Associative polynomial functions over bounded distributive lattices

The associativity property, usually defined for binary functions, can be generalized to functions of a given fixed arity n>=1 as well as to functions of multiple arities. In this paper, we investigate these two generalizations in the case of polynomial functions over bounded distributive lattices and present explicit descriptions of the corresponding associative functions. We also show that, in this case, both generalizations of associativity are essentially the same.Comment: Final versio

Preassociative aggregation functions

The classical property of associativity is very often considered in aggregation function theory and fuzzy logic. In this paper we provide axiomatizations of various classes of preassociative functions, where preassociativity is a generalization of associativity recently introduced by the authors. These axiomatizations are based on existing characterizations of some noteworthy classes of associative operations, such as the class of Acz\'elian semigroups and the class of t-norms.Comment: arXiv admin note: text overlap with arXiv:1309.730

Closed classes of functions, generalized constraints and clusters

Classes of functions of several variables on arbitrary non-empty domains that are closed under permutation of variables and addition of dummy variables are characterized in terms of generalized constraints, and hereby Hellerstein's Galois theory of functions and generalized constraints is extended to infinite domains. Furthermore, classes of operations on arbitrary non-empty domains that are closed under permutation of variables, addition of dummy variables and composition are characterized in terms of clusters, and a Galois connection is established between operations and clusters.Comment: 21 page

Additive decomposability of functions over abelian groups

Abelian groups are classified by the existence of certain additive decompositions of group-valued functions of several variables with arity gap 2.Comment: 17 page

Towards a new method to analyze the soccer teams tactical behaviour : measuring the effective area of play

Recently, new tactical metrics have been developed to increase the match analysis’ potential. Naturally, innovate metrics need some updates in order to improve the utility to the soccer coaches. Thus, this paper aims to update the surface area metric, proposing the effective area of play given some efficacy information’s about team players’ positioning. Furthermore, aim analyzes the effective area of play of each team depending on the state of ball possession and a full match of 7-a-side soccer game in the district final was also analysed. Results showed an inverse correlation between teams’ opposite effective areas of play(rp = -0.681), suggesting the expansion-contraction relationship. Furthermore, was analyzed statistical differences with large effect between the moments with and without ball possession for the team A (F(1; 1506) = 1343.893; p-value ≤ 0.001; η2 = 0.472; Power = 1.000) and B (F(1; 1506) = 968.500; p-value ≤ 0.001; η2 = 0.391; Power = 1.000).info:eu-repo/semantics/publishedVersio

Soccer teams behaviors : analysis if the team distribution in function to ball possession

Innovative tools to soccer analysis are the main concern of the sport performance analysts. Considering team players occupation as one of the fundamental characteristics of soccer success, is too important generate new systems to interpret the post-match reality. These systems must be easy for the coach's applications. Thus, this study proposes an easy tool to understand the team’s collective behaviour in function to their ball possession status. Through the histograms of all team players will be possible understand the most occupied areas by each team, trying understand possible tendencies in the moments with and without ball possession. Were analyzed two teams during an official soccer match, collecting their positions at each instant. Using this tracking was possible perform two heat maps by each team, representing the moments with and without ball possession. Through this method was possible analyze different collective behaviors and explain how could coaches interpret outcomes.info:eu-repo/semantics/publishedVersio

Dynamical Stability and Predictability of Football Players: The Study of One Match

The game of football demands new computational approaches to measure individual and collective performance. Understanding the phenomena involved in the game may foster the identification of strengths and weaknesses, not only of each player, but also of the whole team. The development of assertive quantitative methodologies constitutes a key element in sports training. In football, the predictability and stability inherent in the motion of a given player may be seen as one of the most important concepts to fully characterise the variability of the whole team. This paper characterises the predictability and stability levels of players during an official football match. A Fractional Calculus (FC) approach to define a player’s trajectory. By applying FC, one can benefit from newly considered modeling perspectives, such as the fractional coefficient, to estimate a player’s predictability and stability. This paper also formulates the concept of attraction domain, related to the tactical region of each player, inspired by stability theory principles. To compare the variability inherent in the player’s process variables (e.g., distance covered) and to assess his predictability and stability, entropy measures are considered. Experimental results suggest that the most predictable player is the goalkeeper while, conversely, the most unpredictable players are the midfielders. We also conclude that, despite his predictability, the goalkeeper is the most unstable player, while lateral defenders are the most stable during the match

Hybrid adaptive control of a dragonfly model

Dragonflies show unique and superior flight performances than most of other insect species and birds. They are equipped with two pairs of independently controlled wings granting an unmatchable flying performance and robustness. In this paper, it is presented an adaptive scheme controlling a nonlinear model inspired in a dragonfly-like robot. It is proposed a hybrid adaptive (HA) law for adjusting the parameters analyzing the tracking error. At the current stage of the project it is considered essential the development of computational simulation models based in the dynamics to test whether strategies or algorithms of control, parts of the system (such as different wing configurations, tail) as well as the complete system. The performance analysis proves the superiority of the HA law over the direct adaptive (DA) method in terms of faster and improved tracking and parameter convergence

Application of fractional algorithms in the control of a robotic bird

In this paper, it is studied the dynamics of the robotic bird in terms of time response and robustness. It is analyzed the wing angle of attack and the velocity of the bird, the tail influence, the gliding flight and the flapping flight. The results are positive for the construction of flying robots. The development of computational simulation based on the dynamic of the robotic bird should allow testing strategies and different algorithms of control such as integer and fractional controllers