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.

The genetic signature of Neolithic in Greece

The Neolithic is characterized by the transition from a subsistence economy, based on hunting and gathering, to one based on food producing. This important change was paralleled by one of the most significant demographic increase in the recent history of European populations. The earliest Neolithic sites in Europe are located in Greece. However, the debate regarding the colonization route followed by the Middle-eastern farmers is still open. Based on archaeological, archaeobotanical, craniometric and genetic data, two main hypotheses have been proposed. The first implies the maritime colonization of North-eastern Peloponnesus from Crete, whereas the second points to an island hopping route that finally brought migrants to Central Greece. To test these hypotheses using a genetic approach, 206 samples were collected from the two Greek regions proposed as the arrival point of the two routes (Korinthian district and Euboea). Expectations for each hypothesis were compared with empirical observations based on the analysis of 60 SNPs and 26 microsatellite loci of Y-chromosome and mitochondrial DNA hypervariable region I. The analysis of Y-chromosome haplogroups revealed a strong genetic affinity of Euboea with Anatolian and Middle-eastern populations. The inferences of the time since population expansion suggests an earlier usage of agriculture in Euboea. Moreover, the haplogroup J2a-M410, supposed to be associated with the Neolithic transition, was observed at higher frequency and variance in Euboea showing, for both these parameters, a decreasing gradient moving from this area. The time since expansion estimates for J2a-M410 was found to be compatible with the Neolithic and slightly older in Euboea. The analysis of mtDNA resulted less informative. However, a higher genetic affinity of Euboea with Anatolian and Middle-eastern populations was confirmed. These results taken as a whole suggests that the most probable route followed by Neolithic farmers during the colonization of Greece was the island hopping route.

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.

Size-selective investigations of spectral and emission properties of small particles and nanotubes

