Design and implementation of a mathematical videogame

This paper presents videogames as a very useful tool in high studies with respect to mathematical matters. It describes the implementation of a videogame developed by its authors which makes it possible for students to reinforce mathematical concepts in a motivating environment. With this work we intend to contribute to the process of engaging a bigger number of university teaching professionals and researchers in the use of serious games and the study of their theoretical frameworks, design, development and application of scientific education. With this idea the authors of the present paper have created and developed the videogame “The Math Castle” which consists in a series of tests through which various aspects of Mathematics are dealt with, especially in the areas of Discrete Mathematics, which due to its nature can be particularly well adapted to this kind of activity, Analysis or Geometry. In this paper there lies a complete description of the game developed and the results obtained with it.

Cryptographic properties of Boolean functions defining elementary cellular automata

In this work, the algebraic properties of the local transition functions of elementary cellular automata (ECA) were analysed. Specifically, a classification of such cellular automata was done according to their algebraic degree, the balancedness, the resiliency, nonlinearity, the propagation criterion and the existence of non-zero linear structures. It is shown that there is not any ECA satisfying all properties at the same time.

The Learning of the Mathematical Models to Aid Decision Making in the High Level Engineering Schools?

At present, in the University curricula in most countries, the decision theory and the mathematical models to aid decision making is not included, as in the graduate program like in Doctored and Master´s programs. In the Technical School of High Level Agronomic Engineers of the Technical University of Madrid (ETSIA-UPM), the need to offer to the future engineers training in a subject that could help them to take decisions in their profession was felt. Along the life, they will have to take a lot of decisions. Ones, will be important and others no. In the personal level, they will have to take several very important decisions, like the election of a career, professional work, or a couple, but in the professional field, the decision making is the main role of the Managers, Politicians and Leaders. They should be decision makers and will be paid for it. Therefore, nobody can understand that such a professional that is called to practice management responsibilities in the companies, does not take training in such an important matter. For it, in the year 2000, it was requested to the University Board to introduce in the curricula an optional qualified subject of the second cycle with 4,5 credits titled " Mathematical Methods for Making Decisions ". A program was elaborated, the didactic material prepared and programs as Maple, Lingo, Math Cad, etc. installed in several IT classrooms, where the course will be taught. In the course 2000-2001 this subject was offered with a great acceptance that exceeded the forecasts of capacity and had to be prepared more classrooms. This course in graduate program took place in the Department of Applied Mathematics to the Agronomic Engineering, as an extension of the credits dedicated to Mathematics in the career of Engineering.

Analysis of digital chaotic optical signals

The main objective of this paper is to present some tools to analyze a digital chaotic signal. We have proposed some of them previously, as a new type of phase diagrams with binary signals converted to hexadecimal. Moreover, the main emphasis will be given in this paper to an analysis of the chaotic signal based on the Lempel and Ziv method. This technique has been employed partly by us to a very short stream of data. In this paper we will extend this method to long trains of data (larger than 2000 bit units). The main characteristics of the chaotic signal are obtained with this method being possible to present numerical values to indicate the properties of the chaos.

Transmission of digital chaotic and information-bearing signals in optical communication systems

A new proposal to have secure communications in a system is reported. The basis is the use of a synchronized digital chaotic systems, sending the information signal added to an initial chaos. The received signal is analyzed by another chaos generator located at the receiver and, by a logic boolean function of the chaotic and the received signals, the original information is recovered. One of the most important facts of this system is that the bandwidth needed by the system remain the same with and without chaos.

Analysis of the critical moments in the League ACB 2007-2008

The aim of this paper was to identify the variables that determine winning or losing in the critical moments of the basketball games. A total of forty one critical moments were analyzed, corresponding to 30 games of the regular season from the Spanish Professional League (ACB, season 2007-2008). Games were selected according to the definition of critical moments (described in the available literature), which corresponded to overtime and the last 5 minutes of games with score differences equal or below to six points. The results revealed better values in the winners in defensive rebounds and successful free-throws.

