Statistical discrimination of steroid profiles in doping control with support vector machines

Due to their performance enhancing properties, use of anabolic steroids (e.g. testosterone, nandrolone, etc.) is banned in elite sports. Therefore, doping control laboratories accredited by the World Anti-Doping Agency (WADA) screen among others for these prohibited substances in urine. It is particularly challenging to detect misuse with naturally occurring anabolic steroids such as testosterone (T), which is a popular ergogenic agent in sports and society.     

IEF pattern classification‐derived criteria for the identification of epoetin‐δ in urine

Epoetin‐δ (Dynepo? Shire Pharmaceuticals, Basing stoke, UK) is a synthetic form of erythropoietin (EPO) whose resemblance with endogenous EPO makes it hard to identify using the classical identification criteria. Urine samples collected from six healthy volunteers treated with epoetin‐δ injections and from a control population were immuno‐purified and analyzed with the usual IEF method. On the basis of the EPO profiles integration, a linear multivariate model was computed for discriminant analysis. For each sample, a pattern classification algorithm returned a bands distribution and intensity score (bands intensity score) saying how representative this sample is of one of the two classes, positive or negative. Effort profiles were also integrated in the model. The method yielded a good sensitivity versus specificity relation and was used to determine the detection window of the molecule following multiple injections. The bands intensity score, which can be generalized to epoetin‐α and epoetin‐β, is proposed as an alternative criterion and a supplementary evidence for the identification of EPO abuse.     

Quadrature formulas with positive weights

Recent developments in the theory of stability or contractivity of numerical methods for solving ordinary differential equations (see for instance [4], [5], [8]) have renewed the interest for the study of quadrature formulas with positive weights. Nørsett-Wanner [8] and Burrage [2], [3] have given characterisation of such quadrature formulas of order 2m–2 or 2m–3. In this paper we extend these investigations to the case of formulas of order 2m–4 and then to the case where the order is 2m–7. Finally we use these results to characterise the algebraically stable methods out of a 12-parameter family of implicit Runge-Kutta methods of order 2m–4.     

Predicting Optimal Lengths of Random Knots

In a thermally fluctuating long linear polymeric chain in a solution, the ends, from time to time, approach each other. At such an instance, the chain can be regarded as closed and thus will form a knot or rather a virtual knot. Several earlier studies of random knotting demonstrated that simpler knots show a higher occurrence for shorter random walks than do more complex knots. However, up to now there have been no rules that could be used to predict the optimal length of a random walk, i.e. the length for which a given knot reaches its highest occurrence. Using numerical simulations, we show here that a power law accurately describes the relation between the optimal lengths of random walks leading to the formation of different knots and the previously characterized lengths of ideal knots of a corresponding type.     

Rational Runge-Kutta methods are not suitable for stiff systems of ODEs

The present paper shows that rational RK-methods are not very appropriate to solve stiff differential equations. The CA₀-stability (i.e. componentwise contractivity) is defined and the non-existence of CA₀-stable rational RK-methods is demonstrated. Furthermore it is shown that the stepsizes which can be expected when solving a stiff differential system with a rational or with an explicit linear RK-method are of the same order of magnitude.     

The number of positive weights of a quadrature formula

In this paper we show that the number of positive weights of a quadrature formula is related to the number of rotations of a certain path in the plane. Necessary and sufficient conditions for all weights to be positive can then be obtained. Also, much of classical theory appears in a new light.