This dissertation presents novel methodologies in the field of stochastic computer model calibration and uncertainty quantification. Simulation models are widely used in studying physical systems, which are often represented by a set of mathematical equations. Inference on true physical system (unobserved or partially observed) is drawn based on the observations from corresponding computer simulation model. These computer models are calibrated based on limited ground truth observations in order produce realistic predictions and associated uncertainties. Stochastic computer model differs from traditional computer model in the sense that repeated execution results in different outcomes from a stochastic simulation. This additional uncertainty in the simulation model requires to be handled accordingly in any calibration set up. Gaussian process (GP) emulator replaces the actual computer simulation when it is expensive to run and the budget is limited. However, traditional GP interpolator models the mean and/or variance of the simulation output as function of input. For a simulation where marginal gaussianity assumption is not appropriate, it does not suffice to emulate only the mean and/or variance. We present two different approaches addressing the non-gaussianity behavior of an emulator, by (1) incorporating quantile regression in GP for multivariate output, (2) approximating using finite mixture of gaussians. These emulators are also used to calibrate and make forward predictions in the context of an Agent Based disease model which models the Ebola epidemic outbreak in 2014 in West Africa. The third approach employs a sequential scheme which periodically updates the uncertainty inn the computer model input as data becomes available in an online fashion. Unlike other two methods which use an emulator in place of the actual simulation, the sequential approach relies on repeated run of the actual, potentially expensive simulation. / Doctor of Philosophy / Mathematical models are versatile and often provide accurate description of physical events. Scientific models are used to study such events in order to gain understanding of the true underlying system. These models are often complex in nature and requires advance algorithms to solve their governing equations. Outputs from these models depend on external information (also called model input) supplied by the user. Model inputs may or may not have a physical meaning, and can sometimes be only specific to the scientific model. More often than not, optimal values of these inputs are unknown and need to be estimated from few actual observations. This process is known as inverse problem, i.e. inferring the input from the output. The inverse problem becomes challenging when the mathematical model is stochastic in nature, i.e., multiple execution of the model result in different outcome. In this dissertation, three methodologies are proposed that talk about the calibration and prediction of a stochastic disease simulation model which simulates contagion of an infectious disease through human-human contact. The motivating examples are taken from the Ebola epidemic in West Africa in 2014 and seasonal flu in New York City in USA.

Wetland impacts in the Mid-Atlantic USA are frequently mitigated via wetland creation in former uplands. Regulatory approval requires a site-specific water budget that predicts the annual water level regime (hydroperiod). However, many studies of created wetlands indicate that post-construction hydroperiods frequently are not similar to impacted wetland systems. My primary objective was to evaluate a water budget model, Wetbud (Basic model), through comparison of model output to on-site water level data for two created forested wetlands in Northern Virginia. Initial sensitivity analyses indicated that watershed curve number and outlet height had the most leverage on model output. Addition of maximum depth of water level drawdown greatly improved model accuracy. I used Nash-Sutcliffe efficiency (NSE) and root mean squared error (RMSE) to evaluate goodness of fit of model output against site monitoring data. The Basic model reproduced the overall seasonal hydroperiod well once fully parameterized, despite NSE values ranging from -0.67 to 0.41 in calibration and from -4.82 to -0.26 during validation. For RMSE, calibration values ranged from 5.9 cm to 12.7 cm during calibration and from 8.2 cm to 18.5 cm during validation. My second objective was to select a group of "design target hydroperiods" for common Mid-Atlantic USA wetland types. From > 90 sites evaluated, I chose four mineral flats, three riverine wetlands, and one depressional wetland that met all selection criteria. Taken together, improved wetland water budget modeling procedures (like Wetbud) combined with the use of appropriate target hydroperiod information should improve the success of wetland creation efforts. / Master of Science / Wetlands in the USA are defined by the combined occurrence of wetland hydrology, hydric soils, and hydrophytic vegetation. Wetlands serve to retain floodwater, sediments and nutrients within their landscape. They may serve as a source of local groundwater recharge and are home to many endangered species of plants and animals. Wetland ecosystems are frequently impacted by human activities including road-building and development. These impacts can range from the destruction of a wetland to increased nutrient contributions from storm- or wastewater. One commonly utilized option to mitigate wetland impacts is via wetland creation in former upland areas. Regulatory approval requires a site-specific water budget that predicts the average monthly water levels (hydroperiod). A hydroperiod is simply a depiction of how the elevation of water changes over time. However, many studies of created wetlands indicate that post-construction hydroperiods frequently are not representative of the impacted wetland systems. Many software packages, called models, seek to predict the hydroperiod for different wetland systems. Improving and vetting these models help to improve our understanding of how these systems function. My primary objective was to evaluate a water budget model, Wetbud (Basic model), through comparison of model output to onsite water level data for two created forested wetlands in Northern Virginia. Initial analyses indicated that watershed curve number (CN) and outlet height had the most influence on model output. Addition of a maximum depth of water level drawdown below the ground surface greatly improved model accuracy. I used statistical analyses to compare model output to site monitoring data. The Basic model reproduced the overall seasonal hydroperiod well once inputs were set to optimum values (calibration). Statistical results for the calibration varied between excellent and acceptable for our selected measure of accuracy, the root mean squared error. My second objective was to select a grouping of “design target hydroperiods” for common Mid-Atlantic USA wetland types. From > 90 sites evaluated, I chose four mineral flats, three riverine wetlands, and one depressional wetland that met all selection criteria. Taken together, improved wetland water budget modeling procedures (like Wetbud) combined with the use of appropriate target hydroperiod information should improve the success of wetland creation efforts.