In dieser Arbeit wurde die Elektronenemission von Nanopartikeln auf Oberflächen mittels spektroskopischen Photoelektronenmikroskopie untersucht. Speziell wurden metallische Nanocluster untersucht, als selbstorganisierte Ensembles auf Silizium oder Glassubstraten, sowie ferner ein Metall-Chalcogenid (MoS2) Nanoröhren-Prototyp auf Silizium. Der Hauptteil der Untersuchungen war auf die Wechselwirkung von fs-Laserstrahlung mit den Nanopartikeln konzentriert. Die Energie der Lichtquanten war kleiner als die Austrittsarbeit der untersuchten Proben, so dass Ein-Photonen-Photoemission ausgeschlossen werden konnte. Unsere Untersuchungen zeigten, dass ausgehend von einem kontinuierlichen Metallfilm bis hin zu Clusterfilmen ein anderer Emissionsmechanismus konkurrierend zur Multiphotonen-Photoemission auftritt und für kleine Cluster zu dominieren beginnt. Die Natur dieses neuen Mechanismus` wurde durch verschiedenartige Experimente untersucht. Der Übergang von einem kontinuierlichen zu einem Nanopartikelfilm ist begleitet von einer Zunahme des Emissionsstroms von mehr als eine Größenordnung. Die Photoemissions-Intensität wächst mit abnehmender zeitlicher Breite des Laserpulses, aber diese Abhängigkeit wird weniger steil mit sinkender Partikelgröße. Die experimentellen Resultate wurden durch verschiedene Elektronenemissions-Mechanismen erklärt, z.B. Multiphotonen-Photoemission (nPPE), thermionische Emission und thermisch unterstützte nPPE sowie optische Feldemission. Der erste Mechanismus überwiegt für kontinuierliche Filme und Partikel mit Größen oberhalb von mehreren zehn Nanometern, der zweite und dritte für Filme von Nanopartikeln von einer Größe von wenigen Nanometern. Die mikrospektroskopischen Messungen bestätigten den 2PPE-Emissionsmechanismus von dünnen Silberfilmen bei „blauer“ Laseranregung (hν=375-425nm). Das Einsetzen des Ferminiveaus ist relativ scharf und verschiebt sich um 2hν, wenn die Quantenenergie erhöht wird, wogegen es bei „roter“ Laseranregung (hν=750-850nm) deutlich verbreitert ist. Es zeigte sich, dass mit zunehmender Laserleistung die Ausbeute von niederenergetischen Elektronen schwächer zunimmt als die Ausbeute von höherenergetischen Elektronen nahe der Fermikante in einem Spektrum. Das ist ein klarer Hinweis auf eine Koexistenz verschiedener Emissionsmechanismen in einem Spektrum. Um die Größenabhängigkeit des Emissionsverhaltens theoretisch zu verstehen, wurde ein statistischer Zugang zur Lichtabsorption kleiner Metallpartikel abgeleitet und diskutiert. Die Elektronenemissionseigenschaften bei Laseranregung wurden in zusätzlichen Untersuchungen mit einer anderen Anregungsart verglichen, der Passage eines Tunnelstroms durch einen Metall-Clusterfilm nahe der Perkolationsschwelle. Die elektrischen und Emissionseigenschaften von stromtragenden Silberclusterfilmen, welche in einer schmalen Lücke (5-25 µm Breite) zwischen Silberkontakten auf einem Isolator hergestellt wurden, wurden zum ersten Mal mit einem Emissions-Elektronenmikroskop (EEM) untersucht. Die Elektronenemission beginnt im nicht-Ohmschen Bereich der Leitungsstrom-Spannungskurve des Clusterfilms. Wir untersuchten das Verhalten eines einzigen Emissionszentrums im EEM. Es zeigte sich, dass die Emissionszentren in einem stromleitenden Silberclusterfilm Punktquellen für Elektronen sind, welche hohe Emissions-Stromdichten (mehr als 100 A/cm2) tragen können. Die Breite der Energieverteilung der Elektronen von einem einzelnen Emissionszentrum wurde auf etwa 0.5-0.6 eV abgeschätzt. Als Emissionsmechanismus wird die thermionische Emission von dem „steady-state“ heißen Elektronengas in stromdurchflossenen metallischen Partikeln vorgeschlagen. Größenselektierte, einzelne auf Si-Substraten deponierte MoS2-Nanoröhren wurden mit einer Flugzeit-basierten Zweiphotonen-Photoemissions-Spektromikroskopie untersucht. Die Nanoröhren-Spektren wiesen bei fs-Laser Anregung eine erstaunlich hohe Emissionsintensität auf, deutlich höher als die SiOx Substratoberfläche. Dagegen waren die Röhren unsichtbar bei VUV-Anregung bei hν=21.2 eV. Eine ab-initio-Rechnung für einen MoS2-Slab erklärt die hohe Intensität durch eine hohe Dichte freier intermediärer Zustände beim Zweiphotonen-Übergang bei hν=3.1 eV.

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.

Stimulus-induced gamma activity in the electrocorticogram of freely moving telemetric implanted rats: the neuronal signature of novelty detection

During this thesis a new telemetric recording system has been developed allowing ECoG/EEG recordings in freely behaving rodents (Lapray et al., 2008; Lapray et al., in press). This unit has been shown to not generate any discomfort in the implanted animals and to allow recordings in a wide range of environments. In the second part of this work the developed technique has been used to investigate what cortical activity was related to the process of novelty detection in rats’ barrel cortex. We showed that the detection of a novel object is accompanied in the barrel cortex by a transient burst of activity in the γ frequency range (40-47 Hz) around 200 ms after the whiskers contact with the object (Lapray et al., accepted). This activity was associated to a decrease in the lower range of γ frequencies (30-37 Hz). This network activity may represent the optimal oscillatory pattern for the propagation and storage of new information in memory related structures. The frequency as well as the timing of appearance correspond well with other studies concerning novelty detection related burst of activity in other sensory systems (Barcelo et al., 2006; Haenschel et al., 2000; Ranganath & Rainer, 2003). Here, the burst of activity is well suited to induce plastic and long-lasting modifications in neuronal circuits (Harris et al., 2003). The debate is still open whether synchronised activity in the brain is a part of information processing or an epiphenomenon (Shadlen & Movshon, 1999; Singer, 1999). The present work provides further evidence that neuronal network activity in the γ frequency range plays an important role in the neocortical processing of sensory stimuli and in higher cognitive functions.

