Optimal Supersaturated Designs for Lasso Sign Recovery

Supersaturated designs, in which the number of factors exceeds the number of runs, are often constructed under a heuristic criterion that measures a design's proximity to an unattainable orthogonal design. Such a criterion does not directly measure a design's quality in terms of screening. To address this disconnect, we develop optimality criteria to maximize the lasso's sign recovery probability. The criteria have varying amounts of prior knowledge about the model's parameters. We show that an orthogonal design is an ideal structure when the signs of the active factors are unknown. When the signs are assumed known, we show that a design whose columns exhibit small, positive correlations are ideal. Such designs are sought after by the Var(s+)-criterion. These conclusions are based on a continuous optimization framework, which rigorously justifies the use of established heuristic criteria. From this justification, we propose a computationally-efficient design search algorithm that filters through optimal designs under different heuristic criteria to select the one that maximizes the sign recovery probability under the lasso

On supersaturated experimental design

Abstract is available in the PDF file

LASSO-OPTIMAL SUPERSATURATED DESIGN AND ANALYSIS FOR FACTOR SCREENING IN SIMULATION EXPERIMENTS

Complex systems such as large-scale computer simulation models typically involve a large number of factors. When investigating such a system, screening experiments are often used to sift through these factors to identify a subgroup of factors that most significantly influence the interested response

Optimal Design of Experiments for Dual-Response Systems

abstract: The majority of research in experimental design has, to date, been focused on designs when there is only one type of response variable under consideration. In a decision-making process, however, relying on only one objective or criterion can lead to oversimplified, sub-optimal decisions that ignore important considerations. Incorporating multiple, and likely competing, objectives is critical during the decision-making process in order to balance the tradeoffs of all potential solutions. Consequently, the problem of constructing a design for an experiment when multiple types of responses are of interest does not have a clear answer, particularly when the response variables have different distributions. Responses with different distributions have different requirements of the design. Computer-generated optimal designs are popular design choices for less standard scenarios where classical designs are not ideal. This work presents a new approach to experimental designs for dual-response systems. The normal, binomial, and Poisson distributions are considered for the potential responses. Using the D-criterion for the linear model and the Bayesian D-criterion for the nonlinear models, a weighted criterion is implemented in a coordinate-exchange algorithm. The designs are evaluated and compared across different weights. The sensitivity of the designs to the priors supplied in the Bayesian D-criterion is explored in the third chapter of this work. The final section of this work presents a method for a decision-making process involving multiple objectives. There are situations where a decision-maker is interested in several optimal solutions, not just one. These types of decision processes fall into one of two scenarios: 1) wanting to identify the best N solutions to accomplish a goal or specific task, or 2) evaluating a decision based on several primary quantitative objectives along with secondary qualitative priorities. Design of experiment selection often involves the second scenario where the goal is to identify several contending solutions using the primary quantitative objectives, and then use the secondary qualitative objectives to guide the final decision. Layered Pareto Fronts can help identify a richer class of contenders to examine more closely. The method is illustrated with a supersaturated screening design example.Dissertation/ThesisDoctoral Dissertation Industrial Engineering 201

Theoretical framework for predicting inorganic fouling in membrane distillation and experimental validation with calcium sulfate

A methodology for predicting scaling in membrane distillation (MD), which considers thermodynamics, kinetics, and fluid mechanics, is developed and experimentally validated with calcium sulfate. The theory predicts the incidence of scaling as a function of temperature, concentration, and flow conditions by comparing the nucleation induction time to the residence time and applying an experimental correction factor. The relevant residence time is identified by considering a volume of solution near the membrane surface that contains enough ions to form a nucleus of critical size. The theory is validated with fouling experiments using calcium sulfate as a model scalant over a range of temperatures (40–70 °C), saturation indices, and flow rates. Although the model is validated with a bench-scale MD system, it is hoped to be compatible with large-scale systems that may have significant changes in concentration, temperature, and flow rate along the flow direction. At lower temperatures, the saturation index can be as high as 0.4–0.5 without scaling, but the safe concentration limit decreases with increasing temperature. Increasing the feed flow rate reduces concentration polarization and fluid residence time, both of which decrease the likelihood of fouling. The model is translated into easily readable maps outlining safe operating regimes for MD. The theory and maps can be used to choose safe operating conditions in MD over a wide range of conditions and system geometries.National Science Foundation (U.S.) (1122374

