Variable threshold algorithm for division of labor analyzed as a dynamical system

Division of labor is a widely studied aspect of colony behavior of social insects. Division of labor models indicate how individuals distribute themselves in order to perform different tasks simultaneously. However, models that study division of labor from a dynamical system point of view cannot be found in the literature. In this paper, we define a division of labor model as a discrete-time dynamical system, in order to study the equilibrium points and their properties related to convergence and stability. By making use of this analytical model, an adaptive algorithm based on division of labor can be designed to satisfy dynamic criteria. In this way, we have designed and tested an algorithm that varies the response thresholds in order to modify the dynamic behavior of the system. This behavior modification allows the system to adapt to specific environmental and collective situations, making the algorithm a good candidate for distributed control applications. The variable threshold algorithm is based on specialization mechanisms. It is able to achieve an asymptotically stable behavior of the system in different environments and independently of the number of individuals. The algorithm has been successfully tested under several initial conditions and number of individuals.

Epidemiology of injuries in First Division Spanish football

Abstract The aim was to examine the injuries sustained by Spanish football players in the First Division and to compare injury-related variables in the context of both competition and training. The injury data were prospectively collected from 16 teams (427 players) using a specific web-based survey during the 2008/2009 season. A total of 1293 injuries were identified (145 were recurring injuries). The overall injury incidence was 5.65 injuries per 1000 h of exposure. Injuries were much more common during competition than during training (43.53 vs. 3.55 injuries per 1000 h of exposure, P menor que 0.05). Most of the injuries (89.6%) involved the lower extremities, and overuse (65.7%) was the main cause. Muscle and tendon injuries were the most common types of injury (53.8%) among the players. The incidence of training injuries was greater during the pre-season and tended to decrease throughout the season, while the incidence of competition injuries increased throughout the season (all P menor que 0.05). In conclusion, the results of this study suggest the need for injury prevention protocols in the First Division of the Spanish Football League to reduce the number of overuse injuries in the muscles and tendons in the lower extremities. In addition, special attention should be paid during the pre-season and the competitive phase II (the last four months of the season) in order to prevent training and competition injuries, respectively.