Asymptotic analysis of vertical geothermal boreholes in the limit of slowly varyng heat injection rates

Theoretical models for the thermal response of vertical geothermal boreholes often assume that the characteristic time of variation of the heat injection rate is much larger than the characteristic diffusion time across the borehole. In this case, heat transfer inside the borehole and in its immediate surroundings is quasi-steady in the first approximation, while unsteady effects enter only in the far field. Previous studies have exploited this disparity of time scales, incorporating approximate matching conditions to couple the near-borehole region with the outer unsteady temperatura field. In the present work matched asymptotic expansion techniques are used to analyze the heat transfer problem, delivering a rigorous derivation of the true matching condition between the two regions and of the correct definition of the network of thermal resistances that represents the quasi-steady solution near the borehole. Additionally, an apparent temperature due to the unsteady far field is identified that needs to be taken into account by the near-borehole region for the correct computation of the heat injection rate. This temperature differs from the usual mean borehole temperature employed in the literatura.

Adams methods: implementation as predictor-corrector methods

In this paper, Adams explicit and implicit formulas are obtained in a simple way and a relationship between them is established, allowing for their joint implementation as predictor-corrector methods. It is shown the purposefulness, from a didactic point of view, of Excel spreadsheets for calculations and for the orderly presentation of results in the application of Adams methods to solving initial value problems in ordinary differential equations.

A card Game Description Language

We present initial research regarding a system capable of generating novel card games. We furthermore propose a method for com- putationally analysing existing games of the same genre. Ultimately, we present a formalisation of card game rules, and a context-free grammar G cardgame capable of expressing the rules of a large variety of card games. Example derivations are given for the poker variant Texashold?em , Blackjack and UNO. Stochastic simulations are used both to verify the implementation of these well-known games, and to evaluate the results of new game rules derived from the grammar. In future work, this grammar will be used to evolve completely novel card games using a grammar- guided genetic program.

State Convergence Theory Applied to a Delayed Teleoperation System

State convergence is a control strategy that was proposed in the early 2000s to ensure stability and transparency in a teleoperation system under specific control gains values. This control strategy has been implemented for a linear system with or without time delay. This paper represents the first attempt at demonstrating, theoretically and experimentantally, that this control strategy can also be applied to a nonlinear teleoperation system with n degrees of freedom and delay in the communication channel. It is assumed that the human operator applies a constant force on the local manipulator during the teleoperation. In addition, the interaction between the remote manipulator and the environment is considered passive. Communication between the local and remote sites is made by means of a communication channel with variable time delay. In this article the theory of Lyapunov-Krasovskii was used to demonstrate that the local-remote teleoperation system is asymptotically stable.

Análisis de la estructura del juego y parámetros morfológicos y fisiológicos en bádminton

