Bubbling with L2L^2-almost constant mean curvature and an Alexandrov-type theorem for crystals

A compactness theorem for volume-constrained almost-critical points of elliptic integrands is proven. The result is new even for the area functional, as almost-criticality is measured in an integral rather than in a uniform sense. Two main applications of the compactness theorem are discussed. First, we obtain a description of critical points/local minimizers of elliptic energies interacting with a confinement potential. Second, we prove an Alexandrov-type theorem for crystalline isoperimetric problems

Incidence and management of pulmonary embolism following spinal surgery occurring while under chemical thromboprophylaxis

Patients undergoing spinal surgery are at risk of developing thromboembolic complications even though lower incidences have been reported as compared to joint arthroplasty surgery. Deep vein thrombosis (DVT) has been studied extensively in the context of spinal surgery but symptomatic pulmonary embolism (PE) has engaged less attention. We prospectively followed a consecutive cohort of 270 patients undergoing spinal surgery at a single institution. From these patients, only 26 were simple discectomies, while the largest proportion (226) was fusions. All patients received both low molecular weight heparin (LMWH) initiated after surgery and compressive stockings. PE was diagnosed with spiral chest CT. Six patients developed symptomatic PE, five during their hospital stay. In three of the six patients the embolic event occurred during the first 3 postoperative days. They were managed by the temporary insertion of an inferior vena cava (IVC) filter thus allowing for a delay in full-dose anticoagulation until removal of the filter. None of the PE patients suffered any bleeding complication as a result of the introduction of full anticoagulation. Two patients suffered postoperative haematomas, without development of neurological symptoms or signs, requiring emergency evacuation. The overall incidence of PE was 2.2% rising to 2.5% after exclusion of microdiscectomy cases. The incidence of PE was highest in anterior or combined thoracolumbar/lumbar procedures (4.2%). There is a large variation in the reported incidence of PE in the spinal literature. Results from the only study found in the literature specifically monitoring PE suggest an incidence of PE as high as 2.5%. Our study shows a similar incidence despite the use of LMWH. In the absence of randomized controlled trials (RCT) it is uncertain if this type of prophylaxis lowers the incidence of PE. However, other studies show that the morbidity of LMWH is very low. Since PE can be a life-threatening complication, LMWH may be a worthwhile option to consider for prophylaxis. RCTs are necessary in assessing the efficacy of DVT and PE prophylaxis in spinal patient

KMOS view of the Galactic Centre - II. Metallicity distribution of late-type stars

Knowing the metallicity distribution of stars in the Galactic Centre has important implications for the formation history of the Milky Way nuclear star cluster. However, this distribution is not well known, and is currently based on a small sample of fewer than 100 stars. We obtained near-infrared K-band spectra of more than 700 late-type stars in the central 4 pc^2 of the Milky Way nuclear star cluster with the integral-field spectrograph KMOS (VLT). We analyse the medium-resolution spectra using a full-spectral fitting method employing the G\"ottingen Spectral library of synthetic PHOENIX spectra. The derived stellar metallicities range from metal-rich [M/H]>+0.3 dex to metal-poor [M/H]<-1.0 dex, with a fraction of 5.2(^{+6.0}+{-3.1}) per cent metal-poor ([M/H]<-0.5 dex) stars. The metal-poor stars are distributed over the entire observed field. The origin of metal-poor stars remains unclear. They could originate from infalling globular clusters. For the metal-rich stellar population ([M/H]>0 dex) a globular cluster origin can be ruled out. As there is only a very low fraction of metal-poor stars in the central 4 pc^2 of the Galactic Centre, we believe that our data can discard a scenario in which the Milky Way nuclear star cluster is purely formed from infalling globular clusters.Comment: 18 pages, 9 Figures, accepted for publication in MNRA

Symbolic Policies versus European Reconciliation: the Hungarian ‘Status Law’

International audienceThis chapter is organized as follows. First, it puts the Status Law back in the context of Hungarian symbolic policies and the development of European standards for minority protection after the Cold War. Agenda-setting at the COE and the OSCE is then analyzed to show how the originally bilateral controversy quickly became a ‘European problem’. The third part of the chapter underlines that the circulation of European standards between these European agencies was intrinsically ambiguous. At the international level, each organization interpreted these norms according to its own history, identity and resources, while at the national level politicians contested the ‘European solutions’ that they felt were being imposed on them

