Evaluation of automatic speech recognition (ASR) systems is difficult and costly, since it requires manual transcriptions. This evaluation is usually done by computing word error rate (WER) that is the most popular metric in ASR community. Such computation is doable only if the manual references are available, whereas in the real-life applications, it is a too rigid condition. A reference-free metric to evaluate the ASR performance is \textit{confidence measure} which is provided by the ASR decoder. However, the confidence measure is not always available, especially in commercial ASR usages. Even if available, this measure is usually biased towards the decoder. From this perspective, the confidence measure is not suitable for comparison purposes, for example between two ASR systems. These issues motivate the necessity of an automatic quality estimation system for ASR outputs. This thesis explores ASR quality estimation (ASR QE) from different perspectives including: feature engineering, learning algorithms and applications. From feature engineering perspective, a wide range of features extractable from input signal and output transcription are studied. These features represent the quality of the recognition from different aspects and they are divided into four groups: signal, textual, hybrid and word-based features. From learning point of view, we address two main approaches: i) QE via regression, suitable for single hypothesis scenario; ii) QE via machine-learned ranking (MLR), suitable for multiple hypotheses scenario. In the former, a regression model is used to predict the WER score of each single hypothesis that is created through a single automatic transcription channel. In the latter, a ranking model is used to predict the order of multiple hypotheses with respect to their quality. Multiple hypotheses are mainly generated by several ASR systems or several recording microphones. From application point of view, we introduce two applications in which ASR QE makes salient improvement in terms of WER: i) QE-informed data selection for acoustic model adaptation; ii) QE-informed system combination. In the former, we exploit single hypothesis ASR QE methods in order to select the best adaptation data for upgrading the acoustic model. In the latter, we exploit multiple hypotheses ASR QE methods to rank and combine the automatic transcriptions in a supervised manner. The experiments are mostly conducted on CHiME-3 English dataset. CHiME-3 consists of Wall Street Journal utterances, recorded by multiple far distant microphones in noisy environments. The results show that QE-informed acoustic model adaptation leads to 1.8\% absolute WER reduction and QE-informed system combination leads to 1.7% absolute WER reduction in CHiME-3 task. The outcomes of this thesis are packed in the frame of an open source toolkit named TranscRater -transcription rating toolkit- (https://github.com/hlt-mt/TranscRater) which has been developed based on the aforementioned studies. TranscRater can be used to extract informative features, train the QE models and predict the quality of the reference-less recognitions in a variety of ASR tasks.

In this Ph.D. thesis we discuss results concerning variational convergences for functionals and differential operators on Lipschitz continuous vector fields. The convergences taken into account are gamma-convergence (for functionals) and H-convergence (for differential operators).

Electromagnetism and optimal control stand out as a topics that feature impactful applications in modern engineering, as well as challenging theoretical aspects of mathematical analysis. Within this context, a major role is played by the search of necessary and sufficient conditions characterizing optimal solutions, as they are functional to numerical algorithms aiming to approximate such solutions. In this thesis, three standalone topics in optimization sharing the underlying framework of Maxwell-related PDEs are discussed. First, I present an optimal control problem driven by a quasi-linear magneto-static obstacle problem featuring first-order differential state constraints. The non-linearity allows to suitably model electromagnetic waves in the presence of ferromagnetic materials, while the first-order obstacle is relevant for applications in the field of magnetic shielding. Existence theory and the derivation of an optimality system are addressed with an approximation technique based on a relaxation-penalization of the variational inequality. Second, I analyze an eddy current problem controlled through a dipole type source, i.e. a Dirac mass with fixed position and variable intensity: well-posedness of the state equation through a fundamental solution (of a curl curl - Id operator) approach and first order conditions are dealt with. To conclude, I discuss the computation of the topological derivative for shape functionals constrained to low-frequency electromagnetic problems (closely related to the eddy current model), with respect to the inclusion/removal of conducting material; the results are obtained using a Lagrangian approach and in particular the so-called averaged adjoint method. This approach requires the study of the asymptotic behavior of the solutions of some problems defined in the whole space, and the introduction and consequent analysis of appropriate function spaces.

