Search

Spiker–blocker encounters are a key moment for determining the result of a volleyball rally. The characterization of such a moment using physical–statistical parameters allows us to reproduce the possible ball’s trajectory and then make calculations to set up the defense in an optimal way. In this work, we present a computational algorithm that shows the possible worst scenarios of ball trajectories for a volleyball defense, in terms of the covered area by the block and the impact time of the backcourt defense to contact the ball before it reaches the floor. The algorithm is based on the kinematic equations of motion, trigonometry, and statistical parameters of the players. We have called it the Attack-Block-Court Defense algorithm (the ABCD algorithm), since it only requires the 3D-coordinates of the attacker and the blocker, and a discretized court in a number of cells. With those data, the algorithm calculates the percentage of the covered area by the blocker and the time at which the ball impacts the court (impact time). More specifically, the structure of the algorithm consists of setting up the spiker’s and blocker’s locations at the time the spiker hits the ball, and then applying the kinematic equations to calculate the worst scenario for the team in defense. The case of a middle-hitter attack with a single block over the net is simulated, and an analysis of the space of input variables for such a case is performed. We found a strong dependence on the average impact time and the covered area on both the attack–block height’s ratio and the attack height. The standard deviation of the impact time was the variable that showed more asymmetry, respecting the input variables. An asymmetric case considering more variables with a wing spiker and three blockers is also shown, in order to illustrate the potential of the model in a more complex scenario. The results have potential applications, as a supporting tool for coaches in the design of customized defense or attack systems, in the positioning of players according to the prior knowledge of the opponent team, and in the development of replay and video-game technologies in multimedia systems.

Variogram models are a valuable tool used to analyze the variability of a time series; such variability usually entails a spherical or exponential behavior, and so, models based on such functions are commonly used to fit and explain a time series. Variograms have a quasi-periodic structure for rainfall cases, and some extra steps are required to analyze their entire behavior. In this work, we detailed a procedure for a complete analysis of rainfall time series, from the construction of the experimental variogram to curve fitting with well-known spherical and exponential models, and finally proposed a novel model: quadratic–exponential. Our model was developed based on the analysis of 6 out of 30 rainfall stations from our case study: the Río Bravo–San Juan basin, and was constructed from the exponential model while introducing a quadratic behavior near to the origin and taking into account the fact that the maximal variability of the process is known. Considering a sample with diverse Hurst exponents, the stations were selected. The results obtained show robustness in our proposed model, reaching a good fit with and without the nugget effect for different Hurst exponents. This contrasts to previous models, which show good outcomes only without the nugget effect.

This paper presents an exploratory analysis of the mitochondrial DNA (mtDNA) of 32 species in the subphylum Vertebrata, divided in 7 taxonomic classes. Multiple stochastic parameters, such as the Hurst and detrended fluctuation analysis (DFA) exponents, Shannon entropy, and Chargaff ratio are computed for each DNA sequence. The biological interpretation of these parameters leads to defining a triplet of novel indices. These new functions incorporate the long-range correlations, the probability of occurrence of nucleic bases, and the ratio of pyrimidines-to-purines. Results suggest that relevant regions in mtDNA can be located using the proposed indices. Furthermore, early results from clustering algorithms indicate that the indices introduced might be useful in phylogenetic studies.