An Approach to Constructing Nested Space-Filling Designs for Multi-Fidelity Computer Experiments.

Multi-fidelity computer experiments are widely used in many engineering and scientific fields. Nested space-filling designs (NSFDs) are suitable for conducting such experiments. Two classes of NSFDs are currently available. One class is based on special orthogonal arrays of strength two and the other consists of nested Latin hypercube designs. Both of them assume all factors are continuous. We propose an approach to constructing new NSFDs based on powerful (t, s)-sequences. The method is simple, easy to implement, and quite general. For continuous factors, this approach produces NSFDs with better space-filling properties than existing ones. Unlike the previous methods, this method can also construct NSFDs for categorical and mixed factors. Some illustrative examples are given. Other applications of the constructed designs are briefly discussed.

Orthogonalizing EM: A design-based least squares algorithm.

We introduce an efficient iterative algorithm, intended for various least squares problems, based on a design of experiments perspective. The algorithm, called orthogonalizing EM (OEM), works for ordinary least squares and can be easily extended to penalized least squares. The main idea of the procedure is to orthogonalize a design matrix by adding new rows and then solve the original problem by embedding the augmented design in a missing data framework. We establish several attractive theoretical properties concerning OEM. For the ordinary least squares with a singular regression matrix, an OEM sequence converges to the Moore-Penrose generalized inverse-based least squares estimator. For ordinary and penalized least squares with various penalties, it converges to a point having grouping coherence for fully aliased regression matrices. Convergence and the convergence rate of the algorithm are examined. Finally, we demonstrate that OEM is highly efficient for large-scale least squares and penalized least squares problems, and is considerably faster than competing methods when n is much larger than p. Supplementary materials for this article are available online.

Spatial modeling for refining and predicting surface potential mapping with enhanced resolution.

Quantitatively mapping surface properties with nanometer or even subnanometer resolutions is critical for advanced scanning probe microscopy (SPM) characterization. However, the characterization performance often suffers from noises and artifacts due to instrumentation or environmental limitations. In this paper, we proposed a novel statistical approach with bivariate spatial modeling to efficiently refine and predict surface property mapping. Scanning Kelvin probe microscopy (SKPM) was selected as a representative example to test our proposed method on lateral nanowire assemblies. We revealed that the proposed method can effectively retrieve the artifact-free surface potential distribution by automatically identifying topological artifacts from surface potential maps. Furthermore, the statistical model built upon low spatial resolution was successfully used to predict the potential values from higher-resolution topography data. Compared to conventional regression model, our model is able to predict the surface potential distribution from less raw data but yields much higher accuracy. Through this means, the spatial resolution of SKPM surface potential maps can be significantly improved. This statistics-enabled predictive method opens a new route toward high-precision and high-resolution SPM characterizations without the enhancement of instrumentation capabilities.

A Statistical Approach to Thermal Management of Data Centers Under Steady State and System Perturbations.

Temperature control for a large data center is both important and expensive. On the one hand, many of the components produce a great deal of heat, and on the other hand, many of the components require temperatures below a fairly low threshold for reliable operation. A statistical framework is proposed within which the behavior of a large cooling system can be modeled and forecast under both steady state and perturbations. This framework is based upon an extension of multivariate Gaussian autoregressive hidden Markov models (HMMs). The estimated parameters of the fitted model provide useful summaries of the overall behavior of and relationships within the cooling system. Predictions under system perturbations are useful for assessing potential changes and improvements to be made to the system. Many data centers have far more cooling capacity than necessary under sensible circumstances, thus resulting in energy inefficiencies. Using this model, predictions for system behavior after a particular component of the cooling system is shut down or reduced in cooling power can be generated. Steady-state predictions are also useful for facility monitors. System traces outside control boundaries flag a change in behavior to examine. The proposed model is fit to data from a group of air conditioners within an enterprise data center from the IT industry. The fitted model is examined, and a particular unit is found to be underutilized. Predictions generated for the system under the removal of that unit appear very reasonable. Steady-state system behavior also is predicted well.

A statistics-guided approach to precise characterization of nanowire morphology.

Precise control of nanomaterial morphology is critical to the development of advanced nanodevices with various functionalities. In this paper, we developed an efficient and effective statistics-guided approach to accurately characterizing the lengths, diameters, orientations, and densities of nanowires. Our approach has been successfully tested on a zinc oxide nanowire sample grown by hydrothermal methods. This approach has three key components. First, we introduced a novel geometric model to recover the true lengths and orientations of nanowires from their projective scanning electron microscope images, where a statistical resampling method is used to mitigate the practical difficulty of relocating the same sets of nanowires at multiple projecting angles. Second, we developed a sequential uniform sampling method for efficiently acquiring representative samples in characterizing diameters and growing density. Third, we proposed a statistical imputation method to incorporate the uncertainty in the determination of nanowire diameters arising from nonspherical cross-section spinning. This approach enables precise characterization of several fundamental aspects of nanowire morphology, which served as an excellent example to overcome nanoscale characterization challenges by using novel statistical means. It might open new opportunities in advancing nanotechnology and might also lead to the standardization of nanocharacterization in many aspects.