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.

Investigation of spectral stability of X-ray tubes by simulations and experimental spectrum measurements

L'obiettivo di questo lavoro è quello di analizzare la stabilità di uno spettro raggi X emesso da un tubo usurato per analisi cardiovascolari, in modo da verificare il suo comportamento. Successivamente questo tipo di analisi sarà effettuata su tubi CT. Per raggiungere questo scopo è stato assemblato un particolare set-up con un rivelatore al germanio criogenico in modo da avere la miglior risoluzione energetica possibile ed alcuni particolari collimatori così da ridurre il flusso fotonico per evitare effetti di pile-up. Il set-up è stato costruito in modo da avere il miglior allineamento possibile nel modo più veloce possibile, e con l'obiettivo di rendere l'intero sistema portabile. Il tubo usato è un SRM Philips tube per analisi cardiovascolari; questa scelta è stata fatta in modo da ridurre al minimo i fattori esterni (ottica elettromagnetica, emettitori) e concentrare l'attenzione solo sugli effetti, causati dalle varie esposizioni, sull'anodo (roughness e bending) e sul comportamento di essi durante il surriscaldamento e successivo raffreddamento del tubo. I risultati mostrano come durante un'esposizione alcuni fattori di usura del tubo possono influire in maniera sostanziale sullo spettro ottenuto e quindi alterare il risultato. Successivamente, nell'elaborato, mediante il software Philips di ricostruzione e simulazione dello spettro si è cercato di riprodurre, variando alcuni parametri, la differenza riscontrata sperimentalmente in modo da poter simulare l'instabilità e correggere i fattori che la causano. I risultati sono interessanti non solo per questo esperimento ma anche in ottica futura, per lo sviluppo di applicazioni come la spectral CT. Il passo successivo sarà quello di spostare l'attenzione su un CT tube e verificare se l'instabilità riscontrata in questo lavoro è persiste anche in una analisi più complessa come quella CT.

Small dense particles in the retina observable by spectral-domain optical coherence tomography in age-related macular degeneration

To observe detailed changes in neurosensory retinal structure after anti-VEGF upload in age-related macular degeneration (AMD), by using spectral domain optical coherence tomography (SD-OCT).

Spectral-domain optical coherence tomography use in macular diseases: a review

The introduction of spectral-domain optical coherence tomography (SD-OCT) has improved the clinical value for assessment of the eyes with macular disease. This article reviews the advances of SD-OCT for the diagnostic of various macular diseases. These include vitreomacular traction syndrome, cystoid macular edema/diabetic macular edema, epiretinal membranes, full-thickness macular holes, lamellar holes, pseudoholes, microholes, and schisis from myopia. Besides offering new insights into the pathogenesis of macular abnormalities, SD-OCT is a valuable tool for monitoring macular disease.

Focal cystic high-attenuation lesions: characterization in renal phantom by using photon-counting spectral CT--improved differentiation of lesion composition

To evaluate the capability of spectral computed tomography (CT) to improve the characterization of cystic high-attenuation lesions in a renal phantom and to test the hypothesis that spectral CT will improve the differentiation of cystic renal lesions with high protein content and those that have undergone hemorrhage or malignant contrast-enhancing transformation.

Effects on choroidal neovascularization after anti-VEGF Upload using intravitreal ranibizumab, as determined by spectral domain-optical coherence tomography

It is unclear whether anti-VEGF monotherapy in age-related macular degeneration (AMD) achieves morphologic CNV regression or only stops further CNV growth. In this study, spectral domain-optical coherence tomography (SD-OCT) was used to image CNV structure before and after anti-VEGF treatment.

Repeatability of nerve fiber layer thickness measurements in patients with glaucoma and without glaucoma using spectral-domain and time-domain OCT

The aim of this work is to assess the repeatability of spectral-domain-OCT (SD-OCT) retinal nerve fiber layer thickness (RNFL) thickness measurements in a non-glaucoma group and patients with glaucoma and to compare these results to conventional time-domain-OCT (TD-OCT).

Equivariant inverse spectral theory and toric orbifolds

Let O-2n be a symplectic toric orbifold with a fixed T-n-action and with a tonic Kahler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace Delta(g) operator on C-infinity(O) determines O up to symplectomorphism. In the setting of tonic orbifolds we shmilicantly improve upon our previous results and show that a generic tone orbifold is determined by its equivariant spectrum, up to two possibilities. This involves developing the asymptotic expansion of the heat trace on an orbifold in the presence of an isometry. We also show that the equivariant spectrum determines whether the toric Kahler metric has constant scalar curvature. (C) 2012 Elsevier Inc. All rights reserved.

Quality evaluation of tandem mass spectral libraries

Tandem mass spectral libraries are gaining more and more importance for the identification of unknowns in different fields of research, including metabolomics, forensics, toxicology, and environmental analysis. Particularly, the recent invention of reliable, robust, and transferable libraries has increased the general acceptance of these tools. Herein, we report on results obtained from thorough evaluation of the match reliabilities of two tandem mass spectral libraries: the MSforID library established by the Oberacher group in Innsbruck and the Weinmann library established by the Weinmann group in Freiburg. Three different experiments were performed: (1) Spectra of the libraries were searched against their corresponding library after excluding either this single compound-specific spectrum or all compound-specific spectra prior to searching; (2) the libraries were searched against each other using either library as reference set or sample set; (3) spectra acquired on different mass spectrometric instruments were matched to both libraries. Almost 13,000 tandem mass spectra were included in this study. The MSforID search algorithm was used for spectral matching. Statistical evaluation of the library search results revealed that principally both libraries enable the sensitive and specific identification of compounds. Due to higher mass accuracy of the QqTOF compared with the QTrap instrument, matches to the MSforID library were more reliable when comparing spectra with both libraries. Furthermore, only the MSforID library was shown to be efficiently transferable to different kinds of tandem mass spectrometers, including "tandem-in-time" instruments; this is due to the coverage of a large range of different collision energy settings-including the very low range-which is an outstanding characteristics of the MSforID library.