This dissertation is divided into three different parts. In the first part we analyse collected data on the occurrence of influenza-like illness (ILI) symptoms regarding the 2009 influenza A/H1N1 virus pandemic in two primary schools of Trento, Italy. These data were used to calibrate a discrete-time SIR model, which was designed to estimate the probabilities of influenza transmission within the classes, grades and schools using Markov Chain Monte Carlo (MCMC) methods. We found that the virus was mainly transmitted within class, with lower levels of transmission between students in the same grade and even lower, though not significantly so, among different grades within the schools. We estimated median values of R0 from the epidemic curves in the two schools of 1.16 and 1.40; on the other hand, we estimated the average number of students infected by the first school case to be 0.85 and 1.09 in the two schools. This discrepancy suggests that household and community transmission played an important role in sustaining the school epidemics. The high probability of infection between students in the same class confirms that targeting within-class transmission is key to controlling the spread of influenza in school settings and, as a consequence, in the general population. In the second part, by starting from a basic host-parasitoid model, we study the dynamics of a 2 hosts-1 parasitoid model assuming, for the sake of simplicity, that larval stages have a fixed duration. If each host is subjected to density-dependent mortality in its larval stage, we obtain explicit conditions for coexistence of both hosts, as long as each 1 host-parasitoid system would tend to an equilibrium point. Otherwise, if mortality is density-independent, under the same conditions host coexistence is impossible. On the other hand, if at least one of the 1 host-parasitoid systems has an oscillatory dynamics (which happens under some parameter values), we found, through numerical bifurcation, that coexistence is favoured. It is also possible that coexistence between the two hosts occurs even in the case without density-dependence. Analysis of this case has been based on methods of approximation of the dominant characteristic multipliers of the monodromy operator using a recent method introduced by Breda et al. Models of this type may be relevant for modelling control strategies for Drosophila suzukii, a recently introduced fruit fly that caused severe production losses, based on native parasitoids of indigenous fruit flies. In the third part, we present a starting point to analyse raw data collected by Stacconi et al. in the province of Trento, Italy. We present an extensions of the model presented in Part 2 where we have two hosts and two parasitoids. Since its analysis is complicated, we begin with a simpler one host-one parasitoid model to better understand the possible impact of parasitoids on a host population. We start by considering that the host population is at an equilibrium without parasitoids, which are then introduced as different percentages of initial adult hosts. We compare the times needed by parasitoids to halve host pupae and we found that the best percentage choice is 10%. Thus we decide to fix this percentage of parasitoid introduction and analyse what happens if parasitoids are introduced when the host population is not at equilibrium both by introducing always the same percentage or the same amount of parasitoids. In this case, even if the attack rate is at 1/10 of its maximum value, parasitoids would have a strong effect on host population, shifting it to an oscillatory regime. However we found that this effect would require more than 100 days but we also found that it can faster if parasitoids are introduced before the host population has reached the equilibrium without parasitoids. Thus there could be possible releases when host population is low. Last we investigate also what happens if in nature mortality rates of these species increase and we found that there is not such a big difference respect to the results obtained using laboratory data.

Firstly, I proposed a very simple SIS/SIR model for a general vector-borne disease transmission considering constant population sizes over the season, where contact between the host and the vector responsible of the transmission is assumed to occur only during the summer of each year. I discussed two different types of threshold for pathogen persistence that I explicitly computed: a "short-term threshold" and a "long-term threshold". Later, I took into account the seasonality of the populations involved in the transmission. For a single season, the model consists of system of non linear differential equations considering the various stages of the infection transmission between the vector and the host population. Assuming the overwintering in the mosquito populations, I simulated the model for several years. Finally, I studied the spatial spread of a vector-borne disease throught an impusive reaction-diffusion model and I showed some simulations.

