Yes / Polypropylene is one type of plastic that is widely used in our everyday life. This study focuses on the identification and justification of the optimum process parameters for polypropylene production in a novel pilot plant based fluidized bed reactor. This first-of-its-kind statistical modeling with experimental validation for the process parameters of polypropylene production was conducted by applying ANNOVA (Analysis of variance) method to Response Surface Methodology (RSM). Three important process variables i.e., reaction temperature, system pressure and hydrogen percentage were considered as the important input factors for the polypropylene production in the analysis performed. In order to examine the effect of process parameters and their interactions, the ANOVA method was utilized among a range of other statistical diagnostic tools such as the correlation between actual and predicted values, the residuals and predicted response, outlier t plot, 3D response surface and contour analysis plots. The statistical analysis showed that the proposed quadratic model had a good fit with the experimental results. At optimum conditions with temperature of 75 °C, system pressure of 25 bar and hydrogen percentage of 2%, the highest polypropylene production obtained is 5.82% per pass. Hence it is concluded that the developed experimental design and proposed model can be successfully employed with over a 95% confidence level for optimum polypropylene production in a fluidized bed catalytic reactor (FBCR).

We live in the era of textit{Big Data} with significantly richer computational resources than the last two decades. The concurrence of computation resources and a large volume of data has boosted researchers' desire for developing feasible Markov Chain Monte Carlo (MCMC) algorithms for large parameter spaces. Dirichlet Process Mixture Models (DPMMs) have become a Bayesian mainstay for modeling heterogeneous structures, namely clusters, especially when the quantity of clusters is not known with the established MCMC methods. As opposed to many ad-hoc clustering methods, using Dirichlet Processes (DPs) in models provide a flexible and probabilistic approach for automatically estimating both cluster structure and quantity. While DPs are not fully parameterized, they depend on both a base measure and a concentration parameter that can heavily impact inferences. Determining the concentration parameter is critical and essential, since it adjusts the a-priori cluster expectation, but typical approaches for specifying this parameter are rather cavalier. In this work, we propose a new method for automatically and adaptively determining this parameter, which directly calibrates distances between clusters through an explicit link function within the DP. Furthermore, we extend our method to mixture models with Nested Dirichlet Processes (NDPs) that cluster the multilevel data and depend on the specification of a vector of concentration parameters. In this work, we detail how to incorporate our method in Markov chain Monte Carlo algorithms, and illustrate our findings through a series of comparative simulation studies and applications. / Ph. D. / We live in the era of <i>Big Data</i> with significantly richer computational resources than the last two decades. The concurrence of computational resources and a large volume of data has boosted researcher’s desire to develop the efficient Markov Chain Monte Carlo (MCMC) algorithms for models such as a Dirichlet process mixture model. The Dirichlet process mixture model has become more popular for clustering analyses because it provides a flexible and generative model for automatically defining both cluster structure and quantity. However, a clustering solution inferred by the Dirichlet process mixture model is impacted by the hyperparameters called a base measure and a concentration parameter. Determining the concentration parameter is critical and essential, since it adjusts the apriori cluster expectation, but typical approaches for specifying this parameter are rather cavalier. In this work, we propose a new method for automatically and adaptively determining this parameter, which directly calibrates distances between clusters. Furthermore, we extend our method to mixture models with Nested Dirichlet Processes (NDPs) that cluster the multilevel data and depend on the specification of a vector of concentration parameters. In this work, we have simulation studies to show the performance of the developed methods and applications such as modeling the timeline for building construction data and clustering the U.S median household income data. This work has contributions: 1) the developed methods in this work are straightforward to incorporate with any type of Monte Carlo Markov Chain algorithms, 2) methods calibrate with the probability distance between clusters and maximize the information based on the observations in defined clusters when estimating the concentration parameter, and 3) the methods can be extended to any type of the extension of Dirichlet processes, for instance, hierarchical Dirichlet processes or dependent Dirichlet processes.

