Algorithms for envelope estimation

Envelopes were recently proposed as methods for reducing estimative variation in multivariate linear regression. Estimation of an envelope usually involves optimization over Grassmann manifolds. We propose a fast and widely applicable one-dimensional (1D) algorithm for estimating an envelope in general. We reveal an important structural property of envelopes that facilitates our algorithm, and we prove both Fisher consistency and root-n-consistency of the algorithm.Comment: 30 pages, 2 figures, 2 table

Monte Carlo Simulations of Doped, Diluted Magnetic Semiconductors - a System with Two Length Scales

We describe a Monte Carlo simulation study of the magnetic phase diagram of diluted magnetic semiconductors doped with shallow impurities in the low concentration regime. We show that because of a wide distribution of interaction strengths, the system exhibits strong quantum effects in the magnetically ordered phase. A discrete spin model, found to closely approximate the quantum system, shows long relaxation times, and the need for specialized cluster algorithms for updating spin configurations. Results for a representative system are presented.Comment: 12 pages, latex, 7 figures; submitted to International Journal of Modern Physics C, Proceedings of the U.S.-Japan Bilateral Seminar: Understanding and Conquering Long Time Scales in Computer Simulation

Impurity states in multiband s-wave superconductors: analysis of iron pnictides

We examine the effect of a single, non-magnetic impurity in a multiband, extended s-wave superconductor allowing for anisotropy of the gaps on the Fermi surfaces. We derive analytic expressions for the Green's functions in the continuum and analyse the conditions for the existence of sharp impurity-induced resonant states. Underlying band structure is more relevant for the multiband than for single band case, and mismatch between the bands generically makes the formation of the impurity states less likely in the physical regime of parameters. We confirm these conclusions by numerically solving the impurity problem in a tight-binding parameterization of the bands relevant to pnictide superconductors.Comment: minor corrections, published versio