As one of the emerging optical molecular imaging modalities, bioluminescence tomography is for reconstruction of the light source distribution inside a small animal body from the measured photon data on its surface. Such a light source distribution can be either induced through the excitation of an external light source, or generated by an internal bioluminescent source. The propagation of light within a biological medium is accurately described by the radiative transfer equation. In this thesis, a bioluminescent source recovery problem is considered for the steady state radiative transfer equation. The recovery model is based on the minimization of combined effects of equation residual, boundary condition residual, and boundary measurement residual. The total variation of the light source is taken as one of the regularization terms so that the minimization of surface area of a light source is achieved. An alternating direction multiplier method is applied to decouple the system governing the light distribution and source data. Three different formulations and algorithms are introduced for the total variation regularization term. Convergence analysis is provided for each algorithm and numerical experiments are presented to show the performance of the algorithms.

Heterogeneous energetic materials such as plastic bonded explosives (PBX), pressed explosives etc have very detailed and non-uniform microstructure. The heterogeneities are usually present in the form of binder, voids, microcracks etc. Shock interaction with these heterogeneities leads to local heated regions known as hot spots. It is widely accepted that these hot spots are predominantly the cause of triggering reaction and eventually ignition in these energetic materials. There are various physical mechanisms operating at mesoscale through which hot spot can be created such as void collapse, inter-granular friction in energetic crystals, shock heating of HMX crystals and binder etc. Hence, microstructural heterogeneities can play a vital role for shock initiation in heterogeneous explosives. In the current work, a general framework is established for performing mesoscale simulations on heterogeneous energetic materials. The numerical framework is based on a massively parallel Cartesian grid based Eulerian solver. Narrow band level set approach is used for sharp tracking of the material interfaces. The interfacial conditions are applied using modified ghost fluid method. The use of level set method for interface tracking provides an inherent advantage of using level set based image segmentation algorithm(active contouring) for the representation of explosives microstructure. The image processing approach allows to perform simulation on real geometries than the idealized shapes. The image processing framework is incorporated in the Eulerian solver. The energetic material considered in the current work is HMX. The chemical decomposition of HMX is modeled using Henson Smilowitz chemical kinetic law. Shock analysis is performed on two different samples of HMX based pressed explosives. Also, both two dimensional and three dimensional shock analysis on mock sugar geometry are performed. The effect of shock strength and relative positioning of voids on ignition threshold of porous HMX is studied. The current work is focused towards the development of a computational framework which can replicate the experimental way of studying the shock initiation behavior of energetic materials i.e. using flyer plate simulations.

In this document, we consider coreset and total sensitivity for shape fitting problems. The shape fitting problems that are of considerable interest include: (1) (j, k) projective clustering problem, and (2) circle fitting problem on the plane. In (j, k) projective clustering, we are given a finite set of points P in d-dimensional Euclidean space, and the goal is to find a shape, which is a k-tuple j-flats (affine j-subspace), that best fits P. In circle fitting problem, given an input point set P ⊂ ℝ2, the goal is to find a circle that best fits P. In L1-fitting, the cost of fitting P to a shape F is defined as Σp∈p dist(p, F), where dist(p, F) is the cost of assigning P to F, while in F∞-fitting, maxp∈p dist(pF). We focus on L1-fitting. A coreset is a compact representation of the input point set. For a shape fitting problem, a coreset for a point set P is a weighted point set, with the property that the cost of fitting the coreset to a shape F approximates the cost of fitting P to F, for every shape in the family of shapes. Coreset of small (e.g., constant) cardinality is of interest, because one can afford to use off-shelf, perhaps computationally expensive algorithms to solve the geometric optimization problem for the coreset, and a good solution for the coreset is guaranteed to be also good for the original input. Depending on whether the fitting problem is L1 fitting or L∞ fitting, the coreset is L1 coreset or L∞ coreset, respectively. One way to obtain small coreset is via non-uniform sampling, using the framework by [30]. Given a point set P, the “importance" of each point p∈P is quantified by its sensitivity σp(p), and the total sensitivity of P is the summation of sensitivities at every point, Σp∈PσP(p). It is shown that if one samples the point set P according to the probability distribution imposed by the sensitivities, one obtains coresets of size roughly O(�2P). Total sensitivity of a shape fitting problem quantifies the complexity of the shapes, which is the main object being studied in this thesis. We briefly summarize the main results below. We establish the connection between L∞ coreset and L1 coreset. In particular, we show that shape fitting problems with small L∞ coreset also have small L1 coreset. This connection allows us to use existing work on L∞ coreset to obtain small L1 coreset for the aforementioned shape fitting problems (variants of (j,k) projective clustering, and circle fitting). Consequently, we obtain the first near-linear algorithm for integer (j,k) projective clustering in high dimension. We show that the total sensitivity of shape fitting problem in ℝd depends on the intrinsic dimension of the shapes. For many shape fitting problems, the shapes are low-dimensional: for example, in (j,k) projective clustering, each shape is a union of k j-flats, and each k-tuple of j-flats is contained in a subspace of dimension O(jk). This fact allows us to get a dimension-reduction type result for the (j,k)-projective clustering problems. Specifically, for integer (j,k) projective clustering, the upper bounds of the total sensitivity is improved from O((log n)f(d,j,k)) to O((log n)f(j,k)), where f (j, k) is a function depending on only j, and k, and no longer on the possibly large d. We obtain coreset of size O((log n)2), using the connection between L∞ coreset and L1 coreset. We show that circle fitting problem does not admit coreset of size o((log n). In particular, we show a construction of a point set, such that any 1/100-coreset of P has size at least Ω(log n).

