Admissible predictive density estimation

Let $X|\mu\sim N_p(\mu,v_xI)$ and $Y|\mu\sim N_p(\mu,v_yI)$ be independent $p$-dimensional multivariate normal vectors with common unknown mean $\mu$. Based on observing $X=x$, we consider the problem of estimating the true predictive density $p(y|\mu)$ of $Y$ under expected Kullback--Leibler loss. Our focus here is the characterization of admissible procedures for this problem. We show that the class of all generalized Bayes rules is a complete class, and that the easily interpretable conditions of Brown and Hwang [Statistical Decision Theory and Related Topics (1982) III 205--230] are sufficient for a formal Bayes rule to be admissible.Comment: Published in at http://dx.doi.org/10.1214/07-AOS506 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Shear thickening of highly viscous granular suspensions

We experimentally investigate shear thickening in dense granular suspensions under oscillatory shear. Directly imaging the suspension-air interface, we observe dilation beyond a critical strain $\gamma_c$ and the end of shear thickening as the maximum confining stress is reached and the contact line moves. Analyzing the shear profile, we extract the viscosity contributions due to hydrodynamics $\eta_\mu$, dilation $\eta_c$ and sedimentation $\eta_g$. While $\eta_g$ governs the shear thinning regime, $\eta_\mu$ and $\eta_c$ together determine the shear thickening behavior. As the suspending liquid's viscosity varies from 10 to 1000 cst, $\eta_\mu$ is found to compete with $\eta_c$ and soften the discontinuous nature of shear thickening

Branching ratios of α\alpha-decay to excited states of even-even nuclei

We make a systematic calculation on $\alpha$-decay branching ratios to members of ground-state rotational band and to excited $0^{+}$ states of even-even nuclei by a simple barrier penetration approach. The branching ratios to the excited states of daughter nucleus are determined by the $\alpha$-decay energy, the angular momentum of $\alpha$-particle, and the excitation probability of the daughter nucleus. Our calculation covers isotopic chains from Hg to Fm in the mass regions 180$<$A$<$202 and A$\geq$224. The calculated branching ratios of $\alpha$-transitions are consistent with the experimental data. Some useful predictions are made for future experiments.Comment: 13 pages, 4 figures, Accepted for publication in Nucl. Phys.

Monitoring the Breakdown of Plastic Materials Under Ultraviolet and Visible Light

The accumulation of plastic waste in landfills and especially in water systems is a pressing environmental concern. Every year, roughly 8 million tons of plastic waste escapes into the oceans, which over time can then break down into microplastics, less than a quarter inch in size, that are consumed by ocean wildlife. The plastic degradation can occur by mechanical means, but energy absorbed from sunlight is also involved in the breakdown of plastic materials. If the efficiency of this degradation was increased, solar energy could be used to eliminate plastic waste and regenerate fuels or chemical feedstocks. In this study, films of four commonly used polymer materials (high-density polyethylene, linear low-density polyethylene, polypropylene, and polystyrene) were exposed to UV and visible light radiation to study how light can be used to degrade plastics. During exposure times of 2 – 3 weeks, the samples were periodically monitored by infrared (IR) spectroscopy to obtain information on structural changes occurring within the polymers. The IR spectra showed the growth of a new IR vibration from carbon-oxygen double bonds, indicating that bonds in the polymer material were breaking and then reacting with molecular oxygen or water in the air. The vibrational band became more intense with continued irradiation as well as when left in the dark. Raman spectroscopy has also been utilized to better understand the pathway of photo-degradation. Overall, the results were much more dramatic when using high-energy UV light compared to visible light

Comparison and optimization of ten phage encoded serine integrases for genome engineering in Saccharomyces cerevisiae

