Online games for the teaching of mathematics

In this article we present a didactic experience developed by the GIE (Group of Educational Innovation) “Pensamiento Matemático” of the Polytechnics University of Madrid (UPM), in order to bring secondary students and university students closer to Mathematics. It deals with the development of a virtual board game called Mate-trivial. The mechanics of the game is to win points by going around the board which consists of four types of squares identified by colours: “Statistics and Probability”, “Calculus and Analysis”, “Algebra and Geometry” and “Arithmetic and Number Theory ”. When landing on a square, a question of its category is set out: a correct answer wins 200 points, if wrong it loses 100 points, and not answering causes no effect on the points, but all the same, two minutes out of the 20 minutes that each game lasts are lost. For the game to be over it is necessary, before those 20 minutes run out, to reach the central square and succeed in the final task: four chained questions, one of each type, which must be all answered correctly. It is possible to choose between two levels to play: Level 1, for pre-university students and Level 2 for university students. A prototype of the game is available at the website “Aula de Pensamiento Matemático” developed by the GIE: http://innovacioneducativa.upm.es/pensamientomatematico/. This activity lies within a set of didactic actions which the GIE is developing in the framework of the project “Collaborative Strategies between University and Secondary School Education for the teaching and learning of Mathematics: An Application to solve problems while playing”, a transversal project financed by the UPM.

Integration of SCORM packages into web games

This paper presents a model that enables the integration of SCORM packages into web games. It is based on the fact that SCORM packages are prepared to be integrated into Learning Management Systems and to communicate with them. Hence in a similar way they can also be integrated into web games. The application of this model results in the linkage between the Learning Objects inside the package and specific actions or conditions in the game. The educational content will be shown to the players when they perform these actions or the conditions are met. For example, when they need a special weapon they will have to consume the Learning Object to get it. Based on this model we have developed an open source web platform which main aim is to facilitate teachers the creation of educational games. They can select existing SCORM packages or upload their own ones and then select a game template in which the Learning Objects will be integrated. The resulting educational game will be available online. Details about the model and the developed platform are explained in this paper. Also links to the platform and an example of a generated game will be provided.

A scalable SIEM correlation engine and its application to the Olympic Games IT infrastructure

The security event correlation scalability has become a major concern for security analysts and IT administrators when considering complex IT infrastructures that need to handle gargantuan amounts of events or wide correlation window spans. The current correlation capabilities of Security Information and Event Management (SIEM), based on a single node in centralized servers, have proved to be insufficient to process large event streams. This paper introduces a step forward in the current state of the art to address the aforementioned problems. The proposed model takes into account the two main aspects of this ?eld: distributed correlation and query parallelization. We present a case study of a multiple-step attack on the Olympic Games IT infrastructure to illustrate the applicability of our approach.

Kinematic and heart rate demands in 4x4 vs 7x7 small sided games in professional soccer players

Comparación de las variables cinemáticas y de frecuencia cardiaca en dos posesiones en fútbol

Towards the automatic generation of card games through Grammar-Guided Genetic Programming

We demonstrate generating complete and playable card games using evolutionary algorithms. Card games are represented in a previously devised card game description language, a context-free grammar. The syntax of this language allows us to use grammar-guided genetic programming. Candidate card games are evaluated through a cascading evaluation function, a multi-step process where games with undesired properties are progressively weeded out. Three representa- tive examples of generated games are analysed. We observed that these games are reasonably balanced and have skill ele- ments, they are not yet entertaining for human players. The particular shortcomings of the examples are discussed in re- gard to the generative process to be able to generate quality games

Flammability conditions for ultra-lean hydrogen premixed combustion based on flame-ball analyses

It has been reasoned that the structures of strongly cellular flames in very lean mixtures approach an array of flame balls, each burning as if it were isolated, thereby indicating a connection between the critical conditions required for existence of steady flame balls and those necessary for occurrence of self-sustained premixed combustion. This is the starting assumption of the present study, in which structures of near-limit steady sphericosym-metrical flame balls are investigated with the objective of providing analytic expressions for critical combustion conditions in ultra-lean hydrogen-oxygen mixtures diluted with N2 and water vapor. If attention were restricted to planar premixed flames, then the lean-limit mole fraction of H2 would be found to be roughly ten percent, more than twice the observed flammability limits, thereby emphasizing the relevance of the flame-ball phenomena. Numerical integrations using detailed models for chemistry and radiation show that a onestep chemical-kinetic reduced mechanism based on steady-state assumptions for all chemical intermediates, together with a simple, optically thin approximation for water-vapor radiation, can be used to compute near-limit fuel-lean flame balls with excellent accuracy. The previously developed one-step reaction rate includes a crossover temperature that determines in the first approximation a chemical-kinetic lean limit below which combustión cannot occur, with critical conditions achieved when the diffusion-controlled radiation-free peak temperature, computed with account taken of hydrogen Soret diffusion, is equal to the crossover temperature. First-order corrections are found by activation-energy asymptotics in a solution that involves a near-field radiation-free zone surrounding a spherical flame sheet, together with a far-field radiation-conduction balance for the temperature profile. Different scalings are found depending on whether or not the surrounding atmosphere contains wáter vapor, leading to different analytic expressions for the critical conditions for flame-ball existence, which give results in very good agreement with those obtained by detailed numerical computations.

Effects of coaches' timeouts on basketball teams' offensive and defensive performances according to momentary differences in score and game period.

