Análise não linear de séries temporais e aplicações à Psicologia

Nesta dissertação estudámos as séries temporais que representam a complexa dinâmica do comportamento. Demos especial atenção às técnicas de dinâmica não linear. As técnicas fornecem-nos uma quantidade de índices quantitativos que servem para descrever as propriedades dinâmicas do sistema. Estes índices têm sido intensivamente usados nos últimos anos em aplicações práticas em Psicologia. Estudámos alguns conceitos básicos de dinâmica não linear, as características dos sistemas caóticos e algumas grandezas que caracterizam os sistemas dinâmicos, que incluem a dimensão fractal, que indica a complexidade de informação contida na série temporal, os expoentes de Lyapunov, que indicam a taxa com que pontos arbitrariamente próximos no espaço de fases da representação do espaço dinâmico, divergem ao longo do tempo, ou a entropia aproximada, que mede o grau de imprevisibilidade de uma série temporal. Esta informação pode então ser usada para compreender, e possivelmente prever, o comportamento. ABSTRACT: ln this thesis we studied the time series that represent the complex dynamic behavior. We focused on techniques of nonlinear dynamics. The techniques provide us a number of quantitative indices used to describe the dynamic properties of the system. These indices have been extensively used in recent years in practical applications in psychology. We studied some basic concepts of nonlinear dynamics, the characteristics of chaotic systems and some quantities that characterize the dynamic systems, including fractal dimension, indicating the complexity of information in the series, the Lyapunov exponents, which indicate the rate at that arbitrarily dose points in phase space representation of a dynamic, vary over time, or the approximate entropy, which measures the degree of unpredictability of a series. This information can then be used to understand and possibly predict the behavior.

Dynamic Match Analysis

Recent technological development has enabled research- ers to gather data from different performance scenarios while considering players positioning and action events within a specific time frame. This technology varies from global positioning systems to radio frequency devices and computer vision tracking, to name the most common, and aims to collect players’ time motion data and enable the dynamical analysis of performance. Team sports—and in particular, invasion games—present a complex dynamic by nature based on the interaction between 2 opposing sides trying to outperform 1 another. During match and training situations, players’ actions are coupled to their performance context at different interaction levels. As expected, ball, teammates’, and opponents’ positioning play an important role in this interaction process. But other factors, such as final score, teams’ development level, and players’ expertise, seem to affect the match dynamics. In this symposium, we will focus on how different constraints affect invasion games dynamics during both match and training situations. This relation will be established while underpinning the importance of these effects to game teaching and performance optimization. Regarding the match, different performance indicators based on spatial-temporal relations between players and teams will be presented to reveal the interaction processes that form the crucial component of game analysis. Considering the training, this symposium will address the relationship of small-sided games with full- sized matches and will present how players’ dynamical interaction affects different performance indicators.