Surgery and the Spectrum of the Dirac Operator

We show that for generic Riemannian metrics on a simply-connected closed spin manifold of dimension at least 5 the dimension of the space of harmonic spinors is no larger than it must be by the index theorem. The same result holds for periodic fundamental groups of odd order. The proof is based on a surgery theorem for the Dirac spectrum which says that if one performs surgery of codimension at least 3 on a closed Riemannian spin manifold, then the Dirac spectrum changes arbitrarily little provided the metric on the manifold after surgery is chosen properly.Comment: 23 pages, 4 figures, to appear in J. Reine Angew. Mat

Clinical Applications of Contrast-Enhanced Ultrasound in the Pediatric Work-Up of Focal Liver Lesions and Blunt Abdominal Trauma:A Systematic Review

In pediatrics ultrasound has long been viewed more favorably than imaging that exposes patients to radiation and iodinated contrast or requires sedation. It is child-friendly and diagnostic capabilities have been improved with the advent of contrast-enhanced ultrasound (CEUS). The application of CEUS is indeed promising. However, no ultrasound contrast agent manufactured today is registered for pediatric use in Europe. The contrast agent SonoVue(®) has recently been approved by the FDA under the name of Lumason(®) to be used in hepatic investigations in adults and children. This article reviews the literature with respect to 2 specific applications of CEUS in children: 1) identification of parenchymal injuries following blunt abdominal trauma, and 2) classification of focal liver lesions. Applications were chosen through the CEUS guidelines published by the European Federation of Societies for Ultrasound in Medicine and Biology and World Federation for Ultrasound in Medicine and Biology. Literature was obtained by searching Medline and Pubmed Central (using Pubmed), Scopus database and Embase. CEUS proved to be an effective investigation in the hemodynamically stable child for identifying parenchymal injuries and for the characterization of focal liver lesions. CEUS showed comparable performance to CT and MRI with a specificity of 98% for identifying benign lesions and a negative predictive value of 100%. For the applications reviewed here, CEUS holds promising perspectives and can help reduce radiation exposure and use of iodinated contrast agents in pediatrics, thereby potentially reducing complications in routine imaging

Characterization of the OCO-2 instrument line shape functions using on-orbit solar measurements

Accurately characterizing the instrument line shape (ILS) of the Orbiting Carbon Observatory-2 (OCO-2) is challenging and highly important due to its high spectral resolution and requirement for retrieval accuracy (0. 25 %) compared to previous spaceborne grating spectrometers. On-orbit ILS functions for all three bands of the OCO-2 instrument have been derived using its frequent solar measurements and high-resolution solar reference spectra. The solar reference spectrum generated from the 2016 version of the Total Carbon Column Observing Network (TCCON) solar line list shows significant improvements in the fitting residual compared to the solar reference spectrum currently used in the version 7 Level 2 algorithm in the O₂ A band. The analytical functions used to represent the ILS of previous grating spectrometers are found to be inadequate for the OCO-2 ILS. Particularly, the hybrid Gaussian and super-Gaussian functions may introduce spurious variations, up to 5 % of the ILS width, depending on the spectral sampling position, when there is a spectral undersampling. Fitting a homogeneous stretch of the preflight ILS together with the relative widening of the wings of the ILS is insensitive to the sampling grid position and accurately captures the variation of ILS in the O₂ A band between decontamination events. These temporal changes of ILS may explain the spurious signals observed in the solar-induced fluorescence retrieval in barren areas