Inexact Bregman iteration with an application to Poisson data reconstruction

This work deals with the solution of image restoration problems by an iterative regularization method based on the Bregman iteration. Any iteration of this scheme requires to exactly compute the minimizer of a function. However, in some image reconstruction applications, it is either impossible or extremely expensive to obtain exact solutions of these subproblems. In this paper, we propose an inexact version of the iterative procedure, where the inexactness in the inner subproblem solution is controlled by a criterion that preserves the convergence of the Bregman iteration and its features in image restoration problems. In particular, the method allows to obtain accurate reconstructions also when only an overestimation of the regularization parameter is known. The introduction of the inexactness in the iterative scheme allows to address image reconstruction problems from data corrupted by Poisson noise, exploiting the recent advances about specialized algorithms for the numerical minimization of the generalized Kullback–Leibler divergence combined with a regularization term. The results of several numerical experiments enable to evaluat

An investigation of the object file system and the approximate number system in a non-symbolic arithmetic task

openQuesta tesi riporta la ricerca sperimentale effettuata su un campione di studenti in età prescolare, finalizzata allo studio dei sistemi "object file" e "approximate number" nella risoluzione di compiti aritmetici non simboliciThis thesis reports on the experimental research carried out on a population of pre-school children to investigate the "object file system" and the "approximate number system" in a non-symbolic arithmetic tas

Statistical analysis of oceanographic extreme events

Condizioni ambientali estreme del mare possono avere un forte impatto sulla navigazione e/o sul successo di operazioni di salvataggio. Le tecniche statistiche sono cruciali per quantificare la presenza di eventi estremi e monitorarne variazioni di frequenza e intensità. Gli eventi estremi "vivono" nella coda di una funzione distribuzione di probabilità (PDF), per questo è importante studiare la PDF in punti lontani diverse deviazioni standard dalla media. L’altezza significativa dell’onda (SWH) è il parametro solitamente usato per valutare l’intensità degli stati del mare. L’analisi degli estremi nella coda di una distribuzione richiede lunghe serie temporali per stime ragionevoli della loro intesità e e frequenza. Dati osservativi (i.e. dati storici da boe), sono spesso assenti e vengono invece utilizzate ricostruzioni numeriche delle onde, con il vantaggio che l’analisi di eventi estremi diventa possibile su una vasta area. Questa tesi vuole condurre un’analisi preliminare delle variazioni spaziali dei valori estremi della SWH nel Mediterraneo. Vengono usati dati orari dal modello del Med-MFC (dal portale del CMEMS), una ricostruzione numerica di onde per il Mediterraneo, che sfrutta il modello "WAM Cycle 4.5.4", coprendo il periodo 2006-2018, con risoluzione spaziale 0.042° (~ 4km). In particolare, consideriamo dati di 11 anni (dal 2007 al 2017), concentrandoci sulle regioni del Mar Ionio e del Mar Iberico. La PDF della SWH è seguita piuttosto bene dall’andamento di una curva Weibull a 2 parametri sia durante l’inverno (Gennaio) che durante l’estate (Luglio), con difetti per quanto riguarda il picco e la coda della distribuzione. A confronto, la curva a 3 parametri Weibull Esponenziata sembra essere più appropriata, anche se non è stato trovato un metodo per dimostrare che sia un fit migliore. Alla fine, viene proposto un metodo di stima del rischio basato sul periodo giornaliero di ritorno delle onde più alte di un certo valore di soglia, ritenute pericolose

A singular Riemannian geometry approach to Deep Neural Networks I. Theoretical foundations

Deep Neural Networks are widely used for solving complex problems in several scientific areas, such as speech recognition, machine translation, image analysis. The strategies employed to investigate their theoretical properties mainly rely on Euclidean geometry, but in the last years new approaches based on Riemannian geometry have been developed. Motivated by some open problems, we study a particular sequence of maps between manifolds, with the last manifold of the sequence equipped with a Riemannian metric. We investigate the structures induced trough pullbacks on the other manifolds of the sequence and on some related quotients. In particular, we show that the pullbacks of the final Riemannian metric to any manifolds of the sequence is a degenerate Riemannian metric inducing a structure of pseudometric space, we show that the Kolmogorov quotient of this pseudometric space yields a smooth manifold, which is the base space of a particular vertical bundle. We investigate the theoretical properties of the maps of such sequence, eventually we focus on the case of maps between manifolds implementing neural networks of practical interest and we present some applications of the geometric framework we introduced in the first part of the paper

Predicting toxicity through computers: a changing world

The computational approaches used to predict toxicity are evolving rapidly, a process hastened on by the emergence of new ways of describing chemical information. Although this trend offers many opportunities, new regulations, such as the European Community's 'Registration, Evaluation, Authorisation and Restriction of Chemicals' (REACH), demand that models be ever more robust

Investigating landfill leachate toxicity in vitro: A review of cell models and endpoints

Landfill leachate is a complex mixture characterized by high toxicity and able to contaminate soils and waters surrounding the dumpsite, especially in developing countries where engineered landfills are still rare. Leachate pollution can severely damage natural ecosystems and harm human health. Traditionally, the hazard assessment of leachate is based on physicochemical characterization but the toxicity is not considered. In the last few decades, different bioassays have been used to assess the toxicity of this complex matrix, including human-related in vitro models. This article reviews the cell bioassays successfully used for the risk assessment of leachate and to evaluate the efficiency of toxicity removal of several processes for detoxification of this wastewater. Articles from 2003 to 2018 are covered, focusing mainly on studies that used human cell lines, highlighting the usefulness and adequacy of in vitro models for assessing the hazard involved with exposure to leachate, particularly as an integrative supporting tool for chemical-based risk assessment. Leachate is generally toxic, mutagenic, genotoxic and estrogenic in vitro, and these effects can be measured in the cells exposed to already low concentrations, confirming the serious hazard of this wastewater for human health. Keywords: Landfill leachate, In vitro models, Estrogenicity, Genotoxicity, Human cell line