En este trabajo se ha realizado un análisis de la estructura del juego y de los parámetros morfológicos y fisiológicos en jugadores de bádminton. Para ello se han realizado 4 estudios aplicados. Objetivo: Los objetivos del trabajo han sido: (1) comprobar si existen diferencias entre el lado dominante y no dominante de las medidas antropométricas en jugadores de bádminton de máximo nivel nacional, así como verificar si el lado del cuerpo donde se realiza la medición puede influir en el cálculo de la composición corporal y del somatotipo. (2) Comparar la estuctura temporal y notacional en partidos de individual masculino entre los Juegos Olímpicos de Pekín y de Londres para observar como ha evolucionado el bádminton de 2008 a 2012. (3) Medir la ocurrencia de daño muscular después de un partido simulado de bádminton y su influencia en parámetros físicos y hematológicos. (4) Investigar la efectividad de una bebida energética que contiene cafeína para mejorar el rendimiento físico y el rendimiento en un partido en jugadores de élite de bádminton. Metodología: Para caracterizar el bádminton participaron en esta tesis un total de 78 jugadores de bádminton de élite (63 hombres y 15 mujeres), distribuidos en tres estudios y se analizaron 40 sets de bádminton de individual masculino usando los videos oficiales de los Juegos Olímpicos de Pekín 2008 y Londres 2012. En el primer estudio se tomaron medidas de pliegues cutáneos, diámetros, longitudes y perímetros del lado dominante y no dominante de los jugadores. Se calculó la composición corporal y el somatotipo. En el segundo estudio se analizaron los factores temporales y los factores notacionales de los partidos. En el tercer estudio se midieron la fuerza máxima isométrica, la velocidad en test específicos de bádminton y se tomaron muestras de sangre antes y después de jugar un partido de bádminton de 45 minutos. En el cuarto estudio se realizó un experimento a doble ciego, aleatorizado y controlado con placebo, los jugadores ingirieron 3 mg de cafeína por kilógramo de masa corporal en forma de bebida energética, o la misma bebida sin cafeína (placebo). En este estudio se registraron diferente tests específicos de bádminton (tests de salto, fuerza máxima y test de agilidad) y se jugó un partido simulado de 45 minutos. Resultados y discusión: (1) El porcentaje óseo fue mayor calculado a partir de las mediciones del lado dominante (dominante = 16.37 ± 1.14 %, no dominante = 15.66 ± 1.12 %; P < 0.001), mientras que el porcentaje muscular fue mayor calculado a partir de las mediciones del lado no dominante (dominante = 49.39 ± 2.60 %, no dominante = 50.18 ± 2.69%; P < 0.001). (2) La duración del set (Pekín: 1124.6 ± 229.9 s vs Londres: 1260.3 ± 267.1 s.; P < 0.05), el tiempo real de juego (Pekín: 306.9 ± 45.7 s vs Londres: 354.7 ± 86.5 s; P < 0.05), tiempo de rally, golpeos por rally, tiempo de descanso en el punto 11, tiempo de descanso entre sets y golpeos por rally fueron significativamente mayores en Londres que en Pekín. (3) El partido simulado de bádminton no afectó a la fuerza isométrica máxima (Pre: 1263.6 ± 245.5, Post: 1290.8 ± 240.4 N) o a la velocidad específica de bádminton (Pre: 21.0 ± 1.7, Post: 20.9 ± 1.8 s), sin embargo las concentraciones de mioglobina y de creatina quinasa en sangre aumentaron de 26.5 ± 11.6 a 197.3 ± 70.2 μg • L-1 y de 258.6 ± 192.2 a 466.0 ± 296.5 U • L-1, respectivamente después del partido de bádminton. (4) En comparación con la bebida placebo, la ingesta de la bebida energética con cafeína incrementó la altura del SJ (34.5±4.7 vs. 36.4±4.3 cm; P < 0.05) y del CMJ (37.7 ± 4.5 vs. 39.5 ± 5.1 cm; P < 0.05) y aumentó el número de aceleraciones totales durante el partido (7395 ± 1594 vs. 7707 ± 2033 aceleraciones; P < 0.05). Conclusiones: (1) Existen asimetrías corporales en los jugadores de bádminton de alto nivel, al encontrarse diferencias en los diámetros óseos y en los perímetros entre el lado dominante y no dominante. Al calcular la composición corporal con el lado dominante de los jugadores de bádminton se está sobreestimando el porcentaje óseo e infraestimando el porcentaje muscular. (2) El bádminton está evolucionando hacía rallies más largos con intervalos de descanso mayores, lo que resulta en partidos más largos. (3) El partido de bádminton generó daño muscular, sin embargo, el nivel de daño muscular alcanzado después de un partido de bádminton no produjo una disminución del rendimiento muscular. (4) El uso de una bebida energética