An Arakawa and Gins experimental teaching space : a feasibility study

This essay discusses the benefits of Arakawa and Gins procedural architecture for the development of interdisciplinary and transdisciplinary learning environments. the discussion of how the body is engaged in knoelwdge acquisition leads to a feasibility study undertaken at an Australian University to determine how an experimental, sensory and perceptually-based learning space might be built given the T&L priorties and the fiscal climate in which universitioes curently operat

Shape analysis on Lie groups and homogeneous spaces

In this paper we are concerned with the approach to shape analysis based on the so called Square Root Velocity Transform (SRVT). We propose a generalisation of the SRVT from Euclidean spaces to shape spaces of curves on Lie groups and on homogeneous manifolds. The main idea behind our approach is to exploit the geometry of the natural Lie group actions on these spaces.Comment: 8 pages, Contribution to the conference "Geometric Science of Information '17

Optimally fast incremental Manhattan plane embedding and planar tight span construction

We describe a data structure, a rectangular complex, that can be used to represent hyperconvex metric spaces that have the same topology (although not necessarily the same distance function) as subsets of the plane. We show how to use this data structure to construct the tight span of a metric space given as an n x n distance matrix, when the tight span is homeomorphic to a subset of the plane, in time O(n^2), and to add a single point to a planar tight span in time O(n). As an application of this construction, we show how to test whether a given finite metric space embeds isometrically into the Manhattan plane in time O(n^2), and add a single point to the space and re-test whether it has such an embedding in time O(n).Comment: 39 pages, 15 figure