The aim of the present study was to assess the effects of game timeouts on basketball teams? offensive and defensive performances according to momentary differences in score and game period. The sample consisted of 144 timeouts registered during 18 basketball games randomly selected from the 2007 European Basketball Championship (Spain). For each timeout, five ball possessions were registered before (n?493) and after the timeout (n?475). The offensive and defensive efficiencies were registered across the first 35 min and last 5 min of games. A k-means cluster analysis classified the timeouts according to momentary score status as follows: losing ( ?10 to ?3 points), balanced ( ?2 to 3 points), and winning (4 to 10 points). Repeated-measures analysis of variance identified statistically significant main effects between pre and post timeout offensive and defensive values. Chi-square analysis of game period identified a higher percentage of timeouts called during the last 5 min of a game compared with the first 35 min (64.999.1% vs. 35.1910.3%; x ?5.4, PB0.05). Results showed higher post timeout offensive and defensive performances. No other effect or interaction was found for defensive performances. Offensive performances were better in the last 5 min of games, with the least differences when in balanced situations and greater differences when in winning situations. Results also showed one interaction between timeouts and momentary differences in score, with increased values when in losing and balanced situations but decreased values when in winning situations. Overall, the results suggest that coaches should examine offensive and defensive performances according to game period and differences in score when considering whether to call a timeout.

Corporate social responsibility in portfolio selection: A "goal games" against nature approach

Nowadays, there is an uprising social pressure on big companies to incorporate into their decision-making process elements of the so-called social responsibility. Among the many implications of this fact, one relevant one is the need to include this new element in classic portfolio selection models. This paper meets this challenge by formulating a model that combines goal programming with "goal games" against nature in a scenario where the social responsibility is defined through the introduction of a battery of sustainability indicators amalgamated into a synthetic index. In this way, we have obtained an efficient model that only implies solving a small number of linear programming problems. The proposed approach has been tested and illustrated by using a case study related to the selection of securities in international markets.

Análisis de sistemas dinámicos y complejos en la Liga Profesional de Balonmano de España = Complex and dynamical systems analysis in Spanish Professional Handball League

El propósito de esta tesis fue estudiar el rendimiento ofensivo de los equipos de balonmano de élite cuando se considera el balonmano como un sistema dinámico complejo no lineal. La perspectiva de análisis dinámica dependiente del tiempo fue adoptada para evaluar el rendimiento de los equipos durante el partido. La muestra general comprendió los 240 partidos jugados en la temporada 2011-2012 de la liga profesional masculina de balonmano de España (Liga ASOBAL). En el análisis posterior solo se consideraron los partidos ajustados (diferencia final de goles ≤ 5; n = 142). El estado del marcador, la localización del partido, el nivel de los oponentes y el periodo de juego fueron incorporados al análisis como variables situacionales. Tres estudios compusieron el núcleo de la tesis. En el primer estudio, analizamos la coordinación entre las series temporales que representan el proceso goleador a lo largo del partido de cada uno de los dos equipos que se enfrentan. Autocorrelaciones, correlaciones cruzadas, doble media móvil y transformada de Hilbert fueron usadas para el análisis. El proceso goleador de los equipos presentó una alta consistencia a lo largo de todos los partidos, así como fuertes modos de coordinación en fase en todos los contextos de juego. Las únicas diferencias se encontraron en relación al periodo de juego. La coordinación en los procesos goleadores de los equipos fue significativamente menor en el 1er y 2º periodo (0–10 min y 10–20 min), mostrando una clara coordinación creciente a medida que el partido avanzaba. Esto sugiere que son los 20 primeros minutos aquellos que rompen los partidos. En el segundo estudio, analizamos los efectos temporales (efecto inmediato, a corto y a medio plazo) de los tiempos muertos en el rendimiento goleador de los equipos. Modelos de regresión lineal múltiple fueron empleados para el análisis. Los resultados mostraron incrementos de 0.59, 1.40 y 1.85 goles para los periodos que comprenden la primera, tercera y quinta posesión de los equipos que pidieron el tiempo muerto. Inversamente, se encontraron efectos significativamente negativos para los equipos rivales, con decrementos de 0.50, 1.43 y 2.05 goles en los mismos periodos respectivamente. La influencia de las variables situacionales solo se registró en ciertos periodos de juego. Finalmente, en el tercer estudio, analizamos los efectos temporales de las exclusiones de los jugadores sobre el rendimiento goleador de los equipos, tanto para los equipos que sufren la exclusión (inferioridad numérica) como para los rivales (superioridad numérica). Se emplearon modelos de regresión lineal múltiple para el análisis. Los resultados mostraron efectos negativos significativos en el número de goles marcados por los equipos con un jugador menos, con decrementos de 0.25, 0.40, 0.61, 0.62 y 0.57 goles para los periodos que comprenden el primer, segundo, tercer, cuarto y quinto minutos previos y posteriores a la exclusión. Para los rivales, los resultados mostraron efectos positivos significativos, con incrementos de la misma magnitud en los mismos periodos. Esta tendencia no se vio afectada por el estado del marcador, localización del partido, nivel de los oponentes o periodo de juego. Los incrementos goleadores fueron menores de lo que se podría esperar de una superioridad numérica de 2 minutos. Diferentes teorías psicológicas como la paralización ante situaciones de presión donde se espera un gran rendimiento pueden ayudar a explicar este hecho. Los últimos capítulos de la tesis enumeran las conclusiones principales y presentan diferentes aplicaciones prácticas que surgen de los tres estudios. Por último, se presentan las limitaciones y futuras líneas de investigación. ABSTRACT The purpose of this thesis was to investigate the offensive performance of elite handball teams when considering handball as a complex non-linear dynamical system. The time-dependent dynamic approach was adopted to assess teams’ performance during the game. The overall sample comprised the 240 games played in the season 2011-2012 of men’s Spanish Professional Handball League (ASOBAL League). In the subsequent analyses, only close games (final goal-difference ≤ 5; n = 142) were considered. Match status, game location, quality of opposition, and game period situational variables were incorporated into the analysis. Three studies composed the core of the thesis. In the first study, we analyzed the game-scoring coordination between the time series representing the scoring processes of the two opposing teams throughout the game. Autocorrelation, cross-correlation, double moving average, and Hilbert transform were used for analysis. The scoring processes of the teams presented a high consistency across all the games as well as strong in-phase modes of coordination in all the game contexts. The only differences were found when controlling for the game period. The coordination in the scoring processes of the teams was significantly lower for the 1st and 2nd period (0–10 min and 10–20 min), showing a clear increasing coordination behavior as the game progressed. This suggests that the first 20 minutes are those that break the game-scoring. In the second study, we analyzed the temporal effects (immediate effect, short-term effect, and medium-term effect) of team timeouts on teams’ scoring performance. Multiple linear regression models were used for the analysis. The results showed increments of 0.59, 1.40 and 1.85 goals for the periods within the first, third and fifth timeout ball possessions for the teams that requested the timeout. Conversely, significant negative effects on goals scored were found for the opponent teams, with decrements of 0.59, 1.43 and 2.04 goals for the same periods, respectively. The influence of situational variables on the scoring performance was only registered in certain game periods. Finally, in the third study, we analyzed the players’ exclusions temporal effects on teams’ scoring performance, for the teams that suffer the exclusion (numerical inferiority) and for the opponents (numerical superiority). Multiple linear regression models were used for the analysis. The results showed significant negative effects on the number of goals scored for the teams with one less player, with decrements of 0.25, 0.40, 0.61, 0.62, and 0.57 goals for the periods within the previous and post one, two, three, four and five minutes of play. For the opponent teams, the results showed positive effects, with increments of the same magnitude in the same game periods. This trend was not affected by match status, game location, quality of opposition, or game period. The scoring increments were smaller than might be expected from a 2-minute numerical playing superiority. Psychological theories such as choking under pressure situations where good performance is expected could contribute to explain this finding. The final chapters of the thesis enumerate the main conclusions and underline the main practical applications that arise from the three studies. Lastly, limitations and future research directions are described.