A portable device was constructed which presents moving, computer generated, sine-wave grating slide projections that range in spatial frequency from 0.4 to 20.5 cycles per degree. At each of two different testing sessions, the contrast sensitivities of 60 undergraduate psychology majors were measured at a static, 25 deg/sec, and 50 deg/sec target movement condition. The results indicate that as target velocity was increased, contrast sensitivity decreased at middle and high spatial frequencies but that contrast sensitivity was enhanced at very low spatial frequencies by target movement. Also, the area of peak sensitivity shifted toward lower spatial frequencies as target velocity increased. In addition, test, re-test reliability was demonstrated. The results are consistent with previous Dynamic Visual Acuity (DVA) research which has shown that the ability to resolve fine detail decreases as target velocities increase, presumedly due to limitations in eye movement control. The testing device, which was designed and constructed for the present study, has proven to be a reliable means for measuring dynamic contrast sensitivity (DCS) and has some distinct advantages over existing methods for measuring both DVA and DCS and, as such, will be valuable in future DVA and DCS research. / Master of Science

This research was designed to investigate the relationship between Trait-based Individual differences (neuroticism and extraversion) and glare subjective responses as well as the actual contrast sensitivity when exposed to the same manipulated glare condition. In addition, the relationship between the glare subjective responses and actual contrast sensitivity was investigated. To examine the trait-based individual differences, the International Personality Item Pool (IPIP) was used while the subjective glare experience was examined utilizing modified glare discomfort rating scale. The visual performance was measured through the contrast sensitivity level using adjustable contrast level of the Landolt's C target. This investigation compared 36 individuals (9 high neuroticism scorers, 9 low neuroticism scorers, 9 high extraversion scorers, and 9 low extraversion scorers) on subjective discomfort glare rating responses and visual contrast sensitivity. The study is directed toward improving our understanding of influencing factors on the experience of discomfort glare, which may eventually be applied to the design of glare measurement methods, and toward training and selection of drivers and workers who may work under conditions of glare. Results indicated significant effect of extraversion trait on rating response while insignificant effect on visual related performance was found. The relationships between rating response and visual performance were also found to be quite low in this study. In conclusion, the expected model was supported but only on the extraversion trait. / Master of Science

In large-scale air quality simulations we are interested in the influence factors which cause changes of pollutants, and optimization methods which improve forecasts. The solutions to these problems can be achieved by incorporating adjoint models, which are efficient in computing the derivatives of a functional with respect to a large number of model parameters. In this research we employ first order adjoints in air quality simulations. Moreover, we explore theoretically the computation of second order adjoints for chemical transport models, and illustrate their feasibility in several aspects. We apply first order adjoints to sensitivity analysis and data assimilation. Through sensitivity analysis, we can discover the area that has the largest influence on changes of ozone concentrations at a receptor. For data assimilation with optimization methods which use first order adjoints, we assess their performance under different scenarios. The results indicate that the L-BFGS method is the most efficient. Compared with first order adjoints, second order adjoints have not been used to date in air quality simulation. To explore their utility, we show the construction of second order adjoints for chemical transport models and demonstrate several applications including sensitivity analysis, optimization, uncertainty quantification, and Hessian singular vectors. Since second order adjoints provide second order information in the form of Hessian-vector product instead of the entire Hessian matrix, it is possible to implement applications for large-scale models which require second order derivatives. Finally, we conclude that second order adjoints for chemical transport models are computationally feasible and effective. / Master of Science

