NMR, Metabonomics and Molecular Profiles: Applications to the Quality Assessment of Foodstuffs

Nuclear Magnetic Resonance (NMR) is a branch of spectroscopy that is based on the fact that many atomic nuclei may be oriented by a strong magnetic field and will absorb radiofrequency radiation at characteristic frequencies. The parameters that can be measured on the resulting spectral lines (line positions, intensities, line widths, multiplicities and transients in time-dependent experi-ments) can be interpreted in terms of molecular structure, conformation, molecular motion and other rate processes. In this way, high resolution (HR) NMR allows performing qualitative and quantitative analysis of samples in solution, in order to determine the structure of molecules in solution and not only. In the past, high-field NMR spectroscopy has mainly concerned with the elucidation of chemical structure in solution, but today is emerging as a powerful exploratory tool for probing biochemical and physical processes. It represents a versatile tool for the analysis of foods. In literature many NMR studies have been reported on different type of food such as wine, olive oil, coffee, fruit juices, milk, meat, egg, starch granules, flour, etc using different NMR techniques. Traditionally, univariate analytical methods have been used to ex-plore spectroscopic data. This method is useful to measure or to se-lect a single descriptive variable from the whole spectrum and , at the end, only this variable is analyzed. This univariate methods ap-proach, applied to HR-NMR data, lead to different problems due especially to the complexity of an NMR spectrum. In fact, the lat-ter is composed of different signals belonging to different mole-cules, but it is also true that the same molecules can be represented by different signals, generally strongly correlated. The univariate methods, in this case, takes in account only one or a few variables, causing a loss of information. Thus, when dealing with complex samples like foodstuff, univariate analysis of spectra data results not enough powerful. Spectra need to be considered in their wholeness and, for analysing them, it must be taken in consideration the whole data matrix: chemometric methods are designed to treat such multivariate data. Multivariate data analysis is used for a number of distinct, differ-ent purposes and the aims can be divided into three main groups: • data description (explorative data structure modelling of any ge-neric n-dimensional data matrix, PCA for example); • regression and prediction (PLS); • classification and prediction of class belongings for new samples (LDA and PLS-DA and ECVA). The aim of this PhD thesis was to verify the possibility of identify-ing and classifying plants or foodstuffs, in different classes, based on the concerted variation in metabolite levels, detected by NMR spectra and using the multivariate data analysis as a tool to inter-pret NMR information. It is important to underline that the results obtained are useful to point out the metabolic consequences of a specific modification on foodstuffs, avoiding the use of a targeted analysis for the different metabolites. The data analysis is performed by applying chemomet-ric multivariate techniques to the NMR dataset of spectra acquired. The research work presented in this thesis is the result of a three years PhD study. This thesis reports the main results obtained from these two main activities: A1) Evaluation of a data pre-processing system in order to mini-mize unwanted sources of variations, due to different instrumental set up, manual spectra processing and to sample preparations arte-facts; A2) Application of multivariate chemiometric models in data analy-sis.

Pyrolysis-Gas Chromatography-Mass Spectometry and Chemometric Analysis for the Characterization of Complex Matrices

The present PhD thesis was focused on the development and application of chemical methodology (Py-GC-MS) and data-processing method by multivariate data analysis (chemometrics). The chromatographic and mass spectrometric data obtained with this technique are particularly suitable to be interpreted by chemometric methods such as PCA (Principal Component Analysis) as regards data exploration and SIMCA (Soft Independent Models of Class Analogy) for the classification. As a first approach, some issues related to the field of cultural heritage were discussed with a particular attention to the differentiation of binders used in pictorial field. A marker of egg tempera the phosphoric acid esterified, a pyrolysis product of lecithin, was determined using HMDS (hexamethyldisilazane) rather than the TMAH (tetramethylammonium hydroxide) as a derivatizing reagent. The validity of analytical pyrolysis as tool to characterize and classify different types of bacteria was verified. The FAMEs chromatographic profiles represent an important tool for the bacterial identification. Because of the complexity of the chromatograms, it was possible to characterize the bacteria only according to their genus, while the differentiation at the species level has been achieved by means of chemometric analysis. To perform this study, normalized areas peaks relevant to fatty acids were taken into account. Chemometric methods were applied to experimental datasets. The obtained results demonstrate the effectiveness of analytical pyrolysis and chemometric analysis for the rapid characterization of bacterial species. Application to a samples of bacterial (Pseudomonas Mendocina), fungal (Pleorotus ostreatus) and mixed- biofilms was also performed. A comparison with the chromatographic profiles established the possibility to: • Differentiate the bacterial and fungal biofilms according to the (FAMEs) profile. • Characterize the fungal biofilm by means the typical pattern of pyrolytic fragments derived from saccharides present in the cell wall. • Individuate the markers of bacterial and fungal biofilm in the same mixed-biofilm sample.