Evaluación del rendimiento de jugadores y equipos de fútbol de nivel de élite en diferentes contextos situacionales = Evaluation on Match Performances of Professional Football Players and Teams under Different Situational Conditions = 不同情境条件下高水平足球运动员和运动队的比赛表现分析

El análisis del rendimiento en deportes juega un papel esencial en el fútbol profesional. Aunque el estudio del análisis del juego en fútbol se ha utilizado desde diferentes ámbitos y situaciones, todavía existen diferentes aspectos y componentes del juego que siguen sin estar estudiados. En este sentido existen diferentes aspectos que deben de superar los estudios previos centrados en el componente descriptivo tales como el uso de variables/ indicadores de rendimiento que no se han definido ni estudiado, la validez de los métodos observaciones que no han sido testados con los softwares específicos en fútbol, la aplicación y utilidad de los resultados, así como las limitaciones del estudio de las variables situacionales/contextuales. Con el objetivo de cubrir las citadas limitaciones se han diseñado 6 estudios independientes e inter-relacionados que tratan de estudiar los aspectos anteriormente referidos. El primer estudio evalua la fiabilidad inter-observadores de las estadísticas de juego de la empresa privada OPTA Sportsdata, estos datos son la muestra de estudio de la presente tesis doctoral. Dos grupos de observadores experimentados se requieren para analizar un partido de la liga española de manera independiente. Los resultados muestran que los eventos de equipos y porteros codificados por los inter-operadores alcanzan un acuerdo muy bueno (valores kappa entre 0.86 y 0.94). La validez inter-observadores de las acciones de juego y los datos de jugadores individuales se evaluó con elevados niveles de acuerdo (valores del coeficiente de correlación intraclase entre 0.88 hasta 1.00, el error típico estandarizado variaba entre 0.00 hasta 0.37). Los resultados sugieren que las estadísticas de juego registradas por los operadores de la empresa OPTA Sportsdata están bien entrenados y son fiables. El segundo, tercer y cuarto estudio se centran en resaltar la aplicabilidad del análisis de rendimiento en el fútbol así como para explicar en profundidad las influencias de las variables situacionales. Utilizando la técnica de los perfiles de rendimiento de jugadores y equipos de fútbol se puede evaluar y comparar de manera gráfica, fácil y visual. Así mismo, mediante esta técnica se puede controlar el efecto de las variables situacionales (localización del partido, nivel del equipo y del oponente, y el resultado final del partido). Los perfiles de rendimiento de porteros (n = 46 porteros, 744 observaciones) y jugadores de campo (n = 409 jugadores, 5288 observaciones) de la primera division professional de fútbol Española (La Liga, temporada 2012-13), los equipos (n = 496 partidos, 992 observaciones) de la UEFA Champions League (temporadas 2009-10 a 2012-13) fueron analizados registrando la media, desviación típica, mediana, cuartiles superior e inferior y el recuento de valores de cada indicador de rendimiento y evento, los cuales se presentaron en su forma tipificada y normalizada. Los valores medios de los porteros de los equipos de diferentes niveles de La Liga y de los equipos de diferente nivel de la UEFA Champions League cuando jugaban en diferentes contextos de juego y situaciones (variables situacionales) fueron comparados utilizando el ANOVA de un factor y la prueba t para muestras independientes (localización del partido, diferencias entre casa y fuera), y fueron establecidos en los perfiles de red después de unificar todos los registros en la misma escala derivada con valores estandarizados. Mientras que las diferencias de rendimiento entre los jugadores de los mejores equipos (Top3) y los peores (Bottom3) fueron comparados mediante el uso de diferencias en la magnitud del tamaño del efecto. El quinto y el sexto estudio analizaban el rendimiento del fútbol desde un punto de vista de predicción del rendimiento. El modelo linear general y el modelo lineal general mixto fue empleado para analizar la magnitud de las relaciones de los indicadores y estadísticas de juego con el resultado final del partido en función del tipo de partido (partidos ajustados o todos los partidos) en la fase de grupos de la Copa del Mundo 2014 de Brasil (n = 48 partidos, 