Yes / Apigenin (4′,5,7-trihydroxyflavone, APG) has many potential therapeutic benefits; however, its poor aqueous solubility has limited its clinical applications. In this work, a large scale cocrystal screening has been conducted, aiming to discover potential APG cocrystals for enhancement of its solubility and dissolution rate. In order to reduce the number of the experimental screening tests, three computational prescreening tools, i.e., molecular complementarity (MC), hydrogen bond propensity (HBP), and hydrogen bond energy (HBE), were used to provide an initial selection of 47 coformer candidates, leading to the discovery of seven APG cocrystals. Among them, six APG cocrystal structures have been determined by successful growth of single crystals, i.e., apigenin-carbamazepine hydrate 1:1:1 cocrystal, apigenin-1,2-di(pyridin-4-yl)ethane hydrate 1:1:1 cocrystal, apigenin-valerolactam 1:2 cocrystal, apigenin-(dl) proline 1:2 cocrystal, apigenin-(d) proline/(l) proline 1:1 cocrystal. All of the APG cocrystals showed improved dissolution performances with the potential to be formulated into drug products.

Many medical therapies, such as thermal tumor detection and hypothermia cancer treatments, utilize heat transfer mechanisms of the body. The focus of this work is the development and experimental validation of a method to simultaneously estimate thermal conductivity, volumetric specific heat, and perfusion of in-vivo tissue. The heat transfer through the tissue was modeled using a modified Pennes' equation. Using a least-squares parameter estimation method with regularization, the thermal properties could be estimated from the temperature response to the known applied heat flux. The method was tested experimentally using a new agar-water tissue phantom designed for this purpose. A total of 40 tests were performed. The results of the experiments show that conductivity can be successfully estimated for perfused tissue phantoms. The values returned for volumetric specific heat are lower than expected, while the estimated values of perfusion are far greater than expected. It is believed that the mathematical model is incorrectly accounting between these two terms. Both terms were treated as heat sinks, so it is conceivable that it is not discriminating between them correctly. Although the method can estimate all three parameters simultaneously, but it seems that the mathematical model is not accurately describing the system. In the future, improvements to the model could be made to allow the method to function accurately. / Master of Science

Predicting the performance of complex structures exposed to harsh thermal environments is a crucial issue in many of today's aerospace and space designs. To predict the thermal stresses a structure might be exposed to, the thermal properties of the independent materials used in the design of the structure need to be known. Therefore, a noninvasive estimation procedure involving Genetic Algorithms was developed to determine the various thermal properties needed to adequately model the Outer Wing Subcomponent (OWS), a structure located at the trailing edge of the High Speed Civil Transport's (HSCT) wing tip. Due to the nature of the nonlinear least-squares estimation method used in this study, both theoretical and experimental temperature histories were required. Several one-dimensional and two-dimensional finite element models of the OWS were developed to compute the transient theoretical temperature histories. The experimental data were obtained from optimized experiments that were run at various surrounding temperature settings to investigate the temperature dependence of the estimated properties. An experimental optimization was performed to provide the most accurate estimates and reduce the confidence intervals. The simultaneous estimation of eight thermal properties, including the volumetric heat capacities and out-of-plane thermal conductivities of the facesheets, the honeycomb, the skins, and the torque tubes, was successfully completed with the one-dimensional model and the results used to evaluate the remaining in-plane thermal conductivities of the facesheets, the honeycomb, the skins, and the torque tubes with the two-dimensional model. Although experimental optimization did not eliminate all correlation between the parameters, the minimization procedure based on the Genetic Algorithm performed extremely well, despite the high degree of correlation and low sensitivity of many of the parameters. / Master of Science

In this thesis we develop new mathematical models, using dynamical systems, to represent localized gene delivery of bone morphogenetic protein 2 into bone marrow-derived mesenchymal stem cells and rat calvarial defects. We examine two approaches, using pDNA or cmRNA treatments, respectively, towards the production of calcium deposition and bone regeneration in in vitro and in vivo experiments. We first review the relevant scientific literature and survey existing mathematical representations for similar treatment approaches. We then motivate and develop our new models and determine model parameters from literature, heuristic approaches, and estimation using sparse data. We next conduct a qualitative analysis using dynamical systems theory. Due to the nature of the parameter estimation, it was important that we obtain local and global sensitivity analyses of model outputs to changes in model inputs. Finally we compared results from different treatment protocols. Our model suggests that cmRNA treatments may perform better than pDNA treatments towards bone fracture healing. This work is intended to be a foundation for predictive models of non-viral local gene delivery systems.

