Principal angle, principal azimuth, and principal-angle ellipsometry of film-substrate systems

Principal angle, principal azimuth, and principal-angle ellipsometry of film-substrate systems

Contours of constant principal angle and constant principal azimuth in the complex Îμ plane

Angle Principal Component Analysis

Recently, many l1-norm based PCA methods have been developed for dimensionality reduction, but they do not explicitly consider the reconstruction error. Moreover, they do not take into account the relationship between reconstruction error and variance of projected data. This reduces the robustness of algorithms. To handle this problem, a novel formulation for PCA, namely angle PCA, is proposed....

Angle between principal axis triples

S U M M A R Y The principal axis angle ξ 0, or Kagan angle, is a measure of the difference between the orientations of two seismic moment tensors. It is the smallest angle needed to rotate the principal axes of one moment tensor to the corresponding principal axes of the other. This paper is a conceptual review of the main features of ξ 0. We give a concise formula for calculating ξ 0, but our ...

Dihedral angle principal component analysis of molecular dynamics simulations.

It has recently been suggested by Mu et al. [Proteins 58, 45 (2005)] to use backbone dihedral angles instead of Cartesian coordinates in a principal component analysis of molecular dynamics simulations. Dihedral angles may be advantageous because internal coordinates naturally provide a correct separation of internal and overall motion, which was found to be essential for the construction and i...