Patient self-report of colorectal cancer (CRC) screening remains a critical source of information in determining adherence to recommended guidelines. Accurate assessment is important for clinical decision-making, quality assurance and research. Population subgroup differences can affect self-report accuracy. Studies relying on patient self-report benefit from assessing validity and attempting to quantify measurement error and bias. This study assessed self-reported CRC screening data accuracy - estimating overall and test-specific adherence using four common validity measures (sensitivity, specificity, concordance, and report-to-records ratio [R2R]) - and evaluated associations between predictor variables and accuracy that might explain variation in estimates. 1,399 patients aged 51-80 years from 16 family medicine offices in the Iowa Research Network (IRENE), a practice-based research network (PBRN), completed an investigator-developed questionnaire and had medical records (MRs) available. Comparison of self-report of up-to-date screening with test documentation in the MR was used to estimate validity; multivariable analysis assessed predictors of concordance, or agreement between self-report and test documentation in the MR, for colonoscopy (CSPY). Predictor variables included patient characteristics (age, gender, education, income, insurance status, family history of CRC and IRENE office), healthcare utilization practices (recency of last visit to office and duration of patient status in office) and patient rural-urban residence classified according to a four-category Rural-Urban Commuting Area (RUCA) coding scheme. Sixty percent of patients reported they were up-to-date with CRC screening by any test, while 48% had screening documented in the MR (sensitivity 0.95, specificity 0.73, concordance 0.83 and R2R 1.24). Nearly all documentation was for CSPY (sensitivity 0.94, specificity 0.76, concordance 0.84 and R2R 1.21). Education, insurance source, CRC family history and patient duration in office, when adjusted for all other variables in the final model, were significant (p < 0.05) predictors of concordance. Age modified a significant association with concordance for patient rural-urban residence (p = 0.03) and for recency of last visit (p = 0.04). Self-reported CRC screening validity was generally acceptable, but overreporting was prevalent across all tests. MR documentation of CRC screening was almost exclusively based on CSPY. Concordance between self-reported CSPY and the MR was good but varied with patient characteristics, healthcare utilization practices and rural-urban residence.

The goal of this work is to explain the process through which I develop a character as an actor. I will explain the crucial elements that I believe great actors exude and also where I have been able--and also unable--to adopt these elements. The act of writing down these ideas is beneficial to myself because it requires me to express on paper what could easily be discussed with any other actor endlessly in circles comparing and contrasting processes and tendencies of practice. I will be able to look back to this particular work in the future and see how I have grown and what principles I'm sure I'll possibly still believe are paramount to great acting. I hope this work will also benefit younger actors who might come across my words and realize that they aren't as clueless and off-the-mark as they might think they are as a result of doing this type of work. I could certainly be the one who is clueless--and only time will answer that question. By exploring and expressing the ways in which I work, I hope I am able to offer some tangible insight to the general public as to what an actor actually does in preparation for a role that they might see onstage or in a film.