con cafeína puede ser una ayuda nutricional eficaz para aumentar el rendimiento en el salto y patrones de actividad durante el juego en jugadores de élite de bádminton. ABSTRACT: This study analyzes the structure of the game and the morphological and physiological parameters in badminton players, investigated in four applied studies. Purpose: The purposes of the study were: (1) To check if there are differences between the dominant and non-dominant side in the anthropometric measures of badminton players at the highest national level and verify if the side of the body where the measurements are performed can influence the calculation of the body composition and the somatotype. (2) To compare the temporal and notational structure in men’s singles matches between the Olympic Games in Beijing and London to observe the evolution of badminton between 2008 and 2012. (3) To asses the occurrence of muscle damage after a simulated badminton match and its influence on physical and haematological parameters. (4) To determine the effectiveness of a commercially available energy drink that contains caffeine to improve match performance in elite badminton players. Methods: A total of 78 elite badminton players (63 men and 15 women) participated in this thesis to characterize the sport of badminton distributed in three studies and 40 sets of men’s singles badminton analyzed using the official videos of the Olympic Games of Beijing 2008 and London 2012. In the first study skinfolds, diameters, lengths and perimeters of the dominant and non-dominant side of the players were measured and body composition and somatotype were calculated. In the second study the temporal and notational factors were analyzed. In the third study maximal isometric force and speed in badminton specific tests were measured and blood samples were taken before and after a badminton match of 45 minutes. In the fourth study, a double-blind, randomized placebo-controlled experiment, players ingested 3 mg of caffeine per kilogram of body mass in the form of an energy drink or an identical drink with no caffeine content (placebo). In this study different badminton specific tests (jump tests, handgrip force test and an agility test) were recorded and a simulated badminton match of 45 minutes was played. Results and discussion: (1) The percentage of bone was higher when calculated from measurements of the dominant body side (dominant = 16.37 ± 1.14 %, nondominant = 15.66 ± 1.12 %; P < 0.001), while the muscle percentage was higher when calculated from measurements of the non-dominant side (dominant = 49.39 ± 2.60 %, non-dominant = 50.18 ± 2.69%; P < 0.001). (2) Set duration (Beijing: 1124.6 ± 229.9 s vs. London: 1260.3 ± 267.1 s.; P < 0.05), real time played (Beijing: 306.9 ± 45.7 s vs. London: 354.7 ± 86.5 s; P < 0.05), rally time, shots per rally, rest time at point 11, rest time between sets and shots per rally were significantly higher in London than in Beijing. (3) A simulated badminton match did not affect maximal isometric force (Pre: 1263.6 ± 245.5, Post: 1290.8 ± 240.4 N) or specific badminton speed (Pre: 21.0 ± 1.7, Post: 20.9 ± 1.8 s), however, concentrations of myoglobin and creatine kinase in blood increased from 26.5 ± 11.6 to 197.3 ± 70.2 μg • L-1 and from 258.6 ± 192.2 to 466.0 ± 296.5 U • L-1, respectively after the badminton match. (4) In comparison to the placebo drink, the caffeinated beverage increased height in the SJ (34.5±4.7 vs. 36.4±4.3 cm; P < 0.05) and in the CMJ (37.7 ± 4.5 vs. 39.5 ± 5.1 cm; P < 0.05) and increased the number of total accelerations during the match (7395 ± 1594 vs. 7707 ± 2033 accelerations; P < 0.05). Conclusions: (1) Body asymmetries were found in high level badminton players, due to the differences found in bone diameters and perimeters between the dominant and non-dominant body side. When calculating body composition with the dominant side of the badminton players we are overestimating bone percentage and underestimating muscle percentage. (2) Badminton is evolving towards longer rallies with greater rest intervals, resulting in longer matches. (3) The badminton match generated muscle damage, however, the level of muscle damage reached after a badminton match did not produce a decrease in muscle performance. (4) The ingestion of an energy drink containing caffeine might be an effective ergogenic nutritional supplement to increase jump performance and activity patterns during the game in elite badminton players.

