A bounded transform approach to self-adjoint operators: Functional calculus and affiliated von Neumann algebras

Spectral theory and functional calculus for unbounded self-adjoint operators on a Hilbert space are usually treated through von Neumann's Cayley transform. Based on ideas of Woronowicz, we redevelop this theory from the point of view of multiplier algebras and the so-called bounded transform (which establishes a bijective correspondence between closed operators and pure contractions). This also leads to a simple account of the affiliation relation between von Neumann algebras and self-adjoint operators.Comment: 10 page

MR image reconstruction using deep density priors

Algorithms for Magnetic Resonance (MR) image reconstruction from undersampled measurements exploit prior information to compensate for missing k-space data. Deep learning (DL) provides a powerful framework for extracting such information from existing image datasets, through learning, and then using it for reconstruction. Leveraging this, recent methods employed DL to learn mappings from undersampled to fully sampled images using paired datasets, including undersampled and corresponding fully sampled images, integrating prior knowledge implicitly. In this article, we propose an alternative approach that learns the probability distribution of fully sampled MR images using unsupervised DL, specifically Variational Autoencoders (VAE), and use this as an explicit prior term in reconstruction, completely decoupling the encoding operation from the prior. The resulting reconstruction algorithm enjoys a powerful image prior to compensate for missing k-space data without requiring paired datasets for training nor being prone to associated sensitivities, such as deviations in undersampling patterns used in training and test time or coil settings. We evaluated the proposed method with T1 weighted images from a publicly available dataset, multi-coil complex images acquired from healthy volunteers (N=8) and images with white matter lesions. The proposed algorithm, using the VAE prior, produced visually high quality reconstructions and achieved low RMSE values, outperforming most of the alternative methods on the same dataset. On multi-coil complex data, the algorithm yielded accurate magnitude and phase reconstruction results. In the experiments on images with white matter lesions, the method faithfully reconstructed the lesions. Keywords: Reconstruction, MRI, prior probability, machine learning, deep learning, unsupervised learning, density estimationComment: Published in IEEE TMI. Main text and supplementary material, 19 pages tota

Limited sinking of Phaeocystis during a 12 days sediment trap study

There is a controversy discussion about the contribution of the genus Phaeocystis to the vertical carbon export with evidence for and against sedimentation of Phaeocystis. So far, the presence of Phaeocystis in sinking matter was investigated with methods depending on morphological features (microscopy) and fast degradable substances (biochemical analyses). In this study, we determine the occurrence and abundance of Phaeocystis antarctica in short-term sediment traps and the overlying water column during a 12-day time period in the Atlantic sector of the Southern Ocean with 454-pyrosequencing and microscopy counting. In the sediment trap samples, we only found few sequences belonging to Phaeocystis, which was not reflecting the situation in the water column above. The cell counts showed the same results. We conclude that Phaeocystis cells are not generally transported downwards by active sinking or other sinking processes

Experimental verification of the very strong coupling regime in a GaAs quantum well microcavity

When the coupling between light and matter becomes comparable to the energy gap between different excited states they hybridize, leading to the appearance of a rich and complex phenomenology which attracted remarkable interest in recent years. While the mixing between states with different number of excitations, so-called ultrastrong coupling regime, has been observed in various implementations, the effect of the hybridization between different single excitation states, referred to as very strong coupling regime, has remained elusive. In semiconductor quantum wells such a regime is predicted to manifest as a photon-mediated electron-hole coupling leading to different excitonic wavefunctions for the two polaritonic branches when the ratio of the coupling strength to exciton binding energy approaches unity. Here, we verify experimentally the existence of this regime in magneto-optical measurements on a microcavity with 28 GaAs quantum wells, showing that the average electron-hole separation of the upper polariton is significantly increased compared to the bare quantum well exciton Bohr radius. This manifests in a diamagnetic shift around zero detuning that exceeds the shift of the lower polariton by one order of magnitude and the bare quantum well exciton diamagnetic shift by a factor of two. The lower polariton exhibits a diamagnetic shift smaller than expected from the coupling of a rigid exciton to the cavity mode which suggests more tightly bound electron-hole pairs than in the bare quantum well

Automated geometry measurement and deep rolling of butt welds

During the joining of two metal sheets by welding, a process-specific geometry of the weld is created. The local geometry of the created weld has a decisive influence on its fatigue strength. This is due to stress concentration at the geometric notches. In this paper, a process known from mechanical engineering called deep rolling is applied on butt welds. The influence on the local weld geometry and the local stress concentration after deep rolling is investigated. Additionally, a novel automated measurement system using optical laser line scanning is presented. The system is qualified for the evaluation of the local weld geometry regarding its flank angles and toe radii. The presented investigations show that the deep rolling process influences the stress concentrations determined by 2D-FE-simulations using real scan data. A correlation between the difference in toe radii or local notch stresses before and after deep rolling and the initial flank angle was found. This indicates that there are process and geometry specific conditions for the successful application of the deep rolling process

Observation of hybrid Tamm-plasmon exciton-polaritons with GaAs quantum wells and a MoSe2 monolayer

