Bayesian Quantile Regression for Single-Index Models

Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work, we use a Gaussian process prior for the unknown nonparametric link function and a Laplace distribution on the index vector, with the latter motivated by the recent popularity of the Bayesian lasso idea. We design a Markov chain Monte Carlo algorithm for posterior inference. Careful consideration of the singularity of the kernel matrix, and tractability of some of the full conditional distributions leads to a partially collapsed approach where the nonparametric link function is integrated out in some of the sampling steps. Our simulations demonstrate the superior performance of the Bayesian method versus the frequentist approach. The method is further illustrated by an application to the hurricane data.Comment: 26 pages, 8 figures, 10 table

Gaussian process single-index models as emulators for computer experiments

A single-index model (SIM) provides for parsimonious multi-dimensional nonlinear regression by combining parametric (linear) projection with univariate nonparametric (non-linear) regression models. We show that a particular Gaussian process (GP) formulation is simple to work with and ideal as an emulator for some types of computer experiment as it can outperform the canonical separable GP regression model commonly used in this setting. Our contribution focuses on drastically simplifying, re-interpreting, and then generalizing a recently proposed fully Bayesian GP-SIM combination, and then illustrating its favorable performance on synthetic data and a real-data computer experiment. Two R packages, both released on CRAN, have been augmented to facilitate inference under our proposed model(s).Comment: 23 pages, 9 figures, 1 tabl

Androgen receptor phosphorylation status at serine 578 predicts poor outcome in prostate cancer patients

Purpose: Prostate cancer growth is dependent upon androgen receptor (AR) activation, regulated via phosphorylation. Protein kinase C (PKC) is one kinase that can mediate AR phosphorylation. This study aimed to establish if AR phosphorylation by PKC is of prognostic significance. Methods: Immunohistochemistry for AR, AR phosphorylated at Ser-81 (pARS81), AR phosphorylated at Ser-578 (pARS578), PKC and phosphorylated PKC (pPKC) was performed on 90 hormone-naïve prostate cancer specimens. Protein expression was quantified using the weighted histoscore method and examined with regard to clinico-pathological factors and outcome measures; time to biochemical relapse, survival from biochemical relapse and disease-specific survival. Results: Nuclear PKC expression strongly correlated with nuclear pARS578 (c.c. 0.469, p=0.001) and cytoplasmic pARS578 (c.c. 0.426 p=0.002). High cytoplasmic and nuclear pARS578 were associated with disease-specific survival (p<0.001 and p=0.036 respectively). High nuclear PKC was associated with lower disease-specific survival when combined with high pARS578 in the cytoplasm (p=0.001) and nucleus (p=0.038). Combined high total pARS81 and total pARS578 was associated with decreased disease-specific survival (p=0.005) Conclusions: pARS578 expression is associated with poor outcome and is a potential independent prognostic marker in hormone-naïve prostate cancer. Furthermore, PKC driven AR phosphorylation may promote prostate cancer progression and provide a novel therapeutic target

Spatiotemporal Mapping of Photocurrent in a Monolayer Semiconductor Using a Diamond Quantum Sensor

The detection of photocurrents is central to understanding and harnessing the interaction of light with matter. Although widely used, transport-based detection averages over spatial distributions and can suffer from low photocarrier collection efficiency. Here, we introduce a contact-free method to spatially resolve local photocurrent densities using a proximal quantum magnetometer. We interface monolayer MoS2 with a near-surface ensemble of nitrogen-vacancy centers in diamond and map the generated photothermal current distribution through its magnetic field profile. By synchronizing the photoexcitation with dynamical decoupling of the sensor spin, we extend the sensor's quantum coherence and achieve sensitivities to alternating current densities as small as 20 nA per micron. Our spatiotemporal measurements reveal that the photocurrent circulates as vortices, manifesting the Nernst effect, and rises with a timescale indicative of the system's thermal properties. Our method establishes an unprecedented probe for optoelectronic phenomena, ideally suited to the emerging class of two-dimensional materials, and stimulates applications towards large-area photodetectors and stick-on sources of magnetic fields for quantum control.Comment: 19 pages, 4 figure

