Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

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.

Bundle branch re-entry ventricular tachycardia in a patient with complete heart block

A 58-year-old male patient presented episodes of palpitations in the context of atrioventricular block treated by a dual-chamber pacemaker. Clinical and electrophysiological studies identified the tachyarrhythmia to be bundle branch re-entrant ventricular tachycardia, which was successfully treated by radiofrequency ablation of the proximal right bundle branch.

Signal peptide and helical bundle domains of virulent canine distemper virus fusion protein restrict fusogenicity

Persistence in canine distemper virus (CDV) infection is correlated with very limited cell-cell fusion and lack of cytolysis induced by the neurovirulent A75/17-CDV compared to that of the cytolytic Onderstepoort vaccine strain. We have previously shown that this difference was at least in part due to the amino acid sequence of the fusion (F) protein (P. Plattet, J. P. Rivals, B. Zuber, J. M. Brunner, A. Zurbriggen, and R. Wittek, Virology 337:312-326, 2005). Here, we investigated the molecular mechanisms of the neurovirulent CDV F protein underlying limited membrane fusion activity. By exchanging the signal peptide between both F CDV strains or replacing it with an exogenous signal peptide, we demonstrated that this domain controlled intracellular and consequently cell surface protein expression, thus indirectly modulating fusogenicity. In addition, by serially passaging a poorly fusogenic virus and selecting a syncytium-forming variant, we identified the mutation L372W as being responsible for this change of phenotype. Intriguingly, residue L372 potentially is located in the helical bundle domain of the F(1) subunit. We showed that this mutation drastically increased fusion activity of F proteins of both CDV strains in a signal peptide-independent manner. Due to its unique structure even among morbilliviruses, our findings with respect to the signal peptide are likely to be specifically relevant to CDV, whereas the results related to the helical bundle add new insights to our growing understanding of this class of F proteins. We conclude that different mechanisms involving multiple domains of the neurovirulent A75/17-CDV F protein act in concert to limit fusion activity, preventing lysis of infected cells, which ultimately may favor viral persistence.

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.

The service bundle design in a digital environment

Der Artikel behandelt das Projektieren der Produkt-Service-Verbindung vom Standpunkt der Informationsintegration aus. Der Autor erläutert grundlegende Unterschiede zwischen dem traditionellen und dem modernen Operationsmanagementkonzept. Ergänzend wird die Rolle der logistischen Unterstüzungsanalyse wird betrachtet. Der Artikel stellt das Konzept von CALS (Continuous Acquisition and Life cycle Support) dar, welches als Umgebung, die Datenverteilung zwischen den in den Entwicklungsprozess beteiligten Geschäftspartnern ermöglicht.

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.

White matter microstructure alterations of the medial forebrain bundle in melancholic depression

BACKGROUND The medial forebrain bundle (MFB) is a key structure of the reward system and connects the ventral tegmental area (VTA) with the nucleus accumbens (NAcc), the medial and lateral orbitofrontal cortex (mOFC, lOFC) and the dorsolateral prefrontal cortex (dlPFC). Previous diffusion tensor imaging (DTI) studies in major depressive disorder point to white matter alterations of regions which may be incorporated in the MFB. Therefore, it was the aim of our study to probe white matter integrity of the MFB using a DTI-based probabilistic fibre tracking approach. METHODS 22 patients with major depressive disorder (MDD) (12 melancholic-MDD patients, 10 non-melancholic-MDD patients) and 21 healthy controls underwent DTI scans. We used a bilateral probabilistic fibre tracking approach to extract pathways between the VTA and NACC, mOFC, lOFC, dlPFC respectively. Mean fractional anisotropy (FA) values were used to compare structural connectivity between groups. RESULTS Mean-FA did not differ between healthy controls and all MDD patients. Compared to healthy controls melancholic MDD-patients had reduced mean-FA in right VTA-lOFC and VTA-dlPFC connections. Furthermore, melancholic-MDD patients had lower mean-FA than non-melancholic MDD-patients in the right VTA-lOFC connection. Mean-FA of these pathways correlated negatively with depression scale rating scores. LIMITATIONS Due to the small sample size and heterogeneous age group comparisons between melancholic and non-melancholic MDD-patients should be regarded as preliminary. CONCLUSIONS Our results suggest that the melancholic subtype of MDD is characterized by white matter microstructure alterations of the MFB. White matter microstructure is associated with both depression severity and anhedonia.