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The mathematical background of proving processes in discrete optimization - Exemplification with Research Situations for the Classroom
No full textInternational audienceDiscrete mathematics brings interesting problems for teaching and learning proof, with accessible objects such as integers (arithmetic), graphs (modeling, order) or polyominoes (geometry). Many problems that are still open can be explained to a large public. The objects can be manipulated by simple dynamic operations (removing, adding, ‘gluing’, contracting, splitting, decomposing, etc.). All these operations can be seen as tools for proving. In this paper we particularly explore the field of ‘discrete optimization’. A theoretical background is defined by taking two main axes into account, namely, the epistemological analysis of discrete problems studied by contemporary researchers in discrete optimization and the design of adidactical situations for classrooms in the frame of the Theory of Didactical Situations. Two problems coming from ongoing research in discrete optimization (the Pentamino Exclusion and the Eight Queens problems) are developed and transposed for the classroom. They underscore the learning potentialities of discrete mathematics and epistemological obstacles concerning proving processes. They emphasize the understanding of a necessary condition and a sufficient condition and problematize the difference between optimal and optimum. They provide proofs involving partitioning strategies, greedy algorithms but also primal–dual methods leading to the concept of duality. The way such problems can be implemented in the classroom is described in a collaborative study by mathematicians and mathematics education researchers (Maths à Modeler Research Federation) through the Research Situations for the Classroom project
Phase Field Model for Brittle Fracture in Random Heterogeneous Elastic Media: Forward Numerical Simulations and Sensitivity Analysis
No full textInternational audienceWithin the framework of linear elasticity theory and fracture mechanics, this work addresses the forward numerical simulation of a phase field model [1] for brittle fracture in random heterogeneous elastic materials. Such a phase field model is classically parameterized by the fracture toughness (or critical energy release rate in the sense of Griffith) and the regularization parameter (corresponding to the actual width of the smeared/diffusivecrack representation) which are considered as deterministic and homogeneous parameters. At a given mesoscale, the material is considered as random and heterogeneous with apparent elasticity properties. Various classes of stochastic models and associated random generators for non-Gaussian tensor-valued random elasticity fields with statistical fluctuations in a given material symmetry class and in the (purely) anisotropic class have been proposed [2]. In the present work, we focus on two particular classes of stochastic models, namely (i) the class of random elasticity fields exhibiting almost surely isotropic symmetry properties, and (ii) the class of purely anisotropic random elasticity fields with an isotropic mean elasticity field and anisotropic statistical fluctuations (around the isotropic mean function). A sensitivity analysis is carried out to study the influence of the (hyper)parameters of the aforementioned stochastic models on some statistical quantities of interest related to the force-displacement curve for identification purposes. The proposed approach is illustrated on a classical benchmark problem for brittle fracture, namely a two-dimensional single-edge notched/cracked specimen under pure shear loading.REFERENCES[1] J.-Y. Wu, V.P. Nguyen, C.T. Nguyen, D. Sutula, S. Sinaie, and S.P.A. Bordas. Chapter One - Phase-field modeling of fracture. volume 53 of Advances in Applied Mechanics, pages 1–183. Elsevier, 2020.[2] C. Soize. Uncertainty Quantification: An Accelerated Course with Advanced Applications in Computational Engineering, volume 47 of Interdisciplinary Applied Mathematics. Springer International Publishing, 1st edition, 2017
La critique du travail par le courant de la Wertkritik (critique de la valeur)
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Acerca de un manuscrito fantasma. Mollien artifice de un viaje de Caldas a Quito en 1805
No full textAbout Quito field of Archival City Program: Quito, is an unknown city. However, it is the Spanish-American capital that has best preserved its archives. A paradox that must be understood in order to restore its rank to the one that was long considered the second largest city in South America, just behind Lima. Built on a geological fault, Quito is directly threatened by three volcanoes and rainwater runoff. The 1987 earthquake raised awareness in a new way: the architectural and archival heritage has since been the subject of a real rescue policy, under the aegis of UNESCO. However, this celebrated heritage is nowadays prey to identity claims, heritage policies and urban planning plans that are not very concerned about such legacies. There is little consensus on urban modernity, as illustrated by the recent controversy over the construction of the Metro. Quito – the “Light of America” – deserves to be thought about a possible “past future” would allow planners to avoid many of the mistakes made in Mexico City, Lima or Bogotá. Archival City will contribute to this by providing an exhaustive inventory of archives, innovative mapping and reflection on the urban future. Under the coordination of Georges Lomné (Gustave Eiffel University, France), a large group of researchers are participating in this ambition. They are attached to the best research centers of the city: mainly the University of San Francisco in Quito (coordination: Carlos Espinosa, USFQ) and the Andean University Simon Bolivar, headquarters of Quito (coordination: Guillermo Bustos, UASB).International audienc