Circadian rhythms in mammals are self-sustained repeating activities driven by the circadian gene expression in cells, which is regulated at both transcriptional and posttranscriptional stages. In this work, we first used mathematical modeling to investigate the transcriptional regulation of circadian gene expression, with a focus on the mechanisms of robust genetic oscillations in the mammalian circadian core clock. Secondly, we built a coarse-grained model to study the post-transcriptional regulation of the rhythmicities of poly(A) tail length observed in hundreds of mRNAs in mouse liver. Lastly, we examined the application of Sobol indices, which is a global sensitivity analysis method, to mathematical models of biological oscillation systems, and proposed two methods tailored for the calculation of circular Sobol indices. In the first project, we modified the core negative feedback loop in a mathematical model of the mammalian genetic oscillator so that the unrealistic tight binding between the repressor PER and the activator BMAL1 is relaxed for robust oscillations. By studying the modified extended models, we found that the auxiliary positive feedback loop, rather than the auxiliary negative feedback loop, makes the oscillations more robust, yet they are similar when accounting for circadian rhythms (~24h period). In the second project, we investigated the regulation of rhythmicities in poly(A) tail length by four coupled rhythmic processes, which are transcription, deadenylation, polyadenylation, and degradation. We found that rhythmic deadenylation is the strongest contributor to the rhythmicity in poly(A) tail length and the rhythmicity in the abundance of the mRNA subpopulation with long poly(A) tails. In line with this finding, the model further showed that the experimentally observed distinct peak phases in the expression of deadenylases, regardless of other rhythmic controls, can robustly cluster the rhythmic mRNAs by their peak phases in poly(A) tail length and abundance of the long-tailed subpopulation. In the last project, we reviewed the theoretical basis of Sobol indices and identified potential problems when it is applied to mathematical models of biological oscillation systems. Based on circular statistics, we proposed two methods for the calculation of circular Sobol indices and compared their performance with the original Sobol indices in several models. We found that though the relative rankings of the contribution from parameters are the same across three methods, circular Sobol indices can better quantitatively distinguish the contribution of individual parameters. Through this work, we showed that mathematical modeling combined with sensitivity analysis can help us understand the mechanisms underlying the circadian gene expression in mammalian cells. Also, testable predictions are made for future experiments and new ideas are provided that can enable potential chronopharmacology research. / Doctor of Philosophy / Circadian rhythms are repeating biological activities with ~24h period observed in most living organisms. Disruption of circadian rhythms in humans has been found to be promote cancer, metabolic diseases, cognitive degeneration etc. In this work, we first used mathematical modeling to study the mechanisms of robust oscillations in the mammalian circadian core clock, which is a molecular regulatory network that drives circadian gene expression at transcriptional stage. Secondly, we built a coarse-grained model to investigate the post-transcriptional regulation of the rhythmicities in poly(A) tail length, which are observed in hundreds of mRNAs in mouse liver. Lastly, we examined the application of Sobol indices, which is a global sensitivity analysis method, to mathematical models of biological oscillation systems, and proposed two methods tailored for the calculation of circular Sobol indices. In the first project, we modified a previous mathematical model of the mammalian genetic oscillator so that it sustains robust oscillation with more realistic parameter values. Our analysis of the model further showed that the auxiliary positive feedback loop, rather than the auxiliary negative feedback loop, makes the oscillations more robust. In the second project, we found that rhythmic deadenylation, among the coupled transcription, polyadenylation, and degradation processes, mostly controls the rhythmicity of poly(A) tail length and mRNA subpopulation with long poly(A) tails. Lastly, we reviewed the theoretical basis of Sobol indices and found potential problems when it is applied to mathematical models of biological oscillation systems. Based on circular statistics, we proposed two circular Sobol indices, which can better distinguish the contribution of individual parameters to model outputs than the original Sobol indices. Altogether, we used mathematical modeling and sensitivity analysis to investigate the regulation of circadian gene expression in mammalian cells, providing testable predictions and new ideas for future experiments and chronopharmacology research.

