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

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

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