Diego Napp, Ricardo Pereira, Raquel Pinto and Paula Rocha
It is well known that convolutional codes are linear systems when they are defined over a finite field. A fundamental issue in the implementation of convolutional codes is to obtain a minimal state representation of the code. Compared with the literature on one-dimensional (1D) time-invariant convolutional codes, there exist relatively few results on the realization problem for time-varying 1D convolutional codes and even fewer if the convolutional codes are two-dimensional (2D). In this paper we consider 2D periodic convolutional codes and address the minimal state space realization problem for this class of codes. This is, in general, a highly nontrivial problem. Here, we focus on separable Roesser models and show that in this case it is possible to derive, under weak conditions, concrete formulas for obtaining a 2D Roesser state space representation. Moreover, we study minimality and present necessary conditions for these representations to be minimal. Our results immediately lead to constructive algorithms to build these representations.
João P. Duarte, Óscar Tavares, João Valente-dos-Santos, Vítor Severino, Alexis Ahmed, Ricardo Rebelo-Gonçalves, João R. Pereira, Vasco Vaz, Susana Póvoas, André Seabra, Sean P. Cumming and Manuel J Coelho-e-Silva
The intermittent nature of match performance in youth soccer supports relevance of ability to repeatedly produce high-intensity actions with short recovery periods. This study was aimed to examine the reproducibility of a repeated dribbling ability protocol and, additionally, to estimate the contribution of concurrent tests to explain inter-individual variability in repeated dribbling output. The total sample comprised 98 players who were assessed as two independent samples: 31 players were assessed twice to examine reliability of the protocol; and 67 juveniles aged 16.1 ± 0.6 years were compared by the competitive level (local, n = 34; national, n = 33) to examine construct validity. All single measurements appeared to be reasonably reliable: total (ICC = 0.924; 95%CI: 0.841 to 0.963); ideal (ICC = 0.913; 95%CI: 0.820 to 0.958); worst (ICC = 0.813; 95%CI: 0.611 to 0.910). In addition, the percentage of the coefficient of variation was below the critical value of 5% for total (%CV = 3.84; TEM = 2.51 s); ideal (%CV = 3.90, TEM = 2.48 s). Comparisons between local and national players suggested magnitude effects as follows: moderate (d-value ranged from 0.63 to 0.89) for all repeated sprint ability scores; large for total (d = 1.87), ideal (d = 1.72), worst (d = 1.28) and moderate for composite scores: the fatigue index (d = 0.69) and the decrement score (d = 0.67). In summary, the dribbling protocol presented reasonable reproducibility properties and output extracted from the protocol seemed to be independent from biological maturation.