Quantum Integrability in Non-Linear Sigma Models related to Gauge/String Correspondences

The Thermodynamic Bethe Ansatz analysis is carried out for the extended-CP^N class of integrable 2-dimensional Non-Linear Sigma Models related to the low energy limit of the AdS_4xCP^3 type IIA superstring theory. The principal aim of this program is to obtain further non-perturbative consistency check to the S-matrix proposed to describe the scattering processes between the fundamental excitations of the theory by analyzing the structure of the Renormalization Group flow. As a noteworthy byproduct we eventually obtain a novel class of TBA models which fits in the known classification but with several important differences. The TBA framework allows the evaluation of some exact quantities related to the conformal UV limit of the model: effective central charge, conformal dimension of the perturbing operator and field content of the underlying CFT. The knowledge of this physical quantities has led to the possibility of conjecturing a perturbed CFT realization of the integrable models in terms of coset Kac-Moody CFT. The set of numerical tools and programs developed ad hoc to solve the problem at hand is also discussed in some detail with references to the code.

On the effect of confounding in linear regression models: an approach based on the theory of quadratic forms

The main topic of this thesis is confounding in linear regression models. It arises when a relationship between an observed process, the covariate, and an outcome process, the response, is influenced by an unmeasured process, the confounder, associated with both. Consequently, the estimators for the regression coefficients of the measured covariates might be severely biased, less efficient and characterized by misleading interpretations. Confounding is an issue when the primary target of the work is the estimation of the regression parameters. The central point of the dissertation is the evaluation of the sampling properties of parameter estimators. This work aims to extend the spatial confounding framework to general structured settings and to understand the behaviour of confounding as a function of the data generating process structure parameters in several scenarios focusing on the joint covariate-confounder structure. In line with the spatial statistics literature, our purpose is to quantify the sampling properties of the regression coefficient estimators and, in turn, to identify the most prominent quantities depending on the generative mechanism impacting confounding. Once the sampling properties of the estimator conditionally on the covariate process are derived as ratios of dependent quadratic forms in Gaussian random variables, we provide an analytic expression of the marginal sampling properties of the estimator using Carlson’s R function. Additionally, we propose a representative quantity for the magnitude of confounding as a proxy of the bias, its first-order Laplace approximation. To conclude, we work under several frameworks considering spatial and temporal data with specific assumptions regarding the covariance and cross-covariance functions used to generate the processes involved. This study allows us to claim that the variability of the confounder-covariate interaction and of the covariate plays the most relevant role in determining the principal marker of the magnitude of confounding.

Wordline approach to higher spin fields

The main object of this thesis is the analysis and the quantization of spinning particle models which employ extended ”one dimensional supergravity” on the worldline, and their relation to the theory of higher spin fields (HS). In the first part of this work we have described the classical theory of massless spinning particles with an SO(N) extended supergravity multiplet on the worldline, in flat and more generally in maximally symmetric backgrounds. These (non)linear sigma models describe, upon quantization, the dynamics of particles with spin N/2. Then we have analyzed carefully the quantization of spinning particles with SO(N) extended supergravity on the worldline, for every N and in every dimension D. The physical sector of the Hilbert space reveals an interesting geometrical structure: the generalized higher spin curvature (HSC). We have shown, in particular, that these models of spinning particles describe a subclass of HS fields whose equations of motions are conformally invariant at the free level; in D = 4 this subclass describes all massless representations of the Poincar´e group. In the third part of this work we have considered the one-loop quantization of SO(N) spinning particle models by studying the corresponding partition function on the circle. After the gauge fixing of the supergravity multiplet, the partition function reduces to an integral over the corresponding moduli space which have been computed by using orthogonal polynomial techniques. Finally we have extend our canonical analysis, described previously for flat space, to maximally symmetric target spaces (i.e. (A)dS background). The quantization of these models produce (A)dS HSC as the physical states of the Hilbert space; we have used an iterative procedure and Pochhammer functions to solve the differential Bianchi identity in maximally symmetric spaces. Motivated by the correspondence between SO(N) spinning particle models and HS gauge theory, and by the notorious difficulty one finds in constructing an interacting theory for fields with spin greater than two, we have used these one dimensional supergravity models to study and extract informations on HS. In the last part of this work we have constructed spinning particle models with sp(2) R symmetry, coupled to Hyper K¨ahler and Quaternionic-K¨ahler (QK) backgrounds.

