Abstract
This paper presents a comparative study of the performance of arithmetic and geometric means as rules to combine multiple classifiers. For problems with two classes., we prove that these combination rules are equivalent when using two classifiers and the sum of the estimates of the a posteriori probabilities is equal to one. We also prove that the case of a two class problem and a combination of two classifiers is the only one where such equivalence occurs. We present experiments illustrating the equivalence of the rules under the above mentioned assumptions.

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Abstract
We give an elementary proof of existence and uniqueness of Gibbs states for Holder weight systems on subshifts of finite type. This uses a notion of duality for such subshifts. The approach of Paterson [2] is used to construct a measure with a prescribed Jacobian and the duality is used to produce an invariant measure from this.

Abstract
In this article we show how the accuracy of a rule based first order theory may be increased by combining it with a case-based approach in a classification task. Case-based learning is used when the rule language bias is exhausted. This is achieved in an iterative approach. In each iteration theories consisting of first order rules are induced and covered examples are removed. The process stops when it is no longer possible to find rules with satisfactory quality. The remaining examples are then handled as cases. The case-based approach proposed here is also, to a large extent, new, Instead of only storing the cases as provided, it has a learning phase where, for each case, it constructs and stores a set of explanations with support and confidence above given thresholds. These explanations have different levels of generality and the maximally specific one corresponds to the case itself The same case may have different explanations representing different perspectives of the case. Therefore, to classify a new case, it looks for relevant stored explanations applicable to the new case. The different possible views of the case given by the explanations correspond to considering different sets of conditions/features to analyze the case. In other words, they lead to different ways to compute similarity between known cases/explanations and the new case to be classified (as opposed to the commonly used global metric). Experimental results have been obtained on a corpus of Portuguese texts for the task of part-of-speech tagging with significant improvement.

Abstract
RAMSYS is a web-based infrastructure for collaborative data mining. It is being developed in the SolEuNet European Project for virtual enterprise services in data mining and decision support. Central to RAMSYS is the idea of sharing the current best understanding to foster efficient collaboration. This paper presents the design and rationale of Zeno, a core component of RAMSYS. Zeno is a groupware for discourses on the Internet and, for RAMSYS, aims to provide a “virtual data mining laboratory” to aid data miners in collaboratively producing better solutions to data mining problems. © Springer-Verlag Berlin Heidelberg 2001.

Abstract
This paper presents some aspects of the production, characterization and implementation of fibre Bragg grating as a key element for selective filtering in optical communications. Theory, fabrications and applications of the Fibre Bragg grating for a specific tuneable optical add-drop multiplexer (OADM) are presented. The OADM performance on a 2.48832 Gbit/s dense wavelength division multiplexing optical communications system with 95 km is reported. The power penalty for the removed channels was less than 0.1 dB. We obtain good agreement between the FBG behaviour the OADM performance with the numerical simulations results. Copyright SBMO.