MIRACLE at Ad-Hoc CLEF 2005: Merging and Combining Without Using a Single Approach

This paper presents the 2005 Miracle’s team approach to the Ad-Hoc Information Retrieval tasks. The goal for the experiments this year was twofold: to continue testing the effect of combination approaches on information retrieval tasks, and improving our basic processing and indexing tools, adapting them to new languages with strange encoding schemes. The starting point was a set of basic components: stemming, transforming, filtering, proper nouns extraction, paragraph extraction, and pseudo-relevance feedback. Some of these basic components were used in different combinations and order of application for document indexing and for query processing. Second-order combinations were also tested, by averaging or selective combination of the documents retrieved by different approaches for a particular query. In the multilingual track, we concentrated our work on the merging process of the results of monolingual runs to get the overall multilingual result, relying on available translations. In both cross-lingual tracks, we have used available translation resources, and in some cases we have used a combination approach.

A Schwarz lemma for Kahler affine metrics and the canonical potential of a proper convex cone

This is an account of some aspects of the geometry of Kahler affine metrics based on considering them as smooth metric measure spaces and applying the comparison geometry of Bakry-Emery Ricci tensors. Such techniques yield a version for Kahler affine metrics of Yau s Schwarz lemma for volume forms. By a theorem of Cheng and Yau, there is a canonical Kahler affine Einstein metric on a proper convex domain, and the Schwarz lemma gives a direct proof of its uniqueness up to homothety. The potential for this metric is a function canonically associated to the cone, characterized by the property that its level sets are hyperbolic affine spheres foliating the cone. It is shown that for an n -dimensional cone, a rescaling of the canonical potential is an n -normal barrier function in the sense of interior point methods for conic programming. It is explained also how to construct from the canonical potential Monge-Ampère metrics of both Riemannian and Lorentzian signatures, and a mean curvature zero conical Lagrangian submanifold of the flat para-Kahler space.

The Proper Generalized Decomposition With Application In Problems Of Dynamics

In this paper we address the new reduction method called Proper Generalized Decomposition (PGD) which is a discretization technique based on the use of separated representation of the unknown fields, specially well suited for solving multidimensional parametric equations. In this case, it is applied to the solution of dynamics problems. We will focus on the dynamic analysis of an one-dimensional rod with a unit harmonic load of frequency (ω) applied at a point of interest. In what follows, we will present the application of the methodology PGD to the problem in order to approximate the displacement field as the sum of the separated functions. We will consider as new variables of the problem, parameters models associated with the characteristic of the materials, in addition to the frequency. Finally, the quality of the results will be assessed based on an example.