The choice of measures naturally consistent to estimate and exploit the proximity of objects has been at the core of mathematics for thousand years. The information society has seen during the last decade a considerable – and still growing – amount of works around distortion measures that are particularly relevant to major domains of computer science: computational geometry, machine learning and computer vision. These distortions, that belong to a relatively small number of classes of distortion measures, share many properties. Recent works show that they are the foundations for the modeling of many problems for the three domains cited before, and furthermore they guide, explicitly or implicitly, the performances of algorithms that address these problems from many possible standpoints: complexity-theoretic, informational, generalization, noise tolerance, and more. From each of these standpoints, various authors have shown that, for some particular problems, the careful choice of the distortion is the key to optimality. The aim of project GAIA is to foster ideas from representatives of these three communities, to address common problems, around the study of these families of information distortion (or divergence) measures, containing prominent members such as f-divergences and Bregman divergences. More precisely, this research project principally includes four research topics, that cover the whole spectrum of research (from the most fundamental to the standalone applications): -1: learning the distortion and learning the data (self-improvement properties), where the objective is essentially to automatically identify the best possible (aggregation of) divergences to treat a problem, so as to better tackle fundamental problems like overfitting, no free-lunch, high dimensional problems, and problems alike. -2: geometric and algorithmic meta-principles (invariants) for classes of distortions, where the objective is essentially to identify key properties of the divergences that may be responsible for the extension of properties or algorithms, devised for a single divergence, to the largest possible members of some family. -3: lifting of particular algorithms to handle general distortions, where the objective is essentially to carry out this generalization to some particular problems of high relevance for the members' domains, such as Iterative Closest Points and Statistical/Non linear Manifold Reconstruction. -4: using divergences for high dimensional problems (Computer Vision), where the objective is mainly to address object recognition problems that could be better tackled with a careful use of such distortions, from the standpoints of the induction, selection, and combination of features from very large spaces. On each of these topics, the members of GAIA expect to rely on six main standpoints: Algorithms/Data structures, Classification/Machine learning, Convexity, Geometry, Statistics/Information Theory and Vision

The warming of the climate system is unequivocal and continued emission of greenhouse gases will cause further warming and changes. Islands are particularly vulnerable to Climate Change (CC) consequences but the coarse spatial resolution of available projections makes it difficult to derive valid statements for islands. Moreover, science-based information about the economic impacts of CC in marine and maritime sectors is scarce, and current economic models lack of solid non-market assesment. Policy makers must have accurate information about likely impact chains and about the costs and benefits of possible strategies to implement efficient measures. SOCLIMPACT aims at modelling downscaled CC effects and their socioeconomic impacts in European islands for 2030–2100, in the context of the EU Blue Economy sectors, and assess corresponding decarbonisation and adaptation pathways, complementing current available projections for Europe, and nourishing actual economic models with non-market assessment, by: • Developing a thorough understanding on how CC will impact the EU islands located in different regions of the world. • Contributing to the improvement of the economic valuation of climate impacts by adopting revealed and stated preference methods. • Increasing the effectiveness of the economic modelling of climate impact chains, through the implementation of an integrated methodological framework (GINFORS, GEM-E3 and non-market indicators). • Facilitating climate-related policy decision making for Blue Growth, by ranking and mapping the more appropriate mitigation and adaptation strategies. • Delivering accurate information to policy makers, practitioners and other relevant stakeholders. SOCLIMPACT addresses completely this Work Programme providing advances in the economic valuation of climate-induced impacts, and in climate and economic models, allowing downscaled projections of complex impact chains, and facilitating the resilience capacity of these vulnerable lands.