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.

The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

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.

Reference values for digital X-ray radiogrammetry parameters in children and adolescents in comparison to estimates in patients with distal radius fractures.

The first objective of this study was to determine normative digital X-ray radiogrammetry (DXR) values, based on original digital images, in a pediatric population (aged 6-18 years). The second aim was to compare these reference data with patients suffering from distal radius fractures, whereas both cohorts originated from the same geographical region and were evaluated using the same technical parameters as well as inclusion and exclusion criteria. DXR-BMD and DXR-MCI of the metacarpal bones II-IV were assessed on standardized digital hand radiographs, without printing or scanning procedures. DXR parameters were estimated separately by gender and among six age groups; values in the fracture group were compared to age- and gender-matched normative data using Student's t tests and Z scores. In the reference cohort (150 boys, 138 girls), gender differences were found in bone mineral density (DXR-BMD), with higher values for girls from 11 to 14 years and for boys from 15 to 18 years (p < 0.05). Girls had higher normative metacarpal index (DXR-MCI) values than boys, with significant differences at 11-14 years (p < 0.05). In the case-control investigation, the fracture group (95 boys, 69 girls) presented lower DXR-BMD at 15-18 years in boys and 13-16 years in girls vs. the reference cohort (p < 0.05); DXR-MCI was lower at 11-18 years in boys and 11-16 years in girls (p < 0.05). Mean Z scores in the fracture group for DXR-BMD were -0.42 (boys) and -0.46 (girls), and for DXR-MCI were -0.51 (boys) and -0.53 (girls). These findings indicate that the fully digital DXR technique can be accurately applied in pediatric populations ≥ 6 years of age. The lower DXR-BMD and DXR-MCI values in the fracture group suggest promising early identification of individuals with increased fracture risk, without the need for additional radiation exposure, enabling the initiation of prevention strategies to possibly reduce the incidence of osteoporosis later in life.

Differentiation of Diabetic Macular Edema From Pseudophakic Cystoid Macular Edema by Spectral-Domain Optical Coherence Tomography.

PURPOSE: To differentiate diabetic macular edema (DME) from pseudophakic cystoid macular edema (PCME) based solely on spectral-domain optical coherence tomography (SD-OCT). METHODS: This cross-sectional study included 134 participants: 49 with PCME, 60 with DME, and 25 with diabetic retinopathy (DR) and ME after cataract surgery. First, two unmasked experts classified the 25 DR patients after cataract surgery as either DME, PCME, or mixed-pattern based on SD-OCT and color-fundus photography. Then all 134 patients were divided into two datasets and graded by two masked readers according to a standardized reading-protocol. Accuracy of the masked readers to differentiate the diseases based on SD-OCT parameters was tested. Parallel to the masked readers, a computer-based algorithm was established using support vector machine (SVM) classifiers to automatically differentiate disease entities. RESULTS: The masked readers assigned 92.5% SD-OCT images to the correct clinical diagnose. The classifier-accuracy trained and tested on dataset 1 was 95.8%. The classifier-accuracy trained on dataset 1 and tested on dataset 2 to differentiate PCME from DME was 90.2%. The classifier-accuracy trained and tested on dataset 2 to differentiate all three diseases was 85.5%. In particular, higher central-retinal thickness/retinal-volume ratio, absence of an epiretinal-membrane, and solely inner nuclear layer (INL)-cysts indicated PCME, whereas higher outer nuclear layer (ONL)/INL ratio, the absence of subretinal fluid, presence of hard exudates, microaneurysms, and ganglion cell layer and/or retinal nerve fiber layer cysts strongly favored DME in this model. CONCLUSIONS: Based on the evaluation of SD-OCT, PCME can be differentiated from DME by masked reader evaluation, and by automated analysis, even in DR patients with ME after cataract surgery. The automated classifier may help to independently differentiate these two disease entities and is made publicly available.

Can we constrain the interior structure of rocky exoplanets from mass and radius measurements?

Aims. We present an inversion method based on Bayesian analysis to constrain the interior structure of terrestrial exoplanets, in the form of chemical composition of the mantle and core size. Specifically, we identify what parts of the interior structure of terrestrial exoplanets can be determined from observations of mass, radius, and stellar elemental abundances. Methods. We perform a full probabilistic inverse analysis to formally account for observational and model uncertainties and obtain confidence regions of interior structure models. This enables us to characterize how model variability depends on data and associated uncertainties. Results. We test our method on terrestrial solar system planets and find that our model predictions are consistent with independent estimates. Furthermore, we apply our method to synthetic exoplanets up to 10 Earth masses and up to 1.7 Earth radii, and to exoplanet Kepler-36b. Importantly, the inversion strategy proposed here provides a framework for understanding the level of precision required to characterize the interior of exoplanets. Conclusions. Our main conclusions are (1) observations of mass and radius are sufficient to constrain core size; (2) stellar elemental abundances (Fe, Si, Mg) are principal constraints to reduce degeneracy in interior structure models and to constrain mantle composition; (3) the inherent degeneracy in determining interior structure from mass and radius observations does not only depend on measurement accuracies, but also on the actual size and density of the exoplanet. We argue that precise observations of stellar elemental abundances are central in order to place constraints on planetary bulk composition and to reduce model degeneracy. We provide a general methodology of analyzing interior structures of exoplanets that may help to understand how interior models are distributed among star systems. The methodology we propose is sufficiently general to allow its future extension to more complex internal structures including hydrogen- and water-rich exoplanets.

A Maximum Radius for Habitable Planets

We compute the maximum radius a planet can have in order to fulfill two constraints that are likely necessary conditions for habitability: 1- surface temperature and pressure compatible with the existence of liquid water, and 2- no ice layer at the bottom of a putative global ocean, that would prevent the operation of the geologic carbon cycle to operate. We demonstrate that, above a given radius, these two constraints cannot be met: in the Super-Earth mass range (1-12 M-earth), the overall maximum that a planet can have varies between 1.8 and 2.3 R-earth. This radius is reduced when considering planets with higher Fe/Si ratios, and taking into account irradiation effects on the structure of the gas envelope.

A LAPLACE TRANSFORM PAIR MODEL TO DETERMINE BREMSSTRAHLUNG SPECTRA FROM ATTENUATION DATA (RADIATION, X-RAY, SPECTRAL MODELING)

Every x-ray attenuation curve inherently contains all the information necessary to extract the complete energy spectrum of a beam. To date, attempts to obtain accurate spectral information from attenuation data have been inadequate.^ This investigation presents a mathematical pair model, grounded in physical reality by the Laplace Transformation, to describe the attenuation of a photon beam and the corresponding bremsstrahlung spectral distribution. In addition the Laplace model has been mathematically extended to include characteristic radiation in a physically meaningful way. A method to determine the fraction of characteristic radiation in any diagnostic x-ray beam was introduced for use with the extended model.^ This work has examined the reconstructive capability of the Laplace pair model for a photon beam range of from 50 kVp to 25 MV, using both theoretical and experimental methods.^ In the diagnostic region, excellent agreement between a wide variety of experimental spectra and those reconstructed with the Laplace model was obtained when the atomic composition of the attenuators was accurately known. The model successfully reproduced a 2 MV spectrum but demonstrated difficulty in accurately reconstructing orthovoltage and 6 MV spectra. The 25 MV spectrum was successfully reconstructed although poor agreement with the spectrum obtained by Levy was found.^ The analysis of errors, performed with diagnostic energy data, demonstrated the relative insensitivity of the model to typical experimental errors and confirmed that the model can be successfully used to theoretically derive accurate spectral information from experimental attenuation data. ^