The assessment of change in rural landscape and the analysis of the driving forces. Proposal of a spatial model for the rural built environment

The presented study carried out an analysis on rural landscape changes. In particular the study focuses on the understanding of driving forces acting on the rural built environment using a statistical spatial model implemented through GIS techniques. It is well known that the study of landscape changes is essential for a conscious decision making in land planning. From a bibliography review results a general lack of studies dealing with the modeling of rural built environment and hence a theoretical modelling approach for such purpose is needed. The advancement in technology and modernity in building construction and agriculture have gradually changed the rural built environment. In addition, the phenomenon of urbanization of a determined the construction of new volumes that occurred beside abandoned or derelict rural buildings. Consequently there are two types of transformation dynamics affecting mainly the rural built environment that can be observed: the conversion of rural buildings and the increasing of building numbers. It is the specific aim of the presented study to propose a methodology for the development of a spatial model that allows the identification of driving forces that acted on the behaviours of the building allocation. In fact one of the most concerning dynamic nowadays is related to an irrational expansion of buildings sprawl across landscape. The proposed methodology is composed by some conceptual steps that cover different aspects related to the development of a spatial model: the selection of a response variable that better describe the phenomenon under study, the identification of possible driving forces, the sampling methodology concerning the collection of data, the most suitable algorithm to be adopted in relation to statistical theory and method used, the calibration process and evaluation of the model. A different combination of factors in various parts of the territory generated favourable or less favourable conditions for the building allocation and the existence of buildings represents the evidence of such optimum. Conversely the absence of buildings expresses a combination of agents which is not suitable for building allocation. Presence or absence of buildings can be adopted as indicators of such driving conditions, since they represent the expression of the action of driving forces in the land suitability sorting process. The existence of correlation between site selection and hypothetical driving forces, evaluated by means of modeling techniques, provides an evidence of which driving forces are involved in the allocation dynamic and an insight on their level of influence into the process. GIS software by means of spatial analysis tools allows to associate the concept of presence and absence with point futures generating a point process. Presence or absence of buildings at some site locations represent the expression of these driving factors interaction. In case of presences, points represent locations of real existing buildings, conversely absences represent locations were buildings are not existent and so they are generated by a stochastic mechanism. Possible driving forces are selected and the existence of a causal relationship with building allocations is assessed through a spatial model. The adoption of empirical statistical models provides a mechanism for the explanatory variable analysis and for the identification of key driving variables behind the site selection process for new building allocation. The model developed by following the methodology is applied to a case study to test the validity of the methodology. In particular the study area for the testing of the methodology is represented by the New District of Imola characterized by a prevailing agricultural production vocation and were transformation dynamic intensively occurred. The development of the model involved the identification of predictive variables (related to geomorphologic, socio-economic, structural and infrastructural systems of landscape) capable of representing the driving forces responsible for landscape changes.. The calibration of the model is carried out referring to spatial data regarding the periurban and rural area of the study area within the 1975-2005 time period by means of Generalised linear model. The resulting output from the model fit is continuous grid surface where cells assume values ranged from 0 to 1 of probability of building occurrences along the rural and periurban area of the study area. Hence the response variable assesses the changes in the rural built environment occurred in such time interval and is correlated to the selected explanatory variables by means of a generalized linear model using logistic regression. Comparing the probability map obtained from the model to the actual rural building distribution in 2005, the interpretation capability of the model can be evaluated. The proposed model can be also applied to the interpretation of trends which occurred in other study areas, and also referring to different time intervals, depending on the availability of data. The use of suitable data in terms of time, information, and spatial resolution and the costs related to data acquisition, pre-processing, and survey are among the most critical aspects of model implementation. Future in-depth studies can focus on using the proposed model to predict short/medium-range future scenarios for the rural built environment distribution in the study area. In order to predict future scenarios it is necessary to assume that the driving forces do not change and that their levels of influence within the model are not far from those assessed for the time interval used for the calibration.

Evaluation and management of demersal stocks in the Adriatic: the case of common sole (Solea solea, L.) in the northern and central Adriatic Sea

This PhD thesis aimed to assess the status of common sole, one of the main commercial stocks in the Adriatic Sea, using a mix of conventional and innovative techniques to provide more reliable estimates of stock status compared to past advice. First, a meta-analysis was carried out using data-poor assessment model to analyze the whole catch assemblage of rapido fishery. The outcomes were used to estimate rebuilding time and forecast catches under different harvest control rule scenarios, with a reduction of 20% of fishing effort being suggested as a way to allow most of the species to recover to sustainable levels. Secondly, an ensemble of data-rich assessment models was developed to better incorporate uncertainty by using alternative hypotheses of main parameters. This was the first time an ensemble of models has been used in the Mediterranean to provide management advice. Consistent with data-poor analysis results, the ensemble outcomes indicated that the common sole stock was showing a recovering trend probably due to the effective management actions underway in the area rather than the moderate effort reduction according to the actual management plan. Moreover, back-calculation measurements were used to fit and compare monophasic and biphasic growth curves through the use of non-linear mixed effects models. The analyses revealed that the fitting of the biphasic curve was superior, confirming the theory that growth in size would decrease as a consequence of reproductive effort. A stock assessment simulation showed how the use of the monophasic pattern would result in a critical overestimation of biomass that could lead to a greater risk of overfishing. As a final step, a simulation-testing procedure was applied to determine the best performing reference points using stock-specific characteristic. The procedure could be routinely adopted to increase transparency in reference points calculation enhancing the credibility of scientific advice.