L'hétérogénéité entre les établissements de l'enseignement supérieur et de la recherche
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Posterior probabilistic learning constrained by stochastic PDE and experimental statistical moments of physics observations
No full textInvited LectureInternational audienceWe consider a stochastic boundary value problem (SBVP) on a bounded domain of the three-dimensional space for which the unknown state is the random field Y. The partial differential equation of this SBVP depends on an uncontrolled non-Gaussian tensor-valued random field, G, and on a controlled vector-valued random parameter, W. We also consider a random vector O = obs(Y,G,W) of physics observations. It is assumed that are given the prior non-Gaussian probability model of G and W and experimental targets represented by a vector b of statistical moments E{h(O)} of random vector O (such as the mean vector and a global dispersion parameter). We are interested in estimating the posterior probability model of G and W given the target b. Such a problem belongs to the class of statistical inverse problems and is generally solved by using the maximum likelihood or Bayesian approaches. In the present framework, such statistics methodologies cannot be used for the following reasons. (1) The numerical cost of one evaluation of the stochastic computational model (SCM) that discretizes the SBVP is very high. Consequently, the SCM can only be called a small number of times. (2) The problem is non-Gaussian and is in very high dimension. (3) The experimental realizations of random observation O are unknown; only statistical moments of O, represented by vector b = E{h(O)}, are given as targets. Consequently maximum likelihood and Bayesian methodologies cannot be used. For solving this challenging problem, we propose an approach that can be briefly summarized as follows. (i) A training set having a small number of points is constructed using the SCM: given a realization (g,w) of (G,W) using the prior probability model, the SBVP is solved for computing the corresponding realization y of Y and then the realization o = obs(y,g,w) of O is deduced. (ii) A formulation of an optimization problem based on the Kullback-Leibler minimum cross-entropy principle is proposed for constructing the posterior probability model under the constraint defined by the targets E{h(O)} = b and by the constraint consisting in minimizing the norm of the random residue of the SBVP. (iii) This optimization problem is solved by using a probabilistic learning method from the training set under the introduced constraints. As an application, we present the stochastic homogenization of a 3D random anisotropic elastic medium with uncertain spectrum for which observation O is the reshaping of the fourth-order effective elasticity tensor, C, at macroscale. We consider the case for which there is no scale separation, yielding C as a random tensor
Faut-il continuer à utiliser les catégories écologiques de vers de terre définies par Marcel Bouché il y a 50 ans ? : une vision historique et critique
No full textThe earthworm ecological categories defined by Marcel Bouché between 1971 and 1977 were successful and universally adopted. However, two silent shifts can be detected about their use. The first shift is that most of the authors forgot that the three main categories (anecic, endogeic and epigeic) were indeed the three poles of a ternary plot between which all the existing species should be placed. This is the reason why, intermediate categories were used by Marcel Bouché (epi-anecic, endo-anecic and endo-epigeic and intermediate, i.e. in the centre of the ternary plot). This first shift made a categorical representation out of a continuous world and this leaded to difficulties in assigning accurately some earthworm species. The second shift is the use of ecological categories as functional groups, something Marcel Bouché never did since he never intended to describe the effects of earthworms on their environment. The consequences of these shifts are discussed. In conclusion, we recommend to (i) read the seminal papers (however written in French), (ii) use the intermediate ecological categories in order to better describe the characteristics (and their variability) of earthworm species and (iii) not use the term « functional group » for ecological categories.Las categorías ecológicas de lombrices definidas por Marcel Bouché para las lombrices franceses entre 1971 y 1977 tuvieron un suceso mundial y están ahora utilizadas por todos los autores de todos los continentes. Sin embargo, en la literatura científica pueden detectarse dos cambios de sentido y de uso. El primero es que la mayoría de los autores