Referee Assignment Problem Case: Italian Volleyball Championships

This thesis addresses the formulation of a referee assignment problem for the Italian Volleyball Serie A Championships. The problem has particular constraints such as a referee must be assigned to different teams in a given period of times, and the minimal/maximal level of workload for each referee is obtained by considering cost and profit in the objective function. The problem has been solved through an exact method by using an integer linear programming formulation and a clique based decomposition for improving the computing time. Extensive computational experiments on real-world instances have been performed to determine the effectiveness of the proposed approach.

Prediction Nomogram for 68Ga-PSMA-11 PET/CT in different clinical settings of PSA failure after radical treatment for Prostate Cancer

Objective The objective of this study was to develop a clinical nomogram to predict gallium-68 prostate-specific membrane antigen positron emission tomography/computed tomography (68Ga-PSMA-11-PET/CT) positivity in different clinical settings of PSA failure. Materials and methods Seven hundred three (n = 703) prostate cancer (PCa) patients with confirmed PSA failure after radical therapy were enrolled. Patients were stratified according to different clinical settings (first-time biochemical recurrence [BCR]: group 1; BCR after salvage therapy: group 2; biochemical persistence after radical prostatectomy [BCP]: group 3; advanced stage PCa before second-line systemic therapies: group 4). First, we assessed 68Ga-PSMA-11-PET/CT positivity rate. Second, multivariable logistic regression analyses were used to determine predictors of positive scan. Third, regression-based coefficients were used to develop a nomogram predicting positive 68Ga-PSMA-11-PET/CT result and 200 bootstrap resamples were used for internal validation. Fourth, receiver operating characteristic (ROC) analysis was used to identify the most informative nomogram’s derived cut-off. Decision curve analysis (DCA) was implemented to quantify nomogram’s clinical benefit. Results 68Ga-PSMA-11-PET/CT overall positivity rate was 51.2%, while it was 40.3% in group 1, 54% in group 2, 60.5% in group 3, and 86.9% in group 4 (p < 0.001). At multivariable analyses, ISUP grade, PSA, PSA doubling time, and clinical setting were independent predictors of a positive scan (all p ≤ 0.04). A nomogram based on covariates included in the multivariate model demonstrated a bootstrap-corrected accuracy of 82%. The nomogram-derived best cut-off value was 40%. In DCA, the nomogram revealed clinical net benefit of > 10%. Conclusions This novel nomogram proved its good accuracy in predicting a positive scan, with values ≥ 40% providing the most informative cut-off in counselling patients to 68Ga-PSMA-11-PET/CT. This tool might be important as a guide to clinicians in the best use of PSMA-based PET imaging.

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.

Tensor-Train decomposition for image classification problems

In these last years a great effort has been put in the development of new techniques for automatic object classification, also due to the consequences in many applications such as medical imaging or driverless cars. To this end, several mathematical models have been developed from logistic regression to neural networks. A crucial aspect of these so called classification algorithms is the use of algebraic tools to represent and approximate the input data. In this thesis, we examine two different models for image classification based on a particular tensor decomposition named Tensor-Train (TT) decomposition. The use of tensor approaches preserves the multidimensional structure of the data and the neighboring relations among pixels. Furthermore the Tensor-Train, differently from other tensor decompositions, does not suffer from the curse of dimensionality making it an extremely powerful strategy when dealing with high-dimensional data. It also allows data compression when combined with truncation strategies that reduce memory requirements without spoiling classification performance. The first model we propose is based on a direct decomposition of the database by means of the TT decomposition to find basis vectors used to classify a new object. The second model is a tensor dictionary learning model, based on the TT decomposition where the terms of the decomposition are estimated using a proximal alternating linearized minimization algorithm with a spectral stepsize.

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.

Lesion detection and classification in breast cancer: evaluation of approaches based on morphological features, tracer kinetic modelling and semi-quantitative parameters in MR functional imaging (DCE-MRI)

The diagnosis, grading and classification of tumours has benefited considerably from the development of DCE-MRI which is now essential to the adequate clinical management of many tumour types due to its capability in detecting active angiogenesis. Several strategies have been proposed for DCE-MRI evaluation. Visual inspection of contrast agent concentration curves vs time is a very simple yet operator dependent procedure, therefore more objective approaches have been developed in order to facilitate comparison between studies. In so called model free approaches, descriptive or heuristic information extracted from time series raw data have been used for tissue classification. The main issue concerning these schemes is that they have not a direct interpretation in terms of physiological properties of the tissues. On the other hand, model based investigations typically involve compartmental tracer kinetic modelling and pixel-by-pixel estimation of kinetic parameters via non-linear regression applied on region of interests opportunely selected by the physician. This approach has the advantage to provide parameters directly related to the pathophysiological properties of the tissue such as vessel permeability, local regional blood flow, extraction fraction, concentration gradient between plasma and extravascular-extracellular space. Anyway, nonlinear modelling is computational demanding and the accuracy of the estimates can be affected by the signal-to-noise ratio and by the initial solutions. The principal aim of this thesis is investigate the use of semi-quantitative and quantitative parameters for segmentation and classification of breast lesion. The objectives can be subdivided as follow: describe the principal techniques to evaluate time intensity curve in DCE-MRI with focus on kinetic model proposed in literature; to evaluate the influence in parametrization choice for a classic bi-compartmental kinetic models; to evaluate the performance of a method for simultaneous tracer kinetic modelling and pixel classification; to evaluate performance of machine learning techniques training for segmentation and classification of breast lesion.