Design and Analysis of Screening Experiments Assuming Effect Sparsity

Many initial experiments for industrial and engineering applications employ screening designs to determine which of possibly many factors are significant. These screening designs are usually a highly fractionated factorial or a Plackett-Burman design that focus on main effects and provide limited information for interactions. To help simplify the analysis of these experiments, it is customary to assume that only a few of the effects are actually important; this assumption is known as ‘effect sparsity’. This dissertation will explore both design and analysis aspects of screening experiments assuming effect sparsity. In 1989, Russell Lenth proposed a method for analyzing unreplicated factorials that has become popular due to its simplicity and satisfactory power relative to alternative methods. We propose and illustrate the use of p-values, estimated by simulation, for Lenth t-statistics. This approach is recommended for its versatility. Whereas tabulated critical values are restricted to the case of uncorrelated estimates, we illustrate the use of p-values for both orthogonal and nonorthogonal designs. For cases where there is limited replication, we suggest computing t-statistics and p-values using an estimator that combines the pure error mean square with a modified Lenth’s pseudo standard error. Supersaturated designs (SSDs) are designs that examine more factors than runs available. SSDs were introduced to handle situations in which a large number of factors are of interest but runs are expensive or time-consuming. We begin by assessing the null model performance of SSDs when using all-subsets and forward selection regression. The propensity for model selection criteria to overfit is highlighted. We subsequently propose a strategy for analyzing SSDs that combines all-subsets regression and permutation tests. The methods are illustrated for several examples. In contrast to the usual sequential nature of response surface methods (RSM), recent literature has proposed both screening and response surface exploration using only one three-level design. This approach is named “one-step RSM”. We discuss and illustrate two shortcomings of the current one-step RSM designs and analysis. Subsequently, we propose a new class of three-level designs and an analysis strategy unique to these designs that will address these shortcomings and aid the user in being appropriately advised as to factor importance. We illustrate the designs and analysis with simulated and real data

Silicon Nanocrystal Field-Effect Light-Emitting Devices

We describe the operation of a light-emitting device in which silicon nanocrystals are electrically pumped via the field-effect electroluminescence (EL) mechanism. In contrast to the simultaneous bipolar carrier injection used in conventional p-n junction light-emitting diodes, this device employs sequential unipolar programming of both electrons and holes across a tunneling barrier from the same semiconductor channel. Light emission is strongly correlated with the injection of second carriers into nanocrystals that have been previously programmed with charges of the opposite sign. The properties of this device are well described by the model of a charge injection through Coulomb field modified tunneling processes. We additionally consider limiting performance bounds for potential future devices fabricated from nanocrystals with different radiative emission rates

Impact of Endogenous Bile Salts on the Thermodynamics of Supersaturated Active Pharmaceutical Ingredient Solutions

A variety of formulation strategies have been developed to mitigate the inadequate aqueous solubility of certain therapeutic agents. Among these, achieving supersaturation in vivo is a promising approach to improve the extent of oral absorption. Because of the thermodynamic instability of supersaturated solutions, inhibitors are needed to kinetically hinder crystallization. In addition to commonly used polymeric additives, bile salts, naturally present in the gastrointestinal tract, have been shown to exhibit crystallization inhibition properties. However, the impact of bile salts on solution thermodynamics is not well understood, although this knowledge is essential in order to explore the mechanism of crystallization inhibition. To better describe solution thermodynamics in the presence of bile salts, a side-by-side diffusion cell was used to evaluate solute flux for solutions of telaprevir in the absence and presence of the six most abundant bile salts in human intestinal fluid at various solute concentrations; flux measurements provide information about the solute thermodynamic activity and hence can provide an improved measurement of supersaturation in complex solutions. Trihydroxy bile salts had minimal impact on solution phase boundaries as well as solute flux, while micellar dihydroxy bile salts solubilized telaprevir leading to reduced solute flux across the membrane. An inconsistency between the concentration-based supersaturation ratio and that based on solute thermodynamic activity (the fundamental driving force for crystallization) was noted, suggesting that the activity-based supersaturation should be determined to better interpret any modification in crystallization kinetics in the presence of these additives. These findings indicate that bile salts are not interchangeable from a thermodynamic perspective and provide a foundation for further studies evaluating the mechanism of crystallization inhibition