olvidaron que según Marcel Bouché, las categorías anécicas, epigeas y endogeas no son 3 polos entre los cuales todas las demás especies se proyectan,razón por la que utilizaba categorías intermedias (epi-endogea, epi-anécica, endo-anécica e intermedia). Así pasamos de una visión continua a una visión discreta, lo que plantea problemas para asignar ciertas especies de lombriz. El segundo cambio es que se utilizaron las categorías cada vez más como sinónimo de grupo funcional. Este cambio es problemático porque las categorías definidas por Marcel Bouché nunca tuvieron por objeto describir los efectos de las lombrices sobre su ecosistema. Se discuten las implicaciones de estos cambios. Por otra parte, recomendamos (i) volver a los textos originales, (ii) utilizar las categorías intermedias (o porcentajes de pertenencia a las 3 clases principales) para describir mejor las características de las especies de lombrices y (iii) no utilizar el término «grupo funcional» para hablar de las categorías ecológicas de lombrices.Les catégories écologiques de vers de terre définies par Marcel Bouché sur les vers de terre français entre 1971 et 1977 ont eu un succès mondial et sont maintenant utilisées par tous les auteurs de tous les continents. Cependant, deux glissements de sens et d'usage peuvent être décelés dans la littérature scientifique. Le premier est que la plupart des auteurs ont oublié que selon Marcel Bouché, les catégories anécique, épigée et endogée ne sont que 3 pôles entre lesquels toutes les autres espèces se projettent, raison pour laquelle il utilisait des catégories intermédiaires (épi-endogée, épi-anécique, endo-anécique et intermédiaire). On est donc passé d'une vision continue à une vision discrète, ce qui pose des problèmes pour assigner certaines espèces de vers de terre. Le second glissement est que les catégories ont de plus en plus souvent été utilisées en synonymie de groupe fonctionnel. Ce glissement est problématique car les catégories définies par Marcel Bouché n'ont jamais eu pour but de décrire les effets des vers de terre sur leur écosystème. Les implications de ces glissements sont discutées. Par ailleurs, nous recommandons (i) de revenir aux textes originels, (ii) d'utiliser les catégories intermédiaires (ou des pourcentages d'appartenance aux 3 classes principales) pour mieux décrire les caractéristiques des espèces de vers et (iii) de ne pas utiliser le terme 'groupe fonctionnel' pour parler des catégories écologiques de vers
Rendre compte de la dégradation des milieux aquatiques. Le rôle des savoirs dans la mise en place des politiques de protection des ressources en eau en Afrique subsaharienne
No full textInternational audienceThis article examines the role that the production of knowledge on the ecological state of aquatic ecosystems plays in the implementation of policies for protecting these environments, used for water supply. Based on interdisciplinary research carried out in two sub-Saharan countries (Côte d'Ivoire and Senegal) by a team of sociologists and ecologists, the article shows how expert knowledge of environmental quality assessment interacts with the local actors, existing management structures and with local representations of these environments. Through this interdisciplinary approach, we question the difficulties of integrating a diversity of points of view on water resources. We highlight the obstacles, uncertainties and controversies linked with the production of expertise and its integration into existing management systems. More specifically, we describe the main challenges for institutionalizing long-term monitoring of the water resources (Aquatic Ecosystems Observatories). We also discuss the possibilities and the interest for integrating expert and local knowledge for co-constructing a shared diagnosis.Cet article questionne le rôle de la production des savoirs sur l’état écologique des milieux dans la gestion et la mise en oeuvre de politiques de surveillance et de protection des ressources en eau utilisées pour la production d’eau potable en Afrique subsaharienne. Sur la base d’une recherche interdisciplinaire réalisée en Côte d’Ivoire et au Sénégal par une équipe comprenant des sociologues et des écologues, l’article montre comment des savoirs experts d’évaluation de la qualité des milieux interagissent avec les jeux d’acteurs, les structures de gestion existantes et les représentations locales de ces mêmes milieux. Nous interrogeons à travers cette approche interdisciplinaire les difficultés d’articulation de la diversité de points de vue sur les ressources en eau, ainsi que les freins, les incertitudes et controverses autour de la production de savoirs et de leur intégration dans des dispositifs de gestion. Nous analysons plus particulièrement les principaux défis pour la mise en place des suivis de l’état écologique des milieux aquatiques, ainsi que les possibles contributions des savoirs experts et locaux à la co-construction d’un diagnostic partagé
Fracture behavior of a composite of bone and calcium sulfate/hydroxyapatite
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Correction: Crenn et al. Influence of Anodized Titanium Surfaces on the Behavior of Gingival Cells in Contact with: A Systematic Review of In Vitro Studies. Crystals 2021, 11, 1566
No full textInternational audienceIn the original article [...