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Showing 1 to 6 of 6 for “"Settore MATH-03/B - Probabilità e statistica matematica"”.
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Advanced Statistical Inference for Stochastic Quasi-Reaction Systems
Quasi-reaction systems are often modelled with stochastic differential equations in order to capture the inherent randomness of their dynamics. The traditional local linear approximation methods for the estimation of the reaction rates face significant challenges in certain conditions. When the …
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NETWORKS OF GROUP EQUIVARIANT NON-EXPANSIVE OPERATORS FOR ARTIFICIAL INTELLIGENCE. MODELS, APPLICATIONS AND INTERPRETABILITY.
… explainable by design. In this context, the mathematical theory of Group Equivariant Non-Expansive Operators (GENEOs) has all the credentials to be at the base of a new generation of ML models with desirable geometric properties. This thesis aims to support this claim by investigating GENEO …
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BRIDGING INTERPRETABILITY AND PERFORMANCE IN 3D DEEP LEARNING THROUGH GEOMETRIC INDUCTIVE BIASES
Questa tesi indaga come i geometric inductive biases possano risolvere limitazioni fondamentali nel deep learning 3D, in particolare per applicazioni critiche di sicurezza come l’ispezione delle reti elettriche. Nonostante i progressi significativi nel campo del 3D scene understanding, la maggior …
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ADVANCES IN MEAN-FIELD OPTIMAL CONTROL VIA DYNAMIC PROGRAMMING EQUATIONS
… sullo spazio di Wasserstein delle misure di probabilità di momento secondo finito P2(Rd). In questa tesi, la buona positura di tale equazione in senso viscoso è sempre analizzata direttamente sullo spazio di Wasserstein; non ricorriamo pertanto al lifting dell'equazione su uno spazio di …
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MODELLING AND NUMERICAL STUDY OF MARBLE SULPHATION IN CULTURALE HERITAGE: A RANDOM PDE-ODE SYSTEM
… a numerical point of view a new approach to the mathematical modelling of the degradation process in the context of Cultural Heritage, focusing on the description of the marble sulphation chemical reaction. Our contribution is a numerical analysis of a novel random model of the sulphation …
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COARSE CORRELATED EQUILIBRIA IN CONTINUOUS-TIME MEAN FIELD GAMES
Mean field games (MFGs), an active theme of research since the mid 2000's, arise as the limit formulation of symmetric N-player games with mean field interactions, and they act as a treatable approximation of such games, when the numbers of players is large enough. The usual notion of MFG solution …