Posterior inference on the degrees of freedom parameter in multivariate-t regression models

Economics

Regression models under competing covariance matrices: A Bayesian perspective

Economics

A Bayesian note on competing correlation structures in the dynamic linear regression model

Economics

On Describing Multivariate Skewness: A Directional Approach

Most multivariate measures of skewness in the literature measure the overall skewness of a distribution. While these measures are perfectly adequate for testing the hypothesis of distributional symmetry, their relevance for describing skewed distributions is less obvious. In this article, we consider the problem of characterising the skewness of multivariate distributions. We define directional skewness as the skewness along a direction and analyse parametric classes of skewed distributions using measures based on directional skewness. The analysis brings further insight into the classes, allowing for a more informed selection of particular classes for particular applications. In the context of Bayesian linear regression under skewed error we use the concept of directional skewness twice. First in the elicitation of a prior on the parameters of the error distribution, and then in the analysis of the skewness of the posterior distribution of the regression residuals.Bayesian methods, Multivariate distribution, Multivariate regression, Prior elicitation, Skewness.

Hyperbolic Metamaterial Resonator-Antenna Scheme for Large, Broadband Emission Enhancement and Single Photon Collection

We model the broadband enhancement of single-photon emission from color centres in silicon carbide nanocrystals coupled to a planar hyperbolic metamaterial, HMM resonator. The design is based on positioning the single photon emitters within the HMM resonator, made of a dielectric index-matched with silicon-carbide material. The broadband response results from the successive resonance peaks of the lossy Fabry Perot structure modes arising within the high-index HMM cavity. To capture this broadband enhancement in the single photon emitters spontaneous emission, we placed a simple gold based cylindrical antenna on top of the HMM resonator. We analyzed the performance of this HMM coupled antenna structure in terms of the Purcell enhancement, quantum efficiency, collection efficiency and overall collected photon rate. For perpendicular dipole orientation relative to the interface, the HMM coupled antenna resonator leads to a significantly large spontaneous emission enhancement with Purcell factor of the order of 250 along with a very high average total collected photon rate, CPR of about 30 over a broad emission spectrum, 700 nm to 1000 nm. The peak CPR increases to about 80 at 900 nm, corresponding to the emission of silicon-carbide quantum emitters. This is a state of the art improvement considering the previous computational designs have reported a maximum average CPR of 25 across the nitrogen-vacancy centre emission spectrum, 600 nm to 800 nm with the highest value being about 40 at 650 nm

Adiabatic optical entanglement between electron spins in separate quantum dots

We present an adiabatic approach to the design of entangling quantum operations with two electron spins localized in separate InAs/GaAs quantum dots via the Coulomb interaction between optically-excited localized states. Slowly-varying optical pulses minimize the pulse noise and the relaxation of the excited states. An analytic "dressed state" solution gives a clear physical picture of the entangling process, and a numerical solution is used to investigate the error dynamics. For two vertically-stacked quantum dots we show that, for a broad range of dot parameters, a two-spin state with concurrence $C>0.85$ can be obtained by four optical pulses with durations $\sim 0.1 - 1$ ns.Comment: 7 pages, 5 figure

Fast initialization of the spin state of an electron in a quantum dot in the Voigt configuration

We consider the initialization of the spin-state of a single electron trapped in a self-assembled quantum dot via optical pumping of a trion level. We show that with a magnetic field applied perpendicular to the growth direction of the dot, a near-unity fidelity can be obtained in a time equal to a few times the inverse of the spin-conserving trion relaxation rate. This method is several orders-of-magnitude faster than with the field aligned parallel, since this configuration must rely on a slow hole spin-flip mechanism. This increase in speed does result in a limit on the maximum obtainable fidelity, but we show that for InAs dots, the error is very small.Comment: 4 pages, 4 figure

Revealing the Young Starburst in Haro 3 with Radio and Infrared Imaging

The Wolf-Rayet galaxy Haro 3 (Mrk 35, NGC 3353) was observed at the near-IR and radio wavelengths as part of ongoing program to study the earliest stages of starbursts. These observations confirm that the current episode of star formation is dominated by a single region (region A). While there are knots of recent (~10 Myr) star formation outside of region A, the sources of ionizing radiation as observed in both radio and Br-gamma observations are almost exclusively associated with region A. The derived ionizing flux implies a star formation rate of ~0.6 solar masses per year localized within a radius of ~0.1 kpc. A comparison with observations from HST indicates that one or more of the star clusters in region A are optically obscured. The star clusters in region A have ages at least as young as ~5 Myr, and possibly as young as ~0.1 Myr. The star cluster that appears to be the youngest also exhibits a near-IR excess in its colors, possibly indicating natal dust in very close proximity to the ionizing stars. The difference between optical- and radio-determined ionizing fluxes as well as the near-IR colors indicate an average extinction value of A_V ~2.5 in region A. The total stellar mass associated with the current starburst in region A is inferred from both the near-IR and radio observations to be ~10^6 solar masses. The other main stellar concentrations observed in the near-IR (Regions B1 and B2) are somewhat older than region A, with ages ~8-10 Myr, and the near-IR observations indicate they have stellar masses of ~8x10^4 and ~2x10^4 solar masses, respectively.Comment: 17 pages, 3 figures, to appear in AJ August 200