Background: Phage-encoded serine integrases, such as ϕC31 integrase, are widely used for genome engineering but have not been optimized for use in Saccharomyces cerevisiae although this organism is a widely used organism in biotechnology. Results: The activities of derivatives of fourteen serine integrases that either possess or lack a nuclear localization signal were compared using a standardized recombinase mediated cassette exchange reaction. The relative activities of these integrases in S. cerevisiae and in mammalian cells suggested that the major determinant of the activity of an integrase is the enzyme itself and not the cell in which it is working. We used an inducible promoter to show that six integrases were toxic as judged by their effects upon the proliferative ability of transformed yeast. We show that in general the active phage-encoded serine integrases were an order of magnitude more efficient in promoting genome integration reactions than a simple homologous recombination. Conclusions: The results of our study allow us to identify the integrases of the phage ϕBT1, TP901 ~ nls, R4, Bxb1, MR11, A118, ϕK38, ϕC31 ~ nls, Wβ and SPBC ~ nls as active in S. cerevisiae and indicate that vertebrate cells are more restricted than yeast in terms of which integrases are active

Enhanced co-solubilities of Ca and Si in YAG (Y3Al5O12)

General garnet structure (Ia3-d) is a forgiving host and can accommodate cations of varying sizes and valence states. Studies on highly yttrium doped alumina ceramics with Ca and Si contamination indicated that YAG precipitates in the ceramic had a propensity to allow simultaneous incorporation of small amounts of Ca and Si impurities in their structure. In this study, using chemical synthesis techniques it was shown that YAG can accommodate up to approximately 8 cation % Ca+2 and Si+4 (i.e. Ca+2/Y+3 and Si+4/Y+3) if they are incorporated together. Equilibrium conditions are established by calcining samples at 900 C for 2 hours and cooling the samples to room temperature in the furnace. Disappearing-phase method and energy dispersive X-ray spectroscopy (EDS) were used to determine solubility and co-solubility limits. Beyond the solubility limit phase separation occurred and three crystalline yttrium aluminate phases (YAG, YAP (yttrium aluminate perovskite, YAlO3), YAM (yttrium aluminate monoclinic, Y4Al2O9)) were observed. It is believed that the excess Ca and Si above co-solubility limit precipitate out in the form of an x-ray amorphous anorthite-like glass in the system

Optimal Estimation of Multidimensional Normal Means With an Unknown Variance

Let X ∼ Np(θ, σ2 Ip) and W ∼ σ2 χ2m, where both θ and σ2 are unknown, and X is independent of W. Optimal estimation of θ with unknown σ2 is a fundamental issue in applications but basic theoretical issues remain open. We consider estimation of θ under squared error loss. We develop sufficient conditions for prior density functions such that the corresponding generalized Bayes estimators for θ are admissible. This paper has a two-fold purpose: 1. Provide a benchmark for the evaluation of shrinkage estimation for a multivariate normal mean with an unknown variance; 2. Use admissibility as a criterion to select priors for hierarchical Bayes models. To illustrate how to select hierarchical priors, we apply these sufficient conditions to a widely used hierarchical Bayes model proposed by Maruyama & Strawderman [M-S] (2005), and obtain a class of admissible and minimax generalized Bayes estimators for the normal mean θ. We also develop necessary conditions for admissibility of generalized Bayes estimators in the M-S (2005) hierarchical Bayes model. All the results in this paper can be directly applied in the familiar setting of Gaussian linear regression

Liquid-gas phase transition in hot asymmetric nuclear matter with density-dependent relativistic mean-field models

The liquid-gas phase transition in hot asymmetric nuclear matter is studied within density-dependent relativistic mean-field models where the density dependence is introduced according to the Brown-Rho scaling and constrained by available data at low densities and empirical properties of nuclear matter. The critical temperature of the liquid-gas phase transition is obtained to be 15.7 MeV in symmetric nuclear matter falling on the lower edge of the small experimental error bars. In hot asymmetric matter, the boundary of the phase-coexistence region is found to be sensitive to the density dependence of the symmetry energy. The critical pressure and the area of phase-coexistence region increases clearly with the softening of the symmetry energy. The critical temperature of hot asymmetric matter separating the gas phase from the LG coexistence phase is found to be higher for the softer symmetry energy.Comment: To be published in Phys. Lett.