We propose to extend the concept of private information retrieval by allowing for distortion in the retrieval process and relaxing the perfect privacy requirement at the same time. In particular, we study the trade-off between download rate, distortion, and user privacy leakage, and show that in the limit of large file sizes this trade-off can be captured via a novel information-theoretical formulation for datasets with a known distribution. Moreover, for scenarios where the statistics of the dataset is unknown, we propose a new deep learning framework by leveraging a generative adversarial network approach, which allows the user to learn efficient schemes from the data itself. We evaluate the performance of the scheme on a synthetic Gaussian dataset as well as on the MNIST, CIFAR-10, and LSUN datasets. For the MNIST, CIFAR-10, and LSUN datasets, the data-driven approach significantly outperforms a nonlearning-based scheme which combines source coding with the download of multiple files.

This specific morphology gives rise to several catchments with steep slopes and limited extension [1]. Autumn events, when deep Atlantic troughs more easily enter the Mediterranean area and activate very moist and unstable flow lifted by the mountain range, may determine catastrophic flood on these coastal areas characterized by a high population density (see [2, 3] for a review of climatology and typical atmospheric configurations of extreme precipitations over the Mediterranean area). Just as an example, the November 4th 2011 flood in Genoa determined six deaths and economic damages up to 100 million euros [4, 5, 6, 7]). A common feature in these extreme events are the presence of a quasi-stationary convective system with a spatial extension of few kilometers [8, 9, 10, 11, 12] Medium and long range either deterministic or ensemble Numerical Weather Prediction (NWP) models still struggle to correctly predict both the intensity and the location of these events, which can be triggered and enhanced by very small-scale features. High resolution convection-permitting NWP models manage to partly return a more realistic description of the dynamics of severe thunderstorms. Many studies addressed the role played by different components or settings of NWP models in order to better describe severe convective systems over the Liguria area, such as model resolution, initial conditions, microphysics schemes or small-scale patterns of the sea surface temperature ([6, 13, 14, 15, 16, 17, 18, 17, 19]).

In this article, we prove the completeness of the following game search algorithms: unbounded best-first minimax with completion and descent with completion, i.e. we show that, with enough time, they find the best game strategy. We then generalize these two algorithms in the context of perfect information multiplayer games. We show that these generalizations are also complete: they find one of the equilibrium points.