Dehn filling in relatively hyperbolic groups

We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a relatively hyperbolic group G, we construct a nice combinatorial Gromov hyperbolic model space acted on properly by G, which reflects the relative hyperbolicity of G in many natural ways. Second, we construct two useful bicombings on this space. The first of these, "preferred paths", is combinatorial in nature and allows us to define the second, a relatively hyperbolic version of a construction of Mineyev. As an application, we prove a group-theoretic analog of the Gromov-Thurston 2\pi Theorem in the context of relatively hyperbolic groups.Comment: 83 pages. v2: An improved version of preferred paths is given, in which preferred triangles no longer need feet. v3: Fixed several small errors pointed out by the referee, and repaired several broken figures. v4: corrected definition 2.38. This is very close to the published versio

Social learning in a multi-agent system

In a persistent multi-agent system, it should be possible for new agents to benefit from the accumulated learning of more experienced agents. Parallel reasoning can be applied to the case of newborn animals, and thus the biological literature on social learning may aid in the construction of effective multi-agent systems. Biologists have looked at both the functions of social learning and the mechanisms that enable it. Many researchers have focused on the cognitively complex mechanism of imitation; we will also consider a range of simpler mechanisms that could more easily be implemented in robotic or software agents. Research in artificial life shows that complex global phenomena can arise from simple local rules. Similarly, complex information sharing at the system level may result from quite simple individual learning rules. We demonstrate in simulation that simple mechanisms can outperform imitation in a multi-agent system, and that the effectiveness of any social learning strategy will depend on the agents' environment. Our simple mechanisms have obvious advantages in terms of robustness and design costs

Hyperbolic groups acting improperly

In this paper we study hyperbolic groups acting on CAT(0) cube complexes. The first main result (Theorem A) is a structural result about the Sageev construction, in which we relate quasi-convexity of hyperplane stabilizers with quasi-convexity of cell stabilizers. The second main result (Theorem D) generalizes both Agol's theorem on cubulated hyperbolic groups and Wise's Quasi-convex Hierarchy Theorem.Comment: 52pp. In v3, some unnecessary assumptions are dropped from some technical results, especially in Section 5 and Corollary 6.5. The main results are unchanged, but the improved technical results are expected to be useful in future work. Several other small improvements to the exposition have been mad