Determinants of cesarean delivery, a population-based study in the Emilia Romagna Region

Cesarean Delivery (CD) rates are rising in many parts of the world. In order to define strategies to reduce them, it is important to explore the role of clinical and organizational factors. This thesis has the objective to describe the contemporary CD practice and study clinical and organizational variables as determinants of CD in all women who gave birth between 2005 and June 2010 in the Emilia Romagna region (Italy). All hospital discharge abstracts of women who delivered between 2005 and mid 2010 in the region were selected and linked with birth certificates. In addition to descriptive statistics, in order to study the role of clinical and organizational variables (teaching or non-teaching hospital, birth volumes, time and day of delivery) multilevel Poisson regression models and a classification tree were used. A substantial inter-hospital variability in CD rate was found, and this was only partially explained by the considered variables. The most important risk factors of CD were: previous CD (RR 4,95; 95%CI: 4,85-5,05), cord prolapse (RR 3,51; 95% CI:2,96-4,16), and malposition/malpresentation (RR 2,72; 95%CI: 2,66-2,77). Delivery between 7 pm and 7 am and during non working days protect against CD in all subgroups including those with a small number of elective CDs while delivery at a teaching hospital and birth volumes were not statistically significant risk factors. The classification tree shows that previous CD and malposition/malpresentation are the most important variables discriminating between high and low risk of CD. These results indicate that other not considered factors might explain CD variability and do not provide clear evidence that small hospitals have a poor performance in terms of CD rate. Some strategies to reduce CD could be found by focusing on the differences in delivery practice between day and night and between working and no-working day deliveries.

Maternal Smoking Impact on the Delivery Cost: a population-based study in the Emilia-Romagna region

This doctoral thesis is devoted to the study of the causal effects of the maternal smoking on the delivery cost. The interest of economic consequences of smoking in pregnancy have been studied fairly extensively in the USA, and very little is known in European context. To identify the causal relation between different maternal smoking status and the delivery cost in the Emilia-Romagna region two distinct methods were used. The first - geometric multidimensional - is mainly based on the multivariate approach and involves computing and testing the global imbalance, classifying cases in order to generate well-matched comparison groups, and then computing treatment effects. The second - structural modelling - refers to a general methodological account of model-building and model-testing. The main idea of this approach is to decompose the global mechanism into sub-mechanisms though a recursive decomposition of a multivariate distribution.

Diagnosis and Fault detection in Electrical Machines and Drives based on Advanced Signal Processing Techniques

In the present thesis, a new methodology of diagnosis based on advanced use of time-frequency technique analysis is presented. More precisely, a new fault index that allows tracking individual fault components in a single frequency band is defined. More in detail, a frequency sliding is applied to the signals being analyzed (currents, voltages, vibration signals), so that each single fault frequency component is shifted into a prefixed single frequency band. Then, the discrete Wavelet Transform is applied to the resulting signal to extract the fault signature in the frequency band that has been chosen. Once the state of the machine has been qualitatively diagnosed, a quantitative evaluation of the fault degree is necessary. For this purpose, a fault index based on the energy calculation of approximation and/or detail signals resulting from wavelet decomposition has been introduced to quantify the fault extend. The main advantages of the developed new method over existing Diagnosis techniques are the following: - Capability of monitoring the fault evolution continuously over time under any transient operating condition; - Speed/slip measurement or estimation is not required; - Higher accuracy in filtering frequency components around the fundamental in case of rotor faults; - Reduction in the likelihood of false indications by avoiding confusion with other fault harmonics (the contribution of the most relevant fault frequency components under speed-varying conditions are clamped in a single frequency band); - Low memory requirement due to low sampling frequency; - Reduction in the latency of time processing (no requirement of repeated sampling operation).

Evidence-based polytherapies and long-term mortality after acute myocardial infarction in very old subjects compared with elderly and adults: a nested case-control study

