Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings

We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and Neumann boundary conditions, respectively, at a selected vertex called root. The root is either the central vertex or, in the more challenging problem, a pendant vertex of the star graph. At all other pendant vertices Dirichlet conditions are imposed; at the central vertex, at which a mass may be placed, continuity and Kirchhoff conditions are assumed. We derive conditions on two sets of real numbers to be the spectra of the above Dirichlet and Neumann problems. Our solution for the inverse problems is constructive: we establish algorithms to recover the mass distribution on the star graph (i.e. the point masses and lengths of subintervals between them) from these two spectra and from the lengths of the separate strings. If the root is a pendant vertex, the two spectra uniquely determine the parameters on the main string (i.e. the string incident to the root) if the length of the main string is known. The mass distribution on the other edges need not be unique; the reason for this is the non-uniqueness caused by the non-strict interlacing of the given data in the case when the root is the central vertex. Finally, we relate of our results to tree-patterned matrix inverse problems.

Spectral bounds and basis results for non-self-adjoint pencils, with an application to Hagen-Poiseuille flow

We obtain eigenvalue enclosures and basisness results for eigen- and associated functions of a non-self-adjoint unbounded linear operator pencil A−λBA−λB in which BB is uniformly positive and the essential spectrum of the pencil is empty. Both Riesz basisness and Bari basisness results are obtained. The results are applied to a system of singular differential equations arising in the study of Hagen–Poiseuille flow with non-axisymmetric disturbances.

Generalized fuzzy clustering for segmentation of multi-spectral magnetic resonance images.

An integrated approach for multi-spectral segmentation of MR images is presented. This method is based on the fuzzy c-means (FCM) and includes bias field correction and contextual constraints over spatial intensity distribution and accounts for the non-spherical cluster's shape in the feature space. The bias field is modeled as a linear combination of smooth polynomial basis functions for fast computation in the clustering iterations. Regularization terms for the neighborhood continuity of intensity are added into the FCM cost functions. To reduce the computational complexity, the contextual regularizations are separated from the clustering iterations. Since the feature space is not isotropic, distance measure adopted in Gustafson-Kessel (G-K) algorithm is used instead of the Euclidean distance, to account for the non-spherical shape of the clusters in the feature space. These algorithms are quantitatively evaluated on MR brain images using the similarity measures.

Sleep respiratory disturbances and arousals at moderate altitude have overlapping electroencephalogram spectral signatures

An ascent to altitude has been shown to result in more central apneas and a shift towards lighter sleep in healthy individuals. This study employs spectral analysis to investigate the impact of respiratory disturbances (central/obstructive apnea and hypopnea or periodic breathing) at moderate altitude on the sleep electroencephalogram (EEG) and to compare EEG changes resulting from respiratory disturbances and arousals. Data were collected from 51 healthy male subjects who spent 1 night at moderate altitude (2590 m). Power density spectra of Stage 2 sleep were calculated in a subset (20) of these participants with sufficient artefact-free data for (a) epochs with respiratory events without an accompanying arousal, (b) epochs containing an arousal and (c) epochs of undisturbed Stage 2 sleep containing neither arousal nor respiratory events. Both arousals and respiratory disturbances resulted in reduced power in the delta, theta and spindle frequency range and increased beta power compared to undisturbed sleep. The similarity of the EEG changes resulting from altitude-induced respiratory disturbances and arousals indicates that central apneas are associated with micro-arousals, not apparent by visual inspection of the EEG. Our findings may have implications for sleep in patients and mountain tourists with central apneas and suggest that respiratory disturbances not accompanied by an arousal may, none the less, impact sleep quality and impair recuperative processes associated with sleep more than previously believed.

A new Bayesian approach to the reconstruction of spectral functions

We present a novel approach for the reconstruction of spectra from Euclidean correlator data that makes close contact to modern Bayesian concepts. It is based upon an axiomatically justified dimensionless prior distribution, which in the case of constant prior function m(ω) only imprints smoothness on the reconstructed spectrum. In addition we are able to analytically integrate out the only relevant overall hyper-parameter α in the prior, removing the necessity for Gaussian approximations found e.g. in the Maximum Entropy Method. Using a quasi-Newton minimizer and high-precision arithmetic, we are then able to find the unique global extremum of P[ρ|D] in the full Nω » Nτ dimensional search space. The method actually yields gradually improving reconstruction results if the quality of the supplied input data increases, without introducing artificial peak structures, often encountered in the MEM. To support these statements we present mock data analyses for the case of zero width delta peaks and more realistic scenarios, based on the perturbative Euclidean Wilson Loop as well as the Wilson Line correlator in Coulomb gauge.

