From the Farkas Lemma to the Hahn–Banach Theorem

This paper provides new versions of the Farkas lemma characterizing those inequalities of the form f(x) ≥ 0 which are consequences of a composite convex inequality (S ◦ g)(x) ≤ 0 on a closed convex subset of a given locally convex topological vector space X, where f is a proper lower semicontinuous convex function defined on X, S is an extended sublinear function, and g is a vector-valued S-convex function. In parallel, associated versions of a stable Farkas lemma, considering arbitrary linear perturbations of f, are also given. These new versions of the Farkas lemma, and their corresponding stable forms, are established under the weakest constraint qualification conditions (the so-called closedness conditions), and they are actually equivalent to each other, as well as equivalent to an extended version of the so-called Hahn–Banach–Lagrange theorem, and its stable version, correspondingly. It is shown that any of them implies analytic and algebraic versions of the Hahn–Banach theorem and the Mazur–Orlicz theorem for extended sublinear functions.

Application of Text Summarization techniques to the Geographical Information Retrieval task

Automatic Text Summarization has been shown to be useful for Natural Language Processing tasks such as Question Answering or Text Classification and other related fields of computer science such as Information Retrieval. Since Geographical Information Retrieval can be considered as an extension of the Information Retrieval field, the generation of summaries could be integrated into these systems by acting as an intermediate stage, with the purpose of reducing the document length. In this manner, the access time for information searching will be improved, while at the same time relevant documents will be also retrieved. Therefore, in this paper we propose the generation of two types of summaries (generic and geographical) applying several compression rates in order to evaluate their effectiveness in the Geographical Information Retrieval task. The evaluation has been carried out using GeoCLEF as evaluation framework and following an Information Retrieval perspective without considering the geo-reranking phase commonly used in these systems. Although single-document summarization has not performed well in general, the slight improvements obtained for some types of the proposed summaries, particularly for those based on geographical information, made us believe that the integration of Text Summarization with Geographical Information Retrieval may be beneficial, and consequently, the experimental set-up developed in this research work serves as a basis for further investigations in this field.

New methodology for describing the equilibrium beach profile applied to the Valencia's beaches

Mathematical models used for the understanding of coastal seabed morphology play a key role in beach nourishment projects. These projects have become the fundamental strategy for coastal maintenance during the last few years. Accordingly, the accuracy of these models is vital to optimize the costs of coastal regeneration projects. Planning of such interventions requires methodologies that do not generate uncertainties in their interpretation. A study and comparison of mathematical simulation models of the coastline is carried out in this paper, as well as elements that are part of the model that are a source of uncertainty. The equilibrium profile (EP) and the offshore limit corresponding to the depth of closure (DoC) have been analyzed taking into account different timescale ranges. The results have thus been compared using data sets from three different periods which are identified as present, past and future. Accuracy in data collection for the beach profiles and the definition of the median grain size calculation using collected samples are the two main factors that have been taken into account in this paper. These data can generate high uncertainties and can produce a lack of accuracy in nourishment projects. Together they can generate excessive costs due to possible excess or shortage of sand used for the nourishment. The main goal of this paper is the development of a new methodology to increase the accuracy of the existing equilibrium beach profile models, providing an improvement to the inputs used in such models and in the fitting of the formulae used to obtain seabed shape. This new methodology has been applied and tested on Valencia's beaches.