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Borel-Wadge degrees

Alessandro AndrettaDonald A. Martin — 2003

Fundamenta Mathematicae

Two sets of reals are Borel equivalent if one is the Borel pre-image of the other, and a Borel-Wadge degree is a collection of pairwise Borel equivalent subsets of ℝ. In this note we investigate the structure of Borel-Wadge degrees under the assumption of the Axiom of Determinacy.

Belief functions induced by multimodal probability density functions, an application to the search and rescue problem

P.-E. DoréA. MartinI. Abi-ZeidA.-L. JousselmeP. Maupin — 2010

RAIRO - Operations Research - Recherche Opérationnelle

In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension . We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two...

Belief functions induced by multimodal probability density functions, an application to the search and rescue problem

P.-E. DoréA. MartinI. Abi-ZeidA.-L. JousselmeP. Maupin — 2011

RAIRO - Operations Research

In this paper, we propose a new method to generate a continuous belief functions from a multimodal probability distribution function defined over a continuous domain. We generalize Smets' approach in the sense that focal elements of the resulting continuous belief function can be disjoint sets of the extended real space of dimension . We then derive the continuous belief function from multimodal probability density functions using the least commitment principle. We illustrate the approach on two...

A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations

Martin A. GreplAnthony T. Patera — 2005

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we extend the reduced-basis methods and associated a posteriori error estimators developed earlier for elliptic partial differential equations to parabolic problems with affine parameter dependence. The essential new ingredient is the presence of time in the formulation and solution of the problem – we shall “simply” treat time as an additional, albeit special, parameter. First, we introduce the reduced-basis recipe – Galerkin projection onto a space W N spanned by solutions of the...

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