Given a mapping $f:Xto X$ we naturally associate to it a monotonic map $gg_f:exp Xto exp X$ from the power set of $X$ into itself, thus inducing a generalized topology on $X$. In this paper we investigate some properties of generalized topologies which are defined by such a procedure.

An increased use of free form surfaces in design often results to mass customised components and structural systems which are complex to assemble and expensive to produce. Often to resolve these forms, a tessellation algorithm is used to break the geometry down to manageable components which can be fabricated individually. The issue that can arise is the production of ...

Simulation and game content includes the levels, models, textures, items, and other objects encountered and possessed by players during the game. In most modern video games and in simulation software, the set of content shipped with the product is static and unchanging, or at best, randomized within a narrow set of parameters. However, ideally, if game content could be constantly and automatica...

An important feature of many problem domains in machine learning is their geometry. For example, adjacency relationships, symmetries, and Cartesian coordinates are essential to any complete description of board games, visual recognition, or vehicle control. Yet many approaches to learning ignore such information in their representations, instead inputting flat parameter vectors with no indicati...

Neuroevolution is currently the strongest method on the pole-balancing benchmark reinforcement learning tasks. Although earlier studies suggested that there was an advantage in evolving the network topology as well as connection weights, the leading neuroevolution systems evolve fixed networks. Whether evolving structure can improve performance is an open question. In this article, we introduce...

One of the main goals in developing an autonomous vehicle is programming the action of merging into the traffic lane from an entrance ramp. We seek to create such a behavior through the use of NeuroEvolution of Augmenting Topologies (NEAT) by evolving an agent over many generations to maximize a certain prescribed fitness function, which encourages a smooth merging behavior without crashing. Ou...