Geometrical and Spectral Properties of the Orthogonal Projections of the Identity

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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.

Spectral and variational characterizations of solutions to semilinear eigenvalue problems

Die vorliegende Arbeit befaßt sich mit einer Klasse von nichtlinearen Eigenwertproblemen mit Variationsstrukturin einem reellen Hilbertraum. Die betrachteteEigenwertgleichung ergibt sich demnach als Euler-Lagrange-Gleichung eines stetig differenzierbarenFunktionals, zusätzlich sei der nichtlineare Anteil desProblems als ungerade und definit vorausgesetzt.Die wichtigsten Ergebnisse in diesem abstrakten Rahmen sindKriterien für die Existenz spektral charakterisierterLösungen, d.h. von Lösungen, deren Eigenwert gerade miteinem vorgegeben variationellen Eigenwert eines zugehörigen linearen Problems übereinstimmt. Die Herleitung dieserKriterien basiert auf einer Untersuchung kontinuierlicher Familien selbstadjungierterEigenwertprobleme und erfordert Verallgemeinerungenspektraltheoretischer Konzepte.Neben reinen Existenzsätzen werden auch Beziehungen zwischenspektralen Charakterisierungen und denLjusternik-Schnirelman-Niveaus des Funktionals erörtert.Wir betrachten Anwendungen auf semilineareDifferentialgleichungen (sowieIntegro-Differentialgleichungen) zweiter Ordnung. Diesliefert neue Informationen über die zugehörigenLösungsmengen im Hinblick auf Knoteneigenschaften. Diehergeleiteten Methoden eignen sich besonders für eindimensionale und radialsymmetrische Probleme, während einTeil der Resultate auch ohne Symmetrieforderungen gültigist.

Spectral-Element and Adjoint 3D Full-Wave Tomography for the Lithosphere of Central Italy

The primary objective of this thesis is to obtain a better understanding of the 3D velocity structure of the lithosphere in central Italy. To this end, I adopted the Spectral-Element Method to perform accurate numerical simulations of the complex wavefields generated by the 2009 Mw 6.3 L’Aquila event and by its foreshocks and aftershocks together with some additional events within our target region. For the mainshock, the source was represented by a finite fault and different models for central Italy, both 1D and 3D, were tested. Surface topography, attenuation and Moho discontinuity were also accounted for. Three-component synthetic waveforms were compared to the corresponding recorded data. The results of these analyses show that 3D models, including all the known structural heterogeneities in the region, are essential to accurately reproduce waveform propagation. They allow to capture features of the seismograms, mainly related to topography or to low wavespeed areas, and, combined with a finite fault model, result into a favorable match between data and synthetics for frequencies up to ~0.5 Hz. We also obtained peak ground velocity maps, that provide valuable information for seismic hazard assessment. The remaining differences between data and synthetics led us to take advantage of SEM combined with an adjoint method to iteratively improve the available 3D structure model for central Italy. A total of 63 events and 52 stations in the region were considered. We performed five iterations of the tomographic inversion, by calculating the misfit function gradient - necessary for the model update - from adjoint sensitivity kernels, constructed using only two simulations for each event. Our last updated model features a reduced traveltime misfit function and improved agreement between data and synthetics, although further iterations, as well as refined source solutions, are necessary to obtain a new reference 3D model for central Italy tomography.

Airborne measurements of the spectral surface albedo over Morocco and its influence on the radiative forcing of Saharan dust

This PhD thesis is embedded into the DFG research project SAMUM, the Saharan Mineral Dust Experiment which was initiated with the goal to investigate the optical and microphysical properties of Saharan dust aerosol, its transport, and its radiative effect. This work described the deployment of the Spectral Modular Airborne Radiation Measurement SysTem (SMART-Albedometer) in SAMUM after it has been extended in its spectral range. The SAMUM field campaign was conducted in May and June 2006 in south-eastern Morocco. At two ground stations and aboard two aircraft various measurements in an almost pure plume of Saharan dust were conducted. Airborne measurements of the spectral upwelling and downwelling irradiance are used to derive the spectral surface albedo in its typical range in the experiment region. Typical spectral types are presented and compared to the surface albedo derived from MISR satellite data. Furthermore, the radiative forcing of the observed Saharan dust is estimated in dependence on the surface albedo and its regional variations. A strong dependence of the radiative forcing not only on the surface albedo, but also on the optical properties of the dust aerosol is observed. It is unique to SAMUM that all these influential parameters have been measured in near-source Saharan dust, which made the calculations shown in this work possible.

Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form

In this Thesis we consider a class of second order partial differential operators with non-negative characteristic form and with smooth coefficients. Main assumptions on the relevant operators are hypoellipticity and existence of a well-behaved global fundamental solution. We first make a deep analysis of the L-Green function for arbitrary open sets and of its applications to the Representation Theorems of Riesz-type for L-subharmonic and L-superharmonic functions. Then, we prove an Inverse Mean value Theorem characterizing the superlevel sets of the fundamental solution by means of L-harmonic functions. Furthermore, we establish a Lebesgue-type result showing the role of the mean-integal operator in solving the homogeneus Dirichlet problem related to L in the Perron-Wiener sense. Finally, we compare Perron-Wiener and weak variational solutions of the homogeneous Dirichlet problem, under specific hypothesis on the boundary datum.

Main characteristics of the emission from elliptical galaxies

Elliptical galaxies are one of the most characteristic objects we can find in the sky. In order to unveil their properties, such as their structure or chemical composition, one must study their spectral emission. In fact they seem to behave rather differently when observed with different eyes. This is because their light is mainly brought by two different components: optical radiation arises from its stars, while the X emission is primarly due to a halo of extremely hot gas in which ellipticals seem to be embedded. After a brief classification, the two main processes linked to these phenomena will be described, together with the informations we can collect thanks to them. Eventually, we will take a quick look at the other regions of the electromagnetic spectrum.

Extracting evolutionary information from the spectral decomposition of early-type galaxies.

Holding the major share of stellar mass in galaxies and being also old and passively evolving, early-type galaxies (ETGs) are the primary probes in investigating these various evolution scenarios, as well as being useful means to provide insights on cosmological parameters. In this thesis work I focused specifically on ETGs and on their capability in constraining galaxy formation and evolution; in particular, the principal aims were to derive some of the ETGs evolutionary parameters, such as age, metallicity and star formation history (SFH) and to study their age-redshift and mass-age relations. In order to infer galaxy physical parameters, I used the public code STARLIGHT: this program provides a best fit to the observed spectrum from a combination of many theoretical models defined in user-made libraries. the comparison between the output and input light-weighted ages shows a good agreement starting from SNRs of ∼ 10, with a bias of ∼ 2.2% and a dispersion 3%. Furthermore, also metallicities and SFHs are well reproduced. In the second part of the thesis I performed an analysis on real data, starting from Sloan Digital Sky Survey (SDSS) spectra. I found that galaxies get older with cosmic time and with increasing mass (for a fixed redshift bin); absolute light-weighted ages, instead, result independent from the fitting parameters or the synthetic models used. Metallicities, instead, are very similar from each other and clearly consistent with the ones derived from the Lick indices. The predicted SFH indicates the presence of a double burst of star formation. Velocity dispersions and extinctiona are also well constrained, following the expected behaviours. As a further step, I also fitted single SDSS spectra (with SNR∼ 20), to verify that stacked spectra gave the same results without introducing any bias: this is an important check, if one wants to apply the method at higher z, where stacked spectra are necessary to increase the SNR. Our upcoming aim is to adopt this approach also on galaxy spectra obtained from higher redshift Surveys, such as BOSS (z ∼ 0.5), zCOSMOS (z 1), K20 (z ∼ 1), GMASS (z ∼ 1.5) and, eventually, Euclid (z 2). Indeed, I am currently carrying on a preliminary study to estabilish the applicability of the method to lower resolution, as well as higher redshift (z 2) spectra, just like the Euclid ones.

Spectral estimates and preconditioning for saddle point systems arising from optimization problems

In this thesis, we consider the problem of solving large and sparse linear systems of saddle point type stemming from optimization problems. The focus of the thesis is on iterative methods, and new preconditioning srategies are proposed, along with novel spectral estimtates for the matrices involved.

Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

Antarctic cloud spectral emission from ground-based measurements, a focus on far infrared signatures

The present work belongs to the PRANA project, the first extensive field campaign of observation of atmospheric emission spectra covering the Far InfraRed spectral region, for more than two years. The principal deployed instrument is REFIR-PAD, a Fourier transform spectrometer used by us to study Antarctic cloud properties. A dataset covering the whole 2013 has been analyzed and, firstly, a selection of good quality spectra is performed, using, as thresholds, radiance values in few chosen spectral regions. These spectra are described in a synthetic way averaging radiances in selected intervals, converting them into BTs and finally considering the differences between each pair of them. A supervised feature selection algorithm is implemented with the purpose to select the features really informative about the presence, the phase and the type of cloud. Hence, training and test sets are collected, by means of Lidar quick-looks. The supervised classification step of the overall monthly datasets is performed using a SVM. On the base of this classification and with the help of Lidar observations, 29 non-precipitating ice cloud case studies are selected. A single spectrum, or at most an average over two or three spectra, is processed by means of the retrieval algorithm RT-RET, exploiting some main IR window channels, in order to extract cloud properties. Retrieved effective radii and optical depths are analyzed, to compare them with literature studies and to evaluate possible seasonal trends. Finally, retrieval output atmospheric profiles are used as inputs for simulations, assuming two different crystal habits, with the aim to examine our ability to reproduce radiances in the FIR. Substantial mis-estimations are found for FIR micro-windows: a high variability is observed in the spectral pattern of simulation deviations from measured spectra and an effort to link these deviations to cloud parameters has been performed.

Perturbation theory for spectral subspaces

In der vorliegenden Arbeit wird die Variation abgeschlossener Unterräume eines Hilbertraumes untersucht, die mit isolierten Komponenten der Spektren von selbstadjungierten Operatoren unter beschränkten additiven Störungen assoziiert sind. Von besonderem Interesse ist hierbei die am wenigsten restriktive Bedingung an die Norm der Störung, die sicherstellt, dass die Differenz der zugehörigen orthogonalen Projektionen eine strikte Normkontraktion darstellt. Es wird ein Überblick über die bisher erzielten Resultate gegeben. Basierend auf einem Iterationsansatz wird eine allgemeine Schranke an die Variation der Unterräume für Störungen erzielt, die glatt von einem reellen Parameter abhängen. Durch Einführung eines Kopplungsparameters wird das Ergebnis auf den Fall additiver Störungen angewendet. Auf diese Weise werden zuvor bekannte Ergebnisse verbessert. Im Falle von additiven Störungen werden die Schranken an die Variation der Unterräume durch ein Optimierungsverfahren für die Stützstellen im Iterationsansatz weiter verschärft. Die zugehörigen Ergebnisse sind die besten, die bis zum jetzigen Zeitpunkt erzielt wurden.

Plasmonic nanoparticles as sensors : a novel approach to quantify adsorption and diffusion kinetics

Biosensors find wide application in clinical diagnostics, bioprocess control and environmental monitoring. They should not only show high specificity and reproducibility but also a high sensitivity and stability of the signal. Therefore, I introduce a novel sensor technology based on plasmonic nanoparticles which overcomes both of these limitations. Plasmonic nanoparticles exhibit strong absorption and scattering in the visible and near-infrared spectral range. The plasmon resonance, the collective coherent oscillation mode of the conduction band electrons against the positively charged ionic lattice, is sensitive to the local environment of the particle. I monitor these changes in the resonance wavelength by a new dark-field spectroscopy technique. Due to a strong light source and a highly sensitive detector a temporal resolution in the microsecond regime is possible in combination with a high spectral stability. This opens a window to investigate dynamics on the molecular level and to gain knowledge about fundamental biological processes.rnFirst, I investigate adsorption at the non-equilibrium as well as at the equilibrium state. I show the temporal evolution of single adsorption events of fibrinogen on the surface of the sensor on a millisecond timescale. Fibrinogen is a blood plasma protein with a unique shape that plays a central role in blood coagulation and is always involved in cell-biomaterial interactions. Further, I monitor equilibrium coverage fluctuations of sodium dodecyl sulfate and demonstrate a new approach to quantify the characteristic rate constants which is independent of mass transfer interference and long term drifts of the measured signal. This method has been investigated theoretically by Monte-Carlo simulations but so far there has been no sensor technology with a sufficient signal-to-noise ratio.rnSecond, I apply plasmonic nanoparticles as sensors for the determination of diffusion coefficients. Thereby, the sensing volume of a single, immobilized nanorod is used as detection volume. When a diffusing particle enters the detection volume a shift in the resonance wavelength is introduced. As no labeling of the analyte is necessary the hydrodynamic radius and thus the diffusion properties are not altered and can be studied in their natural form. In comparison to the conventional Fluorescence Correlation Spectroscopy technique a volume reduction by a factor of 5000-10000 is reached.

