55 research outputs found

    On simple arrangements of lines and pseudo-lines in P^2 and R^2 with the maximum number of triangles

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    We give some new advances in the research of the maximum number of triangles that we may obtain in a simple arrangements of n lines or pseudo-lines.Comment: 12 pages, 9 figure

    Algorithm MGB to solve highly nonlinear elliptic PDEs in O~(n)\tilde{O}(n) FLOPS

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    We introduce Algorithm MGB (Multi Grid Barrier) for solving highly nonlinear convex Euler-Lagrange equations. This class of problems includes many highly nonlinear partial differential equations, such as pp-Laplacians. We prove that, if certain regularity hypotheses are satisfied, then our algorithm converges in O~(1)\tilde{O}(1) damped Newton iterations, or O~(n)\tilde{O}(n) FLOPS, where the tilde indicates that we neglect some polylogarithmic terms. This the first algorithm whose running time is proven optimal in the big-O~\tilde{O} sense. Previous algorithms for the pp-Laplacian required O~(n)\tilde{O}(\sqrt{n}) damped Newton iterations or more

    Efficient algorithms for solving the p-Laplacian in polynomial time

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    The pp-Laplacian is a nonlinear partial differential equation, parametrized by p[1,]p \in [1,\infty]. We provide new numerical algorithms, based on the barrier method, for solving the pp-Laplacian numerically in O(nlogn)O(\sqrt{n}\log n) Newton iterations for all p[1,]p \in [1,\infty], where nn is the number of grid points. We confirm our estimates with numerical experiments.Comment: 28 pages, 3 figure

    Partitions of Pearson’s Chi-square statistic for frequency tables:a comprehensive account

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    Sharp condition number estimates for the symmetric 2-lagrange multiplier method

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    Inverting Regional Sensitivity Analysis to reveal sensitive model behaviors

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    We address the question of sensitivity analysis for model outputs of any dimension using Regional Sensitivity Analysis (RSA). Classical RSA computes sensitivity indices related to the impact of model inputs variations on the occurrence of a target region of the model output space. In this work, we invert this perspective by proposing to find, for a given target model input, the region whose occurrence is best explained by the variations of this input. When it exists, this region can be seen as a model behavior which is particularly sensitive to the variations of the model input under study. We name this method iRSA (for inverse RSA). iRSA is formalized as an optimization problem using region-based sensitivity indices and solved using dedicated numerical algorithms. Using analytical and numerical examples, including an environmental model producing time series, we show that iRSA can provide a new graphical and interpretable characterization of sensitivity for model outputs of various dimensions

    Solving large systems on HECToR using the 2-lagrange multiplier methods

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    Comment appuyer les dynamiques collectives au sein des équipes pédagogiques ? Potentiel et limites des dispositifs d'incitation et de soutien dans les établissements d'enseignement supérieur

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    International audienceA partir de 17 études de cas menées dans des universités en France et à l’étranger, ce « point de vue » cherche à étudier comment les dispositifs (ou instruments) d’incitation et de soutien à la transformation pédagogique peuvent appuyer les dynamiques collectives au sein des équipes pédagogiques. Les différents dispositifs observés ont un potentiel significatif pour impulser et soutenir de telles dynamiques de coopération. Dans la pratique cependant, leurs usages se concentrent le plus souvent à l’échelle individuelle, ce qui peut nuire à l’ampleur, la visibilité et la pérennité des transformations pédagogiques visées. En conclusion, 5 hypothèses sont avancées quant aux principaux leviers transversaux qui peuvent être mobilisés pour appuyer des dynamiques collectives à l’échelle des équipes pédagogiques
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