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Controller Synthesis for Timeline-based Games
No full textIn the timeline-based approach to planning, the evolution over time of a setof state variables (the timelines) is governed by a set of temporalconstraints. Traditional timeline-based planning systems excel at theintegration of planning with execution by handling temporal uncertainty. Inorder to handle general nondeterminism as well, the concept of timeline-basedgames has been recently introduced. It has been proved that finding whether awinning strategy exists for such games is 2EXPTIME-complete. However, aconcrete approach to synthesize controllers implementing such strategies ismissing. This paper fills this gap, by providing an effective andcomputationally optimal approach to controller synthesis for timeline-basedgames.Comment: arXiv admin note: text overlap with arXiv:2209.1031
Complex ODEs, singularity theory and dynamics
No full textThese notes are a slightly enlarged version of my habilitation thesis, whereour research interest and main results in the past few years are summarized.Most of the discussion revolves around complex ordinary differential equationsand their underling foliations, singularity theory and dynamical systems.Compared to the original text, a section containing some background material onholomorphic foliations was added. Also some new results obtained in the pastthree years that are in line with the one presented in the habilitation wereincluded
L’analyse de réseaux pour l’étude des coopérations intergouvernementales : le cas du Bureau International d’Éducation (1929-1958)
No full textThis report of the thesis "Recommending utopia? A construction of an intergovernmental cooperation by the International Bureau of Education (IBE) in the middle of the 20th century" (Brylinski, 2022), focuses on the use of network analysis to study intergovernmental cooperation in education. The first part sets out the research questions and the data collected. The second describes how network analyses were applied to the Bulletins and to the Minutes published by the IBE. Then, the third part exposes the results obtained, to illustrate how these techniques are useful to study the staging of States, their interactions and cooperation strategies. Network analysis is thus a relevant method to analyze how governments contributed to the construction of the cause which lied at the heart of the cooperation project, namely peace education. This approach makes it possible to improve our understanding of the circulation and co-construction of knowledge within the framework of an intergovernmental organization and the production of international education recommendations.Ce compte rendu de la thèse "Recommander l’utopie ? Construction d’une coopération intergouvernementale par le Bureau International d’Éducation (BIE) au milieu du 20e siècle" (Brylinski, 2022) porte sur l’intérêt de mobiliser les techniques d’analyse de réseaux pour étudier la coopération intergouvernementale en éducation. La première partie expose les questions de recherche et les données récoltées. La seconde décrit comment l’analyse de réseaux est appliquée aux Bulletins et aux Procès-verbaux publiés par le BIE. Puis, la troisième restitue les résultats obtenus pour illustrer comment ces techniques permettent d’étudier des mises en scène d’États, leurs interactions et stratégies de coopération pour faire-valoir ou marginaliser certains savoirs. Ainsi, l’analyse de réseaux est une méthode pertinente pour révéler comment se construit la cause qui réside au cœur du projet de coopération, à savoir l’éducation pacifique, lorsqu’elle est saisie par des gouvernements. Cette démarche permet d’améliorer notre compréhension de la circulation et la co-construction de savoirs dans le cadre d’une organisation intergouvernementale et de la production des recommandations internationales de l’éducation
Situations pour l'apprentissage de la preuve en mathématiques
No full textResearch on the epistemic, logical, and discursive complexity of proof learning has generated a wealth of literature over the past two decades. The results contribute to a more precise understanding of the difficulties encountered by students and those encountered by teachers. They support the design of situations, especially validation situations in the sense of the Theory of Didactical Situations (TDS—Brousseau, 1998), in which proof is a problem-solving tool. However, there remains the difficulty of grasping proof as an object, recognizing its mathematical specificities and institutionalizing it as such. This is the topic of this text. This text complements those given at the Séminaire national de didactique des mathématiques in 2017 and at CORFEM in 2019. The common theme of these three presentations was the learning and the teaching of proof before the introduction of mathematical proof as the canonical form of proof in mathematics. After an introduction recalling the institutional and scientific context, the first part (sections 2 to 4) is devoted to a review of the state of research, taking into account the reports of outstanding work from different approaches. In the second part (section 5), proposals are made to provide a basis for future research. The conclusion considers the issues raised by the need for situation-specific engineering to encourage and support the genesis and recognition of proof norms in the mathematics classroom, prior to the explicit teaching of the introduction of mathematical proof.La investigación sobre la complejidad epistémica, lógica y discursiva del aprendizaje de la demostración ha generado abundante literatura en las dos últimas décadas. Los resultados contribuyen a una comprensión más precisa de las dificultades a que se enfrentan los alumnos y a cuáles se enfrentan los profesores. Estos resultados, refuerzan la utilidad de la noción de situación; en particular de situación de validación en el sentido de la Teoría de las Situaciones Didácticas (TSD – Brousseau, 1998), en las cuales la prueba funciona como una herramienta de resolución de problemas. Sin embargo, sigue existiendo una dificultad de entender la demostración como objeto, reconocer sus especificidades matemáticas e institucionalizarla como tal. Es en este problema en que se centra este texto, que desarrolla los elementos presentados en la 21ª Escuela de Verano de Didáctica de las Matemáticas. Este texto completa las comunicaciones presentadas en el Séminaire national de didactique des mathématiques (2017) y en el CORFEM (2019). El tema común de estas tres presentaciones fue el aprendizaje y la enseñanza de la prueba antes de la introducción de la demostración como forma canónica de prueba en matemáticas. Tras una introducción en la que se recuerda el contexto institucional y científico, la primera parte (secciones 2 a 4) está dedicada a una revisión del estado de la cuestión retomando los relatos de trabajos destacados desde distintos enfoques. La segunda parte (sección 5) presenta propuestas para sentar las bases de futuras investigaciones. La conclusión aborda