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.

The foodomics approach to investigate the impact of the matrix structure on food quality: applications of magnetic resonance spectroscopy, relaxometry and imaging

The aim of this thesis is to explore the possible influence of the food matrix on food quality attributes. Using nuclear magnetic resonance techniques, the matrix-dependent properties of different foods were studied and some useful indices were defined to classify food products based on the matrix behaviour when responding to processing phenomena. Correlations were found between fish freshness indices, assessed by certain geometric parameters linked to the morphology of the animal, i.e. a macroscopic structure, and the degradation of the product structure. The same foodomics approach was also applied to explore the protective effect of modified atmospheres on the stability of fish fillets, which are typically susceptible to oxidation of the polyunsaturated fatty acids incorporated in the meat matrix. Here, freshness is assessed by evaluating the time-dependent change in the fish metabolome, providing an established freshness index, and its relationship to lipid oxidation. In vitro digestion studies, focusing on food products with different matrixes, alone and in combination with other meal components (e.g. seasoning), were conducted to investigate possible interactions between enzymes and food, modulated by matrix structure, which influence digestibility. The interaction between water and the gelatinous matrix of the food, consisting of a network of protein gels incorporating fat droplets, was also studied by means of nuclear magnetic relaxometry, in order to create a prediction tool for the correct classification of authentic and counterfeit food products protected by a quality label. This is one of the first applications of an NMR method focusing on the supramolecular structure of the matrix, rather than the chemical composition, to assess food authenticity. The effect of innovative processing technologies, such as PEF applied to fruit products, has been assessed by magnetic resonance imaging, exploiting information associated with the rehydration kinetics exerted by a modified food structure.

Essays on social networks, altruism and information diffusion

This dissertation consists of three standalone articles that contribute to the economics literature concerning technology adoption, information diffusion, and network economics in one way or another, using a couple of primary data sources from Ethiopia. The first empirical paper identifies the main behavioral factors affecting the adoption of brand new (radical) and upgraded (incremental) bioenergy innovations in Ethiopia. The results highlight the importance of targeting different instruments to increase the adoption rate of the two types of innovations. The second and the third empirical papers of this thesis, use primary data collected from 3,693 high school students in Ethiopia, and shed light on how we should select informants to effectively and equitably disseminate new information, mainly concerning environmental issues. There are different well-recognized standard centrality measures that are used to select informants. These standard centrality measures, however, are based on the network topology---shaped only by the number of connections---and fail to incorporate the intrinsic motivations of the informants. This thesis introduces an augmented centrality measure (ACM) by modifying the eigenvector centrality measure through weighting the adjacency matrix with the altruism levels of connected nodes. The results from the two papers suggest that targeting informants based on network position and behavioral attributes ensures more effective and equitable (gender perspective) transmission of information in social networks than selecting informants on network centrality measures alone. Notably, when the information is concerned with environmental issues.

Model selection and the vectorial misspecification-resistant information criterion in multivariate time series

The thesis deals with the problem of Model Selection (MS) motivated by information and prediction theory, focusing on parametric time series (TS) models. The main contribution of the thesis is the extension to the multivariate case of the Misspecification-Resistant Information Criterion (MRIC), a criterion introduced recently that solves Akaike’s original research problem posed 50 years ago, which led to the definition of the AIC. The importance of MS is witnessed by the huge amount of literature devoted to it and published in scientific journals of many different disciplines. Despite such a widespread treatment, the contributions that adopt a mathematically rigorous approach are not so numerous and one of the aims of this project is to review and assess them. Chapter 2 discusses methodological aspects of MS from information theory. Information criteria (IC) for the i.i.d. setting are surveyed along with their asymptotic properties; and the cases of small samples, misspecification, further estimators. Chapter 3 surveys criteria for TS. IC and prediction criteria are considered for: univariate models (AR, ARMA) in the time and frequency domain, parametric multivariate (VARMA, VAR); nonparametric nonlinear (NAR); and high-dimensional models. The MRIC answers Akaike’s original question on efficient criteria, for possibly-misspecified (PM) univariate TS models in multi-step prediction with high-dimensional data and nonlinear models. Chapter 4 extends the MRIC to PM multivariate TS models for multi-step prediction introducing the Vectorial MRIC (VMRIC). We show that the VMRIC is asymptotically efficient by proving the decomposition of the MSPE matrix and the consistency of its Method-of-Moments Estimator (MoME), for Least Squares multi-step prediction with univariate regressor. Chapter 5 extends the VMRIC to the general multiple regressor case, by showing that the MSPE matrix decomposition holds, obtaining consistency for its MoME, and proving its efficiency. The chapter concludes with a digression on the conditions for PM VARX models.

Radiocarbon and stable isotopes in the shell organic matrix: a new approach for the use of mollusk shells in the study of human evolution

Mollusk shells are often found in archeological sites, given their great preservation potential and high value as a multipurpose resource. They are often the only available material to use for radiocarbon dating, due to a lack of well-preserved bones in many archeological sites, especially for the key period of the Middle to Upper Paleolithic transition. However, radiocarbon dating on mollusk shells is often regarded as less reliable compared to bones, wood, or charcoals due to the various factors influencing their radiocarbon content (e.g., Isotope fractionation, marine reservoir effect etc.). For the development of more accurate chronologies using shells, it is fundamental to continue improving the precision of the techniques applied, as has been done for other materials (wood and bones). Thus, improving the chemical pretreatment on mollusk shells might allow researchers to obtain more reliable radiocarbon determinations allowing for the construction of new radiocarbon chronologies in archeological sites where so far it has not been possible. Furthermore, mollusk shells can provide information on the climatic and environmental variables present during their growth. Using shells for paleoclimatic reconstruction adds more evidence helpful for the interpretation of scenarios of human migration, adaptation, and behavior. Standard methods for both radiocarbon and stable isotope studies use the carbonate fraction of the shell. However, being biogenic structures, mollusk shells also consist of a minor organic fraction. The shell organic matrix has an important role in the formation of the calcium carbonate structure and is still not fully understood. This thesis explores the potential of using the shell organic matrix for radiocarbon dating and paleoenvironmental studies. The results of the work performed for this thesis represent a starting point for future research to build on, and further develop the approach and methodology proposed here.