This study presents a novel rapid and effective point simplification algorithm based on point clouds without using either normal or connectivity information. Sampled points are clustered based on shape variations by octree data structure, an inner point distribution of a cluster, to judge whether these points correlate with the coplanar characteristics. Accordingly, the relevant point from each...

In this paper, we investigate the heat kernel embedding as a route to graph representation. The heat kernel of the graph encapsulates information concerning the distribution of path lengths and, hence, node affinities on the graph; and is found by exponentiating the Laplacian eigen-system over time. A Young–Householder decomposition is performed on the heat kernel to obtain the matrix of the em...

We realize a two-dimensional kagome lattice for ultracold atoms by overlaying two commensurate triangular optical lattices generated by light at the wavelengths of 532 and 1064 nm. Stabilizing and tuning the relative position of the two lattices, we explore different lattice geometries including a kagome, a one-dimensional stripe, and a decorated triangular lattice. We characterize these geomet...

Recently, research originating in several dierent applications has appeared on un-structured triangular meshes in which the vertex distribution is not locally uniform, i.e. anisotropic unstructured meshes. The techniques used have the common features that the distribution of triangle shapes for the mesh is controlled by specifying a symmetric tensor, and that the anisotropic mesh is the transfo...

Residual distribution schemes are discussed in the context of higher order spatial discretization for hyperbolic conservation laws. The discrete solution is globally continuous, defined by a Finite Element space based on triangular Lagrangian Pk elements. A natural subtriangulation of these elements allows the reuse of simple distribution formula previously developed for linear P1 triangles. Th...

We present parallel algorithms for triangular periodic Sylvester-type matrix equations, conceptually being the third step of a periodic Bartels–Stewart-like solution method for general periodic Sylvester-type matrix equations based on variants of the periodic Schur decomposition. The presented algorithms are designed and implemented in the framework of the recently developed HPC library SCASY a...

We investigate lattice energies for radially symmetric, spatially extended particles interacting via a radial potential and arranged on the sites of a twodimensional Bravais lattice. We show the global minimality of the triangular lattice among Bravais lattices of fixed density in two cases: In the first case, the distribution of mass is sufficiently concentrated around the lattice points, and ...

A long BeppoSAX observation of the Galactic Center region shows that the spectrum of the diffuse X–ray emission from the SgrA Complex can be described with the sum of two thermal plasma models with temperatures of ∼0.6 keV and ∼89 keV. The spatial distribution of the diffuse emission is energy dependent. While the hard X–ray emission has a nearly symmetric distribution elongated along the Galac...

These notes provide an introduction to the local semicircle law from random matrix theory, as well as some of its applications. We focus on Wigner matrices, Hermitian random matrices with independent upper-triangular entries with zero expectation and constant variance. We state and prove the local semicircle law, which says that the eigenvalue distribution of a Wigner matrix is close to Wigner’...