Fundamental group in o-minimal structures with definable Skolem functions

In this paper we work in an arbitrary o-minimal structure with definable Skolem functions and prove that definably connected, locally definable manifolds are uniformly definably path connected, have an admissible cover by definably simply connected, open definable subsets and, definable paths and definable homotopies on such locally definable manifolds can be lifted to locally definable covering maps. These properties allow us to obtain the main properties of the general o-minimal fundamental group, including: invariance and comparison results; existence of universal locally definable covering maps; monodromy equivalence for locally constant o-minimal sheaves – from which one obtains, as in algebraic topology, classification results for locally definable covering maps, o-minimal Hurewicz and Seifert–van Kampen theorems.     

Gromov hyperbolicity of periodic planar graphs

The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it.The main result in this paper is a very simple characterization of the hyperbolicity of a large class of periodic planar graphs.     

Quantification of morphine and its major metabolites M3G and M6G in antemortem and postmortem samples

Morphine is one of the most effective agents for the control of significant pain, primarily metabolized to morphine‐3‐glucuronide (M3G) and morphine‐6‐glucuronide (M6G). While M6G is a potent opioid agonist, M3G has no opioid action and seems to have a role in side‐effects caused by morphine. In this study, a reversed‐phase high‐performance liquid chromatographic method with diode‐array and electrochemical detection was developed for the simultaneous determination of morphine, M3G and M6G in antemortem and postmortem samples (plasma, whole blood, urine, liver, kidney and brain). Morphine, glucuronides and internal standard were extracted by double solid‐phase extraction and the separation was carried out with a Waters Spherisorb® ODS2 reversed‐phase column and potassium phosphate buffer (pH = 2.2)–acetonitrile containing sodium dodecyl sulfate as the mobile phase. The method proved to be specific with good linearity for all analytes in a calibration range from 1 to 600 ng/mL and proved to be accurate and have adequate precision and recovery. Limits of detection in the studied matrices were 0.4–4.5 ng/mL for morphine, 2.7–6.1 ng/mL for M3G and 0.8–4.4 ng/mL for M6G. The proposed method can be successfully applied to quantify morphine and its metabolites in several biological samples, covering the major routes of distribution, metabolism and elimination of morphine. Copyright © 2014 John Wiley & Sons, Ltd.     

Extracting Work Optimally with Imprecise Measurements

Measurement and feedback allows for an external agent to extract work from a system in contact with a single thermal bath. The maximum amount of work that can be extracted in a single measurement and the corresponding feedback loop is given by the information that is acquired via the measurement, a result that manifests the close relation between information theory and stochastic thermodynamics. In this paper, we show how to reversibly confine a Brownian particle in an optical tweezer potential and then extract the corresponding increase of the free energy as work. By repeatedly tracking the position of the particle and modifying the potential accordingly, we can extract work optimally, even with a high degree of inaccuracy in the measurements.     

Gromov hyperbolic cubic graphs

If X is a geodesic metric space and x ₁; x ₂; x ₃ ∈ X, a geodesic triangle T = {x ₁; x ₂; x ₃} is the union of the three geodesics [x ₁ x ₂], [x ₂ x ₃] and [x ₃ x ₁] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. We denote by δ(X) the sharp hyperbolicity constant of X, i.e., δ(X) = inf {δ ≥ 0: X is δ-hyperbolic}. We obtain information about the hyperbolicity constant of cubic graphs (graphs with all of their vertices of degree 3), and prove that for any graph G with bounded degree there exists a cubic graph G* such that G is hyperbolic if and only if G* is hyperbolic. Moreover, we prove that for any cubic graph G with n vertices, we have δ(G) ≤ min {3n/16 + 1; n/4}. We characterize the cubic graphs G with δ(G) ≤ 1. Besides, we prove some inequalities involving the hyperbolicity constant and other parameters for cubic graphs.     

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials II

We present a definition of general Sobolev spaces with respect to arbitrary measures, Wh,p (Ω,μ) for 1 ≤p≤∞. In [RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we consider certain general types of measures, then Cc∞ (R) is dense in thee spaces. As an application to Sobolev orthogonal polynomials, we study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.     

Statistics of extremes for IID data and breakthroughs in the estimation of the extreme value index: Laurens de Haan leading contributions

In the last decades there has been a shift from the parametric statistics of extremes for IID random variables, based on the probabilistic asymptotic results in extreme value theory, towards a semi-parametric approach, where the estimation of the right tail-weight, under a quite general framework, is of major importance. After a brief presentation of classical Gumbel’s block methodology and of later improvements in the parametric framework (multivariate and multi-dimensional extreme value models for largest observations and peaks over threshold approaches), we present a coordinated overview, over the last three decades, of the developments on the estimation of the extreme value index under a semiparametric framework. Laurens de Haan has been one of the leading scientists in the field, (co-)author of many seminal ideas, that he generously shared with dozens (literally) of colleagues and students, thus achieving one of the main goals in a scientist’s life: he gathered around him a bunch of colleagues united in the endeavour of building knowledge. The last section is a personal tribute to Laurens, who fully lives his ideal that co-operation is the heart of Science. To Laurens de Haan, a token of friendship.     

Analysing head coach dismissals in the German “Bundesliga” with a mixed logit approach

This article analyzes the dismissal of head coaches in the top tier of German professional football, the “Bundesliga”. A random parameter logit model is used to analyse the characteristics that are associated with the probability of a coach to be dismissed, taking into account uncontrolled heterogeneity of the data. Policy implications are presented.     

Efficiency in the Greek insurance industry

This paper employs the two-stage procedure of Simar and Wilson (2007) to analyse the effects of deregulation on the efficiency of the Greek insurance industry. The efficiency is estimated by means of data envelopment analysis (DEA). The companies are ranked according to their CRS efficiency score for the period 1994–2003. The first stage results indicate a decline in efficiency over the sample period, while the second stage results confirm that the competition for market shares is a major driver of efficiency in the Greek insurance industry.