Natural attenuation refers to the observed reduction in contaminant concentration via natural processes as contaminants migrate from the source into environmental media. Assessment of the dimensions of contaminant plumes and prediction of their fate requires predictions of the rate of dissolution of contaminants from residual non-aqueous-phase liquids (NAPLs) into the aquifer and the rate of contaminant removal through biodegradation. The available techniques to estimate these parameters do not characterize their confidence intervals by accounting for their relationships to uncertainty in source geometry and hydraulic conductivity distribution. The central idea in this thesis is to develop a flexible modeling approach for characterization of uncertainty in residual NAPL dissolution rate and first-order biodegradation rate by tailoring the estimation of these parameters to distributions of uncertainty in source size and hydraulic conductivity field. The first development in this thesis is related to a distance function approach that characterizes the uncertainty in the areal limits of the source zones. Implementation of the approach for a given monitoring well arrangement results in a unique uncertainty band that meets the requirements of unbiasedness and fairness of the calibrated probabilities. The second development in this thesis is related to a probabilistic model for characterization of uncertainty in the 3D localized distribution of residual NAPL in a real site. A categorical variable is defined based on the available CPT-UVIF data, while secondary data based on soil texture and groundwater table elevation are also incorporated into the model. A cross-validation study shows the importance of incorporation of secondary data in improving the prediction of contaminated and uncontaminated locations. The third development in this thesis is related to the implementation of a Monte Carlo type inverse modeling to develop a screening model used to characterize the confidence intervals in the NAPL dissolution rate and first-order biodegradation rate. The development of the model is based on sequential self-calibration approach, distance-function approach and a gradient-based optimization. It is shown that tailoring the estimation of the transport parameters to joint realizations of source geometry and transmissivity field can effectively reduce the uncertainties in the predicted state variables.

We establish a parameter-dependent pseudo-differential calculus on an infinite cylinder, regarded as a manifold with conical exits to infinity. The parameters are involved in edge-degenerate form, and we formulate the operators in terms of operator-valued amplitude functions.

Inverse problems have gained popularity in statistical research recently. This dissertation consists of two statistical inverse problems: a Bayesian approach to detection of small low emission sources on a large random background, and parameter estimation methods for partial differential equation (PDE) models. Source detection problem arises, for instance, in some homeland security applications. We address the problem of detecting presence and location of a small low emission source inside an object, when the background noise dominates. The goal is to reach the signal-to-noise ratio levels on the order of 10^-3. We develop a Bayesian approach to this problem in two-dimension. The method allows inference not only about the existence of the source, but also about its location. We derive Bayes factors for model selection and estimation of location based on Markov chain Monte Carlo simulation. A simulation study shows that with sufficiently high total emission level, our method can effectively locate the source. Differential equation (DE) models are widely used to model dynamic processes in many fields. The forward problem of solving equations for given parameters that define the DEs has been extensively studied in the past. However, the inverse problem of estimating parameters based on observed state variables is relatively sparse in the statistical literature, and this is especially the case for PDE models. We propose two joint modeling schemes to solve for constant parameters in PDEs: a parameter cascading method and a Bayesian treatment. In both methods, the unknown functions are expressed via basis function expansion. For the parameter cascading method, we develop the algorithm to estimate the parameters and derive a sandwich estimator of the covariance matrix. For the Bayesian method, we develop the joint model for data and the PDE, and describe how the Markov chain Monte Carlo technique is employed to make posterior inference. A straightforward two-stage method is to first fit the data and then to estimate parameters by the least square principle. The three approaches are illustrated using simulated examples and compared via simulation studies. Simulation results show that the proposed methods outperform the two-stage method.

The lymphatic system is responsible for several vital roles in human body, one of which is maintaining fluid and protein balance. There is no central pump in the lymphatic system and the transport of fluid against gravity and adverse pressure gradient is maintained by the extrinsic and intrinsic pumping mechanisms. Any disruption of the lymphatic system due to trauma or injury can lead to edema. There is no cure for lymphedema partly because the knowledge of the function of the lymphatic system is lacking. Thus, a well-developed model of the lymphatic system is crucial to improve our understanding of its function. Here we used a lumped parameter approach to model a chain of lymphangions in series. Equations of conservation of mass, conservation of momentum, and vessel wall force balance were solved for each lymphangion computationally. Due to the lack of knowledge of the parameters describing the system in the literature, more accurate measurements of these parameters should be pursued to advance the model. Because of the difficulty of the isolated vessel and in-situ experiments, we performed a parameter sensitivity analysis to determine the parameters that affect the system most strongly. Our results showed that more accurate estimations of active contractile force and physiologic features of lymphangions, such as length/diameter ratios, should be pursued in future experiments. Also further experiments are required to refine the valve behavior and valve parameters.