Radial basis function approach in nuclear mass predictions

The radial basis function (RBF) approach is applied in predicting nuclear masses for 8 widely used nuclear mass models, ranging from macroscopic-microscopic to microscopic types. A significantly improved accuracy in computing nuclear masses is obtained, and the corresponding rms deviations with respect to the known masses is reduced by up to 78%. Moreover, strong correlations are found between a target nucleus and the reference nuclei within about three unit in distance, which play critical roles in improving nuclear mass predictions. Based on the latest Weizs\"{a}cker-Skyrme mass model, the RBF approach can achieve an accuracy comparable with the extrapolation method used in atomic mass evaluation. In addition, the necessity of new high-precision experimental data to improve the mass predictions with the RBF approach is emphasized as well.Comment: 18 pages, 8 figure

The Peculiar Atmospheric Chemistry of KELT-9b

The atmospheric temperatures of the ultra-hot Jupiter KELT-9b straddle the transition between gas giants and stars, and therefore between two traditionally distinct regimes of atmospheric chemistry. Previous theoretical studies assume the atmosphere of KELT-9b to be in chemical equilibrium. Despite the high ultraviolet flux from KELT-9, we show using photochemical kinetics calculations that the observable atmosphere of KELT-9b is predicted to be close to chemical equilibrium, which greatly simplifies any theoretical interpretation of its spectra. It also makes the atmosphere of KELT-9b, which is expected to be cloudfree, a tightly constrained chemical system that lends itself to a clean set of theoretical predictions. Due to the lower pressures probed in transmission (compared to emission) spectroscopy, we predict the abundance of water to vary by several orders of magnitude across the atmospheric limb depending on temperature, which makes water a sensitive thermometer. Carbon monoxide is predicted to be the dominant molecule under a wide range of scenarios, rendering it a robust diagnostic of the metallicity when analyzed in tandem with water. All of the other usual suspects (acetylene, ammonia, carbon dioxide, hydrogen cyanide, methane) are predicted to be subdominant at solar metallicity, while atomic oxygen, iron and magnesium are predicted to have relative abundances as high as 1 part in 10,000. Neutral atomic iron is predicted to be seen through a forest of optical and near-infrared lines, which makes KELT-9b suitable for high-resolution ground-based spectroscopy with HARPS-N or CARMENES. We summarize future observational prospects of characterizing the atmosphere of KELT-9b.Comment: Accepted by ApJ. 9 pages, 6 figures. Corrected minor errors in Figures 1a and 1b (some line styles were switched by accident), text and conclusions unchanged, these minor changes will be updated in final ApJ proo

The Dynamical Yang-Baxter Relation and the Minimal Representation of the Elliptic Quantum Group

In this paper, we give the general forms of the minimal $L$ matrix (the elements of the $L$-matrix are $c$ numbers) associated with the Boltzmann weights of the $A_{n-1}^1$ interaction-round-a-face (IRF) model and the minimal representation of the $A_{n-1}$ series elliptic quantum group given by Felder and Varchenko. The explicit dependence of elements of $L$-matrices on spectral parameter $z$ are given. They are of five different forms (A(1-4) and B). The algebra for the coefficients (which do not depend on $z$) are given. The algebra of form A is proved to be trivial, while that of form B obey Yang-Baxter equation (YBE). We also give the PBW base and the centers for the algebra of form B.Comment: 23 page

Impacts of urban expansion on relatively smaller surrounding cities during heat waves

Urban-induced thermal stress can threaten human health, especially during heat waves (HWs). The growth of cities further exacerbates this effect. Here, weather research and forecasting (WRF) with an urban canopy model (UCM) is used to assess the effects of megacities and their growth on the thermal regime of proximal cities during heat waves. Analysis of the heat fluxes shows that advection impacts cities downwind. Results indicate that as urban areas change size (50%−100% and 100−150% of their current size), the local 2 m temperature increases by 2.7 and 1.7 °C, and the 2 m specific humidity decreases by 2.1 and 1.4 g kg−1, respectively. A small city downwind is impacted with a 0.3−0.4 °C increase in 2 m temperature. Green roof is a potential mitigation strategy for these regions (i.e., beyond the megacity). With 50% green roofs in an urban area, a 0.5 °C decrease in 2 m temperature and 0.6 g kg−1 increase in specific humidity is simulated. Urbanization upwind of a megacity will contribute to regional climate change