As recently shown in laboratory bench scale experiments, chemotaxis, i.e.the movement of microorganisms toward or away from the concentration gradient of a chemical species, could have a fundamental role in the transport of bacteria through saturated porous media. Chemotactic bacteria could enhance bioremediation by directing their own motions to residual contaminants in less conductive zones in aquifers. The aim of the present work is to develop a proper numerical scheme to define and to quantify the magnitude and the role of chemotaxis in the complex groundwater system framework. We present a new class of meshless Lagrangian particle methods based on the Smooth Particle Hydrodinamics (SPH) formulation of Vila & Ben Moussa, combined with a new Weighted Essentially Non-Oscillatory (WENO) reconstruction technique on moving point clouds in multiple space dimensions. The purpose of this new scheme is to fully exploit the advantages of SPH among traditional meshbased and meshfree schemes and to overcome its inapplicability for modeling chemotaxis in porous media. The key idea is to produce for each particle first a set of high order accurate Moving Least Squares (MLS) reconstructions on a set of different reconstruction stencils. Then, these reconstructions are combined with each other using a nonlinear WENO technique in order to capture at the same time discontinuities and to maintain accuracy and low numerical dissipation in smooth regions. The numerical fluxes between interacting particles are subsequently evaluated using this MLS-WENO reconstruction at the midpoint between two particles, in combination with a Riemann solver that provides the necessary stabilization of the scheme based on the underlying physics of the governing equations. We propose the use of two different Riemann solvers: the Rusanov flux and an Osher-type flux. The use of monotone fluxes together with a WENO reconstruction ensures accuracy, stability, robustness and an essentially non oscillatory solution without the artificial viscosity term usually employed in conventional SPH schemes. To our knowledge, this is the first time that the WENO method, which has originally been developed for mesh-based schemes in the Eulerian framework on fixed grids, is extended to meshfree Lagrangian particle methods like SPH in multiple space dimensions. In the first part, we test the new algorithm on two dimensional blast wave problems and on the classical one-dimensional Sod shock tube problem for the Euler equations of compressible gas dynamics. We obtain a good agreement with the exact or numerical reference solution in all cases and an improved accuracy and robustness compared to existing standard SPH schemes. In the second part, the new SPH scheme is applied to advection-diffusion equation in heterogeneous porous media with anisotropic diffusion tensor. Several numerical test case shows that the new scheme is accurate. Unlike standard SPH, it reduces the occurrence of negative concentration. In the third part, we show the applicability of the new scheme for modeling chemotaxis in porous media. We test the new scheme against analytical reference solutions. Under the assumption of complete mixing at the Darcy scale, we perform different two-dimensional conservative solute transport simulations under steady-state conditions with instant injection showing that chemotaxis significantly affect the quantification of field-scale mixing processes.

The works presented in this thesis are very different one from the other but they all deal with the mathematical modelling of emerging infectious diseases which, beyond being the leitmotiv of this thesis, is an important research area in the field of epidemiology and public health. A minor but significant part of the thesis has a theoretical flavour. This part is dedicated to the mathematical analysis of the competition model between two HIV subtypes in presence of vaccination and cross-immunity proposed by Porco and Blower (1998). We find the sharp conditions under which vaccination leads to the coexistence of the strains and using arguments from bifurcation theory, draw conclusions on the equilibria stability and find that a rather unusual behaviour of histeresis-type might emerge after repeated variations of the vaccination rate within a certain range. The most of this thesis has been inspired by real outbreaks occurred in Italy over the last 10 years and is about the modelling of the 1999-2000 H7N1 avian influenza outbreak and of the 2009-2010 H1N1 pandemic influenza. From an applied perspective, parameter estimation is a key part of the modelling process and in this thesis statistical inference has been performed within both a classical framework (i.e. by maximum likelihood and least square methods) and a Bayesian setting (i.e. by Markov Chain Monte Carlo techniques). However, my contribution goes beyond the application of inferential techniques to specific case studies. The stochastic, spatially explicit, between-farm transmission model developed for the transmission of the H7N1 virus has indeed been used to simulate different control strategies and asses their relative effectiveness. The modelling framework presented here for the H1N1 pandemic in Italy constitutes a novel approach that can be applied to a variety of different infections detected by surveillance system in many countries. We have coupled a deterministic compartmental model with a statistical description of the reporting process and have taken into account for the presence of stochasticity in the surveillance system. We thus tackled some statistical challenging issues (such as the estimation of the fraction of H1N1 cases reporting influenza-like-illness symptoms) that had not been addressed before. Last, we apply different estimation methods usually adopted in epidemiology to real and simulated school outbreaks, in the attempt to explore the suitability of a specific individual-based model at reproducing empirically observed epidemics in specific social contexts.

