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Languages follow many statistical regularities called laws. Perhaps the most popular example is Zipf's law for word frequencies, that relates the frequency of a word with its rank, but other laws have been formulated, such as the law of abbreviation, the law of meaning-distribution, the meaning-frequency law,...and so on (Zipf 1949). About 15 years ago, a family of optimization models was introduced to shed light on the origins of Zipf's law for word frequencies (Ferrer-i-Cancho & Solé 2003, Ferrer-i-Cancho 2005). In that family, language is modelled as a bipartite graph where words connect to meanings and a cost function is defined based on the structure of that graph. A simple Monte Carlo algorithm was used to minimize the cost function while the structure of the graph was allowed to vary. Recently, it has been shown how these models shed light on how children learn words (Ferrer-i-Cancho 2017). The aim of this project is to investigate new versions of these models (e.g., Ferrer-i-Cancho & Vitevitch 2018) in two directions: (1) Providing an efficient implementation of the optimization algorithm. (2) Comparing the statistical properties of the model against the statistical properties of natural communication systems.

The master thesis consists of developing a framework for Group Recommender Systems and investigating the methods for generating recommendations to groups.

This project aims to analyze the prediction capability of Optical Coherence Tomography Angiography (OCTA) images for Diabetes Mellitus (DM) and Diabetic Retinopathy (DR,) in a large high-quality image dataset from previous research projects carried out in the field of Ophthalmology (Fundacio¿ La Marato¿ TV3, Fondo Investigaciones Sanitarias, FIS). OCTA is a newly developed, non-invasive, retinal imaging technique that permits adequate delineation of the perifoveal vascular network. It allows the detection of paramacular areas of capillary non perfusion and/or enlargement of the foveal avascular zone (FAZ), representing an excellent tool for assessment of DR.

We propose to a student or multiple students to work on processing techniques using Deep Learning (Convolutional Neural networks, Generative Adversarial Networks, Semantic Segmentation Networks) to detect and classify marine mammals in photographs and satellite imagery. The computational capacity offered by these new tools will allow the scientific community to better study endangered species and to give an adequate and rapid response to face the current biodiversity crisis.

The goal of this project is to analyze and mitigate bias in collaborative filtering recommender systems.

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