Modelling and classification with quantile-based distributions

In this work, we explore and demonstrate the potential for modeling and classification using quantile-based distributions, which are random variables defined by their quantile function. In the first part we formalize a least squares estimation framework for the class of linear quantile functions, leading to unbiased and asymptotically normal estimators. Among the distributions with a linear quantile function, we focus on the flattened generalized logistic distribution (fgld), which offers a wide range of distributional shapes. A novel naïve-Bayes classifier is proposed that utilizes the fgld estimated via least squares, and through simulations and applications, we demonstrate its competitiveness against state-of-the-art alternatives. In the second part we consider the Bayesian estimation of quantile-based distributions. We introduce a factor model with independent latent variables, which are distributed according to the fgld. Similar to the independent factor analysis model, this approach accommodates flexible factor distributions while using fewer parameters. The model is presented within a Bayesian framework, an MCMC algorithm for its estimation is developed, and its effectiveness is illustrated with data coming from the European Social Survey. The third part focuses on depth functions, which extend the concept of quantiles to multivariate data by imposing a center-outward ordering in the multivariate space. We investigate the recently introduced integrated rank-weighted (IRW) depth function, which is based on the distribution of random spherical projections of the multivariate data. This depth function proves to be computationally efficient and to increase its flexibility we propose different methods to explicitly model the projected univariate distributions. Its usefulness is shown in classification tasks: the maximum depth classifier based on the IRW depth is proven to be asymptotically optimal under certain conditions, and classifiers based on the IRW depth are shown to perform well in simulated and real data experiments.

Data-driven multivariate flood hazard modeling

The present Dissertation shows how recent statistical analysis tools and open datasets can be exploited to improve modelling accuracy in two distinct yet interconnected domains of flood hazard (FH) assessment. In the first Part, unsupervised artificial neural networks are employed as regional models for sub-daily rainfall extremes. The models aim to learn a robust relation to estimate locally the parameters of Gumbel distributions of extreme rainfall depths for any sub-daily duration (1-24h). The predictions depend on twenty morphoclimatic descriptors. A large study area in north-central Italy is adopted, where 2238 annual maximum series are available. Validation is performed over an independent set of 100 gauges. Our results show that multivariate ANNs may remarkably improve the estimation of percentiles relative to the benchmark approach from the literature, where Gumbel parameters depend on mean annual precipitation. Finally, we show that the very nature of the proposed ANN models makes them suitable for interpolating predicted sub-daily rainfall quantiles across space and time-aggregation intervals. In the second Part, decision trees are used to combine a selected blend of input geomorphic descriptors for predicting FH. Relative to existing DEM-based approaches, this method is innovative, as it relies on the combination of three characteristics: (1) simple multivariate models, (2) a set of exclusively DEM-based descriptors as input, and (3) an existing FH map as reference information. First, the methods are applied to northern Italy, represented with the MERIT DEM (∼90m resolution), and second, to the whole of Italy, represented with the EU-DEM (25m resolution). The results show that multivariate approaches may (a) significantly enhance flood-prone areas delineation relative to a selected univariate one, (b) provide accurate predictions of expected inundation depths, (c) produce encouraging results in extrapolation, (d) complete the information of imperfect reference maps, and (e) conveniently convert binary maps into continuous representation of FH.