Análisis de la actividad neuronal y cerebral mediante técnicas de redes complejas

El cerebro humano es probablemente uno de los sistemas más complejos a los que nos enfrentamos en la actualidad, si bien es también uno de los más fascinantes. Sin embargo, la compresión de cómo el cerebro organiza su actividad para llevar a cabo tareas complejas es un problema plagado de restos y obstáculos. En sus inicios la neuroimagen y la electrofisiología tenían como objetivo la identificación de regiones asociadas a activaciones relacionadas con tareas especificas, o con patrones locales que variaban en el tiempo dada cierta actividad. Sin embargo, actualmente existe un consenso acerca de que la actividad cerebral tiene un carácter temporal multiescala y espacialmente extendido, lo que lleva a considerar el cerebro como una gran red de áreas cerebrales coordinadas, cuyas conexiones funcionales son continuamente creadas y destruidas. Hasta hace poco, el énfasis de los estudios de la actividad cerebral funcional se han centrado en la identidad de los nodos particulares que forman estas redes, y en la caracterización de métricas de conectividad entre ellos: la hipótesis subyacente es que cada nodo, que es una representación mas bien aproximada de una región cerebral dada, ofrece a una única contribución al total de la red. Por tanto, la neuroimagen funcional integra los dos ingredientes básicos de la neuropsicología: la localización de la función cognitiva en módulos cerebrales especializados y el rol de las fibras de conexión en la integración de dichos módulos. Sin embargo, recientemente, la estructura y la función cerebral han empezado a ser investigadas mediante la Ciencia de la Redes, una interpretación mecánico-estadística de una antigua rama de las matemáticas: La teoría de grafos. La Ciencia de las Redes permite dotar a las redes funcionales de una gran cantidad de propiedades cuantitativas (robustez, centralidad, eficiencia, ...), y así enriquecer el conjunto de elementos que describen objetivamente la estructura y la función cerebral a disposición de los neurocientíficos. La conexión entre la Ciencia de las Redes y la Neurociencia ha aportado nuevos puntos de vista en la comprensión de la intrincada anatomía del cerebro, y de cómo las patrones de actividad cerebral se pueden sincronizar para generar las denominadas redes funcionales cerebrales, el principal objeto de estudio de esta Tesis Doctoral. Dentro de este contexto, la complejidad emerge como el puente entre las propiedades topológicas y dinámicas de los sistemas biológicos y, específicamente, en la relación entre la organización y la dinámica de las redes funcionales cerebrales. Esta Tesis Doctoral es, en términos generales, un estudio de cómo la actividad cerebral puede ser entendida como el resultado de una red de un sistema dinámico íntimamente relacionado con los procesos que ocurren en el cerebro. Con este fin, he realizado cinco estudios que tienen en cuenta ambos aspectos de dichas redes funcionales: el topológico y el dinámico. De esta manera, la Tesis está dividida en tres grandes partes: Introducción, Resultados y Discusión. En la primera parte, que comprende los Capítulos 1, 2 y 3, se hace un resumen de los conceptos más importantes de la Ciencia de las Redes relacionados al análisis de imágenes cerebrales. Concretamente, el Capitulo 1 está dedicado a introducir al lector en el mundo de la complejidad, en especial, a la complejidad topológica y dinámica de sistemas acoplados en red. El Capítulo 2 tiene como objetivo desarrollar los fundamentos biológicos, estructurales y funcionales del cerebro, cuando éste es interpretado como una red compleja. En el Capítulo 3, se resumen los objetivos esenciales y tareas que serán desarrolladas a lo largo de la segunda parte de la Tesis. La segunda parte es el núcleo de la Tesis, ya que contiene los resultados obtenidos a lo largo de los últimos cuatro años. Esta parte está dividida en cinco Capítulos, que contienen una versión detallada de las publicaciones llevadas a cabo durante esta Tesis. El Capítulo 4 está relacionado con la topología de las redes funcionales y, específicamente, con la detección y cuantificación de los nodos mas importantes: aquellos denominados “hubs” de la red. En el Capítulo 5 se muestra como las redes funcionales cerebrales pueden ser vistas no como una única red, sino más bien como una red-de-redes donde sus componentes tienen que coexistir en una situación de balance funcional. De esta forma, se investiga cómo los hemisferios cerebrales compiten para adquirir centralidad en la red-de-redes, y cómo esta interacción se mantiene (o no) cuando se introducen fallos deliberadamente en la red funcional. El Capítulo 6 va un paso mas allá al considerar las redes funcionales como sistemas vivos. En este Capítulo se muestra cómo al analizar la evolución de la topología de las redes, en vez de tratarlas como si estas fueran un sistema estático, podemos caracterizar mejor su estructura. Este hecho es especialmente relevante cuando se quiere tratar de encontrar diferencias entre grupos que desempeñan una tarea de memoria, en la que las redes funcionales tienen fuertes fluctuaciones. En el Capítulo 7 defino cómo crear redes parenclíticas a partir de bases de datos de actividad cerebral. Este nuevo tipo de redes, recientemente introducido para estudiar las anormalidades entre grupos de control y grupos anómalos, no ha sido implementado nunca en datos cerebrales y, en este Capítulo explico cómo hacerlo cuando se quiere evaluar la consistencia de la dinámica cerebral. Para concluir esta parte de la Tesis, el Capítulo 8 se centra en la relación entre las propiedades topológicas de los nodos dentro de una red y sus características dinámicas. Como mostraré más adelante, existe una relación entre ellas que revela que la posición de un