In this thesis we analyze the relationship between epidemiology and network theory, starting from the observation that the viral propagation between interacting agents is determined by intrinsic characteristics of the population contact network. We aim to investigate how a particular network structure can impact on the long-term behavior of epidemics. This field is way too large to be fully discussed; we limit ourselves to consider networks that are partitioned into local communities, in order to incorporate realistic contact structures into the model. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals infect those belonging to the same community with higher probability than individuals in other communities. We describe the epidemic process as a continuous-time individual-based susceptible–infected–susceptible (SIS) model using a first-order mean-field approximation, both in homogeneous and in heterogeneous setting. For this mean-field model we show that the spectral radius of the smaller quotient graph, in connection with the infecting and curing rates, is related to the epidemic threshold, and it gives conditions in order to decide whether the overall healthy-state defines a globally asymptotically stable or an unstable equilibrium. Moreover we show that above the threshold another steady-state exists that can be computed using a lower-dimensional dynamical system associated with the evolution of the process on the quotient graph. Our investigations are based on the graph-theoretical notion of equitable partition and of its recent and rather flexible generalization, that of almost equitable partition. We also consider the important issue related to the control of the infectious disease. Taking into account the connectivity of the network, we provide a cost-optimal distribution of resources to prevent the disease from persisting indefinitely in the population; for a particular case of two-level immunization problem we report on the construction of a polynomial time complexity algorithm. In the second part of the thesis we include stochasticity in the model, considering the infection rates in the form of independent stochastic processes. This allows us to get stochastic differential equation for the probability of infection in each node. We report on the existence of the solution for all times. Moreover we show that there exist two regions, given in terms of the coefficients of the model, one where the system goes to extinction almost surely, and the other where it is stochastic permanent.

From industrial revolution to the present day, fossil fuels are the main sources for ensuring energy supply. Fossil fuel usages have negative effects on environment that are highlighted by several local or international policy initiatives at support of the big energy transition. The effects urge energy planners to integrate renewable energies into the corresponding energy systems. However, large-scale incorporation of renewable energies into the systems is difficult because of intermittent behaviors, limited availability and economic barriers. It requires intricate balancing among different energy producing resources and the syringes among all the major energy sectors. Although it is possible to evaluate a given energy scenario (complete set of parameters describing a system) by using a simulation model, however, identifying optimal energy scenarios with respect to multiple objectives is a very difficult to accomplished. In addition, no generalized optimization framework is available that can handle all major sectors of an energy system. In this regards, we propose a complete generalized framework for identifying scenarios with respect to multiple objectives. The framework is developed by coupling a multi-objective evolutionary algorithm and EnergyPLAN. The results show that the tool has the capability to handle multiple energy sectors together; moreover, a number of optimized trade-off scenarios are identified. Furthermore, several improvements are proposed to the framework for finding better-optimized scenarios in a computationally efficient way. The framework is applied on two different real-world energy system optimization problems. The results show that the framework is capable to identify optimized scenarios both by considering recent demands and by considering projected demands. The proposed framework and the corresponding improvements make it possible to provide a complete tool for policy makers for designing optimized energy scenarios. The tool can be able to handle all major energy sectors and can be applied in short and long-term energy planning.

This thesis deals with the classical problem of prime numbers represented by polynomials. It consists of three parts. In the first part I collected many results about the problem. Some of them are quite recent and this part can be considered as a survey of the state of the art of the subject. In the second part I present two results due to P. Pleasants about the cubic polynomials with integer coefficients in several variables. The aim of this part is to simplify the works of Pleasants and modernize the notation employed. In such a way these important theorems are now in a more readable form. In the third part I present some original results related with some algebraic invariants which are the key-tools in the works of Pleasants. The hidden diophantine nature of these invariants makes them very difficult to study. Anyway some results are proved. These results make the results of Pleasants somewhat more effective.