challenge. This paper outlines the challenge, its organization, the dataset used, evaluation methods and results of top performing participating solutions. We observe that the top performing approaches utilize a blend of clinical information, data augmentation, and the ensemble of models. These findings have the potential to enable new developments in retinal image analysis and image-based DR screening in particular.

No abstract

Accurate and reliable forecasting of total cloud cover (TCC) is vital for many areas such as astronomy, energy demand and production, or agriculture. Most meteorological centres issue ensemble forecasts of TCC; however, these forecasts are often uncalibrated and exhibit worse forecast skill than ensemble forecasts of other weather variables. Hence, some form of post-processing is strongly required to improve predictive performance. As TCC observations are usually reported on a discrete scale taking just nine different values called oktas, statistical calibration of TCC ensemble forecasts can be considered a classification problem with outputs given by the probabilities of the oktas. This is a classical area where machine learning methods are applied. We investigate the performance of post-processing using multilayer perceptron (MLP) neural networks, gradient boosting machines (GBM) and random forest (RF) methods. Based on the European Centre for Medium-Range Weather Forecasts global TCC ensemble forecasts for 2002-2014, we compare these approaches with the proportional odds logistic regression (POLR) and multiclass logistic regression (MLR) models, as well as the raw TCC ensemble forecasts. We further assess whether improvements in forecast skill can be obtained by incorporating ensemble forecasts of precipitation as additional predictor. Compared to the raw ensemble, all calibration methods result in a significant improvement in forecast skill. RF models provide the smallest increase in predictive performance, while MLP, POLR and GBM approaches perform best. The use of precipitation forecast data leads to further improvements in forecast skill, and except for very short lead times the extended MLP model shows the best overall performance. Keywords Ensemble calibration Á Logistic regression Á Multilayer perceptron Á Total cloud cover Abbreviations CDF Cumulative distribution function CRPS Continuous ranked probability score CRPSS Continuous ranked probability skill score CTRL (ECMWF) Control (forecast) DM Diebold-Mariano (test) ECMWF European Centre for Medium-Range Weather Forecasts ENS (50-member ECMWF) ensemble EPS Ensemble prediction system GBM Gradient boosting machine

No abstract

No abstract

We consider polynomial finite elements of order k _> 1 for the approximation of Stokes and linear elasticity problems which are continuous in the Gauss-Legendre points of the elements sides, i.e., generalize the Crouzeix-Raviart (k = 1), Fortin-Soulie (k = 2) and Crouzeix-Falk (k = 3) elements. We show that, for odd orders, these Gauss-Legendre elements do not possess a CrouzeixVelte decomposition. For even orders, not only a Crouzeix-Velte decomposition can be shown to exist (which is advantageous when solving the corresponding linear equations and eigenvalue problems) but also the grid singularity of the well-known Scott-Vogelius elements is avoided by these elements which are shown to differ from the former ones by nonconforming bubbles. We also consider quadrilateral elements of order k _> 1 where the requirement of a Crouzeix-Velte decomposition is shown to exclude most commonly used elements.

No abstract

The positions of the l = 0 S-matrix poles are calculated in generalized Woods-Saxon (GWS) potential and in cut-off generalized Woods-Saxon (CGWS) potential. The solutions of the radial equations are calculated numerically for the CGWS potential and analytically for GWS using the formalism of Gy. Bencze [1]. We calculate CGWS and GWS cases at small non-zero values of the diffuseness in order to approach the square well potential and to be able to separate effects of the radius parameter and the cut-off radius parameter. In the case of the GWS potential the wave functions are reflected at the nuclear radius therefore the distances of the resonant poles depend on the radius parameter of the potential. In CGWS potential the wave function can be reflected at larger distance where the potential is cut to zero and the derivative of the potential does not exist. The positions of most of the resonant poles do depend strongly on the cut-off radius of the potential, which is an unphysical parameter. Only the positions of the few narrow resonances in potentials with barrier are not sensitive to the cut-off distance. For the broad resonances the effect of the cut-off can not be corrected by using a suggested analytical form of the first order perturbation correction.