Sharp estimates for eigenvalues of integral operators generated by dot product kernels on the sphere

We obtain explicit formulas for the eigenvalues of integral operators generated by continuous dot product kernels defined on the sphere via the usual gamma function. Using them, we present both, a procedure to describe sharp bounds for the eigenvalues and their asymptotic behavior near 0. We illustrate our results with examples, among them the integral operator generated by a Gaussian kernel. Finally, we sketch complex versions of our results to cover the cases when the sphere sits in a Hermitian space.

Optical resonances of sphere-on-plane geometries

The optical resonances of metallic nanoparticles placed at nanometer distances from a metal plane were investigated. At certain wavelengths, these “sphere-on-plane” systems become resonant with the incident electromagnetic field and huge enhancements of the field are predicted localized in the small gaps created between the nanoparticle and the plane. An experimental architecture to fabricate sphere-on-plane systems was successfully achieved in which in addition to the commonly used alkanethiols, polyphenylene dendrimers were used as molecular spacers to separate the metallic nanoparticles from the metal planes. They allow for a defined nanoparticle-plane separation and some often are functionalized with a chromophore core which is therefore positioned exactly in the gap. The metal planes used in the system architecture consisted of evaporated thin films of gold or silver. Evaporated gold or silver films have a smooth interface with their substrate and a rougher top surface. To investigate the influence of surface roughness on the optical response of such a film, two gold films were prepared with a smooth and a rough side which were as similar as possible. Surface plasmons were excited in Kretschmann configuration both on the rough and on the smooth side. Their reflectivity could be well modeled by a single gold film for each individual measurement. The film has to be modeled as two layers with significantly different optical constants. The smooth side, although polycrystalline, had an optical response that was very similar to a monocrystalline surface while for the rough side the standard response of evaporated gold is retrieved. For investigations on thin non-absorbing dielectric films though, this heterogeneity introduces only a negligible error. To determine the resonant wavelength of the sphere-on-plane systems a strategy was developed which is based on multi-wavelength surface plasmon spectroscopy experiments in Kretschmann-configuration. The resonant behavior of the system lead to characteristic changes in the surface plasmon dispersion. A quantitative analysis was performed by calculating the polarisability per unit area /A treating the sphere-on-plane systems as an effective layer. This approach completely avoids the ambiguity in the determination of thickness and optical response of thin films in surface plasmon spectroscopy. Equal area densities of polarisable units yielded identical response irrespective of the thickness of the layer they are distributed in. The parameter range where the evaluation of surface plasmon data in terms of /A is applicable was determined for a typical experimental situation. It was shown that this analysis yields reasonable quantitative agreement with a simple theoretical model of the sphere-on-plane resonators and reproduces the results from standard extinction experiments having a higher information content and significantly increased signal-to-noise ratio. With the objective to acquire a better quantitative understanding of the dependence of the resonance wavelength on the geometry of the sphere-on-plane systems, different systems were fabricated in which the gold nanoparticle size, type of spacer and ambient medium were varied and the resonance wavelength of the system was determined. The gold nanoparticle radius was varied in the range from 10 nm to 80 nm. It could be shown that the polyphenylene dendrimers can be used as molecular spacers to fabricate systems which support gap resonances. The resonance wavelength of the systems could be tuned in the optical region between 550 nm and 800 nm. Based on a simple analytical model, a quantitative analysis was developed to relate the systems’ geometry with the resonant wavelength and surprisingly good agreement of this simple model with the experiment without any adjustable parameters was found. The key feature ascribed to sphere-on-plane systems is a very large electromagnetic field localized in volumes in the nanometer range. Experiments towards a quantitative understanding of the field enhancements taking place in the gap of the sphere-on-plane systems were done by monitoring the increase in fluorescence of a metal-supported monolayer of a dye-loaded dendrimer upon decoration of the surface with nanoparticles. The metal used (gold and silver), the colloid mean size and the surface roughness were varied. Large silver crystallites on evaporated silver surfaces lead to the most pronounced fluorescence enhancements in the order of 104. They constitute a very promising sample architecture for the study of field enhancements.

La PCA per la riduzione dei dati di SPHERE IFS

Nel primo capitolo di questa tesi viene presentata una panoramica dei principali metodi di rivelazione degli esopianeti: il metodo della Velocità Radiale, il metodo Astrometrico, il metodo del Pulsar Timing, il metodo del Transito, il metodo del Microlensing ed infine il metodo del Direct Imaging che verrà approfondito nei capitoli successivi. Nel secondo capitolo vengono presentati i principi della diffrazione, viene mostrato come attenuare la luce stellare con l'uso del coronografo; vengono descritti i fenomeni di aberrazione della luce provocati dalla strumentazione e dagli effetti distorsivi dell'atmosfera che originano le cosiddette speckle; vengono poi presentate le moderne soluzioni tecniche come l'ottica attiva e adattiva, che hanno permesso un considerevole miglioramento della qualità delle osservazioni. Nel terzo capitolo sono illustrate le tecniche di Differential Imaging che permettono di rimuovere efficacemente le speckle e di migliorare il contrasto delle immagini. Nel quarto viene presentata una descrizione matematica della Principal Component Analysis (Analisi delle Componenti Principali), il metodo statistico utilizzato per la riduzione dei dati astronomici. Il quinto capitolo è dedicato a SPHERE, lo strumento progettato per il Very Large Telescope (VLT), in particolare viene descritto il suo spettrografo IFS con il quale sono stati ottenuti, nella fase di test, i dati analizzati nel lavoro di tesi. Nel sesto capitolo vengono mostrate le procedure di riduzione dati e l'applicazione dell'algoritmo di IDL LA_SVD che applica la Principal Component Analysis e ha permesso, analogamente ai metodi di Differenzial Imaging visti in precedenza, di rimuovere le speckle e migliorare il contrasto delle immagini. Nella parte conclusiva, vengono discussi i risultati.