This work comprises several projects that involve optimization of physical systems. By a physical system we understand an object or a process that is governed by physical, mechanical, chemical, biological, etc., laws. Such objects and the related optimization problems are relatively rarely considered in operations research literature, where the traditional subjects of optimization methods are represented by schedules, assignments and allocations, sequences, and queues. The corresponding operations research and management sciences models result in optimization problems of relatively simple structure (for example, linear or quadratic optimization models), but whose difficulty comes from very large number (from hundreds to millions) of optimization variables and constraints. In contrast, in many optimization problems that arise in mechanical engineering, chemical engineering, biomedical engineering, the number of variables or constraints in relatively small (typically, in the range of dozens), but the objective function and constraints have very complex, nonlinear and nonconvex analytical form. In many problems, the analytical expressions for objective function and constraints may not be available, or are obtained as solutions of governing equations (e.g., PDE-onstrained optimization problems), or as results of external simulation runs (black-box optimization). In this dissertation we consider problems of classification of biomedical data, construction of optimal bounds on elastic tensor of composite materials, multiobjective (multi-property) optimization via connection to stochastic orderings, and black-box combinatorial optimization of crystal structures of organic molecules.

Barriers to effective pulmonary drug delivery are inherent to the lung physiology and present a challenge when attempting to bypass the natural defenses against inhaled particles. Inhaled particulate aerosols that deposit in the conducting airways of the lungs can become trapped in the respiratory mucus layer where they are then subjected to rapid clearance by the mucociliary escalator. The details of particle behavior after deposition and before this clearance are not well understood, however. Several physical processes may influence particle behavior on the mucus, including a penetration of particles into the mucus layer or a lateral transport of particles across the lung surface. Particles which deposit onto the respiratory mucus are subject to a number of forces which dictate these behaviors in the lung and may influence the retention of particles in the lungs and the efficacy of pulmonary drug delivery. The goal of this thesis was to investigate the behavior of microparticles deposited on a synthetic mucus model designed to mimic the bulk viscoelastic and surface tension properties of conducting airway mucus. Studies were conducted to determine the effects of mucus surface properties and particle physicochemical properties on the submersion and lateral mobility of single particles and the spreadability of particle-laden droplets at the air-liquid interface. Synthetic mucus gels were developed with viscoelastic properties that mimicked those of non-diseased tracheobronchial mucus. Infasurf, a calf lung surfactant extract, was spread onto the gel surfaces and compressed in a Langmuir trough to attain physiologically relevant surface tensions (~30-34 mN/m) and to analyze surfactant behavior on viscoelastic subphases. Microparticles were aerosolized onto the model mucus surface and imaged by brightfield microscopy at varying surface tensions on gels of varying viscoelastic properties to determine the extent of capillary submersion, in the fluid interface. Lateral transport of microparticles across the surfactant interface was quantified using particle tracking techniques. Finally, the spreading patterns of surfactant-laden droplets containing model drugs or particles were monitored by time-course imaging. Studies revealed that key physicochemical properties, including particle size and hydrophobicity, influenced particle submersion and mobility on the mimetic surfaces. Submersion, transport, and droplet spreadability were all inhibited with increasing gel viscoelastic properties, suggesting that such inhibition would be expected by healthy or disease tracheobronchial mucus. While low surface tensions promoted microparticle submersion into the subphase, the lateral transport and droplet spreadability were inhibited on gels with pre-existing surfactant films. The extent of droplet spreading could be enhanced by adding surfactant to the droplets. Overall, these studies aid our understanding of particle behavior and their fate at lung-like fluid surfaces, which has implications for both pulmonary drug delivery and pulmonary toxicity. Particulate aerosols which are designed to be smaller and more hydrophilic would experience improved mobility in the lungs and potentially gain the ability to submerge through the thick and highly viscous mucus barriers of diseased lungs. In healthy lungs, improved submersion could lead to greater particle retention, reduced mucociliary clearance, and a more effective delivery of drug to the epithelium. Lastly, by adding surfactant to drug containing liquid aerosol droplets, the deposition and distribution of drug could be improved in the peripheral regions of the obstructed lungs of cystic fibrosis patients. Results from these studies provide new knowledge that can be used to predict the behavior of aerosols deposited in the lungs and can aid the design of aerosols for drug delivery applications.

