Measuring the Initial Transient: Reflected Brownian Motion

We analyze the convergence to equilibrium of one-dimensional reflected Brownian motion (RBM) and compute a number of related initial transient formulae. These formulae are of interest as approximations to the initial transient for queueing systems in heavy traffic, and help us to identify settings in which initialization bias is significant. We conclude with a discussion of mean square error for RBM. Our analysis supports the view that initial transient effects for RBM and related models are typically of modest size relative to the intrinsic stochastic variability, unless one chooses an especially poor initialization.Comment: 14 pages, 3 figure

Central Limit Theorems and Large Deviations for Additive Functionals of Reflecting Diffusion Processes

This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting diffusions in which the functional may include a term associated with the cumulative amount of boundary reflection that has occurred. Extending the known central limit and large deviations theory for Markov processes to include additive functionals that incorporate boundary reflection is important in many applications settings in which reflecting diffusions arise, including queueing theory and economics. In particular, the paper establishes the partial differential equations that must be solved in order to explicitly compute the mean and variance for the CLT, as well as the associated rate function for the large deviations principle

Electrohydrodynamic jet printing of PZT thick film micro-scale structures

This paper reports the use of a printing technique, called electrohydrodynamic jet printing, for producing PZT thick film micro-scale structures without additional material removing processes. The PZT powder was ball-milled and the effect of milling time on the particle size was examined. This ball-milling process can significantly reduce the PZT particle size and help to prepare stable composite slurry suitable for the E-Jet printing. The PZT micro-scale structures with different features were produced. The PZT lines with different widths and separations were fabricated through the control of the E-Jet printing parameters. The widths of the PZT lines were varied from 80 μm to 200 μm and the separations were changed from 5 μm to 200 μm. In addition, PZT walled structures were obtained by multi-layer E-Jet printing. The E-Jet printed PZT thick films exhibited a relative permittivity (ɛr) of ∼233 and a piezoelectric constant (d33, f) of ∼66 pC N−1

Distributed ARIMA Models for Ultra-long Time Series

Providing forecasts for ultra-long time series plays a vital role in various activities, such as investment decisions, industrial production arrangements, and farm management. This paper develops a novel distributed forecasting framework to tackle challenges associated with forecasting ultra-long time series by utilizing the industry-standard MapReduce framework. The proposed model combination approach facilitates distributed time series forecasting by combining the local estimators of ARIMA (AutoRegressive Integrated Moving Average) models delivered from worker nodes and minimizing a global loss function. In this way, instead of unrealistically assuming the data generating process (DGP) of an ultra-long time series stays invariant, we make assumptions only on the DGP of subseries spanning shorter time periods. We investigate the performance of the proposed distributed ARIMA models on an electricity demand dataset. Compared to ARIMA models, our approach results in significantly improved forecasting accuracy and computational efficiency both in point forecasts and prediction intervals, especially for longer forecast horizons. Moreover, we explore some potential factors that may affect the forecasting performance of our approach

Forecast combinations: an over 50-year review

Forecast combinations have flourished remarkably in the forecasting community and, in recent years, have become part of the mainstream of forecasting research and activities. Combining multiple forecasts produced from single (target) series is now widely used to improve accuracy through the integration of information gleaned from different sources, thereby mitigating the risk of identifying a single "best" forecast. Combination schemes have evolved from simple combination methods without estimation, to sophisticated methods involving time-varying weights, nonlinear combinations, correlations among components, and cross-learning. They include combining point forecasts and combining probabilistic forecasts. This paper provides an up-to-date review of the extensive literature on forecast combinations, together with reference to available open-source software implementations. We discuss the potential and limitations of various methods and highlight how these ideas have developed over time. Some important issues concerning the utility of forecast combinations are also surveyed. Finally, we conclude with current research gaps and potential insights for future research

Developing a Simple and Rapid Test for Monitoring the Heat Evolution of Concrete Mixtures for Both Laboratory and Field Applications

Recently, activities and interest in monitoring the heat evolution of cement hydration in concrete have increased. This is because the development of early-age concrete properties (such as workability, setting time, strength gain, and thermal cracking resistance) is predominantly influenced by the kinetics of cement hydration. Various test methods are currently available for measuring heat of cement hydration; however, most existing methods require expensive equipment, complex testing procedures, and/or extensive time, thus making them unsuitable for field application. Although ASTM C 186 is used for determining the heat of hydration of cement, there is no standard test method for concrete. The overall object of this three-phase study is to identify, develop, and evaluate a standard test procedure for monitoring pavement concrete using a calorimetry technique. It is envisioned that the newly developed calorimetry test method will be able to verify appropriate concrete proportions, to identify potentially incompatible materials and conditions, and to predict concrete performance. The primary objective of Phase II (presented in this report) is to establish a standard test procedure as well as the methods for interpreting the calorimeter test results. The newly developed calorimeter test is completed more quickly than ASTM C 186, in approximately 24 hours. Among a number of uses, the test can be utilized as a quality control measure for prescreening concrete materials and a prediction tool for early-age cracking. The Phase II results demonstrate that the new calorimetry test method has a high potential for detecting concrete incompatibility problems, predicting fresh concrete properties (such as set time), and assessing hardened concrete performance characteristics (such as strength gain and thermal cracking)