Limit Distribution of Convex-Hull Estimators of Boundaries

Given n independent and identically distributed observations in a set G with an unknown function g, called a boundary or frontier, it is desired to estimate g from the observations. The problem has several important applications including classification and cluster analysis, and is closely related to edge estimation in image reconstruction. It is particularly important in econometrics. The convex-hull estimator of a boundary or frontier is very popular in econometrics, where it is a cornerstone of a method known as `data envelope analysis´ or DEA. In this paper we give a large sample approximation of the distribution of the convex-hull estimator in the general case where p>=1. We discuss ways of using the large sample approximation to correct the bias of the convex-hull and the DEA estimators and to construct confidence intervals for the true function. --Convex-hull,free disposal hull,frontier function,data envelope analysis,productivity analysis,rate of convergence

Asymptotic distribution of conical-hull estimators of directional edges

Nonparametric data envelopment analysis (DEA) estimators have been widely applied in analysis of productive efficiency. Typically they are defined in terms of convex-hulls of the observed combinations of $\mathrm{inputs}\times\mathrm{outputs}$ in a sample of enterprises. The shape of the convex-hull relies on a hypothesis on the shape of the technology, defined as the boundary of the set of technically attainable points in the $\mathrm{inputs}\times\mathrm{outputs}$ space. So far, only the statistical properties of the smallest convex polyhedron enveloping the data points has been considered which corresponds to a situation where the technology presents variable returns-to-scale (VRS). This paper analyzes the case where the most common constant returns-to-scale (CRS) hypothesis is assumed. Here the DEA is defined as the smallest conical-hull with vertex at the origin enveloping the cloud of observed points. In this paper we determine the asymptotic properties of this estimator, showing that the rate of convergence is better than for the VRS estimator. We derive also its asymptotic sampling distribution with a practical way to simulate it. This allows to define a bias-corrected estimator and to build confidence intervals for the frontier. We compare in a simulated example the bias-corrected estimator with the original conical-hull estimator and show its superiority in terms of median squared error.Comment: Published in at http://dx.doi.org/10.1214/09-AOS746 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Kinetic stabilization of Fe film on (4 by 2)-GaAs(100)

We grow Fe film on (4 by 2)-GaAs(100) at low temperature, (~ 130 K) and study their chemical structure by photoelectron spectroscopy using synchrotron radiation. We observe the effective suppression of As segregation and remarkable reduction of alloy formation near the interface between Fe and substrate. Hence, this should be a way to grow virtually pristine Fe film on GaAs(100). Further, the Fe film is found stable against As segregation even after warmed up to room temperature. There only forms very thin, ~ 8 angstrom thick interface alloy. It is speculated that the interface alloy forms via surface diffusion mediated by interface defects formed during the low temperature growth of the Fe film. Further out-diffusion of both Ga and As are suppressed because it should then proceed via inefficient bulk diffusion.Comment: 4 figure

Entanglement between qubits induced by a common environment with a gap

We study a system of two qubits interacting with a common environment, described by a two-spin boson model. We demonstrate two competing roles of the environment: inducing entanglement between the two qubits and making them decoherent. For the environment of a single harmonic oscillator, if its frequency is commensurate with the induced two-qubit coupling strength, the two qubits could be maximally entangled and the environment could be separable. In the case of the environment of a bosonic bath, the gap of its spectral density function is essential to generate entanglement between two qubits at equilibrium and for it to be used as a quantum data bus.Comment: accepted for publication in Physical Review

Quelques plats pour la m\'etrique de Hofer

We show, by an elementary and explicit construction, that the group of Hamiltonian diffeomorphisms of certain symplectic manifolds, endowed with Hofer's metric, contains subgroups quasi-isometric to Euclidean spaces of arbitrary dimension.Comment: 9 pages, minor change

Energy Spectrum of Bloch Electrons Under Checkerboard Field Modulations

Two-dimensional Bloch electrons in a uniform magnetic field exhibit complex energy spectrum. When static electric and magnetic modulations with a checkerboard pattern are superimposed on the uniform magnetic field, more structures and symmetries of the spectra are found, due to the additional adjustable parameters from the modulations. We give a comprehensive report on these new symmetries. We have also found an electric-modulation induced energy gap, whose magnitude is independent of the strength of either the uniform or the modulated magnetic field. This study is applicable to experimentally accessible systems and is related to the investigations on frustrated antiferromagnetism.Comment: 8 pages, 6 figures (reduced in sizes), submitted to Phys. Rev.

Entanglement and Quantum Phase Transitions via Adiabatic Quantum Computation

For a finite XY chain and a finite two-dimensional Ising lattice, it is shown that the paramagnetic ground state is adiabatically transformed to the GHZ state in the ferromagnetic phase by slowly turning on the magnetic field. The fidelity between the GHZ state and an adiabatically evolved state shows a feature of the quantum phase transition.Comment: Revise

Landau diamagnetism and magnetization of interacting diffusive conductors

We show how the orbital magnetization of an interacting disordered diffusive electron gas can be simply related to the magnetization of the non-interacting system having the same geometry. This result is applied to the persistent current of a mesoscopic ring and to the relation between Landau diamagnetism and the interaction correction to the magnetization of diffusive systems. The field dependence of this interaction contribution can be deduced directly from the de Haas-van Alphen oscillations of the free electron gas. Known results for the free orbital magnetism of finite systems can be used to derive the interaction contribution in the diffusive regime in various geometries.Comment: 4 pages, 2 figure

Seed-specific overexpression of the pyruvate transporter BASS2 increases oil content in Arabidopsis seeds

117Ysciescopu

Depletion of density of states near Fermi energy induced by disorder and electron correlation in alloys

We have performed high resolution photoemission study of substitutionally disordered alloys Cu-Pt, Cu-Pd, Cu-Ni, and Pd-Pt. The ratios between alloy spectra and pure metal spectra are found to have dips at the Fermi level when the residual resistivity is high and when rather strong repulsive electron-electron interaction is expected. This is in accordance with Altshuler and Aronov's model which predicts depletion of density of states at the Fermi level when both disorder and electron correlation are present.Comment: 1 tex file and 4 ps file