Rational homotopy theory of automorphisms of manifolds

We study the rational homotopy types of classifying spaces of automorphism groups of smooth simply connected manifolds of dimension at least five. We give dg Lie algebra models for the homotopy automorphisms and the block diffeomorphisms of such manifolds. Moreover, we use these models to calculate the rational cohomology of the classifying spaces of the homotopy automorphisms and block diffeomorphisms of the manifold #^g S^d x S^d relative to an embedded disk as g tends to infinity. The answer is expressed in terms of stable cohomology of arithmetic groups and invariant Lie algebra cohomology. Through an extension of Kontsevich's work on graph complexes, we relate our results to the (unstable) homology of automorphisms of free groups with boundaries.Comment: 83 pages. Revision of v2 prompted by referee comments. Final version, to appear in Acta Mathematic

Graphics Hardware Implementation of the Parameter-Less Self-Organising Map

This paper presents a highly parallel implementation of a new type of Self-Organising Map (SOM) using graphics hardware. The Parameter-Less SOM smoothly adapts to new data while preserving the mapping formed by previous data. It is therefore in principle highly suited for interactive use, however for large data sets the computational requirements are prohibitive. This paper will present an implementation on commodity graphics hardware which uses two forms of parallelism to signi¯cantly reduce this barrier. The performance is analysed experi- mentally and algorithmically. An advantage to using graphics hardware is that visualisation is essentially free", thus increasing its suitability for interactive exploration of large data sets