Covering point sets with two disjoint disks or squares

Open archive-ElsevierWe study the following problem: Given a set of red points and a set of blue points on the plane, find two unit disks CR and CB with disjoint interiors such that the number of red points covered by CR plus the number of blue points covered by CB is maximized. We give an algorithm to solve this problem in O(n8/3 log2 n) time, where n denotes the total number of points. We also show that the analogous problem of finding two axis-aligned unit squares SR and SB instead of unit disks can be solved in O(nlog n) time, which is optimal. If we do not restrict ourselves to axis-aligned squares, but require that both squares have a common orientation, we give a solution using O(n3 log n) time

Demographic and clinical profile of idiopathic pulmonary fibrosis patients in Spain: the SEPAR National Registry

BackgroundLittle is known on the characteristics of patients diagnosed with idiopathic pulmonary fibrosis (IPF) in Spain. We aimed to characterize the demographic and clinical profile of IPF patients included in the IPF National Registry of the Spanish Respiratory Society (SEPAR).MethodsThis is a prospective, observational, multicentre and nationwide study that involved 608 IPF patients included in the SEPAR IPF Registry up to June 27th, 2017, and who received any treatment for their disease. IPF patients were predominantly males, ex-smokers, and aged in their 70s, similar to other registries.ResultsUpon inclusion, meanSD predicted forced vital capacity was 77.6%+/- 19.4, diffusing capacity for carbon monoxide was 48.5%+/- 17.7, and the 6-min walk distance was 423.5m +/- 110.4. The diagnosis was mainly established on results from the high-resolution computed tomography in the proper clinical context (55.0% of patients), while 21.2% of patients required invasive procedures (surgical lung biopsy) for definitive diagnosis. Anti-fibrotic treatment was prescribed in 69.4% of cases, 51.5% pirfenidone and 17.9% nintedanib, overall with a good safety profile.Conclusions The SEPAR IPF Registry should help to further characterize current characteristics and future trends of IPF patients in Spain and compare/pool them with other registries and cohorts