nodo dentro una red está íntimamente correlacionada con sus propiedades dinámicas. Finalmente, la última parte de esta Tesis Doctoral está compuesta únicamente por el Capítulo 9, el cual contiene las conclusiones y perspectivas futuras que pueden surgir de los trabajos expuestos. En vista de todo lo anterior, espero que esta Tesis aporte una perspectiva complementaria sobre uno de los más extraordinarios sistemas complejos frente a los que nos encontramos: El cerebro humano. ABSTRACT The human brain is probably one of the most complex systems we are facing, thus being a timely and fascinating object of study. Characterizing how the brain organizes its activity to carry out complex tasks is highly non-trivial. While early neuroimaging and electrophysiological studies typically aimed at identifying patches of task-specific activations or local time-varying patterns of activity, there has now been consensus that task-related brain activity has a temporally multiscale, spatially extended character, as networks of coordinated brain areas are continuously formed and destroyed. Up until recently, though, the emphasis of functional brain activity studies has been on the identity of the particular nodes forming these networks, and on the characterization of connectivity metrics between them, the underlying covert hypothesis being that each node, constituting a coarse-grained representation of a given brain region, provides a unique contribution to the whole. Thus, functional neuroimaging initially integrated the two basic ingredients of early neuropsychology: localization of cognitive function into specialized brain modules and the role of connection fibres in the integration of various modules. Lately, brain structure and function have started being investigated using Network Science, a statistical mechanics understanding of an old branch of pure mathematics: graph theory. Network Science allows endowing networks with a great number of quantitative properties, thus vastly enriching the set of objective descriptors of brain structure and function at neuroscientists’ disposal. The link between Network Science and Neuroscience has shed light about how the entangled anatomy of the brain is, and how cortical activations may synchronize to generate the so-called functional brain networks, the principal object under study along this PhD Thesis. Within this context, complexity appears to be the bridge between the topological and dynamical properties of biological systems and, more specifically, the interplay between the organization and dynamics of functional brain networks. This PhD Thesis is, in general terms, a study of how cortical activations can be understood as the output of a network of dynamical systems that are intimately related with the processes occurring in the brain. In order to do that, I performed five studies that encompass both the topological and the dynamical aspects of such functional brain networks. In this way, the Thesis is divided into three major parts: Introduction, Results and Discussion. In the first part, comprising Chapters 1, 2 and 3, I make an overview of the main concepts of Network Science related to the analysis of brain imaging. More specifically, Chapter 1 is devoted to introducing the reader to the world of complexity, specially to the topological and dynamical complexity of networked systems. Chapter 2 aims to develop the biological, topological and functional fundamentals of the brain when it is seen as a complex network. Next, Chapter 3 summarizes the main objectives and tasks that will be developed along the forthcoming Chapters. The second part of the Thesis is, in turn, its core, since it contains the results obtained along these last four years. This part is divided into five Chapters, containing a detailed version of the publications carried out during the Thesis. Chapter 4 is related to the topology of functional networks and, more specifically, to the detection and quantification of the leading nodes of the network: the hubs. In Chapter 5 I will show that functional brain networks can be viewed not as a single network, but as a network-of-networks, where its components have to co-exist in a trade-off situation. In this way, I investigate how the brain hemispheres compete for acquiring the centrality of the network-of-networks and how this interplay is maintained (or not) when failures are introduced in the functional network. Chapter 6 goes one step beyond by considering functional networks as living systems. In this Chapter I show how analyzing the evolution of the network topology instead of treating it as a static system allows to better characterize functional networks. This fact is especially relevant when trying to find differences between groups performing certain memory tasks, where functional networks have strong fluctuations. In Chapter 7 I define how to create parenclitic networks from brain imaging datasets. This new kind of networks, recently introduced to study abnormalities between control and anomalous groups, have not been implemented with brain datasets and I explain in this Chapter how to do it when evaluating the consistency of brain dynamics. To conclude with this part of the Thesis, Chapter 8 is devoted to the interplay between the topological properties of the nodes within a network and their dynamical features. As I will show, there is an interplay between them which reveals that the position of a node in a network is intimately related with its dynamical properties. Finally, the last part of this PhD Thesis is composed only by Chapter 9, which contains the conclusions and future perspectives that may arise from the exposed results. In view of all, I hope that reading this Thesis will give a complementary perspective of one of the most extraordinary complex systems: The human brain.

