Hyperspace geography: Visualizing fitness landscapes beyond 4D

Human perception is finely tuned to extract structure about the 4D world of time and space as well as properties such as color and texture. Developing intuitions about spatial structure beyond 4D requires exploiting other perceptual and cognitive abilities. One of the most natural ways to explore complex spaces is for a user to actively navigate through them, using local explorations and global summaries to develop intuitions about structure, and then testing the developing ideas by further exploration. This article provides a brief overview of a technique for visualizing surfaces defined over moderate-dimensional binary spaces, by recursively unfolding them onto a 2D hypergraph. We briefly summarize the uses of a freely available Web-based visualization tool, Hyperspace Graph Paper (HSGP), for exploring fitness landscapes and search algorithms in evolutionary computation. HSGP provides a way for a user to actively explore a landscape, from simple tasks such as mapping the neighborhood structure of different points, to seeing global properties such as the size and distribution of basins of attraction or how different search algorithms interact with landscape structure. It has been most useful for exploring recursive and repetitive landscapes, and its strength is that it allows intuitions to be developed through active navigation by the user, and exploits the visual system's ability to detect pattern and texture. The technique is most effective when applied to continuous functions over Boolean variables using 4 to 16 dimensions.

Bandwidth requirements for shallow, high-resolution seismic reflection

The optimum bandwidth for shallow, high-resolution seismic reflection differs from that required for conventional petroleum reflection. An understanding of this issue is essential for correct choice of acquisition instrumentation. Numerical modelling of simple Bowen Basin coal structures illustrates that, for high-resolution imaging, it is important to accurately record all frequencies up to the limit imposed by earth scattering. On the contrary, the seismic image is much less dependent on frequencies at the lower end of the spectrum. These quantitative observations support the use of specialised high-frequency geophones for high-resolution seismic imaging. Synthetic seismic inversion trials demonstrate that, irrespective of the bandwidth of the seismic data, additional low-frequency impedance control is essential for accurate inversion. Inversion provides no compelling argument for the use of conventional petroleum geophones in the high-resolution arena.