Self-adjoint extensions for confined electrons: From a particle in a spherical cavity to the hydrogen atom in a sphere and on a cone

In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at the wall of the cavity. In this paper, we study this situation in detail both for a free particle and for a hydrogen atom centered in a spherical cavity. For appropriate values of the self-adjoint extension parameter, the bound states localized at the wall resonate with the standard hydrogen bound states. We also examine the accidental symmetry generated by the Runge–Lenz vector, which is explicitly broken in a spherical cavity with general Robin boundary conditions. However, for specific radii of the confining sphere, a remnant of the accidental symmetry persists. The same is true for an electron moving on the surface of a finite circular cone, bound to its tip by a 1/r1/r potential.

Isolation of sphere-forming stem cells from the mouse inner ear

The mammalian inner ear has very limited ability to regenerate lost sensory hair cells. This deficiency becomes apparent when hair cell loss leads to hearing loss as a result of either ototoxic insult or the aging process. Coincidently, with this inability to regenerate lost hair cells, the adult cochlea does not appear to harbor cells with a proliferative capacity that could serve as progenitor cells for lost cells. In contrast, adult mammalian vestibular sensory epithelia display a limited ability for hair cell regeneration, and sphere-forming cells with stem cell features can be isolated from the adult murine vestibular system. The neonatal inner ear, however, does harbor sphere-forming stem cells residing in cochlear and vestibular tissues. Here, we provide protocols to isolate sphere-forming stem cells from neonatal vestibular and cochlear sensory epithelia as well as from the spiral ganglion. We further describe procedures for sphere propagation, cell differentiation, and characterization of inner ear cell types derived from spheres. Sphere-forming stem cells from the mouse inner ear are an important tool for the development of cellular replacement strategies of damaged inner ears and are a bona fide progenitor cell source for transplantation studies.

Cloud Computing in the EU Policy Sphere Interoperability, Vertical Integration and the Internal Market

Cloud computing is a new development that is based on the premise that data and applications are stored centrally and can be accessed through the Internet. Thisarticle sets up a broad analysis of how the emergence of clouds relates to European competition law, network regulation and electronic commerce regulation, which we relate to challenges for the further development of cloud services in Europe: interoperability and data portability between clouds; issues relating to vertical integration between clouds and Internet Service Providers; and potential problems for clouds to operate on the European Internal Market. We find that these issues are not adequately addressed across the legal frameworks that we analyse, and argue for further research into how to better facilitate innovative convergent services such as cloud computing through European policy – especially in light of the ambitious digital agenda that the European Commission has set out.

The Jews of Philadelphia : their history from the earliest settlements to the present time. A record of events and institutions, and of leading members of the Jewish community in every sphere of activity

Henry Samuel Morais

Cisplatin-resistant cells in malignant pleural mesothelioma cell lines show ALDH(high)CD44(+) phenotype and sphere-forming capacity

BACKGROUND Conventional chemotherapy in malignant pleural mesothelioma (MPM) has minimal impact on patient survival due to the supposed chemoresistance of cancer stem cells (CSCs). We sought to identify a sub-population of chemoresistant cells by using putative CSC markers, aldehyde dehydrogenase (ALDH) and CD44 in three MPM cell lines; H28, H2052 and Meso4. METHODS The Aldefluor assay was used to measure ALDH activity and sort ALDH(high) and ALDH(low) cells. Drug-resistance was evaluated by cell viability, anchorage-independent sphere formation, flow-cytometry and qRT-PCR analyses. RESULTS The ALDH(high) - and ALDH(low) -sorted fractions were able to demonstrate phenotypic heterogeneity and generate spheres, the latter being less efficient, and both showed an association with CD44. Cis- diamminedichloroplatinum (II) (cisplatin) treatment failed to reduce ALDH activity and conferred only a short-term inhibition of sphere generation in both ALDH(high) and ALDH(low) fractions of the three MPM cell lines. Induction of drug sensitivity by an ALDH inhibitor, diethylaminobenzaldehyde (DEAB) resulted in significant reductions in cell viability but not a complete elimination of the sphere-forming cells, suggestive of the presence of a drug-resistant subpopulation. At the transcript level, the cisplatin + DEAB-resistant cells showed upregulated mRNA expression levels for ALDH1A2, ALDH1A3 isozymes and CD44 indicating the involvement of these markers in conferring chemoresistance in both ALDH(high) and ALDH(low) fractions of the three MPM cell lines. CONCLUSIONS Our study shows that ALDH(high) CD44(+) cells are implicated in conveying tolerance to cisplatin in the three MPM cell lines. The combined use of CD44 and ALDH widens the window for identification and targeting of a drug-resistant population which may improve the current treatment modalities in mesothelioma.

Functionalization of PAMAM dendrimers with nitronyl nitroxide radicals as models for the outer-sphere relaxation in dentritic potential MRI contrast agents

PAMAM dendrimers functionalized with nitronyl nitroxide radicals were characterized. Quantitative determination of substitution with radicals was performed using EPR and electrochemical methods. The study of the 1H NMR relaxation of the surrounding water showed how the outer-sphere contribution to the relaxivity may be limited by the presence of the dendrimer core.