Refinement criteria for global illumination using convex funcions

In several computer graphics areas, a refinement criterion is often needed to decide whether to go on or to stop sampling a signal. When the sampled values are homogeneous enough, we assume that they represent the signal fairly well and we do not need further refinement, otherwise more samples are required, possibly with adaptive subdivision of the domain. For this purpose, a criterion which is very sensitive to variability is necessary. In this paper, we present a family of discrimination measures, the f-divergences, meeting this requirement. These convex functions have been well studied and successfully applied to image processing and several areas of engineering. Two applications to global illumination are shown: oracles for hierarchical radiosity and criteria for adaptive refinement in ray-tracing. We obtain significantly better results than with classic criteria, showing that f-divergences are worth further investigation in computer graphics. Also a discrimination measure based on entropy of the samples for refinement in ray-tracing is introduced. The recursive decomposition of entropy provides us with a natural method to deal with the adaptive subdivision of the sampling region

A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

Studies of dynamics of physical agent ecosystems

This thesis addresses the problem of learning in physical heterogeneous multi-agent systems (MAS) and the analysis of the benefits of using heterogeneous MAS with respect to homogeneous ones. An algorithm is developed for this task; building on a previous work on stability in distributed systems by Tad Hogg and Bernardo Huberman, and combining two phenomena observed in natural systems, task partition and hierarchical dominance. This algorithm is devised for allowing agents to learn which are the best tasks to perform on the basis of each agent's skills and the contribution to the team global performance. Agents learn by interacting with the environment and other teammates, and get rewards from the result of the actions they perform. This algorithm is specially designed for problems where all robots have to co-operate and work simultaneously towards the same goal. One example of such a problem is role distribution in a team of heterogeneous robots that form a soccer team, where all members take decisions and co-operate simultaneously. Soccer offers the possibility of conducting research in MAS, where co-operation plays a very important role in a dynamical and changing environment. For these reasons and the experience of the University of Girona in this domain, soccer has been selected as the test-bed for this research. In the case of soccer, tasks are grouped by means of roles. One of the most interesting features of this algorithm is that it endows MAS with a high adaptability to changes in the environment. It allows the team to perform their tasks, while adapting to the environment. This is studied in several cases, for changes in the environment and in the robot's body. Other features are also analysed, especially a parameter that defines the fitness (biological concept) of each agent in the system, which contributes to performance and team adaptability. The algorithm is applied later to allow agents to learn in teams of homogeneous and heterogeneous robots which roles they have to select, in order to maximise team performance. The teams are compared and the performance is evaluated in the games against three hand-coded teams and against the different homogeneous and heterogeneous teams built in this thesis. This section focuses on the analysis of performance and task partition, in order to study the benefits of heterogeneity in physical MAS. In order to study heterogeneity from a rigorous point of view, a diversity measure is developed building on the hierarchic social entropy defined by Tucker Balch. This is adapted to quantify physical diversity in robot teams. This tool presents very interesting features, as it can be used in the future to design heterogeneous teams on the basis of the knowledge on other teams.