38 partidos ajustados) y La Liga 2012-13 (n = 320 partidos ajustados). Las relaciones fueron evaluadas mediante las inferencias en la magnitud de las diferencias y se expresaron como partidos extra ganados o perdidos por cada 10 partidos mediante la variable calculada en 2 desviaciones típicas. Los resultados mostraron que, para los 48 partidos de la fase de grupos de la Copa del Mundo 2014, nueve variables tuvieron un efecto positive en la probabilidad de ganar (tiros, tiros a puerta, tiros de contraataque, tiros dentro del área, posesión de balón, pases en corto, media de secuencia de pases, duelos aéreos y entradas), cuatro tuvieron efectos negativos (tiros bloqueados, centros, regates y tarjetas amarillas), y otras 12 variables tenían efectos triviales o poco claros. Mientras que los 38 partidos ajustados, el efecto de duelos aéreos y tarjetas amarillas fueron triviales y claramente negativos respectivamente. En la La Liga, existió un efecto moderado positive para cada equipo para los tiros a puerta (3.4 victorias extras por cada 10 partidos; 99% IC ±1.0), y un efecto positivo reducido para tiros totales (1.7 victorias extrsa; ±1.0). Los efectos de la mayoría de los eventos se han relacionado con la posesión del balón, la cual obtuvo efectos negativos entre equipos (1.2 derrotas extras; ±1.0) pero un efecto positivo pequeño entra equipos (1.7 victorias extras; ±1.4). La localización del partido mostró un efecto positive reducido dentro de los equipos (1.9 victorias extras; ±0.9). Los resultados obtenidos en los perfiles y el modelado del rendimiento permiten ofrecer una información detallada y avanzada para el entrenamiento, la preparación previa a los partidos, el control de la competición y el análisis post-partido, así como la evaluación e identificación del talento de los jugadores. ABSTRACT Match performance analysis plays an important role in the modern professional football. Although the research in football match analysis is well-developed, there are still some issues and problems remaining in this field, which mainly include the lack of operational definitions of variables, reliability issues, applicability of the findings, the lack of contextual/situational variables, and focusing too much on descriptive and comparative analysis. In order to address these issues, six independent but related studies were conducted in the current thesis. The first study evaluated the inter-operator reliability of football match statistics from OPTA Sportsdata Company which is the data resourse of the thesis. Two groups of experienced operators were required to analyse a Spanish league match independently in the experiment. Results showed that team events and goalkeeper actions coded by independent operators reached a very good agreement (kappa values between 0.86 and 0.94). The inter-operator reliability of match actions and events of individual outfield players was also tested to be at a high level (intra-class correlation coefficients ranged from 0.88 to 1.00, standardised typical error varied from 0.00 to 0.37). These results suggest that the football match statistics collected by well-trained operators from OPTA Sportsdata Company are reliable. The second, third and fourth study aims to enhance the applicability of football match performance analysis and to explore deeply the influences of situational variables. By using a profiling technique, technical and tactical performances of football players and teams can be interpreted, evaluated and compared more easily and straightforwardly, meanwhile, influences and effects from situational variables (match location, strength of team and opposition, and match outcome) on the performances can be properly incorporated. Performance profiles of goalkeepers (n = 46 goalkeepers, 744 full match observations) and outfield players (n = 409 players, 5288 full match observations) from the Spanish First Division Professional Football League (La Liga, season 2012-13), teams (n = 496 matches, 992 observations) from UEFA Champions League (seasons 2009-10 to 2012-13) were set up by presenting the mean, standard deviation, median, lower and upper quartiles of the count values of each performance-related match action and event to represent their typical performances and spreads. Means of goalkeeper from different levels of team in La Liga and teams of different strength in UEFA