Seemingly unrelated linear regression for contaminated data based on Gaussian mixtures

In this thesis, new classes of models for multivariate linear regression defined by finite mixtures of seemingly unrelated contaminated normal regression models and seemingly unrelated contaminated normal cluster-weighted models are illustrated. The main difference between such families is that the covariates are treated as fixed in the former class of models and as random in the latter. Thus, in cluster-weighted models the assignment of the data points to the unknown groups of observations depends also by the covariates. These classes provide an extension to mixture-based regression analysis for modelling multivariate and correlated responses in the presence of mild outliers that allows to specify a different vector of regressors for the prediction of each response. Expectation-conditional maximisation algorithms for the calculation of the maximum likelihood estimate of the model parameters have been derived. As the number of free parameters incresases quadratically with the number of responses and the covariates, analyses based on the proposed models can become unfeasible in practical applications. These problems have been overcome by introducing constraints on the elements of the covariance matrices according to an approach based on the eigen-decomposition of the covariance matrices. The performances of the new models have been studied by simulations and using real datasets in comparison with other models. In order to gain additional flexibility, mixtures of seemingly unrelated contaminated normal regressions models have also been specified so as to allow mixing proportions to be expressed as functions of concomitant covariates. An illustration of the new models with concomitant variables and a study on housing tension in the municipalities of the Emilia-Romagna region based on different types of multivariate linear regression models have been performed.

Modelli non lineari statici e dinamici su dati microeconomici: analisi delle condizioni finanziarie delle famiglie italiane

The thesis studies the economic and financial conditions of Italian households, by using microeconomic data of the Survey on Household Income and Wealth (SHIW) over the period 1998-2006. It develops along two lines of enquiry. First it studies the determinants of households holdings of assets and liabilities and estimates their correlation degree. After a review of the literature, it estimates two non-linear multivariate models on the interactions between assets and liabilities with repeated cross-sections. Second, it analyses households financial difficulties. It defines a quantitative measure of financial distress and tests, by means of non-linear dynamic probit models, whether the probability of experiencing financial difficulties is persistent over time. Chapter 1 provides a critical review of the theoretical and empirical literature on the estimation of assets and liabilities holdings, on their interactions and on households net wealth. The review stresses the fact that a large part of the literature explain households debt holdings as a function, among others, of net wealth, an assumption that runs into possible endogeneity problems. Chapter 2 defines two non-linear multivariate models to study the interactions between assets and liabilities held by Italian households. Estimation refers to a pooling of cross-sections of SHIW. The first model is a bivariate tobit that estimates factors affecting assets and liabilities and their degree of correlation with results coherent with theoretical expectations. To tackle the presence of non normality and heteroskedasticity in the error term, generating non consistent tobit estimators, semi-parametric estimates are provided that confirm the results of the tobit model. The second model is a quadrivariate probit on three different assets (safe, risky and real) and total liabilities; the results show the expected patterns of interdependence suggested by theoretical considerations. Chapter 3 reviews the methodologies for estimating non-linear dynamic panel data models, drawing attention to the problems to be dealt with to obtain consistent estimators. Specific attention is given to the initial condition problem raised by the inclusion of the lagged dependent variable in the set of explanatory variables. The advantage of using dynamic panel data models lies in the fact that they allow to simultaneously account for true state dependence, via the lagged variable, and unobserved heterogeneity via individual effects specification. Chapter 4 applies the models reviewed in Chapter 3 to analyse financial difficulties of Italian households, by using information on net wealth as provided in the panel component of the SHIW. The aim is to test whether households persistently experience financial difficulties over time. A thorough discussion is provided of the alternative approaches proposed by the literature (subjective/qualitative indicators versus quantitative indexes) to identify households in financial distress. Households in financial difficulties are identified as those holding amounts of net wealth lower than the value corresponding to the first quartile of net wealth distribution. Estimation is conducted via four different methods: the pooled probit model, the random effects probit model with exogenous initial conditions, the Heckman model and the recently developed Wooldridge model. Results obtained from all estimators accept the null hypothesis of true state dependence and show that, according with the literature, less sophisticated models, namely the pooled and exogenous models, over-estimate such persistence.

