Web. Cette méthodologie met en œuvre les principes d’une pédagogie active collaborative. Elle est proposée aux étudiants de filières universitaires professionnalisées ainsi qu’à leurs tuteurs sous forme de kits. Le site Web mis en place par les étudiants assure la communication entre les différents membres du projet. Nous pensons que les étudiants soumis à cette méthodologie accroissent leur niveau de compétence en gestion de projet, ce que devrait bientôt vérifier une expérimentation en cours

Assistance To Project-Based Learning Support: From Learning Models To Platforms

International audienceFor the research domain we study, Technology Enhanced Learning Systems (TELS), these systems do not consider pedagogical and computer science aspects be unrelated. One of the teachers' major objectives is to define the way of designing, adapting or choosing the accurate platform to support the pedagogy they need to implement. Therefore our work aims to propose an approach to help the teachers to choose a platform of e-learning and deploy their lessons according to the objectives of a Project-Based Collaborative Learning (PBCL) framework. We focused on the choice and adaptation strategy rather than on the design development aspects. In this publication, we define an MDA based approach in order to establish a methodological framework of our research project and therefore meet with our objectives. We will also report on our research progress and propose a state of our work in PBCL modeling

Living Persona Technique applied to HCI Education

International audienceThis paper aims to present an experience report on a new pedagogical technique which applies to the teaching of interactive systems: the Living Persona technique. First, we review the well-known technique of Persona that is used in some processes of realization of interactive systems. In this technique, a Persona represents an archetype of the users interacting in the system to be produced. From this Persona technique, we define the Living Persona one. Within the framework of practical work students have to specify an interactive system, this technique of Living Persona consists in making the teacher play the role of a representative of the contracting authority, who is also potentially a future user of the system to be specified. As a consequence, during his meetings with the students, the teacher has to adopt a behavior in compliance with the state of mind of the users' archetype defined by the Persona. Then we present a pedagogical scenario which integrates this Living Persona technique and we apply it to a practical work in which the students must produce an interactive system specification using the Unified Modeling Language (UML). We show through a classroom experience that the practical work set up provides students with work situations close to professional realities. We evaluate the level of interactions between students and teacher and the extent to which this pedagogy influences some students behaviors. Finally, the continuation of our research is highlighted

Projet en milieu universitaire: vers une gestion collaborative assistée par le web

International audienceThis article presents a Web assisted project management methodology that is based on an active collaborative pedagogy. Students in computer science were provided with a Web site that allowed them to communicate with the members of their project. The authors are of the opinion that this collaborative learning experience helped the students develop their skills in project management and conclude that further study should validate their results.Cet article présente une méthodologie de gestion de projets étudiants assistée par le Web. Cette méthodologie met en œuvre les principes d’une pédagogie active collaborative. Elle est proposée aux étudiants de filières universitaires professionnalisées ainsi qu’à leurs tuteurs sous formede kits. Le site Web mis en place par les étudiants assure la communication entre les différents membres du projet. Nous pensons que les étudiants soumis à cette méthodologie accroissent leur niveau de compétence en gestion de projet, ce que devrait bientôt vérifier une expérimentation en cours