Analyzing the dependence structure of microarray data: a copula–based approach

The main aim of this Ph.D. dissertation is the study of clustering dependent data by means of copula functions with particular emphasis on microarray data. Copula functions are a popular multivariate modeling tool in each field where the multivariate dependence is of great interest and their use in clustering has not been still investigated. The first part of this work contains the review of the literature of clustering methods, copula functions and microarray experiments. The attention focuses on the K–means (Hartigan, 1975; Hartigan and Wong, 1979), the hierarchical (Everitt, 1974) and the model–based (Fraley and Raftery, 1998, 1999, 2000, 2007) clustering techniques because their performance is compared. Then, the probabilistic interpretation of the Sklar’s theorem (Sklar’s, 1959), the estimation methods for copulas like the Inference for Margins (Joe and Xu, 1996) and the Archimedean and Elliptical copula families are presented. In the end, applications of clustering methods and copulas to the genetic and microarray experiments are highlighted. The second part contains the original contribution proposed. A simulation study is performed in order to evaluate the performance of the K–means and the hierarchical bottom–up clustering methods in identifying clusters according to the dependence structure of the data generating process. Different simulations are performed by varying different conditions (e.g., the kind of margins (distinct, overlapping and nested) and the value of the dependence parameter ) and the results are evaluated by means of different measures of performance. In light of the simulation results and of the limits of the two investigated clustering methods, a new clustering algorithm based on copula functions (‘CoClust’ in brief) is proposed. The basic idea, the iterative procedure of the CoClust and the description of the written R functions with their output are given. The CoClust algorithm is tested on simulated data (by varying the number of clusters, the copula models, the dependence parameter value and the degree of overlap of margins) and is compared with the performance of model–based clustering by using different measures of performance, like the percentage of well–identified number of clusters and the not rejection percentage of H0 on . It is shown that the CoClust algorithm allows to overcome all observed limits of the other investigated clustering techniques and is able to identify clusters according to the dependence structure of the data independently of the degree of overlap of margins and the strength of the dependence. The CoClust uses a criterion based on the maximized log–likelihood function of the copula and can virtually account for any possible dependence relationship between observations. Many peculiar characteristics are shown for the CoClust, e.g. its capability of identifying the true number of clusters and the fact that it does not require a starting classification. Finally, the CoClust algorithm is applied to the real microarray data of Hedenfalk et al. (2001) both to the gene expressions observed in three different cancer samples and to the columns (tumor samples) of the whole data matrix.

Valutazione della qualità ed autenticità di prodotti oleari e lattiero caseari mediante metodi fisici di analisi accoppiati a tecniche statistiche multivariate

Questa tesi descrive alcuni studi di messa a punto di metodi di analisi fisici accoppiati con tecniche statistiche multivariate per valutare la qualità e l’autenticità di oli vegetali e prodotti caseari. L’applicazione di strumenti fisici permette di abbattere i costi ed i tempi necessari per le analisi classiche ed allo stesso tempo può fornire un insieme diverso di informazioni che possono riguardare tanto la qualità come l’autenticità di prodotti. Per il buon funzionamento di tali metodi è necessaria la costruzione di modelli statistici robusti che utilizzino set di dati correttamente raccolti e rappresentativi del campo di applicazione. In questo lavoro di tesi sono stati analizzati oli vegetali e alcune tipologie di formaggi (in particolare pecorini per due lavori di ricerca e Parmigiano-Reggiano per un altro). Sono stati utilizzati diversi strumenti di analisi (metodi fisici), in particolare la spettroscopia, l’analisi termica differenziale, il naso elettronico, oltre a metodiche separative tradizionali. I dati ottenuti dalle analisi sono stati trattati mediante diverse tecniche statistiche, soprattutto: minimi quadrati parziali; regressione lineare multipla ed analisi discriminante lineare.

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.

Data assimilation for advanced cross-scale unstructured-grid ocean modeling.

The coastal ocean is a complex environment with extremely dynamic processes that require a high-resolution and cross-scale modeling approach in which all hydrodynamic fields and scales are considered integral parts of the overall system. In the last decade, unstructured-grid models have been used to advance in seamless modeling between scales. On the other hand, the data assimilation methodologies to improve the unstructured-grid models in the coastal seas have been developed only recently and need significant advancements. Here, we link the unstructured-grid ocean modeling to the variational data assimilation methods. In particular, we show results from the modeling system SANIFS based on SHYFEM fully-baroclinic unstructured-grid model interfaced with OceanVar, a state-of-art variational data assimilation scheme adopted for several systems based on a structured grid. OceanVar implements a 3DVar DA scheme. The combination of three linear operators models the background error covariance matrix. The vertical part is represented using multivariate EOFs for temperature, salinity, and sea level anomaly. The horizontal part is assumed to be Gaussian isotropic and is modeled using a first-order recursive filter algorithm designed for structured and regular grids. Here we introduced a novel recursive filter algorithm for unstructured grids. A local hydrostatic adjustment scheme models the rapidly evolving part of the background error covariance. We designed two data assimilation experiments using SANIFS implementation interfaced with OceanVar over the period 2017-2018, one with only temperature and salinity assimilation by Argo profiles and the second also including sea level anomaly. The results showed a successful implementation of the approach and the added value of the assimilation for the active tracer fields. While looking at the broad basin, no significant improvements are highlighted for the sea level, requiring future investigations. Furthermore, a Machine Learning methodology based on an LSTM network has been used to predict the model SST increments.

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.