Covariance approximation for large multivariate spatial data sets with an application to multiple climate model errors

This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate models. Our method allows for a nonseparable and nonstationary cross-covariance structure. We also present a covariance approximation approach to facilitate the computation in the modeling and analysis of very large multivariate spatial data sets. The covariance approximation consists of two parts: a reduced-rank part to capture the large-scale spatial dependence, and a sparse covariance matrix to correct the small-scale dependence error induced by the reduced rank approximation. We pay special attention to the case that the second part of the approximation has a block-diagonal structure. Simulation results of model fitting and prediction show substantial improvement of the proposed approximation over the predictive process approximation and the independent blocks analysis. We then apply our computational approach to the joint statistical modeling of multiple climate model errors.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS478 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions

We reconsider the matrix model formulation of type IIB superstring theory in (9+1)-dimensional space-time. Unlike the previous proposal in which the Wick rotation was used to make the model well-defined, we regularize the Lorentzian model by introducing infrared cutoffs in both the spatial and temporal directions. Monte Carlo studies reveal that the two cutoffs can be removed in the large-N limit and that the theory thus obtained has no parameters other than one scale parameter. Moreover, we find that three out of nine spatial directions start to expand at some "critical time", after which the space has SO(3) symmetry instead of SO(9).Comment: 4 pages, 3 figures; minor corrections, reference added; improved discussions, the version published in PR

A comprehensive evaluation of physical and environmental performances for wet-white leather manufacture

This paper presents the comprehensive evaluation results of physical and environmental performances for a novel wet-white (chrome-free) leather manufacturing. The tanning process is optimized as 15 wt% tannic acid (TA) combination with 4 wt% Laponite nanoclay, giving the leather with shrinkage temperature (Ts) above 86 °C. Inductively coupled plasma-atomic emission spectrometry (ICP-AES) measurements indicate that Laponite can be evenly and tightly bound within the leather matrix, which is further confirmed by scanning electron microscopy and energy dispersive X-ray (SEM-EDX) spectroscopy analysis. The resultant wet-white leathers have reasonable good physical properties that can meet the standard requirements for furniture leather without containing hazardous Cr(VI) and formaldehyde. Further life cycle assessment (LCA) studies shows that tanning process is the main contributor to environmental impact categories in the wet-white tanning process, and tannic acid is the most significant substance factor. Compared to conventional chrome tanning, the wet-white tanning process exhibits much lower abiotic depletion potential (ADP), and reduced global warming potential (GWP) and human toxicity potential (HTP) impacts due to the nature of vegetable tanning; whereas, GWP excluding biogenic carbon and energy consumption are higher owing to prolonged run time.Peer ReviewedPostprint (published version