Dynamical Stability and Predictability of Football Players: The Study of One Match

The game of football demands new computational approaches to measure individual and collective performance. Understanding the phenomena involved in the game may foster the identification of strengths and weaknesses, not only of each player, but also of the whole team. The development of assertive quantitative methodologies constitutes a key element in sports training. In football, the predictability and stability inherent in the motion of a given player may be seen as one of the most important concepts to fully characterise the variability of the whole team. This paper characterises the predictability and stability levels of players during an official football match. A Fractional Calculus (FC) approach to define a player’s trajectory. By applying FC, one can benefit from newly considered modeling perspectives, such as the fractional coefficient, to estimate a player’s predictability and stability. This paper also formulates the concept of attraction domain, related to the tactical region of each player, inspired by stability theory principles. To compare the variability inherent in the player’s process variables (e.g., distance covered) and to assess his predictability and stability, entropy measures are considered. Experimental results suggest that the most predictable player is the goalkeeper while, conversely, the most unpredictable players are the midfielders. We also conclude that, despite his predictability, the goalkeeper is the most unstable player, while lateral defenders are the most stable during the match.

QuEChERS: a new sample preparation approach for the determination of ibuprofen and its metabolites in soils

Ibuprofen is one of the most used active pharmaceutical ingredients worldwide. A new method for the analysis of ibuprofen and its metabolites, hydroxyibuprofen and carboxyibuprofen, in soils is presented. The extraction of these compounds from the soil matrices was performed by using a modified quick, easy, cheap, effective, rugged, and safe (QuEChERS) method. The method involves a single extraction of the investigated compounds with purified water (acidified at pH 2.5 with hydrochloric acid), and a slow and continuous addition of the QuEChERS content, followed by the addition of acidified acetonitrile (1% acetic acid), prior to the determination by liquid chromatography coupled with fluorescence detection (LC–FLD). Validation studies were carried out using soil samples with a range of organic carbon contents. Recoveries of the fortified samples ranged from 79.5% to 101%. Relative standard deviations for all matrix–compound combinations did not exceed 3%. The method quantification limits were ≤22.4 μg kg−1 in all cases. The developed method was applied to the analysis of sixteen real samples.

Application of fractional order concepts in the study of electrical potential

The Maxwell equations, expressing the fundamental laws of electricity and magnetism, only involve the integer-order calculus. However, several effects present in electromagnetism, motivated recently an analysis under the fractional calculus (FC) perspective. In fact, this mathematical concept allows a deeper insight into many phenomena that classical models overlook. On the other hand, genetic algorithms (GA) are an important tool to solve optimization problems that occur in engineering. In this work we use FC and GA to implement the electrical potential of fractional order. The performance of the GA scheme and the convergence of the resulting approximations are analyzed.