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.

Benchmarking the Bayesian reconstruction of the non-perturbative heavy ǪǬ potential

The extraction of the finite temperature heavy quark potential from lattice QCD relies on a spectral analysis of the real-time Wilson loop. Through its position and shape, the lowest lying spectral peak encodes the real and imaginary part of this complex potential. We benchmark this extraction strategy using leading order hard-thermal loop (HTL) calculations. I.e. we analytically calculate the Wilson loop and determine the corresponding spectrum. By fitting its lowest lying peak we obtain the real- and imaginary part and confirm that the knowledge of the lowest peak alone is sufficient for obtaining the potential. We deploy a novel Bayesian approach to the reconstruction of spectral functions to HTL correlators in Euclidean time and observe how well the known spectral function and values for the real and imaginary part are reproduced. Finally we apply the method to quenched lattice QCD data and perform an improved estimate of both real and imaginary part of the non-perturbative heavy ǪǬ potential.

A community-based geological reconstruction of Antarctic Ice Sheet deglaciation since the Last Glacial Maximum

A robust understanding of Antarctic Ice Sheet deglacial history since the Last Glacial Maximum is important in order to constrain ice sheet and glacial-isostatic adjustment models, and to explore the forcing mechanisms responsible for ice sheet retreat. Such understanding can be derived from a broad range of geological and glaciological datasets and recent decades have seen an upsurge in such data gathering around the continent and Sub-Antarctic islands. Here, we report a new synthesis of those datasets, based on an accompanying series of reviews of the geological data, organised by sector. We present a series of timeslice maps for 20 ka, 15 ka, 10 ka and 5 ka, including grounding line position and ice sheet thickness changes, along with a clear assessment of levels of confidence. The reconstruction shows that the Antarctic Ice sheet did not everywhere reach the continental shelf edge at its maximum, that initial retreat was asynchronous, and that the spatial pattern of deglaciation was highly variable, particularly on the inner shelf. The deglacial reconstruction is consistent with a moderate overall excess ice volume and with a relatively small Antarctic contribution to meltwater pulse 1a. We discuss key areas of uncertainty both around the continent and by time interval, and we highlight potential priorities for future work. The synthesis is intended to be a resource for the modelling and glacial geological community.

Four years follow-up after clavicle reconstruction in a child: a case report.

Clavicle reconstruction is a rare operation. In most cases a mid-shaft defect of the clavicle is bridged by using different grafting techniques or musculo-osteous flaps. In some clinical situations where reconstruction is not a suitable option claviculectomy as a salvation procedure has proven to be an acceptable solution. In the paediatric population the challenge of both the cosmetic and the functional result attempting reconstruction of large bone defects is of higher demand. To our knowledge, this is the first case of a successful clavicle reconstruction with a sufficient follow-up using a free vascularised fibula graft in a child. This case provides a technique description, considerations in the paediatric population, an overview of other techniques used, and a long-term follow-up.

ACL reconstruction with physiological graft tension by intraoperative adjustment of the anteroposterior translation to the uninjured contralateral knee.

PURPOSE Fixation of anterior cruciate ligament (ACL) substitutes with non-physiological anteroposterior translation (APT) worsens outcome. The aim was to present a technique for physiological APT adjustment of the transplant in ACL reconstruction and its outcome at midterm. METHODS In a consecutive series of 28 patients (age 32 ± 11 years, 24 male), chronic ACL deficiency was treated by bone-patella-tendon-bone reconstruction. Transplant APT was adjusted to that of the contralateral uninjured ACL, measured 3, 6, and 12 months postoperatively using the Rolimeter. At a median follow-up of 5.3 years (3-8 years), 82% of the patients were re-evaluated with APT measurement and using IKDC-, Tegner-, Lysholm-Scores, conventional radiographs and MRI. RESULTS No differences in APT (mean ± SD) between uninjured and reconstructed knees were observed after adjustment (6 ± 1 versus 6 ± 1 mm, n.s.). Three months postoperatively, a statistically significant increase in APT (7 ± 1 mm) and a further increase at midterm (9 ± 2 mm) were observed. Patients scored "normal" or "nearly normal", respectively, in 79% (IKDC) and 4 (3-9) points (Tegner; median, range) or 89 ± 9 points (Lysholm; mean ± SD). Radiological evaluation showed no, minimal or moderate joint degeneration in 5, 20 and 75% of patients, respectively. MRI confirmed intact ACL transplants in all patients. CONCLUSION ACL reconstruction using the presented technique was considered successful, as patients did not suffer from subjective instability, radiographic analysis did not provide evidence for graft rupture at midterm. However, APT increase and occurrence of degenerative changes in reconstructed knees at the midterm might not be prevented even by restoration of a physiological APT in ACL reconstruction. The Rolimeter can be used for quick and easy intraoperative indirect control of the applied tension to the ACL transplant by measuring the APT to obtain physiological tensioning resulting in a satisfying outcome at midterm. LEVEL OF EVIDENCE IV.