The purpose of this research was to analyze child and clinician factors affecting language therapy outcomes and to analyze the potential bi-directional relationship between child and clinician factors. Transcripts of intervention sessions with one child and one trained examiner were coded for factors relating to children's language ability, examiners' strategies for reaching session targets, and differences in examiners' interactional styles. It was found that differences in children's language ability and examiners' interactional styles did not have a strong relationship with therapy outcomes. Differences were observed in the overall frequency of examiners' strategy use across children; however, examiners were not sensitive to individual children's responsiveness to particular strategies. This is a secondary data analysis on an intervention study, which affects interpretation of the results: variability in examiner and child behaviors was decreased due to adherence to intervention protocol. However, the mismatch between examiner strategies and child responses is of interest. Making clinicians explicitly aware of the many types of elicitation and response strategies available may increase examiners' effectiveness, efficiency, or responsiveness.

The use of testlets in a test can cause multidimensionality and local item dependence (LID), which can result in inaccurate estimation of item parameters, and in turn compromise the quality of item response theory (IRT) true and observed score equating of testlet-based tests. Both unidimensional and multidimensional IRT models have been developed to control local item dependence caused by testlets. The purposes of the current study were to (1) investigate how different levels of LID can affect IRT true and observed score equating of testlet-based tests when the traditional three parameter logistic (3PL) IRT model was used for calibration, and (2) compare the performance of four different IRT models, including the 3PL IRT model, graded response model (GRM), testlet response theory model (TRT), and bifactor model, in IRT true and observed score equating of testlet-based tests with various levels of local item dependence. Both real and simulated data analyses were conducted in this study. Two testlet-based tests (i.e., Test A and Test B) that differed in subjects, test length, and testlet length were used in the real data analysis. For simulated data analysis, two main factors were investigated in this study: (1) testlet length (5 or 10), and (2) LID level within testlets that was defined by testlet effect variance (0, 0.25, 0.5625, 0.75, 1, and 1.5). For the unidimensional IRT models (i.e., 3PL IRT model and GRM), unidimensional IRT true score and observed score equating procedures, explained in Kolen and Brennan (2004), were used. For the two investigated multidimensional IRT models (i.e., 3PL TRT model and bifactor model), the unidimensional approximation of multidimensional item response theory (MIRT) true score equating procedure and the unidimensional approximation of MIRT observed score equating procedure (Brossman & Lee, 2013) were applied. The traditional equipercentile equating method was used as the baseline for comparison in both real data and simulated data analyses. It was found in the study that both testlet length and the LID level affected the performance of the investigated models on IRT true and observed score equating of testlet-based tests. When the traditional 3PL IRT model was used for tests with long testlets, higher levels of local item dependence led to IRT equating results that deviated further away from those obtained from the baseline method. However, the effect of local item dependence on IRT equating results was not prominent for tests with short testlets. Moreover, for tests consisting of long testlets (e.g., a testlet length of 10 or more) and having a very low level of local item dependence (e.g., a LID level of 0.25 or lower), and for tests consisting of short testlets (e.g., a testlet length around 5), all four investigated IRT models worked well in IRT true and observed score equating. For tests with long testlets and a relatively high level of local item dependence (e.g., a LID level of 0.5625 or higher), the GRM, bifactor, and TRT models outperformed the traditional 3PL IRT model in IRT true and observed equating of testlet-based tests. The study suggested that the selection of models for IRT true and observed score equating of testlet-based tests should be considered with respect to the features of the testlet-based tests and the groups of examinees from which the data is collected. It is hoped that this study encourages researchers to identify differences among existing models for IRT true and observed score equating of testlet-based tests with various features, and to develop new models that are appropriate for modeling testlet-based tests to obtain accurate IRT number correct score equating results.

My work is concerned with our perceptions of climate change and our relationship with the environment. Scientific study of historical worldwide climate data shows that global temperatures have been steadily rising for at least the last one hundred years. The concept of the anthropocene—a particular geologic epoch defined by human presence—links climate change specifically to humans and their impact on the environment. Even confronted with the data, many feel disconnected from climate change. While one can detect temperature change of single degrees over the course of seconds or minutes, it is difficult to feel this kind of temperature change over the course of decades. My work for the past three years has been concerned with questions related to how we feel and figure environmental loss. Crafting, mourning, and emotion have continually cropped up in my work as ways of apprehending environmental loss.