Champions League when playing under different situational conditions were compared by using one-way ANOVA and independent sample t test (for match location, home and away differences), and were plotted into the same radar charts after unifying all the event counts by standardised score. While differences between the performances of outfield players from Top3 and from Bottom3 teams were compared by magnitude-based inferences. The fifth and sixth study aims to move from the descriptive and comparative football match analysis to a more predictive one. Generalised linear modelling and generalised mixed linear modelling were undertaken to quantify relationships of the performance-related match events, actions and variables with the match outcome in different types of games (close games and all games) in the group stage of 2014 Brazil FIFA World Cup (n = 48 games, 38 close games) and La Liga 2012-13 (n = 320 close games). Relationships were evaluated with magnitude-based inferences and were expressed as extra matches won or lost per 10 matches for an increase of two standard deviations of a variable. Results showed that, for all the 48 games in the group stage of 2014 FIFA World Cup, nine variables had clearly positive effects on the probability of winning (shot, shot on target, shot from counter attack, shot from inside area, ball possession, short pass, average pass streak, aerial advantage, and tackle), four had clearly negative effects (shot blocked, cross, dribble and red card), other 12 variabless had either trivial or unclear effects. While for the 38 close games, the effects of aerial advantage and yellow card turned to trivial and clearly negative, respectively. In the La Liga, there was a moderate positive within-team effect from shots on target (3.4 extra wins per 10 matches; 99% confidence limits ±1.0), and a small positive within-team effect from total shots (1.7 extra wins; ±1.0). Effects of most other match events were related to ball possession, which had a small negative within-team effect (1.2 extra losses; ±1.0) but a small positive between-team effect (1.7 extra wins; ±1.4). Game location showed a small positive within-team effect (1.9 extra wins; ±0.9). Results from the established performance profiles and modelling can provide detailed and straightforward information for training, pre-match preparations, in-match tactical approaches and post-match evaluations, as well as for player identification and development. 摘要 比赛表现分析在现代足球中起着举足轻重的作用。尽管如今对足球比赛表现分析的研究已经相对完善，但仍有很多不足之处。这些不足主要体现在：研究中缺乏对研究变量的清晰定义、数据信效度缺失、研究结果的实用性受限、比赛情境因素缺失以及过于集中在描述性和对比性分析等。针对这些问题，本论文通过六个独立而又相互联系的研究，进一步对足球比赛表现分析进行完善。 第一个研究对本论文的数据源--OPTA Sportsdata公司的足球比赛数据的信效度进行了实验检验。实验中，两组数据收集人员被要求对同一场西班牙足球甲级联赛的比赛进行分析。研究结果显示，两组收集人员记录下的球队比赛事件和守门员比赛行为具有高度的一致性(卡帕系数介于0.86和0.94)。收集人员输出的外场球员的比赛行为和比赛事件也具有很高的组间一致性(ICC相关系数介于0.88和1.00，标准化典型误差介于0.00和0.37)。实验结果证明了OPTA Sportsdata公司收集的足球比赛数据具有足够高的信效度。 第二、三、四个研究旨在提升足球比赛表现分析研究结果的实用性以及深度探讨比赛情境因素对足球比赛表现的影响。通过对足球运动员和运动队的比赛技战术表现进行档案创建，可以对运动员和运动队的比赛表现进行简直接而直观的呈现、评价和对比，同时，情境变量(比赛场地、球队和对手实力、比赛结果)对比赛表现的影响也可以被整合到表现档案中。本部分对2012-13赛季西班牙足球甲级联赛的参赛守门员(n = 46球员人次，744比赛场次)和外场球员(n = 409球员人次, 5288比赛场次)以及2009-10至2012-13赛季欧洲足球冠军联赛的参赛球队(n = 496比赛场次)的比赛技战术表现进行了档案创建。在表现档案中，各项比赛技战术指标的均值、标准差、中位数和大小四分位数被用来展现守门员、外场球员和球队的普遍表现和表现浮动性。方差分析(ANOVA)被用来对西甲不同水平球队的守门员、欧冠中不同水平球队在不同比赛情境下的普遍表现(各项指标的均值)进行对比，独立样本t检验被用来对比主客场比赛普遍表现的差异。数据量级推断(magnitude-based inferences)的方法则被用来对西甲前三名和最后三名球队外场球员的普遍表现进行对比分析。所有来自不同水平球队的运动员和不同水平运动队的各项比赛指标皆被转换成了标准分数，从而能把他们在各种不同比赛情境下的普遍表现(各项比赛指标的均值)投到相同的雷达图中进行直观的对比。 第五和第六个研究目的在于进行预测性足球比赛表现分析，从而跨越之前固有的描述性和对比性分析。广义线性模型和广义混合线性模型被用来对2014年巴西世界杯小组赛(n = 48 比赛场次，38小分差场次)和2012-13赛季西甲联赛(n = 320小分差场次)的比赛中各表现相关比赛事件、行为和变量与比赛结果(胜、平、负)的关系进行建模。模型中的关系通过数据量级推断(magnitude-based inferences)的方法来界定，具体表现为某个变量增加两个标准差对比赛结果的影响(每10场比赛中额外取胜或失利的场数)。研究结果显示，在2014年巴西世界杯小组赛的所有48场比赛中，9个变量(射门、射正、反击中射门、禁区内射门、控球、短传、连续传球平均次数、高空球争抢成功率和抢断)与赢球概率有清晰的正相关关系，4个变量(射门被封堵、传中、过人和红牌)与赢球概率有清晰的负相关关系，其他12个被分析的变量与赢球概率的相关关系微小或不清晰。而在38场小分差比赛中，高空球争抢成功率由正相关变为微小关系，黄牌则由微小关系变为清晰的负相关。在西甲联赛中，每一支球队增加两个标准差的“射正球门”可以给每10场比赛带来3.4场额外胜利(99%置信区间±1.0场)，而所有球队作为一个整体，每增加两个标准差的“射正球门”可以给每10场比赛带来1.7场额外胜利(99%置信区间±1.0场)。其他大多数比赛相关事件与比赛结果的相关关系与“控球”相关联。每一支球队增加两个标准差的“控球”将会给每10场比赛带来1.2场额外失利(99%置信区间±1.0场)，而所有球队作为一个整体，每增加两个标准差的“控球”可以给每10场比赛带来1.7场额外胜利(99%置信区间±1.4场)。与客场比赛相对，主场能给球队带来1.9 /10场额外胜利(99%置信区间±0.9场)。 比赛表现档案和模型中得出的研究结果可以为俱乐部、足球队、教练组、表现分析师和运动员提供详细而直接的参考信息。这些信息可用于训练指导、赛前备战、赛中技战术调整和赛后技战术表现分析，也可运用于足球运动员选材、培养和发展。

