Minimax estimation with thresholding and its application to wavelet analysis

Many statistical practices involve choosing between a full model and reduced models where some coefficients are reduced to zero. Data were used to select a model with estimated coefficients. Is it possible to do so and still come up with an estimator always better than the traditional estimator based on the full model? The James-Stein estimator is such an estimator, having a property called minimaxity. However, the estimator considers only one reduced model, namely the origin. Hence it reduces no coefficient estimator to zero or every coefficient estimator to zero. In many applications including wavelet analysis, what should be more desirable is to reduce to zero only the estimators smaller than a threshold, called thresholding in this paper. Is it possible to construct this kind of estimators which are minimax? In this paper, we construct such minimax estimators which perform thresholding. We apply our recommended estimator to the wavelet analysis and show that it performs the best among the well-known estimators aiming simultaneously at estimation and model selection. Some of our estimators are also shown to be asymptotically optimal.Comment: Published at http://dx.doi.org/10.1214/009053604000000977 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Modulation Doping of a Mott Quantum Well by a Proximate Polar Discontinuity

We present evidence for hole injection into LaAlO3/LaVO3/LaAlO3 quantum wells near a polar surface of LaAlO3 (001). As the surface is brought in proximity to the LaVO3 layer, an exponential drop in resistance and a decreasing positive Seebeck coefficient is observed below a characteristic coupling length of 10-15 unit cells. We attribute this behavior to a crossover from an atomic reconstruction of the AlO2-terminated LaAlO3 surface to an electronic reconstruction of the vanadium valence. These results suggest a general approach to tunable hole-doping in oxide thin film heterostructures.Comment: 16 pages, 7 figure

Metallic behavior in Si/SiGe 2D electron systems

We calculate the temperature, density, and parallel magnetic field dependence of low temperature electronic resistivity in 2D high-mobility Si/SiGe quantum structures, assuming the conductivity limiting mechanism to be carrier scattering by screened random charged Coulombic impurity centers. We obtain comprehensive agreement with existing experimental transport data, compellingly establishing that the observed 2D metallic behavior in low-density Si/SiGe systems arises from the peculiar nature of 2D screening of long-range impurity disorder. In particular, our theory correctly predicts the experimentally observed metallic temperature dependence of 2D resistivity in the fully spin-polarized system

Electronic charges and electric potential at LaAlO3/SrTiO3 interfaces studied by core-level photoemission spectroscopy

We studied LaAlO3/SrTiO3 interfaces for varying LaAlO3 thickness by core-level photoemission spectroscopy. In Ti 2p spectra for conducting "n-type" interfaces, Ti3+ signals appeared, which were absent for insulating "p-type" interfaces. The Ti3+ signals increased with LaAlO3 thickness, but started well below the critical thickness of 4 unit cells for metallic transport. Core-level shifts with LaAlO3 thickness were much smaller than predicted by the polar catastrophe model. We attribute these observations to surface defects/adsorbates providing charges to the interface even below the critical thickness

Far-infrared spectroscopy of spin excitations and Dzyaloshinskii-Moriya interactions in a Shastry-Sutherland compound SrCu2_2(BO3_3)$_2

We have studied spin excitation spectra in the Shastry-Sutherland model compound SrCu$_2$(BO$_3$)$_2$ in magnetic fields using far-infrared Fourier spectroscopy. The transitions from the ground singlet state to the triplet state at 24 cm$^{-1}$ and to several bound triplet states are induced by the electric field component of the far-infrared light. To explain the light absorption in the spin system we invoke a dynamic Dzyaloshinskii-Moriya (DM) mechanism where light couples to a phonon mode, allowing the DM interaction. Two optical phonons couple light to the singlet to triplet transition in SrCu$_2$(BO$_3$)$_2$. One is $a$-polarized and creates an intra-dimer dynamic DM along the c axis. The other is $c$-polarized and creates an intra-dimer dynamic DM interaction, it is in the $(ab)$ plane and perpendicular to the dimer axis. Singlet levels at 21.5 and 28.6 cm$^{-1}$ anti-cross with the first triplet as is seen in far-infrared spectra. We used a cluster of two dimers with a periodic boundary condition to perform a model calculation with scaled intra- and inter-dimer exchange interactions. Two static DM interactions are sufficient to describe the observed triplet state spectra. The static inter-dimer DM in the c-direction $d_1=0.7$ cm$^{-1}$ splits the triplet state sub-levels in zero field [C\'{e}pas et al., Phys. Rev. Lett. \textbf{87}, 167205 (2001)]. The static intra-dimer DM in the $(ab)$ plane (perpendicular to the dimer axis) $d_2=1.8$ cm$^{-1}$, allowed by the buckling of CuBO$_3$ planes, couples the triplet state to the 28.6 cm$^{-1}$ singlet as is seen from the avoided crossing.Comment: 12 pages with 7 figures, some references correcte

AKARI observation of early-type galaxies in Abell 2218

We describe the AKARI InfraRed Camera (IRC) imaging observation of early-type galaxies (ETGs) in A2218 at z ≅ 0.175. With the imaging capability at 11 and 15 μm, we investigate mid-infrared (MIR) properties of ETGs in the cluster environment. Among our flux-limited sample of 22 optical red sequence ETGs, we find that more than 50% have MIR-excess emission, and the most likely cause of the MIR excess is the circumstellar dust emission from asymptotic giant branch (AGB) stars. The MIR-excess galaxies reveal a wide spread in N3-S11 (3 and 11 μm) colors, indicative of a significant spread (2–11 Gyr) in the mean ages of stellar populations. They are also preferentially located in the outer region, suggesting the environment dependence of MIR-excess ETGs over an area out to a half virial radius

Negative Differential Resistance Induced by Mn Substitution at SrRuO3/Nb:SrTiO3 Schottky Interfaces

We observed a strong modulation in the current-voltage characteristics of SrRuO$_3$/Nb:SrTiO$_3$ Schottky junctions by Mn substitution in SrRuO$_3$, which induces a metal-insulator transition in bulk. The temperature dependence of the junction ideality factor indicates an increased spatial inhomogeneity of the interface potential with substitution. Furthermore, negative differential resistance was observed at low temperatures, indicating the formation of a resonant state by Mn substitution. By spatially varying the position of the Mn dopants across the interface with single unit cell control, we can isolate the origin of this resonant state to the interface SrRuO$_3$ layer. These results demonstrate a conceptually different approach to controlling interface states by utilizing the highly sensitive response of conducting perovskites to impurities

Relativistic Hydrodynamic Cosmological Perturbations

Relativistic cosmological perturbation analyses can be made based on several different fundamental gauge conditions. In the pressureless limit the variables in certain gauge conditions show the correct Newtonian behaviors. Considering the general curvature ($K$) and the cosmological constant ($\Lambda$) in the background medium, the perturbed density in the comoving gauge, and the perturbed velocity and the perturbed potential in the zero-shear gauge show the same behavior as the Newtonian ones in general scales. In the first part, we elaborate these Newtonian correspondences. In the second part, using the identified gauge-invariant variables with correct Newtonian correspondences, we present the relativistic results with general pressures in the background and perturbation. We present the general super-sound-horizon scale solutions of the above mentioned variables valid for general $K$, $\Lambda$, and generally evolving equation of state. We show that, for vanishing $K$, the super-sound-horizon scale evolution is characterised by a conserved variable which is the perturbed three-space curvature in the comoving gauge. We also present equations for the multi-component hydrodynamic situation and for the rotation and gravitational wave.Comment: 16 pages, no figure, To appear in Gen. Rel. Gra