Evaluation of Portable Retroreflectometers

Portable retroreflectometers have been used to compare the reflectivity of the various pavement marking materials. The Mirolux 12 has been used to collect reflectivity data for the products tested for the National Transportation Product Evaluation Program (NTPEP). The Mirolux 12 docs not have a 30 meter geometry, and there has been a desire to explore the possibility of using a retroreflectometer which has a 30 meter geometry which may better simulate the view of a driver. The objective of this report is to compare data taken with the Mirolux 12 and two other portable retroflectometers having the 30 meter geometry

Transformation and Individuation in Giordano Bruno's Monadology

The essay explores the systematic relationship in the work of Giordano Bruno (1548-1600) between his monadology, his metaphysics as presented in works such as De la causa, principio et uno, the mythopoeic cosmology of Lo spaccio de la bestia trionfante, and practical works like De vinculis in genere. Bruno subverts the conceptual regime of the Aristotelian substantial forms and its accompanying cosmology with a metaphysics of individuality that privileges individual unity (singularity) over formal unity and particulars over substantial forms without sacrificing a metaphysical perspective on the cosmos. The particular is individuated as a unique site of desire, continually transforming but able to entrain itself and others through phantasmatic ‘bonding’, the new source of regularity in Bruno’s polycentric universe. Bruno thus tries to do justice to the demands of intelligibility as well as transformative eros. The essay concludes with a note on Bruno’s geometry as it relates to his general conception of form

Developments in GRworkbench

The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, GRworkbench has been significantly extended to facilitate numerical experimentation in analytically-defined space-times. The numerical differential geometric engine has been rewritten using functional programming techniques, enabling objects which are normally defined as functions in the formalism of differential geometry and General Relativity to be directly represented as function variables in the C++ code of GRworkbench. The new functional differential geometric engine allows for more accurate and efficient visualisation of objects in space-times and makes new, efficient computational techniques available. Motivated by the desire to investigate a recent scientific claim using GRworkbench, new tools for numerical experimentation have been implemented, allowing for the simulation of complex physical situations.Comment: 14 pages. To appear A. Moylan, S.M. Scott and A.C. Searle, Developments in GRworkbench. Proceedings of the Tenth Marcel Grossmann Meeting on General Relativity, editors M. Novello, S. Perez-Bergliaffa and R. Ruffini. Singapore: World Scientific 200

Differential geometry of monopole moduli spaces

This thesis was motivated by a desire to understand the natural geometry of hyperbolic monopole moduli spaces. We take two approaches. Firstly we develop the twistor theory of singular hyperbolic monopoles and use it to study the geometry of their charge 1 moduli spaces. After this we introduce a new way to study the moduli spaces of both Euclidean and hyperbolic monopoles by applying Kodaira's deformation theory to the spectral curve. We obtain new results in both the Euclidean and hyperbolic cases. In particular we prove new cohomology vanishing theorems and find that the hyperbolic monopole moduli space appears to carry a new type of geometry whose complexification is similar to the complexification of hyperk\"ahler geometry but with different reality conditions.Comment: 95 pages, author's DPhil thesi

Geometry Helps to Compare Persistence Diagrams

Exploiting geometric structure to improve the asymptotic complexity of discrete assignment problems is a well-studied subject. In contrast, the practical advantages of using geometry for such problems have not been explored. We implement geometric variants of the Hopcroft--Karp algorithm for bottleneck matching (based on previous work by Efrat el al.) and of the auction algorithm by Bertsekas for Wasserstein distance computation. Both implementations use k-d trees to replace a linear scan with a geometric proximity query. Our interest in this problem stems from the desire to compute distances between persistence diagrams, a problem that comes up frequently in topological data analysis. We show that our geometric matching algorithms lead to a substantial performance gain, both in running time and in memory consumption, over their purely combinatorial counterparts. Moreover, our implementation significantly outperforms the only other implementation available for comparing persistence diagrams.Comment: 20 pages, 10 figures; extended version of paper published in ALENEX 201