Breathers are spatially localized and time periodic solutions of extended Hamiltonian dynamical systems. In this paper we study excitation thresholds for (nonlinearly dynamically stable) ground state breather or standing wave solutions for networks of coupled nonlinear oscillators and wave equations of nonlinear Schrödinger (NLS) type. Excitation thresholds are rigorously characterized by varia...

A new technique for computing the differential invariants of a surface from 3D sample points and normals. It is based on a new conformal geometric approach to computing shape invariants directly from the Gauss map. In the current implementation we compute the mean curvature, the Gauss curvature, and the principal curvature axes at 3D points reconstructed by area-based stereo. The differential i...

The straight-line method presented by Papadopulos requires a minimum of three observation wells for determining the transmissivity tensor of a homogeneous and anisotropic aquifer. A simplification of this method was developed for fractured aquifers where the principal directions of the transmissivity tensor are known prior to implementation, such as when fracture patterns on outcropping portion...

The direct variational optimization of the ground-state two-electron reduced-density matrix (2-RDM) is typically performed under ensemble N-representability conditions. Accordingly, variationally obtained 2-RDMs for degenerate ground states may not represent a pure state. When considering only ground-state energetics, the ensemble nature of the 2-RDM is of little consequence. However, the use o...

Great amount of data under varying intrinsic features is thought of as high dimensional nonlinear manifold in the observation space. How to analyze the mapping relationship between the high dimensional manifold and the corresponding intrinsic low dimensional one quantitatively is important to machine learning and cognitive science. In this paper, we propose SVD (singular value decomposition) ba...

Li’s pHd method uses an asymptotic chi-squared test statistic to evaluate a hypothesized dimensionality of a reduceddimension space in a largely nonparametric setting. This statistic is based on an assumed normal distribution of the predictors. When the distributional assumption is violated, a mixture chi-squared test proposed by Cook is theoretically more appropriate. However, both tests may n...