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.

Fractional Order Generalized Information

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.

Nutritonal evaluation of pemphigus foliaceus patients on long term glucocorticoid therapy

Our objective was to compare food intake and nutritional status of Pemphigus Foliaceus patients (PG) on long term glucocorticoid therapy to a Control Group (CG). Fourteen PG female inpatients receiving prednisone (0.33 ± 0.22mg/kg) for at least 12 months and twelve CG subjects were submitted to nutritional evaluation, including anthropometry, urinary creatinine determination and serum biochemical measurements, besides 48-h-based food intake records. Groups were compared by Chi-square, Mann-Whitney and "t" tests. PG patients and CG were paired, respectively, in relation to age (24.7 ± 14.1 vs. 22.0 ± 12.0 years), body mass index (25.8 ± 6.4 vs. 24.0 ± 5.6kg/m2), daily protein intake (132.9 ± 49.8 vs. 95.2 ± 58.9g), and serum albumin (median; range) (3.8; 3.5-4.1 vs. 3.8; 3.6-5.0g/dl). However, PG patients had lower height-creatinine index (64.8 ± 17.6 vs. 90.1 ± 33.4%), and higher daily energy (3080 ± 1099 vs. 2187 ± 702kcal) and carbohydrate (376.8 ± 135.8 vs. 242.0 ± 80.7g) intakes. Despite high food, protein and energy consumption, PG patients on long term glucocorticoid therapy had lower body muscle mass than controls, while showing high body fat stores. These findings are possibly related to combined metabolic effects of long term corticotherapy and inflammatory disease plus corticosteroid-induced increased appetite.

Fractional Order Generalized Information

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.

Multidimensional Scaling Visualization using Parametric Similarity Indices

In this paper, we apply multidimensional scaling (MDS) and parametric similarity indices (PSI) in the analysis of complex systems (CS). Each CS is viewed as a dynamical system, exhibiting an output time-series to be interpreted as a manifestation of its behavior. We start by adopting a sliding window to sample the original data into several consecutive time periods. Second, we define a given PSI for tracking pieces of data. We then compare the windows for different values of the parameter, and we generate the corresponding MDS maps of ‘points’. Third, we use Procrustes analysis to linearly transform the MDS charts for maximum superposition and to build a global MDS map of “shapes”. This final plot captures the time evolution of the phenomena and is sensitive to the PSI adopted. The generalized correlation, the Minkowski distance and four entropy-based indices are tested. The proposed approach is applied to the Dow Jones Industrial Average stock market index and the Europe Brent Spot Price FOB time-series.

Fractional State Space Analysis of Economy Systems

This paper examines modern economic growth according to the multidimensional scaling (MDS) method and state space portrait (SSP) analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis.

Fractional state space analysis of economic systems

This paper examines modern economic growth according to the multidimensional scaling (MDS) method and state space portrait (SSP) analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis.

Connecting free volume with shape memory properties in noncytotoxic gamma-irradiated polycyclooctene

The free volume holes of a shape memory polymer have been analysed considering that the empty space between molecules is necessary for the molecular motion, and the shape memory response is based on polymer segments acting as molecular switches through variable flexibility with temperature or other stimuli. Therefore, thermomechanical analysis (TMA) and positron annihilation lifetime spectroscopy (PALS) have been applied to analyse shape recovery and free volume hole sizes in gamma irradiated polycyclooctene (PCO) samples, as a non-cytotoxic alternative to more conventional PCO crosslinked via peroxide for future applications in medicine. Thus, a first approach relating structure, free volume holes and shape memory properties in gamma irradiated PCO is presented. The results suggest that free volume holes caused by gamma irradiation in PCO samples facilitate the recovery process by improving movement of polymer chains and open t possibilities for the design and control of the macroscopic response.

Tailoring poly(vinylidene fluoride-co-chlorotrifluoroethylene) microstructure and physicochemical properties by exploring its binary phase diagram with dimethylformamide

Poly(vinylidene fluoride-co-chlorotrifluoroethylene), PVDF-CTFE, membranes were prepared by solven casting from dimethylformamide, DMF. The preparation conditions involved a systematic variation of polymer/solvent ratio and solvent evaporation temperature. The microstructural variations of the PVDF-CTFE membranes depend on the different regions of the PVDF-CTFE/DMF phase diagram, explained by the Flory-Huggins theory. The effect of the polymer/solvent ratio and solvent evaporation temperature on the morphology, degree of porosity, β-phase content, degree of crystallinity, mechanical, dielectric and piezoelectric properties of the PVDF-CTFE polymer were evaluated. In this binary system, the porous microstructure is attributed to a spinodal decomposition of the liquid-liquid phase separation. For a given polymer/solvent ratio, 20 wt%, and higher evaporation solvent temperature, the β-phase content is around 82% and the piezoelectric coefficient, d33, is - 4 pC/N.