Template-Based Image Reconstruction from Sparse Tomographic Data

Funder: University of CambridgeAbstract: We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements by deforming a given template image. The image registration is directly incorporated into the variational regularisation approach in the form of a partial differential equation that models the registration as either mass- or intensity-preserving transport from the template to the unknown reconstruction. We provide theoretical results for the proposed variational regularisation for both cases. In particular, we prove existence of a minimiser, stability with respect to the data, and convergence for vanishing noise when either of the abovementioned equations is imposed and more general distance functions are used. Numerically, we solve the problem by extending existing Lagrangian methods and propose a multilevel approach that is applicable whenever a suitable downsampling procedure for the operator and the measured data can be provided. Finally, we demonstrate the performance of our method for template-based image reconstruction from highly undersampled and noisy Radon transform data. We compare results for mass- and intensity-preserving image registration, various regularisation functionals, and different distance functions. Our results show that very reasonable reconstructions can be obtained when only few measurements are available and demonstrate that the use of a normalised cross correlation-based distance is advantageous when the image intensities between the template and the unknown image differ substantially

Medial femoral condyle fracture as a complication of antegrade intramedullary nailing

A 49-year-old man suffered a closed oblique fracture of the middle third of his left femur. Closed reduction and internal fixation by intramedullary (IM) nailing were performed. Per-operative fluoroscopic imaging and initial postoperative X-rays were judged normal and the patient followed the usual rehabilitation protocol. At 3-month follow-up the patient still demonstrated poor knee function and pain. A plain X-ray and a CT scan of the left knee revealed a displaced fracture of the medial femoral condyle. Analysis of the postoperative imaging suggests that the fracture occurred during the insertion of the IM nail. The nail possibly hit the Steinmann traction pin in the distal femur causing the medial condyle fracture. The patient was reoperated; open reduction and internal plate and screw fixation were performed with satisfactory clinical progress postoperatively. The description and illustration of this case is intended to make trauma surgeons aware of this rare but serious complication of IM femoral nailin

Disentangling the Circumnuclear Environs of Centaurus A: III. An Inner Molecular Ring, Nuclear Shocks and the CO to warm H2 interface

We present the distribution and kinematics of the molecular gas in the circumnuclear disk (CND, 400 pc x 200 pc) of Centaurus A with resolutions of ~5 pc (0.3 arcsec) and shed light onto the mechanism feeding the Active Galactic Nucleus (AGN) using CO(3-2), HCO+(4-3), HCN(4-3), and CO(6-5) observations obtained with ALMA. Multiple filaments or streamers of tens to a hundred parsec scale exist within the CND, which form a ring-like structure with an unprojected diameter of 9 x 6 arcsec (162pc x 108pc) and a position angle PA = 155deg. Inside the nuclear ring, there are two leading and straight filamentary structures with lengths of about 30-60pc at PA = 120deg on opposite sides of the AGN, with a rotational symmetry of 180deg and steeper position-velocity diagrams, which are interpreted as nuclear shocks due to non-circular motions. Along the filaments, and unlike other nearby AGNs, several dense molecular clumps present low HCN/HCO+(4-3) ratios (~0.5). The filaments abruptly end in the probed transitions at r = 20pc from the AGN, but previous near-IR H2 (J=1-0) S(1) maps show that they continue in an even ~1000 K), winding up in the form of nuclear spirals, and forming an inner ring structure with another set of symmetric filaments along the N-S direction and within r = 10pc. The molecular gas is governed primarily by non-circular motions, being the successive shock fronts at different scales where loss of angular momentum occurs, a mechanism which may feed efficiently powerful radio galaxies down to parsec scales.Comment: 46 pages. Accepted for publication in Ap

Jeans modelling of the Milky Way's nuclear stellar disc

The nuclear stellar disc (NSD) is a flattened stellar structure that dominates the gravitational potential of the Milky Way at Galactocentric radii 30≲R≲300pc⁠. In this paper, we construct axisymmetric Jeans dynamical models of the NSD based on previous photometric studies and we fit them to line-of-sight kinematic data of the Apache Point Observatory Galactic Evolution Experiment (APOGEE) and silicon monoxide (SiO) maser stars. We find that (i) the NSD mass is lower but consistent with the mass independently determined from photometry by Launhardt et al. Our fiducial model has a mass contained within spherical radius r=100pc of M(r 1. Observations and theoretical models of the star-forming molecular gas in the central molecular zone suggest that large vertical oscillations may be already imprinted at stellar birth. However, the finding σz/σR > 1 depends on a drop in the velocity dispersion in the innermost few tens of parsecs, on our assumption that the NSD is axisymmetric, and that the available (extinction corrected) stellar samples broadly trace the underlying light and mass distributions, all of which need to be established by future observations and/or modelling. (iii) We provide the most accurate rotation curve to date for the innermost 500pc of our Galaxy