Spectral-domain optical coherence tomography findings after severe exogenous endophthalmitis

PURPOSE To report outcomes and assess structural changes in the retina in patients with severe endophthalmitis. METHODS Retrospective, nonrandomized, interventional case series at a tertiary referral centre. Spectral domain optical coherence tomography (OCT) images of both eyes were acquired at least 5 months after pars plana vitrectomy. OCT images were analyzed using retinal layer segmentation. RESULTS Nine patients (46-80 years of age) were included in this study. Average ETDRS visual acuity before treatment was 23 letters and improved to 74 letters. In our cohort we did not find a generalized reduction of retinal layers using automated layer segmentation. CONCLUSION Our findings suggest that prompt treatment of severe endophthalmitis with intravitreal antibiotics followed by pars plana vitrectomy may lead to excellent visual outcomes with minimal damage to the retinal architecture.

Rasmussen's spectral sequences and the \germslN-concordance invariants

Combining known spectral sequences with a new spectral sequence relating reduced and unreduced slN-homology yields a relations hip between the Homflypt-homology of a knot and its slN-concordance invariants. As an application, some of the slN-concordance invariants are shown to be linearly independent.

Investigation of retinal morphology alterations using spectral domain optical coherence tomography in a mouse model of retinal branch and central retinal vein occlusion.

Retinal vein occlusion is a leading cause of visual impairment. Experimental models of this condition based on laser photocoagulation of retinal veins have been described and extensively exploited in mammals and larger rodents such as the rat. However, few reports exist on the use of this paradigm in the mouse. The objective of this study was to investigate a model of branch and central retinal vein occlusion in the mouse and characterize in vivo longitudinal retinal morphology alterations using spectral domain optical coherence tomography. Retinal veins were experimentally occluded using laser photocoagulation after intravenous application of Rose Bengal, a photo-activator dye enhancing thrombus formation. Depending on the number of veins occluded, variable amounts of capillary dropout were seen on fluorescein angiography. Vascular endothelial growth factor levels were markedly elevated early and peaked at day one. Retinal thickness measurements with spectral domain optical coherence tomography showed significant swelling (p<0.001) compared to baseline, followed by gradual thinning plateauing two weeks after the experimental intervention (p<0.001). Histological findings at day seven correlated with spectral domain optical coherence tomography imaging. The inner layers were predominantly affected by degeneration with the outer nuclear layer and the photoreceptor outer segments largely preserved. The application of this retinal vein occlusion model in the mouse carries several advantages over its use in other larger species, such as access to a vast range of genetically modified animals. Retinal changes after experimental retinal vein occlusion in this mouse model can be non-invasively quantified by spectral domain optical coherence tomography, and may be used to monitor effects of potential therapeutic interventions.

Quantitative Analysis of Mouse Retinal Layers Using Automated Segmentation of Spectral Domain Optical Coherence Tomography Images.

PURPOSE Quantification of retinal layers using automated segmentation of optical coherence tomography (OCT) images allows for longitudinal studies of retinal and neurological disorders in mice. The purpose of this study was to compare the performance of automated retinal layer segmentation algorithms with data from manual segmentation in mice using the Spectralis OCT. METHODS Spectral domain OCT images from 55 mice from three different mouse strains were analyzed in total. The OCT scans from 22 C57Bl/6, 22 BALBc, and 11 C3A.Cg-Pde6b(+)Prph2(Rd2) /J mice were automatically segmented using three commercially available automated retinal segmentation algorithms and compared to manual segmentation. RESULTS Fully automated segmentation performed well in mice and showed coefficients of variation (CV) of below 5% for the total retinal volume. However, all three automated segmentation algorithms yielded much thicker total retinal thickness values compared to manual segmentation data (P < 0.0001) due to segmentation errors in the basement membrane. CONCLUSIONS Whereas the automated retinal segmentation algorithms performed well for the inner layers, the retinal pigmentation epithelium (RPE) was delineated within the sclera, leading to consistently thicker measurements of the photoreceptor layer and the total retina. TRANSLATIONAL RELEVANCE The introduction of spectral domain OCT allows for accurate imaging of the mouse retina. Exact quantification of retinal layer thicknesses in mice is important to study layers of interest under various pathological conditions.

Synthesis, spectral, and anti-microbial studies of thioiminium iodides and amine hydrochlorides

To avoid the undesired deprotonation during the addition of organolithium and organomagnesium reagents to ketones, the thioiminium salts, easily prepared from lactams and amides are converted into 2,2-disubstituted and 2-monosubstituted amines by reaction with simple nucleophiles such as organocerium and organocopper reagents. The reaction of thioiminium iodides with organocerium reagents derived by transmetalation of corresponding lithium reagents with anhydrous cerium(III) chloride has been investigated. These thioiminium iodides act as good electrophiles and accept alkylceriums towards bisaddition. The newly synthesized amines have been characterized by 1H and 13C NMR, IR and mass spectra. The amines have been converted into their hydrochlorides and characterized by COSY. These hydrochlorides have been subjected to antimicrobial screening with clinically isolated microorganisms, Staphylococcus aureus, Klebsiella pneumoniae, Pseudomonas aeruginosa, Salmonella typhi and Candida albicans. The hydrochlorides show quite good activity against these bacteria and fungus.