Epigenetic signature in persons with Down Syndrome

Persons affected by Down Syndrome show a heterogeneous phenotype that includes developmental defects and cognitive and haematological disorders. Premature accelerated aging and the consequent development of age associated diseases like Alzheimer Disease (AD) seem to be the cause of higher mortality late in life of DS persons. Down Syndrome is caused by the complete or partial trisomy of chromosome 21, but it is not clear if the molecular alterations of the disease are triggered by the specific functions of a limited number of genes on chromosome 21 or by the disruption of genetic homeostasis due the presence of a trisomic chromosome. As epigenomic studies can help to shed light on this issue, here we used the Infinium HumanMethilation450 BeadChip to analyse blood DNA methylation patterns of 29 persons affected by Down syndrome (DSP), using their healthy siblings (DSS) and mothers (DSM) as controls. In this way we obtained a family-based model that allowed us to monitor possible confounding effects on DNA methylation patterns deriving from genetic and environmental factors. We showed that defects in DNA methylation map in genes involved in developmental, neurological and haematological pathways. These genes are enriched on chromosome 21 but localize also in the rest of the genome, suggesting that the trisomy of specific genes on chromosome 21 induces a cascade of events that engages many genes on other chromosomes and results in a global alteration of genomic function. We also analysed the methylation status of three target regions localized at the promoter (Ribo) and at the 5’ sequences of 18S and 28S regions of the rDNA, identifying differently methylated CpG sites. In conclusion, we identified an epigenetic signature of Down Syndrome in blood cells that sustains a link between developmental defects and disease phenotype, including segmental premature aging.

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.

Approccio network-based alla discriminant analysis mediante HPC per la ricerca di signature ottimali in dati ad alta dimensionalità

Il presente lavoro di tesi si inserisce nell’ambito della classificazione di dati ad alta dimensionalità, sviluppando un algoritmo basato sul metodo della Discriminant Analysis. Esso classifica i campioni attraverso le variabili prese a coppie formando un network a partire da quelle che hanno una performance sufficientemente elevata. Successivamente, l’algoritmo si avvale di proprietà topologiche dei network (in particolare la ricerca di subnetwork e misure di centralità di singoli nodi) per ottenere varie signature (sottoinsiemi delle variabili iniziali) con performance ottimali di classificazione e caratterizzate da una bassa dimensionalità (dell’ordine di 101, inferiore di almeno un fattore 103 rispetto alle variabili di partenza nei problemi trattati). Per fare ciò, l’algoritmo comprende una parte di definizione del network e un’altra di selezione e riduzione della signature, calcolando ad ogni passaggio la nuova capacità di classificazione operando test di cross-validazione (k-fold o leave- one-out). Considerato l’alto numero di variabili coinvolte nei problemi trattati – dell’ordine di 104 – l’algoritmo è stato necessariamente implementato su High-Performance Computer, con lo sviluppo in parallelo delle parti più onerose del codice C++, nella fattispecie il calcolo vero e proprio del di- scriminante e il sorting finale dei risultati. L’applicazione qui studiata è a dati high-throughput in ambito genetico, riguardanti l’espressione genica a livello cellulare, settore in cui i database frequentemente sono costituiti da un numero elevato di variabili (104 −105) a fronte di un basso numero di campioni (101 −102). In campo medico-clinico, la determinazione di signature a bassa dimensionalità per la discriminazione e classificazione di campioni (e.g. sano/malato, responder/not-responder, ecc.) è un problema di fondamentale importanza, ad esempio per la messa a punto di strategie terapeutiche personalizzate per specifici sottogruppi di pazienti attraverso la realizzazione di kit diagnostici per l’analisi di profili di espressione applicabili su larga scala. L’analisi effettuata in questa tesi su vari tipi di dati reali mostra che il metodo proposto, anche in confronto ad altri metodi esistenti basati o me- no sull’approccio a network, fornisce performance ottime, tenendo conto del fatto che il metodo produce signature con elevate performance di classifica- zione e contemporaneamente mantenendo molto ridotto il numero di variabili utilizzate per questo scopo.

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).