Local Trigonometric Methods for Time Series Smoothing.

The thesis is concerned with local trigonometric regression methods. The aim was to develop a method for extraction of cyclical components in time series. The main results of the thesis are the following. First, a generalization of the filter proposed by Christiano and Fitzgerald is furnished for the smoothing of ARIMA(p,d,q) process. Second, a local trigonometric filter is built, with its statistical properties. Third, they are discussed the convergence properties of trigonometric estimators, and the problem of choosing the order of the model. A large scale simulation experiment has been designed in order to assess the performance of the proposed models and methods. The results show that local trigonometric regression may be a useful tool for periodic time series analysis.

Statistical mechanics formalism and methods for the analysis of real networks

This thesis provides a thoroughly theoretical background in network theory and shows novel applications to real problems and data. In the first chapter a general introduction to network ensembles is given, and the relations with “standard” equilibrium statistical mechanics are described. Moreover, an entropy measure is considered to analyze statistical properties of the integrated PPI-signalling-mRNA expression networks in different cases. In the second chapter multilayer networks are introduced to evaluate and quantify the correlations between real interdependent networks. Multiplex networks describing citation-collaboration interactions and patterns in colorectal cancer are presented. The last chapter is completely dedicated to control theory and its relation with network theory. We characterise how the structural controllability of a network is affected by the fraction of low in-degree and low out-degree nodes. Finally, we present a novel approach to the controllability of multiplex networks

Matrix Designs and Methods for Secure and Efficient Compressed Sensing

The idea of balancing the resources spent in the acquisition and encoding of natural signals strictly to their intrinsic information content has interested nearly a decade of research under the name of compressed sensing. In this doctoral dissertation we develop some extensions and improvements upon this technique's foundations, by modifying the random sensing matrices on which the signals of interest are projected to achieve different objectives. Firstly, we propose two methods for the adaptation of sensing matrix ensembles to the second-order moments of natural signals. These techniques leverage the maximisation of different proxies for the quantity of information acquired by compressed sensing, and are efficiently applied in the encoding of electrocardiographic tracks with minimum-complexity digital hardware. Secondly, we focus on the possibility of using compressed sensing as a method to provide a partial, yet cryptanalysis-resistant form of encryption; in this context, we show how a random matrix generation strategy with a controlled amount of perturbations can be used to distinguish between multiple user classes with different quality of access to the encrypted information content. Finally, we explore the application of compressed sensing in the design of a multispectral imager, by implementing an optical scheme that entails a coded aperture array and Fabry-Pérot spectral filters. The signal recoveries obtained by processing real-world measurements show promising results, that leave room for an improvement of the sensing matrix calibration problem in the devised imager.

Algorithms and Models For Combinatorial Optimization Problems

In this thesis we present some combinatorial optimization problems, suggest models and algorithms for their effective solution. For each problem,we give its description, followed by a short literature review, provide methods to solve it and, finally, present computational results and comparisons with previous works to show the effectiveness of the proposed approaches. The considered problems are: the Generalized Traveling Salesman Problem (GTSP), the Bin Packing Problem with Conflicts(BPPC) and the Fair Layout Problem (FLOP).

Study of innovative methods of control in the cereal productive chain for the production of beer and spirits

Researches performed during the PhD course intended to assess innovative applications of near-infrared spectroscopy in reflectance (NIR) in the production chain of beer. The purpose is to measure by NIR the "malting quality" (MQ) parameter of barley, to monitor the malting process and to know if a certain type of barley is suitable for the production of beer and spirits. Moreover, NIR will be applied to monitor the brewing process. First of all, it was possible to check the quality of the raw materials like barley, maize and barley malt using a rapid, non-destructive and reliable method, with a low error of prediction. The more interesting result obtained at this level was that the repeatability of the NIR calibration models developed was comparable with the one of the reference method. Moreover, about malt, new kinds of validation were used in order to estimate the real predictive power of the proposed calibration models and to understand the long-term effects. Furthermore, the precision of all the calibration models developed for malt evaluation was estimated and statistically compared with the reference methods, with good results. Then, new calibration models were developed for monitoring the malting process, measuring the moisture content and other malt quality parameters during germination. Moreover it was possible to obtain by NIR an estimate of the "malting quality" (MQ) of barley and to predict whether if its germination will be rapid and uniform and if a certain type of barley is suitable for the production of beer and spirits. Finally, the NIR technique was applied to monitor the brewing process, using correlations between NIR spectra of beer and analytical parameters, and to assess beer quality. These innovative results are potentially very useful for the actors involved in the beer production chain, especially the calibration models suitable for the control of the malting process and for the assessment of the “malting quality” of barley, which need to be deepened in future studies.