The goal of the project is to build an experimental platform for validating the correctness of analog and mixed-signal circuits, a component of increasing importance for the functioning of modern embedded system. The platform will combine the technologies currently being developed by the partners : an efficient and physically-accurate simulator for large analog and mixed-signal circuits and the methods for covering the state space of such circuits by input signals. The project will be composed of the following 3 activities : - Development of search-based methods for validating large-scale continuous and hybrid systems - Development of numerical analysis techniques for non-smooth dynamical systems - Development of simulation-based validation tools (including generation of circuit equations from high-level models, optimization, etc.)

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 aim of the project is to realize a modeling environment dedicated to Markov models. One part will develop the Perfect Simulation techniques, which allow to sample from the stationary distribution of the process. A second one will develop parallelization techniques for Monte Carlo simulation. A third one will develop numerical computation techniques for a wide class of Markov models. All these developments will be integrated into a programming environment allowing the specification of models and their solution strategy. Several applications will be studied in various scientific disciplines: physics, biology, economics, network engineering.