Efectos de una intervención nutricional personalizada a largo plazo sobre los hábitos alimentarios de jugadores profesionales de baloncesto y su influencia en la percepción del esfuerzo y la fatiga

El presente trabajo consistió en el desarrollo de una intervención nutricional a largo plazo llevada a cabo con jugadores profesionales de baloncesto, en función al cumplimiento de las recomendaciones nutricionales, con los siguientes dos objetivos: 1) valorar los cambios que dicha intervención produce sobre las prácticas nutricionales diarias de estos deportistas y 2) conocer la influencia de las modificaciones nutricionales producidas sobre la tasa de percepción del esfuerzo por sesión (RPE-Sesión) y la fatiga, a lo largo de una temporada competitiva, tanto para entrenamientos como partidos oficiales. Los objetivos del estudio se fundamentan en: 1) la numerosa evidencia científica que muestra la inadecuación de los hábitos nutricionales de los jugadores de baloncesto y otros deportistas respecto a las recomendaciones nutricionales; 2) el hecho ampliamente reconocido en la literatura especializada de que una ingesta nutricional óptima permite maximizar el rendimiento deportivo (a nivel físico y cognitivo), promoviendo una rápida recuperación y disminuyendo el riesgo de enfermedades y lesiones deportivas. No obstante, pocos estudios han llevado a cabo una intervención nutricional a largo plazo para mejorar los hábitos alimentarios de los deportistas y ninguno de ellos fue realizado con jugadores de baloncesto; 3) la elevada correlación entre la percepción del esfuerzo (RPE) y variables fisiológicas relacionadas al desarrollo de un ejercicio (por ej.: frecuencia cardíaca, consumo máximo de oxígeno o lactato sanguíneo) y los múltiples estudios que muestran la atenuación de la RPE durante la realización del ejercicio mediante una ingesta puntual de nutrientes, (especialmente de hidratos de carbono) aunque ninguno fue desarrollado en baloncesto; 4) el estudio incipiente de la relación entre la ingesta nutricional y la RPE-Sesión, siendo éste un método validado en baloncesto y otros deportes de equipo como indicador de la carga de trabajo interna, el rendimiento deportivo y la intensidad del ejercicio realizado; 5) el hecho de que la fatiga constituye uno de los principales factores influyentes en la percepción del esfuerzo y puede ser retrasada y/o atenuada mediante la ingesta de carbohidratos, pudiendo disminuir consecuentemente la RPE-Sesión y la carga interna del esfuerzo físico, potenciando el rendimiento deportivo y las adaptaciones inducidas por el entrenamiento; 6) la reducida evidencia acerca del comportamiento de la RPE-Sesión ante la modificación de la ingesta de nutrientes, encontrándose sólo un estudio llevado a cabo en baloncesto y 7) la ausencia de investigaciones acerca de la influencia que puede tener la mejora del patrón nutricional de los jugadores sobre la RPE-Sesión y la fatiga, desconociéndose si la adecuación de los hábitos nutricionales conduce a una disminución de estas variables en el largo plazo para todos los entrenamientos y partidos oficiales a nivel profesional. Por todo esto, este trabajo comienza con una introducción que presenta el marco teórico de la importancia y función de la nutrición en el deporte, así como de las recomendaciones nutricionales actuales a nivel general y para baloncesto. Además, se describen las intervenciones nutricionales llevadas a cabo previamente con otros deportistas y las consecuentes modificaciones sobre el patrón alimentario, coincidiendo este aspecto con el primer objetivo del presente estudio. Posteriormente, se analiza la RPE, la RPE-Sesión y la fatiga, focalizando el estudio en la relación de dichas variables con la carga de trabajo físico, la intensidad del entrenamiento, el rendimiento deportivo y la recuperación post ejercicio. Finalmente, se combinan todos los aspectos mencionados: ingesta nutricional, RPE percepción del esfuerzo y fatiga, con el fin de conocer la situación actual del estudio de la relación entre dichas variables, conformando la base del segundo objetivo de este estudio. Seguidamente, se exponen y fundamentan los objetivos antes mencionados, para dar lugar después a la explicación de la metodología utilizada en el presente estudio. Ésta consistió en un diseño de estudios de caso, aplicándose una intervención nutricional personalizada a tres jugadores de baloncesto profesional (cada jugador = un estudio de caso; n = 1), con el objetivo de adecuar su ingesta nutricional en el largo plazo a las recomendaciones nutricionales. A su vez, se analizó la respuesta individual de cada uno de los casos a dicha intervención para los dos objetivos del estudio. Para ello, cada jugador completó un registro diario de alimentos (7 días; pesada de alimentos) antes, durante y al final de la intervención. Además, los sujetos registraron diariamente a lo largo del estudio la RPE-Sesión y la fatiga en entrenamientos físicos y de balón y en partidos oficiales de liga, controlándose además en forma cuantitativa otras variables influyentes como el estado de ánimo y el sueño. El análisis de los datos consistió en el cálculo de los estadísticos descriptivos para todas las variables, la comparación de la ingesta en los diferentes momentos evaluados con las recomendaciones nutricionales y una comparación de medias no paramétrica entre el período pre intervención y durante la intervención con el test de Wilcoxon (medidas repetidas) para todas las variables. Finalmente, se relacionaron los cambios obtenidos en la ingesta nutricional con la percepción del esfuerzo y la fatiga y la posible influencia del estado de ánimo y el sueño, a través de un estudio correlacional (Tau_b de Kendall). Posteriormente, se presentan los resultados obtenidos y la discusión de los mismos, haciendo referencia a la evidencia científica relacionada que se encuentra publicada hasta el momento, la cual facilitó el análisis de la relación entre RPE-Sesión, fatiga y nutrición a lo largo de una temporada. Los principales hallazgos y su correspondiente análisis, por lo tanto, pueden resumirse en los siguientes: 1) los tres jugadores de baloncesto profesional presentaron inicialmente hábitos nutricionales inadecuados, haciendo evidente la necesidad de un nutricionista deportivo dentro del cuerpo técnico de los equipos profesionales; 2) las principales deficiencias correspondieron a un déficit pronunciado de energía e hidratos de carbono, que fueron reducidas con la intervención nutricional; 3) la ingesta excesiva de grasa total, ácidos grasos saturados, etanol y proteínas que se halló en alguno/s de los casos, también se adecuó a las recomendaciones después de la intervención; 4) la media obtenida durante un período de la temporada para la RPE-Sesión y la fatiga de entrenamientos, podría ser disminuida en un jugador individual mediante el incremento de su ingesta de carbohidratos a largo plazo, siempre que no existan alteraciones psico-emocionales relevantes; 5) el comportamiento de la RPE-Sesión de partidos oficiales no parece estar influido por los factores nutricionales modificados en este estudio, dependiendo más de la variación de elementos externos no controlables, intrínsecos a los partidos de baloncesto profesional. Ante estos resultados, se pudo observar que las diferentes características de los jugadores y las distintas respuestas obtenidas después de la intervención, reforzaron la importancia de utilizar un diseño de estudio de casos para el análisis de los deportistas de élite y, asimismo, de realizar un asesoramiento nutricional personalizado. Del mismo modo, la percepción del esfuerzo y la fatiga de cada jugador evolucionaron de manera diferente después de la intervención nutricional, lo cual podría depender de las diferentes características de los sujetos, a nivel físico, psico-social, emocional y contextual. Por ello, se propone que el control riguroso de las variables cualitativas que parecen influir sobre la RPE y la fatiga a largo plazo, facilitaría la comprensión de los datos y la determinación de factores desconocidos que influyen