Effetti idrodinamici prodotti dal costume tecnico sul nuotatore

L’introduzione dei costumi tecnici nel nuoto ha portato miglioramenti senza precedenti sulla prestazione. I miglioramenti nella velocità di nuoto sono stati attribuiti dalla letteratura a riduzioni nelle resistenze idrodinamiche sul nuotatore. Tuttavia, gli effetti specifici dovuti all’utilizzo di questo tipo di costume non sono ancora completamente chiariti. Questa tesi aveva l’obiettivo di indagare gli effetti del costume tecnico sul galleggiamento statico, sulla posizione del corpo e sulla resistenza idrodinamica in avanzamento passivo. Nello studio preliminare sono stati misurati la spinta idrostatica, i volumi polmonari dinamici e la circonferenza toracica di 9 nuotatori che indossavano un costume tradizionale o un costume tecnico in gomma sintetica. Indossare il costume tecnico ha determinato una riduzione significativa del galleggiamento statico, e la compressione toracica causata da questo tipo di costume potrebbe avere una relazione con la significativa riduzione dei volumi polmonari misurati quando il nuotatore indossa questo tipo di costume. Un successiva analisi prevedeva il traino passivo di 14 nuotatori che mantenevano la miglior posizione idrodinamica di scivolamento indossando un costume tradizionale, tecnico in tessuto e tecnico in gomma. La posizione del corpo in avanzamento è stata misurata con un’analisi cinematica. La resistenza passiva indossando i costumi tecnici è risultata significativamente minore per entrambi i costumi tecnici rispetto alla prova con costume tradizionale. L’analisi condotta attraverso modelli di regressione lineari ha mostrato che una parte della riduzione della resistenza passiva era legata a proprietà intrinseche dei costumi tecnici. Tuttavia, anche l’area di impatto frontale determinata dall’inclinazione del tronco del soggetto in scivolamento e l’inclinazione degli arti inferiori hanno mostrato una marcata influenza sulla resistenza idrodinamica passiva. Pertanto, la riduzione di resistenza idrodinamica durante lo scivolamento passivo effettuato con costume tecnico da nuoto è attribuibile, oltre all’effetto del materiale di composizione del costume, ad una variazione della posizione del corpo del nuotatore.

A New Prediction Model for Slope Stability Analysis

The instability of river bank can result in considerable human and land losses. The Po river is the most important in Italy, characterized by main banks of significant and constantly increasing height. This study presents multilayer perceptron of artificial neural network (ANN) to construct prediction models for the stability analysis of river banks along the Po River, under various river and groundwater boundary conditions. For this aim, a number of networks of threshold logic unit are tested using different combinations of the input parameters. Factor of safety (FS), as an index of slope stability, is formulated in terms of several influencing geometrical and geotechnical parameters. In order to obtain a comprehensive geotechnical database, several cone penetration tests from the study site have been interpreted. The proposed models are developed upon stability analyses using finite element code over different representative sections of river embankments. For the validity verification, the ANN models are employed to predict the FS values of a part of the database beyond the calibration data domain. The results indicate that the proposed ANN models are effective tools for evaluating the slope stability. The ANN models notably outperform the derived multiple linear regression models.

Mathematical Optimization Applied to Thermal and Electrical Energy Systems

This Thesis aims at building and discussing mathematical models applications focused on Energy problems, both on the thermal and electrical side. The objective is to show how mathematical programming techniques developed within Operational Research can give useful answers in the Energy Sector, how they can provide tools to support decision making processes of Companies operating in the Energy production and distribution and how they can be successfully used to make simulations and sensitivity analyses to better understand the state of the art and convenience of a particular technology by comparing it with the available alternatives. The first part discusses the fundamental mathematical background followed by a comprehensive literature review about mathematical modelling in the Energy Sector. The second part presents mathematical models for the District Heating strategic network design and incremental network design. The objective is the selection of an optimal set of new users to be connected to an existing thermal network, maximizing revenues, minimizing infrastructure and operational costs and taking into account the main technical requirements of the real world application. Results on real and randomly generated benchmark networks are discussed with particular attention to instances characterized by big networks dimensions. The third part is devoted to the development of linear programming models for optimal battery operation in off-grid solar power schemes, with consideration of battery degradation. The key contribution of this work is the inclusion of battery degradation costs in the optimisation models. As available data on relating degradation costs to the nature of charge/discharge cycles are limited, we concentrate on investigating the sensitivity of operational patterns to the degradation cost structure. The objective is to investigate the combination of battery costs and performance at which such systems become economic. We also investigate how the system design should change when battery degradation is taken into account.