Many fields in science and engineering require large-scale numerical simulations of complex systems described by differential equations. These systems are typically multi-physics (they are driven by multiple interacting physical processes) and multiscale (the dynamics takes place on vastly different spatial and temporal scales). Numerical solution of such systems is highly challenging due to the dimension of the resulting discrete problem, and to the complexity that comes from incorporating multiple interacting components with different characteristics. The main contributions of this dissertation are the creation of new families of time integration methods for multiscale and multiphysics simulations, and the development of industrial-strengh tools for sensitivity analysis. This work develops novel implicit-explicit (IMEX) general linear time integration methods for multiphysics and multiscale simulations typically involving both stiff and non-stiff components. In an IMEX approach, one uses an implicit scheme for the stiff components and an explicit scheme for the non-stiff components such that the combined method has the desired stability and accuracy properties. Practical schemes with favorable properties, such as maximized stability, high efficiency, and no order reduction, are constructed and applied in extensive numerical experiments to validate the theoretical findings and to demonstrate their advantages. Approximate matrix factorization (AMF) technique exploits the structure of the Jacobian of the implicit parts, which may lead to further efficiency improvement of IMEX schemes. We have explored the application of AMF within some high order IMEX Runge-Kutta schemes in order to achieve high efficiency. Sensitivity analysis gives quantitative information about the changes in a dynamical model outputs caused by caused by small changes in the model inputs. This information is crucial for data assimilation, model-constrained optimization, inverse problems, and uncertainty quantification. We develop a high performance software package for sensitivity analysis in the context of stiff and nonstiff ordinary differential equations. Efficiency is demonstrated by direct comparisons against existing state-of-art software on a variety of test problems. / Ph. D.

Background: Modifying the gut microbiota through the administration of probiotics during high fat feeding has been shown to attenuate weight gain and body fat accretion while improving insulin sensitivity in animal models. Objective: Our objective was to determine the effects of the probiotic VSL#3 on body weightand composition, skeletal muscle substrate oxidation, and insulin sensitivity and during 4 weeks of high-fat, hypercaloric feeding. We hypothesized that the probiotic would attenuate the body weight and fat gain and adverse changes in insulin sensitivity and substrate oxidation following high fat, hypercaloric feeding in young, non-obese males. Methods: Twenty non-obese males (18-30 y) volunteered to participate in the present study. Following a 2-week eucaloric control diet, subjects underwent a dual x-ray absorptiometry (DXA) to determine body composition, an intravenous glucose tolerance test (IVGTT) to determine insulin sensitivity, a skeletal muscle biopsy for measurement of substrate oxidation. Serum endotoxin was also measured. Subsequently, subjects were randomized to receive either VSL#3 (2 satchets) or placebo during 4 weeks of consuming a high fat (55% fat), hypercaloric diet (+1,000 kcal/day). Macronutrient composition of the high fat diet was 55% fat, 30% carbohydrate, and 15% protein. Results: There were no differences between the groups in subject characteristics or in the dependent variables at baseline. Body weight and fat mass increased less (P<0.045) following the high fat diet with VSL#3 compared to placebo. Insulin sensitivity (and other IVGTT variables) and both glucose and fat oxidation did not change significantly with time or VSL#3 treatment. Serum endotoxin concentration was not different between groups following the high-fat diet. Conclusions: VSL#3, a multi-strain probiotic, attenuated body weight and fat gain following a 4-week high fat, hypercaloric diet compared with a placebo. There were no differences between the VSL and control in circulating endotoxin, insulin sensitivity (and other IVGTT variables) or in skeletal muscle substrate oxidation. / Ph. D.

Anthropometric test devices (ATDs), commonly referred to as crash test dummies, are tools used to conduct aerospace and spaceflight safety evaluations. Finite element (FE) analysis provides an effective complement to these evaluations. In this work a FE model of the Test Device for Human Occupant Restraint (THOR) dummy was developed, calibrated, and validated for use in aerospace and spaceflight impact analysis. A previously developed THOR FE model was first evaluated under spinal loading. The FE model was then updated to reflect recent updates made to the THOR dummy. A novel calibration methodology was developed to improve both kinematic and kinetic responses of the updated model in various THOR dummy certification tests. The updated THOR FE model was then calibrated and validated under spaceflight loading conditions and used to asses THOR dummy biofidelity. Results demonstrate that the FE model performs well under spinal loading and predicts injury criteria values close to those recorded in testing. Material parameter optimization of the updated model was shown to greatly improve its response. The validated THOR-FE model indicated good dummy biofidelity relative to human volunteer data under spinal loading, but limited biofidelity under frontal loading. The calibration methodology developed in this work is proven as an effective tool for improving dummy model response. Results shown by the dummy model developed in this study recommends its use in future aerospace and spaceflight impact simulations. In addition the biofidelity analysis suggests future improvements to the THOR dummy for spaceflight and aerospace analysis. / Master of Science

