For least squares regression, Efron et al. (2004) proposed an efficient solution path algorithm, the least angle regression (LAR). They showed that a slight modification of the LAR leads to the whole LASSO solution path. Both the LAR and LASSO solution paths are piecewise linear. Recently Wu (2011) extended the LAR to generalized linear models and the quasi-likelihood method. In this work we ex...

Solving the so-called geodesic endpoint problem, i.e., finding a that connects two given points on manifold, is at basis of virtually all data processing operations, including averaging, clustering, interpolation and optimization. On Stiefel manifold orthonormal frames, this problem computationally involved. A remedy to use quasi-geodesics as replacement for Riemannian geodesics. Quasi-geodesic...

We solve the two-particle s-wave scattering for an ultracold-atom gas confined in a quasi-one-dimensional trapping potential which is periodically modulated. The interaction between the atoms is included via Fermi's pseudopotential. For a modulated isotropic transverse harmonic confinement, the atomic center of mass and relative degrees of freedom decouple and an exact solution is possible. The...

[1] We compare solute transport experiments to simulations in a partially-saturated, variable-aperture fracture in measured fracture aperture and entrapped-air geometry fields. The computational model tracks particles through a quasi-three-dimensional velocity field that is based on the two-dimensional solution to the Reynolds equation. The model predicts 84% of the relative increase in dispers...

Purely multiplicative comparisons of quantum relative entropy are desirable but challenging to prove. We show such for entropies between comparable densities, including the a density with respect its subalgebraic restriction. These inequalities asymptotically tight in approaching known, as perturbation size approaches zero. Based on these results, we obtain kind inequality known quasi-factoriza...