Analysis of competitiveness in the NBA regular seasons

[EN] Research background and hypothesis. Several attempts have been made to understand some modalities of sport from the point of view of complexity. Most of these studies deal with this phenomenon with regard to the mechanics of the game itself (in isolation). Nevertheless, some research has been conducted from the perspective of competition between teams. Our hypothesis was that for the study of competitiveness levels in the system of league competition our analysis model (Shannon entropy), is a useful and highly sensitive tool to determine the degree of global competitiveness of a league. Research aim. The aim of our study was to develop a model for the analysis of competitiveness level in team sport competitions based on the uncertainty level that might exist for each confrontation. Research methods. Degree of uncertainty or randomness of the competition was analyzed as a factor of competitiveness. It was calculated on the basis of the Shannon entropy. Research results. We studied 17 NBA regular seasons, which showed a fairly steady entropic tendency. There were seasons less competitive (? 0.9800) than the overall average (0.9835), and periods where the competitiveness remained at higher levels (range: 0.9851 to 0.9902). Discussion and conclusions. A league is more competitive when it is more random. Thus, it is harder to predict the fi nal outcome. However, when the competition is less random, the degree of competitiveness will decrease signifi cantly. The NBA is a very competitive league, there is a high degree of uncertainty of knowing the fi nal result.

Breeze-forced oscillations and strongly nonlinear tide-generated internal solitons

Programa de doctorado en Oceanografía

Correlatos da participação no desporto escolar nos ensinos regular e militar, o papel do sexo, idade, estatuto socioeconómico e das atitudes

[POR] Introdução: Em Portugal, além das aulas de educação física, as escolas oferecem tempos destinados ao desporto escolar (DE), que poderão aumentar os níveis de actividade física dos alunos. Objectivo: Analisar os níveis e os correlatos da participação no DEnos ensinos regular e militar, identificando a su a relação com variáveis sociodomográficas e atitudes.

Labeling the nodes in the intrinsic order graph with their weights

[EN] This paper deals with the study of some new properties of the intrinsic order graph. The intrinsic order graph is the natural graphical representation of a complex stochastic Boolean system (CSBS). A CSBS is a system depending on an arbitrarily large number n of mutually independent random Boolean variables. The intrinsic order graph displays its 2n vertices (associated to the CSBS) from top to bottom, in decreasing order of their occurrence probabilities. New relations between the intrinsic ordering and the Hamming weight (i.e., the number of 1-bits in a binary n-tuple) are derived. Further, the distribution of the weights of the 2n nodes in the intrinsic order graph is analyzed…

Complex sochastic boolean systems : new properties of the intrinsic order graph

[EN]A complex stochastic Boolean system (CSBS) is a system depending on an arbitrary number n of stochastic Boolean variables. The analysis of CSBSs is mainly based on the intrinsic order: a partial order relation defined on the set f0; 1gn of binary n-tuples. The usual graphical representation for a CSBS is the intrinsic order graph: the Hasse diagram of the intrinsic order. In this paper, some new properties of the intrinsic order graph are studied. Particularly, the set and the number of its edges, the degree and neighbors of each vertex, as well as typical properties, such as the symmetry and fractal structure of this graph, are analyzed…