The semi-continous quadratic mixture design problem

The semi-continuous quadratic mixture design problem (SCQMDP) is described as a problem with linear, quadratic and semi-continuity con- straints. Moreover, a linear cost objective and an integer valued objective are introduced. The research question is to deal with the SCQMD prob- lem from a Branch-and-Bound perspective generating robust solutions. Therefore, an algorithm is outlined which is rigorous in the sense it iden- ti¯es instances where decision makers tighten requirements such that no ²-robust solution exists. The algorithm is tested on several cases derived from industry

On the minimum number of simplex shapes in longest edge bisection refinement of a regular n-simplex

In several areas like Global Optimization using branch-and-bound methods, the unit n-simplex is refined by bisecting the longest edge such that a binary search tree appears. This process generates simplices belonging to different shape classes. Having less simplex shapes facilitates the prediction of the further workload from a node in the binary tree, because the same shape leads to the same sub-tree. Irregular sub-simplices generated in the refinement process may have more than one longest edge when n\geqslant 3. The question is how to choose the longest edge to be bisected such that the number of shape classes is as small as possible. We develop a Branch-and-Bound (B&B) algorithm to find the minimum number of classes in the refinement process. The developed B&B algorithm provides a minimum number of eight classes for a regular 3-simplex. Due to the high computational cost of solving this combinatorial problem, future research focuses on using high performance computing to derive the minimum number of shapes in higher dimensions

On lower bounds using separable terms in interval B&B for one-dimensional poblems

Interval Branch-and-Bound (B&B) algorithms are powerful methods which aim for guaranteed solutions of Global Optimization problems. Lower bounds for a function in a given interval can be obtained directly with Interval Arithmetic. The use of lower bounds based on Taylor forms show a faster convergence to the minimum with decreasing size of the search interval. Our research focuses on one dimensional functions that can be decomposed into several terms (sub-functions). The question is whether using this characteristic leads to sharper bounds when based on bounds of the sub-functions. This paper deals with separable functions in two sub-functions. The use of the separability is investigated for the so-called Baumann form and Lower Bound Value Form (LBVF). It is proven that using the additively separability in the LBVF form may lead to a combination of linear minorants that are sharper than the original one. Numerical experiments confirm this improving behaviour and also show that not all separable methods do always provide sharper additively lower bounds. Additional research is needed to obtain better lower bounds for multiplicatively separable functions and to address higher dimensional problems

On interval branch-and-bound for additively separable functions with common variables

Interval branch-and-bound (B&B) algorithms are powerful methods which look for guaranteed solutions of global optimisation problems. The computational effort needed to reach this aim, increases exponentially with the problem dimension in the worst case. For separable functions this effort is less, as lower dimensional sub-problems can be solved individually. The question is how to design specific methods for cases where the objective function can be considered separable, but common variables occur in the sub-problems. This paper is devoted to establish the bases of B&B algorithms for separable problems. New B&B rules are presented based on derived properties to compute bounds. A numerical illustration is elaborated with a test-bed of problems mostly generated by combining traditional box constrained global optimisation problems, to show the potential of using the derived theoretical basis

Effectiveness and safety of obeticholic acid in a Southern European multicenter cohort of patients with primary biliary cholangitis and suboptimal response to ursodeoxycholic acid

Background Obeticholic acid (OCA) was recently approved as the only on-label alternative for patients with primary biliary cholangitis (PBC) with intolerance or suboptimal response to ursodeoxycholic acid (UDCA). However, few data are available outside clinical trials. Aim To assess the effectiveness and safety of OCA in a real-world cohort of patients with non-effective UDCA therapy. Methods Open-label, prospective, real-world, multicentre study, enrolling consecutive patients who did not meet Paris II criteria, from 18 institutions in Spain and Portugal. Effectiveness was assessed by the changes in GLOBE and UK-PBC scores from baseline. POISE and Paris II criteria were evaluated after 12 months of OCA . Liver fibrosis was evaluated by FIB-4 and AST to platelet ratio index (APRI). Results One hundred and twenty patients were eligible, median time since PBC diagnosis 9.3 (4.0-13.8) years, 21.7% had cirrhosis, and 26.7% received had previous or concomitant treatment with fibrates. Seventy-eight patients completed at least 1 year of OCA. The Globe-PBC score decreased to 0.17 (95% CI 0.05 to 0.28; P = 0.005) and the UK-PBC score decreased to 0.81 (95% CI -0.19 to 1.80; P = 0.11). There was a significant decrease in alkaline phosphatase of 81.3 U/L (95% CI 42.5 to 120; P < 0.001), ALT 22.1 U/L (95% CI 10.4 to 33.8; P < 0.001) and bilirubin 0.12 mg/dL (95% CI 0 to 0.24; P = 0.044). FIB-4 and APRI remained stable. According to the POISE criteria, 29.5% (23 out of 78) achieved response. The adverse events rate was 35%; 11.67% discontinued (8.3% due to pruritus). Conclusions This study supports data from phase III trials with significant improvement of PBC-Globe continuous prognostic marker score among OCA-treated patients with good tolerability

Measurement of the polarisation of W bosons produced with large transverse momentum in pp collisions at sqrt(s) = 7 TeV with the ATLAS experiment

This paper describes an analysis of the angular distribution of W->enu and W->munu decays, using data from pp collisions at sqrt(s) = 7 TeV recorded with the ATLAS detector at the LHC in 2010, corresponding to an integrated luminosity of about 35 pb^-1. Using the decay lepton transverse momentum and the missing transverse energy, the W decay angular distribution projected onto the transverse plane is obtained and analysed in terms of helicity fractions f0, fL and fR over two ranges of W transverse momentum (ptw): 35 < ptw < 50 GeV and ptw > 50 GeV. Good agreement is found with theoretical predictions. For ptw > 50 GeV, the values of f0 and fL-fR, averaged over charge and lepton flavour, are measured to be : f0 = 0.127 +/- 0.030 +/- 0.108 and fL-fR = 0.252 +/- 0.017 +/- 0.030, where the first uncertainties are statistical, and the second include all systematic effects.Comment: 19 pages plus author list (34 pages total), 9 figures, 11 tables, revised author list, matches European Journal of Physics C versio