sobre estas variables. Finalmente, al ser la RPE-Sesión un indicador directo de la carga interna del entrenamiento, es decir, del estrés psico-fisiológico experimentado por el deportista, la posible atenuación de esta variable mediante la adecuación de los hábitos nutricionales, permitiría aplicar las cargas externas de entrenamiento planificadas, con menor estrés interno y mejor recuperación entre sesiones, disminuyendo también la sensación de fatiga, a pesar del avance de la temporada. ABSTRACT This study consisted in a long-term nutritional intervention carried out with professional basketball players according to nutritional recommendations, with the following two main objectives: 1) to evaluate the changes produced by the intervention on daily nutritional practices of these athletes and 2) to determine the influence of long term nutritional intake modifications on the rate of perceived exertion per session (Session-RPE) and fatigue, throughout a competitive season for training as well as competition games. These objectives are based on: 1) much scientific evidence that shows an inadequacy of the nutritional habits of basketball players and other athletes regarding nutritional recommendations; 2) the fact widely recognized in the scientific literature that an optimal nutrition allows to achieve the maximum performance of an athlete (both physically and cognitively), promoting fast recovery and decreasing risks of sports injuries and illnesses. However, only few studies carried out a long term nutritional intervention to improve nutritional practices of athletes and it could not be found any research with basketball players; 3) the high correlation between the rate of perceived exertion (RPE) and physiological variables related to the performance of physical exercise (e.g.: heart rate, maximum consumption of oxygen or blood lactate) and multiple studies showing the attenuation of RPE during exercise due to the intake of certain nutrients (especially carbohydrates), while none of them was developed in basketball; 4) correlation between nutritional intake and Session-RPE has been recently studied for the first time. Session-RPE method has been validated in basketball players and other team sports as an indicator of internal workload, sports performance and exercise intensity; 5) fatigue is considered one of the main influential factor on RPE and sport performance. It has also been observed that carbohydrates intake may delay or mitigate the onset of fatigue and, thus, decrease the perceived exertion and the internal training load, which could improve sports performance and training-induced adaptations; 6) there are few studies evaluating the influence of nutrient intake on Session-RPE and only one of them has been carried out with basketball players. Moreover, it has not been analyzed the possible effects of the adequacy of players’ nutritional habits through a nutritional intervention on Session-RPE and fatigue, variables that could be decreased for all training session and competition games because of an improvement of daily nutritional intake. Therefore, this work begins with an introduction that provides the conceptual framework of this research focused on the key role of nutrition in sport, as well as on the current nutritional recommendations for athletes and specifically for basketball players. In addition, previous nutritional interventions carried out with other athletes are described, as well as consequential modifications on their food pattern, coinciding with the first objective of the present study. Subsequently, RPE, Session-RPE and fatigue are analyzed, with focus on their correlation with physical workload, training intensity, sports performance and recovery. Finally, all the aforementioned aspects (nutritional intake, RPE and fatigue) were combined in order to know the current status of the relation between each other, this being the base for the second objective of this study. Subsequently, the objectives mentioned above are explained, continuing with the explanation of the methodology used in the study. The methodology consisted of a case-study design, carrying out a long term nutritional intervention with three professional basketball players (each player = one case study; n = 1), in order to adapt their nutritional intake to nutritional recommendations. At the same time, the individual response of each player to the intervention was analyzed for the two main objectives of the study. Each player completed a food diary (7 days; weighing food) in three moments: before, during and at the end of the intervention. In addition, the Session-RPE and fatigue were daily recorded throughout the study for all trainings (training with ball and resistance training) and competition games. At the same time, other potentially influential variables such as mood state and sleeping were daily controlled throughout the study. Data analysis consisted in descriptive statistics calculation for all the variables of the study, the comparison between nutritional intake (evaluated at different times) and nutritional recommendations and a non-parametric mean comparison between pre intervention and during intervention periods was made by Wilcoxon test (repeated measurements) for all variables too. Finally, the changes in nutritional intake, mood state and sleeping were correlated with the perceived exertion and fatigue through correctional study (Tau_b de Kendall). After the methodology, the study results and the associated discussion are presented. The discussion is based on the current scientific evidence that contributes to understand the relation between Session-RPE, fatigue and nutrition throughout the competitive season. The main findings and results analysis can be summarized as follows: 1) the three professional basketball players initially had inadequate nutritional habits and this clearly shows the need of a sports nutritionist in the coaching staff of professional teams; (2) the major deficiencies of the three players’ diet corresponded to a pronounced deficit of energy intake and carbohydrates consumption which were reduced with nutritional intervention; (3) the excessive intake of total fat, saturated fatty acids, ethanol and protein found in some cases were also adapted to the recommendations after the intervention; (4) Session-RPE mean and fatigue of a certain period of the competition season, could be decreased in an individual player by increasing his carbohydrates intake in the long term, if there are no relevant psycho-emotional disorders; (5) the behavior of the Session-RPE in competition games does not seem to be influenced by the nutritional factors modified in this study. They seem to depend much more on the variation of external non-controllable factors associated with the professional basketball games. Given these results, the different characteristics of each player and the diverse responses observed after the intervention in each individual for all the variables, reinforced the importance of the use of a case study design for research with elite athletes as well as personalized nutritional counselling. In the same way, the different responses obtained for RPE and fatigue in the long term for each player due to modification of nutritional habits, show that there is a dependence of such variables on the physical, psychosocial, emotional and contextual characteristics of each player. Therefore it is proposed that the rigorous control of the qualitative variables that seem to influence the RPE and fatigue in the long term, may facilitate the understanding of data and the determination of unknown factors that could influence these variables. Finally, because Session-RPE is a direct indicator of the internal load of training (psycho-physiological stress experienced by the athlete), the possible attenuation of Session-RPE through the improvement in nutritional habits, would allow to apply the planned external loads of training with less internal stress and better recovery between sessions, with a decrease in fatigue, despite of the advance of the season.