Background: Clinical trials have demonstrated that selected secondary prevention medications for patients after acute myocardial infarction (AMI) reduce mortality. Yet, these medications are generally underprescribed in daily practice, and older people are often absent from drug trials. Objectives: To examine the relationship between adherence to evidence-based (EB) drugs and post-AMI mortality, focusing on the effects of single therapy and polytherapy in very old patients (≥80 years) compared with elderly and adults (<80 years). Methods: Patients hospitalised for AMI between 01/01/2008 and 30/06/2011 and resident in the Local Health Authority of Bologna were followed up until 31/12/2011. Medication adherence was calculated as the proportion of days covered for filled prescriptions of angiotensin-converting enzyme inhibitors (ACEIs)/angiotensin receptor blockers (ARBs), β-blockers, antiplatelet drugs, and statins. We adopted a risk set sampling method, and the adjusted relationship between medication adherence (PDC≥75%) and mortality was investigated using conditional multiple logistic regression. Results: The study population comprised 4861 patients. During a median follow-up of 2.8 years, 1116 deaths (23.0%) were observed. Adherence to the 4 EB drugs was 7.1%, while nonadherence to any of the drugs was 19.7%. For both patients aged ≥80 years and those aged <80 years, rate ratios of death linearly decreased as the number of EB drugs taken increased. There was a significant inverse relationship between adherence to each of 4 medications and mortality, although its magnitude was higher for ACEIs/ARBs (adj. rate ratio=0.60, 95%CI=0.52–0.69) and statins (0.60, 0.50–0.72), and lower for β-blockers (0.75, 0.61–0.92) and antiplatelet drugs (0.73, 0.63–0.84). Conclusions: The beneficial effect of EB polytherapy on long-term mortality following AMI is evident also in nontrial older populations. Given that adherence to combination therapies is largely suboptimal, the implementation of strategies and initiatives to increase the use of post-AMI secondary preventive medications in old patients is crucial.

Decomposition Methods and Network Design Problems

Decomposition based approaches are recalled from primal and dual point of view. The possibility of building partially disaggregated reduced master problems is investigated. This extends the idea of aggregated-versus-disaggregated formulation to a gradual choice of alternative level of aggregation. Partial aggregation is applied to the linear multicommodity minimum cost flow problem. The possibility of having only partially aggregated bundles opens a wide range of alternatives with different trade-offs between the number of iterations and the required computation for solving it. This trade-off is explored for several sets of instances and the results are compared with the ones obtained by directly solving the natural node-arc formulation. An iterative solution process to the route assignment problem is proposed, based on the well-known Frank Wolfe algorithm. In order to provide a first feasible solution to the Frank Wolfe algorithm, a linear multicommodity min-cost flow problem is solved to optimality by using the decomposition techniques mentioned above. Solutions of this problem are useful for network orientation and design, especially in relation with public transportation systems as the Personal Rapid Transit. A single-commodity robust network design problem is addressed. In this, an undirected graph with edge costs is given together with a discrete set of balance matrices, representing different supply/demand scenarios. The goal is to determine the minimum cost installation of capacities on the edges such that the flow exchange is feasible for every scenario. A set of new instances that are computationally hard for the natural flow formulation are solved by means of a new heuristic algorithm. Finally, an efficient decomposition-based heuristic approach for a large scale stochastic unit commitment problem is presented. The addressed real-world stochastic problem employs at its core a deterministic unit commitment planning model developed by the California Independent System Operator (ISO).

Noises: a Nuisance and a Resource. Development of New Decomposition Methods of Noisy Data

Noise is constant presence in measurements. Its origin is related to the microscopic properties of matter. Since the seminal work of Brown in 1828, the study of stochastic processes has gained an increasing interest with the development of new mathematical and analytical tools. In the last decades, the central role that noise plays in chemical and physiological processes has become recognized. The dual role of noise as nuisance/resource pushes towards the development of new decomposition techniques that divide a signal into its deterministic and stochastic components. In this thesis I show how methods based on Singular Spectrum Analysis have the right properties to fulfil the previously mentioned requirement. During my work I applied SSA to different signals of interest in chemistry: I developed a novel iterative procedure for the denoising of powder X-ray diffractograms; I “denoised” bi-dimensional images from experiments of electrochemiluminescence imaging of micro-beads obtaining new insight on ECL mechanism. I also used Principal Component Analysis to investigate the relationship between brain electrophysiological signals and voice emission.

Decoding complex flow phenomena via Dynamic Mode Decomposition

In this thesis, the viability of the Dynamic Mode Decomposition (DMD) as a technique to analyze and model complex dynamic real-world systems is presented. This method derives, directly from data, computationally efficient reduced-order models (ROMs) which can replace too onerous or unavailable high-fidelity physics-based models. Optimizations and extensions to the standard implementation of the methodology are proposed, investigating diverse case studies related to the decoding of complex flow phenomena. The flexibility of this data-driven technique allows its application to high-fidelity fluid dynamics simulations, as well as time series of real systems observations. The resulting ROMs are tested against two tasks: (i) reduction of the storage requirements of high-fidelity simulations or observations; (ii) interpolation and extrapolation of missing data. The capabilities of DMD can also be exploited to alleviate the cost of onerous studies that require many simulations, such as uncertainty quantification analysis, especially when dealing with complex high-dimensional systems. In this context, a novel approach to address parameter variability issues when modeling systems with space and time-variant response is proposed. Specifically, DMD is merged with another model-reduction technique, namely the Polynomial Chaos Expansion, for uncertainty quantification purposes. Useful guidelines for DMD deployment result from the study, together with the demonstration of its potential to ease diagnosis and scenario analysis when complex flow processes are involved.