Evaluating Lebesgue constants by Chebyshev polynomial meshes on cube, simplex and ball

We show that product Chebyshev polynomial meshes can be used, in a fully discrete way, to evaluate with rigorous error bounds the Lebesgue constant, i.e. the maximum of the Lebesgue function, for a class of polynomial projectors on cube, simplex and ball, including interpolation, hyperinterpolation and weighted least-squares. Several examples are presented and possible generalizations outlined. A numerical software package implementing the method is freely available online

Fast Gibbs sampling for high-dimensional Bayesian inversion

Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to explore and quantify its uncertainties. In applications where the inverse solution is subject to further analysis procedures, this can be a significant advantage. Alongside theoretical progress, various new computational techniques allow to sample very high dimensional posterior distributions: In [Lucka2012], a Markov chain Monte Carlo (MCMC) posterior sampler was developed for linear inverse problems with $\ell_1$-type priors. In this article, we extend this single component Gibbs-type sampler to a wide range of priors used in Bayesian inversion, such as general $\ell_p^q$ priors with additional hard constraints. Besides a fast computation of the conditional, single component densities in an explicit, parameterized form, a fast, robust and exact sampling from these one-dimensional densities is key to obtain an efficient algorithm. We demonstrate that a generalization of slice sampling can utilize their specific structure for this task and illustrate the performance of the resulting slice-within-Gibbs samplers by different computed examples. These new samplers allow us to perform sample-based Bayesian inference in high-dimensional scenarios with certain priors for the first time, including the inversion of computed tomography (CT) data with the popular isotropic total variation (TV) prior.Comment: submitted to "Inverse Problems

Assessment of efficacy and safety of the herbal medicinal product BNO 1016 in chronic rhinosinusitis

Background: The objective of this clinical trial (CRS-02) was to assess the efficacy, safety and tolerability of two dosages of the herbal medicinal product BNO 1016 (Sinupret extract) in patients with chronic rhinosinusitis (CRS). Methodology: 929 patients suffering from CRS were enrolled in this randomised placebo-controlled trial with a treatment period of 12 weeks. The primary endpoint was the mean Major Symptom Score (MSS) in week 8 and week 12 compared to placebo. Secondary endpoints included further MSS related parameters and responder rates over time. Pharmacoeconomic endpoints were also analysed. Finally, safety and tolerability were evaluated. Results: Sinupret extract was not superior over placebo regarding the primary endpoint. However, the results of the secondary endpoints showed a clear trend towards superior efficacy. Therefore, additional post-hoc sensitivity analyses were performed in patients with a baseline MSS > 9 and persistence of disease > 1 year diagnosed by specialists in otorhinolaryngology.Those patients significantly benefited from Sinupret extract. Therapy was superior for the primary endpoint analysis. Patients were less impaired with respect to work and daily activities. A good safety and tolerability of Sinupret extract was assured in all patients. Conclusions: Sinupret extract can safely be administered in patients with CRS. Although the primary endpoint of the study was not significant, a post-hoc subgroup analysis in patients whose disease was diagnosed by a specialist revealed a pronounced treatment effect. Effects in that subgroup were even stronger with longer disease persistence and stronger severity

Special Issue dedicated to Stefano De Marchi on the occasion of his 60th birthday

As colleagues and friends we dedicate this issue to Stefano De Marchi on the occasion of his 60th birthday, publishing works of some of his collaborators. Stefano has made many important contributions to approximation theory and beyond and is one of the “founding fathers” of this journal. Here we briefly reminisce and recount some of our experiences with Stefano in the spirit of the occasion

Constraints on the star-formation rate of z~3 LBGs with measured metallicity in the CANDELS GOODS-South field

We analyse 14 LBGs at z~2.8-3.8 constituting the only sample where both a spectroscopic measurement of their metallicity and deep IR observations (CANDELS+HUGS survey) are available. Fixing the metallicity of population synthesis models to the observed values, we determine best-fit physical parameters under different assumptions about the star-formation history and also consider the effect of nebular emission. For comparison we determine the UV slope of the objects, and use it to estimate their SFR_UV99 by correcting the UV luminosity following Meurer et al. (1999). A comparison between SFR obtained through SED-fitting (SFR_fit) and the SFR_UV99 shows that the latter are underestimated by a factor 2-10, regardless of the assumed SFH. Other SFR indicators (radio, far-IR, X-ray, recombination lines) coherently indicate SFRs a factor of 2-4 larger than SFR_UV99 and in closer agreement with SFR_fit. This discrepancy is due to the solar metallicity implied by the usual beta-A1600 conversion factor. We propose a refined relation, appropriate for sub-solar metallicity LBGs: A1600 = 5.32+1.99beta. This relation reconciles the dust-corrected UV with the SED-fitting and the other SFR indicators. We show that the fact that z~3 galaxies have sub-solar metallicity implies an upward revision by a factor of ~1.5-2 of the global SFRD, depending on the assumptions about the age of the stellar populations. We find very young best-fit ages (10-500 Myrs) for all our objects. From a careful examination of the uncertainties in the fit and the amplitude of the Balmer break we conclude that there is little evidence of the presence of old stellar population in at least half of the LBGs in our sample, suggesting that these objects are probably caught during a huge star-formation burst, rather than being the result of a smooth evolution.Comment: 16 pages, 13 figures, A&A in press. Matched to the published versio

Delivering effective care through mobile apps:Findings from a multi-stakeholder design science approach

In this paper, we use a design science approach to develop a mobile app for lung cancer patients that facilitates their interactions with their clinicians, manages and reports on their health status, and provides them access to medical information/education. This paper contributes to the information systems literature by demonstrating the value of design science research to co-create solutions that advance health care outcomes through technological innovations. The design process engaged a diverse cast of experts and methods, such as a survey of oncologists and cancer patients, a workshop, roundtables and interviews with leading patient and clinician association representatives and focus groups, including two panels each of clinicians and cancer patients. Our approach also develops actionable knowledge that is grounded in evidence from the field, including design guidelines that recapitulate what we learned from the design-testing-redesign cycles of our artefact