las cuestiones abiertas por la necesidad de una ingeniería de situaciones específica para fomentar y apoyar la génesis y el reconocimiento de las normas de la prueba en el aula de matemáticas antes de la enseñanza explícita de la demostración.Les recherches sur la complexité épistémique, logique et discursive de l’apprentissage de la preuve ont suscité une abondante littérature au cours des deux dernières décades. Leurs résultats contribuent à une compréhension plus précise des difficultés rencontrées par les élèves et de celles du travail des professeurs. Ils confortent la conception de situations, notamment les situations de validation au sens de la Théorie des situations didactiques (TSD – Brousseau, 1998), dans lesquelles la preuve fonctionne comme outil de résolution de problèmes. Cependant, subsiste la difficulté de saisir la preuve comme objet, pour en reconnaitre les spécificités mathématiques et l’institutionnaliser en tant que telle. C’est sur ce problème que porte ce texte. Ce texte complète ceux des exposés faits au Séminaire national de didactique des mathématiques en 2017 et au CORFEM en 2019. Ces trois exposés avaient pour objet commun l’apprentissage et l’enseignement de la preuve en amont de l’introduction de la démonstration comme forme canonique de preuve en mathématique. Après une introduction rappelant le contexte institutionnel et scientifique, une première partie (sections 2 à 4) est consacrée à un état de la recherche en reprenant les comptes-rendus de travaux marquants relevant de différentes approches, une deuxième partie (section 5) avance des propositions pour constituer une base pour les recherches à venir. La conclusion porte sur les questions ouvertes par le besoin d’ingénieries spécifiques des situations pour susciter et accompagner la genèse et la reconnaissance des normes de la preuve dans la classe de mathématique avant l’enseignement explicite de la démonstration
Towards efficient and reliable utilization of automated data collection: Media scrapers applied to news on climate change
No full textAbstract: Automated data collection provides tempting opportunities for social sciences and humanities studies. Abundant data accumulating in various digital archives allows more comprehensive, timely and cost-efficient ways of harvesting and processing information. While easing or even removing some of the key problems, such as laborious and time-consuming data collection and potential errors and biases related to subjective coding of materials and distortions caused by focus on small samples, automated methods also bring in new risks such as poor understanding of contexts of the data or non-recognition of underlying systematic errors or missing information. Results from testing different methods to collect data describing newspaper coverage of climate change in Finland emphasize that fully relying on automatable tools such as media scrapers has its limitations and can provide comprehensive but incomplete document acquisition for research. Many of these limitations can, however, be addressed and not all of them rely on manual control
Generalized Alternating Projections on Manifolds and Convex Sets
No full textIn this paper, we extend the previous convergence results for the generalizedalternating projection method applied to subspaces in [arXiv:1703.10547] tohold also for smooth manifolds. We show that the algorithm locally behavessimilarly in the subspace and manifold settings and that the same rates areobtained. We also present convergence rate results for when the algorithm isapplied to non-empty, closed, and convex sets. The results are based on afinite identification property that implies that the algorithm after an initialidentification phase solves a smooth manifold feasibility problem. Therefore,the rates in this paper hold asymptotically for problems in which thisidentification property is satisfied. We present a few examples where this isthe case and also a counter example for when this is not
Quasi-positive orbifold cotangent bundles: Pushing further an example by Junjiro Noguchi
No full textIn this work, we investigate the positivity of logarithmic and orbifold cotangent bundles along hyperplane arrangements in projective spaces. We show that a very interesting example given by Noguchi (as early as in 1986) can be pushed further to a very great extent. Key ingredients of our approach are the use of Fermat covers and the production of explicit global symmetric differentials. This allows us to obtain some new results in the vein of several classical results of the literature on hyperplane arrangements. These seem very natural using the modern point of view of augmented base loci, and working in Campana's orbifold category
Identities for subspaces of the Weyl algebra
No full textIn this paper we describe the polynomial identities of degree 4 for a certainsubspace of the Weyl algebra A_1 over an infinite field of arbitrarycharacteristic.Comment: 15 pages. In version 2 proofs were expande
An Analysis of Tennenbaum's Theorem in Constructive Type Theory
No full textTennenbaum's theorem states that the only countable model of Peano arithmetic(PA) with computable arithmetical operations is the standard model of naturalnumbers. In this paper, we use constructive type theory as a framework torevisit, analyze and generalize this result. The chosen framework allows for asynthetic approach to computability theory, exploiting that, externally, allfunctions definable in constructive type theory can be shown computable. Wethen build on this viewpoint, and furthermore internalize it by assuming aversion of Church's thesis, which expresses that any function on naturalnumbers is representable by a formula in PA. This assumption provides for aconveniently abstract setup to carry out rigorous computability arguments, evenin the theorem's mechanization. Concretely, we constructivize several classicalproofs and present one inherently constructive rendering of Tennenbaum'stheorem, all following arguments from the literature. Concerning the classicalproofs in particular, the constructive setting allows us to highlightdifferences in their assumptions and conclusions which are not visibleclassically. All versions are accompanied by a unified mechanization in the Coqproof assistant
An Elementary Construction of Modified Hamiltonians and Modified Measures of 2D Kahan Maps
No full textWe show how to construct in an elementary way the invariant of the KHKdiscretisation of a cubic Hamiltonian system in two dimensions. That is, weshow that this invariant is expressible as the product of the ratios of affinepolynomials defining the prolongation of the three parallel sides of a hexagon.On the vertices of such a hexagon lie the indeterminacy points of the KHK map.This result is obtained analysing the structure of the singular fibres of theknown invariant. We apply this construction to several examples, and we provethat a similar result holds true for a case outside the hypotheses of the maintheorem, leading us to conjecture that further extensions are possible.Comment: 30 pages, 7 figure