55 research outputs found
On simple arrangements of lines and pseudo-lines in P^2 and R^2 with the maximum number of triangles
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 FLOPS
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 -Laplacians. We prove
that, if certain regularity hypotheses are satisfied, then our algorithm
converges in damped Newton iterations, or FLOPS,
where the tilde indicates that we neglect some polylogarithmic terms. This the
first algorithm whose running time is proven optimal in the big-
sense. Previous algorithms for the -Laplacian required
damped Newton iterations or more
Efficient algorithms for solving the p-Laplacian in polynomial time
The -Laplacian is a nonlinear partial differential equation, parametrized
by . We provide new numerical algorithms, based on the
barrier method, for solving the -Laplacian numerically in Newton iterations for all , where is the number of
grid points. We confirm our estimates with numerical experiments.Comment: 28 pages, 3 figure
Inverting Regional Sensitivity Analysis to reveal sensitive model behaviors
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
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
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
- …