The relation between the symmetry in halo displays and crystal symmetry is investigated for halo displays that are generated by ensembles of crystals. It is found that, regardless of the symmetry of the constituent crystals, such displays are always left-right (L-R) symmetric if the crystals are formed from the surrounding vapor. L-R symmetry of a halo display implies here that the cross sectio...

A reduced order representation of a large data set is often realized through a principal component analysis based upon a singular value decomposition (SVD) of the data. The left singular vectors of a truncated SVD provide the reduced basis. In several applications such as facial analysis and protein dynamics, structural symmetry is inherent in the data. Typically, reflective or rotational symme...

Stabilizing controllers are developed for a 3D pendulum assuming that the pendulum has a single axis of symmetry and that the center of mass lies on the axis of symmetry. This assumption allows development of a reducedmodel that forms the basis for controller design and global closed-loop analysis; this reduced model is parameterized by the constant angular velocity component of the 3D pendulum...

S U M M A R Y Large scale seismic anisotropy in the Earth’s mantle is likely dynamically supported by the mantle’s deformation; therefore, tomographic imaging of 3-D anisotropic mantle seismic velocity structure is an important tool to understand the dynamics of the mantle. While many previous studies have focused on special cases of symmetry of the elastic properties, it would be desirable for...

The image properties that are crucial for priming for symmetry perception in threedimensional line drawings were examined in four experiments. In all experiments, participants first engaged in a study task, in which they determined the left/right facing direction of individual objects. Following the study task, priming (facilitation in accuracy and/or speed of performance) of symmetry judgement...

We obtain a pointwise, a priori bound for the vorticity of axis symmetric solutions to the 3 dimensional Navier-Stokes equations. The bound is in the form of a reciprocal of a power of the distance to the axis of symmetry. This seems to be the first general pointwise estimate established for the axis symmetric Navier-Stokes equations.

Explorations of the order-disorder transformation in vortex matter in single crystals of tetragonal structured (c/a ∼ 3) borocarbide superconductors, Y Ni2B2C and LuNi2B2C, reveal that vortex arrays experience different effective pinning in different crystallographic directions. We surmise that correlation exists between the large anisotropy in effective pinning/disorder and the differences in ...

We explore how global symmetry can be detected prior to segmentation and under noise and occlusion. The definition of local symmetries is extended to affine geometries by considering the tangents and curvatures of local structures, and a quantitative measure of local symmetry known as symmetricity is introduced, which is based on Mahalanobis distances from the tangent-curvature states of local ...

In this paper we are concerned with producing exhaustive lists of simple monotone Venn diagrams that have some symmetry (non-trivial isometry) when drawn on the sphere. A diagram is simple if at most two curves intersect at any point, and it is monotone if it has some embedding on the plane in which all curves are convex. We show that there are 23 such 7-Venn diagrams with a 7-fold rotational s...

We explore how global symmetry can be detected prior to segmentation and under noise and occlusion. The definition of local symmetries is extended to affine geometries by considering the tangents and curvatures of local structures, and a quantitative measure of local symmetry known as symmetricity is introduced, which is based on Mahalanobis distances from the tangent-curvature states of local ...