According to the Centers for Disease Control, roughly 9.4% of the US population is diabetic, and at least 35% of the US population has metabolic syndrome. These diseases are associated with increased mortality risk, reduced quality of life, and altered taste perception of foods. With increased occurrence of these metabolic diseases, there is a greater need for research oriented towards using lifestyle modifications to combat illness. A relationship between flavanol consumption, health benefits, and taste perception has been well documented. Dietary flavanols are secondary plant metabolites that exist naturally in a wide array of polymerization states. The mechanisms behind the protective effects of flavanols are not entirely understood, particularly when considering how the mean degrees of polymerization (mDP), or average compound size, impacts the health benefits. Moreover, it is known that flavanol mDP influences the sensory attributes of flavanol-rich foods including bitterness and astringency. It is known that obesity and sensitivity to bitterness both influence perception of certain taste attributes such as sweetness and bitterness. The influence of these bitter and astringent sensations determined by flavanol mDP on consumer preferences for flavanol-rich products remains unknown. These influences on preference pose potential barriers to consumption, resulting in the loss of health benefits. The objectives of the research detailed here were i) to determine the effect of dietary consumption of small to medium-sized flavanols on markers of metabolic syndrome that were brought on by diet-induced obesity, ii) to determine how flavanol mDP influences the consumer perception and liking of flavanol-rich, wine-like products based on differences in consumer phenotype, and iii) to explore the potential to manipulate mDP of wine using traditional winemaking techniques. By way of an in vivo mouse model, it was observed that regardless of mDP, flavanols delivered at low dose, as part of a high-fat diet, reduced adipose-derived inflammatory cytokine production but did not prevent associated weight and fat gain. This suggests that small to medium sized flavanols may, at low dose, delay the onset of the pro-inflammatory state, which could ultimately protect against metabolic derangements associated with obesity and diabetes. Regarding the consumer acceptance of wine-like products made from flavanols of different mDP, and therefore different in bitterness and astringency intensity, it was observed in a consumer panel (n = 102) that when segmenting the panelists by body fat % and BMI classification, increased adiposity was associated with decreased ability to differentiate wine samples made with flavanols of different mDP. Moreover, differences in liking and ability to differentiate bitterness and astringency intensities were not as pronounced when segmenting the panelists based on bitterness sensitivity. This suggests that obesity may impact preference for flavanol-rich foods more so than sensitivity to flavor attributes associated with these products. Finally, in an exploratory effort to manipulate mDP of red and rosé wines using traditional winemaking techniques, no differences in mDP were observed in young wines, but significant differences in flavanol concentration were detected. It is hypothesized that aging of these wines could lead to greater differences in mDP, especially for those that had a high flavanol concentration at baseline. Future work will continue to build off these studies so that flavanol-rich products such as red wine can be optimized for health benefits and consumer acceptability of dietary polyphenols. / Ph. D. / According to the Centers for Disease Control, roughly 9.4% of the US population is diabetic, and at least 35% of the US population has metabolic syndrome. These diseases are associated with increased mortality risk, reduced quality of life, and altered taste perception for certain food types. With increased occurrence of these metabolic diseases, there is a greater need for research oriented towards using lifestyle modifications to combat illness. Dietary flavanols, which are potent antioxidants derived from plants, are being explored for their ability to mitigate chronic disease. They exist naturally in a wide variety of sizes and structures depending on plant of origin, growing conditions, and food processing conditions. It is believed that the size of these compounds impacts their health effects and influences their taste profile; smaller compounds are more bitter while larger compounds are more astringent. The purpose of this research was to determine the effect of flavanol supplementation on markers of the metabolic syndrome and how differences in taste due to differences in flavanol size influence consumer liking and perception of winelike products. It was determined in this study that dietary flavanols, delivered at low dose in the context of a high-fat diet can slightly improve fasting blood glucose levels and prevent inflammation. When examining consumer preferences for wines made from dietary flavanols that are distinctly different in terms of bitterness and astringency, it was determined that overall, consumers liked wines that were less intense in terms of bitterness and astringency. However, when examining consumers classified as having a high body fat percentage or high BMI, their ability to differentiate the wines was decreased compared to lean counterparts. These findings suggest that dietary flavanol supplementation at a physiologically relevant dose may improve symptoms of diabetes and metabolic syndrome. Future work confirming these observations in humans is warranted, as are studies devoted to better understanding of the taste preferences of the obese population. This will allow for optimization of flavanol-rich foods that maximize health benefit while also being palatable to consumers.