Andrew J. Hanson

Gravitation, Gauge Theories and Differential Geometry

Stanford Linear Accelerator Center, Stanford, California 94305, USA and The Enrico Fermi Institute and Department of Physics, The University of Chicago, Chicago, illinois, USA Peter B. GILKEY Fine Hall, Box 37. Department of Mathematics, Princeton University, Princeton, New Jersey 08544, USA and Department of Mathematics, University of Southern California, Los Angeles, California 90007, USA and Andrew J. HANSON

Asymptotically flat self-dual solutions to euclidean gravity

In an attempt to find gravitational analogs of Yang-Mills pseudoparticles, we obtain two classes of self-dual solutions to the euclidean Einstein equations. These matries are free from singularities and approach a flat metric at infinity.

Computational strategies for object recognition

This article reviews the available methods for automated identification of objects in digital images. The techniques are classified into groups according to the nature of the computational strategy used. Four classes are proposed: (1) the simplest strategies, which work on data appropriate for feature vector classification, (2) methods that match models to symbolic data structures for situations involving reliable data and complex models, (3) approaches that fit models to the photometry and are appropriate for noisy data and simple models, and (4) combinations of these strategies, which must be adopted in complex situations. Representative examples of various methods are summarized, and the classes of strategies with respect to their appropriateness for particular applications.

Self-Dual Solutions to Euclidean Gravity

Recent work on Euclidean self-dual gravitational fields is reviewed. We discuss various solutions to the Einstein equations and treat asymptotically locally Euclidean self-dual metrics in detail. These latter solutions have vanishing classical action and nontrivial topological invariants, and so may play a role in quantum gravity resembling that of the Yang-Mills instantons.

The relativistic spherical top

The classical theory of the free relativistic spherical top is first developed from a Lagrangian viewpoint. Our method allows the invariant mass to be an arbitrary function of the intrinsic spin. A canonical formalism is established following the approach suggested by Dirac for constrained Hamiltonian systems. There is a second arbitrary function in the theory, in addition to the usual one due to reparametrization invariance. The usual Newton-Wigner variables are supplemented by the Euler angles. The quantum theory of the free top is discussed. The classical theory is generalized to included charged tops with magnetic moments.

Illuminating the fourth dimension

A family of techniques for creating intuitively informative shaded images of 4-D mathematical objects is proposed. The rendering of an object in a 4-D world is described by considering step-by-step how objects might be rendered into images in simpler worlds. The mathematical principles needed to compute projected images of objects and their shadows in D dimensions are outlined. The issues involved in producing shaded images of objects in four dimensions, including extending rendering from 3-D to 4-D, smooth shading, and specularity, are discussed. Results of rendering a Steiner surface, torus, and knotted sphere in four dimensions are presented.<<ETX>>

Interactive visualization methods for four dimensions

Making accurate computer graphics representations of surfaces and volumes (2-manifolds and 3-manifolds) embedded in four-dimensional space typically involves complex and time-consuming computations. In order to make simulated worlds that help develop human intuition about the fourth dimensions, we need techniques that permit real-time, interactive manipulation of the most sophisticated depictions available. We propose the following new methods that bring us significantly closer to this goal: an approach to high-speed 4D illuminated surface rendering incorporating 4D shading and occlusion coding; a procedure for rapidly generating 2D screen images of tessellated 3-manifolds illuminated by 4D light. These methods are orders of magnitude faster than previous approaches, enabling the real-time manipulation of high-resolution 4D images on commercial graphics hardware.<<ETX>>

Interactive methods for visualizable geometry

Interactive computer graphics can provide new insights into the objects of pure geometry, providing intuitively useful images, and, in some cases, unexpected results. Interactive computer graphics systems have opened a new era in the visualization of pure geometry. We demonstrate the fruitful relationship between mathematics and the discipline of computer graphics, emphasizing those areas of low-dimensional geometry and topology where interactive paradigms are of growing importance.<<ETX>>

Search for Charged Current Coherent Pion Production on Carbon in a Few-GeV Neutrino Beam

The SciBooNE Collaboration has performed a search for charged current coherent pion production from muon neutrinos scattering on carbon, nu{sub {mu}}{sup 12}C- {yields} {mu}{sup 12}Cpi{sup +}, with two distinct data samples. No evidence for coherent pion production is observed. We set 90% confidence level upper limits on the cross section ratio of charged current coherent pion production to the total charged current cross section at 0.67 x 10{sup -2} at mean neutrino energy 1.1 GeV and 1.36 x 10{sup -2} at mean neutrino energy 2.2 GeV.

Visualizing Large-Scale Uncertainty in Astrophysical Data

Visualization of uncertainty or error in astrophysical data is seldom available in simulations of astronomical phenomena, and yet almost all rendered attributes possess some degree of uncertainty due to observational error. Uncertainties associated with spatial location typically vary significantly with scale and thus introduce further complexity in the interpretation of a given visualization. This paper introduces effective techniques for visualizing uncertainty in large-scale virtual astrophysical environments. Building upon our previous transparently scalable visualization architecture, we develop tools that enhance the perception and comprehension of uncertainty across wide scale ranges. Our methods include a unified color-coding scheme for representing log-scale distances and percentage errors, an ellipsoid model to represent positional uncertainty, an ellipsoid envelope model to expose trajectory uncertainty, and a magic-glass design supporting the selection of ranges of log-scale distance and uncertainty parameters, as well as an overview mode and a scalable WIM tool for exposing the magnitudes of spatial context and uncertainty.