This work has been supported by the State of Bavaria. C.S. acknowledges financial support by the European Research Council (unLiMIt-2D project). AK acknowledged the support from the HORIZON 2020 RISE project CoExAn (Grant No. 644076). S.H and A.K acknowledge funding by the EPSRC.Strong light matter coupling between excitons and microcavity photons, as described in the framework of cavity quantum electrodynamics, leads to the hybridization of light and matter excitations. The regime of collective strong coupling arises, when various excitations from different host media are strongly coupled to the same optical resonance. This leads to a well-controllable admixture of various matter components in three hybrid polariton modes. Here, we study a cavity device with four embedded GaAs quantum wells hosting excitons that are spectrally matched to the A-valley exciton resonance of a MoSe2 monolayer. The formation of hybrid polariton modes is evidenced in momentum resolved photoluminescence and reflectivity studies. We describe the energy and k-vector distribution of exciton-polaritons along the hybrid modes by a thermodynamic model, which yields a very good agreement with the experiment.Publisher PDFPeer reviewe

3C 220.3: a radio galaxy lensing a submillimeter galaxy

Herschel Space Observatory photometry and extensive multiwavelength followup have revealed that the powerful radio galaxy 3C 220.3 at z=0.685 acts as a gravitational lens for a background submillimeter galaxy (SMG) at z=2.221. At an observed wavelength of 1mm, the SMG is lensed into three distinct images. In the observed near infrared, these images are connected by an arc of 1.8" radius forming an Einstein half-ring centered near the radio galaxy. In visible light, only the arc is apparent. 3C 220.3 is the only known instance of strong galaxy-scale lensing by a powerful radio galaxy not located in a galaxy cluster and therefore it offers the potential to probe the dark matter content of the radio galaxy host. Lens modeling rejects a single lens, but two lenses centered on the radio galaxy host A and a companion B, separated by 1.5", provide a fit consistent with all data and reveal faint candidates for the predicted fourth and fifth images. The model does not require an extended common dark matter halo, consistent with the absence of extended bright X-ray emission on our Chandra image. The projected dark matter fractions within the Einstein radii of A (1.02") and B (0.61") are about 0.4 +/- 0.3 and 0.55 +/- 0.3. The mass to i-band light ratios of A and B, M/L ~ 8 +/- 4 Msun/Lsun, appear comparable to those of radio-quiet lensing galaxies at the same redshift in the CASTLES, LSD, and SL2S samples. The lensed SMG is extremely bright with observed f(250um) = 440mJy owing to a magnification factor mu~10. The SMG spectrum shows luminous, narrow CIV 154.9nm emission, revealing that the SMG houses a hidden quasar in addition to a violent starburst. Multicolor image reconstruction of the SMG indicates a bipolar morphology of the emitted ultraviolet (UV) light suggestive of cones through which UV light escapes a dust-enshrouded nucleus.Comment: 17 pages, 14 Figures, accepted for publication in Ap

Gender differences in paediatric patients of the swiss inflammatory bowel disease cohort study.

PURPOSE: Gender differences in paediatric patients with inflammatory bowel disease (IBD) are frequently reported as a secondary outcome and the results are divergent. To assess gender differences by analysing data collected within the Swiss IBD cohort study database since 2008, related to children with IBD, using the Montreal classification for a systematic approach. METHODS: Data on gender, age, anthropometrics, disease location at diagnosis, disease behaviour, and therapy of 196 patients, 105 with Crohn's disease (CD) and 91 with ulcerative or indeterminate colitis (UC/IC) were retrieved and analysed. RESULTS: THE CRUDE GENDER RATIO (MALE : female) of patients with CD diagnosed at <10 years of age was 2.57, the adjusted ratio was 2.42, and in patients with UC/IC it was 0.68 and 0.64 respectively. The non-adjusted gender ratio of patients diagnosed at ≥10 years was 1.58 for CD and 0.88 for UC/IC. Boys with UC/IC diagnosed <10 years of age had a longer diagnostic delay, and in girls diagnosed with UC/IC >10 years a more important use of azathioprine was observed. No other gender difference was found after analysis of age, disease location and behaviour at diagnosis, duration of disease, familial occurrence of IBD, prevalence of extra-intestinal manifestations, complications, and requirement for surgery. CONCLUSION: CD in children <10 years affects predominantly boys with a sex ratio of 2.57; the impact of sex-hormones on the development of CD in pre-pubertal male patients should be investigated

Sinus histiocytosis with massive lymphadenopathy (Rosai-Dorfman disease) and cirrhosis of the liver: A case report and literature review

Patients with cirrhosis of the liver usually present with a small shrunken liver and a large spleen. The presence of an unusually huge liver should prompt the treating doctor to look for another cause, as this may be treatable and improve the patient’s outcome. In South Africa tuberculosis and lymphoma in the presence of HIV infection should be excluded. Sinus histiocytosis with massive lymphadenopathy and cirrhosis is a rare combination and has not been reported before in the literature. This case is intended to make clinicians aware of this rare combination of diseases

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