We investigate the worst-case behavior of the simplex algorithm on linear programs with 3 variables, that is, on 3-dimensional simple polytopes. Among the pivot rules that we consider, the “random edge” rule yields the best asymptotic behavior as well as the most complicated analysis. All other rules turn out to be much easier to study, but also produce worse results: Most of them show essentia...

BACKGROUND Some studies have reported a ceiling effect in EQ-5D-3L, especially in healthy and/or young individuals. Recently, two further levels have been included in its measurement model (EQ-5D-5L). The purposes of this study were (1) to assess the properties of the EQ-5D-5L in comparison with the standard EQ-5D-3L in a sample of young adults, (2) to foreground the importance of collecting qu...

Fractals have been introduced by Mandelbrot (1975) to define geometrical ensembles, or mathematical sets, that have a fractional dimension. He pioneered the study of very irregular mathematical sets, where the methods of classical calculus cannot be applied. Fractals are not smooth nor differentiable; they are characterized by self-similarity. Their geometrical structure has details at all scal...

INTRODUCTION The new, five-level version of the EQ-5D (EQ-5D-5L) questionnaire has better psychometric properties than the standard three-level version (EQ-5D-3L), including a reduced ceiling effect. Currently, there are few existing population norms for the EQ-5D-5L. The aims of this study were to provide population norms for the EQ-5D-5L in Poland, based on a representative sample of adults, ...

BACKGROUND The EQ-5D is a brief, generic measure of health status that can be easily incorporated into population health surveys. There are two versions of the EQ-5D for use in adult populations, one with 3 response levels in each of the instrument's 5 dimensions (EQ-5D-3L) and one with 5 levels in each dimension (EQ-5D-5L). We compared the two versions as measures of self-reported health statu...

In this paper we give the main ideas to show that a real analytic vector field in R3 with a singular point at the origin is locally topologically equivalent to its principal part defined through Newton polyhedra under non-degeneracy conditions.

We extend Hendriks’ classification theorem and Turaev’s realisation and splitting theorems for PD–complexes to the relative case of PD– pairs. The results for PD–complexes are recovered by restricting the results to the case of PD–pairs with empty boundary. Up to oriented homotopy equivalence, PD–pairs are classified by their fundamental triple consisting of the fundamental group system, the or...