Game theory and reciprocity in some extensive form experimental games

We examine decision making in two-person extensive form game trees using nine treatments that vary matching protocol, payoffs, and payoff information. Our objective is to establish replicable principles of cooperative versus noncooperative behavior that involve the use of signaling, reciprocity, and backward induction strategies, depending on the availability of dominated direct punishing strategies and the probability of repeated interaction with the same partner. Contrary to the predictions of game theory, we find substantial support for cooperation under complete information even in various single-play treatments.

Nonatomic games on Loeb spaces

In the setting of noncooperative game theory, strategic negligibility of individual agents, or diffuseness of information, has been modeled as a nonatomic measure space, typically the unit interval endowed with Lebesgue measure. However, recent work has shown that with uncountable action sets, for example the unit interval, there do not exist pure-strategy Nash equilibria in such nonatomic games. In this brief announcement, we show that there is a perfectly satisfactory existence theory for nonatomic games provided this nonatomicity is formulated on the basis of a particular class of measure spaces, hyperfinite Loeb spaces. We also emphasize other desirable properties of games on hyperfinite Loeb spaces, and present a synthetic treatment, embracing both large games as well as those with incomplete information.

Stochastic game theory: For playing games, not just for doing theory

Recent theoretical advances have dramatically increased the relevance of game theory for predicting human behavior in interactive situations. By relaxing the classical assumptions of perfect rationality and perfect foresight, we obtain much improved explanations of initial decisions, dynamic patterns of learning and adjustment, and equilibrium steady-state distributions.