A Bayesian construction of asymptotically unbiased estimators

A differential geometric framework to construct an asymptotically unbiased estimator of a function of a parameter is presented. The derived estimator asymptotically coincides with the uniformly minimum variance unbiased estimator, if a complete sufficient statistic exists. The framework is based on the maximum a posteriori estimation, where the prior is chosen such that the estimator is unbiased. The framework is demonstrated for the second-order asymptotic unbiasedness (unbiased up to $O(n^{-1})$ for a sample of size $n$). The condition of the asymptotic unbiasedness leads the choice of the prior such that the departure from a kind of harmonicity of the estimand is canceled out at each point of the model manifold. For a given estimand, the prior is given as an integral. On the other hand, for a given prior, we can address the bias of what estimator can be reduced by solving an elliptic partial differential equation. A family of invariant priors, which generalizes the Jeffreys prior, is mentioned as a specific example. Some illustrative examples of applications of the proposed framework are provided.Comment: 28 pages, 2 figure

Si/Ge hole-tunneling double-barrier resonant tunneling diodes formed on sputtered flat Ge layers

We have demonstrated Si/Ge hole-tunneling double-barrier resonant tunneling diodes (RTDs) formed on flat Ge layers with a relaxation rate of 89% by our proposed method; in this method, the flat Ge layers can be directly formed on highly B-doped Si(001) substrates using our proposed sputter epitaxy method. The RTDs exhibit clear negative differential resistance effects in the static current–voltage (I–V) curves at room temperature. The quantized energy level estimation suggests that resonance peaks that appeared in the I–V curves are attributed to hole tunneling through the first heavy- and light-hole energy levels

Superhumps in a Peculiar SU UMa-Type Dwarf Nova ER Ursae Majoris

We report the photometry of a peculiar SU UMa-type dwarf nova - ER UMa for ten nights during 1998 December and 1999 March covering a complete rise to the supermaximum and a normal outburst cycle. Superhumps have been found during the rise to the superoutburst. A negative superhump appeared in Dec.22 light curve, while the superhump on the next night became positive and had large amplitude and distinct waveform from that of the previous night. In the normal outburst we captured, superhumps with larger or smaller amplitudes seem to always exist, although it is not necessarily true for every normal outburst. These results show great resemblance with V1159 Ori (Patterson et al. 1995). It is more likely that superhumps occasionally exist at essentially all phases of the eruption cycles of ER UMa stars, which should be considered in modeling.Comment: 4 pages, 5 figures, Accepted by ApJ Letter

SuprimeCam Observation of Sporadic Meteors during Perseids 2004

We report the serendipitous findings of 13 faint meteors and 44 artificial space objects by Subaru SuprimeCam imaging observations during 11-16 August 2004. The meteors, at about 100km altitude, and artificial satellites/debris in orbit, at 500km altitude or higher, were clearly discriminated by their apparent defocused image sizes. CCD photometry of the 13 meteors, including 1 Perseid, 1 Aquarid, and 11 sporadic meteors, was performed. We defined a peak video-rate magnitude by comparing the integrated photon counts from the brightest portion of the track traversed within 33ms to those from a 0-mag star during the same time duration. This definition gives magnitudes in the range 4.0< V_{vr} <6.4 and 4.1< I_{vr}<5.9 for these 13 meteors. The corresponding magnitude for virtual naked-eye observers could be somewhat fainter especially for the V-band observation, in which the [OI] 5577 line lasting about 1 sec as an afterglow could contribute to the integrated flux of the present 5-10 min CCD exposures. Although the spatial resolution is insufficient to resolve the source size of anything smaller than about 1 m, we developed a new estimate of the collisionally excited column diameter of these meteors. A diameter as small as a few mm was derived from their collisionally excited photon rates, meteor speed, and the volume density of the oxygen atoms at the 100km altitude. The actual column diameter of the radiating zone, however, could be as large as few 100m because the excited atoms travel that distance before they emit forbidden lines in 0.7 sec of its average lifetime. Among the 44 artificial space objects, we confirmed that 17 were cataloged satellites/space debris.Comment: 14 pages, 13 figures, 5 tables, submitted to PAS

Imprint of Gravitational Lensing by Population III Stars in Gamma Ray Burst Light Curves

We propose a novel method to extract the imprint of gravitational lensing by Pop III stars in the light curves of Gamma Ray Bursts (GRBs). Significant portions of GRBs can originate in hypernovae of Pop III stars and be gravitationally lensed by foreground Pop III stars or their remnants. If the lens mass is on the order of $10^2-10^3M_\odot$ and the lens redshift is greater than 10, the time delay between two lensed images of a GRB is $\approx 1$s and the image separation is $\approx 10 \mu$as. Although it is difficult to resolve the two lensed images spatially with current facilities, the light curves of two images are superimposed with a delay of $\approx 1$ s. GRB light curves usually exhibit noticeable variability, where each spike is less than 1s. If a GRB is lensed, all spikes are superimposed with the same time delay. Hence, if the autocorrelation of light curve with changing time interval is calculated, it should show the resonance at the time delay of lensed images. Applying this autocorrelation method to GRB light curves which are archived as the {\it BATSE} catalogue, we demonstrate that more than half light curves can show the recognizable resonance, if they are lensed. Furthermore, in 1821 GRBs we actually find one candidate of GRB lensed by a Pop III star, which may be located at redshift 20-200. The present method is quite straightforward and therefore provides an effective tool to search for Pop III stars at redshift greater than 10. Using this method, we may find more candidates of GRBs lensed by Pop III stars in the data by the {\it Swift} satellite.Comment: 13 pages, 13 figures, accepted for publication in Ap

Spin and interaction effects in quantum dots: a Hartree-Fock-Koopmans approach

We use a Hartree-Fock-Koopmans approach to study spin and interaction effects in a diffusive or chaotic quantum dot. In particular, we derive the statistics of the spacings between successive Coulomb-blockade peaks. We include fluctuations of the matrix elements of the two-body screened interaction, surface-charge potential, and confining potential to leading order in the inverse Thouless conductance. The calculated peak-spacing distribution is compared with experimental results.Comment: 5 pages, 4 eps figures, revise

Anomalous Enhancement of the Boltzmann Conductivity in Disordered Zigzag Graphene Nanoribbons

We study the conductivity of disordered zigzag graphene nanoribbons in the incoherent regime by using the Boltzmann equation approach. The band structure of zigzag nanoribbons contains two energy valleys, and each valley has an excess one-way channel. The crucial point is that the numbers of conducting channels for two propagating directions are imbalanced in each valley due to the presence of an excess one-way channel. It was pointed out that as a consequence of this imbalance, a perfectly conducting channel is stabilized in the coherent regime if intervalley scattering is absent. We show that even in the incoherent regime, the conductivity is anomalously enhanced if intervalley scattering is very weak. Particularly, in the limit of no intervalley scattering, the dimensionless conductance approaches to unity with increasing ribbon length as if there exists a perfectly conducting channel. We also show that anomalous valley polarization of electron density appears in the presence of an electric field.Comment: 10 pages, 3 figure