Hydrophobic/hydrophilic P(VDF-TrFE)/PHEA polymer blend membranes

Polymer blend membranes have been obtained consisting of a hydrophilic and a hydrophobic polymers distributed in co-continuous phases. In order to obtain stable membranes in aqueous environments, the hydrophilic phase is formed by a poly(hydrohyethyl acrylate), PHEA, network while the hydrophobic phase is formed by poly(vinylidene fluoride-co-trifluoroethylene) P(VDF-TrFE). To obtain the composites, in a first stage, P(VDF-TrFE) is blended with poly(ethylene oxyde) (PEO), the latter used as sacrificial porogen. P(VDF-TrFE)/PEO blend membranes were prepared by solvent casting at 70° followed by cooling to room temperature. Then PEO is removed from the membrane by immersion in water obtaining a P(VDF-TrFE) porous membrane. After removing of the PEO polymer, a P(VDF-TrFE) membrane results in which pores are collapsed. Nevertheless the pores reopen when a mixture of hydroxethyl acrylate (HEA) monomer, ethyleneglycol dimethacrylate (as crosslinker) and ethanol (as diluent) is absorbed in the membrane and subsequent polymerization yields hybrid hydrophilic/hydrophobic membranes with controlled porosity. The membranes are thus suitable for lithium-ion battery separator membranes and/or biostable supports for cell culture in biomedical applications.

Photoactivation of butyric acid from 6-aminobenzocoumarin cages

A new benzocoumarin bearing an amino group is proposed as a photocleavable protecting group for carboxylic acids. The novel heterocycle, 6-amino-4-chloromethyl-2-oxo-2H-naphtho[1,2-b]pyran was used in the preparation of ester conjugates of butyric acid, and of the corresponding mono- and di-methylated or ethylated derivatives. The photolability of the ester conjugates was studied by irradiation at selected wavelengths in methanol/HEPES buffer (80:20) solutions, and the release of butyric acid was followed with HPLC/UV and 1H NMR monitoring. Release of the carboxylic acid was faster for the monoalkylated derivatives (approximately within 20 min), at the longer wavelengths of irradiation (350 and 419 nm). The photophysics of the heterocyclic conjugates was also evaluated by both steady state and time-resolved methods.

Flippase (FLP) recombinase-mediated marker recycling in the dermatophyte Arthroderma vanbreuseghemii.

Biological processes can be elucidated by investigating complex networks of relevant factors and genes. However, this is not possible in species for which dominant selectable markers for genetic studies are unavailable. To overcome the limitation in selectable markers for the dermatophyte Arthroderma vanbreuseghemii (anamorph: Trichophyton mentagrophytes), we adapted the flippase (FLP) recombinase-recombination target (FRT) site-specific recombination system from the yeast Saccharomyces cerevisiae as a selectable marker recycling system for this fungus. Taking into account practical applicability, we designed FLP/FRT modules carrying two FRT sequences as well as the flp gene adapted to the pathogenic yeast Candida albicans (caflp) or a synthetic codon-optimized flp (avflp) gene with neomycin resistance (nptII) cassette for one-step marker excision. Both flp genes were under control of the Trichophyton rubrum copper-repressible promoter (PCTR4). Molecular analyses of resultant transformants showed that only the avflp-harbouring module was functional in A. vanbreuseghemii. Applying this system, we successfully produced the Ku80 recessive mutant strain devoid of any selectable markers. This strain was subsequently used as the recipient for sequential multiple disruptions of secreted metalloprotease (fungalysin) (MEP) or serine protease (SUB) genes, producing mutant strains with double MEP or triple SUB gene deletions. These results confirmed the feasibility of this system for broad-scale genetic manipulation of dermatophytes, advancing our understanding of functions and networks of individual genes in these fungi.

High-resolution spatial mapping of changes in the neurochemical profile after focal ischemia in mice.

After ischemic stroke, the ischemic damage to brain tissue evolves over time and with an uneven spatial distribution. Early irreversible changes occur in the ischemic core, whereas, in the penumbra, which receives more collateral blood flow, the damage is more mild and delayed. A better characterization of the penumbra, irreversibly damaged and healthy tissues is needed to understand the mechanisms involved in tissue death. MRSI is a powerful tool for this task if the scan time can be decreased whilst maintaining high sensitivity. Therefore, we made improvements to a (1) H MRSI protocol to study middle cerebral artery occlusion in mice. The spatial distribution of changes in the neurochemical profile was investigated, with an effective spatial resolution of 1.4 μL, applying the protocol on a 14.1-T magnet. The acquired maps included the difficult-to-separate glutamate and glutamine resonances and, to our knowledge, the first mapping of metabolites γ-aminobutyric acid and glutathione in vivo, within a metabolite measurement time of 45 min. The maps were in excellent agreement with findings from single-voxel spectroscopy and offer spatial information at a scan time acceptable for most animal models. The metabolites measured differed with respect to the temporal evolution of their concentrations and the localization of these changes. Specifically, lactate and N-acetylaspartate concentration changes largely overlapped with the T(2) -hyperintense region visualized with MRI, whereas changes in cholines and glutathione affected the entire middle cerebral artery territory. Glutamine maps showed elevated levels in the ischemic striatum until 8 h after reperfusion, and until 24 h in cortical tissue, indicating differences in excitotoxic effects and secondary energy failure in these tissue types. Copyright © 2011 John Wiley & Sons, Ltd.