Estudio del rendimiento bajo presión en los tiros libres en baloncesto, y su influencia sobre el porcentaje de acierto durante el último minuto de juego

El minuto final de un partido ajustado de baloncesto es un momento crítico que está sujeto a multitud de factores que influyen en su desarrollo. Así, el porcentaje de acierto en los tiros libres durante ese periodo de tiempo va a determinar, en muchas ocasiones, el resultado final del partido. La disminución de rendimiento (drop) en esta faceta de juego en condiciones de presión, puede estar relacionada con múltiples variables propias del contexto deportivo estudiado, como por ejemplo: los segundos restantes de posesión, la situación en el marcador (ir ganando, empatando o perdiendo), la localización del partido (jugar en casa o fuera), la fase de competición (fase regular o eliminatorias) o el nivel del equipo (mejores/peores equipos). Además, las características del jugador que realiza los lanzamientos tienen una gran importancia respecto a su edad y años de experiencia para afrontar los momentos críticos, así como el puesto de juego que ocupa en el equipo. En este sentido, la combinación de factores del contexto y del jugador, permiten interactuar en el rendimiento del lanzador en los momentos finales de partido durante sus lanzamientos de tiro libre. El presente trabajo de tesis doctoral tiene como objetivo encontrar aquellas variables más relacionadas con la disminución de rendimiento del jugador en los tiros libres durante el último minuto de juego, y la última serie de tiros libres en los partidos ajustados de baloncesto. Para alcanzar el objetivo del estudio se analizaron 124 partidos ajustados (diferencias iguales o inferiores a 2 puntos) de todas las competiciones (fase regular, playoff y copa del Rey) de la liga ACB durante las temporadas 2011-2012 a 2014-2015. Para el registro de variables se analizó el porcentaje de acierto en los tiros libres del lanzador en la liga regular, partido completo, último minuto y última serie. De este modo se trató de analizar qué variables del contexto y del jugador permitían explicar el rendimiento en los tiros libres durante el último minuto, y la última serie de tiros libres del partido. Por otro lado, se trató de conocer el grado de asociación entre el descenso del rendimiento (drop) en los momentos finales de partido, y las variables estudiadas del jugador: puesto de juego, edad, y años de experiencia profesional; mientras que las variables situacionales consideradas fueron: fase de competición, localización, clasificación, tiempo restante, y diferencia parcial en el marcador. Para el análisis de los datos se realizaron dos modelos estadísticos: 1º) un modelo de regresión lineal múltiple para conocer el efecto de las variables independientes en el porcentaje de aciertos del lanzador en el último minuto, y en la última serie de tiros libres del partido; y 2º) un análisis de regresión logística binomial para analizar la relación existente entre la probabilidad de tener un drop (disminución del rendimiento) y las características del lanzador, y las variables situacionales. Los resultados del modelo de regresión lineal múltiple mostraron efectos negativos significativos en el porcentaje de acierto en los tiros libres durante el último minuto, cuando los lanzadores son los pívots (-19,45%). Por otro lado, los resultados durante la última serie mostraron el efecto negativo significativo sobre la posición de pívot (- 19,30%) y la diferencia parcial en el marcador (-3,33%, para cada punto de diferencia en el marcador) en el porcentaje de acierto en los tiros libres. Las variables independientes edad, experiencia profesional, clasificación en la liga regular, fase de competición, localización, y tiempo restante, no revelaron efectos significativos en los modelos de regresión lineal. Los resultados de la regresión logística binomial revelaron que las variables experiencia profesional entre 13 y 18 años (OR = 4,63), jugar de alero (OR = 23,01), y jugar de base (OR = 10,68) están relacionadas con una baja probabilidad de disminuir el rendimiento durante el último minuto del partido; mientras que ir ganando, aumenta esta probabilidad (OR = 0,06). Además, los resultados de la última serie mostraron una menor disminución del rendimiento del jugador cuando tiene entre 13 y 18 años de experiencia (OR = 4,28), y juega de alero (OR = 8,06) o base (OR = 6,34). Por el contrario, las variables situacionales relacionadas con esa disminución del rendimiento del jugador son las fases eliminatorias (OR = 0,22) e ir ganando (OR = 0,04). Los resultados principales del estudio mostraron que existe una disminución del rendimiento del jugador en su porcentaje de acierto en los tiros libres durante el último minuto y en la última serie de lanzamientos del partido, y que está relacionada significativamente con la edad, experiencia profesional, puesto de juego del jugador, y diferencia parcial en el marcador. Encontrando relación también con la fase de competición, durante la última serie de tiros libres del partido. Esta información supone una valiosa información para el entrenador, y su aplicación en el ámbito competitivo real. En este sentido, la creación de simulaciones en el apartado de aplicaciones prácticas, permite predecir el porcentaje de acierto en los tiros libres de un jugador durante los momentos de mayor presión del partido, en base a su perfil de rendimiento. Lo que puede servir para