Internal characteristics, chemical compounds and spectroscopy of sapphire as single crystals

In this study more than 450 natural sapphire samples (most of basaltic type) collected from 19 different areas were examined. They are from Dak Nong, Dak Lak, Quy Chau, two unknown sources from the north (Vietnam); Bo Ploi, Khao Ploi Waen (Thailand); Ban Huay Sai (Laos); Australia; Shandong (China); Andapa, Antsirabe, Nosibe (Madagascar); Ballapana (Sri Lanka); Brazil; Russia; Colombia; Tansania and Malawi. rnThe samples were studied on internal characteristics, chemical compositions, Raman-, luminescence-, Fourier transform infrared (FTIR)-, and ultraviolet-visible-near infrared (UV-Vis-NIR)- spectroscopy. The internal features of these sapphire samples were observed and identified by gemological microscope, con focal micro Raman and FTIR spectroscopy. The major and minor elements of the samples were determined by electron probe microanalysis (EPMA) and the trace elements by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). rnThe structural spectra of sapphire were investigated by con focal Raman spectroscopy. The FTIR spectroscopy was used to study the vibration modes of OH-groups and also to determine hydrous mineral inclusions in sapphire. The UV-Vis-NIR absorption spectroscopy was used to analyze the cause of sapphire color. rnNatural sapphires contain many types of mineral inclusions. Typically, they are iron-containing inclusions like goethite, ilmenite, hematite, magnetite or silicate minerals commonly feldspar, and often observed in sapphires from Asia countries, like Dak Nong, Dak Lak in the south of Vietnam, Ban Huay Sai (Laos), Khao Ploi Waen and Bo Ploi (Thailand) or Shandong (China). Meanwhile, CO2-diaspore inclusions are normally found in sapphires from Tansania, Colombia, or the north of Vietnam like Quy Chau. rnIron is the most dominant element in sapphire, up to 1.95 wt.% Fe2O3 measured by EPMA and it affects spectral characteristics of sapphire.rnThe Raman spectra of sapphire contain seven peaks (2A1g + 5Eg). Two peaks at about 418.3 cm-1 and 577.7 cm-1 are influenced by high iron content. These two peaks shift towards smaller wavenumbers corresponding to increasing iron content. This shift is showed by two equations y(418.3)=418.29-0.53x andy(577.7)=577.96-0.75x, in which y is peak position (cm-1) and x is Fe2O3 content (wt.%). By exploiting two these equations one can estimate the Fe2O3 contents of sapphire or corundum by identifying the respective Raman peak positions. Determining the Fe2O3 content in sapphire can help to distinguish sapphires from different origins, e.g. magmatic and metamorphic sapphire. rnThe luminescence of sapphire is characterized by two R-lines: R1 at about 694 nm and R2 at about 692 nm. This characteristic is also influenced by high iron content. The peak positions of two R-lines shift towards to smaller wavelengths corresponding to increasing of iron content. This correlation is showed by two equations y(R_2 )=692.86-0.049x and y(R_1 )=694.29-0.047x, in which y is peak position (nm) of respective R-lines and x is Fe2O3 content (wt.%). Two these equations can be applied to estimate the Fe2O3 content of sapphire and help to separate sapphires from different origins. The luminescence is also applied for determination of the remnant pressure or stress around inclusions in Cr3+-containing corundum by calibrating a 0-pressure position in experimental techniques.rnThe infrared spectra show the presence of vibrations originating from OH-groups and hydrous mineral inclusions in the range of 2500-4000 cm-1. Iron has also an effect upon the main and strongest peak at about 3310 cm-1. The 3310 cm-1 peak is shifted to higher wavenumber when iron content increases. This relationship is expressed by the equation y(3310)=0.92x+3309.17, in which y is peak position of the 3310 cm-1 and x is Fe2O3 content (wt.%). Similar to the obtained results in Raman and luminescence spectra, this expression can be used to estimate the Fe2O3 content and separate sapphires from different origins. rnThe UV-Vis-NIR absorption spectra point out the strong and sharp peaks at about 377, 387, and 450 nm related to dispersed Fe3+, a broad band around 557 and 600 nm related to intervalence charge transfer (IVCT) Fe2+/Ti4+, and a broader band around 863 nm related to IVCT of Fe2+/Fe3+. rnGenerally, sapphires from different localities were completely investigated on internal features, chemical compounds, and solid spectral characteristics. The results in each part contribute for identifying the iron content and separate sapphires from different localities order origins. rn