realizar una toma de decisiones más idónea, con el objetivo de lograr el mejor resultado. Del mismo modo, orienta el tipo de proceso de entrenamiento que se ha de seguir, en relación a los jugadores más tendentes al drop, con el objetivo de minimizar el efecto de la presión sobre su capacidad para rendir adecuadamente en la ejecución de los tiros libres, y lograr de esta manera un rendimiento más homogéneo en todos los jugadores del equipo en esta faceta del juego, durante el momento crítico del final de partido. ABSTRACT. The final minute of a close game in basketball is a critical moment which is subject to many factors that influence its development. Thus, the success rate in free-throws during that period will determine, in many cases, the outcome of the game. Decrease of performance (drop) in this facet of play under pressure conditions, may be related to studied own multiple sports context variables, such as the remaining seconds of possession, the situation in the score (to be winning, drawing, or losing) the location of the match (playing at home or away), the competition phase (regular season or playoffs) or team level (best/worst teams). In addition, the characteristics of the player are very important related to his age and years of experience to face the critical moments, as well as his playing position into team. In this sense, the combination of factors in context and player, allows interact about performance of shooter in the final moments of the game during his free-throw shooting. The aim of this present doctoral thesis was find the most related variables to player´s drop in free throws in the last minute of the game and the last row of free-throws in closed games of basketball. To achieve the objective of the study, 124 closed games (less or equal than 2 points difference) were analyzed in every copetition in ACB league (regular season, playoff and cup) from 2011-2012 to 2014-2015 seasons. To record the variables, the percentage of success of the shooter in regular season, full game, last minute, and last row were analyzed. This way, it is tried to analyze which player and context variables explain the free-throw performance in last minute and last row of the game. On the other hand, it is tried to determine the degree of association between decrease of performance (drop) of the player in the final moments, and studied player variables: playing position, age, and years of professional experience; while considered situational variables considered were: competition phase, location, classification, remaining time, and score-line. For data analysis were performed two statistical models: 1) A multiple linear regression model to determine the effect of the independent variables in the succsess percentage of shooter at the last minute, and in the last row of free-throws in the game; and 2) A binomial logistic regression analysis to analyze the relationship between the probability of a drop (lower performance) and the characteristics of the shooter and situational variables. The results of multiple linear regression model showed significant negative effects on the free-throw percentage during last minute, when shooters are centers (-19.45%). On the other hand, results in the last series showed the significant negative effect on the center position (-19.30%) and score-line (-3.33% for each point difference in the score) in the free-throw percentage. The independent variables age, professional experience, ranking in the regular season, competition phase, location, and remaining time, revealed no significant effects on linear regression models. The results of the binomial logistic regression showed that the variables professional experience between 13 and 18 years (OR = 4.63), playing forward (OR = 23.01) and playing guard (OR = 10.68) are related to reduce the probability to decrease the performance during the last minute of the game. While wining, increases it (OR = 0.06). Furthermore, the results of the last row showed a reduction in performance degradation when player is between 13 and 18 years of experience (OR = 4.28), and playing forward (OR = 8.06) or guard (OR = 6.34). By contrast, the variables related to the decrease in performance of the player are the knockout phases (OR = 0.22) and wining (OR = 0.04). The main results of the study showed that there is a decrease in performance of the player in the percentage of success in free-throws in the last minute and last row of the game, and it is significantly associated with age, professional experience, and player position. Finding relationship with the competition phase, during last row of free-throws of the game too. This information is a valuable information for the coach, for applying in real competitive environment. In this sense, create simulations in the section of practical applications allows to predict the success rate of free-throw of a player during the most pressing moments of the game, based on their performance profile. What can be used to take more appropriate decisions in order to achieve the best result. Similarly, guides the type of training process must be followed in relation to the most favorable players to drop, in order to minimize the effect of pressure on their ability to perform properly in the execution of the free-throws. And to achieve, in this way, a more consistent performance in all team players in this facet of the game, during the critical moment in the final of the game.